II.8.1 - Forebay Delay

The essential elements of this submodel include a forebay volume defined by the forebay depth H, a horizontal length scale L, which changes with illumination I, and river flow F (Fig. 49).

Fig. 49 Variables for dam passage delay model

Forebay Input

The number of fish entering the forebay in each dam time slice is determined by the number leaving the reservoir. Since reservoir time slices are longer than dam time slices, input from a reservoir is evenly distributed across the corresponding dam slices according to the formula

(133)

where

• S (t_j | t_i) = number of fish entering the reservoir on increment t_i

  and exiting the reservoir at increment t_j as defined in eq (62)

• J(t) = number of fish entering the forebay on dam slice increment t
• t = hours in a dam time slice, typically set for 2 hours
• T = hours in a reservoir time slice, typically set for 12 hours

Forebay passage is defined in terms of the following equation

(134)

where

• y = fish in forebay
• t = time (resolved to time of day and Julian day)
• J(t) = input to forebay from the reservoir
• p(F,t) = rate at which fish pass from the forebay into the dam
• F = flow through the dam in kcfs.

(135)

where

• t = duration of a dam time slice, typically 2 hours
• Y_t = number of fish in the forebay in the dam time slice t
• p (F, t) = forebay rate coefficient. This depends on the flow F, and an illumination dependent time t as is developed below.

To alter passage according to the diel distribution, the rate coefficient depends on time of day/light level. In addition, CRiSP.1 alters passage according to the river flow relative to the hydraulic capacity of the dam. The forebay rate coefficient is defined

(136)

where

• k = dimensionless constant which is species dependent describing the propensity of the fish to move with the flow
• F(T) = river flow in kcfs which depends on the reservoir time slice
• F_max = hydraulic capacity of a project in kcfs
• V_forebay(t) = effective forebay volume containing fish, which depends on illumination I as a function of time.

(137)

where

• H_forebay = depth of forebay
• L_day = forebay horizontal length scale associated with fish in full daylight
• L_night = forebay horizontal length scale associated with fish in the night. Note: L_day > L_night
• I = illumination which depends on season and time of day
• B(I(t)) = behavioral factor dependent on the illumination.

  This selects the appropriate length scale within a dam time slice. B is zero when the illumination is below a threshold level through the time slice and is one when illumination is above the threshold. For dam time slices in which the illumination crosses the threshold, B is the fraction of time the slice is above the threshold and is a function of the time of day and Julian date. (Fig. 50).

Fig. 50 Relationship between illumination and behavioral factor for dam time slices over a day

The illumination as a function of time of day and Julian date¹ is

(138)

where

• t = hour of day
• local noon = typically 1300 hr with daylight savings time
• D(T) = day length is a function Julian day, T,

  The vernal equinox is day 80 and the mean length of daylight is 14 hr so the equation is

(139)

The time before or after local noon when the threshold is crossed is determined by setting illumination equal to the threshold value and solving for t as

(140)

where

• t = time in hours before or after local noon of the threshold crossing
• I_threshold = light threshold at which fish behavior switches.

Variation in any of the dam delay parameters produce families of curves relating delay probability and time of day for a given fish depth, flow, and day of the year (see examples in Fig. 51).

Fig. 51 Family of trajectories for delay versus time of day under varying noon distance values.

Note that probability of delay does not map directly onto passage frequency. Passage will be affected by delay, but also by the arrival frequency of potential migrants and by the rate of predation that delayed smolts incur in the forebay. If smolt arrival is assumed to be uniform during the day (probably not accurate; A. Giorgi personal communication) and we assign an arbitrary predation loss of 10% during a two-hour time period, the delay probabilities shown in Fig. 51 produce diel passage patterns as shown in Fig. 52 A.

As fish forebay residence time increases they suffer an increasing accumulation of mortality due to predation. As noon distance (L_day) increases from 40 feet to 140 feet, while holding night distance (L_night) constant at 40 feet, mortality increases from 0% to just over 10% during the entire 24-hour cycle (see Fig. 52 B).

Fig. 52 A. Diel passage patterns from by delay probabilities in Fig. 51. B. Mortality experienced by smolts with increasing delay.

Comparison Data

Numerous data sets exist that provide information on diel passage (e.g. Raemhild et al. 1983, Steig and Johnson 1986, Ransom and Sullivan 1989). Very few data sets, however, provide information on the difference between arrival at the dam and actual passage. Diel passage patterns can be summarized simply: more fish pass at night than during the day. Generally peak passage occurs around 2100 hr.

The delay model is calibrated to radio-tag data. Radio tags were inserted into the gut of spring chinook salmon (Oncorhynchus tshawytscha), the fish released, and their movement patterns tracked.The comparison data set comes from John Day Dam and its reservoir (Giorgi et al., 1985).

These data include the date and time of arrival in the forebay for each fish, as well as the date and time of passage through the dam. The mode of passage - powerhouse or spillway - is also noted. The difference between these two times is the delay experienced by each fish. Because our model is based on delays induced at the powerhouse, fish that pass the dams via the spillway have been excluded. There is a significant relationship between the delay experienced and the time of day the fish arrive at the dam (Fig. 53; Kendall's = -0.297, p = 0.0096). Fish arriving during the day experience longer delays; those arriving at night pass the dam quickly.

The data suggest that fish arriving during the day are delayed 2 hours. Since CRiSP currently uses a 2-hour dam time step, this is equivalent to a delay probability of 50% during daylight, and no delay at night. A particular linear combination of model parameters produces these values: any point taken from this linear collection will achieve the desired effect using the values given in Table 39.

These values have a good fit to observed of arrival and passage (Fig. 54).

Fig. 53 Delay as a function of time of day of arrival.

Fig. 54 Arrival and diel passage of spring chinook at John Day Dam, observed and simulated.

Columbia River Salmon Passage Model CRiSP.1.5 Theory, Calibration & Validation Manual
Copyright © 1996, Columbia Basin Research. All rights reserved.