On the performance of three indices of agreement: an easy-to-use r-code for calculating the Willmott indices

Pereira, Heloisa Ramos; Meschiatti, Monica Cristina; Pires, Regina Célia de Matos; Blain, Gabriel Constantino

doi:10.1590/1678-4499.2017054

Cited by 48 publications

(26 citation statements)

References 18 publications

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“…(8)); Willmott's index of agreement (d) (Willmott, 1981) (Eq. (9)), which indicates how well model-produced estimates simulate observed data (Pereira et al, 2018); performance index of Camargo and Sentelhas (1997) (c) (Eq. (10)), which is the result of multiplying r and d, therefore, aggregates the information provided by both indicators, making it easier to visualize; mean error (me) (Eq.…”

Section: Validation Of Results and Statistical Analysismentioning

confidence: 99%

Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Pinto

Nunes

Souza

et al. 2020

Rev. bras. meteorol.

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Two models aimed to estimate solar irradiance were calibrated in six locations in Northeastern Pará (Belém, Cametá, Conceição do Araguaia, Marabá, Soure, and Tucuruí). The first one is the equation of Angström-Prescott (AP), which requires observations of sunshine duration hours. The second model is a modified version of Hargreaves' radiation formula (MH), which requires observations of daily maximum and daily minimum air temperatures. Both models were calibrated to estimate daily and monthly solar radiation. The calibration of both equations for each season (i.e., dry season and wet season) in each location was also tested. AP has an average performance about 74% higher than MH for daily estimates (excluding Soure) and 83% higher than MH for monthly estimates (excluding Soure and Tucuruí). The use of seasonally calibrated equations slightly improves the performance of AP, measured by the performance index, by 0.68% and improves the performance of MH in most locations, when estimating daily solar radiation. The performance of both models is much higher when estimating monthly solar radiation than daily solar radiation, with an increase of the performance index of 10.95% for AP.

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Section: Validation Of Results and Statistical Analysismentioning

confidence: 99%

Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Pinto

Nunes

Souza

et al. 2020

Rev. bras. meteorol.

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“…( 4)-( 7), and refer to modelled and observed data; ̅ and ̅ are the mean values of modelled and observed data; and define the standard deviation of the modelled and observed data; and n is number of observations. In the 95 % confidence interval of each index value was calculated through bootstrap approach as contained in (Pereira et al, 2018).…”

Section: Methodsmentioning

confidence: 99%

“…Nevertheless, the CRU dataset appears to be substantially better than the CPC owing its low error statistics. The proposed by Willmott et al (2012) and demonstrated by Pereira et al (2018) was used to test the level of agreement of the datasets relative to the reference observations over the study domain. The results obtained from the are similar to those from r. However, the range of values obtained using are generally lower but yet credible enough to reveal the accuracy of the datasets.…”

Section: Analysis Of Pdfs For Minimum and Maximum Temperaturesmentioning

confidence: 99%

Validating Gauge-based Spatial Surface Atmospheric Temperature Datasets for Upper Benue River Basin, Nigeria

Salaudeen

Ismail

Adeogun

et al. 2021

Nig. J. Env. Sci. & Tech.

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Like most other countries of Africa, one of the main problems threatening effective impact modelling in Nigeria including Upper Benue river basin, dwells in lack of high-quality in-situ observation datasets at appropriate spatiotemporal scales. Gridded meteorological variables can serve as promising alternatives to in-situ measurements in data sparse regions, but then, require validations to assess quantitatively their level of accuracies and reliabilities. As a consequence, this study makes comparative analysis of two gauge-based, spatially interpolated surface atmospheric temperature datasets with in-situ measurements in seven distinct meteorological stations covering the period of 1982-2006. Correspondingly, spatial analysis and statistical measures were used to assess the performances of the gridded datasets from the Climate Research Unit (CRU) and the Climate Prediction Centre (CPC). Results from spatial distributions depict 8, 11 and 10 °C as observed minimum temperatures and 33, 36, 42 °C as observed maximum temperatures over the Cameroon highland (Gembu), the Jos plateau and at the northern fringes of the basin respectively. Consequently, both the CRU and CPC datasets captured remarkably well the observed temperature gradients along the varying topography, though with differing margins. The interannual variabilities indicate CRU dataset to better capture the signs and magnitudes of the observed anomalies as compared to the CPC data. Moreover, the CRU data was noted to be more outstanding in representing the observed features in seasonal temperature variations over most stations. Also, the shapes of the probability density function (PDF) for both datasets in minimum and maximum temperatures measured closely the shapes of the observed PDF. Trend analysis suggests CRU datasets to better represent the warming and the cooling trends than the CPC. Overall, the CRU datasets are the most outstanding in this study and is therefore preferred for water resource application over the study area.

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“…In this sense, five methods were used to evaluate the residuals calculated by the cross-validation, MSE (6), R 2 (7), square root of the MSE (RMSE) and modified Willmott's concordance index (md) (8), where Z u i is the mean and Ẑ u i is the fitted value. The md index is less sensitive to the presence of outliers and has a range between 0 and 1, where values close to 1 better indicate the model's performance in the prediction [36].…”

Section: Evaluation Of the Modelsmentioning

confidence: 99%

The assessment of annual rainfall field by applying different interpolation methods in the state of Rio Grande do Sul, Brazil

et al. 2021

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An accurate analysis of spatial rainfall distribution is of great importance for managing watershed water resources, in addition to giving support to meteorological studies and agricultural planning. This work compares the performance of two interpolation methods: Inverse distance weighted (IDW) and Kriging, in the analysis of annual rainfall spatial distribution. We use annual rainfall data for the state of Rio Grande do Sul (Brazil) from 1961 to 2017. To determine which proportion of the sample results in more accurate rainfall distribution maps, we use a certain amount of points close to the estimated point. We use mean squared error (MSE), coefficient of determination (R2), root mean squared error (RMSE) and modified Willmott's concordance index (md). We conduct random fields simulations study, and the performance of the geostatistics and classic methods for the exposed case was evaluated in terms of precision and accuracy obtained by Monte Carlo simulation to support the results. The results indicate that the co-ordinary Kriging interpolator showed better goodness of fit, assuming altitude as a covariate. We concluded that the geostatistical method of Kriging using nine closer points (50% of nearest neighbors) was the one that better represented annual rainfall spatial distribution in the state of Rio Grande do Sul.

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On the performance of three indices of agreement: an easy-to-use r-code for calculating the Willmott indices

Cited by 48 publications

References 18 publications

Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Validating Gauge-based Spatial Surface Atmospheric Temperature Datasets for Upper Benue River Basin, Nigeria

The assessment of annual rainfall field by applying different interpolation methods in the state of Rio Grande do Sul, Brazil

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