Chapter 3
Operational Hydrologic Model Validation and INFORM
Ensemble Inflow Forecasts
3.1
INTRODUCTION
We now turn our attention to the land surface hydrology components of
INFORM. In this area, the objective of our work is two fold: (a) to validate and, if
necessary, refine operational hydrologic forecasts of reservoir inflow, and (b) to develop,
implement and test the stand alone hydrologic model that will be used by INFORM for
the intercomparisons of the existing management procedures with the INFORM
integrated forecast-management procedures. As such, this chapter focuses on the
operational hydrologic simulations pertaining to the snow accumulation and ablation
model, Sacramento soil water accounting model, and channel routing procedures, their
validation with historical data for the drainage areas of Folsom and Oroville reservoirs,
the development of a stand-alone semi-distributed hydrologic system applicable to the
upstream areas of the major Sierra Nevada reservoirs, the validation of the model with
data from the Folsom drainage basin, and the use of this stand alone model to produce
ensemble streamflow predictions. Appendix C presents an exhaustive listing of all
available hydrometeorological data collected for the development of the INFORM project
database.
3.2
MODEL DESCRIPTION
The hydrologic model objective for each basin is to represent the basin physical
processes that are driven by atmospheric forcing (e.g., precipitation, temperature) and
basin physical characteristics (topography, land cover), and to generate a streamflow
hydrograph at the basin outlet. The National Weather Service River Forecast System
(NWSRFS) that facilitates operations at the California Nevada River Forecast Center
(CNRFC) contains a variety of hydrologic models and procedures for operational
Chapter 3
3-1
forecasting. The hydrologic model component of the NWSRFS of interest in this work is
a continuous-time simulation model with model states (e.g., snow mass and energy
properties and soil properties) computed at each time step on the basis of initial
conditions and new input. The model consists of three major components: snow
accumulation and ablation (SNOW-17); basin rainfall-runoff model (Sacramento Soil
Moisture Accounting (SAC-SMA)); and unit-hydrograph/channel routing procedures.
A short description of the model components follows.
3.2.1
Snow Model
The snow model used is the NWS Hydro -17. For a detailed description the
interested reader is referred to NOAA Technical Memorandum NWS HYDRO-17
(Anderson 1973) and NOAA Technical Report NWS 19 (Anderson 1976). This model is
constructed to account for the energy and mass balance in the snow pack. The snow
model was developed to run in conjunction with a rainfall-runoff model. The model
states are the energy deficit in the snow pack, an antecedent temperature index that
approximates snow pack temperature, the liquid water equivalent of the snow pack, and
the volume of the liquid water of the snow pack. Energy balance is represented as heat
deficit which is used to refreeze available liquid water in the snow pack. The model
requires input data in the form of Mean Areal Temperature (MAT) and Mean Areal
Precipitation (MAP). The MAT is used as an index to energy exchange across the snowair interface. It is used to compute snow melt heat exchange and to determine snowfall
from rain. During periods with no precipitation but warm temperatures, a seasonally
varied melt factor is used to produce the volume of melt. During rain or snow events a
simplified energy balance approach that considers temperature and precipitation data is
used. The model also accounts for snow soil interface interaction, and liquid water
storage and transmission through the snow pack.
For application of the operational hydrologic model to the mountainous area of
Sierra Nevada, special attention should be given to the snow model. The Sierra Nevada
intermittent seasonal snow pack contributes approximately 70% to the annual flow, and
the interaction of snow melt and accumulation controls seasonal flows and is responsible
Chapter 3
3-2
for the inter-annual flow regime. To better understand factors that affect the model, a
sensitivity analysis of the snow model input and parameters was conducted.
3.2.1.1. Snow Model Sensitivity to Temperature Data.
The MAT data as explained in section 3.2.1 is utilized as an index to radiation
properties, snow pack properties and several threshold parameters. Such model structures
that rely on a single input variable for the calculations of different processes create
dependency among the processes and strong sensitivity to the forcing data. Therefore,
good quality temperature data are required to achieve good model simulations. In
mountainous regions with large heterogeneity of snow cover, such as in the Sierra
Nevada, there is significant temperature heterogeneity and it is difficult to produce
representative mean areal temperature (MAT) for certain basins through the interpolation
of point measurements.
To demonstrate the sensitivity of the model to the MAT values, in the following
case studies we perturbed the MAT data within a range of assumed reasonable
uncertainty due to surface elevation differences. The model sensitivity to the MAT was
demonstrated on the Upper South Fork American (1650 to 3150 meters). We assume that
air temperature is linearly correlated to ground surface elevation by the moist adiabatic
lapse rate (1 deg °C / 150 meter). This approach can be used to derive a temperature
distribution from a topographic data set such as a digital elevation model (DEM).
Temperature differences due to orography in the Upper South Fork American can reach
10 °C. It has been documented however that on the Sierra Nevada western slopes the
temperature gradient is occasionally larger then the moist lapse rate (Knowles 2000).
Thus, the selection of the moist adiabatic rate for this study can be regarded as a
conservative choice.
In this analysis the model sensitivity to temperature is demonstrated using both
systematic and non-systematic perturbation of the MAT values. The basin is divided into
bands of an elevation range of 150 meters, and the MAT was modified based on the lapse
rate elevation at the centroid of each band (see schematic example in Figure 3-1). This
Chapter 3
3-3
segmentation yields 8 temperature bands for the upper region of South Fork with up to 3
and 5 °C MAT increase and decrease, respectively.
+150 meter
Mean basin elevation
-150 meter
-1
MAT +1
Temperature (°C)
Figure 3-1: Schematic of the temperature (abscissa) relation to the elevation (ordinate) by the moist
adiabatic lapse rate.
In the systematic perturbation sensitivity analysis (Figure 3-2) the snow water
equivalent (SWE) was derived for each elevation band (Figure 3-2a) compared with the
SWE simulation derived from the un-perturbed MAT (red line). The areal weighted
SWE from the systematic perturbation is compared to the MAT derived SWE in Figure
3-2b. It can be seen that the differences in temperature due to the lapse rate can create a
range of snow pack response with peaks that can range from about 250 to 2300 mm of
SWE. Moreover during the melting period, the curve that was built from the weighted
systematic error in MAT (Figure 3.2b) has different properties from the nominal run.
Chapter 3
3-4
2500
1200
(b)
(a)
1000
2000
800
1500
(mm)
(mm)
600
1000
400
500
0
200
0
500
1000
0
1500
0
500
1000
1500
6-hour time steps
Figure 3-2: Snow water equivalent (SWE) in the Upper South Fork American for water year 1980 as a
function of systematic perturbation in the MAT: (a) 8 simulations in elevation zones with MAT that ranges
from -5 to +3 oC; (b) areal weighted average of the perturbed simulation. The nominal simulation that uses
the observed (unperturbed) MAT values is shown in red.
In the next set of analyses, the model sensitivity to temperature is examined for
randomly perturbed MAT. That is, in each time step the MAT was sampled randomly
from the distribution of elevations. In Figure 3-3 the sensitivity of the SWE from an
ensemble of 20 nonsystematic temperature perturbations is presented. It can be seen that
the SWE is sensitive to the temperature data and the ensemble provide SWE that are
different from the nominal MAT derived SWE.
Chapter 3
3-5
1400
1200
1000
SWE (mm)
800
600
400
200
0
0
500
1000
1500
6-hour time step
Figure 3-3: Snow water equivalent (SWE) in the Upper South Fork American for water year 1980 as a
function of random perturbation of the MAT. The nominal simulation is provided in red.
3.2.1.2. Sensitivity of the Snow Model to the Model Parameter Values
To provide a better understanding of the snow model response, a sensitivity
analysis with respect to the model parameters was conducted for the North Fork
American River. A list of parameters and their nominal values as calibrated by CNRFC
is provided in Table 3-1.
A central function in the snow model is that which determines the snow cover
area (SCA). This function requires the specification of a snow depletion curve (SDC)
that relates the ratio (R) between the current pack snow water equivalent (SWE) and the
minimum pack water equivalent for which the SCA is 100% (SI). In the nominal run the
SDC is a 45 degree straight line which indicates a 1:1 ratio between R and SCA. To
evaluate the sensitivity of the SDC as a specified parameter in the model, an SDC
function that depends on two parameters (a and b) was established. This SDC curve
consists of three straight lines. The first line for R< 0.33 is defined by parameter a, which
is the angle of the curve with the x-axis; the second line for R> 0.67 is defined by
parameter b, which is the angle with the right y-axis; and the third line for 0.33< R <0.67
Chapter 3
3-6
is a line that connects the end of the first two line segments at locations R = 0.33 and R
=0.67 (see Figure 3-4).
Table 3-1: Snow Model Parameters
Parameters
Nominal
Values
SCF - Snow correction factor
1.15
MFMAX - Maximum melt factor during non rain periods (mm C° 6hr )
1
MFMIN - Minimum melt factor during non rain periods (mm C° 6hr )
0.4
UADJ – Average wind function during rain on snow (mm/mb)
0.15
SI – Mean areal water equivalent above which there is always 100% snow cover (mm)
900
NMF – Negative melt factor (mme C° )
0.15
TIPM – Antecedent weight factor
0.25
PXTEMP - determination of rain from snow (C°)
2
MBASE – base temperature °C
0
-1
-1
-1
PLWHC –Percent liquid water holding capacity
0.02
DAYGM – Snow soil interface melt factor (mm day )
-1
0.3
Figure 3-4: Two-parameter snow depletion curve. Parameters a and b are the angles with respect to the xand y-axis, respectively, as shown.
Chapter 3
3-7
In the sensitivity analyses, the curve was symmetrically changed which implies
that the curve is dependent on one parameter. The case of the nominal curve is a specific
case in which a and b are equal to a 45 degree angle. The sensitivity analysis was
conducted for the water years 1959 and 1960, which represent a relative wet and dry
year, respectively. For each sensitivity run, one parameter value was modified to be
above or below its nominal value by 50%, while other parameters maintained their
nominal values. In Figure 3-5 the nominal SWE is shown in blue while the SWE
corresponding to a 50% under- and over-estimation of the parameter value are shown in
red and black, respectively. The parameters can be classified into sensitive and
insensitive parameters. The sensitive parameters are SCF, MFMAX, MFMIN, SI,
PXTEMP and the SDC; whereas the other parameters ((UADJ, NMF, TIPM, MBASE
PLWHC and DAYGM) are relatively not sensitive on an annual scale.
Snow Water Equivalent
1500
1000
SCF
1000
MFMAX
500
500
0
0
500
1000
1500
2000
2500
0
3000
1000
0
500
1000
MFMIN
0
500
1000
1500
2000
2500
0
3000
0
500
1000
SI
2000
2500
3000
2000
2500
3000
2000
2500
3000
2000
2500
3000
2000
2500
3000
NMF
0
500
1000
1500
2000
2500
0
3000
0
500
1000
1500
1000
TIPM
PXTEMP
500
500
0
500
1000
1000
1500
2000
2500
0
3000
0
500
1000
MBASE
PLWHC
500
0
500
1000
1500
1500
1000
500
2000
2500
0
3000
1000
0
500
1000
1500
1000
DAYGM
500
0
1500
500
1000
0
3000
1000
500
0
2500
500
1000
0
2000
UADJ
500
0
1500
1000
SDC
500
0
500
1000
WY 1959
1500
2000
2500
0
3000
0
500
1000
WY 1959
WY1960
1500
WY1960
Figure 3-5: The nominal simulation of SWE (blue) compared to SWE corresponding to a 50% over- (red)
and under-estimation (black) of the nominal parameter value. Each panel indicates the parameter
perturbed.
Chapter 3
3-8
The following is a summary of the effect of each of the sensitive parameters on
snow model simulations:
•
SCF - clearly has the largest effect on total snow water equivalent simulations. It
has at each time step an over- or under-estimation of up to 70% of the nominal
SWE. However, this effect seams to be symmetric and monotonic for this
analysis.
•
MFMAX - This parameter is involved in the calculation of the rate of melt in non
rainy periods and the calculation of heat deficit in non melt periods. Therefore, as
expected, it affects the declining limb of the SWE. The effect appears to be
monotonic and uniform. The parameter also determines to a large degree the end
of the melting season and the disappearing of the snow pack.
•
MFMIN – Similar to the previous parameter, this parameter has an effect on the
melting part of the annual SWE curve. However sensitivity to changes in this
parameter is shown to be less pronounced than to changes in MFMAX, and this
parameter does not affect melt timing.
•
SI – Changes in this parameter seem to have a significant effect only when they
underestimate the nominal parameter value. It can be seen during the wet year
under-estimation of the nominal value speeds up the pack melting processes.
•
PXTEMP – Changes in this parameter have a clear effect on the overall volume
of the pack. This parameter is best evaluated from single isolated events from the
snow model output, rain plus melt.
•
SDC - That seems to be the parameter that affects significantly the shape of the
SWE graph. In the wet year, the SDC affects mainly the melting process, with an
over-estimation of the equal angles in Figure 3-4 providing a tail of melting that
continues into the summer months. On the other hand, the under-estimation of
the equal angles yields a sharp melting process. The SDC also produces a
significantly different appearance of the SWE pack in the drier year.
Calibration of the model parameters using a physical approach usually implies
that the parameters have to be estimated in a sequential manner. As such, the order in
Chapter 3
3-9
which parameters are selected for the calibration is important with the most sensitive
parameters calibrated first. It is also observed that except from SDC, the other sensitive
parameters have a well identified and predicted effect on the simulation compared to the
nominal. Therefore these parameters can be tuned rather easily in order to match an
observed SWE time series. The SDC curve is the parameter that affects the overall shape
and behavior of snow accumulation and ablation processes the most. This observation
implies that this curve should be estimated first to achieve a reasonable interannual
behavior of the snow pack.
3.2.2 SAC-SMA
The soil water accounting component of the NWSRFS for the study basins in the
INFORM region is the Sacramento soil moisture accounting model (SAC-SMA). It is a
continuous simulation model of the wetting and drying processes in the soil and produces
surface and sub-surface flows that feed the basin channel network. The discrete form of
the model has been described in (Burnash et al. 1973) while a continuous time form is in
(Georgakakos 1986). Koren et al. (2000) and Duan et al. (2001) link the parameters of
the SAC model to watershed soil and land-cover characteristics. The effectiveness of the
SAC model to reproduce high flow conditions under spatially lumped and spatially
distributed implementations is most recently demonstrated by the results of the
Distributed Modeling Intercomparison Project (DMIP) organized by the US National
Weather Service Office of Hydrologic Development (Smith et al. 2004 and Reed et al.
2004). It is noted that in the following discussion we will use interchangeably the terms
soil moisture and soil water to describe depth-integrated soil moisture quantities.
The SAC-SMA model runs operationally at CNRFC over basins of area O(1000
km2) to produce streamflow estimates and forecasts at each of several forecast preparation
times. At the completion of the operational forecast run, the current estimates of the
volumes in each of the model soil water compartments (upper zone tension water, upper
zone free water, lower zone tension water, lower zone free primary and supplementary
water, and additional impervious area water), valid at the forecast preparation time, are
stored. They are used as initial conditions for subsequent forecast runs of the model
Chapter 3
3-10
when new forecast or observed input of mean areal precipitation (or areal rain plus melt
during periods with snow) and mean areal evapotranspiration demand becomes available.
In some cases, the model has been complemented with a state estimator for real time
updating from discharge observations and for generation of variance estimates for the real
time flow forecasts (Georgakakos 2000).
3.2.3 Unit Hydrographs and Channel Routing Procedures
To translate the volume of runoff produced by the operational soil water model
(SAC-SMA) in the form of total channel inflow into streamflow rate, unit hydrographs or
some type of channel routing method are employed within the NWSRFS. For channel
routing models that have the form of a cascade of linear reservoirs, one may associate the
parameters of the channel routing model with those of the unit hydrograph so that the
response is equivalent (e.g., Singh 1992 or Sperfslage and Georgakakos 1996). The
parameters of the unit hydrograph or channel routing model used are estimated as part of
the overall hydrologic model calibration process for specific basins. For the sub basins
under study in the Folsom and Oroville drainages, unit hydrographs are used with
parameters calibrated by the CNRFC. For the INFORM stand-alone hydrologic forecast
system equivalent channel routing models are used with parameters that are estimated as
part of the calibration process.
3.3
EVALUATION OF THE CNRFC MODEL IN THE AMERICAN AND
FEATHER RIVER BASINS
3.3.1 Introduction
Simulations of the operational hydrologic model, run routinely at the CNRFC,
were evaluated for the American and the Feather Rivers. The major objective of the
modeling process is to predict discharge in the basin outlet (inflow to the Folsom and
Oroville Lakes in the American and Feather Rivers, respectively). Although the main
task of the CNRFC is to predict floods, the model is also used, and has the potential to be
Chapter 3
3-11
used, for predictions of a longer hydrologic time response such as required for water
resources management, ecological preservation, long term climate forecast and other.
To plausibly meet these mentioned objectives the model must perform well on
different time scales and under variety of forcing scenarios. These time scales are clearly
manifested by the different modules that represent different processes (i.e., snow, soil
water accounting with runoff production and channel routing). The three modules
represent distinct processes which are closely interlinked, and in the validation processes
it is not a simple task to isolate the contribution of each process to the performance and
overall uncertainty in the simulation. This information regarding model sensitivity and
uncertainty on various time scales is important for the water resources manager for
decision making in reservoir operations. In the present evaluation, the processes are
considered sequentially with an attempt to isolate and identify the strengths and
weaknesses of the three different modules.
3.3.2
Procedure
Simulation runs were conducted by the CNRFC in calibration mode for the
American and Feather Rivers. The evaluation for the American River basins was
conducted using the current operational modeling scheme, although CNRFC is in the
processes of recalibrated and reconfiguring the model for the American River basins. The
current version of the model for the American River includes four sub-basins (North,
Middle and South Forks, and Folsom Local). The first three basins (the Forks) were
further divided into upper and lower basins using an elevation cutoff of 1,500 m (5000
feet) as shown in Figure 3-6.
Chapter 3
3-12
NF -American
MF - American
SF - American
Upper
Upper
Upper
Lower
Lower
Lower
Folsom Local
Figure 3-6: Schematic structure of the current operational hydrologic simulation for the American River
drainage with outlet at Folsom Lake.
The Feather River was subdivided into six sub-basins (Indian Creek, North Fork
at Pulga, Middle Fork at Merrimac, Middle Fork at Clio, Lake Almanor and Lake
Oroville) and each sub-basin was further divided into upper and lower sub-areas using
the 1,500 m elevation cutoff (Figure 3-7).
NF -Lake Almanor
MF - Clio
NF - Indian Creek
Upper
Upper
Upper
Lower
Lower
Lower
MF - Merrimac
NF - Pulga
Upper
Upper
Lower
Oroville Local
Lower
Upper
Lower
Figure 3-7: Schematic structure of the current operational hydrologic simulation for the Feather River
drainage with outlet at Oroville Lake.
Chapter 3
3-13
The model output evaluation was done with data from a variety of sources:
1. Mean daily flow for each of the sub basin outlets. The basin outlets and their
corresponding streamflow gauges are provided in Table 3-2. The inflows to
the lakes are computed flows generated from Lake water level records (also
provided by the CNRFC).
2. Daily snow water equivalent from snow sensors was obtained from the
California Data Exchange Center. http://cdec.water.ca.gov/ . There are 11
snow sensors found in the American River and 8 sensors in the Feather River.
A list of the snow sensors used in this study is provided in Table 3-3.
It is must be noted that in this evaluation study we disregard issues of data quality, and
the errors and uncertainties in this analyses are assumed to be related to the modeling
practices and components. It is expected that the observation sensors which are operated
by multiple agencies have differences in their data quality. However, there is not enough
information to account for these differences at present.
In Table 3-2 the scores of three statistical criteria are presented. The statistical
criteria were computed with a daily discharge time step for the entire available record
with a total of time steps equal to n. The simulations are denoted by S while the
corresponding observations by O. Although the different length of the available time
series used in this evaluation might affect the confidence in the computed criteria values,
all the criteria account for the time series length and, hence, it is reasonable to inter
compare the performance among different cases. The three statistical performance
criteria used are: (1) The correlation coefficient, R = COV ( S , O ) / var( S ) var(O ) . A
score of R equal to 1 indicates perfect linear relationships. (2) Root Mean Square Error,
RMSE = n −1 ∑ ( S − O ) 2 ; and (3) Percent of Daily Absolute Error
PDAE = ∑ S − O / ∑ O , which is an indicator to the degree of daily correspondence, on
average, between the observed and simulated discharges. For the last two measures a
perfect score is equal to 0.
Chapter 3
3-14
________________________________________________________________________
Table 3-2: Performance Statistics for Historical Simulation of the Operational Model
R2
RMSE
PDAE
USGS id
Water Years
American
North Fork
Middle Fork
South Fork
Folsom Dam
0.95
0.94
0.86
0.98
14.1
34.2
27.6
78.9
0.24
0.78
0.44
0.38
11427000
11433300
11444500
10/54 - 9/93 (39)
10/58 - 9/99 (41)
10/64 - 9/93 (39)
10/64 - 9/89 (25)
Feather
North Fork nr. Pulga
Middle Fork nr. Merrimac
Indian Creek
Middle Fork nr. Clio
Lake Almanor
Oroville Local
0.85
0.92
0.95
0.83
0.93
0.94
49.0
25.9
10.6
9.8
12.2
36.1
1.46
0.31
0.29
0.48
0.32
0.40
11404500
11394500
11401500
11392500
11399000
11406800
10/80 - 9/92 (12)
10/60 - 9/79 (19)
10/77 - 9/92 (15)
10/60 - 9/79 (19)
10/81 - 9/97 (18)
10/69 - 9/87 (18)
________________________________________________________________________
The results in this table provide a means for an inter comparison of performance
among different sub-basins. Based on these statistical measures we can state that the
operational model performs well for most sub basins with daily R2 values that are above
0.83, reaching well into the upper 0.90s. It is also apparent that there are clearly some
sub-basins that had superior performance (North Fork American, Indian Creek and
Almanor). It is interesting to note performance for Middle Fork Clio and Folsom Dam.
For the first, the RMSE score is the best (lowest) but the correlation coefficient is the
worst (lowest) with the PDAE being high. For the Folsom Dam, the correlation
coefficient computed was best (highest) among all the sub basins but the RMSE
computed was worst (highest). These results indicate that the measures used represent
specific aspects of the hydrologic response and further evaluation was necessary to
clarify performance as reported next.
Chapter 3
3-15
_______________________________________________________________________
Table 3-3: List of Snow Sensors
Sensors
Feather River:
Kettle Rock (KTL)
Grizzly Ridge (GRZ)
Pilot Peak (PLP)
Gold Lake
(GOL)
Humbug (HMB)
Rattle Snake (RTL)
Bucks Lake (BKL)
Four Trees
(FOR)
Elevation (ft)
Sub-Basins
7300
6900
6800
6750
6500
6100
5750
5150
IIF
MRM, IIF, FTC
MRM, ORD
MRM, FTC
PLG
PLG
PLG
PLG, MRM, ORD
American River:
Schneiders (SCN)
Lake Lois (LOS)
Caples Lake (CAP)
Forni Ridge (FRN)
Silver Lake (SIL)
Van Vleck (VVL)
Huysink (HYS)
Robbs Saddle (RBB)
Greek Store (GKS)
Blue Canyon (BLC)
Robbs Powerhouse (RBP)
8750
8600
8000
7600
7100
6700
6600
5900
5600
5280
5150
SF
MF
SF
SF
SF
SF, MF
NF
SF, MF
MF
NF
SF
3.3.3
Evaluation of Operational Model Performance
A comprehensive evaluation was conducted by comparing the streamflow and the
snow water equivalent simulations to observations. Different types of plots were used
during this process that highlight different performance aspects. A selected set of figures
that highlight various aspects of the hydrologic response are presented in Appendix D. In
this section, Figures from the American River are provided as examples and to aid the
discussion. After a presentation of sample Figures of different types we discuss our
findings.
Figures D-1 through D-16 (in Appendix D) show observed and simulated
hydrographs for different water years for the four sub-basins of the American River and
the six sub-basins of the Feather River. One example in presented in Figure 3-8.
Chapter 3
3-16
Folsom Dam
300
American South Fork
100
250
80
200
60
150
100
40
50
20
100
200
300
Water Year 1971
American Middle Fork
150
100
200
300
Water Year 1971
American North Fork
60
100
40
50
20
100
200
300
Water Year 1971
100
200
300
Water Year 1971
Figure 3-8: Examples of observed (blue) and simulated (red) flows in m3/s (cms) for water year 1971 for
the total flow at Folsom Dam and the outlet of the South, Middle and North Fork of the American River.
Figures 3-9 and 3-10 are duration curves of the transformed flow which provide
insight on the overall systematic errors. The flow discharges in these figures were
transformed using the Box-Cox transformation. The Box-Cox transformation n is used
for visualization purposes. The utilization of the transformation maps the independent
discharge values into a homoscedastic time series with an approximately normal
distribution. The transformation is given by: qt ,transform = ( qtλ − 1) / λ , where λ is set to 0.3
and the units of discharge are m3/s. The duration curves are used to highlight consistent
behavior of the simulations in a variety of flow magnitudes.
Chapter 3
3-17
Figure 3-9: Observed (blue) and simulated (red) duration curves of Box Cox transformed flow for the
basins of the American River
Figure 3-10: Observed (blue) and simulated (red) duration curves of Box Cox transformed flow for the
basins of the Feather River.
Chapter 3
3-18
Figures 3-11 and 3-12 are plots of the simulated flow as a function of the
observed flow at a single time step. These scatter plots enable us to see the overall
functional relationship and the performance of the exceptional events which are distinct
from the crowded cloud of points. The line of perfect correspondence is also shown in
these Figures for reference.
Figure 3-11: Simulated daily flow versus observed Flow in m3/s for the American River.
Chapter 3
3-19
Figure 3-12: Simulated daily flow versus the observed Flow
The cumulative curves in Figures 3-13 and 3-14 are consistency plots that provide
an opportunity to inspect the long-term water yield of the model. They emphasize the
importance of model long-term biases and the significance of monthly water balance. In
cases when the model runs in a semi-distributed mode but the model calibration is done
with performance measures pertaining to downstream aggregate response, it may be that
due to compensation of errors, downstream basins show overall good model performance
even though upstream sub-basins persistently over- or under-estimate the observed flow.
Chapter 3
3-20
Figure 3-13: Observed (blue) and simulated (red) of cumulative flow for the length of the simulation for
the American River sub-basins.
Figure 3-14. Observed (blue) and simulated (red) of cumulative flow for the length of the simulation for
the Feather River sub-basins.
Chapter 3
3-21
The western face in the Sierra Nevada has rapid transitions in flow from late
summer low flow, to winter mid flow and eventually to spring peak flows. It is important
to capture the annual dynamics and the timing of these transitions in the operational
model simulations. In Figures 3-15 and 3-16, the daily Box-Cox transformed values of
simulated versus observed flow are plotted for each month. In Figures 3-17 and 3-18, the
monthly contribution to the annual flow is presented. In this set of Figures, for each
month the mean and the standard deviation of the annual volume fraction are plotted for
the simulated and observed flows.
Figure 3-15: Scatter plots of simulated as a function of the observed monthly flows for the American River
sub-basins.
Chapter 3
3-22
Figure 3-16: Scatter plots of simulated as a function of the observed monthly flows for the Feather River
sub-basins.
Chapter 3
3-23
Figure 3-17: Observed and simulated monthly mean (± standard deviation) flow expressed as a fraction of
annual flow volume for the American River sub-basins.
Chapter 3
3-24
Figure 3-18: Observed and simulated monthly mean (± standard deviation) flow expressed as a fraction of
annual flow volume for the Feather River sub-basins.
Chapter 3
3-25
Another important aspect in the model representation of the natural flows is the
timing of the spring onset pulse. The method used herein to identify the spring pulse is
the cumulative departure method (Aguado et al. 1992; Cayan et al. 2001). This method
identifies the time (day) at which the cumulative departure from that year’s mean daily
flow is most negative. This measure is equivalent to finding the day in which the flow
magnitude shifts from less than average to more then average. This method avoids early
episodic melt events and captures the main shift of the spring melt. However, the
indicated day is also related to basin physiographic characteristics and includes a basin
lag time from snow melt to flow at the basin outlet. Figure 3-19 presents an example
from the North Fork American River sub-basin.
1000
North Fork
American
500
0
CMS
-500
-1000
-1500
100
200
300
Water Year 1960 (days)
Figure 3-19: The observed (black) and simulated (red) cumulative departure of the daily flow from the
annual mean flow at the North Fork American River sub-basin (WY 1960). The circles indicate the
occurrence of the lowest negative deviation and indicate the timing of the spring melt pulse.
Figure 3-20 compares the simulated and observed annual spring pulse at the North
Fork American sub-basin. Spring pulse Figures (such as Figures 3-19 and 3-20) for all
the other sub-basin are provided in Appendix D (Figures D-17 through D-36).
Chapter 3
3-26
Spring Pulse (Julian Day)
North Fork American
200
Simulated
Observed
(a)
150
100
50
Observed - Simulated (Days)
0
60
65
70
75
80
Water Years
85
90
95
65
70
75
80
Water Years
85
90
95
100
(b)
50
0
-50
60
Figure 3-20: (a) Observed (black) and simulated (red) time trace of the spring pulse; (b) Annual
differences between the observed and simulated spring pulse timing.
Last, the snow water equivalent (SWE) output from the model simulation was
compared with snow sensor data located in the corresponding sub-basins. An example of
four years is provided for the South Fork American River sub-basin in Figure 3-21, while
the comparison of snow sensor data to the simulations for the remaining sub-basins is
provided in Appendix D (Figures D-37 through D-44).
Chapter 3
3-27
Figure 3-21: Daily snow water equivalent from snow sensors (dots) and simulated model snow water
equivalent (solid line) for water years 1988 -1991 and for the South Fork American River sub-basin.
Chapter 3
3-28
3.3.4 Discussion of Evaluation Results
The following summarize the major findings from the operational hydrologic
model evaluation:
1. The group of Figures D-1 through D-16 shows that the simulation performance of the
model for some of the sub-basins captures well the overall basin hydrologic response
(e.g., NF -American, Indian Creek, Lake Almanor). On the other hand, in some basins
there are clearly periods in which the model does not perform well; see for example SFAmerican (Figure D-1, D-5, D-6), MF-American (Figures D-5 and D-6), Folsom Dam
(Figure D-6); MF near Clio (Figure D-14), and NF near Pulga (Figure D-13). In many of
theses cases, poor performance during periods of medium and low flow is because of
regulation in upstream reservoirs that alters the downstream natural flow.
2. As exemplified in Figures 3-15 and 3-16, the model fails to reproduce well the August
through September (summer) flow for most of the sub basins. Poor simulation of the
summer month flows is observed even in sub basins for which the model has a good
overall performance (e.g., NF American). The natural discharge in these summer months
is dominated by shallow groundwater flow and springs. Although this flow is of a low
magnitude, it is about 5-10% of the annual flow (e.g., Figures 3-17 and 3-18). This may
cause a cumulative effect on the overall water budget as seen in Figures 3-13 and 3-14.
The performance of the model during the summer months can be attributed to one or
more of the following: (a) streamflow regulation in any existent upstream reservoirs; (b)
errors in model parameters that represent the generation of baseflow in the model; and (c)
errors in basin evapotranspiration during the summer months.
3. The distinct climatological seasons and the intermittent winter snow pack in the Sierra
Nevada cause an intra annual flow variability in the study basins that is represented by
the monthly flow (e.g., Figures 3-17 and 3-18). In addition, winter precipitation may fall
either as snow or as rain. In Figures 3-17 and 3-18, the mean of the monthly flow volume
(solid lines) bracketed by the 1-sigma bounds (symbols) is shown for the observations
Chapter 3
3-29
and simulations. The monthly flow volume is expressed as a fraction of the annual flow
volume. This monthly flow behavior is captured well by the model for the NF-American
and MF- Feather near Merrimac. In other basins, the late winter and early spring
transitions of the monthly volume fraction are not well captured (e.g., Folsom Dam, SFAmerican, MF-American, and NF-Feather near Pulga). It is conjectured that this monthly
behavior is dominated by the model snow pack development, and, thus, can be better
captured by improving the simulation of the snow pack by the snow model. This
conclusion is supported by the water year hydrographs (Figures D-1 through D-16 in
Appendix D). Performance is consistently better in early winter compared to late winter
and spring.
4. Analysis of the snow simulations was conducted by comparing the model-produced
snow water equivalent to corresponding daily observations from point sensors in the
study basins (Figures D-37 through D-44 in Appendix D). This is a qualitative
comparison of point data to model variables that represent an aggregate area. General
conclusions that can be made for all the basins are: (a) performance is reasonable and the
shape of the simulated snow water equivalent curve captures the snow accumulation
period and the major snow storms; (b) usually melt in the model starts earlier than
observed from the sensors; (c) simulations agree well with the sensors that are located in
lower elevations thus indicating that the model may be underestimating the actual basin
snow water equivalent; and (d) the slopes of the depletion curves in the simulations are
less steep then the snow depletion slopes of the sensors. With respect to this latter point,
simulations represent a spatially aggregate response and the slope of the depletion curve
is a function of the spatial distribution of the basin properties rather than the properties of
any particular point. Satellite remote sensing data may be a better ground truth against
which to measure the depletion curve properties.
5. The simulation of the onset of the spring melt pulse is shown in Figures D-17 through
D-26 of Appendix D. It can be seen that for most of the basins the spring onset was
predicted well and it is within a few days at most of the observed spring onset time.
Occasionally there are some years in which the onset was predicted with large deviation
Chapter 3
3-30
from the observed. In some of these cases upstream streamflow regulation altered the
onset signal.
3.3.6
Recommendations
1. Lake operations and water diversions in the upper stream of the basins are a major
difficulty, especially for low and medium flows, when using a model that attempts to
represent the natural system. Although the day-to-day operational decisions pertaining to
upstream reservoirs are difficult to predict for hydrologic modeling purposes, an effort
should be made to incorporate this upstream flow regulation into the model. This will
improve the continuous simulations of the model states and the water balance. Efforts
along these lines have been initiated at the CNRFC for the Folsom Lake drainage.
2. Attention should be given to the parameters of the lower zone in the SAC-SMA model.
Some adjustment will probably improve the performance of the model in the summer
months. The summer flow regime (August through September) constitutes 3-5% of the
annual flow yield. Improving the prediction of the summer flow will also improve model
representation of the baseflow process and will contribute to a better representation in the
wet periods. This activity is underway at the CNRFC as well for the American River
basins.
3. The snow model component should be studied. Major issues that need attention are,
understanding the uncertainty associated with the use of mean areal temperature in the
mountainous area of Sierra Nevada, better representation of the snow spatial distribution,
and improvement of the snow depletion curve representation.
Chapter 3
3-31
3.4
DESIGN AND APPLICATIONS OF THE INFORM STAND-ALONE
HYDROLOGIC MODEL
3.4.1
Introduction
One of the objectives of the INFORM demonstration project is to inter compare
the benefits of the actual forecast – management operations to those of an integrated
forecast-management system that uses climate forecast information (e.g., see Figure 1-2,
Chapter 1). To allow (a) the automated production of ensemble flow forecasts
conditional on climate and weather information and (b) direct integration with the
reservoir management models (see Chapter 4), a stand-alone hydrologic prediction model
was designed and implemented. The model reproduces important features of the CNRFC
operational hydrologic model, including the components for snow accumulation and
ablation, soil water accounting, and channel routing. These components of the stand
alone model were designed and implemented to mirror the analogous components of the
operational CNRFC forecast model. In this section, the implementation of this model is
discussed for the Folsom Lake drainage, and an evaluation of the model performance is
made for the gauged locations within the basin. Lastly, the generation of ensemble
streamflow predictions by the stand-alone model using the National Weather Service
extended streamflow prediction (ESP) algorithm is discussed, and an initial evaluation of
their reliability for the Folsom Lake drainage is presented.
3.4.2
Features of the Stand-Alone Hydrologic Prediction Model
The model consists of a simplified version of the operational snow accumulation
and ablation model (Anderson 1973), the Sacramento soil water accounting model as
described in Georgakakos (1986), and the kinematic channel routing model of
Georgakakos and Bras (1982). The hydrologic basin upstream of a major reservoir site
within the INFORM project region is subdivided into sub-basins considering stream
gauge sites, significant upstream reservoir facilities, available automated precipitation
and temperature sensors, and the topology of the channel network. Those sub-basins that
Chapter 3
3-32
have significant elevation differences within their areas are further subdivided into subareas (up to two sub-areas, in this version of the stand alone model). The snow and the
soil-water models are applied to each of the sub-areas to produce rain plus melt and
channel inflow volumes. These volumes are then fed into the channel routing model and
are carried downstream through the channel network undergoing time distribution,
advection and attenuation. The model produces outflow at all the gauging sites and all
the junctions of the model-channel network, and, of course, at the basin outlet (inflow
point into the reservoir). It is important to note that the stand-alone model is designed to
use the same input as the operational hydrologic forecast model, and its parameters bear
close relationship to the parameters of the operational hydrologic model.
The configuration of the stand-alone model elements is exemplified for the
Folsom Lake drainage in Figure 3-22. The North (NF), Middle (MF) and South (SF)
Fork sub-basins are shown, sub-divided into an upper and a lower sub-area for snow-pack
and soil-water accounting. Channel routing occurs in each sub-basin and at channel
network junctions the inflows are summed. Channel routing is indicated with red arrows
in the Figure. There are four observation sites in the basin, shown with black filled
circles in Figure 3-22. Of these, the one corresponding to the inflow point to Folsom
Lake reports lake levels, which are transformed to naturalized flows. Channel routing
also occurs to junctions without observations (open circles) to allow for the correct
reproduction of the observed hydrograph with a six-hour resolution.
It is noted that the configuration of the model for Folsom Lake is slightly different
than that of the current operational model that treats the entire local area near Folsom
Lake as one sub-basin. In the case of the stand alone model this area is subdivided into
three sub-areas as shown in Figure 3-22, mainly for better channel routing representation.
The mean areal precipitation and temperature for those three sub-areas is the same as that
of the operational model for the local Folsom Lake sub-basin. The volume of water
received in each of the three Folsom local sub-areas for the stand alone model is
proportioned by area. The values of the model parameters used by the operational model
for the snow and soil-water components were used in the stand alone model as well. In
the results presented below, the area depletion curve is a line with a 1:1 slope, and routing
within the snow pack is ignored. Future versions of the model will be enhanced to use
Chapter 3
3-33
arbitrary snow depletion curves and to allow routing of the liquid water within the snow
pack.
MF
SF
Upper
Upper
Lower
Lower
NF
Upper
Lower
MF
Local
SF
Local
NF/MF
Local
Folsom Lake
Figure 3-22: Representation of Folsom Lake drainage by the stand-alone hydrologic prediction model in
INFORM. Sub-basins for which snow-pack and soil-water accounting is done are shown in yellow shade
with sub-divisions into upper and lower sub-areas as appropriate. Routing segments are shown with red
arrows, while junctions are shown with circles (filled black circles indicate gauged sites).
The kinematic channel routing component of the stand alone model for each
channel segment is based on a series of linear reservoirs with identical parameters. The
sum of the inverse of the channel routing model parameters for all the reservoirs
representing a single channel segment is equal to the travel time in the channel segment.
The operational model uses unit hydrographs to reproduce channel processes. For the
Chapter 3
3-34
North, Middle and South Fork sub-basins, the parameters of the channel routing model
were fitted to the unit hydrograph parameters and were used without modification (e.g.,
see Sperfslage and Georgakakos 1996). The parameters of the channel segments
downstream of the Forks were based on preliminary estimates of the travel time in these
segments. Table 3-4 shows the parameter values of the stand alone hydrologic model for
the Folsom Lake drainage sub-basins. The nomenclature is shown in Table 3-5. Table 36 shows the long-term-averaged daily values of evapotranspiration demand by month
(adopted from the operational parametric input files of CNRFC) used by the model.
3.4.3
Evaluation of Stand Alone Model Performance for Folsom Drainage
The stand alone model was used with the available historical data of 6-hourly
mean areal precipitation and temperature from the Folsom Lake drainage to simulate
streamflow in all the channel segments. The simulated inflow to the Folsom Lake and
the flows at the outlet of the North, Middle and South Fork sub-basins may be compared
to available observations at these sites. Although the INFORM model produces 6-hourly
flows, historical streamflow has daily resolution, so daily averages of the simulated flows
were computed to evaluate model performance and to compare it with that of the
operational model (see Section 3.3 above and Appendix D). In the following we discuss
model performance for the Folsom Lake inflows, which will be used in conjunction with
the reservoir decision support system of Chapter 4.
Time series of simulated and observed daily inflows to Folsom Lake are shown in
Figure 3-23 for water years 1965 through 1969. Water year 1965 is a year of
exceptionally high flows (near 5,000 m3/s) while water year 1966 is one of low flows
(less than 300 m3/s), with the other years having peak flows in between. Good agreement
is exhibited for the higher flows and during the winter and spring periods, while the
model has a tendency to overestimate the summer flows in low flow years. As in the
operational model evaluation, upstream reservoir regulation and errors in baseflow
parameters are the likely causes. The agreement between simulated and observed daily
flows throughout the historical period of record may be seen in the scatter plot of Figure
3-24. The plot shows good agreement for the entire range of flows observed.
Chapter 3
3-35
______________________________________________________________________________________
Table 3-4: Nominal Values of Stand Alone Model Parameters*
SNOW PARAMETERS
SCA
MFMAX
MFMIN
NMF
PLWHC
TIPM
MBASE
UADJ
DAYGM
PXTEMP
SI
ELV
PADJ
NFu
1.0
0.86
0.2
0.15
0.04
0.25
1.0
0.04
0.1
2.0
900.
19.86
1.0
NFl
1.0
0.85
0.3
0.15
0.04
0.25
1.0
0.04
0.1
2.0
300.
9.60
1.0
MFu
1.35
0.69
0.12
0.15
0.04
0.25
1.0
0.04
0.1
2.0
1200.
19.81
1.0
MFl
1.0
0.5
0.16
0.15
0.04
0.25
1.0
0.04
0.1
2.0
600.
13.72
1.0
SFu
1.2
0.75
0.2
0.15
0.04
0.25
1.0
0.08
0.1
2.0
1100.
20.29
1.1
SFl
1.0
0.85
0.25
0.15
0.04
0.25
1.0
0.06
0.1
2.0
500.
5.90
1.05
FL
1.0
0.8
0.25
0.15
0.04
0.25
0.0
0.04
0.1
1.0
200.
4.57
0.97
SACRAMENTO MODEL PARAMETERS
NFu
142.000
55.000
312.000
72.000
110.000
0.075
0.001
0.018
20.000
1.400
0.250
0.000
0.010
0.000
1.000
UZTWM
UZFWM
LZTWM
LZFPM
LZFSM
DU
DLPR
DLDPR
EPS
THSM
PF
XMIOU
ADIMP
PCTIM
ETADJ
NFl
161.000
35.000
360.000
72.000
85.000
0.070
0.002
0.030
20.000
1.400
0.350
0.000
0.010
0.000
1.000
MFu
90.000
35.000
270.000
96.000
120.000
0.105
0.001
0.023
48.000
1.300
0.150
0.000
0.000
0.005
1.000
MFl
140.000
45.000
280.000
110.000
110.000
0.115
0.002
0.015
43.000
1.500
0.300
0.000
0.020
0.005
1.000
SFu
100.000
65.000
250.000
125.000
20.000
0.040
0.001
0.007
30.000
2.100
0.250
0.000
0.000
0.000
1.000
SFl
175.000
90.000
600.000
350.000
60.000
0.050
0.001
0.007
100.000
1.100
0.250
0.000
0.000
0.000
1.000
Fl
75.000
15.000
180.000
100.000
80.000
0.062
0.001
0.018
12.000
1.200
0.250
0.100
0.075
0.065
1.000
KINEMATIC CHANNEL ROUTING MODEL PARAMETERS
n
α
NF
3
1.5
MF
3
1.5
SF
3
1.0
MF-NF
2
3.0
MF/NF-F
2
6.0
SF-F
2
2.0
SUB-CATCHMENT AREAS (km2)
Area
NFu
325.4
NFl
556.0
MFu
721.7
MFl
532.7
SFu
780.8
SFl
750.0
Fl
1016.3
_________________________________________________________________________________________
See Table 3-5 for nomenclature used in this Table
*
Chapter 3
3-36
______________________________________________________________________________________
Table 3-5: Nomenclature for Table 3-4
HEADINGS
For Snow
NFu:
NFl:
MFu:
MFl:
SFu:
SFl:
Fl:
and Sacramento Models and for Areas
NORTH FORK UPPER SUB-AREA
NORTH FORK LOWER SUB-AREA
MIDDLE FORK UPPER SUB-AREA
MIDDLE FORK LOWER SUB-AREA
SOUTH FORK UPPER SUB-AREA
SOUTH FORK LOWER SUB-AREA
FOLSOM LAKE LOCAL SUB-BASIN
For Channel Routing Model
NF:
NORTH FORK CHANNEL SEGMENTS
MF:
MIDDLE FORK CHANNEL SEGMENTS
SF:
SOUTH FORK CHANNEL SEGMENTS
MF-NF:
CHANNEL SEGMENT CONNECTING THE OUTLET OF MIDDLE FORK WITH A JUNCTION POINT
DOWNSTREAM OF THE NORTH FORK OUTLET
NF/MF-F: CHANNEL SEGMENT THAT CONNECTS THE JUNCTION POINT DOWNSTREAM OF NORTH FORK
OUTLET WITH FOLSOM LAKE INFLOW POINT
SF-F:
CHANNEL SEGMENT THAT CONNECTS THE OUTLET OF SOUTH FORK WITH FOLSOM LAKE INFLOW
POINT
SNOW MODEL PARAMETERS
SCA:
MFMAX:
MFMIN:
NMF:
PLWHC:
TIPM:
MBASE:
UADJ:
DAYGM:
PXTEMP:
SI:
ELV:
PADJ:
SNOW CATCH ADJUSTMENT FACTOR
MAXIMUM MELT FACTOR (MM DEGC-1 D-1)
MINIMUM MELT FACTOR (MM DEGC-1 D-1)
MAXIMUM NEGATIVE MELT FACTOR (MME DEGC-1 D-1)
FRACTION OF SNOW COVER FOR WATER HOLDING SNOW CAPACITY
PARAMETER FOR ANTECEDENT TEMPERATURE INDEX COMPUTATIONS
BASE TEMPERATURE FOR MELT COMPUTATIONS (DEGC)
AVERAGE DAILY WIND FUNCTION FOR RAIN-ON-SNOW PERIODS (MM MB-1 DAY-1)
CONSTANT MELT AT SNOW-SOIL INTERFACE (MM DAY-1)
TEMPERATURE TO DELINEATE RAIN FROM SNOW (DEGC)
MAXIMUM SWE FOR 100% COVER IN SNOW DEPLETION CURVE (MM)
ELEVATION OF CENTROID OF BASIN (102 M)
PRECIPITATION ADJUSTMENT FACTOR
SACRAMENTO MODEL PARAMETERS
UZTWM:
UZFWM:
LZTWM:
LZFPM:
LZFSM:
DU:
DLPR:
DLDPR:
EPS:
THSM:
PF:
XMIOU:
ADIMP:
PCTIM:
ETADJ:
UPPER ZONE TENSION WATER CAPACITY (MM)
UPPER ZONE FREE WATER CAPACITY (MM)
LOWER ZONE TENSION WATER CAPACITY (MM)
LOWER ZONE FREE PRIMARY WATER CAPACITY (MM)
LOWER ZONE FREE SUPPLEMENTARY WATER CAPACITY (MM)
INTERFLOW RECESSION (6HRS-1)
RECESSION COEFFICIENT FOR LOWER ZONE FREE PRIMARY WATER ELEMENT (6HRS-1)
RECESSION COEFFICIENT FOR LOWER ZONE FREE SUPPLEMENTARY WATER ELEMENT (6HRS-1)
CONSTANT FACTOR IN PERCOLATION FUNCTION
EXPONENT IN PERCOLATIOIN FUNCTION
FRACTION OF PERCOLATION BYPASSING THE LOWER ZONE TENSION WATER ELEMENT
FRACTION OF WATER LOST TO DEEP GROUNDWATER LAYERS
ADDITIONAL IMPERVIOUS AREA MAXIMUM FRACTION
FRACTION OF PERMANENTLY IMPERVIOUS AREA
EVAPOTRANSPIRATION DEMAND ANNUAL ADJUSTMENT FACTOR
CHANNEL MODEL PARAMETERS
nc:
α:
NUMBER OF LINEAR RESERVOIRS REPRESENTING THE CHANNEL SEGMENT UNDER STUDY
COMMON COEFFICIENT OF LINEAR RESERVOIRS WITH INVERSE DESCRIBING TRAVEL TIME
(6HRS-1)
__________________________________________________________________________________________________________
Chapter 3
3-37
_____________________________________________________________________________________
Table 3-6: Daily Values of Evapotranspiration Demand Used by the Sacramento Model for Each Month
(Values in mm/d)
NFu
NFl
MFu
MFl
SFu
SFl
Fl
J
0.760
1.280
0.760
1.280
0.780
1.300
0.860
F
0.780
1.400
1.060
1.860
1.450
2.470
1.120
M
0.820
1.800
1.470
2.520
1.670
2.940
1.640
A
1.030
2.290
1.950
3.110
1.800
3.200
2.480
M
1.800
3.640
2.550
4.110
2.280
3.850
4.150
J
3.040
6.040
4.320
6.330
3.580
7.390
4.560
J
5.260
8.220
5.400
8.650
5.760
9.160
4.640
A
5.570
8.250
6.150
9.730
5.840
8.760
4.100
S
4.100
6.550
4.770
6.950
3.270
3.790
3.220
O
1.940
3.100
2.690
3.120
1.810
2.300
2.200
N
1.140
1.690
1.190
1.440
1.360
2.050
1.230
D
0.910
1.400
0.940
1.250
1.080
1.800
0.880
_________________________________________________________________________________________
Figure 3-23: Simulated (red solid line) and observed (blue dots) daily inflow to Folsom Lake by water
year. Water Years: 1965 – 1969. Flows in m3/s.
Chapter 3
3-38
Figure 3-24: Simulated versus observed daily inflow to Folsom Lake for historical record. Flows in m3/s.
Scatter plots by month between simulated and observed monthly Folsom Lake
inflows, Box-Cox transformed, are shown in Figure 3-25 (compare to Figure 3-15). The
results in Figure 3-25 are similar to those of the upper left panel of Figure 3-15 and show
good model performance for all but the summer months during which biases exist. When
compared to the results in Figure 3-15, it is apparent that the stand alone model performs
similarly to the operational model with somewhat of a wider scatter of the points for
certain months and with a lower bias exhibited in summer months. Further evaluation of
the simulations by the stand alone INFORM hydrologic model may be done using BoxCox-transformed flow duration plots, similar to those of Figure 3-9 which were discussed
earlier in the context of the operational model evaluation. Figure 3-26 shows this type of
plot for the simulated and observed daily Folsom Lake inflow. The model performance
is very similar to that of the operational model (compare Figures 3-25 and upper left
panel of Figure 3-9). That is, the model overestimates the exceedance frequency of a
certain transformed flow that is below the median and underestimates it when the flow is
above the median.
Chapter 3
3-39
Figure 3-25: Scatter plots of simulated as a function of the observed monthly transformed flows for
Folsom Lake inflow.
Folsom Lake Inflow
40
35
Box-Cox Transformed Flow
30
25
20
15
10
5
0
0
10
20
30
40
50
60
Percent Exceedance
70
80
90
100
Figure 3-25: Observed (blue) and simulated (red) duration curves of Box Cox transformed flow for the
Folsom Lake inflow.
Chapter 3
3-40
Lastly, the monthly cycle of the simulated and observed long-term averaged
inflows to Folsom Lake may be seen in Figure 3-26 for the stand alone INFORM model.
This result may be compared to the analogous result obtained for the operational model
shown in Figure 3-17 (upper left panel). The behavior of the INFORM model is similar
to that of the operational model, with less pronounced volume biases during the early
snow melt season (March – April) but with more pronounced biases during the late snow
melt season and in early summer (May – June).
This initial evaluation of the INFORM stand alone hydrologic model for the
Folsom Lake drainage indicates that the model behavior is similar to that of the CNRFC
operational hydrologic model, when both models are forced by the same mean areal
precipitation and temperature data and when they use the same parameter values or, for
the channel routing component, parameter values derived from the unit hydrographs of
the operational model. The performance of the INFORM model with respect to the
observed data appears satisfactory both for high and low flows. Further work aims to
improve performance during the late melt season and during the low flow periods by
incorporating functions that describe the long-term average release policy of the upstream
reservoirs in affected sub-basins of the Folsom Lake drainage.
Lake Folsom Inflow
0.5
0.45
Monthly Fraction of the Annual
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10
11
12
Months
Figure 3-26: Observed and simulated monthly mean (± standard deviation) flow expressed as a fraction of
annual flow volume for the Folsom Lake inflow. Months are from October (1) through September of the
next year (12).
Chapter 3
3-41
3.4.4
Ensemble Forecasting for Reservoir Inflows
Earlier work by the INFORM development team has shown the value of ensemble
forecasting (as opposed to using deterministic forecasts) for operational reservoir
management (see results in Section 1.6 of Chapter 1). Ensemble forecasting is used to
produce likely future reservoir inflows from present conditions (for snow, soil water, and
channel flow) in the upstream basin and from likely future forecasts of mean areal
precipitation and temperature. Important properties of this approach that makes it
indispensable for real time forecasting applications are: (a) the uncertainty in the model
input and parameters may be specified without constraints imposed on model structure
(e.g., additivity and temporal independence of input errors); and (b) it preserves the
strong and time-varying inter dependence of the state vector elements in time for all
sample paths. This latter inter dependence is due to the nature of the physical system that
is reflected in the model and its inputs. The later also makes it impractical to characterize
the state vector process through its full probability density law (joint probability density
for all relevant times), while for reservoir management such temporal dependence of the
forecast flows is critical. In fact it is for the generation of ensemble reservoir inflow
forecasts conditional of weather and climate forecasts that the stand alone hydrologic
component of the previous section was designed and implemented.
Carpenter and Georgakakos (2001) provide the basis of the ensemble forecasting
approach utilized here, while Yao and Georgakakos (2001) use the ensemble forecasts to
produce reservoir management policy and to quantify benefits due to the forecasts. The
interested reader is referred to the above articles for a detailed discussion of the
formulation. In this section, we first extend the feasibility results of Section 1.6 of
Chapter 1 using ensemble climate forecasts (rather than simulations) of ECHAM3 to
condition the input to the hydrologic model used in the feasibility studies, and then we
evaluate the ensemble reservoir inflow forecasts for Folsom Lake produced by the stand
alone INFORM hydrologic model.
Chapter 3
3-42
3.4.4.1 Ensemble Folsom Lake Inflow Forecasts from ECHAM3 Forecasts
The feasibility studies of Carpenter and Georgakakos (2001) summarized in
Section 1.6 of Chapter 1, used ensemble climate model simulations from ECHAM3 to
condition the development of ensemble rain plus melt and evapotranspiration demand
forecasts on basin scales. The ECHAM3 simulations were downscaled by a probabilistic
method. The rain plus melt and evapotranspiration demand forecasts were input to the
Sacramento and channel routing components of a hydrologic model that treated the entire
Folsom Lake drainage as an aggregate unit to produce ensembles of Folsom Lake
inflows. We now extend the previous feasibility study results by using ensemble climate
model forecasts from ECHAM3 to condition the hydrologic model ensemble input. For
this experiment and for comparison purpose we utilize the hydrologic model
configuration and the probabilistic downscaling approach of the earlier feasibility studies.
A set of five ensembles of monthly surface precipitation from ECHAM3 (spatial
resolution approximately 2.8o x 2.8o) was utilized to condition the hydrologic model
input. Use of the ECHAM3 is made at this time because there is no sufficient historical
data for the National Centers of Environmental Prediction (NCEP) climate model
forecasts to develop the required climate-model climatologies (see discussion in Section
2.3 of Chapter 2).
Ensemble Folsom Lake inflow forecasts were produced every five days for the
winter months of the period 1980 – 1993 using two approaches: (a) the National Weather
Service (NWS) extended streamflow prediction (ESP) approach (e.g., Day 1985; Smith et
al. 1991) as enhanced by Carpenter and Georgakakos (2001) to include hydrologic
model uncertainty; and (b) the ensemble forecast approach of Carpenter and
Georgakakos (2001) that is conditioned on climate forecasts. The ensemble Folsom Lake
inflow forecasts in both cases have daily resolution and maximum forecast lead time of
90 days. These ensemble daily inflow forecasts may be used to form ensemble volume
forecasts for volumes of any duration from a day to 90 days or ensemble forecasts of
other derivative quantities such as the peak flow in a given time period, etc.
Of particular interest in large-reservoir operations, when water conservation is a
significant objective for management, is the volume of water inflow integrated over a
Chapter 3
3-43
number of days. Evaluation of the reliability of these derivative forecasts may be done
with the construction of reliability diagrams. These diagrams display the conditional
probability of the observations given the forecasts for a range of forecast frequencies
(e.g., 0-0.1, 0.1-0.2, etc.) They are used as performance measures in conjunction with
the unconditional frequency distribution of the forecasts. The product of the conditional
distribution of observations given the forecasts with the unconditional forecast
distribution is the joint distribution of observations and forecasts. That joint distribution
fully characterizes the properties of the ensemble forecasts with respect to observations
(e.g., Wilks 1995).
Figure 3-27 shows the reliability diagram and associated unconditional frequency
distribution of the ensemble forecasts when the target event pertains to the 30-day
volume. The left panels correspond to the event “30-day volume is in the lower tercile of
its distribution”, while the right panels are for the upper tercile. The perfect reliability
points (open circles) and the associated 95% probability bounds due to sampling error
uncertainty are shown. Ensemble forecasts in a given forecast frequency range with
points outside the 95% bound interval are deemed unreliable at the 5% confidence level
for the particular forecast frequency range. Ensemble forecasts closest to the points of
perfect reliability are best with respect to this performance criterion.
The results of Figure 3-27 may be summarized as follows. The NWS ESP
method that is not conditioned on climate forecasts (blue symbols in the Figure) is
reliable for low forecast frequency ranges for events associated with low 30-day inflow
volumes but it is unreliable for all other ranges except the frequency range (0.9 – 1.0). In
general, the ESP forecasts tend to underestimate the observed frequency substantially.
For instance, they will forecast the chance for a drought (measured by 30-day inflow
volumes) with a much lower frequency of occurrence than observed. For events
associated with high 30-day inflow volumes, the NWS ESP methodology produces
reliable forecasts for all but one forecast frequency range (0.3 – 0.4). In both cases of
target events, the unconditional frequencies indicate that the forecast procedure issues
forecasts in all categories of forecast frequency but favors the low forecast probabilities.
Chapter 3
3-44
30-Day Volumes
Lower Third
1
30-Day Volumes
Upper Third
1
Expected
ESP
ECHAM3-FOR5
Expected
ESP
ECHAM3-FOR5
0.8
Observed Frequency
Observed Frequency
0.8
0.6
0.4
0.2
0.6
0.4
0.2
0
0
0
0.2
0.4
0.6
0.8
1
0
Forecast Frequency
30-Day Volumes - Lower Tercile
0.6
0.8
1
30-Day Volumes - Upper Tercile
300
ESP
ECHAM3-FOR5
250
200
150
100
50
Number of Forecasts
Number of Forecasts
0.4
Forecast Frequency
300
0
0.2
250
200
150
100
50
0
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
Range in Forecast Frequency
ESP
ECHAM3-FOR5
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
Range in Forecast Frequency
Figure 3-27: Reliability diagrams (upper panels) and unconditional frequency distributions of forecasts
(lower panels) for target events of 30-day Folsom Lake inflow volumes being in the lower (left panels) and
upper tercile (right panels) of their distribution. NWS ESP forecasts are in blue and ECHAM3 conditioned
ensemble forecasts are in red. The upper panels show the point of perfect reliability (open circles) and the
95% probability bounds due to sampling error uncertainty.
Compared to the NWS ESP, the ensemble forecasts conditioned on ECHAM3
ensemble forecasts exhibit better performance. The latter ensemble forecasts are reliable
for all forecast frequency ranges (good forecast resolution of forecast frequency ranges)
in both cases of low and high 30-day volume events at the 5% confidence level.
Substantial improvement with respect to the NWS ESP forecasts is noted for the low 30day volume events (pertinent to drought management). The unconditional forecast
distributions corresponding to the climate-forecast conditioned ensembles are similar to
those of the NWS ESP forecasts and tend to favor the lower forecast frequency ranges.
Chapter 3
3-45
These results reinforce the conclusions of Carpenter and Georgakakos (2001)
discussed in Section 1.6 of Chapter 1 regarding the benefits of climate and hydrologic
forecasts for reservoir management. In addition, they form a baseline against which the
ensemble forecasts of the INFORM forecast component may be compared. With respect
to the feasibility study results, this latter component contains the following
improvements: (a) better quality ensemble climate forecasts with higher temporal
resolution (see discussion in section 2.3 of Chapter 2); (b) downscaling procedure that
involves the well validated simplified orographic precipitation model of Section 2.5 of
Chapter 2; (c) improved hydrologic model that involves snow, soil-water and channel
components, and resolves hydrologic processes in sub-basins of the reservoir drainage
basin; (d) higher resolution Folsom Lake inflow forecasts (6 hours). In the next section
we discuss the use of the stand alone INFORM hydrologic model to produce ensemble
Folsom Lake inflow forecasts using the NWS ESP procedure.
3.4.4.2 Ensemble Folsom Lake Inflow Forecasts Using NWS ESP and INFORM Models
The INFORM stand alone hydrologic model, described in section 3.4.2 and 3.4.3
of this Chapter, is used with the NWS ESP procedure to develop retrospective ensemble
flow forecasts of 6-hourly resolution for the period 1958 through 1990. A total of 30
ensemble members were produced once per month on the first day of the month for the
entire record and with a maximum lead time of 90 days (360 6-hour time steps). From
these forecasts 30-day volumes of Folsom Lake inflow were computed, and the reliability
of the ensemble forecasts of 30-day volume was examined. Figure 3-28 shows the
reliability diagrams (upper panels) and the unconditional forecast frequencies (lower
panels) for both events: volume in lower tercile of its distribution (left panels) and
volume in upper tercile of its distribution (right panels).
The reliability diagrams show good reliability and resolution; that is, forecasts
were issued for each forecast range (see lower panels for distribution) and in most cases
are close to the line of perfect reliability. Exceptions to this are forecasts issued for the
forecast ranges (0.2 – 0.3) and (0.8 – 0.9) for the low tercile volume events and (0.8 –
0.9) and (0.9 – 1.0) of the high tercile volume events. It is also apparent that the low
Chapter 3
3-46
tercile volume forecasts have a more uniform distribution of forecasts across the different
forecast ranges while the upper tercile volume forecasts appear sharper (high frequencies
in very low and very high forecast ranges, resembling deterministic forecasts).
Figure 3-28: Reliability diagrams (upper panels) and unconditional forecast frequency distributions (lower
panels) for 30-day inflow volumes to Folsom Lake being in the low tercile (left panels) and in the high
tercile (right panels) of their distribution. The line of perfect reliability and the scalar Brier and Skill scores
are also shown in the upper panels. INFORM stand alone hydrologic model ensemble forecasts were
issued using NWS ESP on the first day of each month for the period October 1958 through September
1990.
The scalar measures of performance, Brier and Skill Score (e.g., Wilks 1995) were
computed to provide summary performance statistics. The Brier score, denoted by B, is
defined by
Chapter 3
3-47
B=
1
N
N
∑( y
i =1
i
− oi ) 2
(3-1)
where N represents the total number of events of record for which a forecast frequency
was computed from the ensemble forecasts, yi is the forecast frequency for event i (e.g.,
30-day volume in the lower tercile of its distribution), and oi represents the observation of
the event forecast that is 1 of the event occurs (i.e., the 30-day volume is indeed in the
lower tercile of its distribution for the event i), and 0 if its does not occur. Perfect
forecasts exhibit Brier scores equal to zero (0) while less accurate forecasts receive
greater Brier scores. This score is bounded by 1.
The Skill score, S, computed in this analysis and expressed as a percent is given
by
S = (1 −
B
) x100
Bc
(3-2)
where B is the Brier score computed from the ensemble model forecasts and Bc is the
Brier score computed from a set of reference forecasts, which are the climatological
relative frequencies of the target events in this case. Thus, the Skill score describes the
percent improvement over climate.
The results of Figure 3-28 indicate good Brier scores and substantial improvement
with respect to forecasts that use climatological probabilities in both cases. The forecasts
issued for low tercile inflow volume events do exhibit better scores, especially skill
scores, indicating that the ensemble forecasts of the INFORM stand alone model would
be particularly useful for predicting drought periods and would likely contribute to better
water conservation practices at Folsom Lake. Additional analyses are in progress, with
more frequent ensemble forecasts issued, with the NWS ESP procedure enhanced by
incorporating hydrologic model uncertainty as in Carpenter and Georgakakos (2001),
and with the ensemble forecasts integrated within the reservoir decision support system
of Chapter 4.
Chapter 3
3-48
3.5
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Chapter 3
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