U.S. Department of the Interior

U.S. Geological Survey

Modeling Managed Flows in the Sacramento/San Joaquin 

Watershed, California, Under Scenarios of Future Change

for CASCaDE2

By Noah Knowles and Collin Cronkite-Ratcliff

Open-File Report 2018–1101
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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Suggested citation:

Knowles, Noah, and Cronkite-Ratcliff, Collin, 2018, Modeling managed flows in the Sacramento/San Joaquin 

watershed, California, under scenarios of future change for CASCaDE2: U.S. Geological Survey Open-File Report 

2018–1101, 38 p., https://doi.org/10.3133/ofr20181101.

ISSN 2331–1258 (online)
iii

Acknowledgments

We thank the California Department of Water Resources for guidance on questions related to the CalSim 2 model. 

We also thank Ann Willis, University of California, Davis, for her guidance and the U.S. Army Corps of Engineers

for providing reservoir operating manuals. We are grateful for support from the Delta Stewardship Council’s

Science Program. 

We thank Michael Dettinger, U.S. Geological Survey (USGS), for his helpful review of this report. We are grateful

for support from the following USGS programs: Priority Ecosystems Science, which is part of the USGS

Ecosystems Mission Area, and the Water Availability and Use Science Program and the National Water Quality

Program, which are part of the Water Mission Area. Finally, we are grateful for the support and collaboration from

our colleagues on the CASCaDE team. Data and associated code generated during this study are available as a 

USGS data release (Knowles and others, 2018).
iv

Contents

1. Introduction................................................................................................................................................ 1

2. Overview of Methods ................................................................................................................................. 3

2.1. Climate Change Scenarios and Downscaling...................................................................................... 3

2.2. Watershed Modeling ........................................................................................................................... 3

3. RVIC Unimpaired Streamflow Simulations and Postprocessing ................................................................ 6

3.1. Overview of RVIC in CASCaDE2 ........................................................................................................ 6

3.2. Bias-Correcting RVIC Unimpaired Flows for Use in Producing C2-CalSim Water-Year Indexes ........ 6

3.3. Transforming Unimpaired RVIC Flows to Managed Flows for Use as C2-CalSim Flow Inputs ........... 8

4. Simulating Managed Streamflows Using C2-CalSim................................................................................. 9

4.1. CalSim 2 Description........................................................................................................................... 9

4.2. Modification of CalSim 2 for CASCaDE2............................................................................................. 9

4.3. Calculation of Indexes Used in C2-CalSim........................................................................................ 13

4.4. Resampling of Remaining Standard CalSim 2 Inputs........................................................................ 14

4.5. Sequential Execution of C2-CalSim Studies...................................................................................... 16

4.6. Automating C2-CalSim Runs............................................................................................................. 17

4.7. Application of C2-CalSim in CASCaDE2: Limitations and Future Work ............................................ 17

5. CRESPI ................................................................................................................................................... 19

5.1. Method .............................................................................................................................................. 19

5.1.1. First Step: Matching Blocks........................................................................................................ 19

5.1.2. Second Step: Smoothing Discontinuities ................................................................................... 20

5.2. Application to CASCaDE2................................................................................................................. 20

5.2.1. Historical Impaired Flow Data .................................................................................................... 21

5.2.2. Effects of Reservoir Storage Levels on Peak Flows................................................................... 23

5.2.2.1. Modeling the Flood Control Reservation.............................................................................. 23

5.2.2.1.1. Shasta Lake ................................................................................................................. 23

5.2.2.1.2. Lake Oroville ................................................................................................................ 25

5.2.2.2. Storage Excess Thresholds................................................................................................. 27

5.2.3. Modeling Separation of Flow by Fremont Weir .......................................................................... 29

6. Combining C2-CalSim and CRESPI Results ........................................................................................... 31

7. Evaluation of Model Performance............................................................................................................ 31

8. Conclusions ............................................................................................................................................. 34

9. References Cited ..................................................................................................................................... 35

Figures

 1. Map of the Bay-Delta watershed, California..................................................................................... 2

 2. Schematic showing the role of watershed modeling in the Computational Assessments of 

 Scenarios of Change for the Delta Ecosystem project phase 2 (CASCaDE2) for the 

 Sacramento-San Joaquin Delta, California .................................................................................... 4

 3. Flowchart showing the modeling of managed daily flows at points throughout the Sacramento

 River Basin, California ................................................................................................................... 5

 4. Graphs showing observation-based, simulated Variable Infiltration Capacity hydrologic model 

 plus Variable Infiltration Capacity routing model (VIC+RVIC), and bias-corrected unimpaired
v

 Sacramento River Basin, California, total monthly flows, and simulated and bias-corrected

 flows versus observation-based flows............................................................................................ 7

 5. Map showing major creeks and rivers in the San Francisco Bay and Sacramento-San Joaquin

 Delta (Bay-Delta) watershed, California, corresponding to CASCaDE2 modified CalSim

 (California Department of Water Resources’ operations model) (C2-CalSim) inflow

 boundaries ................................................................................................................................... 12

 6. Graph showing rule curve for Shasta Lake, California, calculated over the range of ground 

 wetness parameters..................................................................................................................... 25

 7. Rule curve for Lake Oroville, California, calculated over the range of ground wetness

 parameters................................................................................................................................... 27

 8. Graphs showing the 30-day moving maximum storage excess in Shasta Lake and Lake Oroville

 reservoirs, California, versus the 30-day moving maximum daily impaired flow rates ................. 28

 9. Graph showing implementation of culling for Shasta Lake, California ........................................... 29

 10. Graph showing mean daily flow over Fremont Weir versus flow in Yolo Bypass near Woodland,

 California, 1984–2010.................................................................................................................. 30

 11. Evaluation of performance of combined C2-CalSim/CRESPI method for Sacramento River 

 Basin, California, outflows for the historical period, water years 1980–2013 ............................... 32

Tables

 1. Locations in San Francisco Bay and Sacramento-San Joaquin Delta (Bay-Delta) watershed, 

 California, of CASCaDE2 modified CalSim (California Department of Water Resources’ 

 operations model) (C2-CalSim) inflow boundary conditions that are derived from global climate

 model driven Variable Infiltration Capacity routing model (RVIC) daily flow estimates. ............... 11

 2. Streamflow station records from the San Francisco Bay and Sacramento-San Joaquin Delta

 (Bay-Delta) watershed, California, used as historical data in the Computational Assessments of

 Scenarios of Change for the Delta Ecosystem phase 2 (CASCaDE2) resampling algorithm 

 (CRESPI) method ........................................................................................................................ 21

 3. Average annual precipitation measured at eight rain gauges in the vicinity of the Feather River

 Basin, California........................................................................................................................... 26

 4. Intramonthly performance metrics at inflow boundary locations for the San Francisco Bay and

 Sacramento-San Joaquin Delta (Bay-Delta) estuarine hydrodynamical model, Deltares Flow

 Flexible Mesh hydrodynamical model (D-Flow FM) ..................................................................... 33

 5. Intra-WY performance metrics at inflow boundary locations for the San Francisco Bay and 

 Sacramento-San Joaquin Delta (Bay-Delta) estuarine hydrodynamical model, Deltares Flow 

 Flexible Mesh hydrodynamical model (D-Flow FM) ..................................................................... 33
vi

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

Flow Volume

acre-foot 1,233 cubic meters

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F = (1.8 × °C) + 32.

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F – 32) / 1.8.

Abbreviations

AF adjustment factor

ANN artificial neural network

BDCP Bay-Delta Conservation Plan

C2-CalSim CASCaDE2 modified CalSim (CalSim is CDWR’s operations model)

CASCaDE Computational Assessments of Scenarios of Change for the Delta Ecosystem

CASCaDE2 Computational Assessments of Scenarios of Change for the Delta Ecosystem phase 2

CDF cumulative distribution function

CDWR California Department of Water Resources

CMIP5 Coupled Model Intercomparison Project Phase 5

CRESPI CASCaDE2 resampling algorithm

D-Flow FM Deltares Flow Flexible Mesh hydrodynamical model

EC existing conditions

GCM global climate model 

LOCA localized constructed analogs (downscaling method)

LOD level of development

NAA no action alternative

PA preferred alternative

QMBC quantile-mapping bias correction

RCP representative concentration pathway

RMS root-mean-square

RSR ratio of the root mean square error to the standard deviation of observations

RVIC VIC routing model

SLR sea-level rise

USGS U.S. Geological Survey

VIC Variable Infiltration Capacity hydrologic model

WSI-DI Water Supply Index-Delivery Index

WY water year (October 1–September 30)
Modeling Managed Flows in the Sacramento/San Joaquin 

Watershed, California, Under Scenarios of Future Change

for CASCaDE2

By Noah Knowles and Collin Cronkite-Ratcliff

Abstract

Projections of managed flows from the Sacramento River/San Joaquin River watershed, 

California, into the San Francisco Bay and Sacramento-San Joaquin Delta under scenarios of future 

climate change are needed for evaluations of potential impacts on water supply and estuarine 

ecosystems. A new, multiple-model approach for achieving this is described. First, downscaled global

climate model outputs are used to drive an existing Variable Infiltration Capacity/Variable Infiltration 

Capacity Routing (VIC/RVIC) model of Sacramento/San Joaquin hydrology, resulting in projections of 

daily, unimpaired flows (flows unaffected by management infrastructure such as reservoirs, diversions, 

exports, and so on) throughout the watershed. A management model, Computational Assessments of 

Scenarios of Change for the Delta Ecosystem phase 2 (CASCaDE2) modified CalSim (C2-CalSim), 

uses these projections as inputs and produces monthly estimates of reservoir and other infrastructure 

operations and resulting downstream managed flows. A historical resampling algorithm, CASCaDE2 

resampling algorithm (CRESPI), also uses the projected daily unimpaired flows, along with historical 

managed flows, to estimate the daily variability in managed flows (flows that have been altered by 

management infrastructure and actions) throughout the watershed. The monthly and daily managed-flow 

estimates are combined in a way that preserves the multi-decadal variability and century-scale trends 

produced by the C2-CalSim model and the day-to-day variability produced by the CRESPI algorithm.

The performance of the new modeling approach is evaluated at major inflows to the Bay-Delta estuary 

using multiple metrics and found to be satisfactory for the purposes of future scenario evaluation.

1. Introduction

Together, California’s San Francisco Bay and the adjacent upstream delta of the Sacramento and 

San Joaquin Rivers (the “Delta”) are the largest estuary on the west coast of the conterminous United 

States. Although local watersheds contribute inflow into San Francisco Bay, the vast majority of inflows 

to Bay-Delta estuary arrive through the Delta from the combined watershed of the Sacramento and San 

Joaquin Rivers (fig. 1). This watershed’s area is about 30 percent of California’s area and it receives an 

average of 77 million acre-feet of precipitation annually. The Delta is home to vital ecosystems, 

providing habitat for many endangered species and serving as an important stop for migrating birds on 

the Pacific Flyway. The Delta provides drinking water to two-thirds of Californians and is a major 

source of water for California agriculture (National Research Council, 2012). The health of the estuary’s 

ecosystem has long been in decline (for example, Healey and others, 2008). Continued subsidence of 

Delta islands, in conjunction with sea-level rise and the likelihood of major earthquakes, threaten 
2

hundreds of miles of fragile levees (Mount and Twiss, 2005). As a result, the Delta’s ecosystem and the 

role of its waterways as a central conduit for transporting freshwater from north to south are vulnerable. 

In response to these problems, California passed the Sacramento–San Joaquin Delta Reform Act of 

2009 (see http://deltacouncil.ca.gov/enabling-legislation) with the coequal goals of achieving water 

supply reliability and restoring the Delta’s ecosystem. However, critical gaps in our understanding of 

how the Delta may respond to major changes that are likely over the next several decades complicate 

decisions concerning how to achieve these goals.

The Computational Assessments of Scenarios of Change for the Delta Ecosystem project, now 

in its second phase (CASCaDE2), is an interdisciplinary modeling research effort aimed at projecting 

responses of the San Francisco Bay-Delta estuary and the Sacramento/San Joaquin watershed under 

scenarios of future change. The changes being investigated in CASCaDE2 include climate change 

through 2100 and major infrastructure changes, including tunnels under the Delta to provide an 

alternative to through-Delta conveyance of freshwater from north to south. Ultimately, CASCaDE2 is 

aimed at providing an improved understanding and a new capability to model the effects of future 

changes on the Delta ecosystem. A critical step toward that goal is the development of projections of 

managed flows in the Sacramento/San Joaquin watershed under the future scenarios. The methods 

developed and applied to that end in CASCaDE2 are the subject of this report.

A B

 

Figure 1. A, Map of the Bay-Delta watershed, California, with Sacramento and San Joaquin basins shaded 

green and blue, respectively, and major reservoirs labeled in red. The dashed rectangle in A indicates the Delta 

region, which is mapped in B with locations of major Delta freshwater inflows labeled in red. Base map sources: 

U.S. Geological Survey and Esri.
3

2. Overview of Methods

2.1. Climate Change Scenarios and Downscaling

The CASCaDE2 project makes use of 20 climate change scenarios. These correspond to two 

runs each of ten global climate models (GCMs: ACCESS1–0, CanESM2, CCSM4, CESM1-BGC, 

CMCC-CMS, CNRM-CM5, GFDL-CM3, HadGEM2-CC, HadGEM2-ES, and MIROC5. Each model 

was run with two scenarios of future greenhouse gas concentrations, or representative concentration 

pathways (RCPs). The two RCPs evaluated correspond to radiative forcing values in 2100 of 4.5 watts 

per square meter (W/m2) and 8.5 W/m2. These scenarios were selected from the full Coupled Model 

Intercomparison Project Phase 5 (CMIP5) ensemble as suitable for California water-resources 

assessments (California Department of Water Resources, Climate Change Technical Advisory Group,

2015). Outputs from each GCM/RCP scenario were bias-corrected using a recently developed method 

(Pierce and others, 2015) and downscaled using the Localized Constructed Analogs (LOCA) method 

(Pierce and others, 2014), resulting in sets of daily projections of precipitation and near-surface air 

temperature on a 1/16° grid containing the Sacramento/San Joaquin watershed for the period 1950–2100 

(in most cases; some GCM runs end in 2099). Note that the values over the historical period in these 

GCM outputs are simulated climate responses to historical greenhouse gas fluctuations and are 

constrained by no other historical forcings. As such, their interannual and decadal variability differ from 

recorded historical behavior, despite coverage of the same nominal period. In addition to these purely 

GCM-based climate change scenarios, an observation-based dataset (Livneh and others, 2015) on the 

same 1/16° grid was used to provide a historical baseline for comparison with future scenarios for the 

period including water years1 (WYs) 1950–2013. This is also the dataset that Pierce and others (2014) 

used as the historical reference in their GCM bias correction and downscaling.

2.2. Watershed Modeling

The primary goal of the work described in this report was to translate future scenarios of 

downscaled daily precipitation and temperature fields into estimates of daily managed downstream 

flows at points throughout the watershed. Managed flows reflect the influences of reservoirs, diversions, 

groundwater pumping, and so forth, under a set of management goals and criteria. Additionally, a set of 

managed flow “hindcasts” was produced for the historical period using the same modeling tools and the 

observation-based dataset from Livneh and others (2015), providing a historical baseline for comparison 

with the future scenarios. In the CASCaDE2 project, the resulting managed flow projections have 

served as inputs for a new Sacramento watershed sediment model (Stern and others, 2016), and 

managed flows from a subset of the future scenarios are being used to drive a new hydrodynamical 

model of the Bay-Delta estuary called the Deltares Flow Flexible Mesh hydrodynamical model (D-Flow 

FM) (Martyr-Koller and others, 2017) (fig. 2).

 1

A water year is defined as the 12-month period from October 1 of any given year through September 

30 of the following year. The water year is designated by the calendar year in which it ends and which 

includes 9 of the 12 months.
4

Figure 2. Schematic showing the role of watershed modeling in the Computational Assessments of Scenarios of 

Change for the Delta Ecosystem project phase 2 (CASCaDE2) for the Sacramento-San Joaquin Delta, California. 

Downscaled global climate model (GCM) outputs drive watershed and estuary models. Watershed hydrology and 

operations models translate global climate model outputs into managed estuarine inflows.

To produce the managed flow estimates at relevant points throughout the watershed, a 

combination of models was used (fig. 3). First, in simulations performed at Scripps Institution of 

Oceanography by David Pierce (University of California, San Diego, written commun., 2017), the 

Variable Infiltration Capacity (VIC) hydrological model (Liang and others, 1994; Livneh and others,

2013) was driven by the downscaled meteorological data. The resulting simulated fields of gridded 

unimpaired2 surface runoff and subsurface flow were routed to produce unimpaired streamflow 

estimates using the VIC routing model RVIC (Lohmann and others, 1996; Hamman and others, 2016)

configured for the CASCaDE2 spatial domain for this study.

 2 In this document, “impaired” or “managed” flows are flows that have been altered by management 

infrastructure, including reservoirs, diversions, exports, and so on. “Unimpaired” flows are estimates of 

flows that would have occurred without these impairments.
5

Figure 3. Flowchart showing the modeling of managed daily flows at points throughout the San Francisco Bay 

and Sacramento-San Joaquin Delta (Bay-Delta) watershed, California. GCMs, global climate models; LOCA, 

localized constructed analogs; VIC, Variable Infiltration Capacity hydrologic model; RVIC, VIC routing model; 

CASCaDE2, Computational Assessments of Scenarios of Change for the Delta Ecosystem phase 2; CRESPI, 

CASCaDE2 resampling algorithm; C2-CalSim, CASCaDE2 modified CalSim (California Department of Water 

Resources operations model).

The unimpaired streamflow estimates were next translated into managed flows using a 

combination of two methods. First, the freshwater management operations model developed jointly by 

the California Department of Water Resources and the U.S. Bureau of Reclamation, CalSim 2, was 

modified as described in section 4 of this report. The resulting model, which we call C2-CalSim (for 

CASCaDE2 modified CalSim), was driven by inputs derived from the RVIC unimpaired flows. This 

produced corresponding estimates of monthly averaged managed streamflows at outflow points of larger 

basins throughout the watershed. An algorithm to estimate daily managed flows, CRESPI (for 

CASCaDE2 resampling), was implemented using RVIC and C2-CalSim outputs as inputs. CRESPI 

produces daily flow estimates by drawing from recent historical flow patterns and using the other 

models’ outputs to drive the pattern selection process. CRESPI's strength lies in its representation of 

daily flows (as opposed to C2-CalSim's monthly time scale). However, because CRESPI is limited to 

the historical flow regime, the resulting estimates of daily managed flows do not always faithfully 

represent the likely response of freshwater operations to long-term trends in flow patterns associated 

with long-term meteorological trends (manifestations of climate change) present in the GCM outputs. 

For smaller basins, this was not considered an important shortcoming, primarily because the 

contribution of those basins to the overall sediment and flow budgets of the entire Sacramento River 

Basin is relatively small (there were no smaller basins in the San Joaquin watershed studied in 

CASCaDE, just the watershed's total outflow). Also, smaller basins are typically not represented in C2-

CalSim; therefore, for smaller basin outflows, the CRESPI results were used directly. For larger basins, 

however, it was necessary to scale the CRESPI output to more closely represent the response of 

operations to long-term trends as represented in the C2-CalSim output. This scaling was the last step in 

the translation of daily meteorological quantities projected by CMIP5 GCMs into corresponding 

projections of managed daily flows at points throughout the Bay-Delta watersheds. Each of the steps of 

this procedure is discussed in more detail below.
6

3. RVIC Unimpaired Streamflow Simulations and Postprocessing

3.1. Overview of RVIC in CASCaDE2

RVIC is a streamflow routing model designed to accept gridded VIC outputs and generate daily, 

unimpaired streamflow estimates at prescribed points on streams and rivers. The RVIC model was set 

up over the California-Nevada domain (corresponding to the domain of the VIC runs) and configured to 

produce streamflow estimates at the numerous locations throughout the Bay-Delta watershed needed for 

the CASCaDE2 project. For each of these locations, this process included determining the grid cells of 

the VIC hydrology model contained in the associated drainage basin (much of the RVIC configuration 

involved GIS software). The RVIC model takes as input gridded daily surface and subsurface flow 

contributions from each drainage basin’s VIC grid cells and determines the resulting daily flow rate at 

the corresponding downstream outflow location by solving the shallow water equations to simulate the 

routing of the streamflow contributions to the outflow point.

Streamflows were simulated by RVIC for subsequent use in other model components. These

included:

• 16 locations for producing boundary conditions for the watershed sediment model,

• 6 locations for producing D-Flow FM inflow boundary conditions,

• 10 locations for use in generating multiple C2-CalSim water-year indexes (discussed in sections 

3.2 and 4.3),

• 33 locations for use in generating monthly inflows to drive C2-CalSim scenario runs (discussed 

in section 3.3), and 

• 1 location (Shasta Lake inflow) for use in computing Shasta Lake target storages as part of the 

algorithm to convert C2-CalSim monthly outputs to daily flows (discussed in section 5.2.2.1.1).

With some overlap between locations needed for different purposes, daily unimpaired 

streamflow time series at 57 locations were produced. This was done for each of the 20 GCM scenarios 

for the period 1950–2099 (10 GCMs × 2 emissions scenarios). Additionally, a historical (1950–2013) 

“baseline” run of RVIC was performed by using VIC output driven by the gridded, observation-based 

meteorological dataset produced by Livneh and others (2015).

3.2. Bias-Correcting RVIC Unimpaired Flows for Use in Producing C2-CalSim Water-Year Indexes

Once these unimpaired flow estimates were produced, additional processing was needed. The 

historical baseline VIC output (routed with RVIC) generally compares favorably with observation-based 

unimpaired streamflow estimates (fig. 4).
7

Figure 4. Graphs showing (A) observation-based, simulated by the Variable Infiltration Capacity hydrologic 

model plus Variable Infiltration Capacity routing model (VIC+RVIC), and bias-corrected unimpaired Sacramento 

River Basin, California, total monthly flows, and (B) simulated and bias-corrected flows versus observation-based 

flows. A one-to-one line, corresponding to perfect agreement, is shown in black. Unimpaired flow estimates are 

from California Department of Water Resources (2014).

Because this implementation of the VIC model is largely uncalibrated, there are some systematic 

errors in its output; these must be corrected when accurate unimpaired flow estimates are required. In 

particular, low flows are underestimated and high flows are overestimated by the VIC model (fig. 4B).

More accurate unimpaired flow estimates at the monthly scale were needed at 10 of the RVIC 

streamflow output sites to generate water-year indexes used by the C2-CalSim model (discussed in 

section 4.3). To achieve this, a quantile-mapping bias correction (QMBC) was applied to the RVIC 

streamflow outputs.

To apply QMBC, unimpaired flow time series for a historical period, assumed to be accurate, are 

needed for reference. Monthly unimpaired flow data (California Department of Water Resources, 2017)

were obtained for all 10 locations used in the calculation of water-year indexes needed for C2-CalSim. 

At each flow location, the simulated historical baseline flows (based on the Livneh and others 

meteorology dataset [2015]) for the time period covered by the reference data were extracted and paired 

with the reference data.
8

The QMBC method consists of, for each flow location, first estimating values that correspond to 

regularly spaced quantiles of the empirical cumulative distribution functions (CDFs) for that location’s 

pair of historical simulated and reference time series (20 quantiles are used in this study). Then, using 

simulated future-scenario time series, a quantile is generated for each simulated daily flow value by 

interpolating the flow values corresponding to the two nearest mapped quantiles. Next, the biascorrected flow value, corresponding to the same quantile in the reference data, is determined by 

interpolating between the two nearest quantiles in the reference data CDF3

. Finally, any peak flows in 

the future scenarios that exceed the highest flow produced in the baseline simulated flows (which 

corresponds closely to the highest quantile) were mapped by adding to them the difference between the 

highest quantile’s flow value for the reference data and the corresponding flow value in the baseline 

simulation. In this way, the entire simulated future-scenario time series is bias-corrected (see example of 

bias-corrected historical flows in fig. 4A–B). If this bias correction were applied to the same historical 

simulated flow data used to generate the mapping (instead of to the future simulated flows), the 

empirical CDF of the resulting corrected time series would match that of the reference data. This 

approach assumes that biases in the historical simulation remain the same in future simulations. 

Methods of bias-correction that are more sophisticated than QMBC are difficult to implement in 

the current application due to the prohibitively small length of available unimpaired monthly flow 

estimates (Boé and others, 2007). In the future, we may explore approaches to bias-correcting future 

scenarios that preserve changes in statistical moments relative to current climate (for example, Li and 

others, 2010, and Pierce and others, 2015).

Application of QMBC to GCM precipitation output has been shown to have the potential to alter 

trends relative to the uncorrected data (Maurer and Pierce, 2014). The effects of QMBC on trends in 

simulated streamflow are unclear. Because the bias-corrected data are to be used here as monthly 

averages to calculate indexes that largely portray broad annual flow categories, the importance of this 

shortcoming should be minimal.

3.3. Transforming Unimpaired RVIC Flows to Managed Flows for Use as C2-CalSim Flow Inputs

The RVIC outputs needed to generate altered C2-CalSim flow inputs for historical baseline and 

future-scenario C2-CalSim runs required transformation based on historical CalSim 2 input data, which 

represent impaired flows at the model’s boundary points. To generate C2-CalSim inputs for future 

scenarios, a mapping was developed between historical baseline RVIC outputs (calendar years 1950–

2013, based on the Livneh and others [2015] data) and CalSim 2 inputs representing impaired inflows 

from upstream basins (assuming modern infrastructure and freshwater demands in those basins for the 

whole time period). These impaired-inflow inputs to CalSim 2 were produced by the California 

Department of Water Resources for the period covering WYs 1922–2003. The mapping was developed 

for 33 locations representing nearly all of the freshwater input to CalSim 2 (table 1) using the WYs

contained in both datasets: 1951–2003.

The mapping between the 33 RVIC output and CalSim 2 input time series was again achieved 

using QMBC (as described in section 3.2), except that in this case, separate mappings were developed 

for each location for each quarter of the calendar year. This refinement was added because unlike the 

previous flows mapped using QMBC, wherein fairly consistent systematic biases of the VIC and RVIC 

models were being corrected, the mapping here is translating from unimpaired flows to impaired flows 

 3

For the software used—the qmap package in R—it was necessary to subtract the minimum flow of 

simulated and reference time series (that is, the minimum of both time series concatenated together) 

from both time series to avoid spurious zeros in the results.
9

in the rim basins. Because management goals for most reservoirs vary by season, seasonal mappings are 

more appropriate than a single mapping for all seasons. Once the quantile maps were developed for each 

location based on the WY1951–2003 historical datasets, the maps were applied to the future-scenario 

RVIC outputs to generate the corresponding C2-CalSim inputs for these scenarios.

4. Simulating Managed Streamflows Using C2-CalSim

4.1. CalSim 2 Description

The mapped inflows described in section 3.3, along with meteorological data (discussed in 

section 4.3) extracted from the climate-change-scenario downscaled meteorology and historical baseline 

meteorology datasets (Livneh and others, 2015) , were used to drive modified version of a model of 

freshwater management operations—the California Department of Water Resources' CalSim 2 model 

(Draper and others, 2004). CalSim 2 is a management optimization model in which, given inputs of 

reservoir inflows and other inflows, a set of freshwater management decisions that optimally satisfy 

operational goals and constraints is computationally determined on a monthly time step. The results are 

estimates of monthly managed freshwater flows at points throughout the watershed. CalSim 2 has been 

applied in other climate change studies (Brekke and others, 2004, 2009; Dracup and others, 2005;

Vicuna and others, 2007; Anderson and others, 2008).

Prior applications of CalSim 2 outside of the CASCaDE2 project have been based on a fixed, 

historically based pattern of hydrologic variability. The period of these studies has generally begun with 

WY 1922 and, for most relatively recent studies, has ended with WY 2003. The freshwater management 

infrastructure and level of development (corresponding to projected population and agricultural 

irrigation needs) are static over the course of a CalSim 2 run, and the inflows over the historical period 

are taken to represent the range of hydrologic variability present in the watershed. Climate studies

involving CalSim 2 typically apply monthly flow “perturbation” ratios to the standard historical input 

time series. These ratios encapsulate climatological monthly flow changes over time based on separate, 

typically GCM-driven, hydrological model runs. The main limitation of this approach is that the range 

and types of hydrologic variability represented are limited to the recent historical hydroclimatic regime. 

So, for example, 1983 is an unusually wet year in every run, as is 1998, and 1977 is always a very dry 

year and is always followed by a very wet 1978. Possible patterns of interannual and interdecadal 

variability other than those observed in WYs 1922–2003, such as those present in GCM runs, are 

therefore not evaluated in the traditional application of the CalSim 2 model. This is an important 

limitation because such relatively recent historical variability necessarily constitutes a limited subset of 

the possibilities inherent in the climate system, particularly as greenhouse gas concentrations continue to 

increase.

4.2. Modification of CalSim 2 for CASCaDE2

The CASCaDE2 project is designed to directly use downscaled, daily GCM output to drive 

models of the Bay-Delta estuary and watershed to assess the response of these systems not only to longterm meteorological trends, but also to changes in multiyear variability such as droughts and wet years 

and changes in the frequency and magnitude of even shorter term events such as extreme floods. The 

traditional application of CalSim 2, which uses static historically based hydrologic data, therefore does 

not meet CASCaDE2 project needs. The chosen solution was to modify CalSim 2 to accept dynamic 

hydrology. By “dynamic hydrology,” we mean sequences of inputs not constrained to historical 

sequences, generated directly from hydrologic model output. Although traditional CalSim 2 runs cover 
10

WYs 1922–2003 with some runs ending a few years later, the CASCaDE2 implementation of CalSim 2, 

C2-CalSim, simulates WYs 1980–2099. The start date of WY 1980 was chosen because most large 

modern freshwater management infrastructure in the Bay-Delta watershed was constructed and filled by 

that time, so reasonable comparisons between simulated and observed managed flows may be made 

from WY 1980 onward.

CASCaDE2 includes assessment of potential impacts of a massive proposed infrastructure 

project that involves the construction of one or more tunnels under the Delta as an alternative means of 

conveying freshwater from the Sacramento River to the export pumps in the south Delta. The current 

version of this plan is called “California WaterFix.” The predecessor to WaterFix was called the BayDelta Conservation Plan (BDCP). The California Department of Water Resources (CDWR) configured 

CalSim 2 to include the operations of the proposed tunnels and used the model to conduct evaluations of 

the BDCP’s impact. These BDCP CalSim 2 configurations were publicly available, so we used them as 

the starting point for our C2-CalSim modeling. The model files were obtained from the California 

Department of Water Resources, and of the model configurations used to evaluate alternatives for the 

BDCP, two were chosen for use in CASCaDE2. The “No-Action Alternative with Fall X2 

management” (referred to subsequently as NAA) was chosen as our scenario representing minimal inDelta infrastructure change (chapter 3, section 3.5.1 in California Department of Water Resources and 

U.S. Bureau of Reclamation, 2016), and the “Alternative 4 with decision tree,” the California 

Environmental Quality Act preferred alternative (PA), was chosen as our “alternative conveyance” 

scenario (chapter 3, section 3.5.9 in California Department of Water Resources and U.S. Bureau of 

Reclamation, 2016). Another configuration developed for the BDCP study was an “Existing 

Conditions” (EC) run, which used the standard historical CalSim 2 inputs, unaltered for climate change. 

Time series for 33 of the “Existing Conditions” inputs were extracted and used in developing the 

quarterly QMBC mapping between historical baseline RVIC outputs and historical CalSim 2 inputs, 

described in section 3.3. All other input time series from the “Existing Conditions” CalSim 2

configuration were extracted for use in the resampling approach to the generation of future-scenario 

versions of these inputs (described in section 4.4).

The BDCP studies evaluated these and other alternatives by using a perturbation ratio approach

to modify historical CalSim 2 inputs. The perturbation ratios were derived from VIC runs driven by 

downscaled GCM outputs whose trends in precipitation and temperature over the study region fell near 

the medians of trends among select members of the Coupled Model Intercomparison Project Phase 3

GCM ensemble. The individual CalSim 2 inflow inputs that were modified in this manner to represent 

climate change are shown in appendix 5A, section D.3.4 of California Department of Water Resources

and U.S. Bureau of Reclamation (2016) and are reproduced in part in table 1. Locations of the creeks 

and rivers referenced in table 1 are shown in figure 5.
11

Table 1. Locations in San Francisco Bay and Sacramento-San Joaquin Delta (Bay-Delta) watershed, California,

of CASCaDE2 modified CalSim (California Department of Water Resources’ operations model) (C2-CalSim) inflow 

boundary conditions that are derived from global climate model driven Variable Infiltration Capacity routing model 

(RVIC) daily flow estimates. 

[Location numbers are shown in figure 5]

Rim-basin inflows Basin floor inflows

1. Trinity Lake Inflow 14. Clear Creek Inflow to Sacramento River

2. Lewiston Lake Inflow 15. Cottonwood Creek Inflow to Sacramento River

3. Shasta Lake Inflow 16. Cow Creek Inflow to Sacramento River

4. Black Butte Lake Inflow 17. Battle Creek Inflow to Sacramento River

5. Lake Oroville Inflow 18. Paynes Creek Inflow to Sacramento River

6. Folsom Lake Inflow 19. Red Bank Creek Inflow to Sacramento River

7. New Hogan Lake Inflow 20. Antelope Creek Inflow to Sacramento River

8. New Melones Lake Inflow 21. Mill Creek Inflow to Sacramento River

9. New Don Pedro Lake Inflow 22. Deer Creek Inflow to Sacramento River

10. Lake McClure Inflow 23. Elder Creek Inflow to Sacramento River

11. Eastman Lake Inflow 24. Thomes Creek Inflow to Sacramento River

12. Hensley Lake Inflow 25. Big Chico Creek Inflow to Sacramento River

13. Millerton Lake Inflow 26. Butte Creek Spills to Sutter Bypass

27. Stony Creek Inflow to Stony Gorge Reservoir

28. Little Stony Creek Inflow to East Park Reservoir

29. Kelly Ridge Inflow to Feather River

30. Yuba River Inflow to Feather River

31. Bear River Inflow to Feather River

32. Cosumnes River Inflow to Delta

33. Mokelumne River Inflow to Delta
12

Figure 5. Map showing major creeks and rivers in the San Francisco Bay and Sacramento-San Joaquin Delta

(Bay-Delta) watershed, California, corresponding to CASCaDE2 modified CalSim (California Department of Water 

Resources’ operations model) (C2-CalSim) inflow boundaries. See table 1 for names of features. Base map 

sources: U.S. Geological Survey and Esri.

For CASCaDE2, these same inflow inputs were replaced with the values for future scenarios 

generated with the quarterly QMBC approach described in section 3.3. All other time-varying CalSim 2 

inputs were also modified based on future-scenario VIC and RVIC outputs (see sections 4.3 and 4.4). 

Running the C2-CalSim model with these input changes required multiple modifications to the CalSim 

2 configuration files. The modifications included the following steps, which are automated in Bash or 

Python scripts:

1. All model files for a given alternative were extracted to a temporary folder.

2. Pathnames were corrected so C2-CalSim could run on the local file system.
13

3. Dates in the CalSim 2 initial conditions file were modified to implement a WY 1880 start date 

(as opposed to the usual WY 1922 start date). Note that due to technical limitations of CalSim 2, 

the nominal run period for future scenarios is WYs 1880–1999, rather than WYs 1980–2099. 

Only the dates reflect this difference; all other data correspond to the future scenario.

4. All beginning and ending dates in model configuration (“wresl”) files were changed to reflect 

the WY 1880–1999 run time.

5. A new model input parameter, “WYORIG,” was implemented in the configuration and input 

files. This input was needed to make the resampling approach described in section 4.4 work with 

the neural network library used to estimate salinities in the Delta.

4.3. Calculation of Indexes Used in C2-CalSim

Next, some pre-processing was needed to generate time series of key annual indexes needed as 

input to future-scenario C2-CalSim runs. Except where otherwise indicated, these various indexes are 

independent, serve distinct purposes in freshwater management and the CalSim 2 model, and bear no 

quantitative relation to one another. The first index described below is based on meteorological data, 

and the remaining indexes were derived using the bias-corrected unimpaired flows discussed in section

3.2. These indexes are used (in practice and in CalSim 2) in a range of water allocation decisions. Most 

indexes were defined in water-resource management agency documents (for example, State Water 

Resources Control Board, California Environmental Protection Agency, 1995, 1999).

Brief descriptions of these annual indexes and their derivations are listed here:

1. The U.S. Fish and Wildlife Service biological opinion “Action 3” smelt temperature threshold 

crossing date is the annual date on which the average of water temperatures at specific sites 

within the Delta first rises above the critical threshold of 12 degrees Celsius (°C) (U.S. Fish and 

Wildlife Service, 2008). When this threshold is exceeded, specific flow restrictions are 

implemented in CalSim 2. In this calculation, monthly mean air temperatures at the Sacramento 

Executive Airport are assumed to be identical to the water temperatures, as in the BDCP study

(Appendix 5A, section B in California Department of Water Resources and U.S. Bureau of

Reclamation, 2016). These air temperatures were extracted for future scenarios from the 

downscaled climate-change scenarios for the grid cell containing the airport. As in the BDCP 

study, monthly mean values were assumed to occur in the middle of the month, and daily data 

were interpolated between these values to obtain the day and month of the first ascending smelt 

temperature threshold crossing in each WY. These dates typically were in the months of 

February–April. Frequently, in the warmer climates of several of the future scenarios, the 

resulting water temperature estimates were never below the 12 °C threshold. In those cases, the 

date of December 1 was used as the smelt temperature threshold crossing date.

2. The Sacramento River WY type index is based on the total unimpaired Sacramento River Basin 

flow. The index is calculated as follows. First, the following expression is evaluated:

(0.4) × current Apr–Jul runoff forecast (in million acre-feet) + (0.3) × current Oct–Mar 

runoff (in million acre-feet) + (0.3) × previous WY's index (if the previous WY's index 

exceeds 10.0, then 10.0 is used). (1)

Then, based on this calculated value, the index is assigned one of the following integer values 

(qualititative descriptions of the corresponding WY are in parentheses):

1 (Wet): Equal to or greater than 9.2

2 (Above normal): Greater than 7.8, and less than 9.2

3 (Below normal): Greater than 6.5, and equal to or less than 7.8
14

4 (Dry): Greater than 5.4, and equal to or less than 6.5

5 (Critically dry): Equal to or less than 5.4

3. The Oct–Mar Sacramento River index is just the Oct–Mar total Sacramento River Basin outflow 

in million acre-feet.

4. The San Joaquin River WY type index is similar to the Sacramento River WY type index, but 

with a different calculated value:

(0.6) × current Apr–Jul runoff forecast (in million acre-feet) + (0.2) × current Oct–Mar 

runoff (in million acre-feet) + (0.2) × previous WY’s index (if the previous WY's index 

exceeds 4.5, then 4.5 is used). (2)

Based on this calculated value, the index is assigned as:

1 (Wet): Equal to or greater than 3.8

2 (Above normal): Greater than 3.1, and less than 3.8

3 (Below normal): Greater than 2.5, and equal to or less than 3.1

4 (Dry): Greater than 2.1, and equal to or less than 2.5

5 (Critically dry): Equal to or less than 2.1

5. The “SJRAve5” index for a given year is the average of the San Joaquin River WY type index for 

the 5 previous WYs.

6. The Shasta WY index has a more complicated logic; refer to the calc_indexes.py code for details.

7. The “AmerD893” index is based on the Apr–Sept total unimpaired American River flow in 

thousand acre-feet. The index has a value of 1 if the AmerD893 index is greater than 600,000

acre-feet (acre-ft) and a value of 2 otherwise. 

8. The Feather River index has a complicated logic similar to the Shasta WY index. Refer to the 

calc_indexes.py code for details.

9. The Trinity River index is based on unimpaired Trinity River flows. The index values are 

assigned as follows:

If flow is:

less than 650,000 acre-ft, index is 5;

greater than or equal to 650,000 acre-ft and less than 1,025,000 acre-ft, index is 4;

greater than or equal to 1,025,000 acre-ft and less than 1,350,000 acre-ft, index is 3;

greater than or equal to 1,350,000 acre-ft and less than 2,000,000 acre-ft, index is 2;

greater than 2,000,000 acre-feet, index is 1.

10. The Eight-River index is the total unimpaired Sacramento and San Joaquin River flows, in 

thousand acre-feet.

11. The Delta index is the sum of the Jan–May unimpaired Sacramento and San Joaquin River 

flows, in thousand acre-feet.

4.4. Resampling of Remaining Standard CalSim 2 Inputs

With the indexes described in section 4.3 and the major C2-CalSim inflows (table 1) derived 

from GCM-driven RVIC flows generated for all scenarios and for the historical observation-based 

Livneh dataset (Livneh and others, 2015), all remaining C2-CalSim inputs were generated for the 

historical baseline and future-scenario runs by resampling the corresponding inputs from the standard 

input files of the BDCP scenario being evaluated (that is, EC before 2030, or NAA or PA after 2030).

The resampling steps are as follows:

1. Total monthly rim-basin inflows were calculated as the sum of monthly flows over all rim basins 

(table 1). These were calculated using the “Existing Conditions” study inputs and the quarterly 
15

QMBC-mapped C2-CalSim inflows (described in section 3.3) for the historical baseline and 

future scenarios.

2. For each water year in the historical baseline and the future scenarios, a best-match year was 

selected from the “Existing Conditions” rim-basin inflows, where the match metric was 

determined as: 

CCyy = �

1

12 ∑ �QQmm−TTyy,mm�

2 12

mm=1

QQ�TT� (3) 

PPyy = �

1

12 ∑ �QQmm−TTyy−1,mm� 12

mm=1

1

2

(QQ�+TT�) � (4) 

ddyy = CCyy + PPyy⁄25 , (5) 

where

 Qm is total rim-basin flow for a given month (m, where m=1 indicates the first month in 

the WY) in the WY to be matched in the historical baseline or future scenario; 

 Ty,m is total rim-basin flow for a given month (m) in the candidate matching WY (y); 

calculated using rim-basin flows extracted from the “Existing Conditions” study; 

QQ� and TT� are the long-term mean of the total rim-basin flows from the historical baseline or 

future scenario and the long-term mean from the “Existing Conditions” study inputs, 

respectively;

Cy and Py are metrics for current water-year flows and previous water-year flows, respectively; 

and 

dy is the combined metric, with the coefficient 1/25 chosen through an iterative “leave-one-out” 

cross-validation (described below) to optimally represent the combined effects of 

current water-year flows and previous water-year flows on the CalSim 2 inputs being 

resampled. The previous water-year flows are included mainly to represent reservoir 

carry-over storage. 

3. All C2-CalSim inputs, other than the 33 inflows and the 11 indexes derived directly from RVIC 

streamflows, for the water year being matched in the historical baseline or future scenario are 

filled with the corresponding inputs from the best-match year (year with minimum dy) in the 

standard input files of the BDCP scenario being evaluated (EC for years before 2030, or NAA or 

PA after 2030). 

Steps 1–3 are repeated until the C2-CalSim inputs for all 34 years of the historical baseline (WYs 1980–

2013) and 120 years of each future scenario (WYs 1980–2099) have been produced. 

Coefficient selection for the metric dy was carried out by applying the procedure described above 

but using only the EC dataset. The rim-basin inflows for each WY in the EC dataset (WYs 1922–2003) 

were used to select a best-match WY from all other years in the EC dataset (eqs. 3–5). The C2-CalSim 

inputs described in step 3 above from the best-match WY were pulled from the EC dataset to fill the 

corresponding values for the year being matched. This “leave-one-out” procedure was applied to all 

years in the EC dataset, resulting in a cross-validation dataset that was then compared to the original EC 
16

dataset. Evaluation of goodness-of-fit between the two datasets over a range of coefficient values 

resulted in the metric shown in step 2 above.

A record of which water years were selected as best matches for each scenario are also retained 

and added to the C2-CalSim inputs files as values for the WYORIG input variable. CalSim 2 calls a 

separate artificial neural network (ANN) algorithm to generate estimates of salinity and salinity-related 

quantities based on a range of inputs. One of the ANN inputs is the current water-year value. Because 

the ANN is a binary software library that was trained using WYs 1922–2003, the ANN calls in the C2-

CalSim configuration files were altered to use WYORIG (which still varies from 1922 to 2003) instead 

of the model run's current water-year value, which varies from 1980 to 2099 in C2-CalSim. In this way, 

the resampling approach described here extends to this aspect of the ANN calls.

4.5. Sequential Execution of C2-CalSim Studies

Several factors define a given C2-CalSim run. The first is which study is being evaluated: EC, 

NAA, or PA. For CASCaDE2, the EC model configuration is used to represent WYs 1980–2029 (recall 

that for the GCM-derived scenarios, the “historical” period does not correspond to observed historical 

behavior). The NAA and PA studies are used for WYs 2030–2099. This assumes the management 

changes represented in the NAA and PA studies are not put into effect until WY 2030. Another factor 

that affects a given C2-CalSim run is the level of development (LOD), represented as freshwater 

demands corresponding to future projections of population and land use. The EC configuration uses an 

LOD corresponding to the year 2005, and the NAA and PA configurations use a 2030 LOD. Thus, 2030 

seemed an appropriate transition date between model configurations, because of the available LODs and 

the likelihood that any major infrastructure changes (for example, Delta tunnels) would not be 

completed for at least another decade. In the transition from the EC to the NAA or PA studies at 2030, 

the NAA and PA studies were started in 2020 and allowed 10 years to spin up, and the spin-up period 

was discarded. Similarly, the EC portion of the sequence (WYs 1980–1929) was allowed to spin up for 

10 years, and the outputs for WYs 1970–1979 were discarded.

A final factor that should have been included in defining a given study, but in the end was not, 

was the sea level rise (SLR) value used. Because salinities resulting from given inflow patterns increase 

with SLR, more flows are required to meet salinity standards as sea level increases (Anderson and 

others, 2008; Van Lienden and others, 2014). CalSim 2 uses an ANN to estimate salinity and salinityrelated quantities at points throughout the Delta (Chung and Seneviratne, 2009). For the BDCP studies, 

this ANN was trained for conditions corresponding to SLR amounts of 0 centimeters (cm), 15 cm, 30.5 

cm (1 foot [ft]), and 45 cm, resulting in four separate ANNs that could, in theory, be used in a given C2-

CalSim study. Many attempts were made to incorporate the different ANNs into the present study to 

approximate the effects of projected SLR in each scenario on salinity throughout the Delta. These 

attempts were abandoned, however, due to apparent software incompatibilities between the ANN 

binaries and the various configurations of C2-CalSim employed in this study. The ANN corresponding 

to no SLR was used in every case. As SLR increases in a given scenario, the resulting C2-CalSim 

outputs will therefore underestimate the flows required to meet salinity standards, and with regard to 

this aspect of management at least, represent a more optimistic water-management scenario than is 

likely. We may revisit this issue in the future. However, until ANNs are available for much larger 

amounts of SLR (at least 100 cm), even a successful implementation of this approach will significantly 

underestimate the flows needed to repel salinity. See section 4.7 for further discussion of this.
17

4.6. Automating C2-CalSim Runs

With the BDCP study CalSim 2 configuration suitably modified and the C2-CalSim inputs for 

the historical baseline run and for all future-scenario runs generated, and with run segments configured 

to allow for variation in management infrastructure and strategies (as represented in the different BDCP 

studies) and for some variation in LOD, the next step was to run C2-CalSim. Execution of all 20 future 

scenarios and the historical baseline run was automated using Bash, Python, and HEC-DSS Jython 

scripts on Linux, combined with a Windows virtual machine with Cygwin OpenSSH, AutoIt, and 

WRIMS 1.3.0 (the underlying software on which the CalSim 2 model is run) installed.

Initially, the C2-CalSim runs crashed when a particular combination of inputs and state variables 

occurred. This most commonly occurred during very low inflows, though it occasionally occurred 

during very high inflows. It was prohibitively difficult to diagnose these crashes on a case-by-case basis, 

so we decided to moderately increase (or decrease, in the rare cases where the crash was during high 

flows) all inflows listed in table 1 for the month of the crash and restart the run at the beginning of the 

water year during which the crash occurred. This process was automated, successively increasing (or 

decreasing) the crash month's flows until the run was successful or a limit imposed on the multiplicative 

factor being applied to the flows was reached. In the case of only six individual months out of all 

scenarios run, this approach still did not prevent the crash, and a fallback solution of replacing the crash 

month's inflows with inflows from the same month in the previous water year was implemented. In this 

way, all C2-CalSim runs were completed. In nearly all cases, this approach is nudging extreme flows to 

be slightly less extreme, so the overall effect on results is small. The average number of months (over all 

scenarios) whose inflows were altered in this manner was 15 months out of 1,440 over the 120-year 

scenario. The scenario with the most altered months was GFDL-CM3/RCP8.5, which had 35 altered 

months. Averaged over all WYs in a scenario, the maximum (among scenarios) resulting alteration in 

WY-total flow was 0.5 percent, for the GFDL-CM3/RCP8.5 scenario. Averaged over all scenarios, 

flows were altered 0.2 percent.

Finally, all needed flows, diversions, operational time series, and storages were extracted from 

the resulting output files. Time series extracted from the C2-CalSim runs are as follows:

• Reservoir storages: Shasta, Oroville

• Reservoir outflows: Oroville, Keswick, Black Butte Dam, Nimbus, Camp Far West, 

Whiskeytown

• Flows at these locations: Cosumnes, Vernalis, Verona, Yolo Bypass

• Exports: Tracy and Banks pumping plants, North Bay Aqueduct, Rock Slough (Contra Costa 

Water District [CCWD]), Old River+Victoria Canal (CCWD), BDCP “isolated facility” tunnel 

intake (only used in the BDCP PA scenario)

• Other operations: Sacramento Weir flow, number of days per month that C2-CalSim simulated 

the Delta Cross-Channel gates as being open

All steps above were completed for the ECNAA sequence, which will provide flows for the 

CASCaDE2 climate-change-only scenarios, and for the ECPA study, which will provide flows for the 

CASCaDE2 alternative conveyance scenarios.

4.7. Application of C2-CalSim in CASCaDE2: Limitations and Future Work

In attempting to represent the future behavior of a complex freshwater management network like 

California’s, several difficulties are encountered. Projecting freshwater demands is difficult, and for 

CalSim 2, demand scenarios were only available for California’s LOD in 2005 (used in the BDCP EC

study) and the LOD projected for 2030 (used in the PA and other BDCP studies). In CASCaDE2, all 
18

C2-CalSim runs use the 2005 LOD until the beginning of WY 2030, after which they use the 2030 

LOD. This necessarily introduces errors into the results, with a key limitation being that projections well 

past 2030 almost certainly underestimate freshwater demands, barring major changes in California 

water-use patterns and (or) much lower population increases than are currently projected.

Another problem is that freshwater management infrastructure is not static. Representing the 

numerous historical infrastructure changes is difficult, and predicting future changes is impossible. The 

only infrastructure changes considered in CASCaDE2 are those inherent in the different infrastructure 

scenarios—for example, changes including new tunnels and a new notch in Fremont Weir in the PA

configuration as opposed to a largely present-day infrastructure for the climate-change-only (NAA) 

scenarios. For a given scenario, the only changes in freshwater management infrastructure and 

management goals are those associated with the transition from the EC configuration to either the NAA 

or the PA configurations in WY 2030. The results may therefore be interpreted as potential changes that 

additional future adjustments to management infrastructure and goals beyond those represented here 

may be designed to help mitigate.

A limitation of CalSim 2 (and therefore of C2-CalSim) is its treatment of groundwater 

withdrawals, which are allowed in the model to occur at unsustainable levels if other supplies of 

freshwater are insufficient to meet demands. This must be considered when interpreting results. In 

particular, simulated unsustainable withdrawal levels are indicative of an inability to meet freshwater 

demands through other means.

A standard step in new applications of CalSim 2 is to “retrain” the Water Supply Index-Delivery 

Index (WSI-DI) curve for a given hydrologic regime and model configuration. The WSI-DI curve 

relates available water supply (represented by WSI) and deliveries and carryover storage (DI) for the 

State Water Project and the Central Valley Project. A procedure exists for optimizing this curve for a 

given set of inputs. A good description of the WSI-DI curve and the retraining is given in section 3.3.1 

of California Department of Water Resources (2005). Initially, the plan for CASCaDE2 was to use the 

present-day WSI-DI curve for the baseline historical run and for WYs 1980–2019 in all future scenarios 

and to retrain WSI-DI separately for WYs 2020–2059 and 2060–2099 for each scenario. This would 

allow some amount of management “adaptation” to changing hydroclimatic conditions. However, the 

additional model runs involved in the retraining would have increased total model time by a factor of 7,

resulting in about a month of total C2-CalSim run time. This amount of additional time was considered 

prohibitive, and the resulting caveat is that calculated deliveries and carryover storage allocations may 

be suboptimal, particularly later in the future scenarios. Additionally, the intent of the CASCaDE2 C2-

CalSim runs is to explore implications of climate change on managed flows using current management 

infrastructure and strategy, and WSI-DI retraining would be counter to this intent. 

Finally, the failure to include a representation of the effects of SLR in C2-CalSim was discussed 

in section 4.5. This results in an underestimation of Delta outflows required to repel saltwater in the dry 

season and an overestimation of the salinities in the corresponding hydrodynamical simulations. 

Separate CASCaDE2 work (Roseanne Martyr-Koller, University of California, Berkeley, written 

commun.) has resulted in hydrodynamical-model-based estimates of the amount of additional outflow 

needed to meet salinity standards for a range of future SLR values. These results complement the 

present work by quantifying additional outflows that would be needed to meet salinity standards under 

the 20 scenarios evaluated. However, additional work will be needed to understand the feasibility of the 

required additional reservoir releases, given the increasing tensions between supply and demand already 

depicted in the scenario evaluations.
19

5. CRESPI 

C2-CalSim produces monthly estimates of managed flows. For evaluations of estuarine 

hydrodynamics and ecological behavior being undertaken in CASCaDE2, we also need to represent 

daily flow variability. The CRESPI method, described in section 5.1, simulates daily managed flows by 

resampling from the historical record. In order to better simulate the effect of reservoir management on 

peak impaired flows, we partitioned the historical training data used by CRESPI. This partitioning was 

based on whether the reservoir storage was in a state of surplus or deficit. This modification, described 

in section 5.2.2, helps capture the tendency for high flows to occur when reservoirs are storing a surplus 

of water.

5.1. Method

In the CRESPI algorithm, at each location where daily managed flows were needed, we worked 

with time series of two streamflow variables: the unimpaired time series and the impaired time series.

For the historical time series 1950–2013, we had observations of the impaired time series and 

simulations of the unimpaired time series. For the projected time period, we had only the unimpaired 

simulation. We used a resampling-based approach to generate the time series of the impaired variable 

based on the projected unimpaired time series. This approach involves sampling contiguous sections, or 

blocks, of the historical impaired time series and concatenating them to form an impaired time series for 

the projected period. The CRESPI algorithm can be divided into two steps. In the first step, a daily time 

series of the impaired variable is generated without considering dependence or continuity between 

adjacent blocks; in the second step, this time series is re-generated by considering neighboring daily 

values, allowing artifacts from the first step to be reduced.

5.1.1. First Step: Matching Blocks 

The procedure for generating the projected impaired time series using the unimpaired time series 

x is as follows. The algorithm steps through the projected time series month by month. For each month 

m (which varies from 1 to the number of months in the series) of length l (where l can be 28, 29, 30, or 

31, depending on the month and year) of the projected time series, the algorithm extracts the unimpaired 

time series xx�uumm

ff �, where uu is a vector of the time indexes for month m in time series f (for “future”). 

The algorithm then searches all blocks of l days in the historical (h) unimpaired time series for the Nb

most similar blocks xxii(uunn

h) where n ranges from 1 to the number of l-day blocks in the historical time 

series and i ranges from 1 to the predetermined value Nb. In CASCaDE2, a value of Nb=30 was chosen 

after some experimentation. Similarity is measured by the root mean square error between xx�uumm

ff � and 

xxii(uunn

h). 

At this point, a monthly mean constraint can be imposed if available. In CASCaDE2, C2-CalSim 

projections of mean monthly flows were available at many locations of interest throughout the 

watershed. The following approach was tested: from among the Nb similar blocks of daily data, the one 

whose mean best matches the constraint (that is, differs least from the C2-CalSim projection for the 

future month being matched) was selected as the optimal xx(uunn

h). However, this additional restriction on 

the historical impaired data available for matching proved too restrictive and led to unacceptably high 

errors when evaluating historical results against observations. The monthly constraint option of the 

CRESPI method was therefore not implemented for CASCaDE2. 

With no monthly constraint imposed, the most similar block according to the RMS (root-meansquare) measure described above is selected as the optimal xx(uunn

h). When xx(uunnh) has been selected, the 
20

values of the simultaneous block of the impaired variable yy(uunn

h) are copied and inserted into the 

projected time series to become the values of the impaired variable for the current month, yy�uumm

ff �. 

5.1.2. Second Step: Smoothing Discontinuities 

In the first step (section 5.1.1), the daily time series is generated without considering the 

continuity or temporal dependence between adjacent blocks. As a result, time series generated in the 

first step may contain discontinuities at the block boundaries. We smooth these discontinuities by again 

selecting new patterns to estimate the impaired time series. We achieve this task by performing a 

procedure similar to the one described in section 5.1.1. By using the preliminary daily time series of the 

impaired variable for the projected time period generated in the first step, we can now search for the 

best-matching block of the impaired time series directly instead of assigning values to the impaired 

series based on the best match for the unimpaired series. In this step, we also include neighboring values 

of the block in the matching error metric in order to find patterns that are better associated with the 

temporal variability constructed during the first step. For example, for each month m of with length l

days of the projected time series, the algorithm extracts the impaired time series yy�vvmm

ff �, where vv is a 

vector of 2k+l time indexes—l for the month m in the projected time series (f) and k days before and 

after month m. In the application of this method in CASCaDE2, k=7. That is, in this smoothing step, the 

matching block contains the month m, the 7 days preceding the month m (the last 7 days of month m–1), 

and the 7 days following the month m (the first 7 days of month m+1). The number of preceding or 

following days included is zero when estimating streamflow in the first or last month of the projected 

time series, respectively. Although the k neighboring days are included in the match metric, they are 

discarded before inserting the matching block into the projected time series. 

In this second step, any monthly constraint used in step 1 is not re-applied—the algorithm 

searches each block of 2k+l days in the observed historical impaired time series for the single most 

similar block yy(vvnn

h); here, n varies from 1 to the number of 2k+l-day blocks in the historical impaired 

time series. Again, similarity is measured by the root mean square error between yy�vvmm

ff � and yy(vvnn

h). 

This second step reduces discontinuities between adjacent blocks that may have been generated during

the first step.

5.2. Application to CASCaDE2

The CRESPI method is applied individually to each of the points where managed flows are 

required. The unimpaired quantity is the routed streamflow generated by RVIC, and the impaired 

quantity is impaired streamflow at the same location (though the algorithm does not require the two 

quantities be collocated; just that they be strongly related as in upstream and downstream flows, for 

example,). The historical period used is the subperiod within January 1, 1950–December 31, 2013, in 

which the impaired data were observed and suitably representative of modern infrastructure. Where 

CRESPI is applied to a point downstream of either Lake Oroville or Shasta Lake, the historical training 

data are partitioned based on the observed storage minus the target storage, or the “storage excess,” as 

described in section 5.2.2. The projection time period extends from the beginning of the calendar year 

1950 to the end of calendar year 2099 or 2100, depending on the GCM scenario. After application of the 

CRESPI method, the time series were clipped to WYs 1980–2099, commensurate with the C2-CalSim 

results.
21

5.2.1. Historical Impaired Flow Data

The historical impaired flow data on which the future CRESPI projections are based (table 2) 

come from the U.S. Geological Survey (USGS) National Water Information System (NWIS; U.S. 

Geological Survey, 2018. We used historical streamflow data starting from either 1950, the beginning of 

the record, or the date when major upstream impairments went into service, whichever was latest. For 

example, for points below major dams, we used data starting in the water year after the date that dams 

were completed. For some streamflow stations, such as station 11376150 (Eagle Canyon Canal 

Diversion), we set the cutoff date to points where the patterns of flow changed significantly in the 

record. In most cases, these stations were below the impairments. Because no suitable station could be 

identified downstream of Lakewood Dam, station 11425310 (Lakewood), above the dam, was used.

The cutoff date for the data used for the points farthest downstream (Vernalis, Verona, Yolo, and 

Freeport), was the beginning of calendar year 1970 because most of the major dams in the SacramentoSan Joaquin River Basin had been completed by then. Some dams were completed after 1970, the 

largest of these being New Don Pedro Dam in 1971 and New Melones Dam in 1979 (California

Department of Finance, 2008), both in the San Joaquin River Basin.

For the impaired point located below Oroville/Thermalito, the sum of the data from stations 

11406920 (Thermalito) and 11407000 (Oroville) was used.

Table 2. Streamflow station records from the San Francisco Bay and Sacramento-San Joaquin Delta (Bay-Delta)

watershed, California, used as historical data in the Computational Assessments of Scenarios of Change for the 

Delta Ecosystem phase 2 (CASCaDE2) resampling algorithm (CRESPI) method.

[NWIS, National Water Information System database; Rec start, the beginning date of the record; Cutoff, the date before 

which data were excluded; Rec end, the ending date of the record; CDOF, California Department of Finance; YCWA, Yuba 

County Water Agency; CDWR, California Department of Water Resources]

NWIS site 

number

Station name

(upstream dam)

Rec start

(year–month)

Cutoff

(year–month)

Rec end

(year–month)

Note

11388000 Stony Creek below Black 

Butte Dam (Black Butte

Dam)

1955–07 1964–10 1990–09 Dam completed 1963 (CDOF,

2008).

11424000 Bear River near 

Wheatland (Camp Far 

West Dam)

1928–10 1964–10 2013–12 Dam completed 1963 (CDOF,

2008).

11423800 Bear River below Camp 

Far West Reservoir 

(Camp Far West 

Diversion)

1989–10 1989–10 2013–09

11451000 Cache Creek near Lower 

Lake (Cache Creek 

Dam)

1944–10 1950–01 2013–12 Dam completed 1910 (CDOF,

2008).

11376150 North Fork Battle Creek 

below diversion to 

Eagle Canyon Canal 

(Eagle Canyon Canal

Diversion)

1983–10 1995–10 2013–12 Flow behavior change in 1995.

11418000 Yuba River below 

Englebright Dam 

(Englebright Dam)

1941–10 1970–10 2013–12 Yuba River Development 

Project started 1970 (YCWA,

2012).

11447650 Sacramento River at 

Freeport

1948–10 1970–01 2013–12 Far-downstream point (multiple 

major impairments).

11451300 North Fork Cache Creek 

near Clearlake Oaks 

1983–10 1983–10 2013–12 Dam completed 1976 (CDOF,

2008).
22

NWIS site 

number

Station name

(upstream dam)

Rec start

(year–month)

Cutoff

(year–month)

Rec end

(year–month)

Note

(Indian Valley Dam)

11370500 Sacramento River at 

Keswick (Keswick

Dam)

1938–10 1950–01 2013–12 Shasta Dam completed 1945 

(CDOF, 2008).

11425310 Halsey Powerhouse near 

Auburn (Lakewood

Dam)

1980–10 1980–10 2013–09

11376025 North Fork Battle Creek 

below Macumber Dam 

(Macumber Dam)

1980–10 1989–10 2013–12 Dam completed 1907 

(Reynolds and Scott, 1980).

11375700 North Fork Cottonwood 

Creek near Igo 

(Misselbeck Dam)

1956–10 1956–10 1980–09 Dam completed 1920 (CDWR,

1990).

11325500 Mokelumne River at 

Woodbridge

1924–06 1964–10 2013-12 Dam completed 1963 (CDOF,

2008).

11458000 Napa River at Napa 1929–10 1950–01 2013–12

11446500 American River at Fair 

Oaks (Nimbus Dam)

1904–10 1957–10 2013–12 Folsom Dam completed 1956 

(CDOF, 2008).

11376015 North Fork Battle Creek 

below North Battle 

Creek Dam (North 

Battle Creek Dam)

1978–10 1978–10 2013–12 Dam completed 1912 

(Reynolds and Scott, 1980).

11407000 Feather River at Oroville 

(Oroville Dam)

1901–10 1969–10 2013–12 Dam completed 1968 (CDOF,

2008).

11459150 Petaluma River at 

Copland Pumping 

Station

1998–11 1998–11 2013–12

11406920 Thermalito Afterbay 

Release to Feather 

River

1967–11 1969–10 2013–09 Oroville Dam completed 1968 

(CDOF, 2008).

11303500 San Joaquin River near 

Vernalis

1923–10 1970–01 2013–12 Far-downstream point (multiple 

major impairments).

11425500 Sacramento River at 

Verona

1929–10 1970–01 2013–12 Far-downstream point (multiple 

major impairments).

11420700 Dry Creek near Browns 

Valley (Virginia Ranch

Dam)

1964–08 1964–10 1980–10 Dam completed 1963 

(AECOM, 2011).

11372000 Clear Creek near Igo 

(Whiskeytown Dam)

1940–10 1964–10 2013–12 Dam completed 1968 (CDOF,

2008).

11453000 Yolo Bypass near 

Woodland

1939–10 1970–01 2013–12 Far-downstream point (multiple 

major impairments).
23

5.2.2. Effects of Reservoir Storage Levels on Peak Flows

The results of the methods described in section 5.1 can be refined, particularly with regard to 

peak flows, by including information on reservoir storage levels, available as observed historical data 

and as C2-CalSim output for the future scenarios. The effects of California’s two largest reservoirs on 

peak flows are considered here.

The operations of Shasta Lake and Lake Oroville are guided in part by each reservoir’s “rule 

curve,” which determines the amount of the reservoir storage capacity to be reserved for flood control, 

or the “flood control pool” (Willis and others, 2011). The difference between daily storage and the 

target storage level (commonly referred to as “top of conservation” storage) is referred to here as 

“storage excess.” Releases of water from reservoir storage are governed by the release schedule. For 

Shasta Lake and Lake Oroville, the official release schedules require releases when storage excess 

becomes positive (that is, when there is water in the flood control pool).

Peak impaired flows in the lower Sacramento River Basin are associated with reservoir storage 

encroaching (or nearly encroaching) on the flood control pool. In other words, the highest outflows 

occur only when storage excess is relatively high (above zero, or negative but close to zero). In our 

approach, we use the rule curves for two of the major reservoirs in the Sacramento River Basin—Lake 

Oroville and Shasta Lake—to help us identify periods in the historical record where reservoirs were 

operating under similar conditions to those projected. For a given flow location, the largest upstream 

reservoir (Shasta or Oroville) is used to make these determinations.

An empirical storage excess threshold is established for each of these two reservoirs (discussed 

in section 5.2.2.1). Storage levels are interpolated from monthly values based on observations for the 

historical period and on C2-CalSim outputs for the future scenarios. On any future day of the 

simulation, if the storage excess falls below this threshold, blocks from the historical time series may 

not be selected if the maximum daily historical storage excess reached during that block exceeds the 

threshold. However, if the storage excess exceeds this threshold in the future period, the opposite 

restriction is not implemented. This method effectively implements a rule that prevents peak flows from 

being translated downstream of major reservoirs during drought years when the reservoir storage levels 

are below the selected thresholds.

5.2.2.1. Modeling the Flood Control Reservation

The target storage needs to be calculated not only for the future scenarios, but also for the 

historical period because observed data for historical target storages are incomplete. We therefore 

implemented a model to calculate the target storage in Shasta Lake and in Lake Oroville according to 

the guidelines provided in each reservoir’s flood control operations manual. In both cases, the target 

storages calculated for the historical period agreed well with available historical data.

5.2.2.1.1. Shasta Lake

The Shasta Lake rule curve is described in the reservoir operating manual (U.S. Army Corps of 

Engineers, 1977). It is based on a “ground wetness index,” which is computed as:

xt = 0.95 xt–1 + qt , (6)

where 

xt is the ground wetness parameter,

qt is the inflow (in cubic feet per second) for the current day t, and

xt–1 is the parameter for the previous day t–1.
24

xt has the same units as inflow (cubic feet per second) and is constrained by the constants xmin and xmax

(defined in equation 7) such that xmin ≤ xt ≤ xmax.

For each of the projected climate-change scenarios, the impaired inflows to Shasta Lake needed 

for this calculation must be estimated from the unimpaired streamflow produced by RVIC. The inflows 

are estimated by a series of linear regression models, one for each of the 12 calendar months in which 

the impaired inflow is the dependent variable and the unimpaired routed streamflow is the independent 

variable. The observed inflow and unimpaired routed streamflow data from the period 1995–2013 are 

used to train the models. This period was chosen because it had sufficient observed inflow data.

The ground wetness index is initialized to 100,000 cubic feet per second (ft3

/s) on October 1 of 

each year, so that xt(10/01) = 100,000 ft3/s. For a given xt, the target reservoir storage s(xt, t) can take a 

value over the range between a time-invariant minimum storage smin and a maximum storage smax. The 

absolute minimum target storage during the flood season is smin = 3,252,100 acre-feet (acre-ft) , and the 

maximum target storage during the flood season is smax = 4,552,100 acre-ft.

Target storage is calculated as a function of date t and ground wetness parameter xt (fig. 6):

(smin – smax) • (t – 01Oct) / (30Nov – 01Oct) + smax for 01Oct ≤ t < 30Nov

smin for 

30Nov

≤ t < 23Dec , (7)

s(xt,t) = a • (t – 23Dec) / (20Mar – 23Dec) + smin for 23Dec ≤ t < 20Mar

min(smax, smin + a + (smax – smin) • (t – 20Mar) / (15Jun –

20Mar))

for 

20Mar

≤ t 

where

a = (smin – smax) • (xt – xmin) / (xmax – xmin) + (smax – smin),

xmin = 110,000 ft3

/s,

xmax = 530,000 ft3/s,

and subtraction of dates indicates the number of days elapsed between dates.
25

Figure 6. Graph showing rule curve for Shasta Lake, California, calculated over the range of ground wetness 

parameters.

5.2.2.1.2. Lake Oroville

The rule curve for Lake Oroville is described in the reservoir operating manual (U.S. Army 

Corps of Engineers, 1970). The ground wetness index is computed as follows:

xt = 0.97 xt–1 + pt under the condition xmin ≤ xt ≤ xmax , (8)

where 

xt is the ground wetness parameter;

pt is the basin mean precipitation for the current day t; 

xt–1 is the ground wetness parameter for the previous day t–1. xt has the same units as precipitation (units 

of length); 

xmin=3.5; and

xmax=11.0.

The basin mean precipitation is computed as follows (U.S. Army Corps of Engineers, 1970):

pt = (ABP / NAP) • ∑i pt

(i) , (9)

where 

ABP = 44.1 inches (in.) (average basin precipitation for the entire Feather River Basin);

NAP = 412.8 in. (sum of average annual precipitation at eight streamflow stations; table 3); and

pt

(i) is the precipitation recorded on the current day t at the i

th of the eight stations.
26

Table 3. Average annual precipitation measured at eight rain gauges in the vicinity of the Feather River Basin, 

California, (averaging period unknown) (from M. White, California Department of Water Resources (CDWR), written 

commun., April 10, 2013).

[CDEC, California Data Exchange Center]

Station name CDEC station ID Average annual precipitation

(inches)

Oroville Dam ORO 33.4

Strawberry Valley SBY 81

Brush Creek (CDWR) BRS 72.1

Sierraville (CDWR) SVL 26.6

Quincy (CDWR) QCY 41

Camptonville (CDWR) CAM 55.9

De Sabla (CDWR) DES 65.3

Canyon Dam CNY 37.5

Because precipitation projections are not available for each of these eight stations (table 3) for 

the projected climate change scenarios, the basin mean precipitation is calculated directly from the 

gridded downscaled precipitation data, and for the historical baseline it is calculated from the 

meteorological dataset by Livneh and others (2015).

The absolute minimum target storage during the flood season is:

smin(xmax) = 2,788,000 acre-ft , (10)

and the maximum target storage during the flood season is:

s(xmin) = 3,163,000 acre-ft. (11)

During the flood season, the value of smin(xt) then varies linearly between the two values defined in

equations 10-11 as a function of xt:

smin(xt) = s(xmin) + a • (xt – xmin) , (12)

where 

a = (smin(xmax) – s(xmin)) / (xmax – xmin) = (–50,000 acre-ft / ground wetness unit).

Target storage is calculated as a function of date t and ground wetness parameter xt (fig. 7):

(t – 15Sep) • (smin(xt) – smax) / (15Oct – 15Sep) + 

smax 

for 15Sep ≤ t < 15Oct

s(xt,t) = smin(xt) for 15Oct ≤ t < 31Mar , (13)

min(smax, b • (t – 31Mar) + smin(xt)) for 31Mar ≤ t

where b = 10,000 acre-feet per day (acre-ft/d) and smax = 3,538,000 acre-ft is the reservoir’s capacity.
27

Figure 7. Rule curve for Lake Oroville, California, calculated over the range of ground wetness parameters.

5.2.2.2. Storage Excess Thresholds

As mentioned in section 5.2.2, the target storage levels in Shasta Lake and Lake Oroville are 

simulated for each day of the projected time series as well as for the period of the historical training 

data. When searching for matching patterns from the historical training data as described in section

5.1.1, the algorithm checks whether or not the maximum daily storage excess reached during a given 

block exceeds the storage excess threshold. We used storage excess thresholds of –500,000 acre-ft for 

Shasta Lake and –100,000 acre-ft for Lake Oroville. The relations between these storage excess 

thresholds and peak impaired flows can be seen in figure 8. When the 30-day running maximum storage 

excess is plotted against the 30-day running maximum flow, the maximum flow observed within any

30-day window increases when the maximum storage excess is greater than these storage excess 

thresholds.
28 

Figure 8. Graphs showing the 30-day moving maximum storage excess in (A) Shasta Lake and (B) Lake Oroville 

reservoirs, California, versus the 30-day moving maximum daily impaired flow rates. The red lines show the storage 

excess thresholds (–500,000 acre-feet for Shasta and –100,000 acre-feet for Oroville) used to partition the 

historical training data.

The effect of these storage excess thresholds on selection of patterns from the historical data can 

be seen in figure 9. When the maximum storage excess dd within the block for month mm of length l days 

from the projected time series (using notation introduced in section 5.1.1), or mmmm �dd�uumm

ff ��, is below 

the storage excess threshold DD, a given l-day block nn from the historical time series may not be selected 
29 

if the maximum daily storage excess reached during that block, mmmm �dd(uunn

h)�, exceeds the threshold DD. 

The intent of this is to prevent peaks in unimpaired flow from being translated into impaired flow peaks 

when reservoirs have enough space to capture the high flows. 

Figure 9. Graph showing implementation of culling for Shasta Lake, California. The same approach is used for 

Lake Oroville, but with a different threshold). When the maximum storage excess in the projected block is less than 

the storage excess threshold, the algorithm only samples patterns where the maximum storage excess is also 

below this threshold D. 

5.2.3. Modeling Separation of Flow by Fremont Weir

Two of the key locations at which the CRESPI method was used to project impaired flows are 

northern boundary points of the D-Flow FM hydrodynamical model: Sacramento River at Verona and 

Fremont Weir above Yolo Bypass. Flows that do not overtop Fremont Weir proceed downstream to 

Verona, so Fremont Weir has the effect of separating Sacramento River flow into two components. We 

found that the CRESPI method performed better if it was used to project the sum of these two 

components, with the result being subsequently separated into the two flows using the method described 

below. 

Fremont Weir is the primary source of flow into Yolo Bypass (design capacity 343,000 ft3

/s) 

(Russo, Mitch, comp. and ed., 2010). The remaining sources include the Sacramento Weir, downstream 

of Verona, and several west-side tributaries including the Knights Landing Ridge Cut, Cache Creek, 

Putah Creek, and Willow Slough. 

Water flows over Fremont Weir into Yolo Bypass when the Sacramento River exceeds a stage of 

33.5 ft, which corresponds to a flow rate of approximately 62,000 ft3/s at Verona (U.S. Army Corps of 

Engineers, 1999). 
30

Data for daily discharge over Fremont Weir are not available between July 1976 and January 

1984. However, a record of daily flow rates in Yolo Bypass, near Woodland, Calif., is available for the 

full time series from 1970 through 2010. An analysis of the relation between flow over Fremont Weir 

and flow over Yolo Bypass for the period 1984–2010 suggests that flows over Fremont Weir during this 

period can be well approximated by the data from Yolo Bypass at Woodland (fig. 10).

Figure 10. Graph showing mean daily flow over Fremont Weir versus flow in Yolo Bypass near Woodland, 

California, 1984–2010. 

The Woodland data are influenced by the smaller contributions to Yolo Bypass flow from Cache 

Creek and Knights Landing Ridge Cut. Therefore, using the Woodland gauge as a proxy for Fremont 

Weir flows implicitly includes these smaller sources in the estimated flows as well. However, the Yolo 

gauge near Woodland has historically not reported flows under 1,000 ft3

/s. To improve the 

representation of the smaller contributions for Woodland flows under 1,000 ft3

/s, we substitute Cache 

Creek flows for unreported Yolo flows. Cache Creek is the major source of inflow above the Yolo 

gauge other than Fremont Weir, for which observed flows have insufficient temporal coverage to be 

used here. The impact of that omission should be minimal, because overtopping of the Fremont Weir 

occurs infrequently when flows at Yolo near Woodland are less than 1,000 ft3

/s.

A source of uncertainty is that the Fremont Weir flow signal could attenuate by the time it 

reaches the Woodland streamflow station. Also, contributions to Yolo Bypass flow from the Sacramento 

Weir, Putah Creek, and Willow Slough all enter the Bypass below the Woodland gauge and their 

contributions are not included in flow estimates based on that gauge. Keeping these caveats in mind, we 

concluded that the relation depicted in figure 10 is sufficiently strong to justify the use of Woodland 

flows as a proxy for Fremont Weir flows.

With sufficiently complete historical time series for flows at the Sacramento River at Verona and 

Fremont Weir determined, the next step was to determine how to calculate each component based on 

their sum, which was calculated in the previous steps of the CRESPI method. We estimate the flow over 

Fremont Weir by fitting a two-piece linear regression model in which the combined flow is the 

independent variable and the flow in Yolo Bypass is the dependent variable. Two regressions are 

estimated from data where combined Verona and Yolo flow are above or below the 62,000 ft3

/s
31

threshold. The separate fit for combined flows below the threshold allowed for inclusion of the 

occasional Fremont Weir flows that occur below the threshold and for contributions from Cache Creek 

and Knights Landing Ridge Cut. Flows into Yolo Bypass are then estimated by applying the piecewise 

regression to the projected combined flow at Verona.

6. Combining C2-CalSim and CRESPI Results

The projections of daily managed flow produced using the CRESPI method described in section 

5 were used directly for smaller basins, as described in section 2.2. For larger basins, it is important to 

capture the response of management to long-term trends, which could shift managed flow patterns (for 

example, peak flows) beyond the range of those in the historical data used in CRESPI. In those cases, it 

was necessary to scale the CRESPI output to more closely represent the response of operations to longterm trends as represented in the C2-CalSim output.

The approach used was inspired by the “epoch adjustment” method used in other studies (for 

example, Abatzoglou and Brown, 2012). Here, our intent is to retain the representation of daily 

variability provided by CRESPI while also capturing the more dynamic (not constrained to historical 

range) response of operations to long-term trends as represented in the C2-CalSim output. For each 

projection of flows at a given location, a 31-year moving average of monthly averaged flows is 

calculated for each month of the water year (one time series for all Octobers, another for all Novembers, 

and so forth) for WYs 1980–2099. This is done for CRESPI and C2-CalSim outputs. All resulting 

smoothed time series are then divided by their WY 1995 value, corresponding to the WY 1980–2010 

average. This normalizes each time series to its own historical average, which can differ from the 

observed historical average for the GCM scenarios. (Recall that each GCM provides its own realization 

of the historical period, constrained only by historical greenhouse gas concentrations.) An adjustment 

factor (AF) time series is then produced by dividing each smoothed, normalized C2-CalSim-derived 

time series by its CRESPI counterpart. The 12 AF time series for each month of the water year are then 

collapsed into a single monthly AF time series and interpolated to daily time series using a meanpreserving interpolation (Rymes and Myers, 2001). Finally, each daily CRESPI projection is multiplied 

by its corresponding daily AF time series, resulting in a projection of managed flows at a given location 

that possesses realistic daily variability but also preserves long-term trends. 

7. Evaluation of Model Performance

Flow characteristics for observed and modeled impaired Sacramento River Basin outflow (the 

sum of flows from the American River at Nimbus, the Sacramento River at Verona, and in Yolo 

Bypass) for WYs 1980–2013 are shown in figure 11. To evaluate model performance, VIC and RVIC 

were driven by the observation-based Livneh historical meteorological dataset (Livneh and others, 

2015). The resulting RVIC outputs were used to drive C2-CalSim and CRESPI in the usual manner, 

except that in selecting matching historical patterns, the historical resampling of standard CalSim 2 

inputs used in C2-CalSim and the resampling of historical data used in the CRESPI method always 

excluded the WY or pattern being matched (that is, “leave-one-out”).
32

Figure 11. Evaluation of performance of combined C2-CalSim/CRESPI method for Sacramento River Basin, 

California, outflows for the historical period, water years 1980–2013. Tick marks for top two panels are in the 

middle of water years (that is, April 1). A, monthly total major reservoir storage; B, daily flow rates; C, mean annual 

flow rates; D, fraction of total WY flow arriving before April 1; and E, frequency of extreme daily flows exceeding the

99th-percentile threshold for the period shown. 

Simulated and observed total monthly storage in Shasta, Oroville, and Folsom reservoirs (fig. 

11A) agree reasonably well for our purposes, with a correlation coefficient of 0.87 and an RMS error of 

0.83 million acre-feet. Performance for storage in the major reservoirs of the San Joaquin Basin (not 

shown) is similar, with a correlation of 0.85 and RMS error of 0.57 million acre-feet (the observed total 

San Joaquin Basin storage averaged over the period shown is 3.7 million acre-feet). The correlation 

between observed and modeled daily flows (fig. 11B) is 0.88, and the RMS error is 16,617 ft3

/s. A 

tendency to underestimate peak daily flows is evident. Modeled mean annual flow rate (fig. 11C) is 

captured well, though the limited number of data points does not support robust error statistics. Finerscale measures such as intra-annual flow timing and peak flow frequency (fig. 11D-E) capture the 

observed variability reasonably well, though a tendency to underestimate peak flows is again evident in 

the latter. 

The main goal of this work is to provide plausible values for managed daily flow inputs to the 

Bay-Delta estuarine hydrodynamical model, D-Flow FM, under a range of future scenarios. Detailed 
33

performance metrics for the period WY1980–2013 for sites that serve as inflow boundaries for D-Flow 

FM are listed in tables 4-5. The locations of these boundaries are shown in figure 1.

Table 4. Intramonthly performance metrics at inflow boundary locations for the San Francisco Bay and 

Sacramento-San Joaquin Delta (Bay-Delta) estuarine hydrodynamical model, Deltares Flow Flexible Mesh 

hydrodynamical model (D-Flow FM). [%, percent; RSR, ratio of the root mean square error to the standard deviation of observations; r, Pearson’s correlation 

coefficient; See figure 1 for site locations]

Yolo Verona Nimbus Cosumnes Mokelumne Vernalis

Simulated versus observed monthly mean flows

% bias -6.1 -2.0 -0.015 -6.0 -1.7 -1.7

RSR 0.44 0.50 0.57 0.37 0.69 0.87

r 0.90 0.88 0.83 0.93 0.74 0.59

Standard deviation of daily flows within each month

% bias -8.5 -7.6 -6.7 -17 4.1 5.2

RSR 0.47 0.71 0.57 0.43 0.84 0.84

r 0.88 0.73 0.83 0.90 0.60 0.61

Monthly maximum flows

% bias -5.1 -1.9 -1.8 -15 3.8 3.9

RSR 0.47 0.48 0.55 0.55 0.67 0.83

r 0.88 0.89 0.84 0.84 0.75 0.63

Table 5. Intra-WY performance metrics at inflow boundary locations for the San Francisco Bay and SacramentoSan Joaquin Delta (Bay-Delta) estuarine hydrodynamical model, Deltares Flow Flexible Mesh hydrodynamical 

model (D-Flow FM). [%, percent; RSR, ratio of the root mean square error to the standard deviation of observations; r, Pearson’s correlation 

coefficient; See figure 1 for site locations]

Yolo Verona Nimbus Cosumnes Mokelumne Vernalis

Simulated versus observed monthly mean flows

% bias -5.5 -2.3 -0.033 -6.1 -0.23 -1.0

RSR 0.32 0.30 0.40 0.35 0.51 0.66

r 0.95 0.96 0.94 0.97 0.90 0.75

Standard deviation of daily flows within each month

% bias -9.2 7.2 3.4 -6.8 29 24

RSR 0.24 0.40 0.39 0.37 0.56 0.72

r 0.97 0.93 0.92 0.93 0.87 0.74

Monthly maximum flows

% bias -5.8 3.3 2.3 -10 25 22

RSR 0.31 0.42 0.54 0.62 0.66 0.80

r 0.95 0.91 0.84 0.80 0.81 0.67

For each flow site, simulated and observed monthly mean flows were calculated. Also, for each 

month, standard deviation and maximum values for that month’s daily flows were calculated. The 

resulting monthly time series for simulated and observed flows for each site and flow statistic were 

compared using three performance metrics. These are percent bias, which is 100 times the sum of the 

monthly differences between simulated and observed flows divided by the sum of the observed monthly 

flows, the ratio of the root mean square error to the standard deviation of observations (RSR), and the 

Pearson correlation coefficient r. These intramonthly performance statistics are presented in table 4. The 

same statistics but calculated at the WY scale instead of the monthly scale, are in table 5.
34

Intra-WY and intramonthly statistical performance measures are generally satisfactory for the 

purposes of future-scenario evaluation, with the best performance at Yolo, Verona, and Nimbus. The 

magnitudes of biases in mean, standard deviation and maximum are less than 10 percent at these sites, 

though Yolo’s biases are more negative than the others. This reflects the overall tendency of our method 

to underestimate peak flows, which affects performance in Yolo more strongly than other sites because 

the Yolo Bypass is fed primarily by peak flows over Fremont Weir. RSR values at Yolo, Verona, and 

Nimbus are all less than or close to 0.7. Moriasi and others (2007) suggest an RSR of 0.7 as a 

reasonable threshold for streamflow models. Correlation coefficients are all above 0.7. 

At Cosumnes, RSR and r values are good, but bias values are more negative than at other sites, 

particularly for standard deviation and maximum at the intramonthly scale. Underestimation of 

Cosumnes flow means, standard deviations and peaks for the period WY1980–2013 may in part be an 

artifact of the use of training data starting in 1950 in conjunction with positive trends in these flow 

statistics on the Cosumnes (Booth and others, 2006), possibly associated with rising snowlines resulting 

from a warming climate. Such trends may have been more effectively mitigated by reservoirs on the 

other rivers evaluated here than on the largely unimpaired Cosumnes and would not cause similar 

artifacts at those sites. Fortunately, Cosumnes inflows constitute a small fraction of total Delta inflows.

Mokelumne and Vernalis flows have good bias values at the intramonthly scale (table 4), but 

intramonthly RSR values are higher and r values are lower than at the other four sites. Intra-WY 

statistics (table 5) compare similarly, with the exception of high positive biases (>20 percent) in 

standard deviation and WY-maximum daily flow. A key difference between these two sites and the 

other four is that in Vernalis’ upstream watershed (the San Joaquin River Basin) and, to a lesser degree, 

in the Mokelumne River Basin, the total storage capacity is comparable or larger than the basin’s 

average total unimpaired WY flow (Knowles, 2000). In cases such as these, where WY flow volumes 

are comparable or smaller relative to the size of reservoir storage, the CRESPI method as applied here 

does not perform well by the above measures. This is because the method assumes a strong relation

between impaired and unimpaired flows, which is not always the case for these sites. Fortunately, biases 

at the submonthly and monthly scales (table 4), and at the WY scale (table 5, row 1) are very low for 

these sites, and the Sacramento River Basin sites which dominate Delta inflow variability and peaks 

(Yolo, Verona, and Nimbus) perform much better in the metrics for standard deviations and maxima.

Some errors are unavoidable given the nature of this approach and the limitations of the models 

involved. For example, the version of C2-CalSim used to simulate WYs 1980–2013 contains a static 

configuration of management infrastructure and strategies representing conditions in 2005, whereas the 

actual strategies, and to some degree the infrastructure, deviated from this static configuration 

considerably during WYs 1980–2013. Also, the historical period (WYs 1970–2013) used in the CRESPI 

method represents a limited range of hydrologic patterns from which to select matches, and even the 

best matches available may not be good ones, particularly with regard to conditions that occurred 

relatively rarely, such as extreme flows. Indeed, the “leave-one-out” cross-validation ensures that the 

maximum flow for the evaluation period is underestimated. This is a likely reason for the tendency to 

underestimate peaks seen above.

8. Conclusions

The joint application of C2-CalSim, a modified version of the California Department of Water 

Resources CalSim 2 freshwater operations model, and a new algorithm created to estimate daily 

managed flows (CRESPI) provides a new capability for evaluating the response of the freshwater 

management infrastructure to scenarios of future change. Although many caveats and opportunities for 

improvement remain, the basic approach outlined here allows for the direct evaluation of new 
35

hydroclimatic scenarios, such as those derived from GCM outputs. This approach was developed to 

provide plausible estimates of managed downstream flows for inputs to watershed sediment and 

estuarine hydrodynamical and ecological models as part of the CASCaDE2 project but could ultimately 

prove useful for similar projects whose goal is to translate GCM scenarios into downstream boundary 

conditions for studies of regional and local climate change impacts. Some of the methods presented here 

could also be transferable to similar studies in other impaired watersheds. 

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