TMDL Development Using Quantile Regression

Abstract

Quantile Regression (QR) analysis was used to determine the pollutant reductions needed to achieve the dissolved oxygen (DO) cool-water criteria in the Upper John Day River, Oregon. The QR approach was used rather than least-squares methods because QR investigates more properties of the conditional-probability function. Specifically, QR estimates the expected values for the quantiles of the conditional probability function. The QR analysis was performed on a data subset representing a time of the year when river flows were low and there was little irrigation. This is when the digressions of the DO criteria occurred. Once the QR was performed, an empirical model relating DO to water quality parameters was selected from candidate QR equations for the 25th, 33rd, 50th, and 75th-quantiles. The QR equations that related DO to stream temperature (DO-TEMP) were selected from the 22 parameters considered. The DO-TEMP equation for the 75th-quantile was selected as the empirical model to be used based on several model performance statistics. By using the DO-TEMP empirical model and the simulated stream temperature time-series from the temperature TMDL of the Upper John Day River as an input, it was determined that the load allocations for the stream temperature TMDL were sufficient for the DO TMDL. The empirical model would not have been possible without the use of QR. The QR approach provides powerful tools that can be used to explore water quality relationships and provide insights that are not possible using standard least-squares based regression procedures.