Using maximum likelihood to derive various distance-based goodness-of-fit indicators for hydrologic modeling assessment

Cheng, Qinbo; Chen, Xi; Xu, Chong‐Yu; Zhang, Zhicai; Reinhardt‐Imjela, Christian; Schulte, Achim

doi:10.1007/s00477-017-1507-8

Cited by 7 publications

(11 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…RMS is defined as where h o is observed (i.e., the true model) depth of soil layer at location i, h m is the model (i.e., inverted model), and N is the number of observations. If RMS is equal to 0, clearly, the model-simulated results perfectly match the observations; if RMS is greater than 100%, then the model is no better than a predictor using zero (Cheng et al 2018).…”

Section: Effect Of Measurement Errormentioning

confidence: 64%

Evaluation of electrical resistivity tomography (ERT) for mapping the soil–rock interface in karstic environments

et al. 2019

Self Cite

View full text Add to dashboard Cite

Rocky desertification is a significant threat in the karst regions of southwest China. Studies of soil distribution can contribute to protecting and recovering the fragile karst ecosystem that is prevalent in this region. With an underlying aim of being able to assess soil stocks in karstic environments, this study evaluates the use of electrical resistivity tomography (ERT) for delineating the soil-rock interface. Using a synthetic model (that recognizes the three-dimensional nature of the subsurface), experiments are performed to assess the impact of measurement errors and measurement configuration on recovery of the interface. The inverted results show that the accuracy of the delineation of the soil-rock interface decreases with the increase of measurement error and dipole spacing. The results also show the importance of reliable estimation of measurement errors. Field-based applications of ERT at five exposed profiles in southwest China are also reported. For the field data, three-dimensional modelling was necessary to account for the exposed face. The field experiments show that ERT can be effective at delineating the interface between soil and bedrock, but resolution can be limited due to the scale of features or lack of contrast between soil and bedrock. The method shows great promise as a means of assessing, in a non-invasive manner, the soil-bedrock interface, and, perhaps, more significantly, quantifying estimates of total soil stocks, as we seek to quantify the vulnerability or resilience of this important landscape to anthropogenic and natural stresses.

show abstract

Section: Effect Of Measurement Errormentioning

confidence: 64%

Evaluation of electrical resistivity tomography (ERT) for mapping the soil–rock interface in karstic environments

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nevertheless, the larger range of model residuals in Figure 5b than in Figure 4b shows that the performance of model-simulated seepages for the MSE method is better than that for the L approach. Possibly, the MSE method over-calibrates the MF2K-VSF model [16,20].…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, hydrologists have proposed many statistical measures as model efficiency criteria instead of subjective visual judgment to ascertain the goodness of fit of hydrologic models [8][9][10][11][12]. Among these goodness-of-fit indicators, the mean squared error (MSE) (i.e., standard least squares) and its normalization (i.e., Nash-Sutcliffe efficiency (NSE) defined by Nash and Sutcliffe [13] are most widely used [7,9,12,[14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…The maximum likelihood value is in agreement with the best model parameters, which is the so-called maximum likelihood estimation. Moreover, some statistical measures can be reevaluated from the likelihood function viewpoint [16]. For example, numerous authors [14,21,22] pointed out that MSE implies statistical assumptions that model errors should be independent and identically distributed (I.I.D.)…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Inverse Modeling by Separating Model Structural and Observational Errors

Cheng

Chen

Cheng

et al. 2018

Water

Self Cite

View full text Add to dashboard Cite

A practical formal likelihood function (L) is developed to separate model structure errors and observation errors by the separation of correlated and uncorrelated model residuals. L overcomes the time-consuming problem of likelihood functions proposed by previous studies, and combines the Mean Square Error (MSE) and first-order Auto-Regression (AR(1)) models. For comparison of the effect of different error models, MSE, AR(1), and L are used as efficiency criteria to calibrate the three-dimensional variably saturated ground-water flow model (MF2K-VSF) based on the soil tank seepages of rainfall-runoff experiments. Results of L are nearly the same as those of AR(1) due to negligible observational errors. Although all calibrated models well mimic the seepage discharges, MF2K-VSF with MSE cannot capture the groundwater level and soil suction processes because of the considerable autocorrelation of model residuals owing to model inadequacies (e.g., neglect of the soil moisture hysteresis), which obviously violates the statistical assumption of MSE. By contrast, L accounts for the model structural errors and thus enhances the reliability of hydrological simulations.

show abstract

“…Then, two likelihood functions of the NSE and BC-GED are used as the optimization objective functions to calibrate flow and sediment parameters of SWAT with the water balance model and the variable source area concept (SWAT-WB-VSA) in the Baocun watershed, Eastern China [2]. The Nash-Sutcliffe efficiency coefficient (NSE) approach assumes that errors between observed and simulated outcomes follow the Gaussian distribution [22], and the BC-GED approach first utilizes the Box-Cox transformation (BC) to remove the heteroscedasticity of model residuals and then assumes that model residuals after BC transformation follow the generalized error distribution (GED) [23]. Finally, the Bayesian inference results (e.g., posterior distribution of parameter set) of the NSE approach are compared with that of the BC-GED method for studying the effect of likelihood functions.…”

Section: Introductionmentioning

confidence: 99%

The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

Cheng

Chen

Wang³

et al. 2018

Water

Self Cite

View full text Add to dashboard Cite

The soil and water assessment tool (SWAT) is widely used to quantify the spatial and temporal patterns of sediment loads for watershed-scale management of sediment and nonpoint-source pollutants. However few studies considered the trade-off between flow and sediment objectives during model calibration processes. This study proposes a new multi-objective calibration method that incorporates both flow and sediment observed information into a likelihood function based on the Bayesian inference. For comparison, two likelihood functions, i.e., the Nash–Sutcliffe efficiency coefficient (NSE) approach that assumes model residuals follow the Gaussian distribution, and the BC-GED approach that assumes model residuals after Box–Cox transformation (BC) follow the generalized error distribution (GED), are applied for calibrating the flow and sediment parameters of SWAT with the water balance model and the variable source area concept (SWAT-WB-VSA) in the Baocun watershed, Eastern China. Compared with the single-objective method, the multi-objective approach improves the performance of sediment simulations without significantly impairing the performance of flow simulations, and reduces the uncertainty of flow parameters, especially flow concentration parameters. With the NSE approach, SWAT-WB-VSA captures extreme flood events well, but fails to mimic low values of river discharge and sediment load, possibly because the NSE approach is an informal likelihood function, and puts greater emphasis on high values. By contrast, the BC-GED approach approximates a formal likelihood function, and balances consideration of the high- and low- values. As a result, inferred results of the BC-GED method are more reasonable and consistent with the field survey results and previous related-studies. This method even discriminates the nonerodible characteristic of main channels.

show abstract

Using maximum likelihood to derive various distance-based goodness-of-fit indicators for hydrologic modeling assessment

Cited by 7 publications

References 52 publications

Evaluation of electrical resistivity tomography (ERT) for mapping the soil–rock interface in karstic environments

Evaluation of electrical resistivity tomography (ERT) for mapping the soil–rock interface in karstic environments

Improved Inverse Modeling by Separating Model Structural and Observational Errors

The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

Contact Info

Product

Resources

About