Statistical Nonparametric Model for Natural Salt Estimation

Abstract

Many rivers in the Western U.S. suffer from high salinity content due to both natural and human-induced causes. Computer simulation models are often used to estimate future salinity levels and identify mitigation needs. To date, estimation of future natural salt loading has utilized linear relationships between natural flow and natural salt. We develop a nonparametric regression technique to fit a functional relationship between natural flow and natural salt. The main advantages of the nonparametric technique are: (1) No prior assumptions have to be made as to the underlying form of the relationship and (2) any arbitrary relationship (linear or nonlinear) can be modeled. In addition, we develop a resampling scheme to provide confidence intervals of the natural salt estimates from the nonparametric model. We apply this model to data from a stream gauge at Glenwood Springs, Colo., on the Colorado River. We show that the new natural salt model reduces the average overprediction of salt mass shown in the existing natural salt model for the period 1941-1995 by approximately 15% ͑78,000 metric tons͒.

A basin wide stochastic salinity model

“…For details on the methodology and its development for salinity modeling we refer the readers to Prairie et al (2005). The local polynomial approach above also provides estimates of uncertainty assuming the errors to be Normally distributed (Loader, 1999) using regression theory.…”

“…The local polynomial approach above also provides estimates of uncertainty assuming the errors to be Normally distributed (Loader, 1999) using regression theory. Prairie et al (2005) suggested resampling of residuals within the neighborhood of x * and adding them to the mean estimate from step (iii), as a way to obtain asymmetric confidence intervals and also better characterization of the error structure. As mentioned above, this approach was applied successfully in the salt modeling at the Glenwood Springs gauge on the Colorado River.…”

“…As noted above, such a model is crucial for evaluating various management policy options for effective planning, which motivates the present study. To this end, our recent developments of a stochastic nonparametric basin wide streamflow generation model (Prairie et al, 2006b) and nonparametric single-site salinity model (Prairie et al, 2005), provides a unique opportunity to integrate these two into a basin wide salinity and flow generation framework. This forms the basis of the proposed research.…”

“…Mass balance models for estimating salinity were developed by and , which could be coupled with a stochastic streamflow generator. Prairie et al (2005) developed a nonparametric statistical model for simulating salt scenarios consistent with streamflows at a single location. In this, a nonparametric regression based on a local polynomial approach (Loader, 1999) is developed for the salt mass using the streamflow.…”

“…The single site salinity model presented in Prairie et al (2005) uses a nonparametric regression method based on local polynomial estimation, which describes the variability of salt mass as a function of flow. The model is defined as:…”