Statistical Modeling of Daily Water Temperature Attributes on the Sacramento River

Abstract

The Sacramento River is the largest river in California, and an important source of water for agricultural, municipal, and industrial users. Input to the Sacramento River comes from Shasta Lake and is controlled by operators of Shasta Dam, who are challenged with meeting the competing needs of these users while also maintaining a cold water habitat for Endangered Species Act (ESA) listed winter-run Chinook salmon. The cold water habitat goals are constrained by the volume of cold water storage in the lake, which operators attempt to selectively deploy throughout the critical late summer/fall window. To make informed decisions about the release of this limited cold water resource, skillful forecasts of downstream water temperature attributes at the seasonal time scale are crucial. To this end, we offer a generalized linear modeling (GLM) framework with a local polynomial method for function estimation, to provide predictions of a range of daily water temperature attributes (maximum daily water temperature, daily temperature range, number of hours of threshold exceedance, and probability of threshold exceedance/nonexceedance). These attributes are varied in nature (i.e., discrete, continuous, categorical, etc.), and the GLM provides a general framework to modeling all of them. A suite of predictors that impact water temperatures are considered, including current and prior day flow, water temperature of upstream releases, air temperature, and precipitation. A two-step model selection is proposed. First, an objective method based on Bayesian Information Criteria (BIC) is used in a global model to select the best set of predictors for each attribute; then the parameters of the local polynomial method for the selected best set of predictors are obtained using generalized cross validation (GCV). Daily weather ensembles from stochastic weather generators are coupled to the GLM models to provide ensembles of water temperature attributes and consequently, the probability distributions to obtain risk estimates. We demonstrate the utility of this approach by modeling water temperature attributes for a temperature compliance point on the Sacramento River below Shasta Dam. Regulations on the dam depress the water temperature forecasting skill; to show this, we present skillful results from applying the approach to an unregulated location in the Pacific Northwest. The proposed method is general, can be ported across sites, and can be used in climate change studies.