Multiple objective evaluation of a simple phosphorus transfer model

Abstract

Abstract:A simple phosphorus (P) transfer model of the Welland catchment, UK, is evaluated against multiple objective functions using a Monte Carlo approach that combines calibration, identifiability, sensitivity and uncertainty analysis. The model is based on simple conceptual rainfall-runoff and river routing components, combined with estimates of the daily nonpoint source load derived from annual landuse-based export coefficients, disaggregated as a function of the runoff. The model has limited data requirements, consistent with data availability, and is parsimoneous with respect to the number of parameters identified through inverse modelling. The best performing parameter sets capture the main aspects of the observed flow and total P (TP) concentrations and provide a suitable basis for a decision-support tool. However, a trade-off is evident between matching the observed flow peaks, flow recessions and TP concentrations simultaneously, highlighting some limitations of the model structure and/or calibration data. Model analysis indicates that daily nonpoint source load cannot be described as a function of near-surface runoff and land use alone, but that other influences, including seasonality, are important. However, further model development to improve performance is likely to introduce additional complexity (in terms of parameter numbers), and hence additional problems of parameter identifiability and output uncertainty, which in turn raises issues of the information content of the available data.

Sensitivity analysis of a catchment-scale nitrogen model

“…Smith and Wheater, 2004), or to distributed models but only varying a small subset of the parameters (e.g. Anderton et al, 2002).…”

“…Meixner et al, 1999;Wade et al, 2001a;Beck and Chen, 2000;McIntyre et al, 2003) explore the response surface of the model output over a relevant region of the input space-as opposed to a local analysis which typically perturbs the model around the most relevant point in the space. Monte Carlo analysis has also been used as a basis for recursively estimating parameters to indicate model structure errors Smith and Wheater, 2004) and assessing significance of input and calibration data errors . All these cited examples used the simplest form of Monte Carlo analysis-plain random sampling of model input parameters from uniform prior distributions, although other distributions and sampling regimes have been employed (see the review of Kalos and Whitlock, 1986).…”

Diffuse Phosphorus Models in the United States and Europe: Their Usages, Scales, and Uncertainties

“…There have been several studies that have evaluated the uncertainties of P models with different complexities at the watershed scale. These include: Barlund and Tattari (2001) using ICECREAMS and a sensitivity/uncertainty approach called UNCSAM; Beven et al (2006) using GLUE applied to the soil layer model MACRO; Buzas (2001) using fuzzy methods; Johnes (2007) for load estimates and the effect of data resolution; Khadam and Kaluarachchi (2006) using a Bayesian framework with export coefficient models; Kim et al (2006) assessing an in‐river model of P dynamics using the GLUE approach; McFarland and Hauck (2001) using a Monte Carlo assessment of an empirical export coefficient model; McIntyre and Wheater (2004) using a Monte Carlo assessment of in‐stream P transport and mobility; Murdoch et al (2005) using a Monte Carlo assessment of a GIS based model; Preston et al (1992) using a relatively early Monte Carlo study of annual loads; Qian (1997) identifying structure of a P retention model for wetlands; Schaerer et al (2006) using a fuzzy decision support tree for P export; Smith et al (2005) using a Monte Carlo assessment of a hybrid metric‐conceptual model for P exports from agricultural catchments; Smith and Wheater (2004) using a multi‐objective approach (i.e., the use of more than one objective function criterion to evaluate model performance) to P model evaluation; Sohrabi et al (2003) using a Monte Carlo analysis of SWAT2000; Taskinen et al (1994) using a probabilistic assessment of P balance calculations; and van Griensven et al (2006) using a total sensitivity analysis of SWAT for P and other water quality parameters; Dean et al (2008) using a GLUE assessment of INCA‐P. We are sure other examples can be found, however, the consideration of uncertainty in P modeling seems a relatively recent activity.…”

Understanding parameter sensitivity and its management implications in watershed‐scale water quality modeling

“…This Monte Carlo based technique, was first applied to the problem of eutrophication [ Hornberger and Spear , 1980, 1981; Spear and Hornberger , 1980]. It has been used for many different problems, including water quality [ Lence and Takyi , 1992; Spear et al , 1994 ; Smith and Wheater , 2004], population dynamics [ Auslander , 1982], toxicology [ Spear et al , 1991] and nuclear safety [ Cook and Gimblett , 1991]. Recent studies concentrated on integrating GSA into the calibration procedure for hydrologic and soil‐vegetation‐atmosphere transfer (SVAT) models [ Yapo et al , 1998; Bastidas et al , 1999; Demarty et al , 2004, 2005].…”