Scaling-based robust empirical modeling of stream temperature (Tw) across the contiguous U.S.

Abstract:

Stream temperature () controls the biophysical processes occurring in the aquatic environment. Stream temperature typically follows a diurnal pattern due to the variation in climatic drivers (e.g., solar radiation, air temperature). Hydrologic and/or climatic variables data were required to utilize the existing models for the prediction of stream temperature. Furthermore, the site-specificity of these models hinders a robust prediction of fine resolution (e.g., hourly) stream temperature. In light of these limitations, a scaling-based empirical model was developed to predict the diurnal cycle of using a corresponding single reference observation as a scaling parameter. Scaling transformed different diurnal cycles into a common dimensionless diurnal cycle, representing different days and stream sites. An extended stochastic harmonic algorithm (ESHA) was then used to parameterize the dimensionless diurnal cycles by utilizing the hourly observations of stream temperature over the growing season (May ‒ October) for 624 monitoring sites across the contiguous U.S. The study sites incorporated a considerable gradient in latitude, climate (e.g., temperate, tropical), and hydrology (e.g., discharge). The temporal robustness of the daily estimated model parameters leads to aggregate the model parameters across days to obtain the site-specific set of parameters. The relationship between and latitude lead to categorize the station according to their latitudinal position. The latitudinal specific set of parameters were obtained by taking the average of the site-specific set of parameters across stations within each latitude. The high model efficiency (NSE 0.50 to 0.99) and accuracy (RSR = 0.11 to 0.76) confirms the spatiotemporal robustness of latitudinal specific model parameters during the reference hours from 12 P.M. to 3 P.M. The invariability of model parameters with different drivers (climate, hydrology, and water quality) lead to developing a generalized set of model parameter for each reference time. The generalized set of model parameters was able to predict the diurnal cycles at a satisfactory level for 98% stations across the contiguous U.S. and confirms the spatiotemporal robustness of model parameters. The model parameters were spatiotemporally robust, which was further investigated by quantifying the sensitivity and uncertainty measures. The model can predict the entire diurnal cycle of hourly stream temperature from one or a set of the site- and day-specific reference observation(s). The model can help dynamically assess the stream water quality and ecosystem health.