On the deterministic and stochastic use of hydrologic models

Abstract

Environmental simulation models, such as precipitation‐runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed‐parameter precipitation‐runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.

A process‐based insight into nonstationarity of the probability distribution of annual runoff

“…In terms of the p value of the KS test for the DARD, introducing as a random variable is able to significantly improve the performance of the process‐based analytical derivation approach in fitting annual runoff distribution. Therefore, the model error in runoff simulation should be a factor involved in deriving runoff distribution [ Farmer and Vogel , ]. Similar to the performance of the annual runoff model displayed in Figure a, the DARD for the Yangtze River generally has the better fitting effect on the annual runoff distribution than that for the Yellow River.…”

“…Both the trend/change‐point tests and time‐varying moments model are able to provide a primary argument for the nonstationarity of runoff series from statistical perspective, but they are unable to provide a physical insight into how the changes in the hydrological physical mechanisms behind runoff generation will lead to changes in the shape of the runoff frequency curves [ Merz et al ., ]. The nonstationarity of runoff series can originate from nonstationarity in hydrological inputs to hydrological systems, or nonstationarity in watershed characteristics dominating processes of runoff generation and routing, or both [ Blöschl and Sivapalan , ; Merz and Blöschl , , ; Hundecha and Merz , ; Rogger et al ., , , ; Merz et al ., ; Farmer and Vogel , ].…”

Characterizing Uncertainty in Daily Streamflow Estimates at Ungauged Locations for the Massachusetts Sustainable Yield Estimator

“…Figure 1 shows the region used by and . All data used herein have been archived by Farmer and Levin (2017).…”

“…As an inherent symptom of any modeling endeavor, all hydrologic models contain some degree of uncertainty (Montanari and Brath, 2004;Farmer and Vogel, 2016), whether a lumped or distributed conceptual runoff model (Renard et al, 2010) or a statistical model like the algorithms underlying the Massachusetts SYE. Movement away from methods grounded in traditional statistics toward conceptual, process-based models has dissociated our use of and blurred our understanding of model uncertainty to the point that most models are considered as almost purely deterministic tools (Wagener and Wheater, 2005).…”

“…Movement away from methods grounded in traditional statistics toward conceptual, process-based models has dissociated our use of and blurred our understanding of model uncertainty to the point that most models are considered as almost purely deterministic tools (Wagener and Wheater, 2005). Today, most hydrologic models, whether statistical models or rainfall-runoff models, are applied deterministically in management exercises (Montanari and Brath, 2004), but understanding the uncertainties inherent even in deterministic models is necessary for the appropriate use of hydrologic models (Vrugt and Robinson, 2007;Farmer and Vogel, 2016).…”