Confidence intervals of the Kling-Gupta efficiency

Vrugt, Jasper A.; Oliveira, Debora Yumi de

doi:10.1016/j.jhydrol.2022.127968

Cited by 9 publications

(2 citation statements)

References 60 publications

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“…For example, the mean squared log error (MSLE), which corresponds to the lognormal log‐likelihood ℓ 3 , is obtained from ℓ 2 by changing variables

{\ell }_{3}={\ell }_{2}(v(y))+\mathrm{ln}\vert {v}^{\prime }(y)\vert ,

where v , the natural log in this case, can be substituted with other functions to obtain log‐likelihood “equivalents” for normalized squared error (NSE; Nash & Sutcliffe, 1970), mean squared percent error (MSPE), as well as their Laplace equivalents. “Equivalence” here means they are equivalent in a maximum likelihood sense that optimizing on ℓ yields the same parameter set as optimizing on the objective function (but not to be confused with the actual ℓ of NSE, which would be used to estimate a confidence interval; e.g., Vrugt & de Oliveira, 2022). The classic NSE and MSE are only equivalent in the former sense (Appendix ), meaning they are redundant as objectives, so the demonstration uses a common variant of NSE.…”

Section: Objectives To Log Likelihoodsmentioning

confidence: 99%

How to Select an Objective Function Using Information Theory

Hodson,

Over,

Smith

et al. 2024

Water Resources Research

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In machine learning or scientific computing, model performance is measured with an objective function. But why choose one objective over another? According to the information‐theoretic paradigm, the “best” objective function is whichever minimizes information loss. To evaluate different objectives, transform them into likelihoods. The ratios of these likelihoods represent how strongly we should prefer one objective versus another, and the log of that ratio represents the relative information loss (or gain) from one objective to another. In plain terms, minimizing information loss is equivalent to minimizing uncertainty, as well as maximizing probability and general utility. We argue that this paradigm is well‐suited to models that have many uses and no definite utility like the complex Earth system models used to understand the effects of climate change. Furthermore, the benefits of “maximizing information and general utility” extend beyond model accuracy to other important considerations including how efficiently the model calibrates, how well it generalizes, and how well it compresses data.

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“…For example, the mean squared log error (MSLE), which corresponds to the lognormal log‐likelihood ℓ 3 , is obtained from ℓ 2 by changing variables

{\ell }_{3}={\ell }_{2}(v(y))+\mathrm{ln}\vert {v}^{\prime }(y)\vert ,

Section: Objectives To Log Likelihoodsmentioning

confidence: 99%

How to Select an Objective Function Using Information Theory

Hodson,

Over,

Smith

et al. 2024

Water Resources Research

View full text Add to dashboard Cite

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“…The KGE is an enhanced version of the Nash criterion (NSE) [98], which incorporates evaluations of correlation (r), bias (β), and variability (α) [97]. KGE values range from −∞ to 1, where a value of 1 indicates a perfect fit to the in situ data [47,99,100].…”

Section: Evaluation Of Gridded Precipitation Productsmentioning

confidence: 99%

Evaluation of Gridded Rainfall Products in Three West African Basins

Goudiaby,

Bodian,

Dezetter

et al. 2024

Hydrology

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In recent years, accessing rainfall data from ground observation networks maintained by national meteorological services in West Africa has become increasingly challenging. This is primarily due to high acquisition costs and the often sparse distribution of rainfall gauges across the region, which limits their use in hydrological studies and related research. At the same time, the rising availability of precipitation products derived from satellite/earth observations, reanalysis datasets, and in situ measurements presents exciting prospects for hydrological applications. Nonetheless, these datasets constitute indirect measurements, necessitating rigorous validation against ground-based rainfall data. This study comprehensively assesses twenty-three gridded rainfall products, including sixteen from satellites, six from reanalysis data, and one from in situ measurements, across the Senegal, Gambia, and Casamance River basins. Performance evaluation is conducted across distinct climatic zones, both pre- and post-resampling against observed rainfall data gathered from forty-nine rainfall stations over a six-year period (2003–2008). Evaluation criteria include the Kling–Gupta Efficiency (KGE) and Percentage of Bias (PBIAS) metrics, assessed at daily, monthly, and seasonal time steps. The results reveal distinct performance levels among the evaluated rainfall products. RFE, ARC2, and CPC notably yield the highest KGE scores at the daily time step, while GPCP, CHIRP, CHIRPS, RFE, MSWEP, ARC2, CPC, TAMSAT, and CMORPHCRT demonstrate superior performance at the monthly time step. During the rainy season, these products generally exhibit robustness. However, rainfall estimates derived from reanalysis datasets (ERA5, EWEMBI, MERRA2, PGF, WFDEICRU, and WFDEIGPCC) perform poorly in the studied basins. Based on the PBIAS metric, most products tend to underestimate precipitation values, while only PERSIANN and PERSIANNCCS lead to significant overestimations. Spatially, optimal performance of the products is observed in the Casamance basin and the Sudanian and Sahelian climatic zones within the Gambia and Senegal basins. Conversely, in the Guinean zone of the Gambia and Senegal Rivers, the rainfall products displayed the poorest performance.

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Sediment load forecasting from a biomimetic optimization perspective: Firefly and Artificial Bee Colony algorithms empowered neural network modeling in Çoruh River

Katipoğlu,

Kartal,

Pande

2024

Stoch Environ Res Risk Assess

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The service life of downstream dams, river hydraulics, waterworks construction, and reservoir management is significantly affected by the amount of sediment load (SL). This study combined models such as the artificial neural network (ANN) algorithm with the Firefly algorithm (FA) and Artificial Bee Colony (ABC) optimization techniques for the estimation of monthly SL values in the Çoruh River in Northeastern Turkey. The estimation of SL values was achieved using inputs of previous SL and streamflow values provided to the models. Various statistical metrics were used to evaluate the accuracy of the established hybrid and stand-alone models. The hybrid model is a novel approach for estimating sediment load based on various input variables. The results of the analysis determined that the ABC-ANN hybrid approach outperformed others in SL estimation. In this study, two combinations, M1 and M2, with different input variables, were used to assess the model's accuracy, and the best-performing model for monthly SL estimation was identified. Two scenarios, Q(t) and Q(t − 1), were coupled with the ABC-ANN algorithm, resulting in a highly effective hybrid approach with the best accuracy results (R2 = 0.90, RMSE = 1406.730, MAE = 769.545, MAPE = 5.861, MBE = − 251.090, Bias Factor = − 4.457, and KGE = 0.737) compared to other models. Furthermore, the utilization of FA and ABC optimization techniques facilitated the optimization of the ANN model parameters. The significant results demonstrated that the optimization and hybrid techniques provided the most effective outcomes in forecasting SL for both combination scenarios. As a result, the prediction outputs achieved higher accuracy than those of a stand-alone ANN model. The findings of this study can provide essential resources to various managers and policymakers for the management of water resources.

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Confidence intervals of the Kling-Gupta efficiency

Cited by 9 publications

References 60 publications

How to Select an Objective Function Using Information Theory

How to Select an Objective Function Using Information Theory

Evaluation of Gridded Rainfall Products in Three West African Basins

Sediment load forecasting from a biomimetic optimization perspective: Firefly and Artificial Bee Colony algorithms empowered neural network modeling in Çoruh River

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