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On the Validation of Models

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... The hybrid SVR-GWO model is closely followed by the SVR-SHO model. The comparison of two methods and all six stations 1901-19811982Bageshwar 1901-19811982Champawat 1901-19811982Nainital 1901-19811982Pithoragarh 1901-19811982Pantnagar 1961-20002001Garhwal Chamoli 1901-19811982Dehradun 1901-19811982Haridwar 1901-19811982Pauri Garhwal 1901-19811982Rudraprayag 1901-19811982Tehri Garhwal 1955-19971998Uttarkashi 1951-19901991 Table 4 exposed the best prediction of EDI at Pithoragarh station. Similarly, Table 4 outlines the prediction results of SVR-GWO, and SVR-SHO models during the validation period for Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi stations. ...
... The hybrid SVR-GWO model is closely followed by the SVR-SHO model. The comparison of two methods and all six stations 1901-19811982Bageshwar 1901-19811982Champawat 1901-19811982Nainital 1901-19811982Pithoragarh 1901-19811982Pantnagar 1961-20002001Garhwal Chamoli 1901-19811982Dehradun 1901-19811982Haridwar 1901-19811982Pauri Garhwal 1901-19811982Rudraprayag 1901-19811982Tehri Garhwal 1955-19971998Uttarkashi 1951-19901991 Table 4 exposed the best prediction of EDI at Pithoragarh station. Similarly, Table 4 outlines the prediction results of SVR-GWO, and SVR-SHO models during the validation period for Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi stations. ...
... The hybrid SVR-GWO model is closely followed by the SVR-SHO model. The comparison of two methods and all six stations 1901-19811982Bageshwar 1901-19811982Champawat 1901-19811982Nainital 1901-19811982Pithoragarh 1901-19811982Pantnagar 1961-20002001Garhwal Chamoli 1901-19811982Dehradun 1901-19811982Haridwar 1901-19811982Pauri Garhwal 1901-19811982Rudraprayag 1901-19811982Tehri Garhwal 1955-19971998Uttarkashi 1951-19901991 Table 4 exposed the best prediction of EDI at Pithoragarh station. Similarly, Table 4 outlines the prediction results of SVR-GWO, and SVR-SHO models during the validation period for Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi stations. ...
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Drought is a complex natural phenomenon, so, precise prediction of drought is an effective mitigation tool for measuring the negative consequences on agriculture, ecosystems, hydrology, and water resources. The purpose of this research was to explore the potential capability of support vector regression (SVR) integrated with two meta-heuristic algorithms i.e., Grey Wolf Optimizer (GWO), and Spotted Hyena Optimizer (SHO), for meteorological drought (MD) prediction by utilizing EDI (effective drought index). For this objective, the two-hybrid SVR–GWO, and SVR–SHO models were constructed at Kumaon and Garhwal regions of Uttarakhand State (India). The EDI was computed in both study regions by using monthly rainfall data series to calibrate and validate the advanced hybrid SVR models. The autocorrelation function (ACF) and partial-ACF (PACF) were utilized to determine the optimal inputs (antecedent EDI) for EDI prediction. The results produced by the hybrid SVR models were compared with the calculated (observed) values by employing the statistical indicators and through graphical inspection. A comparison of results demonstrates that the hybrid SVR–GWO model outperformed to the SVR–SHO models for all study stations located in Kumaon and Garhwal regions. Also, the results highlighted the better suitability, supremacy, and convergence behavior of meta-heuristic algorithms (i.e., GWO and SHO) for meteorological drought prediction in the study regions.
... The nine locations where field and numerical data were compared are shown in Fig. 2; full validation of the DELFT3D modeling approach is documented in Zarzuelo et al. (2015Zarzuelo et al. ( , 2020Zarzuelo et al. ( , 2021. Figure 2 depicts the correlation and skill coefficients for water levels, east and north velocities, residual currents projected on the axis of the channel, temperature, salinity, and significant wave height. The skill coefficient score is calculated following the formulation proposed by Willmott (1981) to know in more detail the adjustment of the trend and the high and low peaks (Olabarrieta et al., 2011;Zarzuelo et al., 2015). Figure 3 shows the agreement of the temperature and salinity, the two variables with the lowest correlations, between the measured and modeled results. ...
... The period of constituent M2 (12.42 h) is the time required for the phase to complete a 360 • cycle. Willmott, 1981) of the water level, east and north instantaneous velocity, residual velocity, temperature, salinity, and wave height for each station. The color indicates the degree of accuracy (green indicates excellent agreement, yellow-orange indicates good agreement, and red indicates poor agreement). ...
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Estuarine dynamics are highly complex as a result of the temperature and salinity gradients, as well as the multiple interactions between atmospheric, maritime, and hydrological forcing agents. Given the environmental and socioeconomic importance of estuaries and their current and future threats due to human interventions and climate change, it is of vital importance to characterize these dynamics, monitor their evolution, and quantify the expected impacts derived from climate change. This paper presents a hybrid database combining data obtained in six field surveys (in 2012, 2013, and 2015) and results from a physically based 3D numerical model for the Bay of Cádiz (southern Spain), a highly anthropized mesotidal estuary. The 3D dataset includes water levels, currents, density, and wave climate, allowing for an analysis of bay dynamics at different timescales ranging from intratidal processes to seasonal variabilities. The results offer an example of the potential uses of the dataset and include (1) an assessment of the spatial and seasonal variability of the estuarine dynamics and (2) an analysis of the effects of severe weather events. These examples provide convincing evidence regarding how the dataset can be employed in multiple research fields and applications, including ocean–bay interactions, water exchange between basins, longwave and shortwave propagation along creek systems, and energy extraction of tidal waves. Therefore, this hybrid dataset may be of significant interest for stakeholders and scientists from different sectors (water engineering, ecology, urban development, energy, etc.) working on the environmental management of the Gulf of Cádiz and other tidally dominated shallow bays. It can also serve as a benchmark test for numerical hydrodynamic models, infrastructure intervention assessments (e.g., dikes or breakwaters), or renewable energy conversion system models. The dataset is available at https://doi.org/10.5281/zenodo.7484186 (Zarzuelo et al., 2022b).
... Examples include the Pearson correlation coefficient, the Nash-Sutcliffe efficiency and its modified forms, Legates and McCabe's index, relative root mean square error of Loague and Green, Willmott's indices of agreement and their refined versions, Mielke's permutation indices and the associated transformation considered by Watterson. The aforementioned criteria have received considerable attention over the years, beginning with the works on hydrologic and hydroclimatic models: (Nash and Sutcliffe, 1970;McCuen and Snyder, 1975;Willmott, 1981;Willmott, 1982;Mielke, 1984;Willmott et al., 1985;Willmott et al., 2012;Loague and Green, 1991;Legates and McCabe, 1999;Legates and McCabe, 2013;Krause et al., 2005). Some examples of recent applications include (Nas and Berktay, 2010;Meng et al., 2013;Gong et al., 2014;Arslan and Turan, 2015;Duveiller et al., 2016;Ozelkan et al., 2016;Deepika et al., 2020;Ananias et al., 2021;Yang and Xing, 2021). ...
... where a and f denote the means of the actual values a i and the forecasts f i . The original version for k = 2 was proposed by (Willmott, 1981;Willmott, 1982 andWicks, 1980), whereas a modification involving k = 1 was put forward by (Willmott et al., 1985). It is well known that both forms of the measure are bounded from below by zero, with the maximum value of one meaning a perfect match. ...
Article
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Spatial interpolation has been applied for mapping various variables in a wide range of environmental disciplines. This study aims to develop novel tools for examining the relative performance of different interpolation methods. We shall quantify and compare the quality of interpolation models by applying, among others, some inequality indices of error distributions. Such indices can generally be classified as non-dimensional and global. The performance measures explored here provide a valuable supplement to the conventional accuracy assessment, and have so far received only scant attention in the relevant literature. Given a wide range of potential applications for the methods discussed here, the main focus of the paper will be on empirical research concerning variability of soil properties. The eight interpolation methods, i.e., Inverse Distance Weighting (IDW), Modified Shepard’s Method (MS), Radial Basis Function (RBF), Natural Neighbour (NaN), Nearest Neighbour (NeN), Triangulation with Linear Interpolation (TIN), Local Polynomial (LP) and Ordinary Kriging (OK) were applied to estimate spatial distribution of soil pH, nitrogen, potassium and phosphorus content. Biplot methods were applied to visually examine the numerical results on the assessment of prediction quality. The ordinary kriging showed superior performance compared to the competing methods in majority of the cases. Significantly, predictions by kriging approaches revealed substantial improvement by considering data transformations. As concerns the other tested methods, the IDW and the LP algorithms tend to share similar characteristics. In turn, the NeN, RBF and MS algorithms scored relatively small inequality indices, when compared to the other methods. The use of new proposed measures will enable practitioners to gain more insightful and comprehensive evaluations of spatial interpolation techniques.
... To investigate the evaluation of AI models efficiency in the training and testing phases, index of agreement (IOA) , root mean square error (RMSE), mean absolute error (MAE), and scatter index (SI) have been utilized. These statistical criteria were frequently applied to evaluate WQI predictions and other water resources problems, such as stream flow forecasting and soil temperature (e.g., [3,25,30,[36][37][38][39]). ...
... IOA criterion developed by Willmott [36] as a standardized measure of the degree of numerical model estimation error and varied between 0 and 1. The best value of the IOA value was +1. ...
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To restrict the entry of polluting components into water bodies, particularly rivers, it is critical to undertake timely monitoring and make rapid choices. Traditional techniques of assessing water quality are typically costly and time-consuming. With the advent of remote sensing technologies and the availability of high-resolution satellite images in recent years, a significant opportunity for water quality monitoring has arisen. In this study, the water quality index (WQI) for the Hudson River has been estimated using Landsat 8 OLI-TIRS images and four Artificial Intelligence (AI) models, such as M5 Model Tree (MT), Multivariate Adaptive Regression Spline (MARS), Gene Expression Programming (GEP), and Evolutionary Polynomial Regression (EPR). In this way, 13 water quality parameters (WQPs) (i.e., Turbidity, Sulfate, Sodium, Potassium, Hardness, Fluoride, Dissolved Oxygen, Chloride, Arsenic, Alkalinity, pH, Nitrate, and Magnesium) were measured between 14 March 2021 and 16 June 2021 at a site near Poughkeepsie, New York. First, Multiple Linear Regression (MLR) models were created between these WQPs parameters and the spectral indices of Landsat 8 OLI-TIRS images, and then, the most correlated spectral indices were selected as input variables of AI models. With reference to the measured values of WQPs, the WQI was determined according to the Canadian Council of Ministers of the Environment (CCME) guidelines. After that, AI models were developed through the training and testing stages, and then estimated values of WQI were compared to the actual values. The results of the AI models’ performance showed that the MARS model had the best performance among the other AI models for monitoring WQI. The results demonstrated the high effectiveness and power of estimating WQI utilizing a combination of satellite images and artificial intelligence models.
... The predictive performance of the five ML models (GRNN, RBFNN, MLPNN, ANFIS and RF) applied in this study were analysed using various statistical metrics. The following metrics were calculated: mean absolute error (MAE), root mean squared error (RMSE); mean absolute percentage error (MAPE), Pearson's correlation coefficient (r), adjusted coefficient of determination (R 2 adj), index of agreement (d) (Willmott 1981) and confidence coefficient (c). The equations of the metric used in this study to evaluate the predictive performance of the models are given in Table S3. ...
... For all scenarios, adaptative neuro-fuzzy inference system showed the worst predictive performance, with R 2 adj between 0.22 and 0.38 and RMSE ranging from 1.40 to 1.63 µmol m −2 s −1 (Table 5; Figs. 5, 6, 7 and 8). Apart from ANFIS, most machine learning models in the training phase showed a high correlation (r ≥ 0.64) and the indices of agreement were above 0.74 (Willmott 1981), demonstrating a very good fit between the observed and estimated values in the respective ML models, according to the classification index (Camargo and Sentelhas 1997; Table 5). ...
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Soil CO2 emission (FCO2) is a critical component of the global carbon cycle, but it is a source of great uncertainty due to the great spatial and temporal variability. Modeling of soil respiration can strongly contribute to reducing the uncertainties associated with the sources and sinks of carbon in the soil. In this study, we compared five machine learning (ML) models to predict the spatiotemporal variability of FCO2 in three reforested areas: eucalyptus (RE), pine (RP) and native species (RNS). The study also included a generalized scenario (GS) where all the data from RE, RP and RNS were included in one dataset. The ML models include generalized regression neural network (GRNN), radial basis function neural network (RBFNN), multilayer perceptron neural network (MLPNN), adaptive neuro-fuzzy inference system (ANFIS) and random forest (RF). Initially, we had 32 attributes and after pre-processing, including Pearson’s correlation, canonical correlation analysis (CCA), and biophysical justification, only 21 variables remained. We used as input variables 19 soil properties and climate variables in reforested areas of eucalyptus, pine and native species. RF was the best model to predict soil respiration to RE [adjusted coefficient of determination (R² adj): 0.70 and root mean square error (RMSE): 1.02 µmol m⁻² s⁻¹], RP (R² adj: 0.48 and RMSE: 1.07 µmol m⁻² s⁻¹) and GS (R² adj: 0.70 and RMSE: 1.05 µmol m⁻² s⁻¹). Our findings support that RF and GRNN are promising for predicting soil respiration of reforested areas which could help to identify and monitor potential sources and sinks of the main additional greenhouse gas over ecosystems. Graphical abstract
... The CC indicates the degree of linear correlation and RMSE magnitude shows the square root of the mean error between RRPs and observed rainfall data. The CC is insensitive to additive and proportional differences between estimated and observed data (Willmott 1981;Moriasi et al. 2015). Considering the limitations of CC, (Willmott 1981) introduced IA that measures the degree of agreement between model estimates and observations. ...
... The CC is insensitive to additive and proportional differences between estimated and observed data (Willmott 1981;Moriasi et al. 2015). Considering the limitations of CC, (Willmott 1981) introduced IA that measures the degree of agreement between model estimates and observations. The IA ranges from 0 to 1 with higher values indicating better agreement between satellite rainfall estimates and observed rainfall. ...
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Flood risk management studies require reliable estimates of extreme precipitation at high spatial–temporal distribution to force hydrologic models. Recently, Remote Sensing Rainfall Products (RRPs) have gained significant importance in the field of hydrometeorology, but their applicability in urban hydrologic predictions remains uncertain. The current study evaluates the accuracy of RRPs in comparison with observed rainfall and the significance of space–time representation of rain in simulating single and bimodal flood hydrographs. The study is conducted for the Adyar river basin, a rapidly developing urban area in Chennai experiencing frequent floods. Sub-daily rainfall retrievals from Integrated Multi-satellite Retrievals for Global Precipitation Measurement version 6 final run product (IMERG GPM), the near-real-time Global Satellite Mapping of Precipitation (GSMaP_NRT) version 6, GSMaP gauge adjusted (GSMaP_Gauge), Precipitation Dynamic Infrared Rain Rate near real-time (PDIR-Now) and Doppler Weather Radar (DWR) are the Remote sensing Rainfall products (RRPs) selected in the present study. Continuous and categorical statistical indices are selected to evaluate the performance of satellite rainfall estimates for the period from 2001 to 2015. Then the hydrologic utility of RRPs is conducted using the Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS) model for five extreme precipitation events. The RRPs simulated the rising and recession portion of flood hydrographs accurately with a bias in peak discharge. Then, two approaches are selected to further improve the flood hydrograph simulations; 1) Hydrologic model simulations after disaggregating the daily station data to sub-daily scale using time characteristics of RRPs, 2) Hydrologic simulations after bias adjusting the RRPs with station data. The study finds substantial improvements in model results in the two approaches. The disaggregation approach using satellite rainfall estimates has overcome the insufficiency of sub-daily rainfall observations. The bias adjusted radar rainfall data is found as best performing for the flood hydrograph simulations.
... The IOA developed by (Willmott 1981) is a standardised quantity to measure the degree of model prediction error. The value of IOA varies between 0 and 1, where 1 indicates a perfect match, and 0 indicates no agreement (Willmott 1981). ...
... The IOA developed by (Willmott 1981) is a standardised quantity to measure the degree of model prediction error. The value of IOA varies between 0 and 1, where 1 indicates a perfect match, and 0 indicates no agreement (Willmott 1981). IOA is defined as: ...
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Documentation of the skill of a prediction system and its comparison with those of leading modelling centres are crucial in model development. This facilitates understanding the limitations of the existing prediction system and aids in its improvement. The current study compares the extended range prediction skill of the Indian Institute of Tropical Meteorology (IITM) generated real-time forecast with that of the UK Met Office (UKMO) forecast during the boreal summer monsoon season. It is found that both models suffer from biases in the climatological mean state of the monsoon. IITM forecast possesses a skill comparable to UKMO coupled seasonal forecast as compared to the observation in the first two weeks leads over most of the meteorological subdivisions during the monsoon months of June to September. However, at longer leads, the UKMO model outperforms the IITM model, which could be credited to its enhanced skill in predicting the monsoon intraseasonal oscillations and the better representation of monsoon variability at the intraseasonal time scale.
... These metrics are also used to determine δ and distribution in F-DGQM and F-DDQM. The evaluation metrics used are as follows: normalized root mean square error (NRMSE), the percent bias (Pbias), the Nash-Sutcliffe efficiency (NSE) (Nash and Sutcliffe 1970), the modified index of agreement (MD) (Willmott 2013), and the Kling-Gupta efficiency (KGE) (Gupta et al. 2009). The evaluation metrics in this study are presented in Eqs. ...
... MD estimates the sum and proportional difference between the observed and GCM data (Willmott 2013). ...
Article
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Double gamma quantile mapping (DGQM) can outperform single gamma quantile mapping (SGQM) for bias correction of global circulation models (GCMs) using two gamma functions for two segments based on a specific quantile. However, there are two ambiguous points, the use of specific quantile and only Gamma probability distribution function. Therefore, this study introduced a flexible dividing point, δ (%), which can be adjusted to the regionally observed values at the station and consider the combination of various probability distributions for the two separate segments (e.g., Weibull, lognormal, and Gamma). The newly proposed method, flexible double distribution quantile mapping (F-DDQM), was employed to correct the bias of 8 GCMs of Coupled Model Intercomparison Project Phase 6 (CMIP6) at 22 stations in South Korea. The results clearly show a higher performance of F-DDQM than DGQM and Flexible-DGQM (F-DGQM) by 27% and 19%, respectively, in root mean square error. The F-DGQM also performed better in replicating probability distribution, spatial variability and extremes of observed precipitation than other methods. This study contributes to improving the bias correction method for better projection of extreme values.
... Generally, circulation model performance can be evaluated via model-observation comparisons, including temporal comparisons of time series of temperature, salinity and sea surface height at observed locations (e.g., Conlon et al., 2018;Lavaud et al., 2020;Stanev et al., 2019), and spatial comparisons of distributions of velocity along horizontal and vertical transects . The evaluations are commonly represented in quantitative metrics, such as correlation, mean square error, mean absolute error, bias and other self-defined parameters Mark et al., 2008;Pairaud et al., 2011;Sentchev & Yaremchuk, 2016;Willmott, 1981;Xue et al., 2005). Particle tracking models can be evaluated by comparisons between observed drifter tracks and simulated trajectories of passive particles released at the same times and locations (Bouzaiene et al., 2021;Hart-Davis et al., 2018;Kako et al., 2010;Thorpe et al., 2004). ...
... Vertically, the observed velocities were collected from 2 (6) m to the bottom with a bin of 1 (2) m for the nearshore (offshore) transects, so the modeled velocities were also linearly interpolated to the same depths for the assessment. The model performance was assessed using the Willmott Skill (Willmott, 1981): ...
Article
Sections of the coastal Gulf of Maine (GoME) differ in circulation, temperature, salinity, and primary production. These regional differences as well as their temporal changes, together with biological factors, such as the vertical migration, pelagic larval duration, etc., determine marine larval transports, and further affect the population connectivity, and community assembly in the intertidal GoME. To investigate the variations of coastal currents in the GoME, we built a high-resolution circulation model covering the shelf seas from Long Island Sound to the Gulf of St. Lawrence, This model was quantitatively validated with observed sea surface height (SSH), time series of temperature, salinity, and velocity, composite temperature and salinity characteristics from CTD stations, and ADCP transects. Overall, the circulation model successfully reproduced the seasonal and interannual variations of SSH, temperature, salinity, and velocity in the nearshore and coastal GoME, while the performance in predicting velocity in the offshore GoME was less successful. To study the alongshore and cross-shore material transport and population connectivity of Mytilus edulis, we evaluated a particle tracking model with satellite-tracked drifters. It can reproduce the general patterns of drifter tracks in the coastal GoME within the period of a month, though the separation distances between drifters and simulated particles generally accumulate by 3km/day. Our model showed that in the northeast corner of the GoME, the Eastern Maine Coastal Current (EMCC) possesses two cores, an offshore and a nearshore core that peak in summer and spring, respectively. The two cores can be traced back to outflows from the Bay of Fundy along both sides of the Grand Manan Island. The two cores gradually merge as flowing southwestward, but split into two branches again east of Mount Desert Rock, where the nearshore branch flows along the coast to feed the Western Maine Coastal Current (WMCC) (i.e., the connectivity between the EMCC and the WMCC), while the offshore branch turns southward to recirculate in the eastern GoME. The offshore veering occurs further northeastward in late winter and summer, but gradually shifts southwestward from summer to winter. The connectivity between the EMCC and the WMCC generally peaks twice annually, with the highest connectivity in winter and then a secondary peak in late spring or early summer. The WMCC is generally southwestward with an offshore and a nearshore core, fed by the extension of the EMCC and runoff from the Penobscot and Kennebec-Androscoggin Rivers, respectively. A sea level dome can form offshore of Casco Bay during late fall and early winter in some years associated with the northeastward alongshore wind, resulting in the northeastward flows (i.e., the counter-WMCC) on the inshore side of the dome. Diagnosis of momentum balance demonstrates that the EMCC is primarily driven by the offshore pressure gradient force (PG), while both the WMCC and counter-WMCC in late fall and early winter are mainly driven by PG and wind. The general dispersal patterns in the nearshore and coastal GoME consist of relatively uniform grounding along the coast, alongshore transport to the western GoME by the coastal currents and offshore transport to the interior gulf by the wind-driven surface current. Alongshore transport generally follows three prototypical steps: offshore dispersal along with sinking, alongshore transport, and onshore dispersal along with surfacing. Transports to the interior GoME occur prominently offshore of Penobscot Bay and east of Cape Cod, likely due to the offshore veering of EMCC, and variations of isobath inclination, respectively. Inshore of 80 m isobath, the consistent cross-shore flows result in very similar cross-shore transport between years and months, while offshore of 80 m isobath, the influence of variable coastal currents gradually emerges, which alters the cross-shore transport. In the eastern GoME, dispersal of M. edulis larvae exhibits three prototypical patterns: self-seeding, exchanges among beds in the same and neighboring bays, and southwestward alongshore transport. Self-seeding and exchange result in two settlement clusters, in Frenchman Bay and Pleasant-Western Bay, while additional alongshore transport originates in further eastern spawning beds and occurs via the EMCC. Spawning beds that produce a large amount of larvae can modulate the settlements in other beds, and further affect the overall metapopulation. Higher temperature can result in more self-seeding and exchanges among beds in the same and neighboring bays. Moreover, Passamaquoddy Bay, Blue Hill Bay and Penobscot Bay may also contribute to the M. edulis population in the eastern GoME.
... The slope of the submerged trapezoid breakwater in these experiments is 1:2 (Ohyama et al., 1995) and 1:4 (Rao et al., 2021). The agreement index (Wilmott, 1981) is applied to testify the agreement of surface elevation or velocity between the numerical model and the experimental data. The good agreement demonstrates that the two-layer Boussinesq-type model with different values for α (0.13≤α≤0.25) of dispersion coefficient can be applied to wave evolution over a submerged breakwater with a steeper slope as high as 1:2. ...
... Comparison of calculated surface elevations with the experimental dataTo quantitatively describe the degree of simulation of wave surface elevations calculated by the numerical model, the coincidence index d i proposed byWilmott (1981) is used and it can be ...
Conference Paper
Accurate simulation of wave evolution over a submerged trapezoid breakwater requires a high accuracy in both linear and nonlinear properties of the numerical model. The two-layer Boussinesq-type model with highest spatial derivatives being 2 (Liu et al, 2018) is derived with a mild-slope assumption. The model is applied to wave evolution over a submerged trapezoid breakwater with a 1:20 afore slope and 1:10 back slope, good agreement is found (Liu et al., 2019). The applicability of this model in simulating regular wave evolution over a submerged breakwater with slope higher than 1:5 is not known yet. Recently, Sun et al. (2021) reveal that the different values for α (0.13≤α≤0.25) in this two-layer model do not have great effects on the high accuracy of the linear shoaling, linear phase celerity and even third-order nonlinearity for the range of 0<kh ≤ 10 (where k is wave number and h is water depth). The present study investigates the capability and flexibility of the two-layer Boussinesq-type model in modeling of strongly nonlinear nonbreaking wave propagation and transformation over a submerged trapezoid breakwater when the value of dispersion coefficient α is chosen at the interval [0.13, 0.25]. Two available published experimental data (Ohyama et al, 1995; Rao et al, 2021) of wave evolution over a breakwater are used to validate the model. The slope of the submerged trapezoid breakwater in these experiments is 1:2 (Ohyama et al., 1995) and 1:4 (Rao et al., 2021). The agreement index (Wilmott, 1981) is applied to testify the agreement of surface elevation or velocity between the numerical model and the experimental data. The good agreement demonstrates that the two-layer Boussinesq-type model with different values for α (0.13≤ α ≤ 0.25) of dispersion coefficient can be applied to wave evolution over a submerged breakwater with a steeper slope as high as 1:2.
... In addition to validation, i.e., comparison of both simulated and observed values, the model performance was also evaluated by statistical measures like coefficient of determination (R 2 ). Wilmott (1982) pointed out that the main problem of this analysis is that the magnitude of R 2 is not consistently related to the accuracy of prediction where accuracy is the degree to which model predictions approach the magnitude of their observed values. ...
... and While summary measures describe the quality of simulation, difference measures try to locate and quantify errors. The latter includes mean absolute error (MAE), the mean bias error (MBE), the root mean square error (RMSE) and per cent error (PE) (Wilmott, 1982). They are calculated as below : MAE and RMSE indicate the magnitude of the average error. ...
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Lkkj & ihuVxzks ¼ih- ,u- ;w- Vh- th- vkj- vks-½ ekWMy dh izkekf.kdrk fl) djus ds fy, 1987 - 90 ds nkSjku vkuan] xqtjkr esa {ks=h; iz;ksx fd, x, gSaA bl ekWMy dk mi;ksx ew¡xQyh dh QhuksykWth] c<+ksrjh] fodkl vkSj iSnkokj dk iwokZuqeku yxkus ds fy, fd;k x;k gSSA ew¡xQyh ds izfr:fir iq"iu] isfxax] Qyh cuus vkSj Qyh idus dh frfFk;ksa] i.khZ {ks=Qy lwpdkad ¼,y- ,- vkbZ-½ tSoHkkj] 'kSfyax dk izfr’kr rFkk iSnkokj dh rqyuk rhu i)fr;ksa uker% th- ,- ;w- th- 10] th- ,- ;w- th- 2 vkSj vkj- vk-sa - 33 - 1 ls izkIr gq, iszf{kr ekuksa ds lkFk dh xbZ gSA izfr:fir ?kVukØe ls iq"iu ds fy, ,d fnu deh rFkk ik¡p fnu dh c<+r dk] isfxxa ds fy, 2 ls 6 fnuksa dh c<+r] Qyh cuus ds fy, 3 fnu dh deh rFkk 6 fnuksa dh c<+r dk vkSj Qyh idus ds fy, 6 fnu dh deh rFkk 5 fnu rd dh c<+r dk varj ik;k x;k gSA okLrfod ekuksa dh rqyuk esa bl ekWMy ls i.khZ {ks=Qy lwpdkad 91-8 ls 105-8 izfr’kr vkSj 'kSfyax dk izfr’kr 81-5 ls 109-8 ik;k x;k gSA bl ekWMy ls ew¡xQyh dh iSnkokj izsf{kr ekuksa dh rqyuk esa 88-5 ls 112-7 izfr’kr rd ikbZ xbZ gSA bl ekWMy ls izkIr ifj.kkeksa ds vk/kkj ij ij yxkrkj pkj Qlyksa vkSj _rqvksa ds laca/k esa ew¡xQyh dh QhuksYkWkth] c<+ksrjh] fodkl vkSj iSnkokj ds ckjs esa iwokZuqeku larks"ktud ik;k x;k gSA ew¡xQyh dh izsf{kr vkSj izfr:fir iSnkokj ds chp 11 izfr’kr dh ?kVc<+ ikbZ xbZ gS ftlls irk pyrk gS fd ekWMy ds vk/kkj ij fd;k x;k iwokZuqeku larks"ktud gSA ,y- ,- vkbZ- dks NksMdj okLrfod ekuksa vkSj izsf{kr ekuksa esa varj ¼Mh-½ 0-03 vkSj 1-77 ds chp jgk gS ftlls ekWMy ds larks"ktud dk;Z djus dk irk pyrk gSA izfr:i.k v/;;uksa ds ifj.kkeksa ls irk pyrk gS fd tc vf/kd o"kkZ gksus dhs laHkkouk gks rks ew¡xQyh ds chtksa dh lkekU; nwjh rFkk cqokbZ ds lkekU; le; dh vis{kk chtksa dks vf/kd ikl&ikl cksdj rFkk cqokbZ yxHkx ,d lIrkg igys djds ew¡xQyh dh vf/kd iSnkokj izkIr dh tk ldrh gSA Field experiments were conducted at Anand, Gujarat during 1987-90 to validate the PNUTGRO model. The model was used to predict phenology, growth, development and yield of groundnut. The simulated flowering, pegging, pod formation and pod maturity dates, leaf area index (LAI), biomass, shelling % and pod yield of groundnut were compared with the observed values for three cultivars viz., GAUG 10, GAUG 2 and Ro-33-1. The simulated phenological events showed a deviation of –1 to +5 days for flowering, +2 to +6 days for peg formation, -3 to +6 days for pod formation and –6 to +5 days for pod maturity of the crop. The model estimated leaf area index within 91.8 to 105.8% and shelling percentage within 81.5 to 109.8% of the actual values. The model simulated the pod yields within 88.5 to 112.7% of the observed values. The results obtained with the model for the four consecutive crops and seasons revealed satisfactory prediction of phenology, growth, development and yield of groundnut. The percent error between observed and simulated pod yield was 11% which indicated satisfactory prediction by the model. The degree of agreement (d) ranged between 0.03 and 1.77 except for LAI indicating satisfactory performance of the model. Results of simulation studies indicated that when there is a possibility of high rainfall higher pod yield can be achieved by adopting closer spacing and early sowing (one week earlier than normal date of sowing) compared to normal spacing and date of sowing.
... The concept of index of agreement was originally proposed by Willmott in the 1980s and has since then been widely used to "reflect the degree to which the observed variate is accurately estimated by the simulated variate" (Willmott, 1981) in a variety of fields. IOA has gone through several modifications (together referred as Willmott indices) since it was proposed in the original formula (Willmott, 1982;Willmott et al., 1985Willmott et al., , 2012. ...
... The formula of the original form (d) is shown in Table 2 (presented again in Table 3) and the other three (d 1 , d 1 , and d r ) are shown in Table 3. The first version of IOA is proposed over the correlation coefficient for its ability to "discern differences in proportionality and/or constant additive differences between the two variables" (Willmott, 1981), and this version is also the most widely used version in our compiled studies. Compared with R 2 values, the original IOA results in systematically higher values (Valbuena et al., 2019) and thus is being adopted in an increasing number of studies partially because it makes results appear "better". ...
... The SKILL method, which stands for "Skill assessment for Numerical Modeling Evaluation Studies," is an Complimentary Copy approach used to evaluate the performance and accuracy of numerical models in various scientific and engineering fields. It provides a systematic framework for comparing model predictions with observed data and quantifying the model's skill in reproducing real-world phenomena (Wilmott, 1981). ...
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... The SKILL method, which stands for "Skill assessment for Nmerical Modeling Evalation Stdies," is an Complimentary Copy approach used to evaluate the performance and accuracy of numerical models in various scientific and engineering fields. It provides a systematic framework for comparing model predictions with observed data and qantifying the model's skill in reprodcing real-world phenomena (Wilmott, 1981). ...
Chapter
In April 2015, a major chemical fire, followed by the massive use of aqueous film-forming foams (AFFFs), occurred at a petrochemical terminal at the Port of Santos (Southeast Brazil). At least 62,000 L of AFFFs from eight brands were mixed with estuarine waters and used to control the fire, causing the release of large amounts of per-and polyfluoroalkyl substances (PFAS) into the Santos Estuarine System (SES). Perfluorooctane sulfonic acid (PFOS) and perfluorooctanoic acid  Corresponding Athor's Email: denis.abessa@unesp.br. Complimentary Copy D. M. de Souza Abessa, L. Alves Maranho, L. Buruaem Moreira et al. 104 (PFOA), included in the global treaty of the Stockholm Convention, have been detected in AFFFs. The resulting effluent that drained into the estuary was toxic to marine invertebrates, producing adverse effects on marine invertebrates at a 0.01% dilution, much lower than that recommended by AFFFs manufacturers. According to the hydrodynamic model applied, the leaked material spread across the SES by tidal currents and was dispersed in the following weeks. The toxicity of estuarine waters was monitored for up to one year after the event, and adverse effects on different invertebrate species were observed in a space-temporal variable form. The results showed that the fire caused the degradation of estuarine waters in the SES, but other pollution sources also contributed to water toxicity.
... A potential source of discrepancy may be associated with slight variations in location within the physical sill-channel domain where the measured PIV scans are compared directly to BOM velocity profiles obtained at a specific cell location within the model domain. In order to assess the quantitative agreement between the BOM simulation results and the experimental data, the skill score assessment index SK (Wilmott, 1981) and cost function χ (Holt et al., 2005 ) are used to validate the numerical model predictions, and are defined as (5) and ...
... For the evaluation of the performance of the models, the following statistical criteria are applied: RMSE (Root Mean Square Error), R 2 (Linear goodness of fit), NSE (Model efficiency following Nash and Sutcliffe, 1970;Eq. (2.4), and Model Skill presented by Wilmott, (1981) and applied by Warner et al. (2005) to evaluate hydrodynamic models; Eq. (2.5). ...
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Mountain regions play an important role in the global water cycle. Mountainous hydrology and hydraulics, however, are still not fully understood. The Amazon Basin, the largest drainage basin in the world, covers about 40 percent of South America and 66 percent of Bolivia (716500 km2). The sources of the principal tributaries of the Amazon River are located in the Andes mountain range. There-fore, understanding the water cycle in the upstream regions can lead to an im-portant contribution to the comprehension of the low-lands regions (which fre-quently suffer from floods). The Piraí river basin (2705 km2) located in Santa Cruz – Bolivia was selected as case study. This basin begins in a mountainous area and has important low-land areas. Huge variation in topography and lack of complete sets of meteorological data increase the research challenge. Water sources have to be modelled in an integrated way taking into account the physical and natural sub-systems. The approach for such integrated modelling was adapted from the hydrological and hydraulic flood modelling experiences obtained in a more detailed studied case of the Dender basin in Belgium. Investi-gation was made on how the Belgian research outcomes can be transferred, how they can be of use, and how they need to be adjusted to the different conditions of the Bolivian study case. Firstly, data pre-processing was conducted. This involved estimation of potential evapotranspiration taking into account the limited hydro-meteorological data available, testing of methodologies for gap filling of the rainfall records (33 sta-tions with daily series and 14 stations with hourly records) and disaggregation from monthly to daily and from daily to hourly rainfall values. With the com-plete(d) potential evapotranspiration and rainfall series a lumped conceptual rain-fall-runoff model was calibrated and validated for hourly and daily time steps (the study area had 5 gauging stations with hourly discharge data). The implementa-tion and calibration of the rainfall-runoff model was done based on the step-wise process already applied and tested in the Dender case. The hourly disaggregation techniques were tested based on the runoff results. Model efficiencies of around 0.6 for the small sub basins and higher than 0.65 for the large sub basins were obtained. For the daily runoff simulation, the use of 33 stations instead of 14 in-creased the model efficiency. After use of the 33 stations, better results were ob-tained in the peak flow estimations, but underestimations with respect to the ob-servations persisted. A long-term simulation was carried out with the calibrated rainfall-runoff model. The hydrodynamic river processes and related model implementation were stud-ied by means of one-dimensional or quasi two-dimensional (2D) models. For the Dender case, a deep understanding of the quasi-2D implementation and flood-plain modelling were obtained. For the Piraí case, given that the river is influ-enced by morphological changes, the flood modelling methodology had to be ex-tended to account for these changes. This was done through a simplified concep-tual approach. Based on the coupled modelling system (rainfall-runoff and river hydrodynamic models), the rainfall-runoff long-term simulation results and the river flow obser-vations, statistical extreme value analysis was conducted, and synthetic rainfall-runoff hydrographs constructed. These were used for estimation of river and floodplain conditions of given return periods. To reduce model computational times, a conceptual model was identified and calibrated to the results of the more detailed 1D or quasi-2D hydrodynamic mod-el. To support the model structure identification and calibration, a semi-automatic methodology has been developed. The identification and calibration were done based on simulation results with the more detailed hydrodynamic model, includ-ing extreme synthetic and historical events. In this study, MATLAB® environ-ment was selected for implementing the conceptual model. A Conceptual Model Developer tool (CMD) has been developed and tested for the rivers Dender and Piraí with good results.
... In the literature, the modified index of agreement (md) method is thoroughly employed to evaluate the compatibleness between observed data and the output of the gridded GCMs (Noor et al. 2019). It can be between zero (no agreement) and one (perfect agreement) (Willmott 1981). ...
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Since investigating the long-term trends of the renewable energy potential may help in planning sustainable energy systems, this study intends to forecast the renewable energy potential of the East Thrace, Turkey region, in the future based on CMIP6 Global Circulation Models data using the ensemble mean output of the best-performed tree-based machine learning method. To evaluate the accuracy of global circulation models, Kling-Gupta efficiency, modified index of agreement, and normalized root-mean-square error are applied. The best four global circulation models are detected as a result of the comprehensive rating metric, which combines all accuracy performance results into a single metric. Three different machine learning methods, random forest, gradient boosting regression tree, and extreme gradient boosting, are trained using the historical data of the top-four global circulation models and the ERA5 dataset to calculate the multi-model ensembles of each climate variable, and then, the future trends of those variables are forecasted based on the output of ensemble means of best-performed machine learning methods with the lowest out-of-bag root-mean-square error. It is foreseen that there will not be a significant change in the wind power density. The annual average solar energy output potential is found to be between 237.8 and 240.7 kWh/m²/year depending on the shared socioeconomic pathway scenario. Under the forecasted precipitation scenarios, 356–362 l/m²/year of irrigation water could be harvested from agrivoltaic systems. Thereby, it would be possible to grow crops, generate electricity, and harvest rainwater on the same area. Furthermore, tree-based machine learning methods provide much lower error compared to simple mean methods.
... We quantitatively assessed the capability of the model accuracy based on the measured time series of tidal heights and surface salinity at several mooring stations, depth-mean salinity transect and tidal discharge. The model skill score (SS) was determined using the statistical method developed by [22], this ratio widely used in modelling to determine index agreement between observed and modeled [23]: ...
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Flow division at bifurcations is important in controlling material carried from the terrestrial to the coastal zone in tidally influenced deltas. The present study aims to identify the impacts of tides on flow division and freshwater transport in the Berau Delta, East Kalimantan. The Princeton Ocean Model (POM) is applied to simulate the hydrodynamics with forcing from river discharges and tides. Tides at open seas and observed river discharge at upstream locations were used to set model boundaries. Model validation was accomplished by comparing measurements of tidal elevation and salinity time series with model results. The model results reproduce the observed in temporal variations of tidal elevation and salinity. Model results highlight that the tidal amplitude has large influence on discharge division at the tidal junction. Tides enhance equal subtidal flow distribution in the river junctions, with the influence of tide is 15% on subtidal flow distribution in the bifurcations. Freshwater discharge at the Berau Delta flows mainly to the north and middle outlet with 90% of the total discharge. Based on an analysis model results, the decomposition of freshwater transport reveals that advection and tidal pumping are major factor, which are fluctuate in fortnight cycle.
... The RMSE, skill (Willmott 1981), and coefficient of determination (CD) (or R 2 score) were computed for the models. We used the test subset and observed VGC discharge values to calculate these parameters, and from now on, we will call this process the test subset validation step. ...
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Quantitative knowledge of river discharge measurements is essential for understanding coastal and estuarine dynamics and salinity variations. However, direct measurements are scarce for a large portion of rivers in Brazil. In this study, five simple models based on remote sensing and local rainfall datasets (MERGE) for the Ribeira de Iguape catchment are used to estimate the Valo Grande Channel (VGC) discharge on the southeastern coast of Brazil. These models use linear, quadratic, exponential, and two different multiple linear regression methods. The predicted VGC discharge time series resulting from each model is compared with the estimated time series based on in situ data from the Water and Electric Energy Department (DAEE in Portuguese). The estimated time series presented reasonable results, with skills varying from 0.84 to 0.92 and Nash–Sutcliffe efficiency (NSE) indices varying from 0.54 to 0.75, with the highest values corresponding to the multiple linear regression models. This methodology allowed us to reproduce longer time series at a daily frequency, as well as monthly averages between 2000 and 2020.
... The measured data from 14 stations in 2010 were used to validate the model. In this study, the Willmott skill score (SK) was used to evaluate whether the model result is consistent with the observed data (Willmott, 1981). The SK is defined as ...
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The Huangmaohai estuary (HE) is a funnel-shaped microtidal estuary in the west of the Pearl River Delta (PRD) in southern China. Since China reformed and opened up in 1978, extensive human activities have occurred and greatly changed the estuary's topography and modified its hydrodynamics. In this study, we examined the morphological evolution by analyzing remote sensing data with ArcGIS tools and studied the responses of hydrodynamics to the changes in topography from 1977 to 2010 by using the Delft3D model. We took the changes in estuarine circulation during neap tides in dry seasons as an example. The results show that human reclamation caused a narrowing of the estuary, and channel dredging deepened the estuary. These human activities changed both the longitudinal and lateral estuarine circulations. The longitudinal circulation was observed to increase with the deepening and narrowing of the estuary. The lateral circulation experienced changes in both the magnitude and pattern. The momentum balance analysis shows that when the depth and width changed simultaneously, the longitudinal estuarine circulation was modulated by both the channel deepening and width reduction, in which the friction, pressure gradient force, and advection terms were altered. The analysis of the longitudinal vortex dynamics indicates that the changes in the vertical shear of the longitudinal flow, lateral salinity gradient, and vertical mixing were responsible for the change in the lateral circulation. The changes in water depth are the dominant factors affecting lateral circulation intensity. This study has implications for sediment transport and morphological evolution in estuaries heavily impacted by human interventions.
... Amplitude and phase are shown for the M 2 (a, b), S 2 (c, d), N 2 (e, f) and K 1 (g, h) tidal constituents. (Willmott, 1981): ...
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Here we present the first open-access long-term 3D hydrodynamic ocean hindcast for the New Zealand ocean estate. The 28-year 5 km×5 km resolution free-running ocean model configuration was developed under the umbrella of the Moana Project, using the Regional Ocean Modeling System (ROMS) version 3.9. It includes an improved bathymetry, spectral tidal forcing at the boundaries and inverse-barometer effect usually absent from global simulations. The continuous integration provides a framework to improve our understanding of the ocean dynamics and connectivity, as well as identify long-term trends and drivers for particular processes. The simulation was compared to a series of satellite and in situ observations, including sea surface temperature (SST), sea surface height (SSH), coastal water level and temperature stations, moored temperature time series, and temperature and salinity profiles from the CORA5.2 (Coriolis Ocean database for ReAnalysis) dataset – including Argo floats, XBTs (expendable bathythermographs) and CTD (conductivity–temperature–depth) stations. These comparisons show the model simulation is consistent and represents important ocean processes at different temporal and spatial scales, from local to regional and from a few hours to years including extreme events. The root mean square errors are 0.11 m for SSH, 0.23 ∘C for SST, and <1 ∘C and 0.15 g kg−1 for temperature and salinity profiles. Coastal tides are simulated well, and both high skill and correlation are found between modelled and observed sub-tidal sea level and water temperature stations. Moreover, cross-sections of the main currents around New Zealand show the simulation is consistent with transport, velocity structure and variability reported in the available literature. This first multi-decadal, high-resolution, open-access hydrodynamic model represents a significant step forward for ocean sciences in the New Zealand region.
... Statistical methods are used to quantify how simulated values compare to the observed values. Four different efficiency criteria were used to quantitatively assess the performance of the model: coefficient of determination (R 2 ) (Eq. 3) (Willmott 1981), Nash-Sutcliffe efficiency (NSE) (Eq. 4) (Nash and Sutcliffe 1970;O'Connell et al. 1970), root-mean-square error (RSR) (Eq. ...
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This study aims to develop and adapt new methodologies for the foundation of a new hydrological system, essential component of a much-needed decision support spatial system for the Firiza basin and reservoir (North-West of Romania) and other areas situated upstream of a densely populated area. In order to utilize semi-distributed models in basins outside of the USA, in particular the application of an adaptation of the methodology for application of gridded precipitation within HEC-HMS in US regions covered by the hydrologic rainfall analysis projection and the standard hydrologic grid systems has been developed for Romania. This methodology allows for precipitation processing and estimation of loss parameters and runoff transformation parameters to areas outside of the USA and areas that were not covered under the initial formulation of the method. This adaptation enables an alternative forecasting method and a controlled model for the transit of flash floods through reservoirs, which was correlated with the result of precipitation forecast. Multiple sets of parameters have been compiled to represent a wet/typical condition: a snowy and a dry one. All river basin conditions were adjusted according to historical events, and two zone configurations were developed, including the gauge configuration assigned to the transformation and basic flow parameters, and the soil configuration assigned to the loss parameters. Igniș radar provides radar imagery into the future, taking into account advection, growth and decay, allowing for an accurate 0–1 h quantitative precipitation forecast. This capability provides extremely accurate short-term forecasting—80% accuracy over 15 min and 70% accuracy over 30 min—that is vital for near-term flash flood forecasting. The efficiency of the model ranged between the good and very good. The results will be used to manage extreme situations such as flash floods, which can generate major hydrological risk situations for thousands of residents in the Baia Mare urban area, located downstream of this reservoir.
... Proposed by Willmott (1981), the index of agreement is used to identify the degree of conformity between the gauge stations and CHIRPS estimates: ...
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With the advance of remote sensing technologies, meteorological satellites have become an alternative in the process of monitoring and measuring meteorological variables, both spatially and temporally. The present study brings some additional elements to the existent validations of satellite-based precipitation estimates from CHIRPS (Climate Hazards Group Infra-Red Precipitation with Station) all around the world, by analyzing its monthly product in the period 1981–2019 over the central region of the state of São Paulo, Brazil. There are significant variations over time in the number of rain gauges used by CHIRPS at the region, and the product quality has been evaluated under these conditions. Initially, the general relationship between satellite estimates and surface rainfall data is assessed using the linear adjustment and error analysis in both temporal and spatial perspectives, followed by a trend analysis using Laplace test. Results show an average decrease of 20% in R2 values when gauges were not used as anchor/reference stations by CHIRPS; the same behavior is observed for the other metrics. The monthly map analysis, besides the evident impact of the use or not of the gauges as reference stations, showed a better performance of CHIRPS (in terms of R2) during the dry period (April to August) than for the wet period (October to March), especially when anchor stations were not available. On the other hand, CHIRPS tends to underestimate (overestimate) low (high) rain rate events. Finally, despite the changes in product over time, monthly trends showed, in general, the same pattern of variability in rainfall over 38 years and a prevalence toward the reduction of rainfall. In summary, CHIRPS product seems a reasonable alternative for regions that lack historical rainfall information, but a careful analysis on the product diagnosis should be made when temporal analysis is conducted.
... Index of agreement (IOA) is characterized by the match between the departure of each prediction and the departure of each observation from the observed mean and represented as (Willmott 1981) ...
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Tropical cyclones (TCs) are the most distractive natural weather phenomena and cause extensive damage and socioeconomic loss over the North Indian Ocean (NIO) region. Convection and planetary boundary layer (PBL) system play a vital role in the origin and strengthening of the TCs. The various convective and PBL parameterization schemes are available in the statistical model, which integrates these processes. The efficient incorporation of these schemes is vital to enhance the performance of the numerical weather prediction (NWP) model. In the present study, twelve experiments have been designed to carry out the numerical simulations using Advance Research Weather Research and Forecasting (ARW) model. The behavior and performance of the schemes have been evaluated to verify the instantaneous forecast of the TCs. The simulated cyclone track, which is assessed with the Indian Meteorological Department (IMD) best track data, indicates that the vector displacement error and RMSE for the experiment MWBM and YWBM are < 100 km and < 10 km, respectively. The maximum sustained 10-m wind prediction shows MWKF for Luban and YWKF for Titli have the least RMSE value, accounting for 7.13 ms⁻¹ and 9.75 ms⁻¹. The equitable threat score (ETS) at 24-h accumulated rainfall is > 0.4 for MLBM and up to 60 mm in Luban. However, it is > 0.6 for YLBM and up to 40 mm for Titli. Based on the results and keeping the cyclone track, intensity, and rainfall, the BMJ convective scheme with the YSU and MYJ PBL has better predicting skills over the NIO region. The KF scheme has better skills in the prediction of TC intensity.
... The model performance goals include MFE ≤ + 50% and MFB ≤ ± 30%, and the model performance criteria are MFE ≤ + 75% and MFB ≤ ± 60%. IOA indicates the model accuracy and ranges from 0 to 1 (Willmott 1981), IOA = 1 indicating perfect model performance. ...
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... However, all simulations predicted the arrival of a westerly wind front which coincided with the extreme pollen concentration observed at Richmond. Therefore, the WRF simulation with the lowest root-mean-square error (RMSE), highest correlation with observations, and highest Index of Agreement (Willmott, 1981) for wind speed and direction compared to observations was chosen for HYSPLIT backtrajectory simulations. The physics parameterisations of this simulation included: Microphysics WRF single momentum three-class (WSM3), cumulus scheme Kain-Fritsch, long-wave radiation rapid radiative transfer model (RRTM), short-wave radiation scheme Dudhia, boundary layer Yonsei Scheme Uni (YSU), surface layer revised (RMM5), land surface scheme NOAH, 100 vertical levels, and topographic-wind surface roughness parameterisation turned on; the latter improved wind speed agreement with observations. ...
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Inhalation of grass pollen can result in acute exacerbation of asthma, prompting questions about how grass pollen reaches metropolitan areas. We establish typical atmospheric Poaceae (grass) pollen concentrations recorded at two pollen samplers within the Sydney basin in eastern Australia and analyse their correlation with each other and meteorological variables. We determine the effect of synoptic and regional airflow on Poaceae pollen transport during a period of extreme (≥ 100 grains m⁻³ air) concentration and characterise the meteorology. Finally, we tested the hypothesis that most Poaceae pollen captured by the pollen samplers originated from local sources. Fifteen months of daily pollen data, three days of hourly atmospheric Poaceae pollen concentrations and fifteen months of hourly meteorology from two locations within the Sydney basin were used. Weather Research Forecasting (WRF), Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) modelling and conditional bivariate probability functions (CBPF) were used to assess Poaceae pollen transport. Most Poaceae pollen collected was estimated to be from local sources under low wind speeds. Extreme daily Poaceae pollen concentrations were rare, and there was no strong evidence to support long-distance Poaceae pollen transport into the Sydney basin or across the greater Sydney metropolitan area. Daily average pollen concentrations mask sudden increases in atmospheric Poaceae pollen, which may put a significant and sudden strain on the healthcare system. Mapping of Poaceae pollen sources within Sydney and accurate prediction of pollen concentrations are the first steps to an advanced warning system necessary to pre-empt the healthcare resources needed during pollen season.
... In regard to air pollution, PM 10 and PM 2.5 concentrations were simulated. To evaluate the model prediction performance, the squared correlation coefficient (R 2 ), mean absolute percentage error (MAPE), root mean squared error (RMSE), and Willmott's index of agreement ( d ) (Willmott 1981) were calculated between the simulated and measured parameters. ...
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Green Infrastructure (GI) is gaining wide recognition in cooperative research projects seeking to find solutions for climate adaptation in urbanized areas. However, the potential effects of co-produced GI plans and the underlying preparation process are rarely evaluated. To bridge this gap, the aim of this article is to examine what works in addressing environmental burdens in the urban neighborhood of Dortmund Marten, Germany. As part of a larger transdisciplinary process, selective GI measures were delineated in the case study area through a cooperative workshop between scientists and urban planners. Workshop ideas were incorporated into a mitigative scenario considering a hot summer day to quantify the effects of the derived GI measures on thermal comfort and particulate matter dispersion (PM10 and PM2.5). To evaluate the experiences of the science-practice collaboration, the viewpoints of researchers and urban planners on learning effects, knowledge integration, and GI planning were summarized and compared via an online survey. The results indicate that the proposed GI measures could reduce physiological equivalent temperature (PET) by 25 °C. At the same time, additional roadside trees could increase PM10 concentrations by up to 36 µg/m³ due to wind blocking effects. Reflections on the science-practice workshop show that learning effects were higher for the participating researchers than for planning practitioners, while the integration of individual expertise during the workshop was more difficult for academics. These findings point to the importance of continuous reflections on individual understandings in cooperating stakeholder groups and the value of the evaluation of outcomes in transdisciplinary GI planning.
... • Index of agreement and its modified form: The Nash-Sutcliffe efficiency and its modified form is insensitive to the differences associated with the theoretical and the observed luminosities from the respective observed mean [95]. This inspires one to propose two more error estimators, namely the index of agreement and its modified form which takes care of this issue [96][97][98]. The index of agreement is given by, ...
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Regular black holes arising in Einstein gravity coupled to non-linear electrodynamics are worth studying as they can circumvent the r = 0 curvature singularity arising in general relativity. In this work we explore the signatures of regular black holes with a Minkowski core from the quasar continuum spectrum. We use thin-disk approximation to derive the theoretical luminosity from the accretion disk and compare it with the optical data of eighty Palomar Green quasars. Our analysis based on error estimators like the chi-square, the Nash-Sutcliffe efficiency, the index of agreement etc. reveal that optical observations of quasars favor the Kerr scenario compared to black holes in non-linear electrodynamics. The implications are discussed.
... Finally, from the values of total ET 0 observed (O i ) and estimated (E i ) for each interpolator, the Willmott's agreement index d (Willmott, 1981), the BIAS, and the RMSE, were calculated (Ceccherini et al., 2015;Machado et al., 2015;Santos et al., 2018;Xavier et al., 2015). These three metrics are calculated as follows: ...
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The importance of daily data on reference evapotranspiration (ET0) has increased in recent years due to its relevance in planning and decision making regarding irrigated agriculture, water production, and forest restoration. Facing the scarcity of this information measured in loco, the study of interpolation methods capable of representing ET0 becomes important. Therefore, this study aimed to evaluate the adequacy of the Random Forest (RF) method in the spatialization of ET0 in the watersheds of the Mid-South region of the Espírito Santo State, located within the Atlantic Forest biome, Brazil. From this study, it was found that the RF method is the most suitable one for ET0 spatialization when compared to the Angular distance weighting (ADW) and the inverse distance weighting (IDW) techniques. Also, the spatializations carried out by this method were transformed into databases in a grid format and made available online. Furthermore, the RF database was also compared to other ET0 grid databases, and it was concluded that the RF database also carried out a better performance than the other ones.
... Observations applied to evaluate model performance were collected by the United States Environmental Protection Agency Murrell and Lehrter, 2011;Murrell et al., 2013) and the Louisiana Universities Marine Consortium (LUMCON, 2021) and include vertical profiles of temperature, salinity, DO, primary production, and water-column respiration. Model output were compared to observations by calculating model root mean square error (RMSE) according to Stow et al. (2009) and model skill according to Wilmott (1981) as: ...
Article
Complex simulation models are a valuable tool to inform nutrient management decisions aimed at reducing hypoxia in the northern Gulf of Mexico, yet simulated hypoxia response to reduced nutrients varies greatly between models. We compared two biogeochemical models driven by the same hydrodynamics, the Coastal Generalized Ecosystem Model (CGEM) and Gulf of Mexico Dissolved Oxygen Model (GoMDOM), to investigate how they differ in simulating hypoxia and their response to reduced nutrients. Different phytoplankton nutrient kinetics produced 2–3 times more hypoxic area and volume on the western shelf in CGEM compared to GoMDOM. Reductions in hypoxic area were greatest in the western shelf, comprising 72% (∼4,200 km²) of the total shelfwide hypoxia response. The range of hypoxia responses from multiple models suggests a 60% load reduction may result in a 33% reduction in hypoxic area, leaving an annual hypoxic area of ∼9,000 km² based on the latest 5-yr average (13,928 km²).
... Indicadores e coeficientes de comparação entre os distintos métodos com o padrãoA comparação entre o método padrão e os demais foi calculada através da regressão linear (Yi = a + bŶi) para obtenção dos coeficientes a e b e determinação do R². Também foi aplicado o coeficiente de correlação de Pearson (r), a raiz do quadrado médio do erro (RQME), o bo, da equação linear forçada à origem, o índice de Willmott (d)(Willmott, 1981) ...
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A água é um elemento importantíssimo para o desenvolvimento das culturas agrícolas, pois é parte de suas estruturas e meio de transporte de nutrientes. Atender a demanda hídrica da cultura é fundamental para o dimensionamento do sistema de irrigação e contribuir para o aproveitamento sustentável dos recursos hídricos. A evapotranspiração de referência (ETo) é uma das variáveis relacionadas a quantidade de água que deve ser distribuída por unidade de área. Sua determinação pode ser realizada através de diferentes métodos. Este estudo teve por objetivo avaliar dez modelos de estimativa da ETo diária, para a região de Palmeira das Missões-RS. O desempenho dos métodos foi avaliado através de uma série de indicadores estatísticos, em relação ao método FAO Penman-Monteith (FAO-PM). Os dados foram obtidos da estação meteorológica automática de Palmeira das Missões, pertencente ao Instituto Nacional de Meteorologia (INMET) e compreendem o período entre o dia 01/07/2008 a 09/01/2021, com 244 número de amostragens. As avaliações dos métodos foram realizadas utilizando o conjunto total dos dados. Os métodos foram confrontados através de regressão (bo), da regressão linear simples (R²), dos indicadores estatísticos, como o coeficiente de correlação de Pearson (r), índice de Camargo e Sentelhas (c), índice de Willmott (d), erro médio absoluto (MAE) e a raiz quadrada do erro médio absoluto (RQME). Para as condições micrometeorológicas de Palmeira das Missões-RS, os métodos de Penman e Jesen-Haise foram os que melhor estimaram ETo quando comparado com o padrão FAO-PM.
... The index of agreement d [60][61][62] is proposed in order to overcome the insensitivity of Nash-Sutcliffe efficiency and its modified form towards the differences between the theoretical and the observed luminosities from the respective observed mean [59] and its functional form is expressed as follows, ...
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Black holes carrying a magnetic monopole charge are a subject of interest for a long time. In this work we explore the possibility of an observational evidence of such black holes carrying a magnetic monopole, namely the Bardeen rotating black holes. We derive the theoretical spectrum from the accretion disk surrounding a Bardeen black hole using the thin-disk approximation. We compare the theoretically derived spectrum in comparison to the optical data of eighty Palomar Green quasars to constrain the monopole charge parameter $g$ and the spin parameter $a$ of the quasars. From our analysis we note that the Kerr-scenario in \gr\ is observationally more favored than black holes with a monopole charge. We arrive at such a conclusion using error estimators like $\chi^2$, the Nash-Sutcliffe efficiency, the index of agreement and their modified forms. In particular, black holes with $g \geq 0.03$ are outside $99\%$ confidence interval. The implications are discussed.
... The d index defined by Willmott (1981) is given by ...
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The urochloa grass (Urochloa mosambicensis) is a perennial grass, C4 plant, with a high photosynthetic rate and CO 2 fixation, persistent to water deficit, adapted to a wide diversity of soils and hot climate regions. Thus, the objective was to evaluate the urochloa grass growth and define the best models to estimate plant height as a function of nitrogen and phosphate fertilization. The experimental design was completely randomized, in the 2  2 factorial design (presence and absence of nitrogen  presence and absence of phosphorus), with four replications. Was used a dose of nitrogen and phosphorus equivalent to 100 kg.ha-1 of N and 150 kg.ha-1 of P 2 O 5 , respectively. The following models were used: linear, power, gamma and logistic to estimate plant height as a function of the following explanatory variables: days after planting, nitrogen and phosphorus doses. The criteria used to determine the best model(s) were as follows: higher adjusted coefficient of determination, lower Akaike information criterion, lower sum of square of residuals and high Willmott index. The plant height in the absence of nitrogen and phosphorus and when applied 100 kg.ha-1 of N and 150 kg.ha-1 of P 2 O 5 was estimated more accurately by the Gamma model with high power of explanation. The adoption of the Gamma model allows to estimate the U. mosambicensis plant height, in a non-destructive manner, with high precision, speed and low cost, depending of age plant and nitrogen and phosphate fertilization.
... In order to analyze the performance of these models, various efficiency indices, such as Nash-Sutcliffe Efficiency (NSE) (Nash and Sutcliffe, 1970), R 2 determination coefficient, root mean square error (RMSE) (Singh et al. 2005), Mean Absolute Error (MAE) (Willmott et al. 2005), Index of Agreement (Willmott, 1981), Mean Squared Derivative Error (Willmott et al. 2005) and the percent bias (%) (Singh et al. 2005). In addition, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to evaluate the maximum likelihood of models. ...
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Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills. In this paper, we proposed a method for searching the seasonal autoregressive integrated moving average (SARIMA) model parameters to predict the behavior of groundwater time series affected by the issues mentioned. Based on the analysis of statistical indices, 8 stations among 44 available within the Campania region (Italy) have been selected as the highest quality measurements. Different SARIMA models, with different autoregressive, moving average and differentiation orders had been used. By reviewing the criteria used to determine the consistency and goodness-of-fit of the model, it is revealed that the model with specific combination of parameters, SARIMA (0,1,3) (0,1,2) 12, has a high R2 value, larger than 92%, for each of the 8 selected stations. The same model has also good performances for what concern the forecasting skills, with an average NSE of about 96%. Therefore, this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area. © 2021 Journal of Groundwater Science and Engineering Editorial Office
... This method [30] measures the model's accurateness. Based on the agreement between observations and model simulated results, a predictive capability is employed. ...
... The observed data are based on CTD measurements from vessels at sampling stations , as shown by the circles in Fig. 7. The temperature of the bottom-most grid cells from ROMS-L2 agreed well with the observational data, with a correlation coefficient R of 0.9485, root mean square error (RMSE) of 1.432, and model skill score of 0.9735 (a model skill score of one indicates perfect agreement, and zero means complete disagreement; Wilmott, 1981). These results suggest that ROMS-L2 had satisfactory reproducibility in terms of synoptic dynamics, including the Kuroshio path and the oceanic flow field near FNPP1. ...
Article
We developed a three-dimensional prognostic oceanic dispersion model that accounted for the phase transfer of radionuclides between seawater, suspended particles, and seabed sediments with multiscale grain sizes. A detailed hindcast of ¹³⁷Cs in the seabed sediment off the Fukushima coast was conducted to investigate the transfer mechanism of dissolved ¹³⁷Cs derived from the Fukushima Daiichi Nuclear Power Plant (FNPP1) accident toward the seabed sediment. Extensive model-data comparison demonstrated that the model could satisfactorily reproduce the oceanic structure and ¹³⁷Cs concentrations in the seawater and seabed sediment. The model successfully reproduced the major features of the observed spatial variation of the ¹³⁷Cs activities in the sediment, which represented more than 90% of the sedimentary radiocesium existing in the coastal area off Fukushima several months after the accident. Shear stress associated with the resuspension of the seabed sediment was induced by waves near the shore and by current velocity offshore of the study area. The adsorption of ¹³⁷Cs on the seabed sediment differed depending on the particle size, with adsorption on clay being the most substantial. The distribution of ¹³⁷Cs in the sediment off the Fukushima coast was formed mainly owing to adsorption from the dissolved phase by June 2011, when the impact of the direct oceanic ¹³⁷Cs release from FNPP1 was remarkable. After June 2011, seabed sediment became a source of ¹³⁷Cs released to the seawater owing to resuspension with and desorption from the sediment.
... To compare the model results with observations, we used the Skill parameter developed by Wilmott (1981) and used in different estuarine dynamics modeling studies (Ralston et al., 2008;Xing et al., 2013;Toublanc et al., 2013) defined by (Warner et al., 2005) as: ...
Article
In this study we present an approach to calibrate a three-dimensional hydrodynamic model of a salt-wedge estuary, the Araranguá Estuary, southern Brazil, based on the Delft3D-FLOW model. The calibration was carried out in four steps to predict the vertical salinity structure along the estuary in an efficient and effective way. Skill assessment was used to evaluate the calibration quality. The model is forced by water-level elevation along the offshore open boundary and river-discharge inflows from the two major tributaries. The hydrodynamic model was calibrated using field observation of water level, currents and longitudinal salinity structure. Calibration was performed adjusting vertical grid resolution, bottom-friction coefficient and background eddy viscosity. The model achieves high skill values at water level and currents variations during a 113-day period (in 2008) covering a wide range of river discharge and tidal forcing. Water surface fluctuations obtained from the model are in good agreement with the field data. Modeled depth-averaged currents reproduce the temporal pattern of observed data. Longitudinal salinity structure is also well reproduced, although the vertical structure is more diffusive than the observations. Results also demonstrate that the model predicts the overall measured phenomena and the effects of the flash-flood event, with the discharge affecting water level, currents and salinity.
... The model performance was evaluated applying the BOOT Statistical Model Evaluation Software Package (Chang and Hanna 2004). The model acceptance criteria proposed by Chang and Hanna (2004) for air quality models' assessment, establish performance measures for six statistical parameters: (i) the normalized mean square error (NMSE < 1.5) is a measure of scattering and reflects the systematic errors; (ii) the fraction of predictions within a factor of two of observations (FAC2 > 0.5) is the most robust statistic measure since it is not overly influenced by high and low outliers; (iii) the correlation coefficient (r = 1) reflects the linear relationship between two variables; (iv) the root mean square error (RMSE = 0) gives important information about the skill in predicting the magnitude of a variable; (v) the index of agreement (d = 1) provides a standardized measure of the degree of model prediction (Willmott 1981); and (vi) the mean bias error (MBE = 0) can indicate whether the model overestimates or underestimates the concentration values measured. All these statistical parameters were considered in the analysis. ...
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A current challenge in the environmental sciences field is to assess air quality at larger urban areas with high level of spatial resolution and, at the same time, with feasible computational resources time demand. This study provides a sensitivity analysis, focused on the implications of different grid resolutions on air quality results, followed by a performance assessment of the URBan AIR (URBAIR) model, a second-generation Gaussian model, as a tool for air quality management in urban areas. Estarreja area, a city located near an industrial complex, was used as case study, and the most critical air pollutants were investigated: particulate matter (PM10) and nitrogen dioxide (NO2). Three different grid resolutions were tested: 0.1 km, 0.2 km and 0.3 km resolutions. Comparative results revealed that all grids provide similar results regarding the spatial distribution of PM10 and NO2 concentrations, with evident differences in the magnitude of those concentrations and in the required computational time. The source apportionment analysis revealed the great contribution of industrial sources and road transport to NO2 and PM10 concentrations, respectively. The URBAIR model is a useful tool to support decision-makers since it considers the specific characteristics of each city, which make it particularly helpful to assess different origins of air pollution, and so, to select the most effective sectorial measures that should be applied to improve local air quality.
... Willmott's Index for agreement (WI). (Willmott 1981(Willmott , 1982(Willmott , 1984 Legate and McCabe's Index (LMI). McCabe (1999, 2013) shows the level of divergence in prediction by the model from the actual data: ...
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Soil is a heterogeneous medium and due to this, the parameters on which soil slope stability depends, are having high variability, which makes the analysis a complex problem. To take into account the variability in soil parameters, the current research approach is shifting from deterministic approach to probabilistic approach. This paper describes the application of three soft-computing techniques including multivariate adaptive regression spline (MARS), Gaussian process regression (GPR) and functional network (FN) to study the soil slope reliability based on slope stability. The stability of a soil slope of a given height depends on shear strength parameters c (cohesion), ϕ (angle of shearing resistance) and ϒ (unit weight), which are taken as input variables and Factor of Safety of soil slope (FOS) as the output. Also the model performance was assessed using various performance indices i.e. NS, RMSE, VAF, MAE, RSR, Bias Factor, PI, R2, Adj. R2, MAPE, GPI, LMI, U95, tstat and β. The results of the analyses showed that MARS model outperformed GPR and FN models. Therefore, MARS model can be used as a reliable soft computing technique for analyzing soil slope stability.
... However, the associated interpretation with low volume of data should be considered (Abbaszadeh Shahri 2016). Table 4 shows the comparison and efficiencies of several known bedload models with the optimum MLP and hybrid MLP-FA by means of the Nash-Sutcliffe coefficient of efficiency (E NS ) (Nash and Sutcliffe 1970), index of agreement (IA) (Willmott 1981), RMSE, mean absolute percentage error (MAPE) and R 2 . According to given formulation and ranges of used metrics, the model with higher values in R 2 , IA and E NS as well as smaller value in RMSE is Content courtesy of Springer Nature, terms of use apply. ...
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Bedload transport due to approved complexity and challenges has been the subject of different modeling approaches. Due to imprecise of the empirical equations, the potencies of the intelligent techniques in developing more accurate bedload predictive models have been highlighted. In this paper, an optimum hybridized artificial neural network (ANN) with firefly metaheuristic algorithm (FA) through a dynamic setting parameter approach was developed and introduced. The model was applied on 879 datasets including 5 dominant parameters of bedload transport (discharge, flow velocity, slope, depth, mean grain size) from 19 gravel-bed streams of Idaho- USA. Detailed analyses using different analytical error metrics as well as comparison with several empirical equations showed an improved R2-value from 0.1 in empirical equation to 0.95 in hybrid model. The assessed performances of applied model demonstrated for 6.03% progress in ANN and at least 63.08% in empirical equations. According to observed results, the hybrid model with 84.65% accuracy was outperformed than others in providing closer and more compatible outputs to measurements. Referring to carried out sensitivity analysis, the discharge and velocity were identified as the most effective factors on predicted bedload.
... The following performance indices were used as criteria to compare the models with the real leaf area and to choose the best model: a higher coefficient of determination of the model (R²), lower Akaike's information criterion (AIC) defined by Akaike (1974), a lower sum of squares of residuals (SSR), and higher Willmott index (d) defined by Willmott (1981). ...
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Leaf area measurements are used in agronomic studies to evaluate plant growth, light interception, photosynthetic rates, and plant transpiration. It constitute an important indicator of crop productivity, for which the evaluation method must be fast, accurate, and of low cost. The objective of this study was to compare different indirect methods to estimate leaf area in pornunça (Manihot sp.). The research was carried out under field conditions from August 2017 to January 2019 in the semiarid region of Pernambuco State, Northeastern Brazil. Three methods were tested: linear dimensions of leaf (length, width, and the number of lobes), digital image, and leaf scanned image, analyzing 150 healthy leaves from 120 plants of pornunça at different growth stages. The criteria used to determine the best model(s) were a high coefficient of determination, low Akaike information criterion, low sum of squares of residuals, and high Willmott index. Independent of the method of determination, the power models showed the best criteria of adequacy for estimating the leaf area of the pornunça. The digital image, using the power model (Y=LW0.77NL0.49, where L and W are the leaf length and width, and NL is the number of lobes in the leaf) was the best non-destructive method for estimating the leaf area in pornunça plants.
... To examine it, we compare the linear scaling based on Eq. 2 with the model results along the western channel based on Eq. 18. A predictive skill used by Wilmott (1981) and Scully et al. (2009) is adapted to qualify accuracy of prediction as: ...
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The Pearl River Estuary (PRE) is a bell-shaped estuary with a narrow deep channel and wide shoals. This unique topographic feature leads to different dynamics of the subtidal estuarine circulation (SEC) in the PRE compared with a narrow and straight estuary. In this study, the nonlinear dynamics of the SEC in the PRE under mean circumstance are analyzed by using a validated 3D numerical model. Model results show that the nonlinear advections reach leading order in the along-channel momentum balance. Modulated by tide, the nonlinear advections show significant temporal variations as they have much larger values during spring tide than that during neap tide. Unlike straight and narrow estuaries, both tidally and cross-sectionally averaged axial and lateral advections play important roles in driving the SEC in the PRE in which the axial advection dominates the nonlinear effect, but the two nonlinear terms balance each other largely resulting in a reduced nonlinear effect. Despite this, the total nonlinear advection is still comparable with other terms, and it acts as the baroclinic pressure to reinforce the SEC, especially during the ebb tide, suggesting a flood–ebb asymmetry of the nonlinear dynamics in the PRE. In addition, diagnostic analyses of the along-channel vorticity budget show that nonlinear advections also make significant contribution to drive the lateral circulation in the PRE as Coriolis and baroclinic pressure terms, indicating complex dynamics of the circulation in the PRE.
... To evaluate the performance of understudy AI models in terms of quantity, Index of Agreement (IOA), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) were employed. Formulations associated with these statistical measures can be found in the literature (e.g., Willmott, 1981). From these statistical parameters, RMSE and MAE parameters are two wellknown benchmarks, whereas the IOA as a standardized criterion varies from 0 to 1. ...
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Rivers, as one of the freshwater resources, are generally put in the state of jeopardy in terms of quantity and quality due to the development in industry, agriculture, and urbanization. Management of water quality is inextricably bound up with a reliable prediction of the Water Quality Index (WQI) for various purposes. In this way, an accurate estimation of WQI is one of the most challenging issues in the water quality studies of surface water resources. There is a board range of traditional methodologies for the WQI evaluation. Due to the intrinsic limitations of conventional models, Data-Driven Models (DDMs) have been frequently employed to assess the WQI for natural streams. In the present research, WQI values and their typical classifications were obtained by guidelines of the National Sanitation Foundation (NSF). Hence, four well-known DDMs such as Evolutionary Polynomial Regression (EPR), M5 Model Tree (MT), Gene-Expression Programming (GEP), and Multivariate Adaptive Regression Spline (MARS) are employed to predict WQI in Karun River. In this way, 12 Water Quality Parameters (i.e., Dissolved Oxygen, Chemical Oxygen Demand, Biochemical Oxygen Demand, Electrical Conductivity, Nitrate, Nitrite, Phosphate, Turbidity, pH, Calcium, Magnesium, and Sodium) were accumulated from nine hydrometry stations and additionally missing values of water temperature were extracted from images analysis of Landsat-7 ETM⁺. Furthermore, the Gamma Test (GT), Forward Selection (FS), Polynomial Chaotic Expression (PCE), and Principle Component Analysis (PCA) were used to reduce the volume of DDMs-feeding-input variables. Results of DDMs demonstrated that FS-M5 MT had the best performance for the estimation of WQI classification. WQI values for Karun River were assessed in the reliability-based probabilistic framework to consider the effect of any uncertainty and randomness in the input parameters. To this end, the Monte-Carlo scenario sampling technique was conducted to evaluate the limit state function from the DDMs-based-WQI formulation. Based on the qualitative description of the WQI, it was observed that the WQI of Karun River is classified into “Relatively Bad” quality. Moreover, based on the reliability analysis, there is only a 19% chance exists for a specimen from Karun River to have a better quality index.
... The following standard errors statistics, with formulae described in Table 1 (where "o" is the value of the observational data, "f" is the simulated data) were estimated: the BIAS, the root mean square error (RMSE) that gives an overview of the accuracy of simulations, the mean absolute error (MAE), a measure of the absolute values of the model errors, the Pearson's correlation coefficient (COR), the modified Index of Agreement (MIA), developed by (Willmott 1981;Legates and McCabe Jr. 1999) as a standardized measure of the degree of model prediction error, and finally the Nash-Sutcliffe efficiency (Nash and Sutcliffe 1970), NSE, which is a normalized skill score that determines an overall performance and can vary between 1 for perfect agreement and − ∞ for complete disagreement. While the NSE has traditionally been used in hydrological applications, it can also be applied to any type of model data with paired observations of the same quantities (Lee et al. 2018). ...
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This study presents the results of high-resolution dynamical downscaling of 5 km on maximum (TX) and minimum (TN) air temperature and precipitation, for Greece, with the Weather Research and Forecasting (WRF) model. The ERA-Interim (ERA-I) reanalysis dataset is used for initial and boundary conditions. The model results (WRF_5) are evaluated against available ground observations for the period 1980–2004 through the calculation of mean climatology, statistical metrics, and distributions of extreme events on daily, monthly and seasonal scales. WRF_5 model captures very well the geographical distribution of TX and TN of the study area, and illustrates finely the seasonal differences. Statistical results for TX (TN) indicate a cold (warm) bias of − 0.6 °C (1 °C) regarding WRF_5 and − 3 °C (0.5 °C) for ERA-I. The efficiency metrics for temperatures showed a highly improved performance of the model compared to reanalysis for all temporal scales investigated. The observed mean annual cycle and inter-annual variability of precipitation are also well represented by model simulation. Although WRF_5 overestimates rainfall during most of the year, the seasonal pattern of WRF_5 presented similar correlation coefficients for all stations with a range of 0.6–0.85, showing a good model ability to simulate the precipitation in Greece. The results reveal the capability of the configured WRF high resolution model to reproduce the main climatological variables of the study area, outperforming the coarse resolution ERA-Interim in a region that is dominated by highly variable topographic characteristics. This is deemed necessary for undertaking any further studies concerning future climate change impacts in various sectors.
... The correlation coefficient was not calculated since it might be both oversensitive to extreme values and insensitive to proportional differences between model predictions and observations (Legates and McCabe, 1999). The dimensionless SS, previously proposed by Wilmott (1981) and widely used since then to assess the accuracy of hydrodynamic models against HFR estimations (O'Donncha et al., 2015, Vaz et al., 2018, can be defined as: ...
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Storm Gloria (January 19–24, 2020) hit the NW Mediterranean Sea with heavy rainfall, strong easterly winds, and very high waves, causing structural damages and 13 fatalities. The low-lying Ebro Delta (ED) region was severely inundated, ruining rice fields and seaside promenades. A variety of Copernicus Marine Environment Monitoring Service (CMEMS) modeling and observational products were jointly used to examine the fingerprint of Gloria and the response of the upper oceanic layer. According to the results, Gloria can be interpreted as a high-impact once-in-a-decade metocean event where various historical records were beaten. The 99th percentile of several parameters (wind speed, significant wave height, wave period, and surface current velocity), derived from long-term observational time series, was persistently exceeded. The atmospheric surge, albeit not negligible, exerted a secondary role in ED. The ability of a high-frequency radar deployed in this region (HFR-ED) to characterize the striking features of the storm was quantified from both waves and circulation aspects. Consistent radar current observations were subsequently compared against the 5-day-ahead forecast of CMEMS Iberia-Biscay-Ireland (IBI) regional ocean model to determine, from an Eulerian perspective, the strengths and shortcomings in its predictive capabilities. Time-averaged maps of surface circulation, superimposed with fields of Instantaneous Rate of Separation (IROS), were derived to resolve flow features and identify areas of elevated particles dispersion, respectively. The mean and P99 values of IROS almost doubled the historical statistics in the vicinity of the northern Ebro hemidelta. Although IBI predicted moderately well basic features of the storm-induced circulation, results suggests that coastal transport processes, likely modulated by wave-current interactions, were not fully captured. Furthermore, current estimations from other two radar systems, overlooking immediate choke points like the Ibiza Channel and the Strait of Gibraltar, evidenced Gloria’s remote-effect in the anomalous circulation patterns observed, that altered the usual water exchanges between adjacent sub-basins. Finally, three-dimensional outcomes from IBI were used to elucidate the impact of this moving storm at different depth levels. Data analyses illustrated that Gloria caused a large increase in kinetic energy and a significant deepening of the mixed layer depth.
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Conservation efforts have traditionally focused on biodiversity hotspots, overlooking the essential ecological roles and ecosystem services provided by cold spots, the regions that harbour relatively low species diversity. In this study, we used a novel plant species database aggregated at 1˚ grid resolution to predict present and future plant species distribution in major cold spot biogeographic zones of India: Desert, Semi-Arid, Deccan Peninsula, and Gangetic Plain. We employed multiple models: Generalized Linear Model, Generalized Boosted Model, Random Forest, Support Vector Machine, and their ensemble. The results demonstrated reasonable predictive ability, with water and energy variables dominating in all the zones, showing a strong agreement with the field based data. Temperature annual range, annual precipitation, and precipitation of the driest month significantly influenced (r > 0.4) plant species patterns in the Desert and Semi-Arid zone. The ensemble model output improved predictive ability, with reduced root mean square error and enhanced correlation (r = 0.8). Other environmental variables (topography: elevation, and Human Influence Index) showed high correlation in combination with water and energy variables in the Deccan Peninsula. Continuous species loss is anticipated under future climate scenarios across all the zones. Semi-Arid is expected to see the most significant increase, with 69% and 52.5% of grids gaining species in 2050 (RCP4.5) and 69% and 84.7% in 2070 (RCP8.6), mainly attributed to an average precipitation increase. However, the Deccan Peninsula and Gangetic Plain show varying trends from 2050 to 2070, emphasizing the complex interplay of environmental factors influencing biodiversity distribution and dynamics. Our study provides insights into the species richness, potential and future distribution of cold spots in the major Indian biogeographic zones, aligning with climate-driven patterns. Our findings suggest that the ensemble modelling predictions are more accurate than individual models, emphasizing its potential for conservation efforts under rapidly changing climate. The study can provide a guiding tool for developing spatial biodiversity approach in the study region for prioritizing conservation in the face of climate change and help meet sustainable development goals.
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