Precision of tidal datums in the Sacramento River, California. · NPS68-80-007 NAVALPOSTGRADUATESCHOOL Monterey,California THESIS PRECISIONOFTIDALDATUMSINTHE SACRAMENTORIVER,CALIFORNIA

PRECISION OF TIDAL DATUMS IN THE

SACRAMENTO RIVER, CALIFORNIA

Timothy Alan Bouquet

NPS68-80-007

NAVAL POSTGRADUATE SCHOOLMonterey, California

THESISPRECISION OF TIDAL DATUMS IN THE

SACRAMENTO RIVER, CALIFORNIA

by


June 1980

Th<^sis Advisor: W. C. Thompson

Approved for public release; distribution unlimited,

Prepared for: National Ocean Survey (Code C33)6001 Executive BoulevardRockville, Maryland 20852

T 196272

NAVAL POSTGRADUATE SCHOOLMonterey, California

Rear Admiral J. J. Ekelund Jack R, BorstingSuperintendent Provost

This thesis was prepared in conjunction with research supported by

the National Ocean Survey (Code C33) , 6001 Executive Boulevard, Rockville,Maryland 20852 under Purchase Order No, NA80AAG02672,

Reproduction of all or part of this report is not authorized withoutpermission of the Naval Postgraduate School.

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Precision of Tidal Datums in theSacramento River, California

S. TYPE OF RtPOUT * PERIOD COVERED

Master's Thesis;June 198

• PERFORMING ORG. HIÔKT NuMICR

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>• SUPPLEMENTARY NOTES

<• KEY WORDS ! Continue on rovotmo old* II nacoaaaty ana) Identity By Block nunUr;Estuary TidesSacramento RiverComparison of Simultaneous ObservationsTidal DatumsTidal Epoch 1960-1978

20. ABSTRACT (Coniinua on ravoraa alda It nacoaaary and lontntllr »f Block •mar)

A method is developed for extending computed 19-year tidaldatums (1960-1978 epoch) throughout the ocean/river transitionzone of the Sacramento River System using water-level measure-ments from two long-term reference stations, at San Franciscoand Sacramento, and collected over an 18-month period at sevensecondary tide measuring stations located throughout the tran-sition zone. The method uses the standard procedure of theNational Ocean Survey for comparison of simultaneous observations

DD, :°r7 , 1473

(Pape 1)

EDITION OF I MOV 8S ij OBSOLETES/N 10 J-014- A40

1

SECURITY CLASSIFICATION OF THIS PAOB (Whon Data Mniarod)

tf»eu«WTV CUAMIUCATIOM Q» Twit »«Q|^W W»„ g,,,^,

to determine 19-year tidal characteristics as a functionof river level, from which are determined the 19-yearda t urns . The accuracy of tidal da turns , indicated by thestandard deviation, is found to be within 0.1 foot inthe lower bay system and within 0.2 foot upriver.

DD Form 1473

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Approved for public release; distribution unlimited

Precision of Tidal Datums in the

Sacramento River, California

by

Timothy Alan BouquetCartographer, Defense Mapping Agency

B.A., California State University Northridge, 1974

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY)

from the

NAVAL POSTGRADUATE SCHOOLJune 1980

7 KjLfeJUs

ABSTRACT

A method is developed for extending computed 19-year

tidal datums (1960-1978 epoch) throughout the ocean/river

transition zone of the Sacramento River System using water-

level measurements from two long-term reference stations,

at San Francisco and Sacramento, and collected over an

18-month period at seven secondary tide measuring stations

located throughout the transition zone. The method uses

the standard procedure of the National Ocean Survey for

comparison of simultaneous observations to determine 19-year

tidal characteristics as a function of river level, from

which are determined the 19-year datums. The accuracy of

tidal datums, indicated by the standard deviation, is found

to be within 0.1 foot in the lower bay system and within

0.2 foot upriver.

TABLE OF CONTENTS

I. INTRODUCTION- - - - - - 13

II. LOWER SACRAMENTO RIVER SYSTEM - - - - 16

III. TIDAL DATUMS AND RANGES 20

IV. DATA AND EDITING 23

V. PROCEDURES AND ANALYSES 2 5

A. HIGH AND LOW WATERS PROGRAM ----- 25

B. TIDE SELECTION AT PRESIDIO- 26

C. HARMONIC FILTERING PROGRAMS 27

D. COMPARISON OF SIMULTANEOUSOBSERVATIONS PROGRAM 30

E. STATISTICAL ANALYSIS AND GRAPHICS PLOTTING- - - 31

VI. DISCUSSION - 34

A. TIDAL BEHAVIOR IN THE RIVER SYSTEM 34

B. 19 -YEAR DATUMS AND RANGES IN THERIVER SYSTEM 37

1. Seasonal Datum and Range Variation 38

2. Influence of River Flow on19- Year Datums and Ranges 39

3. Relation between Sacramento andOther River Stations 44

4. Accuracy of Datum Determinationfrom Short Observations 44

VII. CONCLUSIONS -------- - 50

TABLES -..-- 57

FIGURES ----- - _--_--_ 77

APPENDIX A - SUPPLEMENTARY FIGURES- - - - - - 115

APPENDIX B - COMPUTER PROGRAMS- ----- 173

1. Comparison of SimultaneousObservation Programs ---------- 173

2. Running Mean Filter Program- - 17 5

3. High and Low Waters Program- ------ 176

LIST OF REFERENCES --------- 177

INITIAL DISTRIBUTION LIST 178

LIST OF TABLES

Table Page

1. Tide Station Locations ------ 57

2. Tide Data -..--583. Tide Data for Sacramento- ----- 59

4. Tidal Datums and Ranges -60

5. Tide Data for Presidio- --- 61

6. Mean Tidal Datums and Ranges in theSacramento River- ---- --62

7. Low Water Tidal Datums and Ranges inthe Sacramento River ---63

8. High Water Tidal Datums and Ranges inthe Sacramento River 64

9. Differences between Maximum and MinimumDatums and Ranges 65

10. Tidal Datums and Ranges withoutRiver Superelevation - 66

11. Statistics for Point Orient from a 28-DayComparison 67

12. Statistics for Benicia from a 28-DayComparison- ----------- --68

13. Statistics for Mallard Island froma 28-Day Comparison 69

14. Statistics for Three Mile Slough froma 28-Day Comparison ---- 70

15. Statistics for Walnut Grove from a

28-Day Comparison --- 71

16. Statistics for Sacramento from a 7-DayComparison ------- 72

Table

17.

18.

19.

20.

Page

Statistics for Sacramento from a14-Day Comparison - -- 73

Statistics for Sacramento from a28-Day Comparison ------- 74

Statistics for Sacramento from a56-Day Comparison 75

Statistical Relationships between MeanRiver Level at Sacramento and at OtherStations • - - - 76

LIST OF FIGURES

Figure Page

1. Lower Sacramento River System ----- 77

2. Mean River Level at Sacramento, 1958-1978 - - - - 78

3. Filtered Running Means and Extracted Tide - - - - 80

4. Simultaneous Water Levels at High Water inthe Sacramento River- ------- 81

5. Mean 19 -Year Tidal Da turns along theSacramento River- --- - 82

6. Mean 19-Year Tidal Ranges along theSacramento River -- 82

7. 19-Year Tidal Datums at Low Water alongthe Sacramento River- ---- -- 83

8. 19-Year Tidal Ranges at Low Water alongthe Sacramento River- - - - - - 83

9. 19-Year Tidal Datums at High Water alongthe Sacramento River - 84

10. 19-Year Tidal Ranges at High Water alongthe Sacramento River - 84

11. 19 -Year Tidal Datums at Sacramento froma 28-Day Comparison ------- 85

12. 19-Year Tidal Ranges at Sacramento froma 28-Day Comparison - 86

13. Tidal Datums at Presidio from a 28-DayRunning Mean - - - - - 87

14. Tidal Ranges at Presidio from a 28-DayRunning Mean - - 88

15. 19-Year Greater Range Relative to MeanRiver Level at Walnut Grove 89

16. Variability of 19-Year MTL along theSacramento River- - 90

Figure Page

17. Variability of 19-Year MLLW along theSacramento River ---- -91

18. Variability of 19-Year MLW along theSacramento River --- ____91

19. Variability of 19-Year MHW along theSacramento River -- . _ 92

20. Variability of 19-Year MHHW along theSacramento River - - 92

21. Variability of 19-Year GR along theSacramento River --------- --93

22. Variability of 19-Year MN along theSacramento River - - - 93

23. Variability of 19-Year DLQ along theSacramento River - 94

24. Variability of 19-Year DHQ along theSacramento River --------- 94

25. Relation between Mean River Level atSacramento and Mean River Level at Other 95River Stations

26. Tidal Datums at Presidio from a 7-DayRunning Mean _--._. 96

27. Tidal Ranges at Presidio from a 7-DayRunning Mean _--__-_-_-97

L o

28. Tidal Datums at Presidio from a 14-DayRunning Mean ----98

29. Tidal Ranges at Presidio from a 14-DayRunning Mean ---------- 99

30. Tidal Datums at Presidio from a 56-DayRunning Mean - 100

31. Tidal Ranges at Presidio from a 56-DayRunning Mean - 101

32. 19-Year Tidal Datums at Sacramento from7-Day Comparisons - -102

10

Figure Page

33. 19-Year Tidal Ranges at Sacramento from7-Day Comparisons- ---- _____ -103

34. 19-Year Tidal Datums at Sacramento from14-Day Comparisons -_-___ -104

35. 19-Year Tidal Ranges at Sacramento from14-Day Comparisons -------------- -105

36. 19-Year Tidal Datums at Sacramento from56-Day Comparisons ----- 106

37. 19-Year Tidal Ranges at Sacramento from56-Day Comparisons - -107

38. 19-Year Mean Range Relative to Mean RiverLevel at Sacramento- --------- 108

39. Variability of the 19-Year MTL withComparison Interval- -- - 109

40. Variability of the 19-Year MLLW withComparison Interval- --------- 110

41. Variability of the 19-Year MLW withComparison Interval --_____-_ -110

42. Variability of the 19-Year MHW withComparison Interval- - ------ -111

43. Variability of the 19-Year MHHW withComparison Interval- -- - -111

44. Variability of the 19-Year GR withComparison Interval _____ .112

45. Variability of the 19-Year MN withComparison Interval- -- - - - - -112

46. Variability of the 19-Year DLQ withComparison Interval - - - 113

47. Variability of the 19-Year DHQ withComparison Interval -- - -113

48. Histogram of Monthly Mean River Levels(NGVD) at Sacramento for the Epoch1960-1978- ------------------ -114

11

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to

Dr. Warren C. Thompson for his guidance and counsel in the

preparation of this thesis and making useful comments. Most

aspects of this thesis are the result of close collaboration

between Dr. Thompson and the author, including the basic

analysis procedure and the definition and interpretation of

datum planes in the riverine and transition zones.

The assistance of Mr. James R. Hubbard, Mr. Howard V.

Krishner, and Mr. Jack E. Fancher of the National Ocean

Survey and Mr. R. M. Oltmann of the U.S. Geological Survey

in the timely procurement and transmission of data is

gratefully recognized. The timely assistance of Duffy

Tegtmeier of the Naval Postgraduate School in the key-

punching of the Sacramento data is truly appreciated.

Special appreciation is given to my loving wife whose

understanding and patience enabled me to complete the

necessary research.

12

I. INTRODUCTION

A tidal datum is a plane of reference for elevations

determined from measurements of the rise and fall of the

tides. Water depths and tide heights are referenced to these

datums . High-water datums are used in the United States

for the determination of property boundaries. A low-water

datum is used for nautical charting so that actual depths

will normally be greater than those charted. In areas of

gradually sloping shoreline, the shoreline position can vary

dramatically with the choice of reference datum.

In tidal rivers, such as the Sacramento River of California,

the distance the measurable tide reaches upriver varies in-

versely with the river stage. At upriver stations the tides

vanish at high river levels. On the navigable rivers

draining the Atlantic slope of the Appalachian Mountains,

the upriver limit of the ocean tides is a well-defined

physiographic boundary known regionally as the fall line.

On the Sacramento River, on the other hand, there is no

convenient natural upriver barrier to the tides. The

National Ocean Survey (NOS) is the responsible agency of the

U.S. Government for tide prediction, nautical charting, and

tidal-datum determination in domestic waters. They are

presented in the Sacramento River, and many other rivers as

well, with the problem of how far up the river system to

13

carry tide guaging for the purpose of tidal datum determina-

tion. This study investigates that problem.

The Sacramento River was chosen for study because of the

availability of tide data collected over a common time period

at a large number of tide stations in the river delta and

the San Francisco Bay System by a cooperative California/

National Ocean Survey tide program conducted in 1977-1979.

NOS is planning both a coastal mapping program and a complete

hydrographic survey of the San Francisco Bay and its tribu-

taries as a part of their intensive investigation in the

San Francisco Bay System.

This study does not directly answer the question of how

far gauging should be carried up the river system, that being

a policy decision to be made by NOS, but presents information

that might serve as a basis for making such a decision.

Data on tidal characteristics and on the quality of tidal

datums in the Sacramento River are presented to provide this

basis. The results may serve as a guide to the solution of

tidal datum surfaces in other tidal rivers as well. Primary

questions addressed include: (1) How do tidal characteris-

tics vary with superelevation of the river (the height of the

river surface above sea level) , (2) with what accuracy can

tidal datums be determined in the river system from a short

series of observations, and (3) what quantitative criteria

might be used to decide whether the river should be judged

14

tidal, or not, for the purpose of datum-plane determination?

The focus of the analysis is primarily on question (2).

This question is examined by computing equvalent 19-year tidal

datums using a short series of tide observations at secondary

tide stations in the river system, derived from comparison

of simultaneous observations at an oceanic reference tide

station having a long tidal history. The standard procedure

for comparison of simultaneous observations used by NOS

[Marmer, 1951] was used as a basis for datum analysis in the

Sacramento River.

This study will in effect develop 19-year datums and

ranges from a series of short observations for tide stations

in the Sacramento River above Presidio, San Francisco to

Sacramento, and then analyze the accuracy of these determined

datums. This will be done using raw hourly heights by first

separating the dominant harmonic tidal components from the

non-harmonic river fluctuations. Then the heights and times

of high and low waters at the secondary tide stations will

be computed for comparison with the same tides at Presidio

to determine the 19-year datums and ranges using the standard

procedure. A least-squares technique will then be used to

define relationships between river levels and computed tidal

datums and ranges. The variability of the determined datums

represents the accuracy of datum determination by the standard

procedure for comparison of simultaneous observation in the

Sacramento River System.

15

II. LOWER SACRAMENTO RIVER SYSTEM

The Sacramento River System considered in this investi-

gation extends approximately from the City of Sacramento,

down the main channel of the Sacramento River to Suisun Bay,

thence along the tidal channel that runs through Suisun and

San Pablo Bays of the San Francisco Bay system to terminate

at the Presidio tide guage in the entrance to the San Francisco

Bay (Figure 1) . Sacramento is located near the upper limit

of tidal influence. Presidio, on the other hand, is con-

sidered here to be situated in an oceanic tidal environment

where daily water-level variations are primarily tidal in

nature. Between these two stations lies the tide-river

transition zone which upriver is subject in diminishing

degrees to the influence of the tides and in increasing

degrees to the influence of the river. Between the City of

Sacramento and Suisun Bay the river traverses the delta of

the Sacramento, San Joaquin, and several smaller rivers.

Water levels in the Sacramento River below the confluence of

the San Joaquin River near Collinsville often reflect runoff

from both major rivers, but above Collinsville the river

level is determined mainly by runoff of the Sacramento.

Nine tide observation stations in the Sacramento River

System were chosen for analysis in order to present a picture

of the tidal and river characteristics throughout the

16

tide-river transition zone (Table 1). These stations were

selected for their even distribution along the river system,

and to represent each tidal regime along the river system.

The Sacramento River at Sacramento, at a distance of about

111 nautical miles (NM) upriver from San Francisco, is about

200 yards wide, and has a charted depth of about 10 feet (low

river stage). At Walnut Grove, downriver 28 NM and below

several meanders, the river is even narrower (about 100

yards wide) and about the same depth. At Three Mile Slough

the river widens to half a mile and is over 20 feet in depth

Further down, the San Joaquin joins the Sacramento as it

empties into Suisun Bay. Collinsville is located at this

juncture. Mallard Island is 4 NM westward of this point and

exhibits similar tides to those at Collinsville. Suisun

Bay widens considerably (to 5 NM) and narrows again at

Benicia, which is at the eastern entrance to Carquinez

Strait. This strait is a constricted channel cut through

rolling hills that connects Suisun Bay with San Pablo Bay

to the west. Port Orient is located in the southern portion

of San Pablo Bay, just 10 NM north of San Francisco. The

long-term primary tide station used for comparisons in this

study is the gauge at Presidio, San Francisco.

This river system presents several interesting features

for tidal studies. These include the extensive lower bay

system in immediate and open communication with the Pacific

17

Ocean through the Golden Gate, the constriction of Carquinez

Strait, the upper bay system comprising mainly Suisun Bay,

and upstream from that the delta region where the tide wave

is divided among numerous tributaries and sloughs.

To relate the datums throughout the river system, all

measurements and datums were reduced to the National Geodetic

Vertical Datum (NGVD) , which is the standard geodetic reference

datum for elevations in the United States. Tide-staff eleva-

tions relative to NGVD are given in Table 2. There is a

possibility of subsidence in the Sacramento River Delta. The

most recent geodetic leveling in the delta was carried out in

1964 and 1965. No attempt was made in this study to deter-

mine or account for subsidence.

Annual variations of river level at Sacramento are so

great as to eliminate any tidal influence during periods

of high water. Figures 2A and 2B show twenty years of mean

monthly water levels at Sacramento, 1958-1978 [Zeile, 1979].

Winter water levels above 20 feet can be seen in some of the

prominent winter peaks. Summer lows are usually, but not

always, below five feet NGVD. Note in Figure 2B the "drought

years" of 1976 and 1977 when the winter water levels were

lower than the average summer lows. Table 3 which includes

statistics for Sacramento is a primary product of this study.

Mean river levels at Sacramento for the 18 -month period of

this study were statistically typical for the river over many

18

years, as can be seen from a comparison with the monthly

mean river level for the 19-year period 1960-1978 (Table 3)

.

Extreme variability of the river during the study period was

not as great as is sometimes found during the previous 19

years

.

19

III. TIDAL DATUMS AND RANGES

Two high waters and two low waters each day characterize

the semi-diurnal mixed tides which are found on the Pacific

coast of the United States. The two high and two low tides

are normally of different heights, thereby providing a higher

high water (HHW) , a lower high water (LHW) , a higher low

water (HLW) and a lower low water (LLW) each day. The sequence

of these four water levels varies throughout the fortnightly

tide cycle. Every 14 days the tides go through a cycle of

both reduced range (neap tides) and increased range (spring

tides) due to changes in phase of the primary lunar and solar

harmonic tidal constituents. Arithmetic means of these water

levels over any chosen observation period produce four primary

tidal datums, MHHW, MLHW, MHLW, and MLLW. From these are

derived the following tidal datums which are the datums used

in navigation and in property boundary determinations:

(1) mean high water, MHW, which is one half of the sum of

the MHHW and the MLHW, (2) mean low water, MLW, which is

similarly the mean of the MHLW and the MLLW, and (3) mean

tide level, MTL, the mean of the MHW and MLW [Marmer, 1951].

These datums are listed in Table 4.

Mean sea level, MSL, is derived from the mean of hourly

heights rather than from water level extremum values. In

this study it was computed only for Presidio for inclusion

20

in Table 5. The terminology mean river level, MRL, is used

interchangeably with mean tide level, MTL, for stations

upriver where the tidal influence is greatly reduced, their

mathematical derivations being the same.

Tidal ranges are a measure of the mean amplitude of the

tide and are derived from differences in elevation of the

tidal datums. The mean range, MN, is the difference between

the MHW and the MLW. The height difference between the MHHW

and the MHW is the diurnal high inequality, DHQ. Similarly,

the difference between the MLW and the MLLW is the diurnal

low inequality, DLQ. The diurnal or greater range, GR, is

the height difference between the MHHW and the MLLW.

By computing tidal datums from observations over a 19-

year period, termed a tidal epoch, virtually all significant

astronomical cycles can be averaged out, thereby providing

datums which, in the absence of eustatic sea level or land

elevation changes, are stable. The period of the longest

tidal constituent of significance, caused by regression of

the moon's nodes, is 18.6 years, but 19 years is used

in practice to average out the larger amplitude yearly tide

cycle. Because of long-term variations in sea level, it is

necessary to specify the 19-year epoch used for computing

datums. The 1960-1978 epoch, which NOS intends to adopt as

a replacement for the 1941-1959 epoch [Hicks, 1980], is used

as the reference for the datums and ranges presented in this

study.

21

The elevations of the tidal datums and ranges for the

epoch 1960-1978 at Presidio, San Francisco, which were used

as the standard for comparison with the secondary stations

in the Sacramento River system are given in Table 5.

Included in Table 5 are the elevations of the previous epoch

of 1941-1959 used in other studies, and the datums for the

18-month period of this study.

22

IV. DATA AND EDITING

The tide observations analyzed in this study were

acquired on magnetic tape, tide gauge analog record, and

paper computer printout from NOS and the U.S. Geological

Survey (USGS) . These are listed in Table 2. Digital tide

data for Presidio for January and February 1978 were unavail-

able, so heights of high and low waters were read directly

off the analog bubbler gauge record supplied by NOS; for these

two months the times of the predicted tides were considered

adequate since they do not affect datum determination by

the comparison of simultaneous observations procedure. Hourly

heights were extracted from both the 15-minute computer print-

out supplied by USGS and the six-minute magnetic tapes

supplied by NOS for systematic computer handling. These

hourly heights were used to compute, by a procedure described

later, the times and heights of high and low waters, which in

turn were used to compute 19-year datums and ranges by the

method of comparison of simultaneous observations. Tide data

for Hercules was not analyzed due to the limited amount of

data available.

Due to equipment malfunctions, gaps occurred in all of

the tide records (Table 2) . Short gaps in the record of up

to three days were interpolated to within 0.1 foot by using

the pattern of the previous and subsequent tides as a guide.

23

Here, ten days of hourly heights were plotted on the same

48-hour graph as five lines centered around the gap. The

missing tides were then interpolated by hand to best fit the

pattern. Gaps longer than three days could not be inter-

polated with acceptable certainty. Mallard Island, Collinsville,

Three Mile Slough, and Walnut Grove contained uneditable gaps,

requiring special handling in computations. All datum and

range computations were performed for the whole study period

of 1/1/78 - 6/30/79 except for the uneditable gaps.

24

V. PROCEDURES AND ANALYSIS

Programs described here extract the tidal component

from the edited hourly heights, determine the heights and

times of high and low waters, sort these tides by daily

type, and then determine tidal datums by the comparison of

simultaneous observations procedure. This procedure compares

the same tides at a short-term or secondary station with a

long-term reference or standard station. Graphical presenta-

tions and analysis of these extended 19-year datums for the

1960-1978 epoch were then produced. The important programs

are included in the Appendix. All computations were performed

on the IBM 360 digital computer at the W. R. Church Computer

Center of the Naval Postgraduate School. Graphics were pro-

duced on the Versatec plotter attached to the computer.

A. HIGH AND LOW WATERS PROGRAM

For the purpose of computing datums by the procedure

of comparison of simultaneous observations, the times and

heights of high and low waters are required. To obtain these

values from the digital hourly height data, a second-degree

polynomial was fitted using a least- squares procedure to the

hourly heights. This parabola-fitting procedure, which is

fully described by Zeile [1979], consists of two steps.

First, four successive hourly heights are scanned in a moving

25

window for a trend or slope. Whenever these heights show a

change in the sign of the differences in successive hourly

heights, this is used as an initial guess for an extreme

water. Upon detection of a change in trend, the five hourly

heights distributed around the sign change are then fitted

with a polynomial. The point on the curve with a zero deriva-

tive is then used as the time and height of the extreme water,

This procedure provides heights accurate within a tenth of a

foot. For a more refined determination of the tide time and

height upriver where the tide wave is clearly assymetrical

,

a third or fourth order polynomial might be more appropriate

for some purposes. This refinement is not justified here in

view of the fact that variations in river height greatly

exceed the accuracy with which tide heights can be determined

B. TIDE SELECTION AT PRESIDIO

In order to determine tidal datums the tides must be

sorted by daily tide type. Since all river stations were

compared with the Presidio reference station, all tides at

Presidio were indexed by daily tide type. It is normally a

simple task to distinguish the higher high, lower high,

higher low, and lower low waters by their relative heights.

When two consecutive high or low waters have the same height,

it is adequate to follow the previous day's pattern.

Since the average period between consecutive tides is a

little longer than six hours, every fortnight there occurs a

26

solar day containing only three tides. For accurate datum

determination it is essential that the tide type of the three

tides be determined. The Manual of Tide Observations [USCGS,

1965, p. 54] recommends for hand comparison that the previous

day's tide pattern be used for a guide to the pattern for the

three-tide day. This procedure usually works well, but is

inadequate on those occasions when a change in tide type

sequence occurs simultaneously with a three-tide day.

Attempts to use the previous day as a guide sometimes failed

early in this study because the day-to-day change in tide

height is occasionally greater than the diurnal high or low

inequality. A satisfactory solution, developed by the author,

is to use the relative heights of the four waters occurring

before noon on the day of the three -tide day as a guide for

the tide or tides in the A.M. and the subsequent four waters

as a guide for the water or waters occurring in the P.M.

This identifies tide types in a consistent manner.

C. HARMONIC FILTERING PROGRAMS

During high river levels at upriver stations the range

of the tide may be reduced to approximately the level of

noise, which has a magnitude of about a tenth of a foot

[Zeile, 1979]. The river height at which tides can be

identified at a given station can be increased by separating

the prominent semi-diurnal and diurnal tidal components from

the non-harmonic river components of the water level. This

27

was done by computing running means of the hourly heights

using averaging intervals determined by the periods of the

harmonic components to be suppressed, i.e., 24 hours for the

solar component and 25 hours for the principal lunar com-

ponent (2M_ = 24.96 hours). Application of these filters

applied singly and in combination is illustrated in Figure 3

for a 24-day series of tide measurements at Presidio. The

upper two curves, displaced vertically for ease of comparison,

show the residual water level remaining after application

of the 25-hour filter (upper curve) and the 24-hour filter

(lower curve) . The middle set of curves shows the effect

of double filtering with both 24 and 25-hour running mean

filters and the triple filter recommended by Godin [1966],

compared with the 24-hour filter. It may be seen in this

example that the double filter eliminates these harmonic

components almost as effectively as the triple filter. Use

of the triple filter, which requires a little more computing

time, yields only an incremental improvement over the double

filter; accordingly, a double filter was used in this study.

The residual, which at river stations represents the river

component of the observed water level history, can then be

subtracted from the hourly heights to extract the tidal com-

ponent to be used in the comparison of simultaneous observa-

tions. This procedure was used for the uppermost river

stations, Walnut Grove and Sacramento, because they both

28

experienced high enough water levels so that the tide would

get lost among the noise.

An additional filter was used to eliminate fictitious

tides (non-tidal water-level fluctuations mistaken for tides)

occurring at Sacramento during periods of high river level.

Zeile [1979] found that an actual tide wave would not arrive

at Sacramento sooner than 6.5 or later than 14.5 hours after

it passed Presidio. Accordingly, the time of tide at

Sacramento was compared to that at Presidio, and if the

lag was less than 6.5 hours it was considered fictitious

and ignored. If the lag was greater than 14.5 hours it was

assumed there was a missed tide; accordingly, the tide was

nevertheless used as an estimate of the missing tide and

also for the next comparison. This crude method produces

an acceptable approximation of the mean river level, but

other datums and ranges derived at river levels above tidal

influence have no significance.

For the lower river stations, where fictitious and missing

tides did not occur, the time lag from when the wave passed

Presidio to the time it arrived at the secondary station was

used to synchronize the array of high and low waters at the

river station with the corresponding waters at the standard

station. Travel times used were from the Tide Tables

[NOS, 1978].

29

D. COMPARISON OF SIMULTANEOUS OBSERVATIONS PROGRAM

Tide observations at all river stations were compared to

those at Presidio, San Francisco using the standard comparison

of simultaneous observations procedure which is explained in

detail by Marmer (1951) . Two assumptions are made in the

use of this procedure: (1) The difference between the mean

tide level over the period of observation and the actual 19-

year mean tide level is the same at both the standard and

subordinate stations, and (2) the ratios of the observed

ranges to the actual 19 -year ranges are the same for both

stations

.

This procedure, which may best be understood from

examination of the program given in the Appendix, first

separates the tides by type (HHW, LHW, HLW, and LLW) at both

stations. The mean of each tide type at the secondary station

is then computed for the comparison period. Differences in

height between the same tide at the reference and secondary

stations are averaged over the comparison interval yielding

mean differences for each tide type. The time differences

in the occurrence of common tides at the two stations are

used to compute the high water and low water time lags

between the two stations. The elevations of the datum planes

and the ranges as described in Table 4 are then computed for

the period of the common tide observations for both stations.

Range ratios are computed using the differences in the common

30

datum elevations between the stations and the ranges at the

secondary station. These are then multiplied by the 19-year

epoch ranges for the Presidio reference station (given in

Table 5) to derive effective 19-year ranges (1960-1978 epoch)

for the subordinate station.

The mean tide level over the observation period for the

secondary station is adjusted to an effective 19-year mean

tide level by applying the difference between the observed

mean tide level and the established 19-year mean tide level

at Presidio to the observed mean tide level at the secondary

station. Effective 19-year high and low water datums are then

computed from the effective 19-year mean tide level and the

19-year ranges.

E. STATISTICAL ANALYSIS AND GRAPHICS PLOTTING

Numerous customized computer programs were written to

produce the many statistical data analyses and graphics

presented in this report. None are included in the Appendix.

The principal products include the following:

1 . Time Series Graphs

Continuous 19-year datums and ranges were generated

and plotted for each river station by the comparison of

simultaneous observations procedure using a running 28-day

observation period and a one-day computation step. Examples

of these time series graphs, which show the seasonal

31

variability of these datums and ranges, appear in Figures 11

and 12 for Sacramento. Similar Graphs for all the river

stations are included in Appendix A.

2

.

Datums and Ranges along the River System

To show the extreme values found in the data during

the study period, a maximum, or peak, and a minimum were

computed for each data set, and are included in Tables 11-19.

Differences between these extreme values are listed in Table 9.

Mean values were computed for each data set over the 18 -month

study period and these are included in Table 6, and plotted

for the length of the river in Figure 5. High water and low

water values from the 18 -month study period are provided for

each 19-year datum and range at each station (Tables 7 and 8).

These statistics are also plotted for the length of the river

system from Presidio to Sacramento (Figures 7-10) .

3. Scatter Plots and Regression Lines

The 19-year datums and ranges were also plotted

against the 28-day mean tide level for each station and are

in Appendix A. For an example of one of these scatter plots,

see Figure 15. A least-squares procedure was used to fit a

straight line of regression to each data set, providing a

mathematical relationship between the 28 -day river level at

each station and the computed 19-year datums and ranges. The stan

dard deviation of each data set about the line of regression was

also computed to provide a measure of the variability of each

32

relationship. The slope and y-intercept of the lines of

regression were tabulated and are included in Tables 11-15

and 18. Graphs of these statistics along the river system

for each datum and range are included in Figures 16-24.

4. Datums and Ranges at Presidio

In order to illustrate the effects and variability

produced on datums and ranges by the use of various observa-

tion periods, tidal datums and ranges for Presidio for the

study period were computed and plotted using simple running

means of the various sample lengths (Figures 13-14, 26-31).

Mean datums and ranges computed for the entire study period

at Presidio are shown in Table 5.

5

.

Comparison of Observation Intervals

To demonstrate the accuracy of datum determination

with various short lengths of comparison, 19-year datums and

ranges were computed using 7, 14, 28, and 56-day observation

periods at Sacramento. Time series graphs of these are

found in Figures 11-12 and 32-37. Scatter graphs of these

datums and ranges against mean river level for each observa-

tion period at Sacramento are found in Appendix A; an example

is shown in Figure 38. Regression statistics for the scatter

graph data are found in Tables 16-19, and are plotted against

the length of comparison in Figures 39-47.

33

VI. DISCUSSION

A. TIDAL BEHAVIOR IN THE RIVER SYSTEM

Many of the characteristic features of tidal behavior

in the river system are illustrated in Figure 4, which

shows a short series of tide waves as they move upriver

from San Francisco Bay during a period of high river stage.

Simultaneous hourly heights for a two-day period are plotted

for eight stations from Presidio to Walnut Grove. The curve

for Sacramento is omitted, the mean river level being over

21 feet on these days and there being effectively no tides.

The figure shows that as tide waves travel upriver, their

range generally decreases and they arrive at each consecu-

tive station at a later time. Less obvious in this example

is asymmetry of the tide wave which develops upriver, the

high tide traveling faster than the low. One can also see

the increase in mean tide level upriver, the gradient of

which is determined by the prevailing river stage. It may be

noted that the MTL gradient increases markedly upriver from

Three Mile Slough where the Sacramento River is confined to

a narrow leveed channel. The increase in MTL can also be

seen in Figure 5, which shows the elevation relative to NGVD

of the derived 19 -year datums throughout the river system

(discussed more fully below) . Note in this figure that MLLW

34

lies below MTL at the Presidio as far as 70 NM upriver from

the Presidio.

Another interesting phenomenon is the increase in tide

range found at some of the lower river stations relative to

the range found at Presidio. According to the Admiralty

Tidal Handbook [1975], as a tide wave moves into a typical

estuary, the range is amplified due to its confinement in

a narrowing channel. This increase exhibited in the

Sacramento River System can be seen in the increased mean

tide range shown in Figure 6 at Point Orient. Note also a

second increase in range found at Three Mile Slough (56 NM

from Presidio) . This apparent increase is due to the lack of

low water (summer) data for the lower two stations,

Collinsville and Mallard Island. Above Point Orient,

Figures 5 and 6 both nicely show the decrease in range

which is generally observed as the tide wave opposes the

river current and gains in elevation. Tidal influence is

found at elevations more than double the MHHW level at

Presidio, demonstrating that the tidal energy indeed climbs

uphill. The DLQ is reduced substantially, whereas the DHQ

is only slightly affected upriver by the increase in eleva-

tion. The data for Figure 5 and 6 are found in Table 6.

Figures 7 and 8 (and Table 7) show the 19-year tidal

datums and tidal ranges, derived from 28-day comparisons,

that correspond to a time of lowest river level during the

35

study period when the tide reaches the farthest upriver. At

these times the computed 19-year datum elevations are lowest

and tide ranges are largest. Figure 7 shows a slight upriver

decrease in elevation of MTL between Point Orient and Benicia

and also between Three Mile Slough and Walnut Grove. Sub-

sidence may be a factor at Three Mile Slough; however, a

comparison of MTL in Figures 5, 7, and 9 suggests that sub-

sidence said to be occurring in the Sacramento-San Joaquin

Delta has been small. This elevation discrepancy may be

entirely due to the lack of data for Three Mile Slough during

the low water summer months.

Figures 9 and 10 (and Table 8) show the computed 19-year

tidal datums and tidal ranges along the Sacramento River

System, derived from 28-day comparisons, that roughly

correspond to the highest water stage in the river system

during the study period. The decrease in tidal ranges upriver

is relatively rapid and there is essentially no tidal influ-

ence at Sacramento. The diurnal high and low water inequali-

ties are seen to disappear upriver so that the tides tend to

become semi-diurnal in type. Note in Figure 9 the flat MTL

in San Pablo Bay and in Suisun Bay, and the gradient found

between Point Orient and Benicia. The latter is considered

to be due to the constriction of the Carquinez Strait.

36

B. 19 -YEAR DATUMS AND RANGES IN THE RIVER SYSTEM

The standard NOS procedure for comparison of simultaneous

observations is used to carry datums from a standard or

primary tide station at which long-term 19-year datums have

been established, to a secondary or subordinate short-term

station. This procedure is more accurate for longer periods

of comparison than for short. The commonly used length of

comparison is one month. This provides estimated 19-year

datums having a standard deviation of 0.13 feet for oceanic

tidal stations on the Pacific Coast within the same tide

regime [Swanson, 1974]. Operational limitations have at

times restricted tide observations to comparison intervals

as short as a week or less, providing reduced accuracy.

Because of the effect of length of comparison on accuracy of

determination, a standard comparison period of 28 days was

chosen for examining the effects of river superelevation on

computed 19-year datums and ranges. A 28-day period was

selected because it minimizes the prominent fortnightly cycle

of spring/neap tides, it is the length of a lunar month, it

approximates the commonly used comparison period of one month,

and also is short enough for convenient computation.

In order to examine the effect of length of the comparison

period on computed 19-year datums and ranges, computations

were also made using a series of intervals of 7, 14, 28, and

56 days duration. This series provides a geometric

37

progression from a short to a longer comparison interval,

including the 14-day interval which approximates the period

of the prominent spring/neap cycle. Longer lengths of

comparison did not provide a significant increase in accuracy

over that given by the 56-day interval.

The results of these comparisons are discussed in

Section B4.

1 . Seasonal Datum and Range Variation

Upriver, the character of the tides varies considerably

throughout the seasons. Figure 11 shows running 19-year datums

at Sacramento derived from 28-day comparisons with the tides at

Presidio using a one-day computational time step. Figure 12

shows the corresponding ranges. Range values shown for the

periods of higher water level, above 10 feet NGVD, are essen-

tially computational noise created by comparison of river

flow fluctuations at Sacramento with real tides at Presidio.

The values for the MTL do present an accurate picture of the

mean water levels in the river. The largest 28-day greater

range, which occurs at lowest river levels, is about a foot

and a half.

Figures 13 and 14, which are presented here for com-

parison with Sacramento, show the variations in the datums

and ranges, respectively, found at Presidio for the same period

These were produced by computing a simple running mean average

of the appropriate high and low waters. The pips and

38

oscillations are computational artifacts resulting from the

three-tide day, and occur with fortnightly frequency. Figure 13

shows fluctuations in the mean tide level which are primarily

due to meteorological effects. The long-period harmonic

fluctuations in tidal range, best shown in Figure 14, are

attributed primarily to the annual and semi-annual harmonic

components of the astronomical tidal forces. Similar graphs

of datums and ranges were produced for 28-day comparisons for

all the river stations and are included in Appendix A.

2 . Influence of River Flow on 19-Year Datums and Ranges

Each 19-year datum and range was plotted against the

28 -day mean tide level used to compute that datum and range

for all of the river stations except Collinsville , and these

graphs are included in Appendix A. Collinsville shows

characteristics very similar to those at Mallard Island due

to their proximity, and therefore has been excluded. With

regard to terminology, mean river level is used inter-

changeably with mean tide level in places where the river

flow is the major influence, even though both are computed

from the mean of the high and low waters. These graphs are

illuminating presentations of the range of 19-year values

which would be expected from a comparison of simultaneous

observations at each station knowing only the 28-day observed

MTL. They also provide information on the variability of

these datums and ranges with changes in river flow. The

39

circular patterns of data points exhibited in many of these

graphs may be due to hydraulic differences between rising and

falling river stages or to variations in contribution from

the San Joaquin River.

In order to quantify the relationship between the

19-year datum or range and the observed 28-day MTL , a least-

squares fit line of regression was computed for each data

pair. The values for these are listed in Tables 11-15 and 18

The slopes given in the tables quantify the influence of the

river flow on the datum or range shown. A zero slope indi-

cates no river influence, a slope of one indicates no tidal

influence, and a negative slope indicates an inverse relation'

ship to river level. The significance of the y-intercept

can be illustrated by imagining a cessation of river flow

into the system. The mean water level of the entire system

will then fall to sea level, and tidal ranges and datums will

be primarily influenced by the geometry of the lower river

system. Assuming the relationships computed from this data

can be extrapolated to this low water case, the y-intercepts

provide estimates of extreme values for the datum or range

at unusually low water levels.

At Walnut Grove, for example, there is a definite

decrease in the range of the tide as the MTL increases; this

can be seen for the period of study in Figure 15. The linear

relationship GR = 3.848 - 0.396 MTL can be fitted to this

40

data with a standard deviation of a tenth of a foot (see

also Table 15). The GR intercept indicates that the largest

28 -day diurnal range that could be expected at Walnut Grove

is about 3.8 feet. The MTL intercept (or x-axis intercept)

provides an estimate of the water level at which there will

be no tide. This calculates to 9 . 7 feet NGVD. The equation

also gives the level at which the tide range equals the tenth

of a foot noise level as 9.5 feet NGVD. These values are

close to the river level at which the tide disappears also

at Sacramento.

Figures 16 through 24 show how these regression

variables for the period of study vary along the river system

for the five datums and four ranges of interest computed

using 28-day observations. These graphs show the relative

influence of the river flow and river system geometry on the

datums and ranges along the river system. The reliability

of these relationships is indicated by the standard deviation,

plotted as squares. The degree of river level influence

on the datums is indicated by the slope, plotted as triangles,

with a zero slope indicating no river influence and a slope

of one indicating no tidal influence. The influence of the

geometry of the river system on the datums and ranges can be

seen in the y-intercept values, plotted as circles, which are

estimates for the 19-year datums or ranges which would be

expected from a cessation of river flow.

41

Figures 16-20 show the variability of the 19-year

MTL, MLLW, MLW, MHW, and MHHW da turns from Presidio to

Sacramento. The general increase of the slope upriver for all

five datums clearly shows an upriver increase in the influence

of river stage on the datums. Even in the lower bay system,

the MTL and high water datums are influenced by river flow

as is shown by the small positive slopes at Point Orient.

The standard deviation for all datums is lowest

in the lower bay system (less than 0.1 foot), and generally

increases upriver. It is 0.15 foot or less for all datums

except for the low water datums at Sacramento, the latter

being 0.18 foot. These small standard deviations indicate

a very close relationship between datum elevations and the

river level, and provide the basis for specifying a set of

19-year datum planes throughout the river system that are

independent of the river level.

Nineteen-year high and low water datums are computed

from the sum of a range and the 19-year mean tide level.

Accordingly, the standard deviation of a high or low water

datum will be equal to the root mean square of the standard

deviation of the 19-year range and 19-year MTL. Any error

in the computation of the 19-year MTL will contribute

significantly to errors in computation of the high and low

water datums; therefore, any improvement in the 19-year

MTL determination in a river system will significantly

improve the datum determinations.

42

Statistics on the 19-year ranges are shown in

Figures 21 and 22. The slopes calculated for the greater

range and mean range show similar patterns, increasing with

increasing mean tide level (positive slope) till about halfway

up the river system, where the superelevation causes a

decrease in range (negative slope). There is a point about

60 NM upriver where the slope is zero, indicating that

the ranges are independent of the river level. At Sacramento

the slope again approaches zero due to the numerous water

level data above the influence of the tides. A more negative

slope value would be found at Sacramento if the regression

was computed only for the low river levels which are subject

to tidal influence. It is interesting to note that in the

lower portions of the river system a tidal range amplification

results with increases in mean tide level.

The effects of river flow on the inequalities are

shown in Figures 23 and 24. The DHQ is little affected by

the changes in river level, the slope of the statistical

distribution being approximately zero regardless of river

level throughout the river system. The variability of the

19-year DHQ averages less than 0.1 foot throughout the river

system, and is about 0.02 foot everywhere below the narrow

channel sector of the river. The DLQ, on the other hand, is

noticeably affected by the superelevation, disappearing in

the upper river even at stages of low river flow.

43

3. Relation between Sacramento and Other River Stations

Figure 25 shows the 28-day mean tide levels for all

the river stations plotted against the mean river levels for

the same 28-day interval at Sacramento. This figure can be

used to estimate the 28-day observed MTL expected for any

station downriver knowing the 28-day mean river level at

Sacramento. Lines of regression were fitted to these rela-

tionships and the statistics from these are shown in Table 20.

Reference can then be made to the individual station graphs

in Appendix A to determine probable values for datums and

ranges at that river level. Using standard tide tables of

predicted tides for San Francisco, the linear relationships

shown in Figure 25, and the real time mean river level at

Sacramento, water levels and tide ranges can be then pre-

dicted for the stations in between.

4

.

Accuracy of Datum Determination from Short Observations

At secondary stations, a short series of tide observa-

tions is compared to a reference station for computation of

19-year datums. A one-year observation interval is a

standard recording period used by NOS for secondary stations

today. Mean datums and ranges were produced for Sacramento

over the 18 -month period of this study and are included in

Table 3. Data limitations restricted the ability in this

study to produce statistics on the reliability of a one-year

length of comparison in the river system. It was also

44

considered that results obtained using one-year data samples

could be accurately extrapolated from the products derived

using shorter sample intervals and that they would not differ

much from the 28 and 56-day results. The latter proved to be

the case. Hydrographic survey limitations occasionally

require comparisons to be made from shorter periods of

observation, NOS Form 248 being used for comparisons of

seven-day or fewer observations.

In this study it was decided to use a series of short-

period observations for the purpose of evaluating the effects

of the length of tide observations on the effective 19-year

datums and ranges produced. Accordingly, four observation

intervals were chosen of 7, 14, 28, and 56 days. Seven days

approximates the shortest series of tide observations generally

used historically in hydrographic surveying, as stated above,

and 28 days approximates the commonly used one-month comparison

interval. It may be noted that the interval of 14 days is the

closest full-day approximation to the prominent fortnightly

cycle of spring/neap tides, and so any averaging over this

period or its multiples would be expected to minimize varia-

tions in the means obtained. The four observation intervals

were also selected to form a geometric progression to simplify

interpolation or extrapolation of results obtained to other

tide observation periods than these.

45

In order to present a picture of how the water levels

can vary over short observation periods and of the effects of

averaging these variations, 7, 14, 28, and 56-day running

means of the tide heights and their differences at Presidio

were computed for the study period. Time series plots of

these are shown in Figures 13 and 14 and 26-31. The varia-

bility of the prominent fortnightly tide cycle can be clearly

seen in Figures 26-29 produced from the 7 and 14-day running

means. Figures 30 and 31, produced from a 56-day running

mean, effectively average out these fortnightly variations.

For contrast, the effects of 7, 14, 28, and 56-day

tide observations at a river station are shown in Figures 11

and 12 and 32-37 for Sacramento. These figures show the

fluctuations of the river to greatly exceed the tidal

influence; nevertheless, the fortnightly spring/neap cycles

appear prominently in the ranges computed from a seven-day

comparison in Figure 33 during low river stages. Figure 36

shows the damping effect of a longer comparison interval on

both the river and spring/neap fluctuations, and Figure 37

shows the corresponding ranges.

Evaluations of the effect of the length of tide

observations over the study period on computed 19-year

datums and ranges were performed using tide data from

Sacramento. Scatter graphs, such as shown in Figure 38 of

the 19-year datums and ranges plotted against the computed

46

mean river level for the same comparison interval , were

prepared for each of the four comparison intervals and are

included in Appendix A. A line of regression, which may be

thought of as a line of datums or ranges, was computed for

each of these scatter graphs and the statistics developed

are given in Tables 16-19 and are graphically summarized

in Figures 39-47. The figures and tables give the slope and

y-axis intercept of the lines of regression and the standard

deviation of the data points about this line, each plotted

against the length of comparison.

The figures show that the slope values and y-intercept

are very nearly independent of the tide observation period.

The standard deviations, however, show a definite decrease

with increased length of comparison for all 19-year datums

and ranges. An eightfold increase in the length of comparison,

from 7 to 56 days, reduces the standard deviation of the

19-year MTL about the short-term observed mean river level

by a factor of two according to Figure 39. A similar reduc-

tion in the standard deviation about the lines of regression

for the other datums and ranges can be seen in Figures 40-47.

The scatter graphs show that most of the variability of these

standard deviations occurs at lower river levels, the tides

disappearing at high water levels.

Swanson [1974] used the standard procedure for com-

parison of simultaneous observations to compute the accuracy

47

)£ datum determination with comparison intervals ranging

:rom one month to one year for oceanic stations in the same

:ide regime. His graphs also show dependency of the the

iccuracy on the length of comparison. The standard deviations

;hown in Figure 42 for MHW and in Figure 43 for MHHW are very

learly identical to the standard deviations for these high

raters found by Swanson [1974, p. 11-12, Figures 8 and 10]

>ver the common sampling interval (one to two months) for the

;tandard method of comparison on the Pacific coast. The

•ate of accuracy change with sampling interval for the over-

.apping data are in agreement; therefore, the rate of change

Letermined by Swanson can be used to estimate the accuracy

rhich would be expected at Sacramento from even longer

:omparison intervals than presented here. Swanson ? s data

l11 pertain to oceanic tide stations where river effects

in the water level are negligible. Thus, it is of particular

.nterest here to note that the dependency of the accuracy of

ligh water datum determination on the length of observation

.s independent of whether the secondary station is located

.n the oceanic or riverine environment.

Accuracy of computed 19-year low water datums show a

similar rate of improvement with longer sampling intervals,

>ut the accuracy of low water datum determination in this

river system is about 401 lower than it is for high water

latums . These determinations for low water datums show

48

standard deviations of up to 0.180 foot at Sacramento, which

is 35% less accurate than the low water standard deviations

found by Swanson for the West Coast. Surprisingly, it is

about the same as the 0.183 foot standard deviation he found

for the Gulf Coast using the standard procedure. The

accuracy of determination of the mean tide level found here

is close to that found by Swanson [1974, p. 12, Figure 10].

49

VII. CONCLUSIONS

The standard method of comparison of simultaneous obser-

vations can be applied in the Sacramento River system in

order to produce internally consistent 19-year datums and

ranges. The validity of using this procedure is based on

the fact that linear relationships can be developed between

the datums and ranges and the river levels. Considering

the variability of river fluctuations, the reduction in

precision of determination that occurs upriver appears

acceptable. Two assumptions are made in the use of the

procedure: (1) The difference between the mean tide level

over the period of observation and the actual 19-year mean

tide level is the same at both the standard and subordinate

stations, and (2) the ratio of the observed ranges to the

actual 19-year ranges is the same for both stations.

In regard to the first assumption, for a secondary

station located where river discharge produces a water-level

superelevation above the ocean level, a weakness of the

standard comparison procedure applied in a river system is

the method of determination of the 19-year MTL. The standard

procedure applies the height difference between the observed

MTL at the primary station and its 19-year MTL, termed a

corrector, to the observed MTL at the secondary station.

This difference may amount to a foot at Presidio for a

50

seven-day observation period and half a foot for a 28-day

period. This difference cannot be expected to travel up-

river as a constant quantity but should undergo a reduction

and/or amplification proportional to that experienced by the

ranges or inequalities. A question remains as how to best

apply this difference upriver. It is possible that the

difference diminishes rapidly upriver as does the diurnal

low inequality. This can be determined with assurance only

from a long series of observations at secondary stations. It

should be pointed out that applying this corrector in a place

where it is inappropriate induces oscillations in the 19-year

MTL which are not real. A comparison of the MTL in Figure 26

with the MTL in Figure 32 shows that the fluctuations are the

inverse of one another, indicating that this MTL corrector

is inappropriately applied at Sacramento.

The second assumption appears valid for all probable mean

river levels at all secondary stations, except Benicia, there

being a well-defined linear correlation between river level

and range reduction or amplification through the river system

(Tables 11-15 and 18, Figures 21 and 22). An unusual situ-

ation occurs at Benicia where it was difficult to get a close

linear fit between the ranges and the mean river level

(Figures 21 and 22) . The diurnal low inequality at low

river levels was found often to behave as if the lowest

waters could not overcome the seaward current through Carquinez

Strait

.

51

Tidal ranges diminish with increased superelevation of

the water level in the Sacramento River, disappearing

completely at certain high river stages except in San Pablo

Bay where some range amplification is seen with the relatively

small superelevation which occurs there. The diurnal low

inequality is affected more by the river superelevation than

is the diurnal high inequality.

The 19-year mean tide levels and high water tidal

datums can be computed in the river system with an accuracy

comparable to that resulting from comparisons in an oceanic

environment found by Swanson [1974] for the same observa-

tion interval. Low water datum determination is less

accurate than high water determination in the river

system. Nineteen-year tidal datums determined from short

comparisons are dependent, though, on the specific super-

elevation of the river.

A method has been developed here having a straightforward

statistical basis, using tide observations collected over

observation periods on the order of a year at secondary river

stations, where a 19-year record is available for both an

oceanic reference station (Presidio) and a river reference

station (Sacramento) , for obtaining the elevation of the

standard tidal datums along the full extent of the river

system in which tidal oscillations occur.

52

The method involves determination of precise values for

19 -year datums and ranges anywhere up the river system in the

following way for a chosen mean river level. For each datum

and range at each river station, precise regression equations

have been developed expressing the computed 19-year datums

and ranges as a function of the river level; these are given

in Tables 11-19. Substituting the chosen river level into

these equations, one can then calculate consistent datums and

ranges by simply multiplying the MTL by the slope and then

adding the y-intercept. For example, the monthly mean river

level at Sacramento for the epoch years 1960-1978 is 7.54 feet

NGVD (Table 3). From the relationships presented in Table 18,

19 -year datums and ranges can then be computed around this

mean river level for Sacramento for the epoch 1960-1978 and

are included in Table 3. It may be noted from the table that

the standard deviation of the mean river level over this 19-year

period of observations is almost five feet.

In the example just considered, the mean of 19 years of

river level measurements was chosen for establishing tidal

datums for the 1960-1978 epoch for Sacramento. However, there

are other logical choices of mean river level that can be

derived from these long-term measurements around which tidal

datums may be desired. These long-term river level measurements

may provide a statistical basis for the choosing of suitable

river levels around which to determine tidal datums. A histo-

gram for this purpose is included as Figure 48 which shows the

53

height distribution of monthly mean river levels at Sacramento

for the eopch years 1960-1978.

For levee design or the determination of property boundaries,

a statistically high river level may be chosen. For navigation

purposes a low level datum would be chosen. With regard to the

latter, it may be noted in Table 3 (upper part) that the tidal

datums at Sacramento cluster about the long-term mean river

level, but that because of the wide variations in river ele-

vation, water levels below MLLW occur much of the time (lower

part). Accordingly, a datum for navigation at Sacramento

would best be chosen at a river level substantially below this

MLLW. In oceanic tide regimes, where tides are the only

influence on water level, fluctuations below the low water

datum chosen for navigation are statistically infrequent

and of small magnitude. In a river environment, a statisti-

cal low water level must be developed for both influences,

river level and tidal fluctuations. The data in Figure 48

might be used to choose a suitable low river level. Some

possible choices for a low water navigation reference at

Sacramento are: (1) the ten-percent quantile water level

(3.58 feet), which approximates the lowest waters in a normal

summer season at Sacramento, (2) the minimum value found in a

19-year record (1.98 feet, for 1960-1978), which is a low

water level in an unusuahly dry summer, and possibly (3) the

hypothetical river level if the river stopped flowing

54

iltogether, which would be calculated by the MTL y-intercepts

ls discussed previously (0.18 feet, Table 10). At any one

>£ these river levels, a MLLW with respect to that level can

ie determined, and used as the nautical charting datum,

fith any one of these choices it would be possible to

establish a datum which is continuous throughout the transition

;one of the Sacramento River System. In practice, tidal

;oning, defining separate da turns for each section of the

•iver, would be required.

With regard to the question raised in the introduction,

'esults obtained here for the Sacramento River System show

:hat there is no natural discontinuity or feature along the

'iver system that can be objectively used to terminate up-

'iver tide measurements for datum determination purposes,

[owever, there are several possible criteria that might be

idopted for this purpose, each requiring an arbitrary speci-

ication: (1) A specified ratio of mean river superelevation

MTL in Table 6) to the mean tide range (MN in Table 6)

,

2) a specified ratio of river variability (manifested by

he MTL in Table 9) to tidal variability (GR in Table 6)

,

3) a specified percentage of time that a tidal influence

>revails (for example, the point where the tide shows some

.nfluence half of the time is where the median river super-

elevation equals the level of no tide; this point is above

line feet upriver from Sacramento.

55

feet this point is upriver from Sacramento) , and (4) the point

above which the river has no tides. The position of the

last choice cannot be determined from the data studied, but

requires knowledge of the river gradient above Sacramento.

Assuming the river gradient is similar above Sacramento to

that below, the tides will travel an additional 100 NM

beyond Sacramento at a low river level , based on the rate

of range decrease along the confined section of the channel

from Walnut Grove to Sacramento indicated in Figure 7

(Table 7)

.

The results of this study raise the following questions:

(1) Can the procedure developed for the Sacramento River

System be applied over the entire Sacramento-San Joaquin

delta region, (2) over what extent of the Sacramento-

San Joaquin delta region can the Sacramento 19-year reference

station be used to determine water levels at other stations,

and (3) is a separate reference station needed on the upper

San Joaquin river system? The California/NOS cooperative

tides program of 1977-1979 involved the synoptic collection

of tide data from some 53 stations throughout the delta

region above Carquinez Strait, and the California Division

of Water Resources maintains some 43 longer term recording

stations in the region. This wealth of data may provide the

means for answering these questions.

56

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58

Table 3. TIDE DATA FOR SACRAMENTO

All elevations and ranges are in feet.

19 -YEAR DATUMMEAN VALUES*

FOR EPOCH 1960-1978MEAN VALUES FOR

STUDY PERIOD 1/78-6/79

MHHW 7.99 NGVD 7.40 NGVD

MHW 7.77 7.17

MRL 7.54 6.85

MLW 7.17 6.53

MLLW 7.07 6.42

19 -YEAR RANGE

GR 0.920 0.947

MN 0.602 0.642

DHQ 0.216 0.224

DLQ 0.100 0.108

STATISTICS FROMMONTHLY MEANWATER LEVELS FOR EPOCH 1960-1978

MEAN

MEDIAN

MAXIMUM

MINIMUM

101 QUANTILE

STD. DEVIATION

7.54 NGVD

5.69

22.55

1.98

3.58

4.73

STUDY PERIOD 1/78-6/79

7.0 7 NGVD

5.27

17.59

3.67

3.75

4.20

*Computed from the mean river level of 7.54 (fromlower part of table) and the relationships foundin Table 18.

59

Table 4. TIDAL DATUMS AND RANGES

Daily Tides: HHW - Higher High Water

LHW - Lower High Water

HLW - Higher Low Water

LLW - Lower Low Water

Tidal Da turns : MHHW - Mean Higher High Water

MHW - Mean High Water =1/2 (MHHW + MLHW)

MLHW - Mean Lower High Water

MTL - Mean Tide Level =1/2 (MHW + MLW)

MHLW - Mean Higher Low Water

MLW - Mean Low Water =1/2 (MHLW + MLLW)

MLLW - Mean Lower Low Water

Tidal Ranges: DHQ - Diurnal High Inequality = MHHW - MHW

DLQ - Diurnal Low Inequality = MLW - MLLW

MN - Mean Range = MHW - MLW

GR - Diurnal or Greater Range= MN + DHQ + DLQ

or = MHHW - MLLW

60

Table 5. TIDE DATA FOR PRESIDIO

All elevations and ranges are in feet.

STUDY PERIODEPOCH 1941-1959 EPOCH 1960-1978 1/78 - 7/79

DATUM STAFF NGVD STAFF NGVD NGVD

MHHW 11.46 2.85 11.60 2.99 3.00

MHW 10.86 2.25 11.00 2.39 2.44

MTL 8.86 0.25 8.95 0.34 0.42

MSL 8.80 0.19 8.90 0.29 0.31

NGVD* 8.61 0.00 8.61 0.00 0.00

MLW 6.87 -1.74 6.90 -1.71 -1.61

MLLW 5.75 -2.86 5.77 -2.84 -2.56

*Geodetic datum

EPOCH EPOCHRANGE 1941-1959 1960-1978

MN 3.99 4.10

GR 5.71 5.83

DHQ 0.60 0.60

DLQ 1.12 1.13

STUDY PERIOD

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5.56

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0.95

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Figure 21. VARIABILITY OF 19-YEAR GREATER RANGESRELATIVE TO MEAN RIVER LEVELS FROM28 -DAY OBSERVATIONS OVER THE STUDYPERIOD.

A SLOPE OF fl BEST FIT LINEOT AXIS INTERCEPT (FEET NGVD)


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20.00 -40.00 60.00 80.00 100.00NAUTICAL MILES FROM PRESIDIO

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STANOARD DEVIATION (FEET)

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APPENDIX A. GRAPHS

POINTORIENT

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M_1_l© THREE

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SLOUGH WALNUTGROVE

SACRAMENTO

Time Series

7-DAY

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14-DAYCOMPARISON

28-

DAY COMPARISON

S6-DAY

COMPARISON

Da turns 8-1 B-l M-l C-l T-l W-l 32 34 11 36

Ranges 0-2 B-2 M-2 C-2 T-2 W-2 33 35 12 37

Scatter Plots

MTL 0-3 B-3 M-3 T-3 W-3 Q-3 R-3 S-3 V-3

MLLW 0-4 B-4 M-4 T-4 W-4 Q-4 R-4 S-4 V-4

MLW 0-5 B-5 M-5 T-5 W-5 Q-5 R-5 S-5 V-5

MHW 0-6 B-6 M-6 T-6 W-6 Q-6 R-6 S-6 V-6

MHHW 0-7 B-7 M-7 T-7 W-7 Q-7 R-7 S-7 V-7

GR 0-8 B-8 M-8 T-8 W-8 Q-8 R-8 S-8 V-8

MN 0-9 B-9 M-9 T-9 W-9 0-9 R-9 S-9 V-9

DLQ 0-10 B-10 M-10 T-10 W-10 Q-10 R-10 S-10 V-10

DHQ 0-11 B-n IM-11 T-ll W-ll Q-n R-ll s-n v-n

All graphs are computed from 28-day comparisons, except as

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APPENDIX B

SU8RCITINE TC CCNFITE 1<3 YE*P TICAL CATUMS FFCM ACOMPARISON OF «INLLTAN«=OL< TICES A"r A SUBORDINATESTATICN FRCN PFES1CIC EPCCh 1963-1^78

KTlvKHtTPlvTPZ ARE SYNCRCMZFC ARRAYS CF HEIGHTSANC T1VES CF H C h ANC LOW VOTERS FOR PRESIDIO ANDTHE SECCNDAPY STATICN RESPECTIVELY

ITYFE IS AN AFFAY CF th« TYPE CF EACH TIDE<1=I-HW,2 = LHW,£=HLV.,4-LHW)

D = CIFFEFEKE CF CIUPNALH = HIGH CR HIGHERL = tCW CF LCWEPN = NEANP = PFIIÂRY CF FFSSICICC = UECUALITYS = SECCNCAFY CF SL ECPC IN A"T =

T = TCTALW - WTER

TPHHfc=0.TPLHW=C.1PHLV=C.TPLLW=C.TSHhW=0.1SLHt» = C,TSt-LW = C,TSLl>=G.LOWPHS=C.HFhs=c.

E=C.C = C.C=C.

SORT EY TYPE CF TICE

CO 3CC I«l>.NCC*PKTVPE»IT>FEU1C-C TC (21C,22C,22C»3AC),KTYPE

SUM THE HIGHER UGH WATERS

310 TPI-HW=TPH-V»4HTimTSHHfc=TSH-HI-T2mHPHS =HlFHS + (TM2m-TM(I) )

A=A+1.GC TC 29«

SUM THE LCWEF HGh WATERS

220 TPLHW = TPLhV + l-Tl(I)T5LHW = TSL(-V-»I-T2n)HFHS=HIFhS-KTV2(I)-TNin I )

E=E*1.GC TC 2S«

173

SUM THE HIGHSF ICV< WATERS

330 TPhLV=TPKMhTim1SHV = TSHHh72<!>L0V.PhS=LCVPHS + (TV2<! l-7fl(IHC=C+1.GG TC 2S C

,

SUM The LCUEF L CW WATERS

340

25S300

7FLLW =7PLIMH71(I)1Slt> = TSltV4M2<I)l0toPhS = LCVPhS-M7M2<! 1-7*1(1) )

C=C+1.C0N7IM£CGNTINIE

CCMPITE 7hE CIPF €F£NC= TC7JLS

CH>W=7S»-l-V>-TFI-mCLhW = TSLI^-lFLHVsCHIW =7SHV-TPHLV*CLLW = TSlLfe-TFLLV*

COMPUTE THE NEAN CIFPE°ENCES

CHf-H V-Chh V /4CMLHW=CLhV/6CMHV> = !>Lfc/CCML1_V=CLIV/CCMHWs.5* (CMH-W + CMLH* t

CMW=,5*(CM-LW40MLLW )

CM1L*. £*<CM-Ia + DVLVO

COMPUTE THE Htl UGH AND LCV» 7IME LAGS

tCV»PhS*LCUFh$/<C+C)HFHS=HIFh</ <A+E)

CGMFITE ThE Ê / N TICES

FM7L=(TPI-l-V»4lPLHV» +TFHLV»47PLLV)/(A>B + C + DIFNTL = Fm-6.61CSHHV« = 1SKh^/ACSLHU =TSll-WECSH>=TSHV»/CCSLLW=1SLLV/CSMHW=.5* (CSH-fc + CSLHW )

SMLV»* # 5 JMCSH> + CSLl>)SMTt=.S*<SM-V»4S*LW)

COMPUTE THE NE4r PANGS ANC INECIAU7IES

SNMSNhfe-SKW5DFQ=C<l-hV-C5t>feSCLQ =DSHfc-CSLLWcni^cm-v*-ckwCHGD=DNHI-V-CMHfcclcd^cm-lv-cmiv.

compute the rajsge 9atics

fmmsmn/ <<m^-cnmrdhq=schc/(schc-dhqo)fcuc=sclc/ (sclc-clcd)

174

COMFITS 19 YE4F NEAN Tire t_cVELS

FROM FRESICIC EFCCH 1960-1976

ML=8.95-»CfTL-SNGVCCMN=4.ic*FNr*CChQ=0.6C*RCI-CCCLQsl .55*FCIC

M.LW=Mlfc-CCLC^v>-NTL-M.5*Cf'N)^HHW = MHW-»CDHCFETUFN

SUBRCLTINc TO CCI^PITE A RUNNING MEAN FROM AN ARRAY CF DATA

NIN IS THE MNEEF CF M5MB*RS IN TH = INPUT ARRAYLTH IS THE NUNEEP CF ARRAY NEVBERS IN EACH MEAN VALCEIDEC IS TH£ IKFENENT CP *Zth CCMPUTATION

( ICEC=Z, EVERN THIRD VEJN IS CCVC^TED)NGUT IS THE NLNEER CF MENeE^S IN THE OUTPUT ARRAY

20

30

SUERCLTINE E CXCAR ( SL ,N IN ,LTH , I DEC ,NOUT)FEAL*4 SM6290)NCLT=CISTAFT=1IEND = IST*F1-»LTH-1IFUENC.C1.NINIP5TUPN

Cci 30 I=I<7*FT,IENDSUN = SUM4«L<I )

KlT=NClT4l!L(NCLT)*Slf'/FlCAT<lTFl1START=IST*FI-»ICECGC TC 2CRETURN

175

THIS SUBROUTINE COMPJTES THE HEIGHTS AND TIMES OF HIGH ANDLOW WATERS FROM AN ARRAY GTIDE OF HOURLY HEIGHTS

LE IS THE NUMBER OF MEMBERS IN GTIOEHEISHT IS AN ARRAY OF HEIGHTSTIME IS AN ARRAY OF TIÊS IN H3JRS AND HUNDREDTHSCTIME IS AN ARRAY OF TIMES OF OAV IN HOURS AND MINUTES

SUBROUTIME HWLW I GT I DE, LE ,HEI GHT , TI ME, CTI ME

)

DIMENSION GTIDEC 12 500), HElSHf (2400)

,

1 TIME(2^00),CTIME(2^00)K3LD=0J=0ID=1

INITIAL GUESS OF HIGH OR LOW WATER

DO 60 K-l.LEB* GTIDE (<) +GT I DE(K + 1)-GTIDE(<>3)-GT IDE <<<*)IF(BU,2,3

1 IC = -1GO TO 4

3 lOl4 CONTINUE

IF(ID+IC)60,5,602 IO-IC5 ID=IC

FIT A SECOND ORDER CURVE TO THE HOURLY HEIGHTS

J = J+1FZ=GTIDE( K)*4.*3riDE(<*l)«-9.*GTIDE<K +2m6.*GTI0E(<«-3)

l«-25. *GTIDE(K+4)FC=GTIDE( K) GTIDE(K-H)«-GTID = (K*2)+GTID = << + 3I

1 +GTIDEU + 4)FL=GTIDE(K)+2.*GTIDE(K-H)+3.*GTIDE(K+2)+<V.*GTIDE(<+3)

+5.*GTIDE( K+<*)

COMPUTE HEI3HT AND TIME FROM THE EXTREMA OF THE CURVE

A2«-(3./ll.)*(((FZ-ll.*FC)/6. )-<15.*FZ-55.*FL)/35.lAl=(FZ-ll .*FC)/SD.-(<374./5 0. 1*A2»A0=FC/5.-3.*Al-ll.*A2TIME<J)=-Al/(2.*42)HEIGHT( J) =AO+TIME(

J

)*A1+TIME< J ) **2*A2TIME(J)=TIME(J)«-=L3AT<«)-2.

COMPUTE TIME IN HOURS AND MINJUTES

TEMPT=TIME<J)*133.TEMPT =.004* A MOO (TEMPT, 100.)CTIME(J) = AMOD(THE( J ) , 24. ) -TE MPT

59 CONTINUE60 CONTINUE

RETURN

176

LIST OF REFERENCES

Coast and Geodetic Survey, 1965, Manual of Tide Observations,

U. S. Department of Commerce, Publication No. 31-li

Godin, G., 1966, Daily Mean Sea Level and Short-PeriodSeiches, International Hydrographic Review , v. XLIII,No. 2, 197T;

Hicks, S. D. , 1980, The National Tidal Datum Convention of1980, Office of Oceanography, Tides and Water LevelsDivision, National Ocean Survey, May 1980 (unpublished).

Hydrographic Department Admiralty, Datums for HydrographicSurveys , Admiralty Tidal Handbook No. 2 , 19 75.

Marmer, H. A., 1951, Tidal Datum Planes , U.S. Departmentof Commerce, Coast and Geodetic Survey, Special Publi-cation No. 135.

National Ocean Survey, Tide Tables 1978 , U.S. Departmentof Commerce.

Swanson, R. L. , 1974, Variability of Tidal Datums andAccuracy in Determining Datums trom Short Seriesof Observations , U. S. Department ot Commerce

,

National Ocean Survey, NOS Tech. Rep. No. 64.

Zeile, F. C. , 1979, Tidal and River Datums in the SacramentoRiver , Master's Thesis, Naval Postgraduate School,Monterey, June 1979.

177

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190195Thesis

BT3'U8 Bouquet

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Precision of tidal datums in the Sacrame

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Precision of tidal datums in the Sacramento River, California. · NPS68-80-007 NAVALPOSTGRADUATESCHOOL Monterey,California THESIS PRECISIONOFTIDALDATUMSINTHE SACRAMENTORIVER,CALIFORNIA