Sensitivity Analysis and Standard Error Development of a River Temperature Model (FLUVIAL-EB): Understanding Predicted River Temperature Response to Atmospheric Observations at the Basin Scale

Abstract

This thesis encompasses three chapters that aim to improve the understanding of a large-lowland river's radiative energy balance and the atmospheric-water surface interactions that control it. In Chapter 1, we develop a sensitivity analysis of a physically-based numerical energy balance model (FLUVIAL-EB) that takes a detailed account of heat energy fluxes in a river system to assess the role of atmospheric variables in river temperature change. We calculate the sensitivity of predicted river temperature to small individual perturbations to several meteorological variables across different seasons, including shortwave radiation, longwave radiation, air temperature, wind speed, vapor pressure, and air pressure. We pay special attention to the perturbation values as early results highlight the need to develop a specialized methodology for perturbing atmospheric variables because each variable operates on differing magnitudes. The coefficient of variation (CV) term is applied to each atmospheric dataset to determine the perturbation value of each variable for each season. We conclude that the CV method provides a standardized measure of the distribution of the observed weather variables and encompasses the seasonal variability within each atmospheric record. Results show that predicted river temperature is particularly susceptible to positive changes in shortwave radiation (+2.6°𝐶𝐶, 25km river distance and +10.3°𝐶𝐶, 150 km river distance) in summer seasons at the longitudinal river basin scale. In Chapter 2, we present a novel Gaussian variance-based, multi-variable error decomposition scheme on the simple standard error equation to account for the contribution of weather data to the error in predicted river temperature. The FLUVIAL-EB model incorporates key atmospheric variables for energy flux and river temperature predictions from the California Irrigation Management Information System (CIMIS) data network. We examine a possible source of error due to the utilization of this data set by using Taylor Series expansion approximations under finite-difference assumptions, where we expand the basic standard error equation to calculate the standard error of predicted river temperature. The equation includes 1) a weighting term (partial derivatives calculated in Chapter 1 that provide a measure of influence on the standard error based on predicted river temperature sensitivities to each atmospheric variable, 2) a Pearson's correlation coefficient term which measures the direction and magnitude of the correlation between two uncorrelated atmospheric variables, and 3) a standard error value for each atmospheric variable that characterizes error due to misrepresentation of the atmosphere directly over the river channel, which we call standard error due to geographic displacement between the weather stations and river channel. Assuming predicted river temperature is only a function of the six critical atmospheric variables, results show error values to be small across all seasons and distances of the river. The most significant error in predicted river temperature occurs during the winter months (± 0.12 °𝐶𝐶) followed by spring, summer, and fall (± 0.08 °𝐶𝐶, ± 0.03 °𝐶𝐶, ± 0.05 °𝐶𝐶, respectively) at the 150 km river distance. Chapter 3 introduces the FLUVIAL-EB model's ability to predict energy fluxes and river temperature along river distance by replacing CIMIS data with gridded regional climate model output. Initially, we hoped to present modeled river temperatures based on atmospheric predictions derived under a high greenhouse gas emission scenario (RCP 8.5) from the fifth-generation Canadian Regional Climate Model (CRCM5). The results presented in Chapter 3 highlight the FLUVIAL-EB model's efficacy in utilizing gridded climate data and motivate future work to incorporate climate predictions into the FLUVIAL-EB model to observe how river temperature reacts under a high-emission greenhouse gas scenario. To conclude, results from this work highlight the need to improve the accuracy and representativeness of weather time-series observations to improve FLUVIAL-EB model predictions of temperature along the length of a river and to incorporate more sources of error to prediction results and model inputs. Results also emphasize the importance of a seasonally based approach to making water management decisions as river temperature sensitivity to the atmosphere fluctuates by a substantial amount depending on the seasons (± 10.3 °𝐶𝐶, in summer at river distance 150km given a + 1.1 𝑊𝑊𝑊𝑊−2 perturbation to shortwave radiation). Finally, the FLUVIAL-EB model can incorporate gridded climate data representing atmospheric conditions derived from high greenhouse gas emission scenarios, making it a valuable tool to assess changes in energy fluxes and river temperature of a large-lowland river in anthropogenic-induced climatic conditions.