Scientific Investigations Report 2007–5008
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5008
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The Detroit Lake model was constructed with CE‑QUAL-W2, a two-dimensional, laterally-averaged, hydrodynamic and water quality model from the USACE (Cole and Wells, 2002). The same model was used in the Oregon Department of Environmental Quality’s TMDL work for the Willamette River, including the Santiam and North Santiam subbasins. CE-QUAL-W2 is capable of simulating hydrodynamics, water temperature, and a number of other water quality constituents, including TDS, and multiple suspended sediment groups. A model grid based on the lake’s bathymetry was developed. Other model inputs included meteorology, inflows and outflows, inflow water temperatures, TDS concentrations, and suspended sediment concentrations. The water balance was calibrated by comparing modeled and measured lake stage for all modeled time periods. The model was calibrated for water temperature, TDS, and suspended sediment through comparisons of model output to measured data. All data used to run the Detroit Lake model, as well as measured profile data, are available online (see section, “Supplemental Material”).
Version 3.12 of CE-QUAL-W2 formed the basis of the Detroit Lake model. This version was modified by USGS project personnel to (1) fix coding errors either posted by CE-QUAL-W2’s development team or found by USGS, (2) add new model output fluxes related to sediment deposition, and (3) enhance model capabilities through the addition of a new subroutine to automatically blend outflows from multiple reservoir outlets to match a user-supplied downstream temperature target. All coding changes were extensively tested to assure proper model performance prior to their use. The blending routines were documented and applied previously by Sullivan and Rounds (2006). CE-QUAL-W2 uses a variable time step to ensure the numerical stability of its computational methods; this time step averaged 52 seconds for the 2002 simulation, 49 seconds for 2003, and 23 seconds for 2005–06.
A geographic information system (GIS) dataset for Detroit Lake was created by combining a digital raster graphic of Detroit Lake with cross sections measured in the field by USGS personnel using acoustic Doppler techniques. Using GIS, the reservoir was divided into model segments (fig. 2). Ten equally spaced cross sections were subsampled from each segment using GIS techniques, then averaged to determine a representative cross section for each model segment.
Segments in CE-QUAL-W2 are grouped together into branches, which connect to form the model grid. The Detroit Lake grid consists of four model branches: The first, or main, branch has 33 segments, extending from the North Santiam River inflow to Detroit Dam. The second branch consists of 11 segments, beginning at the Breitenbush River inflow and connecting to the main branch with a head boundary just downstream of Piety Island in Detroit Lake. The third branch consists of eight segments in the Blowout Creek arm of the lake, and the fourth branch comprises six segments in the Kinney Creek arm. French Creek was modeled as a tributary to the second branch, and Box Canyon Creek was modeled as a tributary to the third branch.
The volume-elevation curve resulting from this model grid was compared to a curve developed for the lake by USACE (fig. 3). From this comparison, the model grid was determined to be an accurate representation of the lake’s bathymetry.
CE-QUAL-W2 requires air temperature, dew point temperature, wind speed, wind direction, and solar radiation or cloud cover data. In late September 2002, a Bureau of Reclamation Agrimet weather station was installed just north of Detroit Lake with funding from USACE. Because the entire 2002 calendar year was modeled, a regression was developed for data collected at this weather station and a Remote Automated Weather Station (RAWS) site at Stayton (located approximately 45 km to the west of Detroit Dam) operated by ODF. This regression was used to extend the record of the Agrimet station back to January 1, 2002. Precipitation at Detroit Dam, reported by the Oregon Climate Service, also was included as input to the Detroit Lake model.
Wind speeds measured at the Agrimet weather station were lower than wind speeds reported on the lake by field crews and estimated by the Beaufort wind force scale, which relates wave heights and descriptions of conditions to wind speed. The lower wind speed at the Agrimet station probably was due to the site’s location in a forest clearing, not directly on or adjoining the lake. For the model, wind speed measured at the Stayton RAWS station was used instead; on average, these wind speeds were 10 to 15 times higher than values reported at the Detroit Agrimet station and more consistent with field observations on the lake.
Streamflow was measured at USGS gaging stations at 30-minute intervals on the main inflows to Detroit Lake including the North Santiam River, Breitenbush River, and Blowout Creek for all modeled time periods. French Creek flows were measured in 2002 and 2003, but not during the 2005–06 storms. Kinney and Box Canyon Creeks were not gaged in any of the modeled years. The inflows from these major ungaged tributaries were estimated using the ratio of each stream’s watershed area to that of Blowout Creek upstream of the Blowout Creek gaging station and multiplying that ratio by the measured streamflow at the Blowout gaging station. Inflows to Detroit Lake generally were high during winter and spring storms, and low during the summer and early autumn.
Most releases from Detroit Lake were routed for power generation through two penstocks with a centerline elevation of 427.6 m (U.S. Army Corps of Engineers, 1953). When another outlet was needed to spill water, such as during a large storm, water was released through outlets with a centerline elevation of 408.4 m. These outlet centerline elevations are 50.6 and 69.8 m below Detroit Lake’s full-pool elevation. Water for power generation was withdrawn from the lake during most of the year, but the amount of water withdrawn varied greatly over the course a day; those data were provided by USACE.
The water-surface elevation in Detroit Lake was measured in the forebay, the part of the lake just upstream of the powerhouse, and these data were compared to the modeled forebay elevations for the water balance calibration. The water-surface elevation of Detroit Lake varied by approximately 35 m in calendar years 2002 and 2003, and almost 30 m during the 2005–06 storms. The lake generally is filled by the end of May for boating and recreational uses, and gradually is drawn down beginning in September to provide storage for flood control through the winter.
Water temperature, specific conductance, and turbidity data were recorded at 30-minute intervals by water quality monitors located in the North Santiam River, Breitenbush River, and Blowout Creek for all modeled years. These constituents were measured in French Creek in 2002 and 2003, but not during the 2005–06 storms. The December 2005–January 2006 French Creek data were estimated through correlations between French Creek and Breitenbush River data for 2002 and 2003. Water temperature, specific conductance, and turbidity were not measured for Kinney or Box Canyon Creeks in any of the modeled time periods. The inflow characteristics of these smaller tributary inflows were assumed to be similar to those in French Creek, which has similar watershed size.
All inflows were relatively cold to start the calendar year, warmed through spring to a maximum temperature in July, and cooled through autumn. Superimposed on this annual water temperature pattern were short term variations due to weather patterns and daily temperature cycles. The temperatures through the year were similar for all gaged inflows, except for Blowout Creek, which could be approximately 5ºC warmer than the other inflows from June through October in the modeled time periods. This warmer temperature may have to do with sensor placement, and this may be investigated in the future by placing a probe in a different location in Blowout Creek.
Inflow specific conductance was lowest during the winter and spring, and reached a maximum in September to early November, repeating the seasonal shift from rainfall and snowmelt (low conductance) to ground water baseflow (higher conductance). The specific conductance in French Creek was the lowest of all gaged inflows, whereas specific conductance was the highest in Breitenbush River, which has geothermal influence. Some spikes (short-lived positive deviations) in specific conductance in Breitenbush River are currently unexplained (Bragg and Uhrich, 2004). To test whether these spikes affected the model results, they were removed for one model run, but were found to make no difference; therefore, the spikes were left unchanged in the final model inputs.
When using CE-QUAL-W2, it is desirable to simulate TDS instead of specific conductance because the model calculates water density as a function of temperature, TDS, and suspended sediment. Specific conductance and TDS are linearly related (Hem, 1985), because ions from dissolved solids make it possible for water to conduct an electric current. For the Detroit Lake model, then, TDS was simulated using TDS inputs that were converted from specific conductance data. According to Hem (1985), the relation between specific conductance and TDS can be described by: TDS = (SC) * A, where SC is specific conductance in microsiemens per centimeter, TDS is in units of milligrams per liter, and A is the slope of the relation between TDS and SC. The value of A generally ranges between 0.55 and 0.75. For the Detroit Lake model, the value of A was estimated to be 0.67. This relation was used to interconvert between SC and TDS.
Although turbidity was recorded at 30-minute intervals at many of Detroit Lake’s inflows, it is not a constituent that can be directly simulated by CE-QUAL-W2. Turbidity is a measure of the light-scattering properties of a liquid, and often can be directly related to the concentration of suspended particulate material in that liquid. Suspended sediment can be directly simulated by CE-QUAL-W2.
Relations between turbidity and total suspended sediment, and between turbidity and “persistent turbidity” — the long-lasting turbidity due to slowly settling small-sized suspended sediment—have been determined for Breitenbush River, French Creek, North Santiam River, and Blowout Creek (updated from Uhrich and Bragg, 2003; table 1). Concentrations for two sediment-size groups were determined for each inflow, using these relations and the measured 30‑minute turbidity data. The larger size group, “sand and silt,” was defined as sediment particles with a diameter larger than 2 µm, and the smaller-size group, “clay,” was defined as particles with a diameter less than or equal to 2 µm. The 2 µm cutoff was based on the persistent turbidity analysis by Uhrich and Bragg (2003). Concentrations of suspended sand and silt were obtained by subtracting the estimated concentration of suspended clay from the estimated total suspended sediment concentration.
Vertical profiles of water temperature, specific conductance, pH, turbidity, and dissolved oxygen were measured with a multiparameter probe in Detroit Lake approximately every 3 weeks from April 2002 to October 2003, and on January 13, 2006. The probes were calibrated and checked during each field trip. Water samples for suspended sediment analysis were taken at several discrete depths with a Van Dorn sampler. Light profiles were measured with a LI-COR LI-193SA spherical quantum sensor. Secchi depths were determined by lowering a Secchi disk into the water and noting the deepest depth at which the disk pattern could still be distinguished. These data were collected in 2002 and 2003 at three sites in Detroit Lake: Kinney, Blowout, and Mongold (fig. 1). The Kinney site, downstream of the Kinney Creek inflow and the site closest to the dam, is the deepest site. The Blowout site, downstream of the Blowout Creek inflow, is of intermediate depth. The Mongold site, downstream of the confluence of the Breitenbush River and North Santiam River arms, is the shallowest of the three main sites. On January 13, 2006, the vertical profiles were taken at four sites: Kinney, Blowout, Mongold-North, and Mongold-South. The latter two sites were upstream of the original Mongold site, on either side of Piety Island in Detroit Lake (fig. 1), and were sampled only in 2006. Water temperature at various depths in the lake also was measured using a string of thermistors suspended at varying depths from a log boom near the dam. Data were collected every hour at 23 depths, from 1 to 80 m, from late May 2003 to early October 2003.
Lake light extinction coefficients, which describe how light is attenuated through the water column, were calculated for each site on each sampling date by three methods using the light profile and Secchi disk data (Sullivan and others, 2006). Light extinction is affected by suspended sediment and algae in the lake, and in turn affects water temperature and the lake heat budget. A seasonal variation in the light extinction coefficient was observed in the lake. The highest light extinction coefficients, approaching 1.0 m-1, occurred in the lake from December through February in 2002 and 2003, presumably due to inflows with high turbidity associated with winter storms. Relatively high light extinction coefficients also were calculated in summer, probably related to algal blooms. The lowest light extinction coefficients occurred in late spring and early autumn. With a regression between average measured suspended sediment concentration in the photic zone and the light extinction data, the light extinction coefficient for water (λH2O), and the light extinction factor for suspended sediment (ε) were calculated to be 0.21 m-1, and 0.14 m2/g, respectively (table 2). The light extinction coefficient (λ) calculated by the model, then, is:
λ = λH20 + λSS , (1)
is light extinction coefficient for lake water with no suspended sediment,
is ε * SS,
is light extinction factor for suspended sediment, and
is suspended sediment concentration.
The fraction of solar radiation absorbed at the water surface (β), was set as 0.40, estimated from the light extinction coefficients and the equation (Cole and Wells, 2002):
β = 0.27 ln(λ) + 0.61 . (2)
To plot and compare model output with measured profile lake data, modeled TDS concentrations were converted to specific conductance by the relation discussed section “Inflow Water Temperature and Water Quality Data.” Similarly, measured turbidity data from the vertical profiles were converted to suspended sediment concentrations by developing a relation between measured turbidity and measured suspended sediment in the lake, using data that had been collected at the same depth and the same time. This relation took the form:
SST = 0.7893 * Tb0.8361, R2 = 0.72 , (3)
is total suspended sediment concentration in mg/L, and
is turbidity, in FNU (Formazin nephelometric units, FNU, are similar to nephelometric turbidity units, NTU, but are from turbidity measurements made with infrared light, not white light [Anderson, 2005]).
From this regression, the standard error in the predicted suspended sediment concentration for each turbidity was 1.74 mg/L. Thus, the model may not be able to fit suspended sediment concentrations converted from measured turbidity with less error than this, because these derived values have about 1.7 mg/L of error intrinsic to the estimation.
Goodness-of-fit statistics were calculated between measured profile data and model output at the same location and time. Three statistics were calculated: mean error (ME), mean absolute error (MAE), and root mean square error (RMSE). ME is defined as the average difference between measured data and modeled values and is used as an indication of model bias. MAE is the average of the absolute values of differences between measured data and modeled values. RMSE is the square root of the mean of the squared differences. Both MAE and RMSE give an indication of the magnitude of the model’s prediction uncertainty for a typical data point. RMSE is similar to a standard error of the mean for the model’s uncertainty.
Water temperature, specific conductance, and turbidity were measured at 30-minute intervals in the North Santiam River at Niagara, downstream of Detroit Dam (fig. 1). These data were useful for comparisons to model output for the outflow from Detroit Lake. However, the intervening 6 km reach between Niagara and the Detroit Lake outflow includes Big Cliff Reservoir and several small unmeasured tributary inflows. Thus, goodness-of-fit statistics were not calculated for these comparisons.
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