GEOS 4430 Lecture Notes:Quantification and Measurement of the

Hydrologic Cycle

Dr. T. Brikowski

Fall 2011

file:hydro_cycle.tex,v (1.30), printed September 8, 2011

Hydrologic Budget

Misc. information and data sources:

• Texas Regional Water planning homepage

• Region C 2011 water plan Executive

Summary

1

Hydrologic Budget

• Hydrologic budget is simply an H2O mass balance{rate of

mass in

}−{

rate of

mass out

}={change in

storage

}(1)

• usually assume density of water constant, then make a

volume balance instead

• estimating these components is a large part of hydrology,

and can sometimes be quite difficult

2

Hydrologic Budget (cont.)

• For a watershed (topographic basin) water balance is (Fig.

1): {rate of

mass in

}= P︸︷︷︸

Precipitation

(2){rate of

mass out

}= Qs︸︷︷︸

Runoff

+ E + T︸ ︷︷ ︸Evapotranspiration

+ R︸︷︷︸Recharge

+ Qg︸︷︷︸Groundwater Discharge

(3)

3

Basin Hydrologic Cycle

Figure 1: Hydrologic cycle for a watershed, after Domenico and

Schwartz [Fig. 1.2, 1990].

4

Evaporation

Misc. information and data sources:

• U.S. Evaporation climatology (calculated)

• U.S. raw evaporation data

• Daily pan (or actual?) evaporation at DFW

lakes

• moisture sensor rebate for NTMWD

customers

5

Importance of Evapotranspiration

• 2/3 of precipitation in the U.S. returns to the atmosphere by

evapotranspiration

• in arid regions ouptput by ET can exceed 90% of basin water

inputs

• in humid regions (e.g. Western Washington) ET can be as

little as 10% of input

6

Evaporation: Physical Process

• endothermic process (requires energy input) (Fig. 2)

• requires relative humidity ≤ 100

(relative humidity) =(absolute humidity)

(saturation humidity)· 100

humidity =(kg water)(m3 air)

• absolute humidity is the current moisture content of the air

• saturation humidity is temperature dependent, the dewpointis the temperature at which saturation humidity becomes

equal to the absolute humidity. See Fetter [Table 2.1, 2001]

7

Water Phase Diagram

Figure 2: Phase diagram for H2O, after Tindall and Kunkel

[1999]. Energy (e.g. heating) is required to drive water across

the two-phase boundary into the vapor field (area to right of

curve).8

Evaporation: Measurement

• Direct methods:

– pan evaporation (land pan, Figs. 3–4):

∗ observe evaporation from a standard-sized shallow metal

pan

∗ best to measure precipitation input separately (i.e. make

a quantitative water balance for pan)

∗ apply empirical relationship to estimate lake or plant

evaporation (Fig. 6)

– lysimeter (Fig. 5)

∗ a cannister containing “natural” soil, installed at ground

level

∗ weigh (and perform water balance) to determine moisture

content changes due to evaporation9

• Indirect methods:

– Energy budget. 540 calgm energy required to transform water

to vapor at room temperature. Not all energy recieved by

surface water is used for evaporation though:

Qs︸︷︷︸incoming solar rad.

− Qrs︸︷︷︸reflected solar rad.

− Qlw︸︷︷︸IR radiation out

−

Qh︸︷︷︸turbulent exchange

− Qe︸︷︷︸latent heat of vap.

+

Qv︸︷︷︸heat brought in by water flow

− Qe︸︷︷︸heat carried out by vapor

=

Qθ︸︷︷︸change in heat content

(4)

– Bowen energy ratio: monitor soil T profile, incoming solar10

radiation and heat radiated to atmosphere at soil surface

(combines Qh & Qe in Eqn. 4, see Hillel [p. 290, 1980]

– Eddy correlation method

∗ directly measure water vapor flux using wind speed,

humidity measurements, i.e. micro-meteorology

∗ more recently used to measure CO2 fluxes, e.g. ABLE

experiment

– soil chloride profile (Cl mass balance, e.g. paleoclimate

studies)

11

NOAA Evaporation Pan

Figure 3: Example of NOAA standard evaporation pan, from

Wikipedia.

12

U.S. Pan Evaporation Contours

Figure 4: U.S. Pan Evaporation Contours, showing general

distribution of open-water evaporation. See original data at

NWS.13

Weighing Lysimeter

Figure 5: Example of commercial weighing lysimeter. Note

variety of sensors, and monitoring of natural and lysimeter

conditions. See UMS for installation details.

14

Transpiration

• Transpiration is evaporation from plants

• underside of leaves contain pores (stoma) which open for

photosynthesis during the day

• water drawn into plant by roots to provide support and

transport nutrients is lost via stoma

• hence length of day is an important constraint on

transpiration

• see animation for a helpful visualization

15

Evapotranspiration: Physical Process

• Transpiration is evaporation from plants

• underside of leaves contain pores (stoma) which open for

photosynthesis during the day

• water drawn into plant by roots to provide support and

transport nutrients is lost via stoma

• hence length of day is an important constraint on

transpiration

• ET is combined bare soil evaporation and plant transpiration16

• transpiration predominant mechanism for water loss from soil

in all but the driest climates [can be 15-80% of basin water

losses, Fetter, 2001] (Fig. 6)

• phreatophytes (plants with roots to water table) are generally

most important, except in agricultural settings

• for shallow-rooted plants, ET ceases when soil moisture drops

below wilting point (plant root suction less than soil suction)

17

ET From Cornfield

Figure 6: ET From Cornfield, showing ratio of ET to open-pan

evaporation. Recall that actual evaporation from open water is

usually about 0.7 times the pan evaporation. After [Fig. 5-1,

Dunne and Leopold, 1978].18

Evapotranspiration: Estimation/Measurement

• Measurement

– Lysimeters (containing soil and plants)

– phytometer - “plant-in-a-box”, airtight transparent

enclosure (lab or field), monitor humidity of air; unnatural

conditions and therefore questionable data

• Estimation

– Thornthwaite Method (empirical formula, inputs are

T, latitude, season; emphasizes meteorological controls,

ignores soil moisture changes, Fig. 7)

Et = 1.6[

10TaI

]a(5)

19

where Et is potential evaporation in cmmo, Ta is mean

monthly air temperature in ◦C , I is an annual heat index,

and a is a cubic polynomial in I

– Blaney-Criddle method, adds a crop factor (empirical

estimate of vegetative growth and soil moisture effects);

most popular method, calibrated for U.S. only

Et = (0.142Ta + 1.095)(Ta + 17.8)kd (6)

where k is an empirical crop factor (bigger for thirsty

crops or fast-growth periods), d is the monthly fraction of

daylight hours.

– Penman Equation:

∗ use vapor pressure, net radiation, T to calculate

∗ fairly popular, but inaccurte (most parameters estimated)20

∗ intended to mimic pan evaporation, so tends to over-

estimate ET (e.g. Fig. 9).

∗ Note [Fig. 2.1 Fetter, 2001] is essentially a graphical

solution of this equation

∗ see various Ag. schools for free software (e.g. U. Idaho).

– Remote sensing:

∗ early efforts developed species-specific ET rates for a

locale, estimate distribution, growth rate, etc. from

multi-spectral images, calculate spatially-variable ET

rates Czarnecki [e.g. 1990], Owen-Joyce and Raymond

[e.g. 1996]

∗ more recently use energy balance approach, e.g. China

study comparison with lysimeter data

21

Thornthwaite Method

Figure 7: Graphical solution of Thornthwaite Method, indicating primary

dependence on mean air temperature and “heat index” (a U.S.-calibrated

indicator of daily temperature range). After [Fig. 5-4, Dunne and Leopold,

1978]. See also online calculator.22

FAO Penman-Montieth Equation

• worldwide standard method developed by UN Food and

Agriculture Organization

• envisions a “reference crop”, accounts for energy balance and

“resistance” to ET (i.e. computes reduction from open-water

evaporation rate, Fig. 8)

• computes potential evaporation (i.e. maximum possible)

• schematic version of equation:

ETo =(net energy flux) + (wind) · (RH)

resistances23

where the energy flux is solar input minus infrared radiation

and reflection out, resistances are rs and ra as shown in Fig.

8

24

Setting: FAO Penman-Monteith Equation

Figure 8: Penman-Monteith setting, showing origin of

resistance terms. After FAO.

25

ET Method Comparison

Figure 9: Comparison of ET estimation methods. After [Fig.

5-3, Dunne and Leopold, 1978]. See also Castaneda-Rao-2005.

26

ET Estimation ReviewAs hydrogeologists, you’ll probably consider the following

methods to predict ET, in order of increasing difficulty and

accuracy (see also FAO Summary) and FAO training manuals:

• Land pan evaporation data: apply appropriate pan

coefficients and nearby pan data to estimate reservoir, or

even crops (rarely). See Wikipedia summary

• Forms of energy balance

– Thornthwaite: meteorology/climate only, ignore vegetation

effects. OK for annual average

– Blaney-Criddle: adds crop effect. Simple, widely used

and broadly inaccurate, better at monthly variations, good

when only temperature data is known27

– Penman: original Penman eqn. mimics pan evaporation

curve, accounts for radiation and convective (wind) flux,

i.e. most terms in (4)

– Penman-Monteith: world standard, assumes realistic

“reference crop”. Provides most inter-comparable results.

28

Typical ET Values

Figure 10: Typical values for ETo, in mmday for climate types and

temperature range. After UN FAO. See current UTD/TAMU

values.

29

ET Example: Colorado River

• Colorado River basin (Fig. 11) over-allocated (Fig. 13), so

components of water balance there are very important (17.5Mac−ft

yr allocated, actual flow averages 14.5 Mac−ftyr )

• very difficult-to-measure aspect of this is ET

• Tamarisk (salt cedar)

• introduced as decorative plant in 1870’s, has spread through

most of watershed (colonization rate 3 km2

yr )

• individual ET rates 2.5 myr

• 1984 total consumptive use, Lower Basin 7x106 acre−ftyr

[Owen-Joyce and Raymond, 1996]30

• of that 15% lost through ET, 6% by natural phreatophytes

(primarily tamarisk), 18% exported to AZ, 67% exported to

CA

• see USGS biennial consumptive use studies

31

Tamarisk Invasion/Control

• current distribution monitored by USGS

• other organizations organize remediation (e.g. Tamarisk

Coalition)

• see TRO Assessment report 2008 for current status of

mitigation/impact

32

Colorado River Hydrologic Basin

Figure 11: Colorado River Basin Compact states, and important

localities, from [Barnett and Pierce, 2008].

33

Colorado River Profile

Figure 12: Topographic profile of Colorado River, showing

river gradient and major impoundments. After Keller [p. 281,

1996].

34

Colorado River Water Allocation

Figure 13: Colorado River Basin Compact allocation and average

discharge. After Keller [p. 282, 1996]. See Wikipedia summary of

shortage plans.35

Evaporation and Climate Change

36

Pan Evaporation Declining

Figure 14: Temporal trends in pan evaporation. Across the US and most

of the world pan evaporation rates have declined since the 1940’s. Numbers

are precipitation trends in mmdecade, [Lawrimore and Peterson, 2000].

37

Global Humidity Increasing

Figure 15: Temporal trends in specific humidity: lower atmospheric

moisture content has been steadily increasing, upper atmosphere (300mB)

moisture decreasing, consistent with brightening. Data from NCDC, based

on analysis of GPS satellite signals, this plot from The Blackboard.38

Evaporation and Global Dimming/Brightening

Figure 16: Observed and modeled global warming and dimming. Light

lines show individual IPCC model results. These warming models include

dimming effects, and the “evaporation paradox”, after [Schmidt et al., 2007].

See Wild [2009] for good summary of brightening/dimming observations.39

Climate Forcings

Figure 17: Model results of 20th century climate, with contributions from

various forcings. Observed warming best matched by effect of greenhouse

gas emissions, moderated through 1990 by particulates (“sulfate”, combined

natural and anthropogenic effects). See also Wikipedia summary.40

Precipitation

Useful data sources:

• National Weather Service flood prediction

data

• Intellicast TX-OK 7-day cumulative precip

from NEXRAD data

• Intellicast current hourly lightning strikes

41

Precipitation: Physical Process

• condensation caused by cooling of the air mass, usually

during lifting

– In Texas mostly during frontal storms (“blue norther’s”)

(Fig. 18)

– See example of March 3, 2000 frontal storm: radar

animation, surface weather map, and lightning record

• local climate effects can be important in hydrology

– frontal precipitation (most common precip. in winter, see

Texas annual precip. distribution, Fig. 19)

– convective precipitation (thunderstorms, most common in

summer)42

– e.g. in temperate arid regions snow is predominant

recharge contributer, even if not predominant form of

precip.

– orographic effect: heavier precip. on upwind side of

topographic highs, lower than average on downwind side

– coastal states often affected by tropical cyclones (e.g.

similar effect from upper atmosphere low at DFW 2009,

Fig. 20)

43

Frontal Precipitation Model

Figure 18: Cross-section through frontal storm, showing the

special case of an occluded front. After Dingman [2002].

44

North Texas Monthly Normal Climate

Figure 19: North Texas monthly normals (after RSSWeather.

See also NOAA Southern Regional Climate Data Center.

45

4-Day Storm Event Cumulative Precipitation

Figure 20: Cumulative precipitation is often highly heterogeneous. 7 day

cumulative precipitation from high-level low pressure system in North Texas.

Sept. 7-14, 2009 (from Intellicast).46

Precipitation: Measurement

One of the most easily measured hydrologic cycle fluxes

• NOAA uses a variety of automated gauges (Fig. 21)

• see modern summary at Wikipedia and summary of

automated airport weather stations, the “gold standard”

of weather data worldwide

• Two basic station networks: primary monitoring stations

(usually major airports) and cooperative stations (usually

not run by NOAA, data quality uncertain). See Fig. 22

• this data accessible for free from .edu IP addresses at National

Climate Data Center (NCDC)

47

Rain Gauge Examples

Figure 21: Examples of recording rain gauges, after Dunne and

Leopold [1978].

48

NOAA Weather Station Network

Figure 22: NOAA Weather Station Network, after Dingman

[2002].

49

Treating Precipitation HeterogeneityPrecipitation usually extremely variable in space and time.

Hard to go from point measurements to regional input, must

use:

• arithmetic average, assumes uniform density of precip. or

stations

• Theissen polygon method: area-weighted average.

Equivalent of natural-neighbor interpolation

• Isohyetal: contouring, includes some concept of local

meteorology

• NEXRAD radar: use to estimate areal variability of rainfall,

calibrate with ground measurements,50

– accuracy can be controversial, but now standard for runoff

models (see Applied Surface Water Modeling Notes re:

NEXRAD)

– cumulative estimates avaliable nationwide (intended for

flood prediction) at NCDC Hydro Prediction Service

51

Engineering Characterization of Precipitation

See Applied Surface Water Modeling Notes topics:

• Introduction: Design approaches in treating rainfall

• Rainfall data adjustments

• Rainfall data sources (online data)

52

Recharge

53

Recharge

• Physical processes

– infiltration - losses = recharge

– infiltration = precipitation - runoff

– runoff occurs when precip. exceeds infiltration capacity of

soil (Hortonian overland flow)

• Measurement

– Direct: lysimeters

– Indirect

∗ Water table fluctuation

· assumes changes in water level in shallow wells reflect

recharge54

· see USGS summary

· also computer program to develop Master Recession

Curve for well water levels

∗ Chemical mass balance: Cl, 3H, δD , δ18O

· Cl method (assumes all input is atmospheric, OK if

no Cl-sediments in basin; N.B. Cl = 0 in evaporated

water) [Dettinger, 1989]

CII︸︷︷︸Infiltrated mass

+ CPP︸ ︷︷ ︸Precipitation

+ CQQ︸ ︷︷ ︸Runoff

= 0

I =PCPCI

− QCQCI

(7)

· Also note that in many desert basins the runoff is 0,

simplifying (7)

∗ Determine Baseflow (hydrograph separation)55

∗ Use empirical relations based on other basins: e.g.

Maxey-Eakin [Watson et al., 1976], uses rainfall and

elevation maps to estimate recharge, calibrated to basins

of “known” recharge

• see excellent summary of methods and results for desert

basins [Hogan et al., 2004] (and online review)

56

Bibliography

57

Tim P. Barnett and David W. Pierce. When will Lake Mead go dry? Water Resour. Res., 44(W03201), 29 March 2008. doi: 10.1029/2007WR006704. URL http://www.agu.org/journals/pip/wr/2007WR006704-pip.pdf.

J. B. Czarnecki. Geohydrology and evapotranspiration at franklin lake playa, inyo county,california. Ofr 90-356, Denver, CO, 1990.

M. D. Dettinger. Reconnaissance estimates of natural recharge to desert basins in nevada, u.s.a., by using chloride-balance calculations. J. Hydrol., 106:55–78, 1989.

S. L. Dingman. Physical Hydrology. Prentice Hall, Upper Saddle River, NJ, 07458, 2nd edition,2002. ISBN 0-13-099695-5.

P. A. Domenico and F. W. Schwartz. Physical and Chemical Hydrogeology. John Wiley &Sons, New York, 1990. ISBN 0-471-50744-X.

T. Dunne and L. B. Leopold. Water in Environmental Planning. W. H. Freeman, New York,1978. ISBN 0-7167-0079-4.

C. W. Fetter. Applied Hydrogeology. Prentice Hall, Upper Saddle River, NJ, 4th edition, 2001.ISBN 0-13-088239-9.

D. Hillel. Applications of soil physics. Academic Press, New York, 1980. ISBN 0-12-348580-0.

James F. Hogan, Fred M. Phillips, and Bridget R. Scanlon, editors. Groundwater Rechargein a Desert Environment: The Southwestern United States, volume 9 of Water Scienceand Application. Amer. Geophys. Union, 2004. URL http://www.agu.org/cgi-bin/agubooks?topic=AL&book=HYWS0093584&search=Scanlon.

E. A. Keller. Environmental Geology. Prentice Hall, Upper Saddle River, NJ, 1996. 7th Ed.,ISBN 0-02-363281-X.

Jay H. Lawrimore and Thomas C. Peterson. Pan evaporation trends in dry andhumid regions of the united states. Journal of Hydrometeorology, 1(6):543, 2000.ISSN 1525755X. URL http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=5716377&site=ehost-live.

58

S. J. Owen-Joyce and L. H. Raymond. An accounting system for water and consumptive usealong the colorado river, hoover dam to mexico. Water-supply paper, U.S. Geol. Survey,Washington, D.C., 1996.

G. A. Schmidt, A. Romanou, and B. Liepert. Further comment on ”a perspective on globalwarming, dimming, and brightening”. EOS, 88(45):473, 11 2007.

J. A. Tindall and J. R. Kunkel. Unsaturated Zone Hydrology for Scientists and Engineers.Prentice-Hall, Upper Saddle River, N.J., 1999. ISBN 0-13-660713-6.

P. Watson, P. Sinclair, and R. Waggoner. Quantitative evaluation of a method for estimatingrecharge to the desert basins of nevada. J. Hydrol., 31:335–357, 1976.

M. Wild. Global dimming and brightening: A review. J. Geophys. Res., 114, 2009. doi:10.1029/2008JD011470.

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