Hydrologic modeling in dynamic catchments: A data assimilation approach

Abstract

The transferability of conceptual hydrologic models in time is often limited by both their structural deficiencies and adopted parameterizations. Adopting a stationary set of model parameters ignores biases introduced by the data used to derive them, as well as any future changes to catchment conditions. Although time invariance of model parameters is one of the hallmarks of a high quality hydrologic model, very few (if any) models can achieve this due to their inherent limitations. It is therefore proposed to consider parameters as potentially time varying quantities, which can evolve according to signals in hydrologic observations. In this paper, we investigate the potential for Data Assimilation (DA) to detect known temporal patterns in model parameters from streamflow observations. It is shown that the success of the DA algorithm is strongly dependent on the method used to generate background (or prior) parameter ensembles (also referred to as the parameter evolution model). A range of traditional parameter evolution techniques are considered and found to be problematic when multiple parameters with complex time variations are estimated simultaneously. Two alternative methods are proposed, the first is a Multilayer approach that uses the EnKF to estimate hyperparameters of the temporal structure, based on apriori knowledge of the form of nonstationarity. The second is a Locally Linear approach that uses local linear estimation and requires no assumptions of the form of parameter nonstationarity. Both are shown to provide superior results in a range of synthetic case studies, when compared to traditional parameter evolution techniques.PUBLICATIONS characteristics of the time series of system states (such as peak flow, base flows, volume of runoff, soil moisture storage fluctuations etc.) [Moussa and Chahinian, 2009;Efstratiadis and Koutsoyiannis, 2010;Westerberg et al., 2011]. Multiobjective criterion type approaches have shown promise in defining parameter spaces which provide improved simulations over a range of characteristics, but trade-offs are almost always required [Madsen, 2003;Efstratiadis and Koutsoyiannis, 2010].One possible approach to improve the applicability of hydrologic models over long time scales is to allow the model parameters to evolve with time. Time varying parameter systems have been investigated in fundamental systems theory over the last few decades [e.g., Richards, 1983;Schwartz and Ozbay, 1990;Mohammadpour and Scherer, 2012], the most common being Linear Time Variant systems where the state space transition matrix is time varying [e.g., Khalil, 1996]. A well-known example of a time varying parameter system is the variation in aerodynamic coefficients during take-off, cruising and landing for high speed aircraft [e.g., Tomas-Rodriguez and Banks, 2010]. In hydrologic applications, model parameterizations would adjust to varying climatic regimes and/or changes in catchment conditions based on signals in the input and observed data under such a framework. It can be argued that time var...

Time-varying parameter models for catchments with land use change: the importance of model structure

“…Previous work proposed the use of models whose parameters vary with time in response to signals of change in observations. The so-called Locally Linear (LL) Dual EnKF time-varying parameter estimation algorithm (Pathiraja et al, 2016a) was applied to two sets of small (< 350 ha) paired experimental catchments with deforestation occurring under experimental conditions (rapid clearing of 100 and 50 % of land surface) (Pathiraja et al, 2016b). Here we demonstrate the efficacy of the method for a larger catchment experiencing more realistic land cover change, while also investigating the importance of the chosen model structure in ensuring the success of the time-varying parameter estimation method.…”

“…A data-assimilation-based framework for estimating timevarying parameters was presented in Pathiraja et al (2016a). The approach relies on an ensemble Kalman filter (EnKF) (Evensen, 1994) to perform sequential joint state and parameter updating.…”

“…The method was verified against multiple synthetic case studies as well as for two small experimental catchments experiencing controlled land use change (Pathiraja et al, 2016a, b). The algorithm is summarized below; for full details refer to Pathiraja et al (2016a).…”

“…practical alternative to sequential Monte Carlo/particle filter methods that propagate the full probability density through time but suffer from several implementation issues, even in moderate dimensional systems. The LL Dual EnKF method of Pathiraja et al (2016a) works by sequentially proposing parameters, updating these using the ensemble Kalman filter and available observations and subsequently using these updated parameters to propose and update model states. An approach for proposing parameters in the time-varying setting was also presented, for cases where no prior knowledge of parameter variations is available.…”

“…They can also be used to determine whether land cover changes (and not solely meteorological factors) contribute to observed changes in streamflow dynamics in retrospective studies where the lack of a paired control catchment precludes such an assessment. Pathiraja et al (2016a) presented an ensemble Kalman filter based algorithm (the so-called Locally Linear (LL) Dual EnKF) to estimate time variations in model parameters. The method sequentially assimilates observations into a numerical model in real time to generate improved estimates of model states, fluxes and parameters based on their respective uncertainties.…”