Assessment of model uncertainty for soil moisture through ensemble verification

Abstract

[1] The Community Land Model (CLM2.0) has been used to simulate land surface processes in a small corn field. The subdivision of grid cells into patches in the CLM2.0 was explored for the generation of Monte Carlo simulations for use in calibration and ensemble generation. A distributed multiobjective calibration was developed for the optimal estimation of parameters and initial state variables for 36 soil moisture profiles. Since the resulting parameter and initial state values did not lead to perfect simulations for soil moisture, and in order to better understand the forecast uncertainty, ensemble runs were generated. The ensembles generated by CLM2.0 have been verified by several methods that are commonly used in meteorology. It was shown that the perfect model approach cannot be applied for bounded hydrological applications and that perturbation of parameters is a necessity to obtain a realistic assessment of the forecast error. Perturbation of forcings only captures more of the model uncertainty than perturbation of initial conditions only, but also causes a too limited spread in the ensembles. The generation of ensemble members through perturbation of the parameter set, found through calibration, does not necessarily result in ensembles that surround the calibrated deterministic control run for soil moisture. This is partially due the nonlinearity of the model in the parameters. It may also indicate that some parameter sets are not robust and not appropriate to perturb for ensemble generation. Consequently, the resulting ensemble mean may not represent the best forecast or a priori state estimation. During periods of extreme drought or precipitation, the ensemble probability density function (pdf) deviates far from normality and the model behaves very nonlinearly. For state estimation, methods like the ensemble Kalman filter are best suited for the propagation of the first moments to account for the nonlinear dynamics during crucial events for hydrological simulations. However, the a posteriori estimate for this technique will only be optimal in the limited class of linear filters, since the underlying pdfs cannot be assumed to be Gaussian.

Disentangling timing and amplitude errors in streamflow simulations

“…Related to that, we provide and test several quality criteria to evaluate deterministic uncertainty ranges. The skill of uncertainty ranges is still rarely evaluated in hydrology (Franz and Hogue, 2011), and most of the available methods such as rank probability scores (Duan et al, 2007), rank histograms, or the usage of different moments of the probability density function (De Lannoy et al, 2006) were developed in climatology (Gneiting et al, 2008;Franz and Hogue, 2011). These approaches typically quantify ensemble spread and thus are probabilistic approaches to evaluate uncertainty estimation.…”

Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe?

“…In particular, only three parameters were selected: Wmax, Ks and Kc, for which the relative standard deviations were expressed as percentage α of the absolute value of the parameter, i.e., σWmax = α1Wmax, σKs = α2Ks, and σKc = α3Kc. The model error estimation was performed by varying the values of the percentages αi (i = 1,2,3) along with σp (σT was assumed constant) in a way that two ensemble verification measures (Test #1 and Test #2 onward) commonly used in meteorology [29] were satisfied. That is, if the ensemble spread sp is large enough, the temporal mean of the ensemble skill <sk> should be similar to the temporal average of the ensemble spread <sp>…”

“…The authors highlighted that inappropriate model error assumptions can lead to circumstances in which the assimilation of surface SM can degrade the performance of open loop simulations. De Lannoy et al [29] proposed using two ensemble indexes statistics previously employed in weather forecast analysis for calibrating the model error parameters and for giving an estimate of the model error, while in a recent paper Alvarez-Garreton et al [22] used a methodology that maximizes the likelihood of observing historical streamflow data given the calibrated model parameters and the model parameter errors. Despite the effort made by these studies, a clear guideline for a proper model error assessment appears to be a long way off from reaching a final solution.…”

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund–Potsdam–Jena (LPJ) model as an example

“…In this work, a new approach was established to ascertain which subset or combination of relatively more sensitive and important parameters causes maximum uncertainty in numerical simulation and forecast results because the parameters combination should be considered to reduce the uncertainty of numerical simulation, such as the data assimilation method and the optimal method (Vrugt et al 2005;De Lannoy et al 2006). After first providing an overview of the new approach in Section 2, we then describe its methodology in more detail in Section 3, as well as the experimental procedures used to test it.…”