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NPS68-80-007
NAVAL POSTGRADUATE SCHOOLMonterey, California
THESISPRECISION OF TIDAL DATUMS IN THE
SACRAMENTO RIVER, CALIFORNIA
by
Timothy Alan Bouquet
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.
SECURITY CLASSIFICATION OF THIS » * c. e rattan Data Bntoroal)""
REPORT DOCUMENTATION PAGE• t NuTsm
READ INSTRUCTIONSBEFORE COMPLETING FORM
»EPC
NPS68-80-007
2. OOVT ACCESSION NO > RECIPIENTS CATALOG NUMICH
4 TlTL£i«ii(Ju»IIIH)
Precision of Tidal Datums in theSacramento River, California
S. TYPE OF RtPOUT * PERIOD COVERED
Master's Thesis;June 198
• PERFORMING ORG. HI^OKT NuMICR
7. »uThO»'ii *. CONTRACT Off GRANT «UMBERr«;
Timothy Alan Bouquet
» PERFORMING ORGANIZATION NAME AnO AOORESS
Naval Postgraduate SchoolMonterey, California 93940
10. PROGRAM ELEMENT. PROJECT TASKAREA a WORK UNIT NUMBERS
NOAA Purchase OrderNA80AAG02672
II CONTROLLING OFFICE NAME >NO AOORESS
National Ocean Survey (Code C33)
6001 Executive BoulevardRockville, Maryland 20852
12. REPORT DATE
June 19 80IS. MUMIIR OF RAGES
18214 MONITORING AGENCY NAME A AQORESSCI/ liltlormnt (MM Cantralllna Olllco)
Naval Postgraduate SchoolMonterey, California 93940
It. SECURITY CLASS, (ol thia report)
UnclassifiedISA. OCCL ASStFl CATION/ DOWN GRAOlMG
SCNEOULE
16. DISTRIBUTION STATEMENT (ol tnia *a»ori)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (ol Ihm m*,,rmct mnlorod In Block 30. II tSlllmtont trmm K*+ori)
>• 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
S/N 0*1^2-014-6601 sccuai*v eLAMiPiCATioN o' *>• **o*r»»««« o«»« #»«•'•*>
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
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
4.05
5.56
0.56
0.95
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Figure 10. 19-YEAR TIDAL RANGES AT HIGH WATER ALONG THESACRAMENTO RIVER SYSTEM FROM 28 -DAY COMPARISONS
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Figure 18. VARIABILITY OF 19 -YEAR MEAN LOW WATERSRELATIVE TO MEAN RIVER LEVELS FROM 28-
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Figure 20. VARIABILITY OF 19-YEAR MEAN HIGHER HIGHWATERS RELATIVE TO MEAN RIVER LEVELSFROM 28 -DAY OBSERVATIONS OVER THESTUDY PERIOD.
92
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1 2ff. OQ
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)
STANDARD DEVIATION (FEET)
Figure 22.
20.00 -40.00 60.00 80.00 100.00NAUTICAL MILES FROM PRESIDIO
VARIABILITY OF 19 -YEAR MEAN RANGERELATIVE TO MEAN RIVER LEVELS FROM28-DAY OBSERVATIONS OVER THE STUDYPERIOD.
oo
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Figure 23. VARIABILITY OF 19 -YEAR DIURNAL LOWINEQUALITIES RELATIVE TO MEAN RIVERLEVELS FROM 28 -DAY OBSERVATIONSOVER THE STUDY PERIOD.
A SLOPE OF A BEST FIT LINE
OT AXIS INTERCEPT (FEET NGVD)
STANOARD DEVIATION (FEET)
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Figure 24. VARIABILITY OF 19 -YEAR DIURNAL HIGHINEQUALITIES RELATIVE TO MEAN RIVERLEVELS FROM 28-DAY OBSERVATIONS OVERTHE STUDY PERIOD.
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108
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A SLOPE OF fl BEST FIT LINEOT AXIS INTERCEPT CFEET NGVD)
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Figure 43.
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.
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VARIABILITY OF 19 -YEAR MEAN RANGES RELATIVE TO MEANRIVER LEVELS WITH COMPARISON INTERVAL AT SACRAMENTO
112
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OT AXIS INTERCEPT (FEET NGVD)
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VARIABILITY OF 19 -YEAR DIURNAL HIGH INEQUALITIESRELATIVE TO MEAN RIVER LEVELS WITH COMPARISONINTERVAL AT SACRAMENTO.
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APPENDIX A. GRAPHS
POINTORIENT
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MALLARD
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M_1_l© THREE
MILE
SLOUGH WALNUTGROVE
SACRAMENTO
Time Series
7-DAY
COMPARISON
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
otherwise indicated. All scatter plots are relative to NGVD.
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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 = PFII^ARY 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 ^E / 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 TI^ES 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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182
BoUguet 1 90 J 95
' Ca^ifornia>
/
190195Thesis
BT3'U8 Bouquet
Precision of tidaldatums in the Sacra-mento River, California.