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PRECIPITATION AND PUMPING EFFECTS ON GROUNDWATER
LEVELS IN CENTRAL WISCONSIN
By
Jessica Haucke
A Thesis
Submitted in Partial Fulfillment
Of the Requirement for the Degree
MASTER OF SCIENCE
IN
NATURAL RESOURCES
(WATER RESOURCES)
College of Natural Resources
UNIVERSITY OF WISCONSIN
Stevens Point, Wisconsin
May 2010
i
Acknowledgements
I would like to thank my advisor Dr. Katherine Clancy for the time and effort that
she put in helping me to finish this project. Her encouragement and belief in my abilities
were deeply appreciated.
I would also like to extend a thank you to Dr. George Kraft who provided me with
the funding and idea for this project, and whose knowledge and support were greatly
valued.
Thank you to the rest of my committee Dr. Nathan Wetzel and Dr. David Ozsvath,
whose expertise in statistics and groundwater were important to this project.
I would also like to thank Jake Macholl my fellow graduate student for his help
and advice.
Finally I extend a sincere thanks to my friends for their help and support, to my
family who encouraged my scientific endeavors, and to the love of my life Troy, for his
constant positive attitude.
ii
Abstract
Central Wisconsin has the greatest density of high capacity wells in the state, most of
which are used for agricultural irrigation. Irrigated agriculture has been growing steadily
in the region since the 1950’s, when irrigation systems and high capacity wells became
inexpensive and easy to install. Recent low lake and river levels have increased concerns
that unfettered groundwater pumping for irrigation will undermine the availability of
groundwater to support surface waters and domestic uses. However, pumping remains
mostly unregulated.
Some research has quantified the magnitude of groundwater level declines due to
irrigation pumping, but no studies have identified its relation to climatic precipitation
changes. Changes in precipitation can exacerbate or mask the effect of groundwater
pumping. In this study, six groundwater monitoring wells and five climate stations were
examined for shifts in groundwater levels and precipitation changes. Through statistical
analysis, significant precipitation increases were identified in the southern part of the
study area which averaged 2.7 mm per year, but no significant change was determined for
the northern portion. Bivariate analysis identified water level declines with the region in
the years 1974, 1992 and 1999 for irrigated land covers. The range in years depended
upon the density of wells within the region and the influence of changes in precipitation.
Multiple regression explained, predicted and quantified the interaction between
precipitation and pumping. Wells located in areas with many high capacity wells showed
iii
a decline in water levels of up to 1.28 meters. In the southern portion of the study area,
where increases in precipitation occurred, this decline was thought to be masked.
iv
Table of Contents
Acknowledgements ......................................................................................................... i
Abstract .......................................................................................................................... ii
Table of Contents .......................................................................................................... iv
List of Tables................................................................................................................. vi
List of Figures ............................................................................................................. viii
List of Appendices ........................................................................................................ xii
Introduction .....................................................................................................................1
Study Area and Methods ..................................................................................................7
Site Description ...........................................................................................................7
Data Description ..........................................................................................................9
Groundwater Data ....................................................................................................9
Precipitation Data .................................................................................................. 13
Statistical Analyses .................................................................................................... 17
Data Analysis......................................................................................................... 17
Trend Analysis ....................................................................................................... 19
Mann-Whitney Test ............................................................................................... 20
Bivariate Analysis .................................................................................................. 21
Multiple Regression and ANCOVA ....................................................................... 22
Data Analysis Summary ......................................................................................... 24
Results and Discussion .................................................................................................. 25
Precipitation Changes................................................................................................. 25
Annual Trends ....................................................................................................... 25
Seasonal Trends ..................................................................................................... 30
Step Increase in Precipitation ..................................................................................... 35
Bivariate Analysis ...................................................................................................... 37
v
Control Monitoring Wells ...................................................................................... 38
Test Monitoring Wells ........................................................................................... 43
Multiple Regression and ANCOVA ........................................................................... 50
Hancock: Test Well ............................................................................................... 52
Plover: Test Well ................................................................................................... 54
Bancroft: Test Well ................................................................................................ 56
Coloma: Test Well ................................................................................................. 58
Wautoma: Control Well ......................................................................................... 60
Amherst Junction: Control Well ............................................................................. 62
Multiple Regression Summary ............................................................................... 64
Conclusions ................................................................................................................... 65
Literature Cited ............................................................................................................. 68
Appendices .................................................................................................................... 74
Appendix 1 ................................................................................................................ 74
Appendix 2 ................................................................................................................ 75
Appendix 3 ................................................................................................................ 78
Appendix 4 ................................................................................................................ 83
Appendix 5 ................................................................................................................ 86
Appendix 6 ................................................................................................................ 89
Appendix 7 ................................................................................................................ 93
Appendix 8 .............................................................................................................. 100
vi
List of Tables
Table 1. USGS monitoring wells used for data analyses. Plover 1 represents the original
well number and Plover 2 is the replacement number. ......................................................9
Table 2. Available data for USGS monitoring wells used in this study. ........................ 12
Table 3. COOP climate stations within the study region. .............................................. 13
Table 4. P-values from the Kendall’s tau trends test for annual precipitation at the six
precipitation stations from 1955-2008 and for the composite central division data for two
time periods (1955-2008 and 1933-2008). P-value <0.05 indicate a significant trend and
+ indicates that the direction of the trend is positive. ...................................................... 28
Table 5. P-values for Kendall's tau trend test from 1955-2008 at COOP locations and for
the composite central division cumulative seasonal precipitation data. ........................... 32
Table 6. The difference in seasonal median values and p-values for 1955-1998 vs. 1999-
2008. ............................................................................................................................. 35
Table 7. Results for changes in the median cumulative annual precipitation using the
Mann-Whitney test for before and after 1970. P-value < 0.05 indicates a step increase in
precipitation................................................................................................................... 37
Table 8. Results from multiple regression models which quantify increases and declines
in monitoring well water elevations (m) possibly due to pumping or the step increase in
precipitation. The step increase at Wautoma was between 1972 and 1973 and the
increase at Amherst Junction was between 1962 and 1963. ............................................ 65
Table 9. Name, county, period of record, and the cluster number for lakes used in this
analysis.......................................................................................................................... 79
Table 10. Time breaks for binary regression variables and the number of measurements
during each time period for lakes in data analysis. ......................................................... 80
vii
Table 11. Change in lake levels between the early and late time period. Positive
numbers represent a decline and negative numbers represent increases in lake surface
elevations. All results use the Wautoma monitoring well as the main explanatory
variable. * indicates a significant p-value of less than 0.05. ........................................... 81
Table 12. Change in lake levels between the early and late time period. Positive
numbers represent a decline and negative numbers represent increases in lake surface
elevations. All results used the Amherst Junction monitoring well as the main
explanatory variable. * indicates a significant p-value of less than 0.05. ....................... 82
Table 13. Cumulative summer (June-August) precipitation from the NOAA COOP
climate station in Stevens Point. .................................................................................... 84
Table 14. . Yearly cumulative precipitation from NOAA COOP climate station in
Stevens Point. Data was divided into two groups between 1970 and 1971 to compare
median values between the two time periods. ................................................................. 87
Table 15. Raw data for the first step of the bivariate analysis, which is the
standardization of the two data sets. ............................................................................... 90
Table 16. The raw data for equations that calculate the test statistic for the change in
mean in the bivariate analysis. ....................................................................................... 91
Table 17. Critical values for To for different levels of significance. .............................. 92
Table 18. Raw input data for multiple regression analysis with ANCOVA for the
Hancock monitoring well from the 1960-2008 growing season (May-September). ......... 94
viii
List of Figures
Figure 1. The central sands region and its topography and high capacity wells. ..............8
Figure 2. Land used for irrigated crops from the 1944-2007 farm census for five
counties in Central Wisconsin. .........................................................................................8
Figure 3. Yearly average monitoring well measurements (m) for test and control
locations. Depth to water measurements were subtracted from 1964 values for
comparison purposes. .................................................................................................... 11
Figure 4. The location of monitoring wells and climate stations used in this study. ...... 12
Figure 5. Annual Precipitation from the five weather stations and the interpolated data
set at Wautoma. The horizontal line represents the average for the time period. ............ 14
Figure 6. Annual composite precipitation from the central division (division 5) for 1933-
2008. ............................................................................................................................. 16
Figure 7. Monthly values from 1933-2008 for the Central Division 24-month Standard
Precipitation Index. Negative numbers represent the probability of observing a dry
period over a 24-month period and positive numbers are the probability of observing a
wet period over 24-months. ........................................................................................... 16
Figure 8. Temporal trends for annual precipitation (1955-2008) at the 5 COOP climate
stations, Wautoma, and the composite central division data. Triangles indicate significant
increasing trends (p-value < 0.05). Circles indicate no significant trend (p-value > 0.05).
Monitoirng well locations are lightly shaded in the background. .................................... 27
Figure 9. Annual Precipitation from 1955-2008 for climate stations, the interpolated data
set at Wautoma and the central composite data. Additionally, the composite central
division annual precipitation for the time period 1933-2008. The trend line and equation
indicate the magnitude of the changes in precipitation through time. .............................. 29
ix
Figure 10. Seasonal Kendall’s tau trends for cumulative monthly data from 1955-2008.
Each bar represents the direction of the data through time. Bars are plotted: spring,
summer, fall and winter respectively. Solid bars indicate a significant trend and hollow
bars indicate no significant trend. Note that Hancock and Montello, in the southern
region, show increasing trends in summer, winter and summer respectively................... 32
Figure 11 Median values for seasonal precipitation comparing 1955-1998 and 1999-2008.
* indicates a significant difference between median values (p-value < 0.05). ................. 34
Figure 12. Bivariate results for a change in mean at Wautoma monitoring well using
Amherst Junction as the stationary data set (1958-2008). The dashed line represents the
95% critical value, Ti is the difference in the two data series being tested, and the vertical
line is the peak year (To) which occurred one year before the change in mean. This
discontinuity in mean is associated with the step increase in precipitation between 1970
and 1971. ....................................................................................................................... 40
Figure 13. Bivariate results for a change in mean at Wautoma monitoring well for a time
period after the step increase in precipitation (1972-2008) using Amherst Junction as the
stationary data set. The dashed line represents the critical value. Statistics (Ti) below this
line indicate no change in mean, establishing a stationary period between 1972-2008. ... 40
Figure 14. Graphs A (Top), B (middle) and C (Bottom) of bivariate results for changes
in mean at the Amherst Junction monitoring well for three different time periods: 1958-
2008, 1958-1999, and 1962-1999 (A-C). Horizontal dashed lines represent the 95%
critical value, Ti is the difference in data sets, and vertical lines represent the peak (To),
the year after To is the change in mean. .......................................................................... 42
Figure 15. Bivariate results for a change in mean at Hancock monitoring well when
compared to Wautoma for the time period 1972-2008. The change in mean occurred in
1999, one year after the last peak in the plateau in 1998. ................................................ 44
Figure 16. Bivariate results for a change in mean at Plover monitoring well when
compared to Amherst Junction for the time period 1962-1999. The first peak in the graph
was in 1973 with the change in mean occurring in 1974................................................. 45
x
Figure 17. Bivariate results for a change in mean at the Plover monitoring well when
compared to Wautoma for the time period 1972-2008. The peaks in the graph plateau
from 1989 to 1998 indicate a time period of continuous change. .................................... 47
Figure 18. Graphs A (Top) and B (Bottom) of bivariate results for a change in mean at
the Bancroft monitoring well when compared to Wautoma (A) from 1972-2008 and to
Amherst Junction (B) from 1962-1999. The peak in both graphs is in 1991 indicating
that the change in mean occurs in 1992. ......................................................................... 48
Figure 19. Bivariate results for a change in mean at Coloma compared to Wautoma for
the time period 1972-2008. A peak occurred in 1973 indicating a change due to pumping
in 1974. ......................................................................................................................... 49
Figure 20. Graphs A (Top) and B (Bottom) of observed and predicted multiple
regression results at the Hancock monitoring well for the growing season (May-
September) 1960-2008. Graph A includes the STPC after 1972 and graph B includes
PC1 which began to affect monitoring well levels in 1999. ............................................ 54
Figure 21. Graphs A (Top) and B (Bottom) of observed and predicted multiple
regression results at the Plover monitoring well for the growing season (May-September)
1960-2008. Graph A includes PC1 which occurred after 1973 and graph B includes PC2
added after 1998. ........................................................................................................... 56
Figure 22. Graphs A (Top) and B (Bottom) of observed and predicted multiple
regression results at the Bancroft monitoring well for the growing season (May-
September) 1960-2008. Graph A shows the response to the SPI06 before PC1 was added.
Graph B includes the pumping covariate that occurred after 1991. ................................. 58
Figure 23. Observed and predicted multiple regression results at the Coloma monitoring
well for the growing season (May-September) 1960-2008. The graph shows the response
of PC1 after 1973........................................................................................................... 59
Figure 24 Graphs A (Top) and B (Bottom) of observed and predicted multiple regression
results at the Wautoma monitoring well for the growing season (May-September) 1960-
2008. Graph A shows the response to the SPI24 before the STPC was added. Graph B
includes the STPC that occurred after 1972.................................................................... 61
xi
Figure 25. Graphs A (Top), B (Middle) and C (Bottom) of observed and predicted
multiple regression results at the Amherst Junction monitoring well for the growing
season (May-September) 1960-2008. Graph A shows just the SPI24, graph B includes
the water level decline that occurred after 1999 and graph C contains the increased water
levels after 1962. ........................................................................................................... 63
Figure 26. The location of Long Lake Saxeville not to be confused with Long Lake
Oasis near Plainfield Wisconsin. .................................................................................... 75
Figure 27. WDNR lake surface elevations and citizen measured beach length for similar
dates at Long Lake Saxeville. ........................................................................................ 77
Figure 28. Long Lake Saxeville lake surface elevations converted from beach length
using regression equation 1. Measurements were taken from 6-1-1947 to 6-1-2007. ...... 77
Figure 29. The location of lakes and clusters used in data analysis. Lakes were grouped
into clusters according to geographic proximity. ............................................................ 79
xii
List of Appendices
Number Title Page
1 Lake Level Records 74
2 Lake Level Records: Long Lake Saxeville 75
3 Lake Level Records: Regression Analysis (ANCOVA) Results 78
4 Kendall’s Tau Trend Analysis 83
5 Mann-Whitney Test 86
6 Bivariate Test 89
7 Multiple Regression with ANCOVA 93
8 Magnitude of Seasonal Precipitation from 1955-2008 100
1
Introduction
The Wisconsin central sands is a loosely-defined region characterized by a thick
(often >30 m) mantle of sandy materials overlying rocks of low permeability. Landforms
are composed of glacial outwash plains and terminal moraine complexes associated with
the Wisconsin Glaciation (Figure 1). The region contains more than 80 lakes (> 5 ha),
over 1000 km of headwater streams and wetlands. Lakes, streams and wetlands are
mostly groundwater fed. Irrigated land covers about 31% of the area of interest (Figure 2)
which is farmed for potatoes, canning vegetables (sweet corn, snap peas, peas), field corn,
soybeans and others. Other land covers include non-irrigated agriculture (field corn,
forages, soybeans and others), coniferous and deciduous forests, grassland, scrubland and
wetlands. Irrigated agriculture is the largest user of groundwater in this region and has
steadily increased since around the 1950’s (Figure 2). This study focuses on the
“headwater” or upland part of the central sands, east of wetlands or drained wetlands.
Groundwater elevations indicate a divide that separates westerly flow to the Wisconsin
River and its tributaries, from easterly flow to headwater streams of the Fox and Wolf
Watersheds.
The groundwater supply in Central Wisconsin is vital to domestic water demands
as well as those of agriculture, industry and municipalities. For example three counties in
Central Wisconsin, Portage, Adams, and Waushara, use 78 billion gallons of groundwater
per year. Of the 78 billion gallons, approximately 87% or 67 billion gallons of
2
groundwater is used for irrigation (USGS, 2005). Soil type is the main reason for such a
heavy dependence on the groundwater supply. The majority of soils in this region are
highly permeable sands and gravels resulting from past glaciations. These sandy soils
have a low water holding capacity, which stores little moisture for plants (Weeks and
Stangland, 1971). Sandy soils discouraged irrigation agriculture until improved
technology, developed in the 1950’s, created inexpensive irrigation systems (Schultz,
2004). Since the 1950’s irrigation has become a dominant feature in Central Wisconsin,
and may be a reason for groundwater related stresses such as declines in surface and
groundwater levels.
In some regions of Central Wisconsin, groundwater related stresses are reflected
in surface water declines. In 2005-2009, reaches of the Little Plover River, a
groundwater fed stream in Plover, Wisconsin, intermittently dried up (Clancy, et al.,
2009). Long Lake, a groundwater fed lake located near Plainfield, Wisconsin (32
kilometers south of Plover), has also dried (Lowery et al, 2009). The most highly
stressed surface water resources occur in areas where there is a greater amount of
irrigation.
Suggested reasons for declines in surface and groundwater levels are intensive
groundwater pumping and drier weather. Precipitation records from the National
Oceanic and Atmospheric Administration (NOAA), combined with the Palmer Drought
Index and the Standard Precipitation Index, indicate that Central Wisconsin has received
close to average annual rainfall for the past five years. Despite near average precipitation
3
totals, questions remain about the effects and interactions of precipitation on groundwater
levels.
Many studies have been conducted throughout the United States that relate
groundwater pumping to declines in surface waters or decreases of water levels in
monitoring wells (Prinos et al., 2002; Sheets and Bossenbroek, 2005; Mair et al., 2007;
Skinner et al., 2007; Mayer and Congdon, 2008). In Wisconsin, the consumption of
groundwater and its effects on surface waters and groundwater levels have been studied
substantially. Weeks and Stangland (1971) examined the development of present and
future irrigation in the sand-plain area and its effects on streamflow and groundwater
levels in the late 1960’s. Stephenson (1974) discussed irrigation and the groundwater
supply throughout Wisconsin. Gotkowitz and Hart (2008) looked at groundwater
consumption and land use in Waukesha Wisconsin. Clancy et al (2009) examined
groundwater use and its potential effects on the Little Plover River in Plover Wisconsin,
and Kraft and Mechenich (2010) studied groundwater pumping and its effects on
groundwater, lake, and streamflow levels in the central sands of Wisconsin. The
relationship between groundwater pumping and declines in surface and groundwater
levels is well established, but the interaction between changes in climate, groundwater
withdrawals and the water table response are not as well understood (Lettenmaier et al.,
2008).
The direct measurement of the surface and groundwater response to pumping is
presumably complicated by changes in precipitation which have occurred in some parts
4
of Wisconsin. Increases in precipitation in the central part of the United States were
noted by Lettenmaier et al. (1994) and McCabe and Wolock (2002). More recently
Juckem et al. (2008) compared time periods 1941-1970 to 1971-2000 and found that
wetter conditions have occurred in southwestern Wisconsin from 1971-2000. These
wetter conditions were thought to be the result of a sudden shift in precipitation called a
“step increase.” This step increase in precipitation may have masked the true effects of
groundwater pumping pressures in some areas of Central Wisconsin (Kraft and
Mechenich, 2010).
The hypothesis for this study is that precipitation has changed groundwater levels
in some regions of the study area, but that pumping may be influencing surface and
groundwater levels more than what can be described by changes in precipitation alone.
To address the hypothesis three questions were examined: 1) is there a change in
groundwater levels presumably due to precipitation and/or pumping and where do they
occur in the study region? 2) If there is a change, when does it show up in the
groundwater records? And, 3) how much does the potential change created by
precipitation or pumping take away or add to current groundwater levels?
An important concept for this study was stationarity. A formal definition is a
random process where all statistical properties do not vary with time (Haag, 2005).
Stationarity is fundamental to water resources and has been used to evaluate and manage
risks to water supplies, water works and floodplains (Milly et al., 2008). Stationarity
describes a process in which natural systems fluctuate within an unchanging range of
5
variability (Milly et al., 2008). When non-stationarity develops, it indicates that a shift
has occurred between the relationships of hydrologic data within a region. Non-
stationarity can be caused by changes in data collection methods or physical changes,
such as a fluctuation in precipitation, or water diversion like groundwater pumping.
(Maronna and Yohai, 1978; Potter, 1981).
Stationarity may be difficult to detect when unknown variables or multiple
variable influence the system. To recognize these impacts the concept of a “covariate”
also plays an important role in this study. A covariate is a statistical term that has been
used to identify an interaction which is not measured but is observed in the record
(Webster et al., 1996; Doll et al., 2002; Mayer and Congdon, 2008). A covariate may be
binary and is often referred to as either a hidden, lurking or dummy variable. According
to Helsel and Hirsch (2002), a covariate influences the dependant variable but is not
appropriately expressed as a continuous variable. A covariate might be used for locations,
such as stations, aquifers, positions or cross sections. It could also be used for time, such
as day and night, summer and winter, or before and after an event such as a flood or a
drought. In this study, time related to changes possibly due to pumping and precipitation
may be represented by a covariate.
Groundwater pumping and changes in precipitation were thought to be the two
main covariates affecting groundwater levels in Central Wisconsin. Observations of
pumping and changes in precipitation have no records associated with their impact on
groundwater levels; therefore, a binary data set was developed for each covariate. For
6
example, when pumping was thought not to be having an effect on the groundwater
record the data set was defined as “off”. When pumping potentially began to impact
groundwater levels, the data set was defined as “on.” Because the covariates are
disconnected from the continuous groundwater data, they may or may not actually
represent groundwater pumping or changes in precipitation.
To examine the hypothesis questions, multiple statistical approaches were used.
Kendall’s tau trend test was used to determine if and where a change in precipitation
occurred. A trend is defined as an increase or decrease of data values over time (Helsel
and Hirsch, 2002). The Mann-Whitney test, which calculates a difference in median
values, was used to determine if a step increase in precipitation occurred. Bivariate
analysis indicated when changes showed up in the groundwater record, presumably
caused by pumping and the step increase in precipitation. Multiple regression models
quantified, explained and predicted the changes due to precipitation or pumping on
groundwater levels. Corroborated findings from these statistical techniques were used to
form conclusions.
Multiple robust statistical techniques were used because water resource and
precipitation data are noisy and can be problematic when it comes to meeting the
underlying assumptions of statistical analysis (Helsel and Hirsch, 2002). Precipitation
data contained outliers and did not have a normal distribution. However, yearly average
groundwater levels from monitoring wells were normally distributed. A 95% confidence
interval (α = 0.05) was used following statistical convention.
7
Study Area and Methods
Site Description
The Central Wisconsin area of interest is shown in Figure 1. The area is
approximately 11,200 square kilometers, of which 31% is cultivated crops (2001 USGS
National Land Cover Database), and is bordered on the west by the Wisconsin River.
The eastern boundary was delineated using ecoregions (EPA, 2000) and glacial deposits
(WGNHS, 1976). Streams and lakes of this area are well connected to shallow,
unconfined, sand and gravel aquifers (Weeks and Stangland, 1971). Agriculture and
domestic water supplies also come from these aquifers.
The topography influences farming types and other land uses. Irrigated
agriculture is concentrated on flat sandy areas which make up approximately 40% of the
region and contain approximately 70% its high capacity wells (2009 Wisconsin
Department of Natural Resources (WDNR) Water, Well, and Related Data Files) (Figure
1). Irrigation is sparser in hilly regions of the study area where large scale farming is less
practical.
In this study monitoring wells are distinguished based on their location within the
area of interest. Monitoring wells located in areas with a High Density of high capacity
Wells (HDW), predominantly in the flat plains, are referred to as “test wells.”
Monitoring wells located in areas with a Low Density of high capacity Wells (LDW),
generally in the hills region, are referred to as “control wells.”
8
Figure 1. The central sands region’s topography and high capacity wells.
Figure 2. Land used for irrigated crops from the 1944-2007 farm census for five counties in Central
Wisconsin.
0
50
100
150
200
250
300
350
400
1940 1950 1960 1970 1980 1990 2000 2010
Sq
uare K
ilom
ete
rs
Adams County
Marquette County
Portage County
Waupaca County
Waushara County
9
Data Description
Groundwater Data
Groundwater level data from six U.S. Geological Survey (USGS) monitoring
wells were used for this study (Table 1) (USGS, 2009). Well names are based on the
locale or quadrangle. The six monitoring wells were chosen based on two rationales: the
length and consistency of available records (Table 2), and the location within the study
area (Figure 4). Amherst Junction and Wautoma wells are located in areas with a LDW
and were considered “control wells.” Four wells (Bancroft, Coloma, Hancock and Plover)
are located in areas with a HDW and were considered “tests wells.” Test wells were
expected to be influenced by groundwater pumping, while control wells were expected to
be minimally influenced. Data represent depth in meters below the land surface. Depth
to water was subtracted from benchmarked elevations to obtain water elevations.
Table 1. USGS monitoring wells used for data analyses. Plover 1 represents the original well number and
Plover 2 is the replacement number.
Well Number Latitude Longitude
Locale or
Quadrangle
Well
Depth
(m)
Elevation
Datum
(m)
442810089194501 44°28'10" 89°19'45" Amherst Junction 5.3 341.38
441833089315601 44°18'33" 89°31'56" Bancroft 3.7 327.45
441454089432801 44°14'54" 89°43'28" Coloma NW 4.7 315.16
440713089320801 44°07'13" 89°32'08" Hancock 5.5 329.18
442623089302701 44°26'23" 89°30'27" Plover 1 5.8 334.95
442622089302901 44°26'22" 89°30'29" Plover 2 5.8 333.17
440345089151701 44°03'45" 89°15'17" Wautoma 4.3 266.09
10
Daily automated measurements existed for monitoring wells near Hancock and
Wautoma. Monthly field measurements were the only type of data that existed for
monitoring wells near Amherst Junction, Bancroft, Coloma NW and Plover. Annual
average water levels were used as a statistic for comparisons (USGS, 2010) (Figure 3).
Yearly values were obtained from averaged daily and monthly values. Both monthly and
yearly data sets were used in data analyses.
Field observations from the monitoring well near Plover were recorded under two
different well numbers. Well number 442623089302701 was used prior to April 14,
2006 and was replaced by well number 442622089302901. These well measurements
were combined and referenced to a common datum. Both well numbers are represented
in Table 1.
11
Figure 3. Yearly average monitoring well measurements (m) for test and control locations. Depth to water
measurements were subtracted from 1964 values for comparison purposes.
-3
-2
-1
0
1
2
3
1950 1960 1970 1980 1990 2000 2010
Sta
ndar
diz
ed D
epth
to W
ater
(M
)
Plover
Hancock
Bancroft
Coloma NW
-3
-2
-1
0
1
2
3
1950 1960 1970 1980 1990 2000 2010
Sta
nd
ard
ized
Dep
th to W
ater
(M
)
Wautoma
Amherst Junction
12
Figure 4. The location of monitoring wells and climate stations used in this study.
Table 2. Available data for USGS monitoring wells used in this study.
Locale or Quadrangle
First
Measurement
Last
Measurement
Total # of
Measurements
Average # of
Measurements
per Month
Type of Measurements
Available
Amherst Junction 7/2/1958 10/23/2008 1702 3.1 Field
Bancroft 9/7/1950 12/22/2008 1583 2.3 Field
Coloma NW 8/8/1951 12/22/2008 693 1.5 Field
Hancock 5/1/1951 12/31/2008 17896 26.9 Automated Daily/Field
Plover 12/1/1959 12/22/2008 1098 1 Field
Wautoma 4/18/1956 12/31/2008 16435 27.8 Automated Daily/Field
13
Precipitation Data
Long term monthly precipitation data (≥ 50 years), from the cooperative observer
(COOP) station network, were accessed online through the National Climate Data Center
(NCDC, 2009). Five weather stations in Central Wisconsin, located at the Hancock
Experimental Farm, Montello, Stevens Point, Waupaca, and Wisconsin Rapids, were
used in this study (Table 3, Figure 4). Yearly (Figure 5) and seasonal values were used in
data analyses and were calculated from monthly observations. Missing monthly
measurements were interpolated using a weighted average of the three closest COOP
stations.
Table 3. COOP climate stations within the study region.
Station Name COOP ID # Period of Record
Hancock Experimental Farm 473405 1931-2008
Montello 475581 1955-2008
Stevens Point 478171 1931-2008
Waupaca 478951 1931-2008
Wisconsin Rapids 479335 1931-2008
Annual precipitation totals from 1931-2008 for the town of Wautoma were
calculated using the Inverse Distance Weighting Method (Tomczak, 1998; Malvic and
Durekovic, 2003; Serbin and Kucharik, 2009). This method was used to develop the
Wautoma interpolated data set. The 12 closest COOP stations within 50 miles with
sufficient records were used to determine the annual totals at Wautoma. Annual
14
interpolated totals were not calculated during years when there were less than 12 stations
contributing to the data (Figure 5).
Figure 5. Annual Precipitation from the five weather stations and the interpolated data set at Wautoma.
The horizontal line represents the average for the time period.
400
600
800
1000
1200
1400
1930 1950 1970 1990 2010
mm
Hancock 1931-2008
400
600
800
1000
1200
1400
1950 1960 1970 1980 1990 2000 2010
mm
Montello 1955-2008
400
600
800
1000
1200
1400
1930 1950 1970 1990 2010
mm
Stevens Point 1931-2008
400
600
800
1000
1200
1400
1930 1950 1970 1990 2010
mmWaupaca 1931-2008
400
600
800
1000
1200
1400
1930 1950 1970 1990 2010
mm
Wisconsin Rapids 1931-2008
400
600
800
1000
1200
1400
1930 1950 1970 1990 2010
mm
Wautoma 1931-2008
Average = 782.7 mm Average = 823.3 mm
Average = 807.7 mm Average = 802.9 mm
Average = 797.9 mm Average = 789.9 mm
15
In addition to precipitation data from COOP stations throughout the study region,
composite precipitation (Figure 6) and the Standard Precipitation Index (SPI) (Figure 7)
were obtained from NCDC for climate division 5 (Central) (NCDC, 2010). Annual and
seasonal composite precipitation were used as a comparison to the COOP stations. The
SPI is a normalized index that quantifies precipitation deficits, can be calculated for any
desired duration, and takes into account time scales in the analysis of wet and dry periods
for water availability and use (Guttman, 1998; Mayer and Congdon, 2008). The SPI was
used because it improved the explanation and prediction of groundwater fluctuations in
multiple regression models and it is better at representing wet and dry periods than the
Palmer Drought Index (Mayer and Congdon, 2008). Time scales available for the SPI
through the NCDC are 1, 2, 3, 6, 9, 12, and 24-month. The 24-month SPI was used in
analyses because there was less variability associated with long term durations (Guttman,
1998), and the values reflected monitoring well water levels more accurately in multiple
regression models.
Statistical analyses included both annual and seasonal precipitation data. The five
COOP stations, the interpolated Wautoma values, and the composite central division
precipitation measurements were used in yearly analyses. Seasonal analyses included
data from the five COOP stations, and the composite central division values. Monthly 6
and 24-month SPI values during the growing season were used in multiple regression
models as a proxy for actual precipitation.
16
Figure 6. Annual composite precipitation from the central division (division 5) for 1933-2008.
Figure 7. Monthly values from 1933-2008 for the Central Division 24-month Standard Precipitation Index.
Negative numbers represent the probability of observing a dry period over a 24-month period and positive
numbers are the probability of observing a wet period over 24-months.
400
600
800
1000
1200
1400
19
33
19
36
19
39
19
42
19
45
19
48
19
51
19
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84
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87
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90
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93
19
96
19
99
20
02
20
05
20
08
Precip
itati
on
(m
m)
-3
-2
-1
0
1
2
3
1933
1935
1937
1939
1941
1943
1945
1947
1949
1951
1953
1955
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2008
Norm
ali
zed
Prob
ab
ilit
y
Average = 805.0 mm
17
Statistical Analyses
Data Analysis
The objective of the data analysis was to predict, quantify, and explain changes in
groundwater levels possibly due to pumping and precipitation. Pumping often cannot be
observed in the monitoring well record until a threshold is reached (Mayer and Congdon,
2008). For this study, a threshold year marks the end of a time period before which there
is no discernable decline in groundwater levels. The approach used to quantify the
possible hidden effect of pumping was multiple regression with ANCOVA. Without any
data, potential pumping can only be expressed as a binary variable. As a binary variable,
the possible pumping effect is either “on” or “off” and the date of the switch is
determined by testing for a threshold year.
In addition to the possible pumping influence, there was the added influence from
changes in precipitation that potentially played a role in groundwater fluctuations.
Studies in Southwestern Wisconsin indicate a step increase in precipitation in the early
1970’s which affected baseflow (McCabe and Wolock, 2002; Juckem et al., 2008). This
step increase in precipitation, which is a statistically significant shift in the mean value
over a short period of time (one to two years), occurred in some areas of the study region.
The shift in precipitation potentially complicated the analyses by masking any possible
impact thought to be due to pumping. For this reason, the step increase in precipitation
was also considered to have a hidden effect on groundwater levels, similar to pumping.
18
The precipitation-step-increase covariate was also treated as a binary variable; however,
from Juckem et al. (2008) it was established that the “switch” would occur sometime in
the early 1970’s. Precipitation trends helped determine areas of the study region where
the step increase may have occurred, and multiple regression with ANCOVA quantified
that interaction with pumping. The 6 and 24-month SPI, used in regression models, was
a composite data set for all of central Wisconsin and therefore did not detect changes at
specific locations.
Several statistical tests were used to extract the implied groundwater impacts
caused by the two covariates. These tests include: Kendall’s tau trend test, the Mann-
Whitney test, bivariate analysis, and multiple regression with ANCOVA. The trend test
established spatial and temporal differences in yearly and seasonal precipitation
throughout the study area and established regions where the covariate for the step
increase in precipitation might have occurred. The Mann-Whitney test confirmed the
existence of a step increase at some stations after 1970 by measuring the difference in
median values for data before 1970 and after 1971. Bivariate analysis measured the
change in mean between control and test monitoring well observations through time and
was calculated to determine the potential pumping covariate threshold year (a specific
year when pumping may have been detected). Finally, multiple regression models were
used to quantify, explain, and predict the effects of the covariates on monitoring well
water elevations. An example of each statistical technique can be found in the attached
appendices.
19
Trend Analysis
Kendall’s tau, a nonparametric statistical technique, has been regularly used to
examine linear trends in precipitation (Kunkel et al., 1999; Andresen et al., 2001;
Huntington et al., 2004). Trends in precipitation, which are increases or decreases in data
values over time, were evaluated to determine if and where changes in precipitation
occurred in the study area. In addition, an increased trend in precipitation during the
same time period that declines were measured in monitoring well water levels indicated a
potential impact due to pumping.
Trends were calculated for yearly and seasonal precipitation totals. The period of
record used for trend analysis was 1955-2008. This time period was based on the shortest
precipitation record at the Montello COOP climate station (Table 3). Annual trend
analysis included Wautoma’s interpolated precipitation data, the five COOP climate
stations, and the composite central division values. Seasonal trends (spring: March-May,
summer: June-August, fall: September-November and winter: December-February)
included the five COOP stations and the composite central division data. Calculations of
precipitation trends through time were made online using the Free Statistics and
Forecasting Software website (Wessa, 2008). An example of this test with summer
precipitation totals is given in Appendix 4.
Median seasonal precipitation values were examined for 1999-2008 at the five
COOP climate stations and for composite central division data. This was done to
20
determine if recent precipitation during a specific season has been lower than in the past
(1955-1999), possibly contributing to declines in monitoring well water elevations.
Mann-Whitney Test
The Mann-Whitney test, a non-parametric version of the t-test, was used to
corroborate findings from the trend tests and to determine if a step increase in
precipitation occurred between 1970 and 1971 at some climate stations. The difference
between the Mann-Whitney and the t-test, is that Mann-Whitney calculates a difference
in the median instead of a difference in mean (Helsel and Hirsch, 2002). This test was
used for precipitation records because these data contained outliers that skewed the
distribution.
The period of record used to find the difference in median values for annual
precipitation was 1933-2008. This produced a similar number of data points on either
side of the 1970, 1971 time break (n = 38 years). Four of the five COOP stations had
data for the 1933-2008 time period. Montello had a shorter available record before 1970
(1955-1970, n = 15). The composite central division data was tested for two periods:
1933-2008 and 1955-2008. The longer time period (1933-2008) was used to confirm that
the shorter time period (1955-2008) produced similar trend results. The Mann-Whitney
test was calculated in Mini Tab (version 15) and an example is given in Appendix 5.
21
Bivariate Analysis
A bivariate analysis tests for a difference in the means of two linearly correlated
data sets (Potter, 1981). The bivariate technique uses time series measurements and has
commonly been used to evaluate climate data such as precipitation, evaporation and
temperature (Buishand, 1982, Bücher and Dessens 1991; Kirono and Jones, 2007). In
this study, bivariate analyses were used to evaluate changes in groundwater levels at
monitoring wells. To meet the requirement of normal data, yearly average depth to water
measurements from monitoring wells were used in the analysis.
The bivariate analysis was used to find the threshold year when the potential
pumping covariate started to affect monitoring well levels. This was accomplished by
examining non-stationarity, or a change in mean, between correlated test and control
monitoring well records. The results from the bivariate technique determined the year,
direction, and magnitude of the change in mean caused by non-stationarity (Potter, 1981).
The bivariate analysis uses a regional stationary series which consists of multiple
stations around a test station. The regional series is assumed to be independent and free
of systematic change (Kirono and Jones, 2007). Due to the lack of available monitoring
well records, multiple stations could not be used to develop a regional stationary series.
Therefore, individual control locations (Amherst Junction or Wautoma) were considered
the stationary regional series, which was similar to the methods of Kirono and Jones
(2007).
22
Bivariate analysis was initially tested on the control monitoring wells, Amherst
Junction and Wautoma, to develop stationary periods of record for each well. The time
period from 1958-2008 was used based on the shorter data set at Amherst Junction.
These stationary periods were developed so that the control locations could serve as the
regional series in further analysis with test monitoring wells.
Once the stationary periods were established at the control sites, the bivariate test
was used to determine the threshold year possibly caused by the pumping covariate at the
test monitoring wells: Bancroft, Coloma NW, Hancock and Plover. Control sites located
within the closest proximity to the test sites were used as the stationary data set. The
results for this test were calculated in Microsoft Office Excel 2007 and an example can
be found in Appendix 6.
Multiple Regression and ANCOVA
Multiple regression was the primary statistical technique used for this research
and supported findings from the previous analyses. Multiple regression is used in many
situations when knowledge of the system indicates that there is more than one variable
needed to explain a result (Helsel and Hirsch, 2002). In groundwater studies, multiple
regression has been used to predict and explain groundwater levels (Ferguson and St.
George, 2003, Mayer and Congdon, 2008). Regression models have been used to
develop equations to measure stage fluctuations in lakes (House, 1985), estimate the
23
magnitude and frequency of floods for ungaged rivers (Jennings et al., 1994), measure
groundwater recharge (Perez, 1997, Gerbert et al., 2007), runoff (Lee and Chung, 2007),
and as an estimation of streamflow depletion from irrigation (Burt et al., 2002). Multiple
regression is considered a useful tool for analyzing complex hydrologic data (Kufs, 1992).
Linear multiple regression equations using ANCOVA were developed to quantify
changes potentially due to the two covariates: the step increase in precipitation and
pumping. ANCOVA is the addition of the covariate variables to the regression models.
Covariates used at specific monitoring well locations were identified using Kendall’s tau
and the bivariate analysis. Slope coefficients of the covariate binary variables
represented the change in monitoring well water elevations. The main purpose of this
technique is to use independent variables to explain and predict the dependant variable:
test monitoring well water elevations (Helsel and Hirsch, 2002). Multiple regression was
well suited for this task because more than one independent variable was needed to
explain monitoring well levels. In this study, multiple regression used variables
developed from the previously described analyses. The model results detected
differences in groundwater levels, predicted measurements, explained trends and
explored the implied precipitation and pumping interaction on water levels in monitoring
wells.
Regression models were created for each monitoring well to distinguish the
changes possibly due to pumping from changes possibly due to a step increase in
precipitation. At control monitoring wells, the step increase in precipitation was
24
examined graphically to determine if changes in precipitation were the same throughout
the study area.
Monthly monitoring well water elevations for the growing season, May through
September, were used for multiple regression analyses. The growing season months were
chosen to limit complexity due to snowpack infiltration rates and because most
groundwater use occurs during the growing season. To achieve parsimony in the model,
the selection of applicable variables was kept small. Three variables provided the best
results: the 6 or 24-month SPI, the binary variable for the potential step increase in
precipitation, and the binary variable for the potential increased impact of groundwater
pumping. The time breaks used to change the binary variables from “off” to “on” were
established with the trends test and the bivariate analysis. Regression tests were
processed with PROC REG in SAS version 8.2. An example of the multiple regression
analysis with ANCOVA is given in Appendix 7.
Data Analysis Summary
Trend analysis and the Mann-Whitney test were used to determine if and where
pumping and the step increase in precipitation may have occurred. The bivariate analysis
used those results to determine when pumping potentially started to impact groundwater
levels and also reconfirmed precipitation changes. Finally, multiple regression with
ANCOVA used results from the previous tests to quantify, explain, and predict
monitoring well water elevations through time.
25
Results and Discussion
Precipitation Changes
Increases or decreases in annual and seasonal precipitation affect groundwater
levels and can exacerbate or mask the impact of groundwater loss (such as pumping).
Spatial and temporal trends were analyzed to determine if and where changes in
precipitation occurred in the study region. A significant trend would require removing
that effect, so the possible impacts of groundwater pumping would not be masked.
To determine when precipitation trends began to impact groundwater levels,
differences in median values were analyzed with the Mann-Whitney test. A difference in
the median value from one time period to the next was considered a step increase in
precipitation. Both the test for trends and the difference in median values were used to
corroborate findings and results.
Annual Trends
Trends in annual precipitation were examined to determine if spatial and/or
temporal differences existed in the study region. Annual trend results for the composite
central division data consisted of two time period, 1955-2008 and 1933-2008. The longer
time period 1933-2008 was included to determine if the shorter time period was sensitive
to changes in precipitation or introduced any bias. The shorter time period 1955-2008
26
was used for all precipitation data sets (the five COOP climate stations, the interpolated
data set at Wautoma, and the composite central division records) because data from one
of the COOP climate stations (Montello) began in 1955.
Figure 8 illustrates the results of the spatial difference in annual precipitation
trends, where circles represent no trend and triangles represent increased trends
(significant decreasing trends were not found). The magnitudes of the trends are shown
in Figure 9. Increasing trends added to the complexity of the data analysis. Three
stations, Hancock, Montello, and Wautoma, in the southern part of the study area show
increased trends in annual cumulative precipitation while stations in the northern part of
the study area, Stevens Point, Waupaca, Wisconsin Rapids, show no trend.
There was no significant trend found for the longer or shorter time period
associated with the composite central division precipitation (Table 4, Figure 9).
Increased precipitation near the control monitoring well at Wautoma required finding a
different calibration period with which to compare test monitoring wells. A different
calibration period was needed because an increase in precipitation through time would
minimize the results of potential pumping impacts at test locations where there was no
increase in precipitation. Increased precipitation near the test monitoring well at
Hancock required removing the effect of the trend so that the implied effect from
groundwater pumping was not dampened.
Trends in annual precipitation throughout the study area alone do not explain
declines in water levels at monitoring wells. Precipitation varies from year to year and
27
affects groundwater levels and hydrologic flow paths especially if annual totals have been
above or below average for long periods (Weeks and Stangland, 1971, Webster et al.,
1996). Long term declines in precipitation would help to explain decreases in surface
and groundwater levels, but increased precipitation though time may be hiding the
impacts of pumping. For this reason precipitation was examined in smaller time
increments.
Figure 8. Temporal trends for annual precipitation (1955-2008) at the 5 COOP climate stations, Wautoma,
and the composite central division data. Triangles indicate significant increasing trends (p-value < 0.05).
Circles indicate no significant trend (p-value > 0.05). Monitoirng well locations are lightly shaded in the
background.
28
Table 4. P-values from the Kendall’s tau trends test for annual precipitation at the six precipitation stations
from 1955-2008 and for the composite central division data for two time periods (1955-2008 and 1933-2008).
P-value <0.05 indicate a significant trend and + indicates that the direction of the trend is positive.
location p-value
Hancock 0.025* (+)
Montello 0.026* (+)
Stevens Point 0.391
Waupaca 0.876
Wautoma 0.042* (+)
Wisconsin Rapids 0.970
Composite 1 (1933-2008) 0.093
Composite 2 (1955-2008) 0.109
* indicates significant p-value < 0.05
+ indicates the direction of the trend
29
Figure 9. Annual Precipitation from 1955-2008 for climate stations, the interpolated data set at Wautoma
and the central composite data. Additionally, the composite central division annual precipitation for the time
period 1933-2008. The trend line and equation indicate the magnitude of the changes in precipitation
through time.
y = 2.8466x - 4847.2400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005
mm
Hancock 1955-2008
y = 3.2525x - 5619.8400
600
800
1000
1200
1400
1950 1960 1970 1980 1990 2000 2010
mm
Montello 1955-2008
y = 1.1024x - 1382400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005
mm
Stevens Point 1955-2008
y = 0.5538x - 271.95400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005m
m
Waupaca 1955-2008
y = 2.1319x - 3420.1400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005
mm
Wautoma 1955-2008
y = -0.0035x + 808.01400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005
mm
Wisconsin Rapids 1955-2008
y = 0.9181x + 769.63400
600
800
1000
1200
1400
19
33
19
37
19
41
19
45
19
49
19
53
19
57
19
61
19
65
19
69
19
73
19
77
19
81
19
85
19
89
19
93
19
97
20
01
20
05
mm
Composite 1933-2008
y = 1.7076x - 2572.1400
600
800
1000
1200
1400
1955 1965 1975 1985 1995 2005
mm
Composite 1955-2008
30
Seasonal Trends
Annual precipitation data were divided into four seasons: spring (March-May),
summer (June-August), fall (September-November) and winter (December-February).
Data from the five COOP stations were used along with the composite central division
precipitation from 1955-2008. The spatially interpolated data set at Wautoma was not
used because interpolations were only calculated for yearly data. Seasonal trends were
analyzed to determine what time of the year increases in precipitation occurred in the
southern part of the study area. Seasonal precipitation data from 1999-2008 were also
examined to determine if a particular time of the year during the last ten years has been
drier.
Summer precipitation increased at Hancock, Montello and for the composite
central division precipitation. Additionally a significant increasing trend was found
during the winter at Hancock (Figure 10). Spring precipitation at all locations showed no
significant trend. Fall precipitation decreased at all sites except Montello, but not
significantly (P-value = <0.05) (Table 5). Figures illustrating the magnitude of the
seasonal trends at each location can be found in Appendix 8.
McCabe and Wolock (2002) proposed that the trends in precipitation were
spurred by increases in fall and winter precipitation totals. The seasonal trend results for
Central Wisconsin indicate that summer was a more likely season for the increase in
31
precipitation to have occurred, with winter contributions possibly from precipitation or
added snowfall.
Groundwater recharge from May through September is substantially less than
during the rest of the year due to evapotranspiration even though most precipitation in
Central Wisconsin (60%) falls during that time (Weeks and Stangland, 1971, USDA,
2006). This indicates that an increase in summer precipitation may not increase recharge.
The lack of increased trends during the spring or fall, when groundwater recharge is the
greatest in Central Wisconsin, may suggest that groundwater recharge is not able to keep
up with the demand for groundwater use (Table 5).
32
Figure 10. Seasonal Kendall’s tau trends for cumulative monthly data from 1955-2008. Each bar
represents the direction of the data through time. Bars are plotted: spring, summer, fall and winter
respectively. Solid bars indicate a significant trend and hollow bars indicate no significant trend. Note that
Hancock and Montello, in the southern region, show increasing trends in summer, winter and summer
respectively.
Table 5. P-values for Kendall's tau trend test from 1955-2008 at COOP locations and for the composite
central division cumulative seasonal precipitation data.
Location Spring Summer Fall Winter
Hancock 0.134 0.004* (+) 0.460 0.009* (+)
Montello 0.561 0.003* (+) 0.654 0.447
Stevens Point 0.556 0.156 0.347 0.107
Waupaca 0.771 0.300 0.236 0.230
Wisconsin Rapids 0.676 0.665 0.230 0.241
Composite 0.633 0.011* (+) 0.612 0.136
* indicates significant p-value < 0.05
+ indicates the direction of the trend
33
The median values for seasonal precipitation from 1955-1998 were compared to
1999-2008 to determine whether the last ten years have been drier. These results are
illustrated in Figure 11. Differences between the median values for the two time periods
and the p-values are given in Table 6. Median values indicate that the total amount of
precipitation in the last 10 years has increased at Hancock during the spring and winter
while fall precipitation at Waupaca has decrease during the fall.
The comparison of median precipitation values suggests that around Hancock
where significant declines in surface and groundwater levels have occurred, precipitation
has increased or is not significantly different during the current time period (1999-2008).
Kraft and Mechenich (2010) imply that the increase in precipitation during this recent
period has masked the rapid expansion of irrigation so that the full effect of pumping in
areas where there is a HDW will not be evident in groundwater record until drier
conditions occur.
Declines in precipitation at Waupaca during the fall may indicate less infiltration
and less recharge to groundwater. Drier falls in the northern part of the study region in
areas with fewer high capacity wells may be exasperating the effect of groundwater
consumption.
34
Figure 11 Median values for seasonal precipitation comparing 1955-1998 and 1999-2008.
* indicates a significant difference between median values (p-value < 0.05).
0
100
200
300
400
Hancock Waupaca Stevens Point Wisconsin Rapids Montello CompositeSp
rin
g P
recip
itati
on
(m
m)
Spring 1955-1998
1999-2008
0
100
200
300
400
Hancock Waupaca Stevens Point Wisconsin Rapids Montello Composite
Su
mm
er P
recip
itati
on
(m
m)
Summer1955-1998
1999-2008
0
100
200
300
400
Hancock Waupaca Stevens Point Wisconsin Rapids Montello Composite
Fall
P
recip
itati
on
(m
m)
Fall1955-1998
1999-2008
0
100
200
300
400
Hancock Waupaca Stevens Point Wisconsin Rapids Montello CompositeWin
ter
Precip
itati
on
(m
m)
Winter1955-1998
1999-2008
*
*
*
35
Table 6. The difference in seasonal median values and p-values for 1955-1998 vs. 1999-2008.
SPRING SUMMER FALL WINTER
Location
Difference
(mm) p-value
Difference
(mm) p-value
Difference
(mm) p-value
Difference
(mm) p-value
Hancock 43.3 0.028 45.5 0.106 -23.5 0.275 23.8 0.005
Waupaca 3.1 0.903 -26.7 0.350 -48.3 0.045 18.7 0.133
Stevens Point 19.7 0.256 21.1 0.385 -40.8 0.091 16.2 0.157
Wisconsin
Rapids 13.1 0.429 14.2 0.730 -29.2 0.164 10.4 0.456
Montello 22.4 0.333 70.4 0.051 -14.6 0.616 17.5 0.161
Composite 13.3 0.410 38.9 0.093 -27.3 0.229 17.9 0.071
Step Increase in Precipitation
The Mann-Whitney test was used to determine whether a step increase in
precipitation occurred between 1970 and 1971 and confirmed spatial differences found in
results from annual precipitation trends. Annual cumulative precipitation from the COOP
climate stations, Wautoma’s interpolated data and the composite central division
precipitation were tested. Differences in median values were compared for before and
after 1970, which was the same year Juckem et al. (2008) used to find a step increase in
precipitation (Table 7). A longer time period (1933-2008) was used when the data were
available, so that there was an equal number of observations on either side of the break
between 1970 and 1971 (n = 38). Juckem et al. (2008) used a shorter time period, 1941-
2000, to determine a step increase in precipitation, but for this study the longer period
was used to capture the most current precipitation records.
36
A significant increase in annual precipitation between 1970 and 1971 indicated
the existence of a step increase in precipitation. Climate stations lacking a significant
trend in annual precipitation were interpreted as having no step change (Table 7). Annual
average precipitation for Central Wisconsin is 760 to 840 mm (USDA, 2006). Most of
the median values in Table 7 fit into this range except for locations where significant
increases occurred (Hancock, Montello and Wautoma). Precipitation outside the annual
average range indicated more dramatic climate shifts in the southern part of the study
area and justified the use of the step increase covariate.
The difference in median annual precipitation before and after 1970 and 1971 for
the composite central division data was calculated for two time periods: 1933-2008 and
1955-2008. The longer data set resulted in a significant difference in median values (p-
value = 0.0412), while the shorter data set indicated no difference (p-value = 0.0569).
This indicates that the longer data set (1933-2008) was sensitive enough to pick out the
step increase in precipitation where as the shorter composite data set (1955-2008) was not.
This differs from the annual precipitation trends which found no significant trends for
either time period mentioned above (Table 4).
37
Table 7. Results for changes in the median cumulative annual precipitation using the Mann-Whitney test
for before and after 1970. P-value < 0.05 indicates a step increase in precipitation.
Location of COOP
Climate Stations
Time
Period
Median Value
(mm)
Time
Period
Median Value
(mm)
Median Difference
(mm)
P-Value for Difference
>0
Hancock 1933-1970 735.84 1971-2008 837.18 101.3 0.018*
Montello 1955-1970 707.64 1971-2008 892.56 184.9 0.013*
Stevens Point 1933-1970 774.45 1971-2008 818.39 43.9 0.486
Waupaca 1933-1970 778.26 1971-2008 835.91 57.7 0.066
Wautoma 1933-1970 734.82 1971-2008 848.36 113.5 0.007*
Wisconsin Rapids 1933-1970 761.75 1971-2008 835.66 73.9 0.379
Composite 1 1933-1970 764.29 1971-2008 850.65 86.4 0.041*
Composite 2 1955-1970 762.76 1971-2008 850.65 87.9 0.057
* indicates significant p-values < 0.05
Bivariate Analysis
The bivariate test, developed by Maronna and Yohai (1978), was used to
determine the year that changes in groundwater levels occurred at monitoring wells. This
was accomplished by finding non-stationarity in the monitoring well records.
Discontinuity of the mean represents non-stationarity. Douglas et al. (2000) used the
water balance equation to illustrate that non-stationarity was analogous with changes in
groundwater levels. They defined stationary conditions as changes in water levels
through time equal to zero. When the amount of precipitation entering the system or
groundwater leaving the system changed, non-stationarity existed.
The change in groundwater levels at test monitoring wells was used to determine
a threshold, when groundwater pumping may have shown up in the record. At test
38
monitoring wells, non-stationarity was associated with groundwater leaving the system
possibly via pumping. At some test locations there was an additional discontinuity from
increasing precipitation entering the system (the step increase in precipitation). Pumping
is documented prior to the beginning of the monitoring well records (Figure 2), so the test
for stationarity or non-stationarity is somewhat limited by the length of the data sets.
Control Monitoring Wells
The bivariate test detects the year, magnitude and direction of a systematic change
in the mean between a test series and a second correlated stationary series. Control
locations at Amherst Junction and Wautoma were considered the second correlated
stationary series and the test series because both control locations were thought to be
influenced by the covariate that represented the step increase in precipitation and the
pumping covariate. For this reason, the bivariate test was initially used to identify a
period of stationarity between the control monitoring wells.
The control monitoring well at Wautoma was thought to the least influenced by
anthropogenic processes (i.e., pumping) due to the low density of irrigation wells. The
bivariate test was calculated using Wautoma as the test series and Amherst Junction as
the second stationary series for 1958-2008. Amherst Junction, a control well not greatly
influenced by pumping, is located in the northern part of the study area where no step
increase in precipitation occurred between 1970 and 1971.
39
In Figure 12, a single discontinuity in the mean at Wautoma occurred in 1973, the
year after the peak in the graph (1972). The dashed horizontal line in Figure 6 represents
the 95% critical value. The peak, To, represents the maximum value of the difference (Ti)
between the Wautoma and Amherst Junction data series. To occurs the year before the
change in mean (Potter, 1981), therefore non-stationarity was interpreted to occur after To
(after 1973).
Non-stationarity that occurred in 1973 at the Wautoma monitoring well indicated
that the increase in precipitation contributed to an increase in groundwater levels. The
change in stationarity at Wautoma with respect to Amherst Junction occurs about the
same time as a step increase in precipitation is suspected for the area. Similar results
were found by Lettenmaier et al. (1994) when they used the bivariate test to determine
that increases in stream baseflow could be connected to increases in precipitation.
A stationary period from 1972-2008 was established at Wautoma, which included
the peak (1972), but excluded the years prior (1958-1971). Figure 13 illustrates that with
the years prior to 1972 excluded, Ti does not reach the critical value, which suggests a
change in mean did not occur at Wautoma for the new time period (1972-2008). The
results for the new stationary period implied that the only change to the monitoring well
at Wautoma had to do with the step increase in precipitation which occurred around 1970.
40
Figure 12. Bivariate results for a change in mean at Wautoma monitoring well using Amherst Junction as
the stationary data set (1958-2008). The dashed line represents the 95% critical value, Ti is the difference
in the two data series being tested, and the vertical line is the peak year (To) which occurred one year before
the change in mean. This discontinuity in mean is associated with the step increase in precipitation
between 1970 and 1971.
Figure 13. Bivariate results for a change in mean at Wautoma monitoring well for a time period after the
step increase in precipitation (1972-2008) using Amherst Junction as the stationary data set. The dashed
line represents the critical value. Statistics (Ti) below this line indicate no change in mean, establishing a
stationary period between 1972-2008.
0
5
10
15
20
25
30
1958 1968 1978 1988 1998 2008
Ti
Critical Value
0
5
10
15
20
25
30
1972 1977 1982 1987 1992 1997 2002 2007
Ti
Critical Value
To in 1972
41
To find a stationary period at the Amherst Junction control well, Amherst
Junction was used as the test series and Wautoma was the second correlated stationary
series. In the Wautoma record it was found that non-stationarity was associated with the
step increase in precipitation, but not with a decline presumed to be due to fewer
pumping wells. Amherst Junction is located in the northern part of the study area where
there was a small or no step increase in precipitation (Waupaca p-value = 0.066 in Table
6). Therefore, the entire Wautoma record (1958-2008) was used to establish a stationary
period at Amherst Junction.
Two shifts in mean occurred in the Amherst Junction record. Although the
bivariate test was designed to detect a single change in mean, it can be sensitive to
multiple changes with the largest shift identified as the primary break and the smaller
shift identified as the secondary break (Kirono and Jones, 2007). The first change in
mean occurred in 2000 after the peak in 1999 (Figure 14A). The bivariate test was
reevaluated without 2000-2008 and identified another change in mean which occurred
during in the early 1960’s (Figure 14B). Three peaks were found in the years 1961, 1962,
and 1965. Multiple peaks meant that from 1962-1966, there were multiple adjustments
and responses occurring at the monitoring well. To identify the longest possible
stationary period at Amherst Junction, data prior to the first change in mean (1962) were
left out. When 1958-1961 were excluded from the bivariate calculation, a stationary
period from 1962-1999 was established (Figure 14C).
42
Figure 14. Graphs A (Top), B (middle) and C (Bottom) of bivariate results for changes in mean at the
Amherst Junction monitoring well for three different time periods: 1958-2008, 1958-1999, and 1962-1999 (A-
C). Horizontal dashed lines represent the 95% critical value, Ti is the difference in data sets, and vertical
lines represent the peak (To), the year after To is the change in mean.
0
5
10
15
20
25
30
1958 1968 1978 1988 1998 2008
Critical Value
0
5
10
15
20
25
30
1958 1963 1968 1973 1978 1983 1988 1993 1998
Ti
0
5
10
15
20
25
30
1962 1967 1972 1977 1982 1987 1992 1997
To = 1999
To = 1961, 1962, 1965
43
Using the bivariate test, two stationary periods were found in the records of the
control monitoring wells. At Wautoma the stationary period was from 1972-2008 and at
Amherst Junction it was from 1962-1999. The stationary periods at the control wells
were important to establish, because they were used to detect a change in mean at the test
monitoring wells. Non-stationarity at the test monitoring wells indicated the year when a
threshold was reached where groundwater pumping was suspected to have a measureable
impact on groundwater levels.
Test Monitoring Wells
To find the threshold year for the potential pumping covariate at test monitoring
wells, bivariate analysis was calculated using the control monitoring wells as the
stationary data set. The bivariate analysis determined the year, magnitude and direction
of non-stationary periods which may have been caused by pumping. Control wells
closest in distance to test wells were compared due to similar precipitation patterns.
The Wautoma control well was used to find the implied pumping covariate
threshold at Hancock, because both were influenced by the step increase in precipitation
and because of proximity. Wautoma’s stationary period (1972-2008) did not include the
time period before 1970. After 1971, the step increase in precipitation had already
occurred. Therefore, the effect of precipitation did not influence the determination of the
pumping threshold year at Hancock.
44
The outcome of the bivariate test at Hancock indicated that although 1994 was the
peak year, the results plateau from 1994-1998 (Figure 15). Potter (1981) mentions that
while a plateau does not create a clear estimate of the exact year of change, it
demonstrates that the bivariate test is sensitive to any change taking place. The plateau
may coincide with a ramp up of groundwater pumping between 1994 and 1998. The last
peak in the plateau (1998) was selected as To which resulted in a non-stationarity, or a
second stationary period after 1999. Multiple regression models corroborated 1999 as the
possible pumping threshold year. The bivariate analysis results for Hancock indicate that
an increase in the magnitude of groundwater pumping during the mid to late 1990’s may
have caused declines in groundwater levels.
Figure 15. Bivariate results for a change in mean at Hancock monitoring well when compared to Wautoma
for the time period 1972-2008. The change in mean occurred in 1999, one year after the last peak in the
plateau in 1998.
0
5
10
15
20
25
30
1972 1977 1982 1987 1992 1997 2002 2007
Ti
Critical Value
To = 1994-1998
45
The Plover test well was initially compared to the Amherst Junction control well
(1962-1999) because Amherst Junction was the closest control location. The bivariate
results for the comparison show two peaks in the Plover record between 1962 and 1999
(Figure 16). The first peak, in 1973, signified non-stationarity at Plover starting in 1974.
A second, higher peak occurred in 1986 indicating an additional non-stationary period
starting in 1987. In a previous study, using double mass curves, Clancy et al. (2009)
determined that groundwater declines became noticeable in the Little Plover River
around 1973. The first peak in Figure 16 was similar to results from Clancy et al. (2009).
Therefore, 1973 was chosen as the first potential pumping threshold year instead of 1986,
even though 1986 represented a slightly higher peak.
Figure 16. Bivariate results for a change in mean at Plover monitoring well when compared to Amherst
Junction for the time period 1962-1999. The first peak in the graph was in 1973 with the change in mean
occurring in 1974.
0
5
10
15
20
25
30
1962 1967 1972 1977 1982 1987 1992 1997
Ti
Critical Value
To = 1986 To = 1973
46
The multiple peaks indicated a possible second non-stationary period, so the
Plover test well was compared with the Wautoma control well. The second comparison
to the Wautoma control well was used to determine whether additional declines in
groundwater levels occurred later in the record. The Wautoma stationary period (1972-
2008) started close to the first identified threshold year at Plover (1973) (Figure 16).
Therefore, the earlier non-stationary peak found when Plover was compared to Amherst
Junction did not influence the comparison of Plover to Wautoma.
The bivariate test using Wautoma as the correlated stationary series identified an
additional non-stationarity period at Plover between 1972 and 2008. Figure 17 illustrates
a plateau for the years 1989-1998 resulting in multiple peak values. The year 1999 was
identified as the second possible pumping threshold because it represented the end of the
plateau period or a period of continuous change.
47
Figure 17. Bivariate results for a change in mean at the Plover monitoring well when compared to
Wautoma for the time period 1972-2008. The peaks in the graph plateau from 1989 to 1998 indicate a time
period of continuous change.
The Bancroft test well was compared to both Amherst Junction (1962-1999) and
Wautoma (1972-2008) because Bancroft is located between the two control locations.
Figure 12A shows results with Wautoma (1972-2008) as the stationary data set. The
1991 peak year indicated a change in mean in 1992. The year 1992 represented the
pumping threshold. The results were the same when Bancroft was compared to the
Amherst Junction stationary time period (1962-1999) (Figure 12B). The comparison
with Amherst Junction also suggests that the step increase in precipitation may not have
occurred at Bancroft because no increase in groundwater levels took place in the early
1970’s.
0
5
10
15
20
25
30
1972 1977 1982 1987 1992 1997 2002 2007
Ti
Critical Value
1989-1998
48
Figure 18. Graphs A (Top) and B (Bottom) of bivariate results for a change in mean at the Bancroft
monitoring well when compared to Wautoma (A) from 1972-2008 and to Amherst Junction (B) from 1962-
1999. The peak in both graphs is in 1991 indicating that the change in mean occurs in 1992.
The Coloma test well was only compared to the Wautoma control location (1972-
2008) because Coloma records were poorly correlated with the Amherst Junction records.
The Coloma comparison to Wautoma (1972-2008) indicated a peak in 1973 associated
with non-stationarity that occurred in 1974 (Figure 13). The discontinuity in the mean
which occurred in 1974 was assumed to be associated with potential pumping impacts
because the direction of the change given in the bivariate results was negative. The non-
stationarity could also be the result of the test being sensitive to values at the beginning or
0
5
10
15
20
25
30
1972 1977 1982 1987 1992 1997 2002 2007
Ti
Critical Value
0
5
10
15
20
25
30
1962 1967 1972 1977 1982 1987 1992 1997
Ti
To = 1991
To = 1991
49
end of the record. For comparison purposes, the peak at Coloma was associated with a
possible pumping threshold in 1974 similar to the first threshold year found at the Plover
test well.
Figure 19. Bivariate results for a change in mean at Coloma compared to Wautoma for the time period
1972-2008. A peak occurred in 1973 indicating a change due to pumping in 1974.
In summary, the bivariate analysis indicated the year and direction of the change
in mean potentially associated with pumping at the test monitoring wells. At all four test
wells, non-stationarity represented the possible pumping threshold year. The threshold at
Hancock was in 1999, at Bancroft it was in 1992, at Coloma it occurred in 1974 and at
Plover the first threshold was in 1974 with an additional pumping covariate that surfaced
at the end of the 1990’s (1999). The bivariate results were applied to multiple regression
equations as binary variables that are “off” before the threshold year and “on” after.
0
5
10
15
20
25
30
1972 1977 1982 1987 1992 1997 2002 2007
Ti
Critical Value
To = 1973
50
Multiple Regression and ANCOVA
Multiple regression equations were developed for each monitoring well.
Regression models used growing season (May-September) water elevations for 1960-
2008. Equations were developed using the 6 and 24-month Standard Precipitation Index
(SPI) and the suggested step increase in precipitation and pumping covariates.
Covariates appeared in some equations and not others, depending on whether potential
impacts from covariates were identified in previous statistical tests. Some regression
equations contained two pumping covariates, which possibly represented increases in the
magnitude of pumping during different time periods. Equations for each monitoring well
are:
Hancock = 0.35·SPI24+0.48·STPC+-0.97·PC1+325.74 R2 = 0.77 Eq. 1
Plover = 0.33·SPI24+-0.39·PC1+-0.89·PC2+330.49 R2 = 0.69 Eq. 2
Bancroft = 0.15·SPI06+-0.28·PC1+326.01 R2 = 0.36 Eq. 3
Coloma = 0.30 SPI24 +-0.21 PC1 + 312.55 R2 = 0.24 Eq. 4
Wautoma = 0.20·SPI24+0.36·STPC+264.78 R2 = 0.63 Eq. 5
Amherst Junction = 0.42·SPI24+1.40·WLI-0.92·WLD+338.73 R2 = 0.57 Eq. 6
where monitoring well locations are water elevations (m), SPI24 is the standard
precipitation index for 24-months, SPI06 is the standard precipitation index for six
months, STPC is the step increase in precipitation covariate that was “off” until 1972 and
51
“on” after 1973 (m), PC1 is the initial pumping covariate that switched from “off” to “on”
depending on location (m), PC2 is a second pumping covariate at the Plover location that
that was “off” until 1998 and “on” from 1999-2008 (m), WLI is the increase in
groundwater levels at the Amherst Junction location after 1962 (m), WLD is the decrease
at the Amherst Junction location after 1999 (m), and the number at the end of each
equation is the elevation constant (m). Models and all variables at all locations were
significant (p-value <0.05).
The SPI24 was the primary precipitation variable chosen for this study because of
work done by Mayer and Congdon (2008). They found that because the SPI24 is
standardized, the SPI variable in regression equations will have the least influence during
normal precipitation periods, when SPI values are close to zero. Other precipitation
variables such as moving averages or lags will have less influence during dry conditions
when values are close to zero, and more influence under wet conditions as values get
larger (Mayer and Congdon, 2008). The SPI appears in all regression equations as the
main driving variable because it represents the systematic response to wet and dry
periods that occurs at monitoring wells in the study region.
The 24-month time period was used a majority of the time in this study, but the
SPI can be calculated for any time period desired. The SPI24 was used in all regression
models except at Bancroft. At Bancroft, the 6 month SPI was a better fit in the regression
model due to what was thought to be a quicker response time to precipitation events. The
SPI24 slope coefficients for all monitoring wells, not including Bancroft, were different.
52
This was possibly due to different well response times and to the well location within the
groundwater table. Monitoring wells located higher in the water table responded quicker
to changes in the aquifer than those located lower in the water table (Webster et al., 1996).
In the regression equations, the SPI24 slope coefficients illustrate this rate of change.
To better illustrate monitoring well responses to the SPI and the possible pumping
and step increase in precipitation covariates, the Multiple Regression and ANCOVA
section is broken down into subsections based on each monitoring well.
Hancock: Test Well
At the Hancock test monitoring well the step increase in precipitation covariate
(STPC) and a pumping covariate (PC1) affected water elevations through time. Equation
1 indicates that the increase in groundwater levels potentially due to the STPC after 1973
was 0.48 m. When groundwater declines became measurable in 1999, that decline at the
Hancock monitoring well was 0.97 m, in spite of increases possibly created by
precipitation. If the suggested step increase in precipitation had not occurred, the net
decline in groundwater levels may have been approximately 1.45 m. Although pumping
was developed before 1999, the STPC may have reduced the measureable impact
pumping had on groundwater levels. Because precipitation may have masked the effects
of pumping at Hancock, it may be difficult to calculate the full effect that potential
pumping had on groundwater levels from 1973-1998.
53
Figure 20A shows the observed groundwater levels at Hancock for the growing
season and predicted water elevations which include STPC in the regression model. The
vertical lines represent the threshold years found with the bivariate analysis. Differences
between predicted and observed values at the end of the graph indicate that the bivariate
test was indeed sensitive to a decline in groundwater levels that occurred at the Hancock
monitoring well. Figure 20B includes PC1 and shows the predicted results of Equation 1.
Before 1973, only the SPI24 was used to predict the Hancock monitoring well
water elevations. With the addition of the STPC, the regression model was able to
accurately predict monitoring well levels using only the suggested increase due to
precipitation until 1998. After 1999, the groundwater decline was more than the previous
response in the record to wet and dry periods. The PC1 variable modified the suggested
precipitation response to accurately predict observed monitoring well water levels after
1999. The withdrawal of groundwater was considered the main reason for declines at the
Hancock monitoring well during the end of the record because annual and seasonal
precipitation totals were higher than during the previous time periods.
54
Figure 20. Graphs A (Top) and B (Bottom) of observed and predicted multiple regression results at the Hancock monitoring well for the growing season (May-September) 1960-2008. Graph A includes the STPC after 1972 and graph B includes PC1 which began to affect monitoring well levels in 1999.
Plover: Test Well
It was assumed that the Plover monitoring well was not influenced by the STPC
that occurred at Hancock because there was no significant increasing trend and no
difference in median seasonal precipitation values. For these reasons it is implied that
pumping was the driver of groundwater levels and began to influence the water
324
325
326
327
328
329
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Han
cock
Wate
r E
levati
on
s (m
) Hancock Observed
Hancock Predicted
324
325
326
327
328
329
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Han
cock
Wate
r E
levati
on
s (m
)
1972, 1973
1998, 1999
R2 = 0.77
55
elevations at the Plover location starting in 1974. Before 1974, precipitation was thought
to be the main driver of water levels in the Plover monitoring well, although pumping
developed in the area prior to the 1970’s. The first response potentially due to pumping
(PC1) occurred between 1974 and 1998 and resulted in a water level decline of 0.39
meters (Figure 21A). The additional groundwater decline (PC2) after 1998 decreased
water levels an additional 0.89 m (Equation 2). The net decline in water elevation at the
Plover monitoring well for both periods was 1.28 m. At Hancock the net decline, if a
precipitation-step-increase had not occurred, was approximated to be around 1.45 m.
Both wells responded to a potential ramp up in pumping at around the same time (1999),
and it seems feasible that an additional pumping impact at Hancock may have been
measured earlier if there had not been a STPC at Hancock after 1972.
In Figure 21A the effect of PC1 is illustrated. The regression model for Plover
over-compensates for the larger decline at the end of the record by predicting lower water
elevations in the mid 1970’s through the mid 1980’s. With the addition of PC2 after
1998, the model adjusts during the mid 1970’s through the mid 1980’s to an improved
prediction of well water elevations (Figure 21B). Figure 21B indicates that there is a
third possible pumping response that occurs around 2005. However, the difference did
not affect stationarity, so there was no justification for adding another covariate.
56
Figure 21. Graphs A (Top) and B (Bottom) of observed and predicted multiple regression results at the
Plover monitoring well for the growing season (May-September) 1960-2008. Graph A includes PC1 which
occurred after 1973 and graph B includes PC2 added after 1998.
Bancroft: Test Well
The Bancroft monitoring well responded to a suggested pumping covariate after
1991, but the regression model was different from other monitoring well results. The
regression equation (Equation 3) indicated that after 1991, water elevations declined by
0.28 m. Before 1991, water elevations responded to the SPI for six months instead of 24-
328
329
330
331
332
333
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
Plo
ver W
ell
Ele
vati
on
s (m
) Plover Observed
Plover Predicted
328
329
330
331
332
333
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
Plo
ver
Wel
l E
levati
on
s (m
)1973, 1974
1998, 1999
R2 = 0.69
57
months used at the other monitoring wells. The quicker response to wet and dry periods
over a shorter duration was apparent in the fluctuation of water elevations throughout the
growing season record, but the magnitude of the range in the water level response was
not as great (Figure 22). The range of water levels in the Bancroft record was
approximately 1.5 meters. This was small when compared to the range of water levels at
the Plover monitoring well, which was almost four meters during the course of the record.
Small fluctuations in Bancroft water levels may also be the reason SPI06 was only able to
approximate the middle of the range of growing season values and was not able to
properly predict peaks and troughs.
Despite not being able to predict peaks and troughs, the Bancroft regression
model was able to pick up the decline in water levels after 1991. This is shown in Figure
22A as a departure of the predicted values from the middle of the range of data. When
PC1 was added after 1991, the model again adjusts to the middle of the data range and is
better able to predict some of the peaks and troughs earlier in the record, before the
addition of the suggested pumping covariate. It is important to note that in Figure 22B,
the predicted values after 2005 are closer to the observed peaks instead of in the middle
of the observed range. This could possibly be the result of a similar pumping influence
noted at the end of the Plover Record.
58
Figure 22. Graphs A (Top) and B (Bottom) of observed and predicted multiple regression results at the
Bancroft monitoring well for the growing season (May-September) 1960-2008. Graph A shows the
response to the SPI06 before PC1 was added. Graph B includes the pumping covariate that occurred after
1991.
Coloma: Test Well
The regression model at Coloma contained one suggested pumping covariate that
began after 1973. The decline in groundwater levels was 0.21 m (Equation 4). Coloma’s
324
325
326
327
328
329
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Ban
croft
Well
Ele
vati
on
s (m
)Bancroft Observed
Bancroft Predicted
324
325
326
327
328
329
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Ba
ncroft
Well
Ele
va
tion
s (m
)
1991, 1992
R2 = 0.36
59
growing season record (May-September) was spotty with several missing monthly values.
For this reason, the model did not predict Coloma water elevations as well, compared to
other regression equations (Figure 23). The monitoring well response was more dramatic
with respect to wet periods than it was with respect to dry periods. This may indicate that
a rolling average or a lag in precipitation may have been better precipitation variables to
use with this monitoring well instead of the SPI24. A rolling average or lag in
precipitation would have resulted in a greater response from the regression model to
wetter periods as precipitation values increased and less response to drier periods when
precipitation values were smaller (Mayer and Congdon, 2008).
Figure 23. Observed and predicted multiple regression results at the Coloma monitoring well for the
growing season (May-September) 1960-2008. The graph shows the response of PC1 after 1973.
310
311
312
313
314
315
1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006
Colo
ma W
ell E
levati
on
s (m
)
Coloma ObservedColoma Predicted
R2 = 0.24
60
Wautoma: Control Well
The regression model for the monitoring well at Wautoma included only the
SPI24 and the STPC. The STPC that was identified between 1972 and 1973 added 0.36
m to monitoring well water levels (Equation 5). This was similar to the response from
the step increase in precipitation at Hancock (STPC = 0.48 m). When the Wautoma
regression model was calculated without the step increase, the model adjusted its
predicted values to the time period after 1972. Figure 24A shows that predicted water
elevations before 1972 were lower, and when the STPC was included the predicted water
elevations adjusted downward before 1972 (Figure 24B).
The Wautoma monitoring well water elevations show little fluctuation and the
regression model predicts more sharp peaks and troughs than what actually existed in the
data. The smaller range in the Wautoma record was similar to the smaller range found in
the Bancroft record, but additionally there was little difference in water elevations at
Wautoma during the growing season. This lack of response to seasonal fluctuations
throughout the record may be due to Wautoma’s position in the groundwater flow system
which is lower than any of the other monitoring wells (elevation datum 266 meters).
Additionally, the Wautoma monitoring well does not respond quickly to precipitation
events as shown in Equation 5 with the SPI24 slope coefficient of 0.20. The rate of
change is lowest among monitoring wells where the 24-month SPI was used. The slow
response might explain the model’s attempt to include nonexistent peaks and troughs.
61
Figure 24 Graphs A (Top) and B (Bottom) of observed and predicted multiple regression results at the
Wautoma monitoring well for the growing season (May-September) 1960-2008. Graph A shows the
response to the SPI24 before the STPC was added. Graph B includes the STPC that occurred after 1972.
263
264
265
266
267
268
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Wau
tom
a W
ell
Ele
vati
on
s (m
)
Wautoma observed
Wautoma Predicted
263
264
265
266
267
268
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Wa
uto
ma
Well
Ele
va
tion
s (m
)
1972, 1973
Adjusted R2 = 0.63
62
Amherst Junction: Control Well
The Amherst Junction monitoring well responded to two shifts in the record
between 1960 and 2008. After 1999, water levels in the monitoring well declined by 0.92
m (Equation 6). Although Amherst Junction is thought to be influenced by groundwater
pumping, the monitoring well is located in an area with fewer high capacity wells and
therefore the influence from pumping was thought not to be as great. Pumping may have
contributed to the decrease in water levels, but the magnitude of the response may have
been caused by less precipitation. At the beginning of the record there was an increase in
the Amherst Junction water elevations. This increase after 1962 predicted by the
regression model was 1.40 m.
A possible explanation for the shifts in the Amherst Junction monitoring well
levels before 1962 and after 1999 could partially be due to the well’s location. The
Amherst Junction well is located on the shores of Lake Emily in western Portage County.
During three different occasions in the well’s record, there were values measured above
the land surface. The location of the monitoring well could also explain the large
fluctuations in water elevations through the record and during the growing season.
Figure 25A illustrates the predicted regression results from the SPI24 for Amherst
Junction water elevations. The regression model in Figure 25A, which only includes the
SPI24 precipitation variable, clearly shows the breaks in the record before 1962 and after
1998. Figures 25B and C include the addition of the two other variables (WLI and WLD).
63
The predicted values from the model are improved, although it seems the variations in
Amherst Junction’s record are too large for the model to accurately explain.
Figure 25. Graphs A (Top), B (Middle) and C (Bottom) of observed and predicted multiple regression
results at the Amherst Junction monitoring well for the growing season (May-September) 1960-2008. Graph
A shows just the SPI24, graph B includes the water level decline that occurred after 1999 and graph C
contains the increased water levels after 1962.
338
339
340
341
342
343
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Amherst Observed
Amherst Predicted
338
339
340
341
342
343
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Am
herst
Ju
ncti
on
Well
Ele
va
tion
s (m
)
338
339
340
341
342
343
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
1962, 1963 1998, 1999
1962, 1963
R2 = 0.57
64
Multiple Regression Summary
At test and control monitoring wells, changes in water elevations were a response
potentially due to pumping or changes in precipitation patterns (Table 8). Suggested
pumping at Hancock may have been masked by the step increase in precipitation. If
masking had not occurred, the net decline may have been similar to the net decline found
at Plover without the suggested step increase in precipitation. The effect of the step
increase at Hancock was thought to be similar to that found at Wautoma, even though
Wautoma showed little variation in groundwater fluctuations. At monitoring wells where
there was a quicker response to precipitation events (Bancroft, Coloma and Amherst
Junction), the possibility of using different precipitation variables may better help predict
water elevations. Table 8 quantifies changes in groundwater levels at each monitoring
well.
65
Table 8. Results from multiple regression models which quantify increases and declines in monitoring well
water elevations (m) possibly due to pumping or the step increase in precipitation. The step increase at
Wautoma was between 1972 and 1973 and the increase at Amherst Junction was between 1962 and 1963.
Location of
Monitoring Wells
Increase in
G.W. Levels
From STPC
and WLI
Decline in
G.W. Levels
From PC1
and WLD
Decline in
G.W. Levels
From PC2
Net Decline
in G.W.
Levels
(1960-2008)
Hancock 0.48 (1973) 0.97 (1999) NA 0.97
Plover NA 0.39 (1974) 0.89 (1998) 1.28
Bancroft NA 0.28 (1991) NA 0.28
Coloma NA 0.21 (1973) NA 0.21
Wautoma 0.36 (1973) NA NA NA
Amherst Junction 1.40 (1962) 0.92 (1999) NA 0.92
STPC: Step Increase in Precipitation Covariate
PC1: Pumping Covariate One
PC2: Pumping Covariate Two
WLI: Water Level Increase (Amherst Junction)
WLD: Water Level Decrease (Amherst Junction)
Conclusions
Surface and groundwater levels have declined in some regions of the study area
possibly due to groundwater withdrawals. Groundwater levels have also increased in
other regions due to a suggested step increase in precipitation. Three questions were
addressed in this study: 1) Is there a change in groundwater levels potentially due to
precipitation and/or pumping and where do they occur in the study region? 2) If there is a
change, when does it show up in the groundwater records? 3) What are the quantitative
differences in groundwater levels associated with increases or decreases in groundwater
levels?
66
Annual and seasonal trends revealed that precipitation increases occurred in the
southern part of the study area and were generally associated with summer rainfall. In
the northern part of the study region, no significant trend was detected so a spatial
difference between the northern and southern part of the study area had to be taken into
account when examining the potential pumping/precipitation interaction. The Mann-
Whitney test confirmed trend tests and identified those locations where a step increase in
precipitation occurred between 1970 and 1971.
The year that the implied effect of pumping and precipitation may have become
measureable in the record was identified using the bivariate test. At the Hancock and
Wautoma monitoring wells, the suggested step increase in precipitation resulted in an
increase in groundwater elevations between 1972 and 1973. At the monitoring wells of
Plover and Coloma, pumping potentially started to influence groundwater levels between
1973 and 1974. Plover area may have experienced an increase in the magnitude of
groundwater withdrawals between 1989 and 1999. The Hancock location experienced a
decrease in groundwater levels beginning in 1999. The Bancroft monitoring well was
potentially affected by groundwater withdrawals starting in 1991, which was the
beginning of a time period where both Hancock and Plover experienced declines in
groundwater levels that spanned over multiple years. These time breaks were used to
quantify changes which may have been due to pumping and precipitation.
Multiple regression equations developed using binary covariate variables
represented the potential impacts of pumping and precipitation and revealed declines in
67
groundwater levels. An increase in precipitation added an average of 0.42 m to
groundwater levels at Hancock and Wautoma. At Hancock, the increase in groundwater
levels was thought to mask the effects of pumping earlier in the record, making the
quantification of groundwater declines before 1999 difficult. The net decline in
groundwater levels at the Plover monitoring well was 1.28 m. The monitoring wells at
Coloma and Bancroft experienced smaller decreases, and had an average decline of 0.25
m. The smaller decreases were associated with smaller groundwater fluctuations thought
to be caused by the closer proximity to groundwater discharge areas.
The conclusions confirm the hypothesis for this study. Increases in precipitation
have changed monitoring well levels by increasing groundwater levels in some regions of
the study area. Groundwater levels have declined in other regions of the study area
despite increases in precipitation. The use of multiple statistical approaches and the
corroboration with recent studies by Clancy et al., (2009) and Kraft and Mechenich (2010)
give a strong inference that there is limit to the sustainability of surface and groundwater
systems. My hope is twofold: 1) that these conclusions will help managers of
groundwater resources understand the interaction between changes in precipitation and
groundwater, and 2) that the results will supplant the concept of an unending supply of
groundwater in Wisconsin.
68
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74
Appendices
Appendix 1
Lake Level Records
Long Lake-Saxeville was considered an additional long term data source. It was
representative of a data source in a LDW (Figure 4) and it had long, continuous records.
For these reasons, Long Lake-Saxeville was analyzed using multiple regression analysis
with ANCOVA. Data for Long Lake, Saxeville was recorded by the Saalsaa/Ziemer
family who live on the lake. The measurements were taken from a high water mark
down to the water’s edge, representing beach length. Beach length was converted to lake
surface elevations through a process explained in Appendix 2. Average yearly values
were calculated from measurements taken one to three times per year from 1947 to 2007.
Fifteen other lakes with stage measurements were chosen for closer examination
of groundwater fluctuations (records available from Waushara County and WDNR).
These lakes’ surface elevations were compared to the monitoring wells water elevations
at Amherst Junction and Wautoma using multiple regression with ANCOVA. Lakes
were located in areas with both LDW and HDW. These analyses and results can be
found in Appendix 3. Quantified results from the examination of lake stages were used
to corroborate quantified results of changes at monitoring wells.
75
Appendix 2
Lake Level Records: Long Lake Saxeville
Raw Data: Excel Workbook “Long Lake Saxeville”
Workbook Location: G:\usr\projects\Centrallake&streams\lake levels
Summary
Long Lake Saxeville is located approximately five miles northeast of Wild Rose (Figure
26) in an area with few high capacity pumping wells. Because there is little groundwater
pumping at this location, lake surface elevations should respond similarly to the
monitoring well located at Wautoma where there is little groundwater pumping.
Initially Long Lake Saxeville had too few measurements to warrant an analysis of the
data. Additional data was acquired from the Saalsaa/Ziemer family who live on the lake.
The additional data were shoreline measurements that extended from a high water mark
to the water’s edge. Measurements were made from 1947 to 2007. Shoreline
measurements were plotted against the lake’s surface elevation measurements obtained
from the Wisconsin Department of Natural Resources (WDNR) in Waushara County.
The equation from the regression line of the plot was used to convert the Saalsaa/Ziemer
reported beach length into elevations. Converted Long Lake Saxeville elevations were
compared to water level elevations at Wautoma.
Figure 26. The location of Long Lake Saxeville not to be confused with Long Lake Oasis near Plainfield
Wisconsin.
0 2.51.25 Miles$ 0 2.5 51.25 Kilometers
LONG
LAKE
WILD
ROSE
PO
RT
AG
EW
AU
PA
CA
PORTAGEWAUSHARA
WAUPACAWAUSHARA
Explanation
County Boundary
Wild Rose
Long Lake Saxeville
76
Data
The Saalsaa/Ziemer family measured the beach distance from a shoreline high water
mark, which they established as a benchmark, to the edge of the water on Long Lake
Saxeville. The beach length above water was used as the proxy for lake surface levels.
Lower values indicated higher Lake surface levels. The Saalsaa/Ziemer lake
measurements date from 6-1-1947 to 6-1-2007. Prior to 1958 measurements were made
periodically. After 1958 measurements were made one to three times per year.
In addition to the Saalsaa/Ziemer shoreline measurements, there were 14 lake surface
elevations taken by the Wisconsin Department of Natural Resources (WDNR) between
11-4-1987 and 7-31-2007. The WDNR values were used to convert the Saalsaa/Ziemer
measured beach lengths into lake surface elevations. Converted values expanded the
Long Lake Saxeville data and allowed further evaluation of water level changes through
time.
To convert the measured beach lengths to lake elevations, WDNR elevations were
matched with the Saalsaa/Ziemer beach lengths for similar dates. These two data sets
were plotted against each other (Figure 27). Measurements from the WDNR and
Saalsaa/Ziemer family were made during the same month or within a month or two of
each other. The dates and values for these matches can be found in the excel file named
“Long Lake Saxeville”, which is located at G:\usr\projects\Centrallake&streams\lake.
The equation from the trend line in Figure 27 was rearranged and used to convert
citizen’s measurements into water surface elevations. The equation is:
X = (y – 10343) / -11.81 Eq. 7
where X is the converted lake surface elevations (ft), and y is the citizen’s reported beach
length. The citizen’s converted elevations were plotted against time and are illustrated in
Figure 28.
77
Figure 27. WDNR lake surface elevations and citizen measured beach length for similar dates at Long
Lake Saxeville.
Figure 28. Long Lake Saxeville lake surface elevations converted from beach length using regression
equation 1. Measurements were taken from 6-1-1947 to 6-1-2007.
Conclusions
The Saalsaa/Ziemer measurements of beach length at Long Lake Saxeville were
successfully converted to water surface elevations using data from the WDNR. Multiple
regression analysis with ANCOVA was used to identify and quantify changes to the
converted Long Lake elevations. Wautoma monitoring well water elevations were used
as the main explanatory variable and threshold years were established by Kraft and
Mechenich (2010). An example of regression analysis can be found in Appendix 7 and
results for Long Lake Saxeville regression analysis can be found in Appendix 3.
y = -11.81x + 10343
R² = 0.95
0
10
20
30
40
50
60
70
870 871 872 873 874 875 876
Cit
izen
Rep
orte
d B
each
Len
gth
(ft
)
WDNR Lake Surface Elevations (ft)
866
868
870
872
874
876
878
1945 1955 1965 1975 1985 1995 2005
Co
nve
rted
Lak
e Su
rfac
e El
evat
ion
s (f
t)
78
Appendix 3
Lake Level Records: Regression Analysis (ANCOVA) Results
Raw Data: Excel Workbook “lakewell”
Workbook Location: G:\usr\projects\Centrallake&streams\lake levels
Summary
Fifteen lakes with extended records used to identify and quantify changes in lake levels
(Table 9). The records for 14 of the 15 lakes came from Waushara County DNR lake
surface elevations files. Data from the 15th lake, Long Lake Saxeville, was discussed in
Appendix 2.
Lake surface elevations were analyzed using water elevations at two monitoring wells
within the study area: Wautoma and Amherst Junction. These two monitoring wells were
used as the main explanatory variables in multiple regression with ANCOVA. Multiple
regression was used to determine pumping impacts between an earlier (prior to large
scale pumping) and later time period (after pumping began to affect lake records).
Presumably these two monitoring wells show less influence from pumping and thus serve
as controls.
When the Wautoma monitoring well was used in the regression models, the results
indicated that lakes in areas where there was little influence from groundwater pumping
showed little to no change through time. Lakes located in regions where groundwater
pumping was heavy show a decline. This change was thought to be the result of
increased development of high capacity pumping wells.
When Amherst Junction was used in the regression models, lakes in areas with little
groundwater pumping showed an increase in surface elevations. Lakes in areas where
there is a greater density of high capacity wells show no change. The difference between
the results using Amherst Junction and using Wautoma may be due to differences in the
climate or the development of pumping in the Amherst Junction area.
Lake Records
A majority of the lakes are located in Waushara County and were grouped according to
their geographic proximity to each other. Sharon Lake is located in Marquette County
and represents one of the two lakes not grouped with any other lakes due to distance
(Pleasant Lake is the second). Groups were referred to as clusters. Lake clusters are
79
given in Table 8 and illustrated in Figure 29. Clusters 1 and 5 were thought to be
influenced by groundwater pumping while the other clusters were not.
Table 9. Name, county, period of record, and the cluster number for lakes used in this analysis.
Lake Name County
# of
levels
First
Measurement
Last
Measurement
Ave. #
Years
Between
Levels
Cluster
#
Fish Lake Waushara 11 7/10/1973 8/3/2007 3.1 1
Huron Lake Waushara 13 7/3/1973 8/3/2007 2.62 1
Long Lake Oasis Waushara 23 8/16/1961 8/3/2007 2 1
Pine Lake Hancock Waushara 15 7/10/1973 8/3/2007 2.27 1
Gilbert Lake Waushara 28 5/10/1962 7/30/2007 1.62 2
Kusel Lake Waushara 26 9/30/1963 7/30/2007 1.69 2
Long Lake Saxeville Waushara 82 6/1/1947 7/1/2007 1.35 2
Pine Lake Springwater Waushara 27 2/8/1961 7/30/2007 1.72 2
Big Silver Lake Waushara 23 5/15/1966 8/1/2007 1.79 3
Burghs Lake Waushara 18 9/7/1973 8/1/2007 1.88 3
Irogami Lake Waushara 24 1/1/1931 8/1/2007 3.19 3
Lake Lucerne Waushara 22 9/30/1963 8/1/2007 1.99 3
Witter's Lake Waushara 20 10/6/1963 8/3/2007 2.19 3
Sharon Lake Marquette 72 11/17/1984 5/31/1994 0.13 4
Pleasant Lake Waushara 21 7/9/1964 8/3/2007 2.05 5
Figure 29. The location of lakes and clusters used in data analysis. Lakes were grouped into clusters
according to geographic proximity.
0 52.5 Miles
0 5 102.5 Kilometers
GR
EE
N
LA
KE
MA
RQ
UE
TT
E
$Explanation
County Boundary
Lakes
Cluster #1
Cluster #2
Cluster #3
Cluster #4Cluster #5
80
Monitoring well water elevations (Amherst Junction and Wautoma) were used as
explanatory variables in multiple regression models to determine if lake surface
fluctuations were impacted by groundwater pumping. An earlier time period (Table 10)
was compared to a later time period (Table 10) using a binary variable that was “off”
during the early period and “on” during the later time period. An example of this
approach can be found in Appendix 7. Many of the lakes had few measurements taken
over a long period of time. Due to spotty and inconsistent measurements, most threshold
years occurred pre and post 1993 (Table 10). Without long term consistent lake
measurements, conclusions were only used as a comparison to other thesis data analyses.
Table 10. Time breaks for binary regression variables and the number of measurements during each time
period for lakes in data analysis.
Lake Name
Cluster
# Early
Early
n Late
Late
n
Fish Lake 1 1973-1989 3 1993-2007 8
Huron Lake 1 1973-1987 4 1993-2007 9
Long Lake Oasis 1 1961-1972 10 1981-2007 10
Pine Lake Hancock 1 1973-1987 4 1993-2007 11
Gilbert Lake 2 1962-1987 16 1993-2007 12
Kusel Lake 2 1963-1989 15 1993-2007 11
Long Lake Saxeville 2 1959-1974 29 1999-2007 12
Pine Lake Springville 2 1961-1989 15 1993-2007 12
Big Silver Lake 3 1966-1989 13 1993-2007 8
Burghs Lake 3 1973-1987 7 1993-2007 11
Lake Irogami 3 1961-1988 7 1993-2007 10
Lake Lucern 3 1963-1987 11 1993-2007 11
Witter's Lake 3 1963-1987 9 1993-2007 11
Sharon Lake 4 1984-1989 39 1990-1994 33
Pleasant Lake 5 1964-1989 7 1993-2007 14
Lake Levels vs. the Wautoma Monitoring Well
Lake surface elevations were analyzed using water elevations from the Wautoma
monitoring well as the main explanatory variable in multiple regression models. Binary
variables were included which were “off” during the early time period and “off” during
the late time period (Table 10). P-values less than 0.05 indicate a significant increase or
decrease in lake surface elevations between the two time periods (Table 11). Declines
are positive numbers and increases in lake surface elevations are negative numbers.
These results are given in Table 11.
81
Table 11. Change in lake levels between the early and late time period. Positive numbers represent a
decline and negative numbers represent increases in lake surface elevations. All results use the Wautoma
monitoring well as the main explanatory variable. * indicates a significant p-value of less than 0.05.
Lake Name
Cluster
#
Decline
(ft) P-Value 95% CI
Fish Lake 1 2.7 0.029* ± 2.3
Huron Lake 1 3.6 0.009* ± 2.5
Long Lake Oasis 1 0 0.951 ± 1.6
Pine Lake Hancock 1 3.2 0.001* ± 1.6
Gilbert Lake 2 0.3 0.257 ± 0.6
Kusel Lake 2 0.5 0.136 ± 0.7
Long Lake Saxeville 2 0 0.961 ± 0.9
Pine Lake Springville 2 0.8 0.004* ± 0.5
Big Silver Lake 3 -0.6 0.218 ± 1.0
Burghs Lake 3 0.9 0.037* ± 0.8
Lake Irogami 3 0 0.996 ± 0.6
Lake Lucern 3 -1.7 0.004* ± 1.1
Witter's Lake 3 -0.4 0.333 ± 0.8
Sharon Lake 4 -0.1 0.273 ± 0.1
Pleasant Lake 5 1.5 0.001* ± 0.8
Lake results varied according to cluster #. Clusters 1 and 5 are in regions where there is a
high density of high capacity pumping wells and indicate that groundwater pumping may
be affecting water levels. Clusters 2, 3, and 4 are in regions where there are few high
capacity pumping wells and show little change indicating that groundwater pumping may
not be effecting their surface elevations.
Lake Levels vs. the Amherst Junction Monitoring Well
Lake surface elevations were calculated with the Amherst Junction monitoring well as the
main explanatory variable in a similar manner as described with the Wautoma monitoring
well. The Amherst Junction well is located near Lake Emily in Portage County and is
thought to be influenced by recent groundwater pumping development in the area.
Regardless of this, the monitoring well is in an area with a low density of high capacity
wells and serves as a control. Results using the same time periods listed in Table 10 are
given in Table 12.
82
Table 12. Change in lake levels between the early and late time period. Positive numbers represent a
decline and negative numbers represent increases in lake surface elevations. All results used the Amherst
Junction monitoring well as the main explanatory variable. * indicates a significant p-value of less than 0.05.
Lake Name
Cluster
#
Decline
(ft) P-Value 95% CI
Fish Lake 1 1.5 0.270 ± 2.9
Huron Lake 1 2.0 0.328 ± 4.3
Long Lake Oasis 1 -1.8 0.009* ± 1.3
Pine Lake Hancock 1 1.4 0.178 ± 2.2
Gilbert Lake 2 -1.0 <0.001* ± 0.5
Kusel Lake 2 -1.0 <0.001* ± 0.5
Long Lake Saxeville 2 -1.5 <0.001* ± 0.7
Pine Lake Springville 2 -0.3 0.295 ± 0.4
Big Silver Lake 3 -3.0 <0.001* ± 1.2
Burghs Lake 3 -1.2 0.061 ± 1.3
Lake Irogami 3 0.9 0.004* ± 0.5
Lake Lucern 3 -2.9 <0.001* ± 0.9
Witter's Lake 3 -1.9 <0.001* ± 0.9
Sharon Lake 4 -0.9 <0.001* ± 0.2
Pleasant Lake 5 0.5 0.233 ± 0.8
The results in Table 12 indicate that in clusters 1 and 5 declines are not significant.
These lakes, although in areas where there is a high density of high capacity wells, do not
show any changes through time when compared to the Amherst Junction monitoring well.
The table also indicates that are significant increases in a majority of the lakes in clusters
2, 3, and 4 where there is a low density of high capacity wells.
Conclusions
When lakes in areas that are not as affected by potential groundwater pumping are
analyzed using Amherst Junction’s monitoring well as the explanatory variable, lake
surface elevations show a significant increase. This could indicate that lakes in clusters 2,
3, and 4 follow the patterns of the Wautoma monitoring well instead of the Amherst
Junction monitoring well. It could also indicate that Amherst Junction was possibly
affected by groundwater pumping from 1999-2008 or that the climate was drier in the
northeastern part of the study area. This is investigated within this study and also in the
report by Kraft and Mechenich (2010).
83
Appendix 4
Kendall’s Tau Trend Analysis
Raw Data: Excel Workbook “Monthly and yearly precip records”
Workbook Location: G:\usr\projects\Centrallake&streams\Trend Analysis
Summary
Kendall’s tau was used to determine trends for annual and seasonal cumulative
precipitation. Trends are increases or decreases in the data through time. Kendall’s tau is
a number between 1 and -1. Zero represents no trend and anything close to 1 or -1
represents positive or negative trends. In this report a step by step procedure is
documented to illustrate how trends were calculated. Summer precipitation totals from
the Stevens Point COOP climate stations from 1955-2008 were used in this example.
Procedure
1. Monthly precipitation data was collected from the NOAA website for Stevens Point,
Wisconsin from 1955-2008.
http://www.ncdc.noaa.gov/oa/climate/climatedata.html#monthly.
2. Missing data was interpolated using a weighted average, based on distance, with the
three closest climate stations.
3. Data was sorted by month and grouped according to season. Summer months
consisted of June through August. Summer records were totaled to produce a cumulative
summer precipitation amount. Summer precipitation data is given in Table 13.
84
Table 13. Cumulative summer (June-August) precipitation from the NOAA COOP climate station in
Stevens Point.
year Summer Precip. @ St. Pt. (mm) year
Summer Precip. @ St. Pt. (mm)
1955 207.8 1993 398.5 1956 307.3 1994 377.7 1957 229.1 1995 344.9 1958 258.8 1996 320.8 1959 309.4 1997 300.0 1960 213.4 1998 336.3
1961 355.1 1999 407.4 1962 306.6 2000 402.3 1963 197.9 2001 307.8 1964 342.1 2002 438.2 1965 300.2 2003 245.6 1966 230.9 2004 280.4 1967 303.5 2005 307.3 1968 311.7 2006 224.5
1969 274.1 2007 310.4 1970 264.9 2008 224.8
1971 300.5 1972 317.8 1973 244.6 1974 243.8 1975 279.7
1976 200.4 1977 218.7 1978 368.0 1979 311.7 1980 365.8 1981 261.6 1982 339.1 1983 233.4 1984 446.8
1985 239.8 1986 327.2 1987 286.5 1988 225.6 1989 188.7 1990 355.6 1991 173.2 1992 241.6
5. An online statistical calculator was used to determine if there was a significant trend
in the precipitation data. The website is called “Free Statistics and Forecasting Software”
and can be found at http://www.wessa.net/rwasp_kendall.wasp.
6. Years were entered into the X data box and precipitation was entered into the Y data
box as shown below.
85
7. The data were computed and the output table was called “Kendall tau Rank
Correlation”. The 2-sided P-value and Kendall tau were examined. If the 2-sided P-
value was less than <0.05 then there was a significant trend. The Kendall tau number
indicated the direction of the trend. In example shown below there was no trend but the
data tracked positively.
86
Appendix 5
Mann-Whitney Test
Raw Data: Excel Workbook “Monthly and yearly precip records”
Workbook Location: G:\usr\projects\Centrallake&streams\Trend Analysis
Summary
The Mann-Whitney test, a non-parametric version of the t-test, was used to corroborate
findings from the trend tests and to determine if a step increase in precipitation occurred
between 1970 and 1971. The Mann-Whitney test calculates a difference in median data
values. This test was used for the precipitation data. In this example yearly cumulative
precipitation from Stevens Point was compared for two time periods: 1933-1970 and
1971-2008 to determine if there was a difference in median value.
Procedure
1. Monthly precipitation data was collected from the NOAA website for Stevens Point,
Wisconsin from 1933-2008.
http://www.ncdc.noaa.gov/oa/climate/climatedata.html#monthly.
2. Missing data was interpolated using a weighted average, based on distance, with the
three closest climate stations.
3. Monthly values were totaled to produce cumulative yearly precipitation at the Stevens
Point COOP climate station. Yearly totals were divided into two groups: group 1
contained data from 1933-1970 and group 2 contained data from 1971-2008. Data values
are given in Table 14.
87
Table 14. . Yearly cumulative precipitation from NOAA COOP climate station in Stevens Point. Data was
divided into two groups between 1970 and 1971 to compare median values between the two time periods.
Year
St. Pt. Precip. (mm) Year
St. Pt. Precip. (mm)
1933 690.9
1971 863.6 1934 858.8
1972 822.2
1935 936.0
1973 982.5 1936 631.7
1974 652.5
1937 755.9
1975 725.2
1938 1324.1
1976 548.9 1939 661.9
1977 924.3
1940 990.1
1978 812.3 1941 899.9
1979 831.6
1942 1093.7
1980 862.3 1943 850.6
1981 708.2
1944 785.6
1982 944.4 1945 1036.8
1983 816.4
1946 733.3
1984 1139.7 1947 795.3
1985 845.6
1948 521.5
1986 881.4 1949 677.9
1987 718.8
1950 743.2
1988 636.0 1951 869.2
1989 736.1
1952 647.4
1990 847.3 1953 725.4
1991 820.4
1954 999.2
1992 921.3 1955 657.6
1993 929.1
1956 694.4
1994 803.9 1957 694.9
1995 836.4
1958 647.7
1996 791.2 1959 943.4
1997 672.6
1960 677.9
1998 734.6 1961 883.2
1999 786.1
1962 739.9
2000 880.4 1963 620.5
2001 861.6
1964 788.4
2002 989.1 1965 999.5
2003 712.2
1966 626.1
2004 912.6 1967 763.0
2005 772.7
1968 893.3
2006 726.4 1969 853.7
2007 752.9
1970 881.4 2008 763.8
5. These data were entered into Minitab version 10 and the Mann-Whitney test was
chosen from the nonparametric stats tab. The first sample was yearly precipitation at
Stevens Point from 1933-1970. The second sample was yearly precipitation at Stevens
Point from 1971-2008, as shown below.
88
6. The results were given in the Minitab output displayed below. St. PT. Precip. (mm) is
the record from 1933-1970. St. Pt. Precip. (mm)_1 is the record from 1971-2008. The
last line gives the p-value for the difference in median between the two time periods. The
p-value of 0.4864 indicated that there was no significant difference between the median
precipitation values at Stevens Point for the two time periods 1933-1970 vs. 1971-2008.
Mann-Whitney Test and CI: St. Pt. Precip. (mm), St. Pt. Precip. (mm)_1 N Median
St. Pt. Precip. (mm) 38 774.3
St. Pt. Precip. (mm)_1 38 818.4
Point estimate for ETA1-ETA2 is -27.4
95.1 Percent CI for ETA1-ETA2 is (-85.8,38.4)
W = 1395.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.4864
The test is significant at 0.4864 (adjusted for ties)
89
Appendix 6
Bivariate Test
Raw Data: Excel Workbook “bivariate control wells” and “bivariate test wells”
Workbook Location: G:\usr\projects\Centrallake&streams\Bivariate Analysis
Summary
The bivariate test was used to determine the year that changes in groundwater levels
occurred at monitoring wells. This was accomplished with a series of equations
calculated in Microsoft Excel 2007. Depth to water measurements were used from each
monitoring well. In this example the test well at Bancroft was being compared to the
control well at Wautoma. Wautoma was used as the stationary regional series.
Procedure
1. Depth to water measurements for Bancroft and Wautoma were collected from the
USGS website http://nwis.waterdata.usgs.gov/wi/nwis/gwlevels.
2. An average was taken of daily and monthly values to obtain yearly data.
3. Records from 1972-2008 were used because of the stationary period established at the
Wautoma control monitoring well.
4. The first set of equations standardized both series. The equations are given below and
the raw data for this standardization is given in Table 15.
Let xj' be the regional series and yj
' the series to be tested, both of length n.
Step 1 : Standardize series.
Let X 1 n x j'
j =1
n
; Y 1 n yj'
j1
n
; Sx 1 n xj' X
2
j1
n
1 2
; S y 1 n yj' Y
2
j1
n
1 2
.
For all 1 j n, let xj x j' X Sx and yj yj
' Y Sy .
90
Table 15. Raw data for the first step of the bivariate analysis, which is the standardization of the two data
sets.
year
xj' Wautoma (ft below
land surface)
yj' Bancroft (ft below
land surface) xj yj
1972 4.22 4.7 1.554736164 -0.71362049
1973 2.27 4.23 -1.10921175 -1.41615378
1974 2.24 4.68 -1.15152682 -0.74589234
1975 2.59 4.99 -0.67346009 -0.28663913
1976 3.35 5.24 0.364381488 0.086969565
1977 4.40 5.35 1.7948163 0.249570026
1978 4.12 4.61 1.423057296 -0.84767278
1979 2.99 3.95 -0.1214397 -1.83817024
1980 3.22 4.52 0.19241326 -0.98048384
1981 3.80 5.00 0.987360534 -0.26677953
1982 3.53 4.53 0.615613789 -0.96818443
1983 2.42 4.32 -0.9031398 -1.28582517
1984 1.92 4.29 -1.58466889 -1.32430314
1985 2.47 4.47 -0.83223158 -1.05743979
1986 1.96 4.15 -1.52444269 -1.52662279
1987 2.66 5.05 -0.57786908 -0.19602971
1988 3.49 5.39 0.554316369 0.320319845
1989 4.40 5.34 1.803674195 0.237157777
1990 3.68 4.68 0.811413868 -0.74340989
1991 3.46 4.61 0.511249755 -0.84519033
1992 3.10 5.92 0.026910178 1.104773977
1993 1.86 5.28 -1.66557593 0.146209844
1994 2.17 6.03 -1.24709479 1.267374438
1995 2.54 5.70 -0.74096044 0.768402031
1996 2.44 5.36 -0.8800923 0.263471745
1997 2.69 5.50 -0.52817863 0.480437856
1998 3.15 5.46 0.098986969 0.417135387
1999 2.97 5.52 -0.15274886 0.511468479
2000 3.10 5.59 0.02430204 0.606591441
2001 2.68 5.21 -0.55308934 0.046009144
2002 2.49 5.66 -0.80669149 0.708823236
2003 2.94 6.58 -0.19276133 2.080624987
2004 3.19 5.45 0.151959857 0.403481913
2005 3.77 6.41 0.936218537 1.825925639
2006 4.20 6.43 1.528470279 1.858693976
2007 4.20 6.13 1.522030596 1.4150802
2008 3.33 5.34 0.343272031 0.243895855
Average Average
n=37 3.08 5.18
St. Deviation St. Deviation
0.732476016 0.671379811
5. The second set of equations computed the test statistic which determined the
difference between the two data sets. The raw data including all equation results are
given in Table 16 and the equations are given below.
91
Table 16. The raw data for equations that calculate the test statistic for the change in mean in the bivariate
analysis. i xj’ cumulative Xi Yj’ cumulative Yi Sxy Fi Di Ti
1 1.554736164 1.554736164 -0.71362049 -0.71362 -1.10949 34.51565 1.20714 1.407596
2 0.445524412 0.222762206 -2.12977427 -1.06489 1.570814 36.89508 1.186969 2.828714
3 -0.70600241 -0.23533414 -2.87566661 -0.95856 0.858915 36.81919 0.985018 2.832742
4 -1.3794625 -0.34486562 -3.16230573 -0.79058 0.19304 36.46661 0.802967 2.412729
5 -1.01508101 -0.2030162 -3.07533617 -0.61507 0.03169 36.76172 0.657727 1.978114
6 0.779735291 0.129955882 -2.82576614 -0.47096 0.447932 36.87906 0.602197 1.933808
7 2.202792587 0.314684655 -3.67343892 -0.52478 -1.20629 36.14507 0.760156 3.409716
8 2.081352884 0.26016911 -5.51160916 -0.68895 0.223227 36.30912 0.978849 6.274497
9 2.273766144 0.252640683 -6.492093 -0.72134 -0.18866 36.24091 1.056921 7.931013
10 3.261126678 0.326112668 -6.75887253 -0.67589 -0.26341 35.54262 1.078509 8.677694
11 3.876740467 0.352430952 -7.72705696 -0.70246 -0.59603 35.05567 1.185173 10.94791
12 2.973600663 0.247800055 -9.01288213 -0.75107 1.16128 35.90945 1.238201 12.83974
13 1.388931774 0.106840906 -10.3371853 -0.79517 2.098582 36.77122 1.274236 14.48127
14 0.556700191 0.039764299 -11.3946251 -0.8139 0.880035 36.96439 1.326315 16.27709
15 -0.9677425 -0.06451617 -12.9212478 -0.86142 2.327249 36.895 1.426131 19.2506
16 -1.54561158 -0.09660072 -13.1172776 -0.81983 0.11328 36.73693 1.412684 19.15032
17 -0.99129521 -0.05831148 -12.7969577 -0.75276 0.177559 36.89306 1.370062 18.30409
18 0.812378987 0.045132166 -12.5597999 -0.69777 0.427755 36.9286 1.383074 18.78121
19 1.623792855 0.085462782 -13.3032098 -0.70017 -0.60321 36.71474 1.493921 21.7854
20 2.13504261 0.10675213 -14.1484001 -0.70742 -0.4321 36.50394 1.618469 25.27386
21 2.161952788 0.102950133 -13.0436262 -0.62113 0.02973 36.4853 1.515939 21.90103
22 0.496376861 0.022562585 -12.8974163 -0.58625 -0.24352 36.97237 1.46084 20.2414
23 -0.75071793 -0.03263991 -11.6300419 -0.50565 -1.58054 36.93524 1.317481 16.0483
24 -1.49167837 -0.06215327 -10.8616399 -0.45257 -0.56936 36.73613 1.253552 14.00155
25 -2.37177067 -0.09487083 -10.5981681 -0.42393 -0.23188 36.30621 1.258834 13.41785
26 -2.8999493 -0.11153651 -10.1177303 -0.38914 -0.25376 35.91203 1.253612 12.54805
27 -2.80096233 -0.10373935 -9.70059487 -0.35928 0.041291 35.92489 1.271984 12.20019
28 -2.95371119 -0.10548969 -9.18912639 -0.32818 -0.07813 35.71904 1.287196 11.59401
29 -2.92940915 -0.10101411 -8.58253495 -0.29595 0.014741 35.63141 1.302132 10.8962
30 -3.48249848 -0.11608328 -8.53652581 -0.28455 -0.02545 34.8632 1.436228 11.74025
31 -4.28918997 -0.13836097 -7.82770257 -0.25251 -0.5718 33.34035 1.495374 10.7802
32 -4.4819513 -0.14006098 -5.74707758 -0.1796 -0.40106 32.35468 1.228581 6.074469
33 -4.32999144 -0.13121186 -5.34359567 -0.16193 0.061313 31.74465 1.398185 6.368212
34 -3.39377291 -0.09981685 -3.51767003 -0.10346 1.709465 32.82201 1.097437 3.134502
35 -1.86530263 -0.05329436 -1.65897606 -0.0474 2.840959 35.16091 0.667813 0.85332
36 -0.34327203 -0.00953533 -0.24389586 -0.00677 2.153795 36.87889 0.164517 0.027935
37 8.60423E-15 2.32547E-16 -6.3283E-14 -1.7E-15 0.083723 #DIV/0! #DIV/0! #DIV/0!
sum
To max
9.091696 25.27386
Step 2 : Compute test statistics.
For all 1 i n, let Xi 1 i xj
j1
i
; Yi 1 i yj
j1
i
; Sxy xj
j1
n
yj ;
Fi n Xi2ni n i ; Di SxyXi nYi n n i Fi
Ti i n i Di2Fi n2 Sxy
2 ; T0 max Ti .
Let i0* be the value of i for which Ti is a maximum.
92
6. The third step is to conduct the test as written below.
7. The Ti column in Table 16 is the calculated difference between the two data sets. To is
the maximum value of all the Tis and represents the peak difference. The year after To is
considered the year that the change in mean took place.
8. To determine if the year after To represented a significant change in the mean between
the two data sets, To is measured against critical values in Table 17. In this case To is
greater than the critical value and therefore represented a change in the mean at the
Bancroft monitoring well in 1992. To and the year where a change in mean occurred are
highlighted in Tables 15 and 16.
Table 17. Critical values for To for different levels of significance.
Critical Values of To
Significance Level
n 0.25 0.10 0.05 0.01
10 4.7 6.0 6.8 7.9
15 4.9 6.5 7.4 9.3
20 5.0 6.7 7.8 9.8
30 5.3 7.0 8.2 10.7
40 5.4 7.3 8.7 11.6
70 5.9 7.9 9.3 12.2
100 6.0 7.9 9.3 12.5
Step 3 : Conduct test.
Compare T0 to the critical value for the appropriate n and the desired significance level.
If T0 exceeds the critical value, reject the null hypothesis; that is, assume that the mean
of y j' has changed in the year after i0
* by an amount equal to SyD
i0* .
93
Appendix 7
Multiple Regression with ANCOVA
Raw Data: Excel Workbooks located in monitoring well folders “SAS Output”
Workbook Location: G:\usr\projects\Centrallake&streams\Multiple Regression and
ANCOVA
Summary
Multiple regression equations were developed for each monitoring well. Regression
models used growing season (May-September) water elevations for 1960-2008.
Equations were developed using the Standard Precipitation Index (SPI), the step increase
in precipitation covariate and pumping covariates. In this example the Hancock
monitoring well was used to show the steps taken to calculate the multiple regression
model.
Procedure
1. Depth to water measurements for Hancock were collected from the USGS website
http://nwis.waterdata.usgs.gov/wi/nwis/gwlevels. Depth to Water measurements were
converted to water elevations by subtracting the well elevation datum (329.18 meters).
2. Monthly water elevations at Hancock were sorted to include only growing season
values (May - September.
3. The Standard Precipitation Index (SPI) data was obtained from the National Climate
Data Center (NCDC) for Central Wisconsin Division 5 at
http://www7.ncdc.noaa.gov/CDO/CDODivisionalSelect.jsp#.
4. The 24-month SPI values were sorted by month to include growing season values.
The raw data for the Hancock water elevations and the SPI for the growing season, 1960-
2008 are given in Table 18.
94
Table 18. Raw input data for multiple regression analysis with ANCOVA for the Hancock monitoring well
from the 1960-2008 growing season (May-September).
Month
Month
# Year
Hancock
Well
Elevations
(m)
Step
Increase in
Precipitation
Covariate
Pumping
Covariate SPI24
may con. 5 1960 325.98 0 0 0.49
june 6 1960 326.20 0 0 0.65
july 7 1960 326.18 0 0 0.50
august 8 1960 326.10 0 0 0.75
september 9 1960 326.05 0 0 0.92
may con. 5 1961 326.18 0 0 0.65
june 6 1961 326.23 0 0 0.88
july 7 1961 326.14 0 0 0.99
august 8 1961 326.10 0 0 0.68
september 9 1961 326.04 0 0 0.86
may con. 5 1962 326.42 0 0 0.32
june 6 1962 326.47 0 0 0.42
july 7 1962 326.40 0 0 0.52
august 8 1962 326.32 0 0 0.51
september 9 1962 326.24 0 0 0.26
may con. 5 1963 325.97 0 0 0.05
june 6 1963 325.94 0 0 0.02
july 7 1963 325.93 0 0 0.05
august 8 1963 325.95 0 0 -0.13
september 9 1963 325.89 0 0 -0.53
may con. 5 1964 325.19 0 0 -1.33
june 6 1964 325.12 0 0 -1.62
july 7 1964 325.04 0 0 -1.35
august 8 1964 324.96 0 0 -1.67
september 9 1964 324.93 0 0 -1.27
may con. 5 1965 324.93 0 0 -1.04
june 6 1965 324.98 0 0 -1.12
july 7 1965 324.95 0 0 -1.11
august 8 1965 324.89 0 0 -0.79
september 9 1965 324.91 0 0 0.10
may con. 5 1966 325.67 0 0 0.75
june 6 1966 325.67 0 0 0.72
july 7 1966 325.67 0 0 0.48
august 8 1966 325.66 0 0 0.57
september 9 1966 325.59 0 0 -0.10
may con. 5 1967 325.45 0 0 -0.19
june 6 1967 325.41 0 0 0.62
july 7 1967 325.52 0 0 0.29
august 8 1967 325.46 0 0 0.02
september 9 1967 325.39 0 0 -1.14
may con. 5 1968 324.96 0 0 -1.03
june 6 1968 325.13 0 0 -0.29
july 7 1968 325.33 0 0 -0.23
august 8 1968 325.38 0 0 -0.39
september 9 1968 325.39 0 0 0.26
may con. 5 1969 325.60 0 0 0.58
june 6 1969 325.69 0 0 0.42
july 7 1969 325.79 0 0 0.60
august 8 1969 325.78 0 0 0.38
september 9 1969 325.71 0 0 0.41
may con. 5 1970 325.21 0 0 0.34
june 6 1970 325.60 0 0 -0.34
july 7 1970 325.63 0 0 -0.40
95
august 8 1970 325.51 0 0 -0.49
september 9 1970 325.44 0 0 -0.53
may con. 5 1971 325.80 0 0 -0.30
june 6 1971 325.92 0 0 -0.80
july 7 1971 325.92 0 0 -0.57
august 8 1971 325.83 0 0 -0.35
september 9 1971 325.76 0 0 -0.24
may con. 5 1972 325.92 0 0 -0.54
june 6 1972 325.92 0 0 -0.47
july 7 1972 325.83 0 0 -0.38
august 8 1972 325.75 0 0 0.38
september 9 1972 325.86 0 0 0.69
may con. 5 1973 327.19 1 0 2.24
june 6 1973 327.34 1 0 1.97
july 7 1973 327.31 1 0 1.60
august 8 1973 327.16 1 0 1.65
september 9 1973 327.03 1 0 1.74
may con. 5 1974 326.89 1 0 2.13
june 6 1974 326.90 1 0 2.12
july 7 1974 326.84 1 0 1.98
august 8 1974 326.73 1 0 1.52
september 9 1974 326.63 1 0 0.58
may con. 5 1975 326.59 1 0 -1.07
june 6 1975 326.60 1 0 -0.88
july 7 1975 326.49 1 0 -0.94
august 8 1975 326.44 1 0 -0.36
september 9 1975 326.65 1 0 -0.55
may con. 5 1976 326.67 1 0 -0.43
june 6 1976 326.58 1 0 -0.79
july 7 1976 326.40 1 0 -0.57
august 8 1976 326.26 1 0 -0.92
september 9 1976 326.14 1 0 -1.07
may con. 5 1977 325.48 1 0 -1.45
june 6 1977 325.44 1 0 -1.44
july 7 1977 325.37 1 0 -1.11
august 8 1977 325.25 1 0 -1.78
september 9 1977 325.21 1 0 -1.46
may con. 5 1978 325.85 1 0 -1.58
june 6 1978 325.91 1 0 -1.05
july 7 1978 325.97 1 0 -0.72
august 8 1978 325.91 1 0 -0.35
september 9 1978 326.03 1 0 0.52
may con. 5 1979 326.70 1 0 1.41
june 6 1979 326.78 1 0 1.18
july 7 1979 326.71 1 0 1.21
august 8 1979 326.66 1 0 1.59
september 9 1979 326.73 1 0 1.09
may con. 5 1980 326.47 1 0 0.68
june 6 1980 326.54 1 0 0.66
july 7 1980 326.50 1 0 0.18
august 8 1980 326.52 1 0 1.01
september 9 1980 326.63 1 0 0.88
may con. 5 1981 326.68 1 0 -0.07
june 6 1981 326.54 1 0 0.01
july 7 1981 326.40 1 0 -0.12
august 8 1981 326.22 1 0 -0.21
september 9 1981 326.13 1 0 0.16
may con. 5 1982 326.17 1 0 0.36
june 6 1982 326.14 1 0 0.09
july 7 1982 326.14 1 0 0.55
august 8 1982 326.16 1 0 -0.30
september 9 1982 326.14 1 0 -0.72
96
may con. 5 1983 326.54 1 0 0.51
june 6 1983 326.65 1 0 0.27
july 7 1983 326.55 1 0 0.29
august 8 1983 326.42 1 0 0.48
september 9 1983 326.52 1 0 0.75
may con. 5 1984 326.73 1 0 0.87
june 6 1984 326.75 1 0 1.39
july 7 1984 326.72 1 0 1.01
august 8 1984 326.62 1 0 1.10
september 9 1984 326.55 1 0 1.45
may con. 5 1985 327.05 1 0 1.41
june 6 1985 326.90 1 0 1.45
july 7 1985 326.76 1 0 1.49
august 8 1985 326.60 1 0 1.39
september 9 1985 326.50 1 0 1.55
may con. 5 1986 326.77 1 0 1.67
june 6 1986 326.64 1 0 1.25
july 7 1986 326.58 1 0 1.57
august 8 1986 326.54 1 0 1.43
september 9 1986 326.50 1 0 2.46
may con. 5 1987 326.68 1 0 1.23
june 6 1987 326.63 1 0 1.22
july 7 1987 326.63 1 0 1.31
august 8 1987 326.46 1 0 0.93
september 9 1987 326.34 1 0 0.62
may con. 5 1988 326.22 1 0 0.11
june 6 1988 326.04 1 0 -0.46
july 7 1988 325.86 1 0 -0.80
august 8 1988 325.73 1 0 -0.60
september 9 1988 325.70 1 0 -1.41
may con. 5 1989 325.76 1 0 -0.88
june 6 1989 326.01 1 0 -1.07
july 7 1989 325.92 1 0 -1.18
august 8 1989 325.75 1 0 -1.22
september 9 1989 325.65 1 0 -1.45
may con. 5 1990 325.42 1 0 -0.85
june 6 1990 325.59 1 0 0.10
july 7 1990 325.78 1 0 -0.03
august 8 1990 325.82 1 0 0.20
september 9 1990 325.93 1 0 -0.08
may con. 5 1991 326.13 1 0 0.15
june 6 1991 326.36 1 0 0.13
july 7 1991 326.34 1 0 0.31
august 8 1991 326.22 1 0 0.35
september 9 1991 326.11 1 0 0.67
may con. 5 1992 326.14 1 0 0.81
june 6 1992 326.17 1 0 -0.02
july 7 1992 326.06 1 0 0.06
august 8 1992 325.95 1 0 -0.41
september 9 1992 325.91 1 0 0.40
may con. 5 1993 326.52 1 0 0.86
june 6 1993 326.77 1 0 1.68
july 7 1993 327.02 1 0 2.04
august 8 1993 327.20 1 0 2.27
september 9 1993 327.21 1 0 2.41
may con. 5 1994 326.85 1 0 1.52
june 6 1994 326.87 1 0 1.58
july 7 1994 326.80 1 0 2.15
august 8 1994 326.74 1 0 2.38
september 9 1994 326.65 1 0 1.93
may con. 5 1995 326.15 1 0 0.83
june 6 1995 326.18 1 0 -0.14
97
july 7 1995 326.10 1 0 -0.78
august 8 1995 325.99 1 0 -0.21
september 9 1995 326.13 1 0 -0.42
may con. 5 1996
1 0 0.29
june 6 1996 326.36 1 0 0.88
july 7 1996 326.51 1 0 0.35
august 8 1996
1 0 0.01
september 9 1996 326.25 1 0 -0.45
may con. 5 1997 326.01 1 0 -0.28
june 6 1997 326.04 1 0 0.10
july 7 1997 326.11 1 0 0.38
august 8 1997 326.23 1 0 -0.10
september 9 1997 326.16 1 0 -0.01
may con. 5 1998 325.96 1 0 -0.39
june 6 1998 325.92 1 0 -0.23
july 7 1998 325.90 1 0 -0.60
august 8 1998
1 0 -0.23
september 9 1998
1 0 -0.08
may con. 5 1999 325.59 1 1 0.04
june 6 1999 325.46 1 1 0.11
july 7 1999 325.38 1 1 0.79
august 8 1999 325.62 1 1 0.58
september 9 1999 325.63 1 1 0.36
may con. 5 2000 325.24 1 1 0.16
june 6 2000 325.40 1 1 0.19
july 7 2000 325.56 1 1 0.38
august 8 2000 325.46 1 1 0.48
september 9 2000 325.43 1 1 0.76
may con. 5 2001 325.55 1 1 0.96
june 6 2001 325.73 1 1 1.22
july 7 2001 325.67 1 1 0.19
august 8 2001 325.53 1 1 0.36
september 9 2001 325.56 1 1 0.86
may con. 5 2002 325.43 1 1 1.25
june 6 2002 325.86 1 1 1.11
july 7 2002 326.55 1 1 1.14
august 8 2002 326.39 1 1 1.00
september 9 2002 326.35 1 1 1.00
may con. 5 2003 325.68 1 1 0.57
june 6 2003 325.69 1 1 0.15
july 7 2003 325.51 1 1 0.24
august 8 2003 325.30 1 1 0.06
september 9 2003 325.15 1 1 -0.12
may con. 5 2004 325.10 1 1 0.71
june 6 2004 325.53 1 1 0.51
july 7 2004 325.82 1 1 0.47
august 8 2004 325.68 1 1 0.49
september 9 2004 325.61 1 1 0.00
may con. 5 2005 325.29 1 1 0.09
june 6 2005 325.19 1 1 0.04
july 7 2005 325.02 1 1 0.23
august 8 2005 325.08 1 1 0.29
september 9 2005 325.04 1 1 0.36
may con. 5 2006 324.94 1 1 -0.46
june 6 2006 325.01 1 1 -1.12
july 7 2006 324.85 1 1 -1.09
august 8 2006 324.72 1 1 -1.10
september 9 2006 324.72 1 1 -0.76
may con. 5 2007 324.82 1 1 -0.62
june 6 2007 324.69 1 1 -0.65
july 7 2007 324.48 1 1 -0.83
august 8 2007 324.43 1 1 -0.08
98
september 9 2007 324.69 1 1 -0.28
may con. 5 2008 325.22 1 1 0.45
june 6 2008 325.39 1 1 1.22
july 7 2008 325.43 1 1 1.53
august 8 2008 325.36 1 1 1.18
september 9 2008 325.27 1 1 1.01
5. The step increase in precipitation covariate and the pumping covariate were added to
the raw data in Table 18. The covariates were switch from “off” (0) to “on” (1) based on
dates determined by the bivariate test.
6. The data set from Table 18 was imported into SAS statistical software version 9.2.
PROC REG was coded into the program editor. The consisted of the Hancock well
elevations (hwellele) equal to the SPI for 24-months (SP24), the step increase in
precipitation covariate (z) and the pumping covariate (z2) as shown below.
7. The regression test was run and the output file is shown below. P-values at the bottom
of the output indicate that all variables in the model are significant (p-value <0.05).
Under the parameter estimates column are the slope coefficients for each variable. These
coefficients also indicate the amount of change that occurs for each variable. For
99
example the slope coefficient for the pumping covariate (z2) is -0.96819 indicating that
pumping has contributed to a decline of 0.97 meters in Hancock well water elevations.
R2 values are located in the middle of the output sheet and indicate how well the
regression equation predicated Hancock water elevations.
100
Appendix 8
Magnitude of Seasonal Precipitation from 1955-2008
y = 0.6923x - 1158.10
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Hancock Spring 1955-2008
y = 0.3431x - 4530
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Montello Spring 1955-2008
y = -0.1296x + 473.370
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Wisconsin Rapids Spring 1955-2008
y = 0.2406x - 259.20
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Stevens Point Spring 1955-2008
y = 0.1095x + 8.24360
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Waupaca Spring 1955-2008
y = 0.1556x - 88.6760
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Composite Spring 1955-2008
101
y = 2.0435x - 3750.70
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Hancock Summer 1955-2008
y = 2.3905x - 4439.10
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Montello Summer 1955-2008
y = 0.9397x - 1569.20
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Stevens Point Summer 1955-2008
y = 0.7696x - 1229.10
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Waupaca Summer 1955-2008
y = 0.4107x - 518.220
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Wisconsin Rapids Summer 1955-2008
y = 1.4115x - 2500.20
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Composite Summer 1955-2008
102
y = -0.5088x + 12110
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Hancock Fall 1955-2008
y = 0.0599x + 93.610
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Montello Fall 1955-2008
y = -0.4645x + 1127.20
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Stevens Point Fall 1955-2008
y = -0.8195x + 18330
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Waupaca Fall 1955-2008
y = -0.6777x + 15480
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Wisconsin Rapids Fall 1955-2008
y = -0.4247x + 1049.60
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Composite Fall 1955-2008
103
y = 0.4964x - 908.15
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Hancock Winter1955-2008
y = 0.417x - 729.84
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Montello Winter1955-2008
y = 0.4768x - 860.32
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Stevens Point Winter1955-2008
y = 0.5018x - 899.1
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Waupaca Winter1955-2008
y = 0.4042x - 716.17
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
W isconsin Rapids Winter1955-2008
y = 0.5653x - 1032.8
0
100
200
300
400
500
600
1955 1965 1975 1985 1995 2005 2015
Precip
itati
on
(m
m)
Composite Winter1955-2008
![Langer–Schwartz–Kampmann–Wagner precipitation ......capillary effects and diffusion fluxes couplings [33]. Prior works using LSKW precipitation modelling have been performed](https://img.dokumen.tips/doc/110x75/61339b45dfd10f4dd73b3283/langeraschwartzakampmannawagner-precipitation-capillary-effects-and.jpg)
