COMPARISON OF ANNUAL CALCULATED AND ANNUAL MEASURED
RUNOFF IN THE BLACK CREEK WATERSHED
Giovanni J. Del Papa
B.S. Humboldt State University, 1996
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SUMMER
2010
©2010
Giovanni J. Del Papa
ALL RIGHTS RESERVED
ii
COMPARISON OF ANNUAL CALCULATED AND ANNUAL MEASURED
RUNOFF IN THE BLACK CREEK WATERSHED
A Project
by
Giovanni J. Del Papa
Approved by:
_________________________________________, Committee Chair
Saad Merayyan, PhD
__________________________________________, Second Reader
John Johnston, PhD, P.E.
____________________________________
Date
iii
Student: Giovanni J. Del Papa
I certify that this student has met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to
be awarded for the Project.
_________________________________, Graduate Coordinator _______________
Cyrus Aryani, PhD, P.E., G.E.
Date
Department of Civil Engineering
iv
Abstract
of
COMPARISON OF ANNUAL CALCULATED AND ANNUAL MEASURED
RUNOFF IN THE BLACK CREEK WATERSHED
by
Giovanni J. Del Papa
Long-duration rainfall totals are sometimes used to calculate runoff volumes for
sizing and design of storm water containment structures. Rainfall totals are also used to
determine runoff-volume-based fines for illicit storm water dischargers. The objective of
this project is to evaluate how well the Soil Conservation Service Method estimates
annual runoff based upon annual accumulated rainfall. In particular, calculations of
annual runoff using a single value of annual rainfall with daily and storm event runoff
coefficients were performed to test how well calculated annual runoff volume compares
to measured annual runoff volume.
The Black Creek watershed located in the Central California foothills was
selected for the current study because it is gaged, and its land use has not changed much
over the data record under evaluation. Land use and soil type data from Calaveras
County were used to produce an area-weighted runoff coefficient (one of four cases
analyzed). Topography data from the United States Geological Survey (USGS)
quadrangles were used to delineate the watershed. Sixteen years of overlapping runoff
and rainfall data from the USGS and the California State Climatologist were utilized in
v
the project. The USGS data provided measured runoff volumes, and the California State
Climatologist data provided measured rainfall totals for the same set of years.
Additionally, 38 individual Black Creek hyetographs and their corresponding
hydrographs were selected from the California Data Exchange Center (CDEC). The
CDEC data allowed for the empirical development of minimum, average, and maximum
runoff coefficients (the other three cases analyzed). The CDEC data provided less data
overlap than the other two sources and was used only to derive runoff coefficients.
Based upon the data and the assumptions used in this project, the calculated
annual runoff volumes overestimate the actual measured annual runoff at the 99.99
percent significance level for all four cases investigated. The average theoretical runoff
volumes were 77 to 135 percent higher than the measured runoff volumes over the 16
water years of data for the four cases investigated.
vi
A CN value was calculated based upon the 16 years to data by minimizing the
sum of the squared residuals (the difference between the calculated and measured runoff
volumes). This CN value is much lower than those of the four cases analyzed and may
represent an “annual” runoff coefficient for the Black Creek watershed.
These results appear consistent with the work of Critchley et. al. (1991) and they
could serve as a warning for those considering using event-based calculations and runoff
coefficients for estimating long-duration runoff from long-duration rainfall totals. These
results could be incentive to the hydrologic industry to investigate and develop better
volume-based hydrologic methods to estimate long-duration runoff volumes.
_________________________________________, Committee Chair
Saad Merayyan, PhD
_________________________________________
Date
vii
DEDICATION
I would like to dedicate this project in loving memory of my father who, among many
other things, faithfully collected and recorded rainfall data in a spiral bound notebook
during my childhood.
viii
ACKNOWLEDGEMENTS
The concept of this project has been on my mind for the better part of the last decade, and
I want to thank my advisor Professor Saad Merayyan for allowing me to pursue this work
and for his mentoring and advice.
I would also like to thank the following:

All of my engineering instructors who helped to prepare me to take on and
complete such a project.

My friends and family who stood behind me during the preparation of this project.

Condor Earth Technologies, Inc. for allowing me the time and for their support
during the preparation of this project.
Thanks to you all.
Giovanni J. Del Papa
ix
TABLE OF CONTENTS
Dedication ............................................................................................................................. viii
Acknowledgments.................................................................................................................... ix
List of Tables ........................................................................................................................... xi
List of Figures ........................................................................................................................ xii
Chapter
1. INTRODUCTION .............................................................................................................. 1
2. LITERATURE REVIEW ................................................................................................... 5
Rational Method .......................................................................................................... 5
Soil Conservation Service Method .............................................................................. 8
Hydrograph Methods ................................................................................................. 12
Long-Term Runoff Approaches by Others ................................................................ 14
3. METHODS AND ANALYSIS ......................................................................................... 17
Description of the Study Area.................................................................................... 19
Sources of the Data .................................................................................................... 23
Hydrologic Data ......................................................................................................... 26
CN Weighting ............................................................................................................ 27
Back-Calculated CN Values ...................................................................................... 29
Comparison of Calculated and Measured Runoff Volumes ...................................... 36
4. DISCUSSION OF RESULTS........................................................................................... 41
5. CONCLUSIONS............................................................................................................... 45
Appendices on CD .................................................................................................................. 47
Appendix A. USGS Daily Flow Data
Appendix B. State Climatologist Yearly Rainfall Totals
Appendix C. CDEC Hourly Rainfall and Flow Data
Appendix D. GIS Polygon Data Used for Weighted
Appendix E. Hyetographs and Hydrographs from 38 Black Creek Storms
Appendix F. Calculations of Differences between Calculated and Measured Water Year
Runoff ............................................................................................................. 48
References ............................................................................................................................... 54
x
LIST OF TABLES
1.
Table 1 Geographic Adjustment Factor ..................................................................... 27
2.
Table 2 Land Use and Soil Type................................................................................ 28
3.
Table 3 CN(II) Values ............................................................................................... 28
4.
Table 4 CN Weighting ............................................................................................... 29
5.
Table 5 Back-Calculated CN Values of Selected Storms .......................................... 35
6.
Table 6 Summary of Average Measured and Calculated Runoff Volumes ............... 37
7.
Table 7 Summary of Statistics and Confidence Intervals .......................................... 42
xi
LIST OF FIGURES
1.
Figure 1. Black Creek Watershed Location Map....................................................... 21
2.
Figure 2. Black Creek Watershed Map ...................................................................... 22
3.
Figure 3. Black Creek Land Use Map ....................................................................... 24
4.
Figure 4. Black Creek Hydrologic Soils Map ............................................................ 25
5.
Figure 5. Black Creek Hydrograph Example – January 25, 2001 Storm................... 32
6.
Figure 6. Dot Plot of CN Values for Selected Storms from
1997 to 2001 .............................................................................................................. 34
7.
Figure 7. Measured versus Calculated Runoff ........................................................... 38
8.
Figure 8. Measured versus Calculated Runoff CN = 31.52 ....................................... 40
xii
1
Chapter 1
INTRODUCTION
The purpose of the current study is to evaluate how well a theoretical method
estimates long-duration storm water runoff based upon long-duration accumulated
rainfall. For the purposes of this study, long-duration is defined as a time period longer
than that of a single storm event. In particular, this study considers annual water year
rainfall and runoff totals.
Storm water discharges are regulated under the amended Clean Water Act (EPA,
1987), these regulations have placed requirements on certain dischargers to monitor and
test their storm water runoff quality. Waivers to monitoring and testing have included
containing all annual runoff, all runoff from certain storms, and/or all runoff from
selected wet seasons have been provided as possible alternatives to monitoring and
testing. Additionally, illicit dischargers can be fined based upon the volume of runoff
discharged over the period of violation. One example of an enforcement action is the
Administrative Civil Liability Complaint R5-2009-0541 imposed on the Madera County
Road Department by the California Regional Water Quality Control Board - Central
Valley Region (California Regional Water Quality Control Board, 2009). In that
administrative civil liability (ACL) example there were 242 days during the rainy season
of non-compliance with the National Pollutant Discharge Elimination System General
Permit for Storm Water Discharges Associated with Construction Activity Order 99-08DWQ (NPDES No. CAS000002) (Construction General Permit). According to this ACL,
the discharger could be fined $10,000 per violation per day plus $10 per gallon of storm
2
water, when the volume of untreated water discharged exceeds 1,000 gallons. This ACL
example does not include calculations of runoff volume or a per gallon fine.
Hydrograph methods and simplistic methods such as the Rational Method and the
Soil Conservation Service (SCS) Method are commonly utilized to estimate runoff from a
single storm event. These methods are often used to determine the peak volumetric flow
rate and/or volume of runoff from a storm event with a selected return interval. Agencies
typically require that storm drain pipes be sized to pass the peak volumetric flow from a
specific storm (e.g. the 10-year, 24-hour storm) and that detention basins be sized to
contain up to double the runoff volume produced from a specified storm. For example,
the San Joaquin County Department of Public Works generally requires that storm drains
be designed to pass the peak flow of a 10-year storm or that retention basins be sized to
contain the runoff from two 10-year, 48-hour storms in urban areas (San Joaquin County,
1997). Many of these methods can be calibrated to closely predict runoff from single
storm events.
The more difficult problem is how to predict the runoff from a year of rainfall on
an ungaged watershed. For yearly rainfall totals, rainfall depths for various return
periods can be determined from probabilistic and statistical methods. The 100-year wet
season, for example, represents the depth of annual rainfall total that would have a 1/100
chance of being exceeded in any given year. The rainfall total for a given year would
consist of many storms contributing to the annual total. These time-distributed storms
would result in many individual runoff hydrographs. It may be tempting to apply a shortterm rainfall-runoff method such as the Rational Method to the season’s total rainfall to
3
quickly calculate a yearly runoff volume. The validity of this approach is the subject of
this project.
This project investigates how well one method used for short-term predictions of
runoff predicts runoff from longer term, multiple storm event rainfall accumulation. In
particular, the original Soil Conservation Service (SCS) equation for runoff volume is
applied to a small, gaged watershed to determine whether the method underestimates,
matches, or overestimates measured yearly runoff volumes. This project could be
considered an exploratory exercise in volume-based hydrology (VBH) because it
considers runoff volume using the original volume-based form of the SCS equation.
Reese (2009) argues for a shift from peak flow-based hydrology to VBH because the rate
at which the volume of runoff moves through a watershed is the basis for flow-based
hydrology. Reese (2009) describes VBH as a means to address water scarcity, runoff
volume reduction , stormwater pollution reduction, erosion reduction and habit
protection, and flood control. The intent of this project is to perform a single calculation
of annual runoff using a single value of annual rainfall and storm event runoff
coefficients to test how well the calculated (theoretical) annual runoff volumes compare
to measured annual runoff volumes.
The scope of the project includes:
1.
Selecting a gaged watershed with historical flow data and nearby
annual rainfall data.
2.
Estimating runoff coefficients for the watershed based on land use, the
hydrologic condition, and the hydrologic soil type of the watershed.
4
3.
Calculating water year runoff volumes based upon the water year
rainfall totals using the estimated runoff coefficients
4.
Comparing the water year calculated runoff volumes to the actual
measured water year runoff volumes and determining the statistical
significance of the differences of the two samples.
5
Chapter 2
LITERATURE REVIEW
Early civilizations such as those along the Tigris and Euphates Rivers, the Nile
River, the Indus River in India, and the Huang-Ho River in China are evidence of early
civilization’s realization of the importance of water for survival (Biswas, 1970).
Evidence exists of man-made hydraulic structures dating back to 4,000 B.C. (Bedient, et
al., 2008). Early water supply, drainage, and containment structures were probably
designed by trial and error. If a supply channel did not supply enough water it was likely
enlarged over time until the capacity met the demand. Eventually engineering
philosophy evolved from simply reacting to natural events to trying to predict them.
Philosophy of controlling nature evolved into one of trying to understand nature. Rain
gages emerged at different times in different parts of the world with some of the earlier
recorded gages in India in the fourth century B.C. (Biswas, 1970). During the 1600’s, the
first documented quantitative hydrologists emerged. During this time the French
naturalist Pierre Perrault published “The Origin of Springs”, one of the first recorded
comparisons of rainfall and stream flow response based upon his observations of the
Seine River (Biswas, 1970).
Rational Method
In the mid-1800’s Irish engineers including Thomas Mulvaney investigated a relationship
between event-based rainfall and peak discharge that eventually evolved to become the
6
widely known Rational Method (Beven, 2001). The general form of the Rational Method
is:
Q p  kCIA
Eq. 1
where:
Qp
= peak flow rate in cubic feet (meters) per second
k
= conversion factor 1.008 (English) or 1/360 (metric)
C
= dimensionless runoff coefficient of the watershed
I
= rainfall intensity in units of inches (millimeters) per hour for a selected return
period and duration equal to the time of concentration tc
tc
= the time for rainfall in the most remote location of the watershed to appear as
runoff at the watershed outlet
A
= area of the watershed in units of acres (hectares)
The early form of this Rational Method equation was designed to predict peak flow and
was not intended to predict the entire runoff hydrograph. Reese (2006) describes the
Rational Method as a conveyance model designed for peak flow. This Rational Method
approach is likely the first recorded academic approach to estimating flood flow for the
purpose of sizing drainage conveyances (Biswas, 1970).
The Rational Method also has volumetric forms. An example in English units
taken from the Improvement Standards for San Joaquin County Department of Public
Works (San Joaquin County, 1997) is:
7
V
CAR
12
Eq. 2
where:
V
= volume of runoff in units of acre-feet
C
= representative runoff coefficient of the watershed
A
= area of the watershed in units of acres
R
= rainfall depth of the selected event in units of inches
The Rational Method is simplistic and is likely the most widely-used method to
design storm drain systems (Chow, et al., 1988). It is widely used by government
agencies and municipalities around the Central Valley in California. Many of these
agencies require use of the Rational Method or forms of it in the design of storm drainage
features unless the method faces limitations or other methods can be justified and
approved. One limit to the use of the Rational Method is watershed area. In large
watersheds, surface storage and hydrograph timing become an issue affecting the
accuracy of the Rational Method. Bedient et al. (2008) limit use of the Rational Method
to watershed surface areas of a few square miles. The San Joaquin County Hydrology
Manual limits the use of the Rational Method to watershed surface areas less than 640
acres (San Joaquin County, 1997). The Improvement Standards for San Joaquin County
Department of Public Works limit the use of the Rational Method to watersheds generally
less than 200 acres (San Joaquin County, 1997).
8
The Merced County Storm Drainage Design Manual (Merced County, undated)
no longer specifies use of the Rational Method but now specifies the Soil Conservation
Service (SCS) Method outlined in Technical Release 55 (TR-55) (NRCS, 1986). NRCS
is the acronym for the Natural Resources Conservation Service which was formerly the
SCS. Additionally, the Merced County Storm Drainage Design Manual states that “the
American Public Works Association recommends that the Rational Method be used for
drainage areas not exceeding 20 acres in size” (Merced County, undated). The focus of
this project is on areas larger than those recommended for the Rational Method.
Soil Conservation Service Method
In the mid 1900’s the SCS investigated methods for determining rainfall loses
within a watershed. Victor Mockus presented the SCS Method for estimating direct
runoff from storm rainfall in Chapter 10, Section 4, Hydrology, of the National
Engineering Handbook (SCS, 1972). Victor Mockus is one of the main developers of
the SCS Method and is the author of the above-referenced Chapter 10 of the National
Engineering Handbook. The SCS Method was originally designed to predict the volume
of runoff based upon daily rainfall (Reese, 2006).
In the following description of the SCS Method, the variable (Q) for actual runoff
potential, as presented by Victor Mockus (SCS, 1972), has been replaced with (Pe) to
avoid confusion with the industry’s use of the symbol Q as the peak flow or peak
discharge in units of volume per time.
9
The SCS assumes that the depth of runoff (Pe) is always less than the total depth
of storm rainfall (P) and that the depth of runoff being retained in the watershed (Fa) is
less than or equal to a maximum storage potential (S). Additionally, there is an amount
of water lost or abstracted (Ia) before ponding begins, so the total potential runoff is:
Pe  P  I a
Eq. 3
The general hypothesis is that the ratio of actual storage to storage potential is equal to
the ratio of actual runoff to runoff potential. The ratio equality is presented as:
Fa
Pe

S
P  Ia
Eq. 4
To balance mass:
P  Pe  I a  Fa
Eq. 5
Solving the Equation 5 for Fa, substituting Fa into Equation 4, and solving for Pe results in
the general form of the SCS equation:
Pe 
 P  I a 2
P  I a  S 
Eq. 6
Based upon experimental study watersheds, the initial abstraction Ia is 20 percent of the
potential for storage S or Ia =0.2S (Chow, et al., 1988). Substituting Ia = 0.2S into the
general equation results in:
Pe
2

P  0.2S 

P  0.8S 
Eq. 7
10
The SCS plotted Equation 7 for many watersheds to produce a range of curves that
empirically relate rainfall depth to runoff depth. These curves were then standardized
using a dimensionless curve numbering (CN) system where the CN would range from 0
to 100. A CN of 100 would represent completely impervious conditions. The
relationship between the storage potential S and the CN value is given by the relationship
below:
S
CN
 10
1000
Eq. 8
It should be noted that the CN curves developed by the SCS are dependent on the
assumption that the initial abstraction Ia is 0.2S. Reese (2006) states that the value of
0.2S may not be appropriate for all circumstances, and that varying Ia would require
developing an entirely new set of CN curves.
CN values take into consideration the land use, the hydrologic condition, and the
hydrologic soil type of the watershed (McCuen, 2005). The hydrologic soil types are
broken down into A, B, C, and D where A is the most permeable with the lowest runoff
potential and D is the least permeable with the highest runoff potential. Hydrologic soil
type B is less permeable than A, C is less permeable than B, and D is less permeable than
C. Soils classified as A likely consist of loose sandy soils whereas soils classified as D
likely consist of dense clay or rock. The SCS has tabulated CN values for various soil
types, land uses, and land conditions. Because watersheds usually consist of a mix of soil
types and land uses, a CN value representative of the entire watershed of interest is
usually estimated by the method of area-weighting to produce a composite CN value.
The area-weighting of CN values can be generalized as:
11
m
CN w 
 CN
i 1
 Ai
i
Eq. 9
m
A
i 1
i
where:
CN w
= weighted CN value of the entire watershed
m
= number of subareas of the watershed
CNi
= CN value of subarea i based upon its soil, land use, and land condition
Ai
= area of subarea i
The antecedent moisture content of a watershed’s soils also impacts the CN value.
The SCS lists three antecedent moisture conditions (AMC). The driest conditions is
AMC(I) and the wettest is AMC(III) with AMC(II) falling in between these two values.
The values for CN(I) (i.e. the CN associated with the driest AMC) and CN(III) were
empirically derived to fit the lower and upper thirds of the CN(II) curves, respectively
(SCS, 1972). From Chow et al. (1988), the applicable curve numbers can be calculated
from:
CN ( I ) 
4.2CN ( II )
10  0.058CN ( II )
Eq. 10
and
CN ( III ) 
23CN ( II )
10  0.13CN ( II )
Eq. 11
Mockus stated in an 1996 verbal interview with Victor Ponce of San Diego State
University, “that SCS developed the runoff curve number method for small basins, less
12
than 400 square miles” and that “the method was developed for events, but it was based
on daily data, because that was the only data available in large quantities” (Ponce, 1996).
Advantages of the SCS Method include the consideration of soil types, antecedent
moisture conditions, and initial abstraction. An apparent disadvantage of the SCS
Method is that the CN curves are based upon daily rainfall totals and the assumption that
Ia is 0.2S. Recently, the SCS Method has become more widely used because the
tabulated curve numbers ease the incorporation of soil and vegetation data sets in
Geographical Information Systems (GIS) for use in rainfall-runoff modeling (Beven,
2001). This is one of the major reasons it was selected for this project.
Hydrograph Methods
To predict rainfall-runoff response over time, storage and routing come into play.
A hydrograph consists of the runoff response with time on the x-axis and the volumetric
flow rate plotted on the y-axis for a particular point of interest in a watershed.
Components of a typical hydrograph include a rising limb, a crest, and a receding limb.
The crest of the hydrograph represents the peak volumetric flow rate of the storm event.
The area under the hydrograph represents the total volume of runoff generated from a
rain event. The shape of a hydrograph is dependent on the characteristics of the
watershed and the duration and intensity of the storm event (Bedient, et al., 2008).
Probably the first attempt at considering the effects of time and area were made by Ross
in 1921 (Beven, 2001). Ross considered a watershed to be divided up into zones with
each zone having a different travel time to the watershed’s outlet. The closest zone to the
13
outlet would produce runoff in the first time step; the next zone would contribute in two
time steps, and so on. The resulting histogram at the watershed outlet would represent
the time-area summation of these pulses considering the delays for each zone to
contribute its pulse. In 1932 Sherman considered the time delays of runoff as a time
distribution without considerations of individual areas. He then normalized the runoff
response into what he referred to as a “unitgraph” which we now call a unit hydrograph
(Beven, 2001). The unit hydrograph can be scaled up to represent different volumes of
effective rainfall runoff. The question of how much effective rainfall (the portion of total
rainfall that becomes actual runoff) to route still presented a problem. Effective rainfall
is influenced by such things as rainfall intensity and duration, soil types, land cover, and
antecedent moisture condition. In 1933 Robert Horton considered runoff generation as
occurring after the infiltration capacity of a soil is reached (Beven, 2001). Since that time
many other excess infiltration equations have been developed. The unit hydrograph and
an infiltration equation are the basic components of a hydrologic model. Because there
may likely be streamflow before a storm occurs, the consideration of baseflow becomes
important. It was found that effective rainfall is more closely related to gaged discharge
if the hydrograph is separated into baseflow and a storm runoff component (Beven,
2001). A variety of hydrograph methods have been developed including Snyder’s,
Clark’s, and the SCS unit hydrograph methods (Bedient, et al., 2008). Unit hydrograph
methods such as the SCS unit hydrograph, Snyder’s method, and the Clark’s method are
frequently used due to their accuracy and simplicity (Bedient, et al., 2008). The SCS
unit hydrograph utilizes Equation 7, described above, to determine the total depth/volume
14
of runoff under the hydrograph, but takes the concept of the SCS Method beyond just
depth or volume of runoff to evaluate total runoff over time. The SCS unit hydrograph
distributes the total runoff volume from Equation 7 over time by considering the peak
flow rate, the time it takes to reach a peak flow, and the time it takes for the peak flow to
recede.
Hydrograph methods were not considered in the current study because the focus
of the project is on the relationship of long-duration rainfall-runoff, and not on any single
storm event hydrograph. To utilize individual hydrographs, one would need to have all of
the individual hydrographs for the duration of interest. For ungaged watersheds this
would not be possible.
Long-Term Runoff Approaches by Others
Others have contemplated evaluating long-term runoff based upon the long-term
precipitation record. For example, in the paper “Modifications to the SCS-CN Method
for Long-Term Hydrologic Simulation” (Geetha et al., 2007), two modified SCS Methods
are considered for long-term, day-to-day, continuous simulation. These modified
methods allow for a daily estimation of runoff that can be summed to estimate yearly and
long-term runoff. The first allows for varying the CN between CN(I), CN(II), and
CN(III) based upon the cumulative rainfall over the previous five days. Prior to
estimating the current day’s runoff, the CN value is selected based upon predetermined,
discrete rainfall criteria. If the 5-day rainfall is below a lower threshold then CN(I) is
used, if it is greater than an upper threshold then CN(III) is used, and if it falls between
15
the upper and lower threshold then CN(II) is used. In the second method, daily CN
values are not allowed to vary directly by prior rainfall but by antecedent soil moisture.
The antecedent moisture amount is still based upon the previous five days of rainfall, but
available soil storage each day is tracked and utilized to directly estimate the CN value of
the current day allowing for more of a continuous estimating of CN as opposed to the
discrete method described above. The work of Geetha et al., (2007) describes the
successful application of these modified methods for predicting long-term runoff based
upon long-term rainfall given gaged information for model calibration. These methods
would not be applicable in a watershed where daily rainfall data is unavailable or for
statistical wet seasons, such as the 100-year wet season where the distribution of day-today rainfall would not be available.
In the manual, “Water Harvesting- A Manual for Design and Construction of
Water Harvesting Schemes for Plant Production”, Critchley et al., (1991) consider design
of water harvesting schemes to support annual crops. The authors of this document
discourage the use of runoff coefficients derived for watersheds from other geographical
areas. They also discourage using runoff coefficients derived from large watersheds for
small watersheds. Instead, they recommend that runoff coefficients be empirically
derived/back-calculated from measured rainfall and runoff in the project area. They
suggested that the runoff coefficient (K) be derived from:
K
Runoff (units of depth)
Rainfall (units of depth)
Eq. 12
16
Where runoff is a percentage (K) of rainfall for the rainstorm of interest as shown below:
Runoff  K x Rainfall
Eq. 13
They also state that not every rainfall event will produce runoff because threshold
rainfall, the amount of water stored in a watershed before runoff begins, must be
exceeded prior to runoff forming. Additionally, Critchley et al., (1991) describe
assessing annual or seasonal runoff coefficients. The annual or seasonal runoff
coefficient is estimated by:
K
Yearly (seasonal) Total Runoff (units of depth)
Yearly (seasonal) Total Rainfall (units of depth)
Eq. 14
Furthermore, the authors discuss the difference between annual runoff coefficients and
runoff coefficients derived from individual storms. According to Critchley, et al.:
“The annual (seasonal) runoff coefficient differs from the runoff coefficients
derived from individual storms as it takes into account also those rainfall events
which did not produce any runoff. The annual (seasonal) runoff coefficient is
therefore always smaller than the arithmetic mean of runoff coefficients derived
from individual runoff-producing storms.”
On the other hand, in the Stormwater Effects Handbook, Burton and Pitt, (2002)
state that small rain depths are associated with small volumetric runoff coefficients (Rv)
whereas larger rains produce larger Rv values. An average Rv value is assumed to
overestimate small rains and under-predict larger rains although the annual average may
be acceptable given that the rainfall data is representative of a complete set of annual
rain.
17
Chapter 3
METHODS AND ANALYSIS
The intent of this project is to investigate the potential difference between annual
calculated runoff volumes and annual measured runoff volumes. The project entails
selection of a small, gaged watershed, free of major dams and free of changes in land use
over the period of the data set in order to compare calculated and measured annual total
runoff volumes on a yearly basis. To make this comparison, annual runoff volumes are
compiled along with annual rainfall totals for the same time period. A single calculation
of annual runoff is performed based upon a single value of annual rainfall using CN
values from literature and back-calculated event CN values. Water year rainfall totals are
transformed into theoretical runoff depths using the SCS Method. These theoretical
runoff depths are then transformed into theoretical runoff volumes by multiplying by the
watershed area. The total measured runoff volume and the calculated runoff volume are
then compared on a yearly basis. Statistical analysis is used to determine if the two
samples, measured and calculated, are from the same population, and a visual evaluation
is made to see how the samples compare to one another. The two samples are considered
dependent because the values in each sample rely on the same input, i.e. the annual
rainfall. For this reason, the samples are treated as paired observations. The purpose of
pairing the observations is to reduce the experimental variance error (Walpole, et al.,
2007). The differences between the measured and calculated runoff for each year are
calculated to develop a confidence interval around the true mean of the sample
18
differences. As presented in Walpole (2007), the structure of the confidence interval is as
follows:
d t
,

2
sd
n
 d  d  t
,

2
sd
n
Eq. 15
where:
d
= sample mean of differences
sd
= standard deviation of differences
n
= number of observations in sample
d
= true mean of the population of differences
t/2,
= critical value from t-distribution

= n-1 degrees of freedom

= one minus the decimal confidence level
If zero is not contained in the confidence interval then the samples are statistically
different at the selected confidence level, where the confidence level is 1 – . If zero is
contained in the confidence interval then the samples are not statistically different at the
selected confidence interval.
As stated in the previous chapter, the Rational Method was not considered in the
current analysis due to the size of the selected watershed. Hydrograph methods were not
considered in the current analysis because they focus on relatively short–duration (event)
rainfall-runoff relationships and the water year consists of many hydrographs. Utilizing
hydrograph methods for long-term runoff estimations would require a watershed to have
19
daily and/or event rainfall data which is not always the case. Attempting to use
hydrograph methods for statistical return periods such as the 100-year wet season would
require that the distribution of event rainfall making up such a season be available.
The purpose of the current analysis was not to calibrate or accurately model a
particular watershed, but to use a gaged watershed to evaluate the SCS Method of
relating long-duration rainfall depth to long-duration runoff volume.
Description of the Study Area
The Black Creek watershed was selected for analysis in the current study. Black
Creek is located in the Sierra Nevada foothills approximately 35 miles east of Stockton,
California. Figure 1 depicts the general location of the Black Creek watershed. Black
Creek flows into Tulloch Reservoir on the Stanislaus River. Tulloch Reservoir is part of
the Tri-Dam Project that includes Beardsley Reservoir, Donnells Reservoir, and Tulloch
Reservoir. The Tri-Dam project supplies water to irrigation districts serving the nearby
areas of the San Joaquin Valley (Oakdale and South San Joaquin Irrigation Districts,
2010).
The Black Creek watershed was selected because it is relatively small in size, it is
not influenced by runoff related to melting of a snow pack, it does not contain any major
reservoirs, and due to its rural nature, its land use likely has not changed much over the
last 50 years. The Black Creek watershed also has a gaging station located near the
bridge on O’Byrnes Ferry Road in Calaveras County. The gaging station is operated by
20
the United States Geologic Survey (USGS) and collects both stream flow data and
rainfall data.
The watershed was delineated utilizing topography from four 7.5 minute USGS
Quadrangles entitled “Angels Camp”, “Copperopolis”, “New Melones Dam”, and “Salt
Springs Valley”. Figure 2 depicts the delineated watershed overlaid on the USGS
quadrangles and the location of the gaging station at the outlet of the watershed.
21
FIGURE 1. BLACK CREEK WATERSHED LOCATION MAP
22
FIGURE 2. BLACK CREEK WATERSHED MAP
23
The delineated watershed is approximately 14.36 square miles or 9,189 acres.
The land use consists of grasslands, sparse oak trees and grassland, dense stands of oaks
and other trees, and areas of brush. The topography varies from mild rolling hills to
steeper terrain. Figure 3 shows vegetation and land use of the watershed as depicted on
aerial photographs furnished on the Calaveras County website (Calaveras County, 2002).
The hydrologic soil type of the watershed is primarily C with a small percentage of D.
Figure 4 depicts the hydrologic soil types of the watershed. The hydrologic soil types of
the watershed are based upon the GIS coverage furnished on the Calaveras County
website (Calaveras County, 2003) and the Calaveras County Soil-Vegetation Handbook
(Stone and Irving, 1982).
Sources of the Data
The United States Geological Survey (USGS) gaging station on Black Creek was
the main source of hydrologic data. The USGS website provided approximately 26 years
of daily flow data for the station from August 24, 1982 to September 9, 2009 (USGS,
2009). Appendix A contains the daily flow data from the USGS.
24
FIGURE 3. BLACK CREEK LAND USE MAP
25
FIGURE 4. BLACK CREEK HYDROLOGIC SOILS MAP
26
Daily rainfall data was not available on the USGS website, but the California
Department of Water Resources (DWR) State Climatologist website provided 20 years of
annual rainfall totals for the New Melones Dam station from 1979 to 1999 (California
Department of Water Resources, 1999). The New Melones Dam station is located
approximately 5.5 miles to the east of the Black Creek station. Appendix B contains the
data from the State Climatologist.
DWR’s California Data Exchange Center (CDEC) website provided
approximately 12 years of hourly tipping bucket rainfall data from September 23, 1997 to
September 13, 2009 for the Black Creek station (California Department of Water
Resources, 2009). Additionally, the CDEC website provided approximately 12.5 years of
hourly flow data from March 7, 1997 to September 13, 2009 for this station (California
Department of Water Resources, 2009). Appendix C contains the hourly rainfall and
flow data from CDEC.
Hydrologic Data
The 16-year overlap between the USGS daily flow data and the State
Climatologist water year totals was selected for this study because it provided the largest
overlap of measured rainfall and measured stream flow. The New Melones Dam rainfall
data were geographically adjusted to the Black Creek Station using a ratio of annual
average rainfall from the GIS raster of annual average precipitation in California
produced by Daily and Taylor (1998). The GIS raster is an isohyetal map coverage of
27
average rainfall in California. Table 1 depicts the annual average precipitation taken
from the GIS raster at New Melones and at the Black Creek station. The geographic
adjustment factor is then calculated as the ratio of the average annual precipitation values
shown in Table 1.
Table 1 – Geographic Adjustment Factor
Station
Average Annual Rainfall
from GIS Raster (inches)
Black Creek
24.03
New Melones Dam
26.72
Adjustment Factor
0.8993
The New Melones rainfall data from the State Climatologist was then multiplied by
0.8993 (the calculated geographic adjustment factor) to adjust this data to the Black
Creek watershed. The daily flow data from the USGS was processed into water year
volumetric totals.
CN Weighting
An area- weighted CN value was calculated using hydrologic soils type and land
uses. The soil data and land use data were analyzed using GIS methods to determine the
acreages of soil and land use combinations. Table 2 provides the results from the GIS
analysis of the land use and soil type acreages for the Black Creek watershed. Appendix
D contains GIS polygon data used to generate Table 2.
28
Grass and Trees
Brush
Woods
Total
Table 2 – Land Use and Soil Type
Soil Type C
Soil Type D
Alluvial
(acres)
(acres)
(acres)
5,305.17
1,958.44
20.30
489.98
11.39
0.00
1,175.92
227.90
0.00
6,971.07
2,197.73
20.30
Total
(acres)
7,283.91
501.37
1,403.82
9,189.10
CN values for antecedent moisture condition II, CN(II), taken from Chow et al. (1988)
for the land use and soil types are shown in Table 3.
Table 3 – CN(II) Values (Chow et al., 1988)
Table 3 – CN Values
Soil Type C
Soil Type D
Land Use
Grass and Trees
Brush
Woods
74
70
70
80
77
77
Alluvial
98
98
98
The alluvial category is actually listed by Stone and Irving (1982) as an unclassified soil
type, described only as “higher alluvial terraces and plains”. It is assumed to be a
cemented alluvium for the purpose of this study. Table 4 depicts the calculations for the
weighted CN (CNw).
29
Complex
Grass C
Grass D
Grass
Alluvial
Brush C
Brush D
Woods C
Woods D
Total
Table 4 – CN Weighting
Area
Ai
(acres)
CNi
Ai*CNi
5305.17
74
392582.33
1958.44
80
156675.45
20.30
489.98
11.39
1175.92
227.90
9189.11
98
70
77
70
77
CNw
1989.49
34298.91
877.40
82314.56
17548.19
686286.33
74.68
The resulting area-weighted CN(II) is 74.68. The resulting area-weighted CN(I) and
CN(III) are 55.33 and 87.15, respectively based upon Equations 10 and 11.
Back-Calculated CN Values
It is possible that CN values from literature may not be representative of the
conditions in the watershed of interest. CN values from literature do not directly account
for AMCs between AMC(I) and AMC(II) or between AMC(II) and AMC(III) or
conditions dryer than AMC (I) and wetter than AMC(III). Additionally, CN values from
literature may not be representative of the exact soil types and land use within the
watershed of interest. Back-calculated CN values inherently represent the antecedent
moisture conditions, the land use, and soils of the watershed at the time of the actual
storm event under consideration. For this reason, the hourly rainfall and stream flow data
from CDEC for the Black Creek station were used to back-calculate CN values for
30
selected storms between 1997 and 2001. Additionally, CN weighting is the common
method for watersheds without rainfall and flow data, so the back-calculated values
provide for a check of the reasonableness of the CN values from literature.
Each month of hourly rainfall and runoff data was reviewed and some of the
isolated storms that produced runoff were selected for analysis. Rainfall and runoff
events that merged together were for the most part not selected for analysis. Multiple
back-to-back storms that created problems in separating one storm from the other and
problems separating their baseflows were avoided. Additionally, if there were data
missing during the storm, the storm was not selected unless the break in missing data was
generally on the order of three hours or less. In the case where there was an hour or two
of flow data missing, the missing data was interpolated for use in the analysis. A total of
38 runoff-producing storms were selected. It should be noted that an attempt was made to
select storms from all months of the wet season. With this in mind, the selected storms
are still not likely to be representative of the entire data record. Figure 5 depicts the
January 25, 2001 storm which provides an example hyetograph and hydrograph of a
evaluated storm. The hydrograph shows the flow rate in cubic feet per second on the y–
axis and the date and time on the x-axis. Additionally, the hyetograph shows incremental
hourly rainfall in inches depicted on the secondary y-axis. Appendix E contains the
hydrographs and hyetographs of the 38 storms selected for use in this study.
The direct runoff volume was estimated by first removing base flow using the
constant discharge or straight line method as presented in Chow, et. al, (1988). The area
under the hydrograph was estimated by dividing the hydrograph into trapezoids and then
31
summing the areas of the trapezoids to calculate with the total volume using Equation 17
as presented in Bedient, et al., (2008).
V   Q dt
Eq. 16
where:
V
= volume of direct runoff (acre-inches in this study)
dt
= time step (one hour in this study)
Q
= average flow rate over the time step (cfs converted to acre-inches per hour in
this study)
32
FIGURE 5. BLACK CREEK HYDROGRAPH EXAMPLE – JANUARY 25, 2001
STORM
33
The resulting direct runoff volume of the storm in acre-inches was then converted into
depth of excess precipitation Pe by dividing by the acreage of the watershed. Pe and the
total measured precipitation P for the event were then used in the general form of the SCS
equation with the assumption that Ia is 0.2S. The general form of the SCS Method
equation is presented again below,
Pe 
P  0.2S 2
P  0.8S 
Eq. 7
Equation 7 was then solved for S. Then the CN value for the storm was back calculated
from:
S
CN
 10
1000
Eq. 8
Rearranging Equation 8 for CN results in:
CN  1000 ( S  10)
Eq. 17
A dot plot graph showing the resulting CNs for the 38 selected storms is presented in
Figure 6. Figure 6 also shows the CN(I), CN(II), and CN(III) from the CN weighting to
allow the reader to compare them to the back-calculated CN values. Table 5 provides a
summary of the selected storms and the back-calculated CN values.
34
FIGURE 6. DOT PLOT OF CN VALUES OF SELECTED STORMS FROM 1997 TO
2001
35
Table 5 – Back-Calculated CN Values of Selected Storms
Storm Date
12/12/1997
4/23/1998
5/2/1998
5/4/1998
5/16/1998
5/28/1998
10/24/1998
11/23/1998
12/3/1998
12/5/1998
12/13/1998
12/20/1998
1/31/1999
2/6/1999
2/20/1999
2/25/1999
3/3/1999
3/8/1999
3/30/1999
4/5/1999
5/2/1999
11/19/1999
4/16/2000
5/6/2000
5/14/2000
10/26/2000
1/8/2001
1/23/2001
1/25/2001
2/9/2001
2/19/2001
4/6/2001
4/18/2001
11/24/2001
11/28/2001
12/14/2001
12/20/2001
12/30/2001
Minimum
Average
Maximum
Rainfall P
(inches)
0.35
1.12
0.80
0.92
0.48
1.20
0.40
0.28
0.52
0.20
0.24
0.12
0.72
4.48
1.12
0.24
0.60
0.48
0.44
1.56
0.52
0.68
1.60
0.80
2.00
1.28
0.48
0.96
0.52
1.64
1.28
0.96
1.08
0.76
0.52
0.48
1.08
0.68
Runoff Pe
(inches)
0.0049
0.0617
0.0409
0.0610
0.0288
0.0475
0.0016
0.0021
0.0079
0.0015
0.0035
0.0019
0.1647
3.8183
0.5213
0.0187
0.0893
0.0378
0.0118
0.2505
0.0093
0.0051
0.0480
0.0091
0.0690
0.0052
0.0044
0.0118
0.0277
0.2842
0.4940
0.0133
0.0292
0.0021
0.0031
0.0052
0.0882
0.3263
CN
88.25
75.68
81.01
80.05
88.17
72.66
85.24
89.67
83.62
92.38
91.65
95.7
90.42
94.21
92.55
82.25
60.14
69.78
76.16
77.64
83.96
78.17
65.17
76.15
60.68
64.37
83.83
72.9
86.91
77.54
89.53
73.2
73.07
74.75
82.1
84.1
78.6
95.53
60.14
80.73
95.70
36
The maximum back-calculated CN value from the selected storms is 95.70 and
occurred in December of 1998. The minimum back-calculated CN value is 60.14 and
occurred in March of 1999. The average back-calculated CN value from the 38 storms is
80.73. This range of back-calculated CN values nearly encompass the range of
antecedent moisture condition CNs from CN(I) (55.33) to CN(III) (87.15) described in
the CN Weighting section and shown on Figure 6. Due to their empirical nature, the
back-calculated CN values inherently reflect the actual moisture, soil, and land use
conditions of the watershed that occurred during the selected storm. The back-calculated
values are generally in agreement with the CN values from literature.
Comparison of Calculated and Measured Runoff Volumes
Water year measured flow volumes from 1983 to 1999 were generated from
average daily flow rates in cubic feet per second recorded at the USGS Black Creek
station. Theoretical water year flow volumes were then calculated from the State
Climatologist annual rainfall totals (P) using the weighted and back-calculated CN values
in Equations 7 and 8. Four cases comparing the calculated and measured runoff volumes
were investigated. Case 1 uses the area-weighted CN(II) based upon Chow et al. (1988);
Case 2 is the minimum back-calculated CN; Case 3 is the average back-calculated CN;
and Case 4 is the maximum back-calculated CN. Averages for the calculated and
measured annual runoff volumes were then calculated over the 16 years of data for each
of the cases investigated. Table 6 presents a summary of the average calculated and
average measured runoff volumes rounded to the nearest 5 acre-feet (ac-ft) for the 16
37
water years evaluated. Table 6 also shows the percent difference between the average
calculated and average measured runoff volumes. Detailed calculations of the data
presented in Table 6 can be found in Appendix F.
Table 6 – Summary of Average Measured and Calculated Runoff Volumes
Case
Description
CN Value
Average
Average
Percent
Measured
Calculated
Difference
Runoff (ac-ft) Runoff (acft)
1
2
3
4
Weighted
Min BackCalculated
Avg BackCalculated
Max BackCalculated
74.68
7,505
15,344
104
60.14
7,505
13,290
77
80.73
7,505
16,080
114
95.70
7,505
17,670
135
Figures 7 is a plot of measured runoff versus the calculated runoff for each year analyzed
and for each of the four cases. This plot also shows the equality line y = x between
calculated and measured runoff. In every case, the calculated runoff exceeds the equality
line including Case 2, the lowest CN value considered in the four cases.
38
Figure 7. MEASURED RUNOFF VERSUS CALCULATED RUNOFF
39
All of the cases analyzed exceeded the measure runoff indicating that the CN values were
too high. Consequently, the Excel Solver function was used to find the CN value that
would minimize the sum of the residuals squared as defined by Equation 19.
r
n
2
2
  Vci  Vmi 
Eq. 18
i 1
where:
r
= the residual Vci - Vmi
n
= number of residual (16 years in this study)
Vci
= calculated volume of runoff from year i
Vmi
= measured volume of runoff from year i
The calculated CN value from the Excel Solver minimization is 31.52 which is
significantly less than the values used in the four cases analyzed. Figure 8 is a plot of
measured runoff versus the calculated runoff using the calculated CN value. Figure 8
illustrates a much better correlation between measured and calculated annual runoff than
those shown in Figure 7. Appendix F contains the calculation table for the calculated CN
of 31.52.
40
Figure 8. MEASURED RUNOFF VERSUS CALCULATED RUNOFF CN = 31.52
41
Chapter 4
DISCUSSION OF RESULTS
This chapter contains a comparison of the back-calculated CNs to CNs from
literature as well as a discussion of the results of comparing measured annual runoff to
calculated runoff using the SCS Method.
Recall that CN(I) represents the drier range of AMC and that CN(III) represents
the wetter AMC with CN(II) falling in between. Referring back to Figure 6, the backcalculated CNs for the most part span the range of the area-weighted CNs calculated from
literature sources. The back-calculated values seem to extend a little higher than the
CN(III) in the wetter months (November, December, January, and February). The CN(II)
value seems to fall midway between the back-calculated data especially for the months of
May and October. All the back-calculated CNs exceed the CN(I) value. No runoffproducing storms during the drier summer months (June through September) were
included in the selection of the 38 storms used in the back-calculations so it is not
possible to make a sound comparison of CNs for the drier months. It should be expected
that the range of back-calculated values would encompass the full range of weighted CNs
because the CN(I) and CN(III) values were empirically derived by the SCS to fit the
lower and upper thirds of the CN(II) curves (SCS, 1972). So extreme AMC values
should produce actual or back-calculated CN values that fluctuate beyond the SCScalculated range from CN(I) to CN(III). Again, it is not possible in this study to make a
42
conclusion about CN(I) during the summer months because no runoff-producing storms
were found in the data set utilized.
Prior to initiating this study, there was an expectation that the calculated runoff
would exceed the measured runoff. Referring to Figure 7, the calculated runoff volumes
did exceed the measured runoff volumes for the 16 years of data and for all four cases
analyzed. For the 16 water years of data, the difference between theoretical and
measured runoff was statistically significant at the 99.99 percent level for all four cases
analyzed. Table 7 summarizes the statistical analysis performed including the lower
limits (LL) and upper limits (UL) of the confidence level intervals rounded to the nearest
one acre-foot. Note that zero is not contained in any of the confidence intervals
indicating that the population means are different at the indicated significance level.
Case
1
2
3
4
Table 7 - Summary of Statistics and Confidence Intervals
n n-1
t/2
Description
Statistical

LL
Significance
(ac-ft)
Level
Weighted
Min BackCalculated
Avg BackCalculated
Max BackCalculated
UL
(ac-ft)
0.9999
0.9999
0.0001
0.0001
16
16
15
15
5.239
5.239
3,090
1,225
12,587
10,345
0.9999
0.0001
16
15
5.239
3,782
13,367
0.9999
0.0001
16
15
5.239
5,323
15,006
Of considerable interest is the best-fit calculated CN of 31.52. This value is considerably
less than the back-calculated CNs based on storm events and the CNs from the literature.
Recall that the tabulated CNs developed by the SCS are based upon daily rainfall.
Likewise, the back-calculated CN values represent event rainfall. The lower CN value of
43
31.52, based on annual runoff appears to be an example of the smaller “annual” runoff
coefficient described in Critchley et al. (1991).
In the four cases analyzed the calculated runoff volume exceeds the measured
runoff volume. This finding could have design and cost implications if event-based CNs
are used for storm water containment structures that have annual runoff or long-term
runoff design criteria Use of event-based runoff coefficients for design of long-duration
containment systems could lead to conservatively over sizing the system. However, over
sizing the system would inherently lead to additional construction and land costs beyond
that required to capture the actual runoff volume. Additionally, the overestimation, if
used to fine long-duration dischargers could lead to fines in excess of that “earned” for
the volume actually discharged.
Probably the biggest reason for the overestimation of calculated runoff is due to
using CN values which were originally generated from daily and event rainfall in a
calculation based on annual rainfall. The basic form of the SCS equation is blind to the
rainfall distribution in time and only considers total runoff depth or volume based upon
total rainfall. Depending on the size and duration of the storm event and the antecedent
moisture conditions not all recorded rainfall events may lead to runoff even though they
are included in the cumulative rainfall total. Additionally as mentioned in Reese (2009),
the assumption that Ia equals 0.2S may not be correct for the circumstances including
those of the Black Creek watershed. A higher value of Ia might assist in reducing
calculated runoff down towards equality with the measured runoff but would require
developing a new set of CN curves. It may be better to develop annual runoff
44
coefficients or to evaluate annual runoff volume by summing individual storm event
volumes if storm event data is available in the watershed of interest. In many cases,
storm event data is not available. Critchley et al. (1991) discusses generating annual
runoff coefficients because they take into account those rainfall events that do not
produce runoff. For example, a watershed may receive ten isolated 0.1 inch rainfall
events of which none result in runoff. In the annual data set, this would be one inch of
rain that likely would not have contributed to the runoff total even though it would be
included in the calculation for the annual runoff. For this reason, the annual CN values
would be expected to be smaller than the event-based CN values. The CN value of 31.52
calculated in this study indeed fits with this expectation and seems to collaborate with
Critchley et al. (1991).
45
Chapter 5
CONCLUSIONS
The purpose of this project was to evaluate the ability of the SCS Method, using
CN values generated from daily and storm event data, to estimate annual storm water
runoff based on annual accumulated rainfall. Sixteen years of gaged annual runoff
volumes were compared to calculated runoff. Four cases were analyzed in this study
which included an area-weighted CN assuming AMC(II), and minimum, average, and
maximum CN values back-calculated from 38 actual storm events in the Black Creek
watershed.
The results of this study indicate that the SCS Method utilizing CN values from
the literature and CN values back-calculated from storm events overestimate the annual
runoff at the 99.99 percent significance level for all four cases. Average values of
calculated runoff were 77 to 135 percent larger than the average measured runoff
volumes. A CN value of 31.52 was calculated from the 16 years of data. This may
represent an “annual” CN value for calculating annual runoff. A relationship between
annual and event CN values can not be made from this study because the CN value of
31.52 only represents a single data point. This could present an opportunity for future
work.
Future work could include the development of “annual” CN values by conducting
similar analyses on many other watersheds of varying characteristics. It may be possible
to develop a relationship between the “daily” CN values from literature for use in
46
generating “annual” CN values. Other future work could include developing “annual”
Rational Method C values using a methodology similar to the one presented here.
The results of this study could serve as a warning for those considering using
event-based or daily-based calculations and runoff coefficients for estimating longduration runoff from long-duration rainfall totals. The results of this study could be
incentive to the hydrologic industry to investigate and develop better volume-based
hydrologic methods to estimate long-duration runoff volumes.
The results of this study are based upon the assumptions provided herein
and a limited number of data collected by others. They are applicable to only the Black
Creek watershed as delineated in this study. Changes to the land use of the watershed
will likely change these results. Watersheds of differing sizes, terrains, soil types, land
uses, and storm patterns will likely produce different results.
47
APPENDICES ON CD
48
APPENDIX F
Calculations of Differences between Calculated and Measured Water Year Runoff
9717.32
4323.99
14229.24
1538.06
234.33
1284.79
596.61
2411.72
4397.97
10933.35
584.83
14791.97
9912.44
16277.32
20738.86
8107.68
7505.03
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Average
Percent Greater
Std. Deviation
n

Confindence Interval

t/2
LL
UL
Water Year
Measured
Runoff Volume
Vm
(ac-ft)
12.69
5.65
18.58
2.01
0.31
1.68
0.78
3.15
5.74
14.28
0.76
19.32
12.94
21.26
27.08
10.59
24.06
21.08
32
14.14
13.67
18.48
17.75
17.6
14.33
40.37
17.84
47.58
31.4
32.09
52.75
24.8
Measured Rainfall
Depth
P
(in)
Case 1 CN = 74.68
Measured
Runoff Depth
Pe
(in)
21.64
18.96
28.78
12.72
12.29
16.62
15.96
15.83
12.89
36.31
16.04
42.79
28.24
28.86
47.44
22.30
Geographically
Adjusted Rain
0.8993*P
(in)
Weighted
18.04
15.42
25.07
9.39
8.99
13.15
12.51
12.38
9.56
32.53
12.59
38.97
24.54
25.15
43.60
18.69
Calculated
Runoff Depth
Pet
(in)
15343.72
104%
13815.30
11807.78
19201.35
7192.75
6885.15
10066.38
9579.66
9479.79
7317.35
24911.57
9639.60
29844.71
18793.02
19262.61
33387.19
14315.30
Calculated
Runoff Volume
Vc
(ac-ft)
3625.45
16
15
0.9999
0.0001
5.2391
3,090
12,587
7838.69
4097.98
7483.79
4972.11
5654.69
6650.82
8781.58
8983.05
7068.06
2919.38
13978.22
9054.78
15052.74
8880.59
2985.30
12648.33
6207.62
Volume
Difference
Vc - Vm
(ac-ft)
49
9717.32
4323.99
14229.24
1538.06
234.33
1284.79
596.61
2411.72
4397.97
10933.35
584.83
14791.97
9912.44
16277.32
20738.86
8107.68
7505.03
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Average
Percent Greater
Std. Deviation
n

Confindence Interval

t/2
LL
UL
Water Year
Measured
Runoff Volume
Vm
(ac-ft)
12.69
5.65
18.58
2.01
0.31
1.68
0.78
3.15
5.74
14.28
0.76
19.32
12.94
21.26
27.08
10.59
24.06
21.08
32
14.14
13.67
18.48
17.75
17.6
14.33
40.37
17.84
47.58
31.4
32.09
52.75
24.8
Measured Rainfall
Depth
P
(in)
Case 2 CN = 60.14
Measured
Runoff Depth
Pe
(in)
21.64
18.96
28.78
12.72
12.29
16.62
15.96
15.83
12.89
36.31
16.04
42.79
28.24
28.86
47.44
22.30
Geographically
Adjusted Rain
0.8993*P
(in)
15.31
12.82
22.11
7.20
6.84
10.67
10.08
9.95
7.35
29.41
10.15
35.75
21.60
22.19
40.32
15.94
Calculated
Runoff Depth
Pet
(in)
Minimum Back-Calculated
13289.91
77%
11727.57
9813.28
16933.97
5514.21
5235.38
8170.64
7715.28
7622.08
5627.52
22519.55
7771.27
27375.84
16536.65
16993.61
30874.59
12207.08
Calculated
Runoff Volume
Vc
(ac-ft)
3481.31
16
15
0.9999
0.0001
5.2391
1,225
10,345
5784.88
2010.24
5489.29
2704.72
3976.15
5001.05
6885.84
7118.68
5210.36
1229.55
11586.20
7186.44
12583.86
6624.21
716.29
10135.73
4099.40
Volume
Difference
Vc - Vm
(ac-ft)
50
9717.32
4323.99
14229.24
1538.06
234.33
1284.79
596.61
2411.72
4397.97
10933.35
584.83
14791.97
9912.44
16277.32
20738.86
8107.68
7505.03
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Average
Percent Greater
Std. Deviation
n

Confindence Interval

t/2
LL
UL
Water Year
Measured
Runoff Volume
Vm
(ac-ft)
12.69
5.65
18.58
2.01
0.31
1.68
0.78
3.15
5.74
14.28
0.76
19.32
12.94
21.26
27.08
10.59
24.06
21.08
32
14.14
13.67
18.48
17.75
17.6
14.33
40.37
17.84
47.58
31.4
32.09
52.75
24.8
Measured Rainfall
Depth
P
(in)
Case 3 CN = 80.73
Measured
Runoff Depth
Pe
(in)
21.64
18.96
28.78
12.72
12.29
16.62
15.96
15.83
12.89
36.31
16.04
42.79
28.24
28.86
47.44
22.30
Geographically
Adjusted Rain
0.8993*P
(in)
19.02
16.37
26.10
10.24
9.83
14.06
13.42
13.28
10.41
33.59
13.50
40.05
25.56
26.18
44.69
19.67
Calculated
Runoff Depth
Pet
(in)
Average Back-Calculated
16079.80
114%
14561.21
12532.78
19986.12
7842.65
7527.85
10768.63
10274.55
10173.11
7970.05
25722.26
10335.43
30670.99
19575.46
20047.72
34222.20
15065.73
Calculated
Runoff Volume
Vc
(ac-ft)
3659.19
16
15
0.9999
0.0001
5.2391
3,782
13,367
8574.77
4843.89
8208.79
5756.87
6304.59
7293.53
9483.84
9677.94
7761.39
3572.08
14788.91
9750.60
15879.02
9663.03
3770.41
13483.35
6958.06
Volume
Difference
Vc - Vm
(ac-ft)
51
9717.32
4323.99
14229.24
1538.06
234.33
1284.79
596.61
2411.72
4397.97
10933.35
584.83
14791.97
9912.44
16277.32
20738.86
8107.68
7505.03
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Average
Percent Greater
Std. Deviation
n

Confindence Interval

t/2
LL
UL
Water Year
Measured
Runoff Volume
Vm
(ac-ft)
12.69
5.65
18.58
2.01
0.31
1.68
0.78
3.15
5.74
14.28
0.76
19.32
12.94
21.26
27.08
10.59
24.06
21.08
32
14.14
13.67
18.48
17.75
17.6
14.33
40.37
17.84
47.58
31.4
32.09
52.75
24.8
Measured Rainfall
Depth
P
(in)
Case 4 CN = 95.70
Measured
Runoff Depth
Pe
(in)
21.64
18.96
28.78
12.72
12.29
16.62
15.96
15.83
12.89
36.31
16.04
42.79
28.24
28.86
47.44
22.30
Geographically
Adjusted Rain
0.8993*P
(in)
21.11
18.43
28.25
12.19
11.77
16.09
15.44
15.30
12.36
35.77
15.52
42.26
27.71
28.33
46.90
21.77
Calculated
Runoff Depth
Pet
(in)
Maximum Back-Calculated
17669.69
135%
16163.48
14112.23
21629.78
9336.69
9013.42
12322.79
11820.43
11717.21
9467.39
27392.83
11882.37
32357.49
21216.68
21691.74
35917.55
16672.89
Calculated
Runoff Volume
Vc
(ac-ft)
3696.44
16
15
0.9999
0.0001
5.2391
5,323
15,006
10164.66
6446.16
9788.24
7400.53
7798.63
8779.09
11038.00
11223.82
9305.49
5069.42
16459.48
11297.54
17565.52
11304.24
5414.43
15178.70
8565.21
Volume
Difference
Vc - Vm
(ac-ft)
52
Sum
Average
Percent Greater
Std. Deviation
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Water Year
7505.03
12.69
5.65
18.58
2.01
0.31
1.68
0.78
3.15
5.74
14.28
0.76
19.32
12.94
21.26
27.08
10.59
Pe
(in)
Vm
(ac-ft)
9717.32
4323.99
14229.24
1538.06
234.33
1284.79
596.61
2411.72
4397.97
10933.35
584.83
14791.97
9912.44
16277.32
20738.86
8107.68
Measured
Runoff Depth
Measured
Runoff Volume
24.06
21.08
32
14.14
13.67
18.48
17.75
17.6
14.33
40.37
17.84
47.58
31.4
32.09
52.75
24.8
P
(in)
21.64
18.96
28.78
12.72
12.29
16.62
15.96
15.83
12.89
36.31
16.04
42.79
28.24
28.86
47.44
22.30
0.8993*P
(in)
Geographically
Adjusted Rain
Calculated CN = 31.52
Measured Rainfall
Depth
7.66
5.88
12.93
2.33
2.13
4.43
4.05
3.97
2.41
19.03
4.10
24.57
12.52
13.00
28.65
8.13
Pet
(in)
7455.58
-1%
5869.44
4500.31
9904.64
1783.38
1630.75
3393.73
3100.29
3041.02
1846.44
14571.06
3136.02
18810.97
9584.05
9952.92
21940.57
6223.73
Vc
(ac-ft)
Calculated
Calculated
Runoff Depth Runoff Volume
2990.27
-49.45
-3847.88
176.32
-4324.60
245.31
1396.42
2108.94
2503.68
629.30
-2551.54
3637.72
2551.20
4018.99
-328.39
-6324.40
1201.72
-1883.95
r = Vc - Vm
(ac-ft)
Volume
Difference
134165130.53
14806209.62
31088.64
18702164.80
60179.20
1949987.54
4447623.54
6268417.84
396012.39
6510332.01
13232974.75
6508602.40
16152304.96
107838.89
39997997.65
1444126.17
3549270.11
r2
53
54
REFERENCES
Beven, K. J., (2001). Rainfall-Runoff Modeling. England: John Wiley & Sons Ltd
Bedient, P. B., Huber, W. C., & Vieux, B.E. (2008). Hydrology and Floodplain Analysis.
New Jersey: Prentice-Hall, Inc.
Biswas, A. K., (1970). History of Hydrology. Amsterdam: North-Holland Publishing
Company
Burton, G. A., & Pitt, R.E. (2002). Stormwater Effects Handbook. New York: Lewis
Publishers
Calaveras County (2002). Aerial Photos. Accessed 25 July 2010 at Calaveras County
website:
ftp://ccwgov.co.calaveras.ca.us/GIS/Raster_Data/Aerial_Photos/2002_2ft_Color_
DOI/JPEG_Format/
Calaveras County (2003), Calaveras County GIS Coverage of Soil Types. Accessed 25 July
2010 at Calaveras County website:
ftp://ccwgov.co.calaveras.ca.us/GIS/Vector_Data/_ZippedShapeFiles/Soil_Types.
zip
California Department of Water Resources. State Climatologist. (1999) New Melones
Rainfall Data Station Number B30 6270 00. Accessed 25 July 2010 at DWR
website:
http://www.water.ca.gov/floodmgmt/hafoo/csc/climate_data/#
California Department of Water Resources. California Data Exchange Center. (2009). Black
Creek Hourly Flow and Precipitation Data Station BCC. Accessed 25 July 2010
at DWR website:
http://cdec.water.ca.gov/cgiprogs/selectQuery?station_id=bcc&sensor_num=&dur_code=D&start_date=&en
d_date=now
California Regional Water Quality Control Board – Central Valley Region. (2009).
Administrative Civil Liability Complaint R5-2009-0541 in the Matter of Madera
County Resource Management Agency. Accessed 16 July 2010 at website:
http://www.swrcb.ca.gov/rwqcb5/board_decisions/tentative_orders/madera_co_r
ma/r5-2009-0541_enf.pdf
55
Chow, V. T., Maidment, D. R., & Mays, L.W. (1988). Applied Hydrology. New York:
McGraw-Hill, Inc.
Critchley, W., Siegert, K., & Chapman, C. (1991). Water Harvesting – A Manual for the
Design and Construction of Water Harvesting Schemes for Plant Production.
Natural Resources Management and Environmental Department – Food and
Agriculture Organization of the United Nations. Accessed 25 July 2010 at
website:
http://www.fao.org/docrep/U3160E/u3160e05.htm#TopOfPage
Daily, C. & Taylor, G. (1998). GIS Raster of California Average Annual Precipitation
1961 to 1990. Oregon: Water and Climate Center of Natural Resources
Conservation Service.
Geetha, K., Mishra, S. K., Eldho, T. I., Rastogi, A. K., & Pandey, R. P. (2007). Modifications
to SCS-CN Method for Long-Term Hydrologic Simulation. Journal of Irrigation
and Drainage Engineering. ASCE. Vol. 133, Issue 5.
McCuen, R. H. (2005). Hydrologic Analysis and Design. Upper Saddle River NJ: Pearson
Prentice Hall.
Merced County. (undated). Storm Drainage Design Manual. Department of Public Works.
Natural Resources Conservation Service (1986). Urban Hydrology for Small Watersheds.
Technical Release No. 55. Second Edition. U.S. Department of Agriculture,
Washington D.C.
Oakdale and South San Joaquin Irrigation Districts (2010). The Tri-Dam Project. Accessed
25 July 2010 at website:
http://www.tridamproject.com/
Ponce, V.M. (1996). Notes of My Conversation with Vic Mockus. Accessed 25 July 2010 at
the San Diego State University website:
http://mockus.sdsu.edu/
Reese, A.J. (2006). Voodoo Hydrology. Stormwater – The Journal for Surface Water Quality.
July-August Issue. Accessed 03 August 2010 at website:
http://www.stormh2o.com/july-august-2006/urban-hydrology-methods.aspx
Reese, A.J. (2009). Volume-Based Hydrology. Stormwater – The Journal for Surface Water
Quality. September Issue. Accessed 03 August 2010 at website:
http://www.stormh2o.com/september-2009/volume-based-hydrology.aspx
San Joaquin County. (1997). Hydrology Manual.. Department of Public Works.
56
San Joaquin County. (1997). Improvement Standards. Department of Public Works.
Soil Conservation Service (1972). National Engineering Handbook. Section 4. Hydrology.
U.S. Department of Agriculture, Washington D.C.: U.S. Government Printing
Office
Stone, C. O., & Irving, D. M. (1982). Calaveras County Soil-Vegetation Handbook. San
Andreas, CA: Calaveras County Farm Advisor’s Office
United States Environmental Protection Agency (1987). Water Quality Act of 1987.
Accessed 25 July 2010 at website:
http://www.epa.gov/npdes/pubs/cwatxt.txt
United States Geological Survey (2009). Black Creek Mean Daily Discharge USGS Station
11299600. Accessed 25 July 2010 at USGS website:
http://waterdata.usgs.gov/nwis/dv?cb_00060=on&format=rdb&begin_date=190001-05&end_date=2010-01-05&site_no=11299600&referred_module=sw
United States Geological Survey. (1962). Angels Camp, Calif. Quadrangle. Photo-inspected
1973
United States Geological Survey. (1962). Copperopolis, Calif. Quadrangle. Photo-revised
1987
United States Geological Survey. (1962). New Melones, Calif. Quadrangle. Photo-revised
1987
United States Geological Survey. (1962). Salt Springs Valley, Calif. Quadrangle.
Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2007). Probability & Statistics for
Engineers & Scientists. Upper Saddle River NJ: Pearson Prentice Hall.