II.3.3 - Scenario Mode Flow Generation

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

• t = Julian day (t = 1 to 365)
• Y_t = estimated daily flow
• m = mean annual flow computed over a 10 year period
• p = fraction of mean annual for the scenario
• e_t = stochastic error term
• F_t = Fourier term

(17)

• a_k, b_k = Fourier coefficients estimated for each river
• = 2/365

(18) where

• r_t = randomly generated variable from a normal distribution centered on 0 with variance appropriate for dry and wet years as described above. The switch from dry year to wet year variance parameters occurs at p = 0.4.
• e₀ = 0.

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

• dV = change in reservoir volume in acre-ft
• dt = time increment, typically 1 day
• F_U = unregulated natural flow into the reservoir in kcfs
• F_R = regulated flow out of the reservoir, which is controlled by the user under volume constraints in kcfs

(20) where

• V(i) = reservoir volume time step i with units of acre-ft
• t = one day increment
• F_U and F_R = unregulated and regulated flows in kcfs
• c = 1983.5 is a conversion factor

  acre-ft = (86400 s/d) * (0.023 acre-ft/ k ft³) * (k ft³ / s) * (d)

  V = (86400) * (0.023) *(F) * ( t)

  V = 1983.5 * (F) * ( t)

(21)

with constraints on reservoir outflow and volume defined by the algorithm

________________________________________________

if V_request(i+1) > V_max then

V_request(i+1) = V_max

F_R(i) = F_U(i) + [V(i) - V_max ] / c

else

if V_request(i+1) < V_min then

V_request(i+1) = V_min

if F_request(i) > F_U then

F_R(i) = F_U(i)

else

F_R(i) = F_request(i)

else

F_R (i) = F_request(i) (22)

_________________________________________________

where

• F_R = outflow from reservoir according to the constraints
• F_U = unregulated inflow to reservoir
• V_request = requested outflow from reservoir
• F_request = requested outflow from reservoir
• V(i) = reservoir volume in reservoir time step i
• V_max = maximum reservoir volume
• V_min = minimum reservoir volume

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

(23) where

• = 2/365
• k = value between 1 and 4

(24)

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

Data

The daily flow from Hydrodata, a CD-ROM database marketed by Hydrosphere, Inc., were obtained for the following locations and dates:

• Clearwater River @ Orifino, Idaho: Oct. 1980 - Sept. 1989
• Salmon River @ Whitebird, Idaho: Oct. 1980 - Sept. 1989
• Grande Ronde River @ Troy, Oregon: Oct. 1980 - Sept. 1989
• Imnaha River @ Imnaha, Oregon: Oct. 1980 - Sept. 1989

Table 5 shows parameters estimated for the unregulated headwater modulators. Parameters mod_coeffs_a and mod_coeffs_b correspond to a_k and b_k 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 US Army Corps of Engineers, North Pacific Division and processed as in Table 6. Data were obtained for the following locations and dates:

• North Fork Clearwater River Oct. 1973 - Sept. 1991
• Grand Coulee Dam Oct. 1971 - Sept. 1991
• Brownlee Dam Oct. 1981 - Sept. 1991

Maximum Unregulated Flows

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

Storage Reservoirs Parameter Values

Storage reservoirs volumes are obtained from Project Data and Operating Limits (1989 a and b) and are given in Table 8.

Desired reservoir elevation levels for flood control, obtained from Project Data and Operating Limits (1989 a and b), are presented in Table 9. This is not used by CRiSP.1 at the present time.