Scientific Investigations Report 2007–5185
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5185
The Willamette flow and temperature models were constructed using CE‑QUAL‑W2, a two-dimensional (longitudinal, vertical) model from the U.S. Army Corps of Engineers (Cole and Wells, 2002). CE‑QUAL‑W2 is a physically based mechanistic model that simulates gravity- and wind-driven flow through a network of interconnected river channels or reservoir reaches by using channel geometry and slope, bottom friction, wind shear, density effects, and upstream/downstream flow or water-level data. Algorithms to calculate the effect of hydraulic structures such as weirs, pumps, and spillways are included. Horizontal and vertical velocities, flow, and stage are simulated.
Water temperature is modeled in CE‑QUAL‑W2 by using a detailed expression of the energy budget of the water body. The model includes algorithms to calculate the effects of both topographic and vegetative shading. Using latitude, longitude, time of day, and the water body’s orientation, the model determines at each time step the presence or absence of a topographic or vegetative shadow on the water surface, the length of any shadow, and the degree to which that shadow shields the water body from solar radiation. Model inputs include meteorological data, topographic shading angles, tree-top elevations, distance to the vegetation, and solar-reduction factors associated with the riparian canopy that vary by location. This detailed representation of the heat budget and the effects of riparian shading was one of the major reasons that ODEQ chose to use CE‑QUAL‑W2 for the Willamette temperature TMDL analysis.
In addition to modeling flow and water temperature, CE‑QUAL‑W2 can simulate many water-quality constituents, including conservative and nonconservative tracers, bacteria, different forms of nitrogen (nitrate and ammonia) and phosphorus, multiple phytoplankton and epiphyton groups, dissolved oxygen, multiple suspended-sediment groups, and dissolved and particulate organic matter. These capabilities were not used in the Willamette temperature TMDL application but may be used to build on these models in the future. CE‑QUAL‑W2 has open source code, good documentation, and a large user community. In addition, it has a long history of successful application to a wide range of lake, reservoir, estuary, and river systems (Cole and Wells, 2002). USGS users have found that CE‑QUAL‑W2 is capable of simulating water temperature with a mean absolute error of 0.5 to 1.0°C (Bales and others, 2001; Green, 2001; Rounds and Wood, 2001; Sullivan and Rounds, 2005 and 2006).
The Willamette modeling suite is composed of nine submodels. These models can be linked together by passing the output of any upstream models to the input of downstream models. Such connections can be made using filters and scripts so that the linkages are automatic and transparent. The nine submodels include:
In general, these models include the entire main-stem Willamette River and most of its major tributaries as far upstream as the first major dam on each tributary (fig. 1). Version 3.12 of CE‑QUAL‑W2 was used to build all submodels. The Santiam and North Santiam River model was constructed by USGS (Sullivan and Rounds, 2004). The South Santiam River model was constructed by ODEQ with assistance from Dr. Scott Wells’ research team at Portland State University (PSU). The rest of the models were constructed by the PSU modeling team (Annear and others, 2004a and 2004b; Berger and others, 2004).
All models were calibrated to measured temperatures at many locations for June 1 to October 31, 2001, and April 1 to October 31, 2002. The summer of 2001 was a drought period, with low flows at or near post-dam 7Q10 low-flow levels in many of the modeled rivers. The 7Q10 is the lowest 7-day average streamflow that would be expected to occur once in 10 years. Hydrologic conditions in 2002, in contrast, were more typical. The models’ water-temperature predictions were in good agreement with measured data; mean absolute errors generally were less than 1.0°C (Berger and others, 2004; Sullivan and Rounds, 2004).
All submodels originally were calibrated and run with a slightly modified form of CE‑QUAL‑W2, based on version 3.12 from August 19, 2003. The PSU modeling team made one enhancement to that code, which created several new output files. These custom outputs contained the daily maximum water temperature from each segment in the model at a user-specified output frequency, calculated using either the surface temperature, a volume-weighted temperature, or a flow-weighted temperature. Having these quantities pre-calculated by the model simplified the post-processing of model results. Further modifications were made to the model code by the USGS for this investigation to make the models easier to use and to eliminate some minor problems. The details of the USGS code changes are described in appendix A. The models used in this investigation are available online from the USGS project website (see section, “Supplemental Material”).
After receiving the Willamette models from ODEQ, USGS staff performed a detailed review and found a few problems that required attention. Several modifications were made to the models to correct errors, remove instabilities, and make the results more usable.
For each of the modeled point sources, a spreadsheet was crafted by ODEQ staff to calculate the allowable effluent flows and temperatures that result from each source’s wasteload allocation formula. The resulting time series of flow and temperature were used in the Willamette temperature models. The spreadsheet calculations, however, were not entirely consistent with the TMDL’s final wasteload allocation formulas. Two errors were discovered, both of which relate to the calculation and use of an adjustment factor (“a”) in the point-source flow-scaling equation of the TMDL (see Oregon Department of Environmental Quality, 2006b, for more details on the TMDL’s point-source allocation framework). USGS staff corrected these errors in the point-source spreadsheets, and the allowable point-source flows and temperatures were recalculated. The changes were largest for those point sources that discharge to the Willamette River and its tributaries upstream of the Santiam River (river mile [RM] 108.5); the modeled point-source discharges increased slightly at certain times of the year. For the rest of the point sources, the changes were small and typically negligible.
The Tri-City wastewater treatment plant (WWTP), which discharges to the lower Willamette River at about RM 25.5, was inadvertently modeled by ODEQ with flows and temperatures calculated for the Wacker Siltronics point source. The Tri-City WWTP is a larger source than Wacker, with higher flows and somewhat similar temperatures. After correcting this error, the modeled cumulative temperature effect of the point sources increased slightly in the lower Willamette River.
The additional flow in a river contributed by a point-source discharge has an effect on downstream temperatures—the magnitude of which depends on river flow and point-source flow. Downstream of dams, increasing streamflow through point-source additions can slightly modify downstream patterns in the 7-day moving average of the daily maximum (7dADM) temperature. Such changes in downstream temperature patterns can complicate the analysis of cumulative point-source heating effects because temperature changes resulting from travel-time modifications are complex and difficult to disentangle from the more straightforward point-source heating effects. Because of this problem, ODEQ modeled most of the point sources with an associated upstream withdrawal of the same magnitude in an attempt to eliminate the travel-time artifact. The Cottage Grove WWTP did not have an associated time-of-travel offset (withdrawal) in the original ODEQ model. By adding such an offset, a slight travel-time anomaly in the Coast Fork model results was eliminated.
Two specific model instabilities were identified and eliminated. The first occurred in the Coast Fork model and affected the simulated 7dADM water temperature for RMs 195.6–186.4 for April 18–24, 2002. This instability was eliminated by reducing the model’s maximum allowable time step from April 16–26, 2002. The second instability occurred in the upper Willamette model and affected the 7dADM water temperature for RMs 94.8–85.5 for October 2–27, 2002. The problem was caused by slightly increased flows on day 277, and only occurred for model runs that included point sources in the Santiam River system. The Santiam sources (WWTPs at Jefferson, Stayton, Lebanon, and Sweet Home), though small, were large enough to cause the slightly elevated Willamette flows that triggered the instability. These sources had not been given time-of-travel offsets by ODEQ in the original model runs; adding such offsets was sufficient to eliminate the instability. By removing these instabilities and their associated artifacts in the modeled 7dADM temperatures, the model results were more usable.
The temperatures assigned to the distributed tributaries (ground water and ungaged tributaries) of the upper Willamette model for branches 1-6 were not consistent in the ODEQ models. Different temperatures were used for the model runs that included point sources, as compared to model runs that had no point sources. The distributed tributary temperatures in the former were slightly higher than those used in the latter, resulting in a small additional temperature increase in the “with point sources” model run that was not caused by the point sources. This problem was fixed by consistently assigning these temperatures to those used in the “without point sources” run.
Because of the relatively large time steps used in the lower Willamette River model, different model runs did not necessarily calculate their daily maximum water temperatures from the same time of day. The maxima could have been extracted from model results that were several minutes apart. This timing discrepancy led to temperature differences, when comparing two model runs, on the order of several hundredths of a degree or more, which in turn led to problems in subsequent data analysis, particularly when adding together the results of many model runs. The solution was to decrease the maximum time step in the lower Willamette River model from 360 to 60 seconds, and use a slightly different version of the model that determined the daily maximum temperature by using information from every time step rather than a user-specified number of times per day (see appendix A).
In assessing the heating effects of point and nonpoint sources on the river system, ODEQ opted to use daily temperature maxima from the river surface for every submodel except the upper, middle, and lower Willamette River. In those three submodels, the flow-weighted daily maxima were used. The lower Willamette River model, however, produces some anomalies in the flow-weighted daily maximum water temperatures that appear when 7dADM temperatures from two different model runs are subtracted. This “noise” is compounded when adding the effects from multiple model runs, making those results unusable for some purposes. Tests showed that the volume-weighted daily maximum temperatures, which do not contain this sort of noise, could be used in place of the flow-weighted daily maximum temperatures for the lower Willamette River without losing any pertinent information. In this work, therefore, USGS used the volume-weighted daily maxima rather than the flow-weighted daily maxima from the lower Willamette River model.
U.S. Department of the Interior | U.S. Geological Survey
URL: https://pubs.usgs.gov/sir/2007/5185
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