A refined index of model performance

Willmott, Cort J.; Robeson, Scott M.; Matsuura, Kenji

doi:10.1002/joc.2419

Cited by 1,066 publications

(565 citation statements)

References 16 publications

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“…Daily data were divided into two seasons -dry and rainy, for a detailed To assess model performance, we correlated the estimated values to those of the standard method using the coefficient of determination (r²) of the linear regression. As statistical indicators, the following indices were used: a) agreement index (d) by WILLMOTT et al (2012) Figure 3a shows the averages of ET0 simulations in decennial scale. By contrasting PO, ASCE-PM, PT, BC and HS against the standard (FAO-56), it becomes evident that the less complex methods BC and HS, which use temperature and solar radiation, had conflicting data.…”

Section: Methodsmentioning

confidence: 99%

Comparison of Methods for Estimating Reference Evapotranspiration: An Approach to the Management of Water Resources Within an Experimental Basin in the Brazilian Cerrado

Gotardo

Gomes

2016

Eng. Agríc.

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ABSTRACT:This study aimed to compare methods for estimating reference evapotranspiration using an experimental basin in the Brazilian Cerrado, for water management purposes. For that, we estimated daily reference evapotranspiration over a certain period (time series between 1982 and 2012) through different empirical methods. These methods consisted of Blaney-Criddle (BC), Hargreaves & Samani (HS), ASCE Penman-Monteith (ASCE-PM), Penman (1948Penman ( /1963) (PO), Priestley-Taylor (PT), which were all compared to the standard Penman-Monteith FAO-56 (PM-FAO56). Based on statistics, ASCE-PM, P and BC methods should be recommended for cerrado areas, either in rainy or dry seasons. After these, the PT also stood out. Among the less complex methods, based on temperature and energy data, PT method is recommended whether climatological data are scarce either in rainy or dry seasons. Yet, HS reached the greatest errors, a broad data spread and low estimate accuracy, but showing better performance in dry periods, thus remaining under restricted use.

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Section: Methodsmentioning

confidence: 99%

Comparison of Methods for Estimating Reference Evapotranspiration: An Approach to the Management of Water Resources Within an Experimental Basin in the Brazilian Cerrado

Gotardo

Gomes

2016

Eng. Agríc.

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“…During this retransformation, a correction factor of e 0.5σ 2 according to [25] where σ equals the standard deviation of the residual was applied to avoid prediction bias. To evaluate the validation (measured vs. predicted biomass), we calculated the R 2 , the RMSE, Willmott's refined index of model performance [26] and the mean relative error of the prediction (calculated by dividing the absolute difference between measured and predicted biomass by the measured biomass and calculating the mean). Willmott's refined index of model performance is a dimensionless indicator of model performance reaching from −1 to 1.…”

Section: Resultsmentioning

confidence: 99%

“…Willmott's refined index of model performance is a dimensionless indicator of model performance reaching from −1 to 1. It "indicates the sum of the magnitudes of the differences between the model-predicted and observed deviations about the observed mean relative to the sum of the magnitudes of the perfect-model (P i = O i , for all i) and observed deviations about the observed mean" [26] and is calculated using the equation…”

Section: Resultsmentioning

confidence: 99%

“…Overall, high coefficients of determination R 2 > 0.8 were reached, confirming the validity of the CSM-derived plant heights, with an RMSE in the single-digit centimeter range. The noon acquisition time shows the highest R 2 and lowest RMSE as well as the joint-highest Willmott's refined index of model performance [26] and thus the best result in estimating the real plant height when compared to the manual plant height measurements performed using a ruler. Therefore, we use the plant heights per plot derived from this acquisition date in the further statistical analysis and regression of plant height and biomass.…”

Section: Plant Height Measurementsmentioning

confidence: 97%

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Estimating Barley Biomass with Crop Surface Models from Oblique RGB Imagery

Brocks

Bareth

2018

Remote Sensing

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Non-destructive monitoring of crop development is of key interest for agronomy and crop breeding. Crop Surface Models (CSMs) representing the absolute height of the plant canopy are a tool for this. In this study, fresh and dry barley biomass per plot are estimated from CSM-derived plot-wise plant heights. The CSMs are generated in a semi-automated manner using Structure-from-Motion (SfM)/Multi-View-Stereo (MVS) software from oblique stereo RGB images. The images were acquired automatedly from consumer grade smart cameras mounted at an elevated position on a lifting hoist. Fresh and dry biomass were measured destructively at four dates each in 2014 and 2015. We used exponential and simple linear regression based on different calibration/validation splits. Coefficients of determination R 2 between 0.55 and 0.79 and root mean square errors (RMSE) between 97 and 234 g/m 2 are reached for the validation of predicted vs. observed dry biomass, while Willmott's refined index of model performance d r ranges between 0.59 and 0.77. For fresh biomass, R 2 values between 0.34 and 0.61 are reached, with root mean square errors (RMSEs) between 312 and 785 g/m 2 and d r between 0.39 and 0.66. We therefore established the possibility of using this novel low-cost system to estimate barley dry biomass over time.

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“…The parameter that best expresses roughness was selected based on the following indicators: Root Mean Square Error -RMSE (Willmott et al, 2012) …”

Section: Methodsmentioning

confidence: 99%

Internal surface roughness of plastic pipes for irrigation

Rocha

Marques

Camargo

et al. 2017

Rev. bras. eng. agríc. ambient.

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A B S T R A C TAssuming that a roughness meter can be successfully employed to measure the roughness on the internal surface of irrigation pipes, this research had the purpose of defining parameters and procedures required to represent the internal surface roughness of plastic pipes used in irrigation. In 2013, the roughness parameter Ra, traditional for the representation of surface irregularities in most situations, and the parameters Rc, Rq, and Ry were estimated based on 350 samples of polyvinyl chloride (PVC) and low-density polyethylene (LDPE) pipes. Pressure losses were determined from experiments carried out in laboratory. Estimations of pressure loss varied significantly according to the roughness parameters (Ra, Rc, Rq, and Ry) and the corresponding pipe diameter. Therefore, specific values of roughness for each pipe diameter improves accuracy in pressure losses estimation. The average values of internal surface roughness were 3.334 and 8.116 µm for PVC and LDPE pipes, respectively. Rugosidade interna de tubos plásticos utilizados em irrigação R E S U M OObjetivou-se, no presente estudo, estabelecer os parâmetros de amplitude das irregularidades da superfície interna de tubos plásticos para irrigação, assim como procedimentos para sua obtenção e representação utilizando-se um rugosímetro de bancada. Durante o ano de 2013 foram avaliados 350 perfis de rugosidade de tubos de PVC e polietileno de baixa densidade (PEBDL), sendo determinados os parâmetros de rugosidade Ra, clássico para a representação das irregularidades de superfícies na maioria das situações, além dos parâmetros adicionais Rc, Rq e Ry. Determinações hidráulicas de perda de carga foram realizadas em laboratório para comparação com a perda de carga obtida pela aplicação dos parâmetros de rugosidade. Evidenciou-se diferença significativa de desempenho estatístico dos parâmetros de rugosidade (Ra, Rq, Rc e Ry) de acordo com o diâmetro do tubo e, portanto, constatou-se que a adoção de valores de rugosidade específicos para cada diâmetro contribui para a exatidão das estimativas de perda de carga. A rugosidade média para tubos de PVC e PEBDL foi 3,334 e 8,116 µm, respectivamente.

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A refined index of model performance

Cited by 1,066 publications

References 16 publications

Comparison of Methods for Estimating Reference Evapotranspiration: An Approach to the Management of Water Resources Within an Experimental Basin in the Brazilian Cerrado

Comparison of Methods for Estimating Reference Evapotranspiration: An Approach to the Management of Water Resources Within an Experimental Basin in the Brazilian Cerrado

Estimating Barley Biomass with Crop Surface Models from Oblique RGB Imagery

Internal surface roughness of plastic pipes for irrigation

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