Scientific Investigations Report 2007–5185

**U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5185**

Model results were analyzed using the same general method used by ODEQ in the development of the Willamette temperature TMDL. That method may be summarized as follows:

- Determine the 7-day moving average of the daily maximum (7dADM) water temperature for every model segment and every day simulated in each model run. Flow-weighted daily maximum temperatures were used for the upper and middle Willamette River models. Volume-weighted daily maximum temperatures were used for the lower Willamette River model (ODEQ used flow-weighted, as discussed previously). Surface daily maximum temperatures were used for all other submodels.
- Subtract the 7dADM temperatures for the “without point sources” baseline model run from the 7dADM temperatures for the target model run (for example, a “with point sources” run) for every model segment and every simulated day. The result is a distribution of 7dADM temperature differences at each location in the model. The “without point sources” baseline run typically was the Natural Thermal Potential, or NTP, run.
- Determine the 95
^{th}percentile of the 7dADM temperature differences at each location. Data were grouped together in several different ways to calculate these percentiles, either for all of 2001 and 2002, or by month, or by a fish-use designation time period defined in Oregon’s temperature standard. In the calculation of the 95^{th}percentile, data points were included from a particular location and time only if they adhered to two particular criteria. If the criteria are met, then the data point is included; if either is not met, then the data point is excluded from the computation of the 95^{th}percentile. Those criteria are:- a. The 7dADM temperature from the NTP run at that time exceeds the numeric criteria of the temperature standard at some point downstream. The focus is on the most critical conditions, when the allowable temperature increase is most restricted by the standard.
- b. The modeled daily average flow at the appropriate point of maximum impact (POMI) is equal to or greater than the post-dam 7
*Q*_{10}low-flow statistic at that location. The POMI is the location of a cumulative point-source heating maximum determined on the basis of model results. POMI locations are at or near Albany in the upper Willamette River model, in the Newberg pool or at Salem in the middle Willamette River model, and in the Portland Harbor for the lower Willamette River model. Local POMIs were used for the Coast Fork and McKenzie River models. 7*Q*_{10}flow values were obtained from the ODEQ’s Willamette temperature TMDL document (Oregon Department of Environmental Quality, 2006b).

This analysis method was discussed with ODEQ staff prior to its use, and it was agreed that this method was very similar, if not identical, to the method used by ODEQ to analyze model results for the TMDL.

Note that at least six different common methods can be used to compute percentiles, and no good agreement exists as to which is preferred. The SAS statistics package alone offers five separate methods for calculating percentiles (SAS Institute, 1990). ODEQ staff relied on Microsoft^{©} Excel to compute percentiles, and Excel’s method, though related, does not match any of those offered by SAS. Most of these percentile methods differ in their assumptions for the intervals that surround each ranked data point; as a result, the computations differ most when applied at the extremes of the distribution, such as at the 5^{th} or 95^{th} percentile. In this analysis, the method documented by Helsel and Hirsch (2002) and identical to SAS Proc Univariate’s definition 4 was used to compute the 95^{th} percentiles. This method is widely applied, but may result in slightly higher 95^{th} percentiles with some datasets, as compared to those computed by Excel.