CRiSP1.6 Theory & Calibration Manual: III.2 - Total Dissolved Gas Calibration

III.2 - Total Dissolved Gas Calibration

WES Linear and Exponential Curves

The majority of the total dissolved gas (TDG) calibration work is based on published documents by Waterways Experiment Station (WES), U.S. Army Corps of Engineers. Some of WES's calibrations were not used because of structural modifications to the dam or additional data that suggested a different dynamic. For these dams, the calibration of the new production equations were developed from the gas monitoring station data¹. The empirical equations derived from the WES calibrations depend on spill alone, and hence if there are significant structural or operational changes to a specific dam, new calibrations would most likely needed.

Different day and night spill patterns for adult and juvenile fish passage at the dams require different production equations. In the case where there is no discernible difference between night and day gas production, the day and night equations are set to be the same.

Table 46 Lower Snake and Lower Columbia dams, gas production curves using linear or exponential models.

Project	%TDG =		Reference
BON			WES 1996
TDA		juvenile pattern (night)	WES 1997a
		adult pattern (day)	WES 1997a
JDA		juvenile pattern (night) 1998 (with new deflectors)
		adult pattern (day) 1998 (with new deflectors)
		Before 19981	WES 1997a
MCN			WES 1997a
IHR		1998 (with 2 additional deflectors), current
		1997 (with new deflectors)
		Before 1997	WES 1997a
LMN		juvenile pattern (night)
		adult pattern (day)a
LGS		juvenile pattern (night)	WES 1997a
		adult pattern (day)a	WES 1996
LWG		(1996)	WES 1997a
		(1995), current	WES 1997a

1 In CRiSP.1, an upper bound of roughly 145% was added to these equations.

For Lower Granite (LWG) and The Dalles (TDA) dams, WES (1997a) reference gave the production curve in the terms of q_s, discharge per spillbay. Here, q_s was converted to Q_s/n assuming the total discharge Q_s was uniformly distributed between the number n of spillbays. In general, because of possible construction or repairs at a dam, the number of spillbays will have to be set separately for each year. For example, the number of spillbays in use for Lower Granite was different for 1995 and 1996.

In the cases where the WES (1996) equations were used-Bonneville Dam, Lower Monumental juvenile pattern, and Little Goose juvenile pattern-there was no new recommendation in the 1997 documentation. In fact, the authors felt that there was not a good fit available. The equations given in WES (1996) were nevertheless taken as a starting point for the new gas production model.

For the upper Columbia dams, the "best" fitting of the empirical gas production equations was chosen based on available hourly tailrace TDG data from 1995-1998. The bounded exponential equation performed well in all cases and is applied to all upper Columbia dams except Wells Dam, which uses the linear equation. The results of this calibration are shown in Table 47.

Table 47 Upper Columbia dams and Dworshak Dam gas production curves using linear or exponential model

Project	%TDG =
PRD
WAN
RIS
RRH
WEL	Night
	Day
CHJ
DWR

There was no data for Hells Canyon Dam, so a "generic" set of coefficients was used for this dam. The bounded exponential model, the one predominantly used for the other dams, was chosen and the coefficients were set for moderate gas production

Table 48 Hells Canyon Dam gas production curves using exponential model

Project	% TDG =
HCY

.

These calibrations are based on spill and typically represent the river best in moderate to high levels of spill. All gas production curves break down when spill is only a few kcfs. In this case, the spill flow retains the dissolved gas level of the forebay.

Exponential Empirical Equation

The parameters in Table 49 were obtained by fitting the exponential empirical submodel to the rating curves. This is the backup model under some circumstances for the dams listed in the table.

Table 49 Values for exponential empirical TDG model

Dam	a	b	k
Default	30.0	0.025	0.03
Bonneville	30.0	0.025	0.03
McNary	30.0	0.025	0.03
Priest Rapids	30.0	0.025	0.03
Wanapum	30.0	0.025	0.03
Rock Island	30.0	0.025	0.03
Rocky Reach	30.0	0.025	0.03
Chief Joseph	30.0	0.025	0.03
Little Goose	45.483192	0.010609	0.03
Lower Granite	30.0	0.025	0.03
Dworshak	34.5	0.007248	0.03
Hells Canyon	32.35294	0.025	0.03

Hyperbolic Empirical Equation

This model is retained for backward compatibility. The calibration is applied to the hyperbolic empirical model given by eq (90) where

• G = percent supersaturation above 100%
• Q_s = spillway flow volume in kcfs
• a, b and h = coefficients specific to each dam, derived from TDG rating curves provided by the U.S. Army Corps of Engineers.

Data for fitting these parameters were obtained from rating curves provided by Bolyvong Tanovan of the U.S. Army Corps of Engineers, North Pacific Division, Portland, OR. The graphs showing observed TDG concentrations in supersaturation for spill flows were copies of in-house documents (un-referenced and unpublished). The graphs were identified with the codes NPDEN-WC, DLL/KPA, 8MAR79. The ruling of the rating curves allowed a precision of kcfs and % saturation.

The parameters in Table 50 were obtained by fitting the hyperbolic submodel of eq (90) to the rating curves using a nonlinear "amoeba" routine from Press et al. (1992). Constraints on fitted parameters were

0 a 50

0 b 0.12

0 h 100.

The hyperbolic gas model is used as the backup equation at John Day Dam, only.

Table 50 Values for hyperbolic empirical TDG model

Dam	a	b	h
Default	30.00	0.0250	6.00
John Day to 1995	45.00	0.0250	6.00
John Day 1996, 1997	36.11	0.0250	6.00
John Day 1998, current	25.00	0.0247	7.67

GasSpill 1 and GasSpill 2 Mechanistic Equations

The mechanistic TDG saturation submodels were calibrated using flow/spill/gas saturation data from the rating curve data from 1984 to 1990. This data set was supplied by Tom Miller of the Walla Walla District, U.S. Army Corps of Engineers. The data originated from the Columbia River Operations Hydrological Monitoring System (CROHMS) database. 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 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 (98) where:

• K₂₀ = entrainment coefficient
• E = energy loss rate
• P = forebay percent saturation
• a, b, and c = coefficients calculated from multiple linear regression of data in Table 51.

For each dam, K₂₀ is calculated from data using:

(138)

where

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

  where

  • P₀ = barometric pressure in atmospheres (assume P₀ is 1)
  • sgr = specific gravity of roller (usually 1)
  • = 0.0295 (density of water)
  • D = stilling basin depth in feet
  • Y₀ =
  • H = hydraulic head in ft is obtained from information in Table 52
  • g = 32.2 (gravitational constant)

    and

• .

GasSpill 2 is used as the backup model at the dams listed in Table 51. GasSpill 1 is not currently calibrated for any dams.

Table 51 Parameters for GasSpill 2 model equation

Dam	L	Basin Floor Elev.	gate wd	# gates	sgr	a	b	c
Default GasSpill 2						3.31	0.41	-0.032
The Dalles	170.0	55.0	60	23	0.50	37.00	3.255	-0.394
Ice Harbor	178.0	304.0	60	10	1.0	28.05	1.38	-0.284
Lower Monumental	218.7	392.0	50	8	1.0	-2.55	4.53	0.018
Wells	30.0	670.0	46	11	1.0	27.84	2.40	-0.281

.

Table 52 Variables for reservoir geometry, in feet

Dam	Max. Forebay Elevation	Full Pool Depth at Head	Full Pool Forebay Depth	Elevation Spillway Crest	Normal Tailwater Elevation
Bonneville	82.5	68	93	24	16
The Dalles	182.3	85	105	121	80
John Day	276.5	105	149	210	163
McNary	357	75	105	291	269
Ice Harbor	446	100	110	391	343
Lower Monumental	548.3	100	118	483	440
Little Goose	646.5	98	140	581	540
Lower Granite	746.5	100	140	681	638
Priest Rapids	488	82.5	101.0		416
Wanapum	575	83.5	116		497
Rock Island	619	54	84		558
Rocky Reach	710	93	108.4		614
Wells	791	72	1111		707.4

K Entrainment

Model runs of CRiSP1.6 were used to determine the optimal value of the parameter k_entrain. This method is computationally intensive, but has certain advantages over simpler regressions. In particular, water travel time is computed based on river geometry and input information on flows and elevations and does not need to be input into the regression for each simulation.

For each dam in turn, CRiSP.1.6 was run with historical data sets from 1995 through 1998, and for each year, a range of k_entrain values between 0 and 1 was used to obtain total dissolved gas (TDG) output at the forebay of the downstream dam. CRiSP.1 produces values for the left and right side of the segment. These values were averaged to produce a single value for the downstream forebay. Then the output was compared to the Columbia River DART database on a day-by-day basis.

To examine the k_entrain values at Priest Rapids (PRD) and Ice Harbor (IHR), values at both dams were varied simultaneously since they both contribute to mixed waters at the confluence of the Snake and Columbia rivers.

The overall success of the k_entrain parameter for each of the model runs was determined by taking the mean sum of squares (MSS) for all days when there was both an observation and a model prediction:

. (139)

A second test examined the sensitivity of the mixing coefficient _dam to a range of changes in k_entrain. This involved a series of runs for various levels of _dam and k_entrain.

The k_entrain values change from year to year. The optimized k_entrain values for each year and dam are shown in Table 32; the analysis was restricted to values of TDG > 100% for both the observed DART values and the CRiSP.1 model predicted values. Ice Harbor, Priest Rapids and Bonneville dams were not evaluated.

Where CRiSP.1 is poor at fitting the data, even with the entrainment coefficient, other avenues should be explored: values of other gas parameters, accuracy of flow and spill archives, accuracy of historical gas data, functional form of the entrainment coefficient, etc.

Examples of the optimization profiles for 1998 are shown in Fig. 55. Sensitivity of gas production to the _dam values is very limited. Variation in the MSS was 1% or less across the range of theta from 0 to 10 for all the dams tested in 1997 and 1998. The only significant sensitivity was for Wanapum (WAN) in 1995 (11%) and 1997 (7.5%).

Fig. 55 Example of optimization of k_entrain values for 1998 for Wanapum (WAN), Rock Island (RIS), Little Goose (LGS), and Lower Granite (LWG).

¹ As of 1998, all major dams in the Columbia Basin have fixed gas monitoring stations in the tailwater recording water quality data.

CRiSP1.6 Theory & Calibration Manual: III.2 - Total Dissolved Gas Calibration