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Monthly mean differences in the reference ET between the original FAO56-PM and modified calculations using the calibrated coefficients (DifET). The open circles, open triangles, and black circles denote the monthly mean DifET based on step 1, 2, and 3, respectively
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Penman-type evapotranspiration (ET) methods are widely used in irrigation water management and water resource planning. To determine the daily reference ET using Penman-type methods, net longwave radiation must be estimated through an empirical net longwave radiation equation based on meteorological data. This paper presents the coefficients of the...
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Citations
... The equation proposed by Allen et al. (1998) adversely overestimated R nl in Argentina (Carmona et al. 2017) and the Czech Republic (Kofroňová et al. 2019). Irmak et al. (2010) compared the procedures for determining the coefficients required to estimate R nl , and several authors (Kjaersgaard et al. 2009;Irmak et al. 2010;Matsui and Osawa 2015) have examined calibrations of coefficient sets-focusing on each factor-in the net longwave equation. In contrast, considering the challenge of accurate observation of net longwave radiation, it is assumed to be constant in the adopted method (Shaw 1956;Kaminsky and Dubayah 1997;Alados et al. 2003). ...
Net longwave radiation, which is an essential factor in evapotranspiration, is generally estimated by multiplying the net emissivity under clear-sky conditions by the effect of cloudiness. In this study, we proposed a phenomenon-specific daily net longwave radiation function, in the form of a difference between the upward longwave radiation and the downward longwave radiation, for the Penman–Monteith evapotranspiration equation and the Penman evaporation equation. In addition, we verified the net longwave radiation equation by comparing the observed downward longwave radiation with that estimated by the downward longwave radiation equation derived from the well-known net longwave radiation equations in the Penman–Monteith evapotranspiration equation and the Penman evaporation equation. The downward longwave radiation equation constituting the proposed net longwave radiation equation w1ith four calibrated parameters had an RMSE of 8.60 W m⁻² and MBE of − 4.37 W m⁻² and is more accurate than the downward longwave radiation equations derived from the general net longwave radiation equations at Tateno, Japan.
... The inversion of the net long-wave radiation is generally carried out with multiple methods such as the Penman method, Brunt method, and Deng Genyun method, and the net long-wave radiation algorithm recommended by the FAO, which have the same structure but different empirical coefficients (Allen et al., 1998;Ren et al., 2006). However, the applicability of these various methods varies greatly in different regions, it is, therefore, necessary to carry out localization and verification of these methods according to the specific conditions, and to take into account the influence of the complex terrain in order to improve the applicability of these methods (Matsui and Osawa, 2015). ...
The surface net radiation as an important component of the surface radiation budget has attracted wide attention; however, it is still an enormous challenge to carry out an accurate estimation of the surface net radiation in areas with complex terrain due to the scarcity of radiation observation sites and high-spatial heterogeneity of the influencing factors of the surface net radiation. Taking the Haihe River Basin as the study area, this study estimated the surface net radiation under clear-sky conditions from 2001∼2019 based on an improved algorithm of the net long-wave radiation, and the solar short-wave radiation in terms of direct radiation, diffuse sky radiation, and reflected radiation from the surrounding terrain. In this study, the regional meteorological factors were inverted based on remote sensing data to make up for the deficiency of meteorological factor interpolation. The solar short-wave radiation was corrected by considering the comprehensive influence of the atmosphere, underlying surface, and terrain, and the net long-wave radiation was optimized by localizing the algorithm coefficients. The results showed the correlation coefficient between the estimated and observed surface net radiation reached approximately 0.9, indicating the accuracy of this improved method is acceptable. Besides, the results suggested the surface net radiation was significantly influenced by the terrain, the highest value of which occurred on the south slope, followed by that on the southwest slope, west or southeast slopes, and the lowest value occurred on the north slope. In addition, there was the highest surface net radiation in summer, and there was the lowest and most frequently negative surface net radiation in winter. This study makes up for the shortcomings of the traditional spatial interpolation of meteorological factors and previous empirical formulas, and can therefore provide an important methodological foundation for the research on the surface radiation, climate, and hydrology in the areas with complex terrain.
... The 48PM method has been widely applied globally (Li et al. 2016;Matsui & Osawa 2015;Xu et al. 2010), but it is limited by severe errors before parameter redetermination. For instance, R MSE of data by the 48PM method was between 1.18 and 2.13 mm/d (Li et al. 2016) in Sichuan, above 1.1 mm/d in Kunshan, Jiangsu (Xu et al. 2010), and about 0.5 mm/d in the middle and lower reaches of Yangtse River (Jia et al. 2016). ...
To achieve accurate evaluation of evapotranspiration of reference crops (ET0) in Jiangxi, China, in the absence of systematic climatological data, with reference to the FAO-56 Penman–Monteith (P-M) equation, the Priestley-Taylor (P–T) method, the Makkink method, the Hargreaves-Samani (H–S) method, the Irmak-Allen (I-A) method, the Penman1948 (48PM) method, the Penman-Van Bavel (PVB) method, the Baier-Robertson (B-R) method, the improved Baier-Robertson (M-B-R) method, the Schendel (Sch) method, the Turc method, the Jensen-Haise (J-H) method, and the Brutsaert-Stricker (B-S) method were used to evaluate the daily climatological data collected by 26 weather stations in Jiangxi, China, and 17 weather stations in adjacent provinces. The results were compared with each other and parameter rate determination was conducted. The results indicated that the Turc method exhibited optimized applicability before parameter rate determination and the average root mean square error (RMSE) and the average normalized root mean square error (NRMSE) by this method were 0.39 mm/d and 0.157 mm, respectively. However, parameter rate determination led to negligible improvement in accuracy for this method. The Turc method could be directly applied in Jiangxi (except Nanchang). For special distribution of error after parameter rate determination, all methods exhibited significant errors in Northern Jiangxi. Herein, the 48PM method and the B-S method showed good applicability after parameter rate determination and RMSE and NRMSE of data by these methods ranged in 0.06 ~ 0.34 mm/d and 0.08 ~ 0.27, 8 ~ 27%, respectively, and their d-indices were close to 1. The annual over-estimations in weather stations in Jiangxi were below 30 mm. In the absence of data about relative humidity and wind speed, the P–T method was an appropriate simplified method for Jiangxi. In this case, α was slightly lower than the default value (1.05 ~ 1.18), RMSE was within 0.21 ~ 0.66 mm/d, and NRMSE was within 0.08 ~ 0.308 ~ 30%. Accuracy of RMSE, d-index, and NRMSE of data by the P–T method, the I-A method, and the PVB method was consistent with all stations, while that by the Mak method was slightly lower, which could be attributed to severe over-estimation in July and August. RMSE of the H–S method, the B-R method, the M-B-R method, the J-H method, and the Sch method were above 0.75 mm/d and these methods were not suitable for accurate evaluation of ET0 in Jiangxi, China. The annual ET0 was calculated by various methods (except the 48PM method and the B-S method) exhibited significant variation around 2003. This may be attributed to significant changes in certain meteorological factors over recent years.
... εgrass is the emissivity of a grass surface according to FAO-56 Penman-Monteith reference evapotranspiration (Allen et al. 235 1998) and was set to εgrass = 0.98 (Matsui & Osawa, 2015). Input for L* and L↓ was taken from the reference stations as the measurements are not influenced by surrounding objects and we assume that the atmospheric conditions are the same for the whole city area (Blankenstein & Kuttler, 2004). ...
The future increase in urban population will lead to progressing urbanization with urban sprawl and densification. Urbanized areas show distinct changes in their hydrological behaviour, water quality and climate. In the last decades, the ability of urban hydrological models to represent the dynamic hydrological behaviour of the different surface types has been improved continuously. Dissenting from the urban surface which is mostly represented in high spatial resolution, the climatic input to these models, such as precipitation and potential evapo(transpi)ration, is usually observed at one or several reference climate stations that are representing a mesoscale urban foot print area or rural conditions. From urban climate studies it is known, that the meteorological variables that are governing potential evapotranspiration (Ep) can be highly variable even on a small spatial scale. Consequently, we expect Ep at the street level to be affected by this variability as well. We observed the urban microclimate with a mobile climate station and a rotational principle at 16 different locations in two differently oriented street canyons with vegetated and non-vegetated sections, respectively, during three seasons (spring, summer, autumn) in Freiburg, in southwestern Germany. With these observations, we simulated Ep at the street level using FAO-56 Penman-Monteith reference evapotranspiration and compared it to reference Ep derived at a rooftop station. We found that Ep on street level is negatively influenced by changes in shortwave radiation and that it is barely sensitive to changes in the other input climate variables. Significant linear relationships between the relative differences in hourly and daily short-wave radiation input and Ep at the street level have been established. The application of these relationships allows to simulate Ep at the street level for any location in a city based on simulated (or observed) short wave time series and observations at a reference climate station. Our findings can be transferred easily to existing urban hydrologic models to improve modelling results with a more precise estimate of potential evapotranspiration on street level.
... Since the data of actual duration of sunshine for RnlFAO24 is often unavailable, the FAO56 method serves as a basis for the estimation of Rnl (Kjaersgaard et al., 2009). However, these formulas cannot be used universally, meaning that a comparison with site-specific conditions is necessary (Matsui and Osawa, 2015). They contain several coefficients recommended by Allen et al. (1998) that originate in local calibration based on site-specific conditions. ...
... Confirming the results of this study, Carmona et al. (2017) also reported overestimation of RnlFAO56 approach in the temperate and sub-humid climate regime of Tandil (Argentina). Conversely, the Rnl was somewhat underestimated in other locations (Matsui and Osawa, 2015;Yin et al., 2008). This can be explained by the non-reference conditions that are likely to be present at every location except the ones were the coefficients were derived. ...
... As a result, many researchers have agreed that the calibration of coefficients (expressing the cloudiness factor and atmospheric emissivity) should be carried out based on local conditions (Allen et al., 1998;Carmona et al., 2014;Jensen et al., 1990;Kjaersgaard et al., 2007bKjaersgaard et al., , 2009Matsui and Osawa, 2015;Müller et al., 2014;Yin et al., 2008). The calibration of RnlFAO56 coefficients can give rise to a significant improvement compared to measured radiation values (e.g. ...
Longwave radiation, as part of the radiation balance, is one of the factors needed to estimate potential evapo-transpiration (PET). Since the longwave radiation balance is rarely measured, many computational methods have been designed. In this study, we report on the difference between the observed longwave radiation balance and modelling results obtained using the two main procedures outlined in FAO24 (relying on the measured sunshine duration) and FAO56 (based on the measured solar radiation) manuals. The performance of these equations was evaluated in the April-October period over eight years at the Liz experimental catchment and grass surface in the Bohemian Forest (Czech Republic). The coefficients of both methods, which describe the influence of cloudiness factor and atmospheric emissivity of the air, were calibrated. The Penman-Monteith method was used to calculate the PET. The use of default coefficient values gave errors of 40-100 mm (FAO56) and 0-20 mm (FAO24) for the seasonal PET estimates (the PET was usually overestimated). Parameter calibration decreased the FAO56 error to less than 20 mm per season (FAO24 remained unaffected by the calibration). The FAO56 approach with calibrated coefficients proved to be more suitable for estimation of the longwave radiation balance.
... The humidity index is a physical quantity that is ideal to characterize wet and dry surface conditions (Hulme et al., 1992;Dikmen and Hansen, 2009). There are many kinds of calculation methods (Yin et al., 2008;Matsui and Osawa, 2015) and the definition of the normalized variable of the humidity index equal to or less than À0.5 is defined as extreme drought (Gavil an and Castillo-Llanque, 2009). In this paper, we chose the FAO PenmaneMonteith model, modified from the original PenmaneMonteith model by the FAO in 1998, to calculate the frequency of extreme drought. ...
... . The FAO56-PM formula has been applied extensively and globally. The accuracy of the common net long-wave radiation equations adopted in Penman-type evapotranspiration formulas was examined in Japan based on observations [13,14]. Regional formulas were established separately for plains and plateaus in China by Tong using measured air temperature, sunshine duration, and water vapor pressure [15]. ...
... T applied extensively and globally. The accuracy of the common net adopted in Penman-type evapotranspiration formulas was e observations [13,14]. Regional formulas were established separately fo Tong using measured air temperature, sunshine duration, and water v method was improved by Deng based on observed data at the Beijing Formulas to estimate Rnl on the Tibetan Plateau were provided by Ji variation characteristics and empirical formulas for estimating the n the oceans were also studied [19][20][21][22][23][24]. ...
Based on surface radiation balance data and meteorological observations at 19 radiation stations in China from 1993 to 2012, we assessed the applicability of seven empirical formulas for the estimation of monthly surface net long-wave radiation (Rnl). We then established a revised method applicable to China by re-fitting the formula using new observational data. The iterative solution method and the multivariate regression analysis method with the minimum root mean square error (RMSE) were used as the objective functions in the revised method. Meanwhile, the accuracy of the CERES (Clouds and the Earth's Radiant Energy System) estimated Rnl was also evaluated. Results show that monthly Rnl over China was underestimated by the seven formulas and the CERES data. The Tong Hongliang formula with lowest errors was the best among the seven formulas for estimating Rnl over China as a whole, followed by the Penman and the Deng Genyun formulas. The estimated Rnl based on the CERES data also showed relatively higher precision in accordance with the three formulas mentioned above. The FAO56-PM formula (Penman-Monteith formula recommended in the No. 56 report of the Food and Agriculture Organization) without calibration was not applicable to China due to its low accuracy. For individual stations, the Deng Genyun formula was the most accurate in the eastern plain area, while the Tong Hongliang formula was suitable for the plateau. Regional formulas were established based on the geographical distribution of water vapor pressure and elevation over China. The revised national and regional formulas were more accurate than the seven original formulas and the CERES data. Furthermore, the regional formulas produced smaller errors than the national formula at most of the stations. The regional formulas were clearly more accurate than the Deng Genyun formula at stations in Northwestern China and on the Tibetan Plateau. They were also more accurate than the Tong Hongliang formula at the stations located in the eastern area. Therefore, the regional formulas developed in this study are recommended as the standard climatology formulas to calculate monthly Rnl over China.
... Meteorological variables are commonly used to estimate net longwave radiation: water vapour pressure, air temperature, and downward shortwave radiation or sunshine duration, as in the Food and Agricultural Organization of the United Nations (FAO)-56 Penman equation [17,27,52]. The daily net longwave radiation equation coefficients based on the FAO- 56 Penman equation have been applied to various situations in many countries and regions. ...
... where a 1 and b 1 are coefficients, and e a is the water vapour pressure (kPa). The cloudiness factor is [52]: ...
... In this study, Equation (17) has been adopted for the cloudiness factor. The empirical coefficients (c 2 and d 2 ) are fitting parameters, which are obtained using Equations (11) In this paper, the three calibration methods described by Hiroyuki [52] were used to calibrate the parameters a 1 , b 1 , c 2 and d 2 . First, the two coefficients (a 1 and b 1 ) in Equation (15) are calibrated to minimize the root-mean-square error (RMSE) of the estimated longwave downward radiation when the relative sunshine duration value exceeds 0.95 (step 1). ...
Net radiation plays an essential role in determining the thermal conditions of the Earth’s surface and is an important parameter for the study of land-surface processes and global climate change. In this paper, an improved satellite-based approach to estimate the daily net radiation is presented, in which sunshine duration were derived from the geostationary meteorological satellite (FY-2D) cloud classification product, the monthly empirical as and bs Angstrom coefficients for net shortwave radiation were calibrated by spatial fitting of the ground data from 1997 to 2006, and the daily net longwave radiation was calibrated with ground data from 2007 to 2010 over the Heihe River Basin in China. The estimated daily net radiation values were validated against ground data for 12 months in 2008 at four stations with different underlying surface types. The average coefficient of determination (R²) was 0.8489, and the averaged Nash-Sutcliffe equation (NSE) was 0.8356. The close agreement between the estimated daily net radiation and observations indicates that the proposed method is promising, especially given the comparison between the spatial distribution and the interpolation of sunshine duration. Potential applications include climate research, energy balance studies and the estimation of global evapotranspiration.
To achieve accurate evaluation of evapotranspiration of reference crops (ET0) in Jiangxi, China in the absence of systematic climatological data, with reference to the FAO-56 Penman-Monteith (P-M) equation, the Pristley-Taylor (P-T) method, the Makkink method, the Hargreaves-Samani (H-S) method, the Irmak-Allen (I-A) method, the Penman1948 (48PM) method, the Penman-Van Bavel (PVB) method, the Baier-Robertson (B-R) method, the improved Baier-Robertson (M-B-R) method, the Schendel (Sch) method, the Turc method, the Jensen-Haise (J-H) method, and the Brutsaert-Stricker (B-S) method were used to evaluate the daily climatological data collected by 26 weather stations in Jiangxi, China and 17 weather stations in adjacent provinces. The results were compared with each other and parameter rate determination was conducted. The results indicated that the Turc method exhibited optimized applicability before parameter rate determination and the average root mean square error (RMSE) and the average normalized root mean square error (NRMSE) by this method were 0.39 mm/d and 0.157 mm, respectively. However, parameter rate determination led to negligible improvement in accuracy for this method. The Turc method could be directly applied in Jiangxi (except Nanchang). For special distribution of error after parameter rate determination, all methods exhibited significant errors in Northern Jiangxi. Herein, the 48PM method and the B-S method showed good applicability after parameter rate determination and RMSE and NRMSE of data by these methods ranged in 0.06 ~ 0.34 mm/d and 0.08 ~ 0.27, 8 ~ 27% respectively, and their d-indices were close to 1. The annual over-estimations in weather stations in Jiangxi were below 30 mm. In the absence of data about relative humidity and wind speed, the P-T method was an appropriate simplified method for Jiangxi. In this case, α was slightly lower than the default value (1.05 ~ 1.18), RMSE was within 0.21 ~ 0.66 mm/d, and NRMSE was within 0.08 ~ 0.308 ~ 30%. Accuracy of RMSE, d-index, and NRMSE of data by the P-T method, the I-A method, and the PVB method were consistent with all stations, while that by the Mak method was slightly lower, which could be attributed to severe over-estimation in July and August. RMSE of the H-S method, the B-R method, the M-B-R method, the J-H method, and the Sch method were above 0.75 mm/d and these methods were not suitable for accurate evaluation of ET0 in Jiangxi, China. The annual ET0 was calculated by various methods (except the 48PM method and the B-S method) exhibited significant variation around 2003. This may be attributed to significant changes in certain meteorological factors over recent years.
