CRiSP1.6 Theory & Calibration Manual: II.2 - Flows INDEXTOCPREVNEXT

II.2 - Flows

II.2.1 - Overview of Flow Computation

This section defines the theory for calculation of flows in CRiSP.1. Flow information is treated differently for the Monte Carlo and Scenario modes. In the Monte Carlo Mode, average flows over defined periods at the dams are read as input from flow archive files (see Hydroregulation Models for more information on flow archive files). The period average flows are then modulated to give simulated daily flows at the dams. Using this information, flows in the headwaters are calculated with an upstream propagation algorithm. Finally, flows through river segments are calculated from the headwaters with the downstream propagation algorithm. In the Scenario Mode, flows can be specified at headwaters using modulators based on historical flows or using the pointer to draw a curve in the GUI. Outflows from storage reservoirs are specified according to the volume constraints of the reservoirs. Finally, river flows are produced using the downstream propagation algorithm which combines storage reservoir flows and unregulated headwater flows.

II.2.2 - Monte Carlo Flow Calculation

When running CRiSP.1 in the Monte Carlo Mode, flow information is specified at dams from flow archive files generated by one of several hydroregulation models. CRiSP.1 uses a step-wise process to calculate daily headwater flows. These steps are as follows:

  1. read period-averaged flows at dams from the flow archive file
  2. modulate period-averaged dam flows to give daily dam flows
  3. modulate losses in reservoirs
  4. propagate upstream flows to determine daily headwater flows as well as gains and losses from river segments
  5. propagate downstream flows through all river segments using the headwater flows and gains and losses in river segments.

Calculation of river flows in Monte Carlo Mode begins with flows at the dams and distributes upstream flows to achieve a mass balance. The procedure uses water conservation equations for losses/gains in river segments, flows in unregulated streams, and flows from storage reservoirs. Definitions for flow calculations (Fig. 5) are as follows:

Fig. 5 Main objects for the Flow submodel



Hydroregulation Models

Flow for the Monte Carlo runs are usually obtained from flow archive files that are generated from runs of hydroregulation models maintained by two agencies:

The models provide flow on a monthly or bimonthly basis over the entire Columbia Basin hydrosystem and are themselves complex models with many variables and special conditions. As a result, these models are not available to be run directly, although outputs of model runs are available for use in CRiSP.1 (the flow.data directory distributed with CRiSP.1 contains flow archive files for 1961 through 1994).

The models use information on natural runoff, regional electrical demand and storage capacity of the reservoirs to model the stream flow on a period averaged basis. The models use historical flow records for natural runoff and generate river flows that meet power generation demand in monthly periods. The exceptions to the monthly periods are April and August which are each divided into two periods. In addition, the HYDROSIM model provides elevations of all reservoirs.

The flow archive file can be used in Monte Carlo Mode as the source for flow, planned spill, and elevation. Information contained in a flow archive file includes:

Flow Modulation

Flow inputs in the Monte Carlo Mode runs consist of predicted daily flow averaged over monthly or bimonthly intervals at each dam used in CRiSP.1. This input generated from HYDROSIM or HYSSR flow archive files typically looks like Fig. 6 below. While this record retains most of the annual and seasonal flow variations, actual historic river flows (Fig. 7) exhibit considerable weekly and daily variations that are not replicated by the hydroregulation models used as flow data for CRiSP.1.

The purpose of the flow modulator is to more accurately simulate real flow patterns encountered by adding variations at finer time-scales consistent with historic flows. These variations include both random and deterministic components.

Fig. 6 Hydroregulation model simulated input - Wells, 1981



Fig. 7 Historic flows at Rocky Reach (next dam downstream from Wells), 1981



Spectral Analysis of Flow

The CRiSP.1 modulators were developed from the following analysis of flows in the Columbia River system. The goal was to develop a modulator that represented daily and weekly variations in flow and had the same spectral qualities as the flows in the river system as it is now operated.

A spectral analysis of an eleven-year time series (1979-1989) of flows revealed the general trend is a decline in spectral power that is qualitatively similar to a pink noise spectrum1. In addition, the spectrum has distinct peaks at frequencies of 1/7, 2/7, 3/7 etc., indicating a seven day cycle (Fig. 8).

This spectrum suggest several distinct processes. The weekly component is the result of flow decreasing on weekends when electric power consumptions is less. The pink noise element of the spectrum is probably the result of seasonal and short term correlations in weather patterns that alter the power consumption and unregulated runoff directly.

Fig. 8 Spectrogram: eleven year time series



Modulator Applications

The strategy for using period averaged archive flows to simulate flows with the spectral qualities of the actual ones involves adding flow variations at several points in the system (Fig. 5). These variations are produced by modulators. Since flows start in the headwaters and are summed downstream, flow variation can be added sequentially according to the manner by which they are produced. First, the archive flows are prescribed at all dams. Next, three modulations are applied. Weekly and daily modulations are added at the regulated headwaters to reproduce variations that occur between dams from additions and subtractions of water in the river segments and a loss modulation is added at downstream dams. After modulation, an upstream propagation process is applied to calculate the flows in unregulated headwaters. This forces the total modulation into the unregulated streams. In the case of the weekly modulation this is an artifact since it is induced by hydrosystem operation. The error is not significant though, since the weekly modulation is a small fraction of the total variation.

Fig. 9 Points of flow modulation in system based on Fig. 5



Weekly Modulators

The weekly modulation, applied in the regulated headwaters, simulates hydrosystem power generation patterns in which electrical demand decreases on weekends. The modulators, producing lower flows on weekends and higher flows midweek (Fig. 10), are approximated with a three-term Fourier series with fixed amplitude. The equation is:

(1)

where

The offset is calculated so that for any year from 1900 to 2100 the minimum value of F(t) occurs on Sunday.

Fig. 10 Weekly shape pattern



Daily Modulators

Daily modulation simulates all variations not associated with the weekly and seasonal variations. A discrete realization of an Ornstein-Uhlenbeck (O-U) process (Gardiner 1985) was used to generate the daily variation. The process has two important characteristics: variations are slightly correlated from one day to the next and variances stabilize over time. This is a correlated random walk in which autocorrelation decays in time. The stochastic differential equation for an O-U process is:

(2)

where

An O-U process has a conditional probability density function (Goel and Richter-Dyn 1974):

(3)

where the mean and variance of the process are defined:

(4)

. (5)

When rt is large enough that exp(-2rt) is negligible, m and V2 tend to be constant values and the time series is stationary.

Changing the continuous differential equation into a discrete one with t = 1 reservoir time step, and rearranging gives:

. (6)

The value r = 0 gives an unbiased random walk and r = 1 gives a series of uncorrelated normal variates.

For the modulators, a system in stochastic equilibrium is sought such that m = 0. Taking F0 = y = 0 gives m = 0, and discarding the first 35 iterations yields stable variance for any value of r useful in this context. Modulator parameters selected for the different portions of the system are given in Table 1 and are based on daily flow data for the years 1979 to 1989 at Wells and Lower Granite dams.

Table 1 Daily modulator parameters
River j rj
Upper Columbia 13 0.5
Lower Columbia 13 0.5
Snake 7 0.5


Random daily variation is added by a numerical form of an Ornstein-Uhlenbeck (O-U) random process created for each run (Fig. 11).

Fig. 11 O-U shape; r = 0.5, = 13



Monte Carlo Flow Modulator Validation

Using daily flow records for Ice Harbor, Priest Rapids and John Day dams during 1981, monthly and bimonthly (April and August) average daily flows were computed and appended to a CRiSP.1 flow archive from which CRiSP.1 generated modulated flows for these dams. Graphs of observed and model-produced flows for the first 300 days of the year at John Day Dam appear in Fig. 12. The model appears to produce realistic patterns of flow variation that mimic natural flows very well.

At a finer scale, however, note that CRiSP-modulated flows generally exhibit less variability than do observed flows, e.g. compare January and July (Fig. 13). In general, modulated flows are about as variable as observed flows in January, but clearly less variable than observed flows in July. This is also reflected in the variance around the mean flow, given in Table 2. This phenomenon is probably due at least partially to "step-like changes" of flows in July that do not occur in January. There is some variation around the mean due solely to that trend, and this will not be captured in a purely random modulation scheme.

Fig. 12 Flows at John Day Dam, 1981



Fig. 13 January and July flows at John Day Dam, 1981



Table 2 Variance about mean flow for observed and modulated flows at three dams in 1981
Dam Month Variance about monthly mean flow
Observed Modeled
John Day January 728.38 287.54
July 1620.08 401.74
Priest Rapids January 67.34 160.29
July 512.97 170.42
Ice Harbor January 247.65 156.96
July 149.83 61.83


Flow Loss

The term loss represents withdrawals from the system, mainly for irrigation. These withdrawals are positive in CRiSP.1. Negative losses are return flows through ground water.

The loss data in a segment represents the change in flow that occurs between the flow input (calculated from the flow of upstream segments) and the flow output (stored as data in the segment). Where not specified, flow loss is set to zero.

During the upstream propagation operation, new flow loss values are computed for reaches that lie between two dams. A dam is said to have no component of unregulated flow if no unregulated headwater flow enters the dam without first flowing through some regulation point.

For each reach r enclosed between a dam and upstream regulation points (Fig. 14), a new flow loss FL(r) is set by distributing any mass imbalance over all reaches between the dam and/or regulated inflow points in proportion to the maximum allowable flow in each reach:

(7)

where

Note: maximum allowable flows are set in the river description file, columbia.desc, using the flow_max token.

Flow loss is not modified by the upstream propagation in any reach not fully enclosed by regulated headwaters or dams. After appropriate loss values are set, flow loss in every segment is used as input data for unregulated headwater calculations.

Fig. 14 Diagram of reach structure for loss calculation



Reservoir Loss Modulation

At downstream dams, variations in flow from losses due to irrigation and evaporation and additions from surface and subsurface ground water flows are accounted for with loss modulators. The intensity of this variation is based on the differences in flows observed at adjacent dams as indicated in period averaged hydroregulation model flows (Fig. 15).

Fig. 15 Inputs at Rocky Reach minus inputs at Wells, 1981





The loss modulation is simulated with a white noise process (Fig. 16). A normal variate random factor is added to modulated flows of all run-of-river dams. The equation is:

(8)

where

Table 3 Flow loss modulator parameter for eq (8)
Dam i (kcfs) Dam i (kcfs)
Bonneville 11.0 Little Goose 5.4
The Dalles 4.1 Priest Rapids 4.0
John Day 17.0 Wanapum 5.0
McNary 12.75 Rock Island 2.65
Ice Harbor 2.75 Rocky Reach 3.0
Lower Monumental 2.4 Wells 6.5


Fig. 16 Random factor modulation at Rocky Reach, 1981



Headwater Computation

Once flows are modulated at dams and the losses and gains are calculated, the headwater flows can be calculated with the algorithms described below.

Regulated Headwater

Regulated headwaters are storage reservoir outflows for the Monte Carlo Mode. No losses are considered for storage reservoir flows other than the dam outflow.

Unregulated Headwaters

Each unregulated headwater is examined. If the flow for a given headwater has not yet been computed, then flow for that and all adjacent unregulated headwaters are calculated.

The region of computation for a segment is defined as all segments within the river map subgraph with endpoints consisting of the nearest downstream dam, and the nearest regulation points or headwaters upstream from the dam. An example of a region with several unregulated headwaters is given in Fig. 17.

Fig. 17 Region of regulated FR and unregulated FU rivers



To calculate the unregulated headwater flows, first the total unregulated flow input to dam r (D(1) in Fig. 17) is computed by subtracting the total regulated flow from flow at dam r. The equation is:

(9)

where

The total unregulated flow is then distributed over all unregulated tributaries upstream of dam r in proportion to each tributary's maximum flow, as specified in columbia.desc by the flow_max token. The flow coefficient K at each unregulated headwater i is the percentage of total unregulated flow contributed by that headwater and is defined:

(10)

where

Finally, the flow at each unregulated headwater in the region of the dam FU(i) is defined:

. (11)

The logic for the unregulated flow calculation is complete except when flow at any unregulated headwater falls below the minimum set in columbia.desc for that headwater, which can be zero. In this case:

(12)

and then for each reach r enclosed by dams the new loss FL(r) is:

(13)

where

Downstream Propagation

Downstream propagation of flow in the Monte Carlo Mode is computed after modulation, flow loss and unregulated headwater flows are computed. Starting at a headwater, flow is propagated by traversing the downstream segments, subtracting loss at each to determine new flow values, and adding flows together at confluences. Thus, flows are assigned at each segment in a downstream recursive descent traversal. The flow for each day is:

(14)

where

Combined Modulated Flow

The modulators are combined with archive flows to give daily flows at the dams according to the equation:

(15)

where

Minima are defined at each dam in the yearly input data file, base.dat by default, under the flow_min token. If the flow drops below the minimum, it is set to the minimum flow. Note: flow minima also exist in the columbia.desc file and are used to set minimum flows in river segments.

Table 4 Flow minimum (kcfs) at dams.
Dam Fmin(i) Dam Fmin(i)
Bonneville 100.0 Dworshak 1.0
The Dalles 0.0 Hells Canyon 5.0
John Day 50.0 Priest Rapids 0.0
McNary 0.0 Wanapum 0.0
Ice Harbor 9.5 Rock Island 0.0
Lower Monumental 11.5 Rocky Reach 0.0
Little Goose 11.5 Wells 0.0
Lower Granite 11.5 Chief Joseph 35.0


II.2.3 - Scenario Mode Flow Generation

In the Scenario Mode, seasonal flows for unregulated (i.e., un-dammed) streams are identified on a daily basis. These can be set by the user simply by drawing headwater seasonal flows when using the graphical user interface, or they can be generated from modulators that distribute the total annual headwater runoff according to the historical seasonal patterns.

Unregulated headwater flows connect directly to the river mainstem or to storage reservoirs. For storage reservoirs, the user can set the schedule of outflow according to constraints of the volume of the reservoir and the inflow. System flows are determined by unregulated stream flows and regulated flows from storage reservoir dams.

Headwater Modulation

In the Scenario Mode, flow from unregulated headwaters are modeled by the following equation:

(16)

where

(17)

The equation given for Ft above is a smooth Fourier estimate for the annual stream flow for each river, in units of multiples of the mean. For each scenario, an error term is randomly generated to incorporate the expected fluctuations. In the wet season (spring) when the exact fluctuations are more difficult to predict, there tends to be more pronounced deviations from the modeled curve. For this reason, the error component is generated from a low variance normal distribution in the dry season, and a higher variance normal distribution in the wet season. Also, since daily flows tend to be highly correlated, the generated (independent) error estimates (rt) are artificially correlated according to the following equation:

(18)

where

The user chooses the type of year to be modeled relative to an average year, which is designated by p = 1. CRiSP.1 multiplies this proportion of the appropriate average flow parameter, m times (Ft + et), which yields an estimate for daily flow for the Scenario Mode flow.

Reservoir Volume and Flow

The storage reservoirs receive flows from the headwaters which are set by the Scenario Flow Modulators or directly by the user. The flow out of the storage reservoirs can be set by the user under constraints established by the maximum and minimum volume of the storage reservoirs. The equation describing the reservoir usable volume is:

(19)

where

The volume for each reservoir is determined by a reservoir time step increment from a numerical form of the volume equation:

(20)

where

The user requests reservoir output FR with the following constraints. 1) The user is allowed to draw any flow curve for reservoir withdrawal as long as the reservoir is between minimum and maximum operating volumes. 2) If a request requires a volume exceeding the allowable range, CRiSP.1 alters the request to fit within the volume constraints. The algorithm is:

(21)

with constraints on reservoir outflow and volume defined by the algorithm2

where

Theory for Parameter Estimation

Average daily flow (designated flow_mean) was computed for all available years. Each daily flow was divided by that year's average. Elements of the resulting series were denoted by , where t = day_of_year. Next, the first nine terms of a Fourier series were computed with a fast Fourier transform. Since the mean of each series was 1, corresponding to the normalized annual mean flow, it follows a0 = 1.0. The remaining Fourier coefficients were estimated according to the equations:

(22)

where

The residual time series, Rt were computed by the equation:

. (23)

The residuals were split into high-variance and low-variance parts, and sample standard deviations computed. The julian day when high flow variance begins and ends are mod_start_hi_sigma and mod_end_hi_sigma, respectively. Period average high and low standard deviation are mod_hi_sigma and mod_lo_sigma, respectively.

Data

Daily flows from Hydrodata, a CD-ROM database marketed by Hydrosphere, Inc., were obtained for the following locations and dates.

Flow modulator parameter estimates derived from flow data listed above were compared to modulator parameters estimated from flows over the previous 10 years at the same location (Oct 1970-Sep 1980). The parameters were slightly different, but graphs of smooth flow curves were nearly identical for Clearwater, Salmon, and Imnaha rivers. The Grande Ronde had a different shape, so for this river the parameters were adjusted to include all data from 1970 to 1989.

Table 5 shows parameters estimated for the unregulated headwater modulators. Parameters mod_coeffs_a and mod_coeffs_b correspond to ak and bk respectively. Table 6 shows data for regulated headwaters, i.e., Columbia above Grand Coulee Dam, North Fork Clearwater above Dworshak Dam, and Snake River above Brownlee Dam. Daily mean flow observations for each year were obtained from the U.S. Army Corps of Engineers, North Pacific Division and processed as in Table 6. Data were obtained for the following locations and dates.

Table 5 Unregulated headwater flow parameter values

Deschutes Clear-water Middle Fork Salmon Wenatchee Methow
flow mean 5.00 8.79 5.00 11.24 5.00 5.00
mod coeffs a0 1.00 1.00 1.00 1.00 1.00 1.00
mod coeffs a1 0.00 -0.76 0.00 -0.84 0.00 0.00
mod coeffs a2 0.00 0.09 0.00 0.34 0.00 0.00
mod coeffs a3 0.00 0.10 0.00 -0.06 0.00 0.00
mod coeffs a4 0.00 -0.14 0.00 -0.09 0.00 0.00
mod coeffs b0 0.00 0.00 0.00 0.00 0.00 0.00
mod coeffs b1 0.00 0.87 0.00 0.50 0.00 0.00
mod coeffs b2 0.00 -0.72 0.00 -0.64 0.00 0.00
mod coeffs b3 0.00 0.35 0.00 0.44 0.00 0.00
mod coeffs b4 0.00 -0.16 0.00 -0.25 0.00 0.00
mod lo sigma 0.05 0.06 0.05 0.04 0.05 0.05
mod hi sigma 0.25 0.29 0.25 0.20 0.25 0.25
mod start hi sigma 46.00 46.00 46.00 86.00 46.00 46.00
mod end hi sigma 196.00 196.00 196.00 196.00 196.00 196.00


Table 6 Regulated headwater flow parameter values

Columbia Headwater Snake Headwater North Fork Clearwater
flow mean 110.00 21.50 5.00
mod coeffs a0 1.00 1.00 1.00
mod coeffs a1 -0.24 0.03 -0.51
mod coeffs a2 0.20 -0.13 -0.04
mod coeffs a3 0.00 0.01 0.16
mod coeffs a4 -0.04 0.00 -0.15
mod coeffs b0 0.00 0.00 0.00
mod coeffs b1 0.13 0.35 0.88
mod coeffs b2 -0.10 -0.16 -0.62
mod coeffs b3 0.10 0.05 0.16
mod coeffs b4 -0.02 -0.06 -0.08
mod lo sigma 0.06 0.05 0.23
mod hi sigma 0.08 0.10 0.31
mod start hi sigma 96.00 96.00 46.00
mod end hi sigma 196.00 196.00 196.00


Maximum Unregulated Flows

Observed maximum flows in the tributaries were obtained from the peak flow data in Hydrodata, a CD-ROM database marketed by Hydrosphere, Inc. The data record length was variable (Table 7).

Table 7 Maximum unregulated flow (kcfs)
Unregulated River Maximum Flow
Wind 30
Hood 30
West Fork Hood 15
East Fork Hood 15
Klickitat 39
Warm Springs 8
Umatilla 18
Walla Walla 21
Tucannon 5
Clearwater 166
Middle Fork Clearwater 78
Red 10
Salmon 129
Little Salmon 10
Rapid River 10
South Fork Salmon 19
Pahsimeroi 1
East Fork Salmon 4
Redfish 1
Yakima 64
Wenatchee 31
Entiat 6
Methow 33
Grande Ronde 36
Imnaha 6




Storage Reservoirs Parameter Values

Storage reservoirs volumes obtained from U.S. Army Corps of Engineers (1989a, 1989b) are given in Table 8.

Table 8 Storage reservoirs; shaded items are used in model
Reservoir Max Pool ft. Min Pool ft. Usable Storage in acre-ft. Powerhouse Hydraulic Capacity (kcfs)
Grand Coulee 1290 1208 5,185,500 280
Libby Dam 2459 2287 4,979,599 24.1
Hungry Horse 3565 3336 3,161,000 8.9
Duncan 1897 1794 1,398,600 20
Mica 2478 2320 7,770,0001 41.6
Coulee total2

22,494,699
Dworshak 1605 1445 2,015,800 10.5
Brownlee 2080 1976 975,318 34.5
1 estimated
 2 In the model, all storage reservoirs above Grand Coulee are summed to represent the combined storage capacity of the upper Columbia system.


Desired reservoir elevation levels for flood control obtained from U.S. Army Corps of Engineers (1989a, 1989b) are presented in Table 9. This is not used by CRiSP.1 at the present time.

Table 9 Storage reservoirs flood control elevation rule curves
Reservoir Date (Elevation in ft.)
Libby Dam Nov 1 (2459) Dec 1 (2448) Jan 1 (2411) -
Dworshak Sept. 1 (1600) Oct 1 (1586) Nov 15 (1579) Dec 15 (1558)


II.2.4 - Flow / Velocity / Elevation

The river velocity used in fish migration calculations is related to river flow and pool geometry and varies with pool drawdown as a function of the volume. The pool is represented as an idealized channel having sloping sides and longitudinal sloping bottom. As a pool is drawn down, part of it may return to a free flowing stream that merges with a smaller pool at the downstream end of the reservoir. The submodel is illustrated in Fig. 18 and Fig. 19. The important parameters are as follows:

Other parameters illustrated in Fig. 18 are used to develop the relationships between the parameters listed above and water velocity and pool volume. They are not named explicitly.

Pool Volume

Reservoir volume depends on elevation. Elevation is measured in terms of E, the elevation drop below the full pool level. The volume calculation is based on the assumptions that the width of the pool at the bottom and the pool side slopes are constant over pool length. As a consequence of these two assumptions, the pool width at the surface increases going downstream in proportion to the increasing depth of the pool downstream. When E >Hu, the drawn down elevation is below the level of the upstream end and the upper end of the segment becomes a free flowing river section that connects to a pool downstream in the segment. When E < Hu, the reservoir extends to the upper end of the segment and for mathematical convenience CRiSP.1 calculates a larger volume and subtracts off the excess. The volume relationship (as a function of elevation drop for E positive measured downward) is developed below.

The total volume is defined:

. (24)

The equation for V1 is developed as follows. Note that when E Hu, the volume V1 divides into two parts:

(25)

where V' is a side volume and V" is the thalweg3 volume. They are defined:

(26)

where

(27)

(28)

. (29)

Combining these terms, when E Hu it follows pool volume is:

. (30)

In terms of the fundamental variables in equations (25) to (30) this is:

(31)

for E Hu and x L.

Fig. 18 Pool geometry for volume calculations showing perspectives of a pool and cross-sections; the pool bottom width remains constant while the surface widens in the downstream direction.



Recall from eq (24) that when the pool elevation drop is less than the upper depth (so E < Hu and x = L), the pool volume is described by the equation . The term V1(E) is the volume of the pool extended longitudinally above the dam where the depth is Hu, so as to form the same triangular longitudinal cross-section as before. This is done so that the volume can still be expressed by eq (31). The term V2(E) is the excess volume of the portion of the pool above the dam and can be expressed:

. (32)

Summarizing, the volume relationship as a function of elevation drop, for E positive measured downward, is:

where

.

The equation for full pool volume can be expressed:

. (33)

When the bottom width is zero the full pool volume becomes:

. (34)

Water Velocity

Water velocity through a reservoir is described in terms of the residence time T and the length of the segment L. The residence time in a segment depends on the amount of the reservoir that is pooled and free flowing (Fig. 19).

Fig. 19 Reservoir with free flowing and pooled portions



The equations for residence time are:

(35)

where

The velocity in the segment is:

. (36)

The velocity with the above units is in thousands of feet per second. Combining equations (31), (32), (35) and (36) the segment velocities are:

for E Hu (37)

and

for E < Hu (38)

where

Flow / Velocity Calibration

The calibration of the volume equation requires determining the average pool slope from the pool volume. The equation is the smaller angle of the two forms:

(39)

where

This scheme using eq (39) reflects the volume versus pool elevation relationship developed for each reservoir by the U.S. Army Corps of Engineers. Capacity versus elevation curves were obtained from several dams to check the accuracy of our volume model. The figures below show data points from these curves versus CRiSP.1's volume curve for two dams. Fig. 20 illustrates Lower Granite Pool with model coefficients of Hu = 40 ft., Hd = 118 ft, = 80.7o, L = 53 miles, W = 2000 ft, and Wanapum Pool with model coefficients Hu = 42 ft., Hd = 116 ft, = 87.0o, L = 38 miles, W = 2996.1 ft.

Fig. 20 Pool elevation vs. volume for Lower Granite and Wanapum pools



Table 10 Geometric data on Columbia River system
Segment L Elev1 MOP2 V A3 W Hu Hd
Units miles ft MSL ft MSL kaf k ft 2 feet feet feet o of arc
Bonneville 46.2 77.0 70.0 565 101.8 3643 22 93 88
The Dalles 23.9 160.0 155.0 332 114.6 3624 60 105 87
John Day 76.4 268.0 257.0 2,370 255.9 5399 34 149 86.9
McNary 61 340.0 335.0 1,350 182.6 5153 40 105 88
Hanford Reach 44 --- --- 131 24.6 3213 29 29 ---
Priest Rapids 18 488.0 465.0 199 91.2 3208 32 101 87
Wanapum 38 572.0 539.0 587 127.4 2996 42 116 87.0
Rock Island 21 613.0 609.0 113 44.4 982 15 44 64.4
Rocky Reach 41.8 707.0 703.0 430 84.8 1815 37 108 84.5
Wells 29.2 781.0 767.0 300 84.8 3023 91 111 86
Chief Joseph 52 956.0 930.0 516 81.9



Ice Harbor 31.9 440.0 437.0 407 105.2 2154 18 110 83.3
L. Monumental 28.7 540.0 537.0 377 108.4 1937 42 118 81.3
Little Goose 37.2 638.0 633.0 365 80.9 2200 40 140 78.2
Lower Granite 53 738.0 733.0 484 75.3 2000 48 140 80.7
1 Elev is normal full pool elevation, in feet above mean sea level.
 2 MOP is minimum operating pool elevation.
 3 A is surface area.


The water particle residence time in a segment is given in eq (35). The pool volume velocity/travel time equation was tested against particle travel time calculations for Lower Granite Pool as reported by the U.S. Army Corps of Engineers in the 1992 reservoir drawdown test (Wik et al. 1993) (Fig. 21).

Fig. 21 Water particle travel time vs. flow for CRiSP.1 (points) and Army Corps calculations (lines) at two elevations full pool (0) and 38 ft below full pool for Lower Granite Dam.



II.2.5 - Temperature

River temperature is computed in two stages. First, hydrosystem temperature inputs are calculated from mixing headwater temperatures according to the equation:

(40)

where

Second, changes to the temperatures within the hydrosystem are made by adding (s,t) for each day t at site s where the true (t) for the site is known.

Headwater temperatures are identified for the Snake River using measured temperatures from Lower Granite Dam as available in the U.S. Army Corps of Engineers CROHMS database. Head water temperatures for the upper Columbia are identified from CROHMS and supplemented using data collected at streamflow gaging stations by the U.S. Geological Survey (see Fig. 45 for locations).

1 Pink noise is random pattern that exhibits some correlation for short time scales
 2
if Vrequest(i+1) > Vmax then
Vrequest(i+1) = Vmax
FR(i) = FU(i) + [V(i) - Vmax] / c
else
if Vrequest(i+1) < Vmin then
Vrequest(i+1) = Vmin
if Frequest(i) > FU then
FR(i) = FU(i)
else
FR(i) = Frequest(i)
else
FR(i) = Frequest(i)

 3 A thalweg is the longitudinal profile of a canyon.
CRiSP1.6 Theory & Calibration Manual: II.2 - Flows INDEXTOCPREVNEXT
Please direct questions or comments to:
web@cbr.washington.edu
Columbia Basin Research,
School of Aquatic & Fishery Sciences,
University of Washington