II.7.2 - Calibration

Empirical Equation

The calibration is applied to the hyperbolic empirical model given by eq (113) where

• N_s = percent supersaturation above 100%
• F_s = spillway flow volume in kcfs
• a, b and h = coefficients specific to each dam, derived from nitrogen rating curves provided by the Corps of Engineers.

The parameters in Table 36 were obtained by fitting the hyperbolic submodel of eq (113) to the rating curves using a nonlinear "amoeba" routine from Numerical Recipes (Press et al. 1988). Constraints on fitted parameters were: 0 a 50, 0 b 0.12, 0 h 100.

Mechanistic Equation

The mechanistic nitrogen saturation submodel (see Mechanistic Equation section II.7.1) was calibrated using flow/spill/gas saturation data from the rating curve data 1984 to 1990 at most projects. (This data set was supplied by Tom Miller of the Walla Walla District of the U.S. Army Corps of Engineers.) The data originated from the Columbia River Operations Hydrological Monitoring System (CROHMS) data base. At each dam the data consisted of: hourly flow and spill, forebay saturation, forebay elevation, tailrace elevation, and temperature, all measured throughout the summer. Using the same gas dissipation mechanism as was used in earlier versions of CRiSP.1, the tailrace gas saturation was back-calculated from the next dam downstream.

For each point in time the three parameters a, b, and c below were estimated using a multiple linear regression of the equation defining K₂₀ in terms of the energy loss rate, the forebay concentration, and the entrainment coefficient. The mechanistic model for GasSpill 2 assumes that these parameters are related as is given by eq (121) where

• K20 = entrainment coefficient
• E = energy loss rate
• Cf = forebay concentration
• a, b, and c = coefficients calculated from multiple linear regression of data in Table 37.

(132)

where

• T = water temperature in the forebay in degrees C.
• S = spill in kcfs
• W = spillway width (gates x width/gate)
• L = stilling basin length in feet
• Nfb = forebay gas saturation
• Nsw = back-calculated spillway gas saturation

where

• sgr = specific gravity of roller (usually 1)
• = 0.0295
• d = stilling basin depth in feet
• y₀ =
• H = hydraulic head in ft is obtained from information in Table 38
• G = 32.2 (gravitational constant)

and

No data were available for Wanapum Dam thus preventing calibration of both Wanapum and Rock Island, the dam immediately upstream. In these cases the initial calibration of Water Resources Engineers Inc. (WRE 1971) was used as the calibration.

The spill program of 1994 presented an opportunity to recalibrate Gasspill parameters using up-to-date data at a variety of spill levels, including some observations at very high levels that had not previously occurred. Daily average gas levels were compared to those estimated using previously calibrated GasSpill parameters, and parameters were adjusted on a dam by dam basis to bring model predictions into closer agreement with observed data. Required changes were quite small, but the improvement of fit was noticeable; current estimates and observed gas levels are shown for several points in the system in Fig. 46. Note that in all four graphs the predicted and observed saturation tracks do not differ significantly (chi-squared goodness-of-fit test, in all cases p>0.05).

Fig. 46 Comparison of observed and modeled gas supersaturation for 1994 data. Lower Granite Pool Chi-square = 1.88, p>0.05. Ice Harbor Pool Chi-square = 3.38, p>0.05. Priest Rapids Pool Chi-square = 2.01, p>0.05. Bonneville Pool Chi-square = 1.08, p>0.05.