Effect of Parameter Distributions on Uncertainty Analysis of Hydrologic Models

Abstract

Increasing concern about the accuracy of hydrologic and water quality models has prompted interest in procedures for evaluating the uncertainty associated with these models. If a Monte Carlo simulation is used in an uncertainty analysis, assumptions must be made relative to the probability distributions to assign to the model input parameters. Some have indicated that since these parameters can not be readily determined, uncertainty analysis is of limited value. In this article we have evaluated the impact of parameter distribution assumptions on estimates of model output uncertainty. We conclude that good estimates of the means and variances of the input parameters are of greater importance than the actual form of the distribution. This conclusion is based on an analysis using the AGNPS model.

Sampling‐Based Methods for Uncertainty Propagation in Flood Modeling Under Multiple Uncertain Inputs: Finding Out the Most Efficient Choice

“…In fact, such non-uniform distributions can be generated from the cumulative distribution functions of the uniform distributions (Equations 1-3) by means of the Inverse Transform Sampling (Steinbrecher & Shaw, 2008) or the Box-Muller algorithm (Box & Muller, 1958). However, these non-uniform distributions would have the same data means and standard deviations, and thus may not significantly change the findings of this study (Haan et al, 1998). Rather, there is an impending need for producing well-characterized uncertainty with statistically rigorous estimation of the potential underlying correlations in their domain of variations, followed by model-based reduction of the uncertainty space (Stefanescu et al, 2012).…”

“…According to Haan et al. (1998), the choice of which probability distributions to adopt to model the uncertain hydrological parameters is less important than acquiring good estimates of their means and standard deviations. In this work, therefore, the input random variables are generated based on given means and standard deviations from surveyed uncertainty ranges in published resources (Section 2.1), and using uniform, or rectangular, probability distributions are recommended (https://www.isobudgets.com/type-a-and-type-b-uncertainty/#type-b-uncertainty-definition; https://physics.nist.gov/cuu/Uncertainty/typeb.html) to conservatively model such Type‐B uncertainty (i.e., with equal probabilities) (Apel et al., 2004).…”

Watershed Response to Legacy Phosphorus and Best Management Practices in an Impacted Agricultural Watershed in Florida, U.S.A.

“…All parameters were assumed to have uniform distributions with values representing reductions (expressed as fractions) from the Baseline TCNS WAM setup. While parameter probability distributions can have impacts on sensitivity analysis results, assuming uniform distributions is recommended when only the basic information (uncertainty range) is available [88,91]. The upper limits of the parameter uncertainty ranges were assigned based on the values for the corresponding parameters in the FBMP setup [74] and past WAM applications for restoration assessments [70,73].…”

Uncertainty analysis of 100-year flood maps under climate change scenarios

“…The existing uncertainty in the input parameters can arise from different sources, such as inconsistent or unavailable data, measurement errors, sampling errors and selection of a probability distribution function (PDF). Determining the input uncertainty is one of the major tasks in flood uncertainty analyses since many parameters are not directly measurable, it is generally not possible to collect a large, random sample of parameter values and test various PDFs for their ability to describe uncertainty in the parameters (Haan et al, 1998). Among various uncertain input parameters required for flood simulation, estimation of precipitation is a significant challenge due to several reasons such as complex and chaotic nature of weather, unavailable or incomplete records and the estimation methods.…”

“…Generally, the uncertainty associated with inputs is defined through assigning particular PDFs to the inputs. However, as it is mentioned earlier it is often difficult to identify the correct and representative PDF for the inputs and several studies have shown the importance of this issue (e.g., Haan et al, 1998, Merz and Thieken, 2009, Winter et al, 2018, Annis et al, 2020, Moccia et al, 2021.…”