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The objective of this study was to assess the accuracy of estimating evapotranspiration (ET) using the FAO-56 Penman-Monteith (FAO-56-PM) model, with measured and estimated net radiation (Rn
_{measured} and Rn
_{estimated}, respectively), the latter obtained via five different models. We used meteorological data collected between August 2005 and June 2008, on a daily basis and on a seasonal basis (wet vs. dry seasons). The following data were collected: temperature; relative humidity; global global solar radiation (Rs); wind speed and soil heat flux. The atmospheric pressure was determined by aneroid barograph, and sunshine duration was quantified with a Campbell-Stokes recorder. In addition to the sensor readings (Rn
_{measured}), five different models were used in order to obtain the Rn
_{estimated}. Four of those models consider the effects of cloud cover: the original Brunt model; the FAO-24 model for wet climates; the FAO-24 model for dry climates, and the FAO-56 model. The fifth was a linear regression model based on Rs. In estimating the daily ET0 with the FAO-56-PM model, Rn
_{measured} can be replaced by Rn
_{estimated}, in accordance with the FAO-24 model for dry climates, with a relative error of 2.9%, or with the FAO-56 model, with an error of 4.9%, when Rs is measured, regardless of the season. The Rn
_{estimated} obtained with the fifth model has a relatively high error. The original Brunt model and FAO-24 model for wet climates performed more poorly than did the other models in estimating the Rn and ET0. In overcast conditions, the original Brunt model, the FAO-24 model for wet climates, the FAO-24 model for dry climates, the FAO-56 model and the model of linear regression with Rs as the predictor variable tended to overestimate Rn and ET, those estimates becoming progressively more accurate as the cloud cover diminished.

The model employed in order to quantify the consumption of water by crops includes the concept of evapotranspiration (ET), which is the rate at which water is transferred into the air from a reference surface. The model uses the FAO-56 Penman-Monteith (FAO-56-PM) equation, with a grass height of 0.12 m, an albedo of 0.23 and a surface resistance of 70 s·m^{−1} [

The application of the FAO-56-PM model requires measurements of net radiation (Rn), soil heat flux, air temperature, humidity, atmospheric pressure and wind speed. Specifically in the case of Rn, there are procedures for estimating its value, as described by various authors [_{measured} and Rn_{estimated}, respectively) to be compared [

The net radiometer is the most widely used instrument for the measurement of Rn. However, Rn is not often measured in weather station networks [

Various studies have evaluated measured or estimated ET on several times scales, Rn having been measured by different instruments or estimated by different models [

Many researchers, in the absence of experimental observations, have estimated Rn from empirical relationships based on physical considerations or other meteorological data [

Rn is the meteorological element that has the greatest influence on ET and represents the main source of energy used in various physical-biological processes. Furthermore, it is the main parameter used in many of the models that estimate the transfer of water from vegetated surfaces into the atmosphere. It is therefore important to measure or estimate Rn accurately. In the present study, we aimed to evaluate the accuracy of estimated evapotranspiration on a daily scale during dry and wet seasons, testing various Rn estimation formulae for non-ir- rigated grass in Brazil.

Measurements were taken at the agrometeorological station of the São Paulo State University School of Agricultural and Veterinary Sciences, located in the city of Jaboticabal, Brazil (21˚14'05''S; 48˚17'09''W, altitude: 615.01 m). The surface studied was covered by grass. According to the Köppen climate classification system [

The experimental data were collected from August 2005 to June 2008?monthly meteorological data (

The months of January, February, March, October, November and December were considered the wettest months, whereas April, May, June, July, August and September were considered the driest months [

ET by the FAO-56-PM model, as described by [

Month | T (˚C·day^{−1}) | RH (%·day^{−1}) | P (mm·day^{−1}) | U_{2} (m·s^{−1}·day^{−1}) | n (h·day^{−1}) | Rn (MJ·m^{−2}·day^{−1}) |
---|---|---|---|---|---|---|

Jan | 23.7 | 78.4 | 412.7 | 1.7 | 5.4 | 10.1 |

Feb | 24.0 | 78.1 | 348.6 | 1.6 | 7.0 | 11.7 |

Mar | 24.0 | 73.3 | 86.8 | 1.5 | 7.5 | 10.8 |

Ap | 22.7 | 71.8 | 168.7 | 1.5 | 7.9 | 11.5 |

May | 19.2 | 66.9 | 166.9 | 1.9 | 7.1 | 9.2 |

Jun | 19.5 | 63.2 | 8.7 | 1.0 | 7.4 | 9.2 |

Jul | 19.3 | 55.9 | 80.5 | 1.9 | 7.7 | 9.9 |

Aug | 22.0 | 54.3 | 0.0 | 1.1 | 9.3 | 12.6 |

Sep | 22.8 | 56.2 | 1.3 | 1.5 | 8.0 | 13.3 |

Oct | 24.8 | 63.7 | 35.0 | 2.1 | 7.6 | 10.3 |

Nov | 23.7 | 66.8 | 129.4 | 2.4 | 7.4 | 11.5 |

Dec | 23.8 | 73.2 | 194.8 | 2.3 | 6.7 | 11.4 |

Full Period | 22.5 | 66.9 | 1633.4 | 1.7 | 7.4 | 10.9 |

T, air temperature; RH, air relative humidity; P, rainfall; U_{2}, wind speed―2 m; n, sunshine duration; Rn, net radiation.

where G is the soil heat flux (MJ·m^{−2}·day^{−1}), γ is the psychrometric coefficient (kPa·˚C^{−1}); T is the mean temperature (˚C); U_{2} is the mean wind speed at a height of 2 m (m·s^{−1}), e_{s} is the saturated vapor pressure (kPa), given by the expression:

e_{a} is the actual vapor pressure (kPa), given by the expression:

where RH is relative humidity (%) and s is the slope of the curve of vapor pressure (kPa·˚C^{−1}), given by the expression:

An automated data logger (CR10X; Campbell Scientific, Logan, UT) was installed on the reference surface in order to collect the following data (from the following instruments): temperature and relative humidity at 1.5 m above the surface (CS500 probe; Vaisala, Helsinki, Finland); Rs (CM3 pyranometer; Kipp & Zonen, Delft, The Netherlands); wind speed at 2 m above the surface (014A-L-34 wind speed sensor; Met-One Instruments, Grants Pass, OR), and Rn (NR-Lite net radiometer; Kipp & Zonen). Measurements of Rn were corrected for the effects of wind according to the manufacturer’s recommendation. The soil heat flux was obtained with a heat flux plate (HFT3; REBS Inc., Seattle, WA) installed at a depth of 3.5 cm. The atmospheric pressure was obtained by aneroid barograph (290; Lambrecht Meteorological Instruments, Göttingen, Germany), and sunshine duration was quantified with a Campbell-Stokes recorder (L-1603; Lambrecht Meteorological Instruments).

In addition to the Rn_{measured}, Rn_{estimated} was obtained by combining the Angström-Prescott equations for shortwave radiation components with the Brunt equation for the longwave radiation component emitted by the atmosphere. Thus, the Rn_{estimated} values were obtained using four models that take into account the effects of cloud cover and a fifth model involving linear regression with Rs as the predictor variable:

Rn_{BRUNT}: original equation of Brunt [

where Rs is the global solar radiation (MJ·m^{−2}·day^{−1}), r is the reflection coefficient of grass, T is the mean temperature (K), ea is the actual vapor pressure in the air (mmHg), n is the number of hours of sunshine duration (h), and N is the photoperiod (h).

Rn_{FAO-24W} and Rn_{FAO-24D}: the Brunt equation, as adapted, in two forms [

Rn_{FAO-56}: FAO-56 equation [

where

where Rso is the global solar radiation without the presence of clouds (MJ·m^{−2}·day^{−1}), z is the altitude (m), Ra is the extraterrestrial radiation (MJ·m^{−2}·day^{−1}), G_{sc} is the solar constant (0.0820 MJ·m^{−2}·min^{−1}), d_{r} is the relative Earth-Sun distance (rad), δ is the solar declination (rad), φ is latitude (rad), ω_{s} is the solar hour angle (rad), and J is the Julian day of the year (1 to 365 or 366).

Rn_{Rs}: equation for estimating the Rn at Jaboticabal linear regression with global solar radiation as the predictor variable, as proposed by André and Volpe [

where Rs is the global solar radiation (MJ·m^{−2}·day^{−1}).

We adopted the cloud cover classification system proposed [_{T}) which is the ratio between incident global solar radiation and extraterrestrial radiation: K_{T} < 0.35 (overcast), 0.35 ≤ K_{T} < 0.55 (broken clouds), 0.55 ≤ K_{T} ≤ 0.65 (scattered clouds) and K_{T} > 0.65 (clear sky).

We compared the estimation of ET based on Rn_{measured} with that based on Rn_{estimated} using the five models mentioned previously, through the statistical indicators simple linear regression analysis through the origin (y = bx), index of agreement (d), mean relative error (MRE) and efficiency (EF) [

where d is the index of agreement, Pi is the ET estimated by the FAO-56-PM model with Rn_{estimated} via the model in question (Rn_{BRUNT}; Rn_{FAO}_{-}_{24W}; Rn_{FAO}_{-24D}; Rn_{FAO}_{-56}; or Rn_{Rs}), O_{i} is the ET estimated by the FAO-56-PM model with Rn_{measured} (the standard), _{estimated} via the alternative model in question, _{measured}, and n is the number of observations.

Analyzing the mean monthly ET values shown in _{measured} ET with the Rn_{estimated} ET from the various models, we can see that the models in which the Rn_{estimated} most closely approximated the Rn_{measured} were the Rn_{FAO-24D} and Rn_{FAO-56} models. In addition, the Rn_{Rs} equation was shown to have overestimated Rn, whereas there was an underestimation of Rn when the Brunt and FAO-24D equations were applied.

Initially, we analyzed the dry and wet months separately to determine the effect of seasonality of rainfall (Ta- ble 2).

Despite the similarity of the equations applied in the Rn_{FAO-24D} and Rn_{FAO-56} models, which differ only in the effect of cloud cover, there were significant differences between those two models. When we analyzed the dry months separately from the wet months, the Rn_{FAO}_{-56} model underestimated the cloud cover, by 8.5% in the dry months and 22.9% in the wet months, resulting in the estimated ET being 1.6% and 2.8% higher in the dry and wet months, respectively, relative to the estimates obtained with the Rn_{FAO}_{-24D} model. When we analyzed the dry and wet months together, the Rn_{FAO}_{-56} model underestimated the cloud cover by 15.2%, increasing the estimated ET by 4.9% (

Rn estimation formulae | N | ET with Rn_{estimated} | b | R^{2} | d | MRE | EF |
---|---|---|---|---|---|---|---|

(mm·day^{−1}) | (mm·day^{−1}) | ||||||

ET (Rn_{measured}), dry month | 1063 | 3.64c | - | - | - | - | - |

ET (Rn_{measured}), wet month | 4.56C | ||||||

ET (Rn_{BRUNT}), dry month | 1063 | 3.19d | 0.8787 | 0.9536 | 0.9942 | 0.45 | 0.9807 |

ET (Rn_{BRUNT}), wet month | 4.26D | 0.9267 | 0.9391 | 0.9978 | 0.30 | 0.9917 | |

ET (Rn_{FAO-24W}), dry month | 1063 | 3.21d | 0.8852 | 0.9534 | 0.9947 | 0.43 | 0.9823 |

ET (Rn_{FAO-24W}), wet month | 4.30D | 0.9339 | 0.9407 | 0.9981 | 0.26 | 0.9923 | |

ET (Rn_{FAO-24D}), dry month | 1063 | 3.79c | 1.0355 | 0.9827 | 0.9990 | 0.15 | 0.9955 |

ET (Rn_{FAO-24D}), wet month | 4.64C | 1.0095 | 0.9628 | 0.9990 | 0.08 | 0.9950 | |

ET (Rn_{FAO-56}), dry month | 1063 | 3.85b | 1.0531 | 0.9746 | 0.9983 | 0.21 | 0.9918 |

ET (Rn_{FAO-56}), wet month | 4.77B | 1.0374 | 0.9703 | 0.9985 | 0.20 | 0.9927 | |

ET (Rn_{Rs}), dry month | 1063 | 4.69a | 1.2804 | 0.9630 | 0.9829 | 1.05 | 0.9075 |

ET (Rn_{Rs}), wet month | 5.59A | 1.2196 | 0.9668 | 0.9886 | 1.03 | 0.9413 |

N, number of observations; b, slope of the regression line; R^{2}, coefficient of determination; d, index of agreement; MRE, mean relative error; EF, efficiency. Means followed by the same letter in the same column do not differ at the 5% level by t-test.

Rn estimation formulae | N | ET (mm) | b | R^{2} | d | MRE (mm) | EF | Rn (MJ·m^{−2}) | b | R^{2} | d | MRE (MJ·m^{−2}) | EF |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

ET (Rn_{medido}) | 1063 | 4.1c | - | - | - | - | - | 9.3e | - | - | - | - | - |

ET (Rn_{BRUNT}) | 1063 | 3.7d | 0.908 | 0.835 | 0.996 | 0.4 | 0.986 | 7.7d | 0.814 | 0.707 | 0.968 | 1.6 | 0.892 |

ET (Rn_{FAO-24W}) | 1063 | 3.8d | 0.915 | 0.937 | 0.996 | 0.3 | 0.987 | 7.9d | 0.836 | 0.716 | 0.970 | 1.4 | 0.895 |

ET (Rn_{FAO-24D}) | 1063 | 4.2bc | 1.020 | 0.975 | 0.999 | 0.1 | 0.995 | 9.8c | 1.013 | 0.842 | 0.986 | 0.5 | 0.905 |

ET (Rn_{FAO-56}) | 1063 | 4.3b | 1.044 | 0.975 | 0.998 | 0.2 | 0.992 | 10.2b | 1.057 | 0.895 | 0.984 | 0.9 | 0.813 |

ET (Rn_{Rs}) | 1063 | 5.1a | 1.244 | 0.965 | 0.986 | 1.0 | 0.924 | 13.8a | 1.425 | 0.801 | 0.949 | 4.4 | 0.589 |

N, number of observations; b, slope of the regression line; R^{2}, coefficient of determination; d, index of agreement; MRE, mean relative error; EF, efficiency. Means followed by the same letter in the same column do not differ at the 5% level by t-test.

joint analyses of dry and wet months, for any of the models. This, together with the values for slope, coefficient of determination, index of agreement, MRE and efficiency (

When comparing the mean Rn_{measured} ET for the entire period (4.1 mm·day^{−1}, _{estimated} ET for the entire period obtained via the Rn_{BRUNT} and Rn_{FAO-24W} models, we found that those two models unde-

restimated the ET by 10.8% and 7.9%, respectively, whereas ET was overestimated by 2.4%, 4.9% and 24.4%, respectively, when we used the models Rn_{FAO-24D}, Rn_{FAO-56} and Rn_{Rs}. A slope of the regression equation that is closer to 1 indicates a better estimate of the ET. The best fit (slope = 1.020) was obtained with the Rn_{FAO}_{-24D} model, as confirmed by t-test (_{FAO}_{-24D} model, followed by the models Rn_{FAO}_{-56} models, Rn_{FAO}_{-}_{24W}, Rn_{BRUNT} and Rn_{Rs}. In the present study, the strongest correlation with the Rn_{measured} was achieved via the Rn_{FAO}_{-24D} model. For the study period as a whole, the MRE of Rn (MJ·m^{−2}·day^{−1}) was 1.6, 1.5, 0.5, 0.9 and 4.4, respectively, for the models Rn_{BRUNT}, Rn_{FAO-24W}, Rn_{FAO-24D}, Rn_{FAO-56} and Rn_{Rs} (

Some authors, such as [

Given that estimates of ET obtained via the FAO-56-PM model are affected by the method employed in obtaining Rn, [

For the Jaboticabal region, the Rn_{Rs} model André and Volpe [

In the present study, despite the high correlation between Rn and Rs, Rs overestimated Rn by 48.4% according to the methodology of André and Volpe [_{Rs} model overestimated the daily ET by 24.4% (

Significant errors can be made in estimating the ET when Rn is not correctly measured or estimated, with differences of as much as 2.2 MJ·m^{−2}·day^{−1} [_{estimated} was 0.2 - 5.1 MJ·m^{−2}·day^{−1} for clear sky days, 0.01 - 3.5 MJ·m^{−2}·day^{−1} for days with scattered clouds, 0.4 - 3.1 MJ·m^{−2}·day^{−1} for days with broken clouds and 1.3 - 2.7 MJ·m^{−2}·day^{−1} for overcast days (

The model used in obtaining Rn and, specifically, the way in which the effect that cloud cover has on the longwave component is calculated, can cause significant errors in the estimation of daily ET by the Penman- Monteith model [

The Rn depends heavily on the Rs, which is in turn dependent on other factors, such as the effect of cloud cover, increases in cloud cover decreasing the Rs and Rn fluxes and consequently decreasing the ET. This is because the clear sky condition reveals the dependence of Rn on cloud cover [

When ET is estimated by the Penman-Monteith model on the basis of Rn estimated by the Rn_{Rs} model, the effect of cloud cover is embedded in the term Rs, but varies slightly in comparison with that of the Rn estimation models in which the effect of cloud cover is taken into account. This is because cloud cover has a major influence on variations in net longwave radiation and consequently on estimates of ET. The Rn_{Rs} model limits variations that other models allow, because it sets fixed values for the seasons. [_{T} and air temperature, normally used to estimate Rn, be incorporated into new elements, such as Rs and pressure of water vapor, to improve the credibility of the estimates. As cloud cover de creases, the net longwave radiation balance becomes more negative and therefore has a greater effect on the calculation of the Rn_{estimated}, bringing it into closer proximity with the Rn_{measured} (

Clearness Rn estimation formulae | N | ET (mm) | b | R^{2} | d | MRE (mm) | EF | Rn (MJ·m^{−2}) | b | R^{2} | d | MRE (MJ·m^{−2}) | EF |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Clear sky | |||||||||||||

ET (Rn_{medido}) | 692 | 4.5bc | - | - | - | - | - | 10.2c | - | - | - | - | - |

ET (Rn_{BRUNT}) | 692 | 3.9d | 0.879 | 0.926 | 0.992 | 0.6 | 0.976 | 7.8d | 0.775 | 0.806 | 0.964 | 2.4 | 0.912 |

ET (Rn_{FAO-24W}) | 692 | 4.0d | 0.886 | 0.927 | 0.993 | 0.5 | 0.978 | 7.9d | 0.788 | 0.808 | 0.967 | 2.3 | 0.919 |

ET (Rn_{FAO-24D}) | 692 | 4.6c | 1.004 | 0.933 | 0.998 | 0.1 | 0.994 | 10.4c | 0.998 | 0.816 | 0.994 | 0.2 | 0.974 |

ET (Rn_{FAO}_{-}_{56}) | 692 | 4.7bc | 1.025 | 0.960 | 0.999 | 0.1 | 0.993 | 10.8b | 1.038 | 0.890 | 0.995 | 0.6 | 0.970 |

ET (Rn_{Rs}) | 692 | 5.7a | 1.250 | 0.917 | 0.983 | 1.2 | 0.903 | 15.3a | 1.443 | 0.743 | 0.948 | 5.1 | 0.593 |

Scattered clouds | |||||||||||||

ET (Rn_{medido}) | 127 | 4.4bc | - | - | - | - | - | 10.4c | - | - | - | - | - |

ET (Rn_{BRUNT}) | 127 | 4.0d | 0.918 | 0.856 | 0.996 | 0.3 | 0.988 | 9.0d | 0.857 | 0.605 | 0.985 | 1.4 | 0.959 |

ET (Rn_{FAO-24W}) | 127 | 4.0d | 0.924 | 0.859 | 0.997 | 0.3 | 0.989 | 9.1d | 0.867 | 0.612 | 0.987 | 1.3 | 0.962 |

ET (Rn_{FAO-24D}) | 127 | 4.4c | 0.994 | 0.896 | 0.998 | 0.01 | 0.994 | 10.4c | 0.988 | 0.698 | 0.995 | 0.01 | 0.979 |

ET (Rn_{FAO-56}) | 127 | 4.5bc | 1.030 | 0.932 | 0.990 | 0.2 | 0.993 | 11.1b | 1.047 | 0.809 | 0.995 | 0.65 | 0.974 |

ET (Rn_{Rs}) | 127 | 5.2a | 1.184 | 0.910 | 0.991 | 0.8 | 0.954 | 13.9a | 1.318 | 0.786 | 0.976 | 3.5 | 0.847 |

Broken clouds | |||||||||||||

ET (Rn_{medido}) | 155 | 3.2d | - | - | - | - | - | 7.3e | - | - | - | - | - |

ET (Rn_{BRUNT}) | 155 | 3.3d | 1.017 | 0.877 | 0.996 | 0.1 | 0.971 | 7.7e | 1.028 | 0.633 | 0.989 | 0.4 | 0.932 |

ET (Rn_{FAO-24W}) | 155 | 3.4d | 1.021 | 0.880 | 0.996 | 0.1 | 0.971 | 7.8d | 1.037 | 0.643 | 0.989 | 0.5 | 0.929 |

ET (Rn_{FAO-24D}) | 155 | 3.5c | 1.075 | 0.912 | 0.994 | 0.3 | 0.959 | 8.5c | 1.137 | 0.746 | 0.984 | 1.2 | 0.873 |

ET (Rn_{FAO-56}) | 155 | 3.6bc | 1.103 | 0.928 | 0.992 | 0.4 | 0.947 | 8.9bc | 1.184 | 0.817 | 0.979 | 1.6 | 0.799 |

ET (Rn_{Rs}) | 155 | 4.0a | 1.219 | 0.882 | 0.986 | 0.7 | 0.908 | 10.4a | 1.410 | 0.767 | 0.962 | 3.1 | 0.726 |

Overcast | |||||||||||||

ET (Rn_{medido}) | 89 | 1.8c | - | - | - | - | - | 3.7c | - | - | - | - | - |

ET (Rn_{BRUNT}) | 89 | 2.1ab | 1.142 | 0.927 | 0.987 | 0.3 | 0.922 | 5.1b | 1.223 | 0.760 | 0.932 | 1.3 | 0.530 |

ET (Rn_{FAO-24W}) | 89 | 2.1ab | 1.145 | 0.929 | 0.986 | 0.3 | 0.920 | 5.1b | 1.231 | 0.766 | 0.930 | 1.4 | 0.516 |

ET (Rn_{FAO-24D}) | 89 | 2.2ab | 1.186 | 0.941 | 0.981 | 0.4 | 0.887 | 5.5b | 1.325 | 0.818 | 0.909 | 1.8 | 0.278 |

ET (Rn_{FAO-56}) | 89 | 2.4a | 1.262 | 0.949 | 0.964 | 0.6 | 0.710 | 6.3a | 1.448 | 0.866 | 0.874 | 2.5 | 0.826 |

ET (Rn_{Rs}) | 89 | 2.4a | 1.294 | 0.872 | 0.959 | 0.6 | 0.800 | 6.4a | 1.628 | 0.777 | 0.888 | 2.7 | 0.120 |

N, number of observations; b, slope of the regression line; R^{2}, coefficient of determination; d, index of agreement; MRE, mean relative error; EF, efficiency. Means followed by the same letter in the same column do not differ at the 5% level by t-test.

As can be seen in _{measured}, because net shortwave radiation is directly dependent on Rs, the proportional contribution of net shortwave radiation increasing in parallel with increases in Rs. Determining the net longwave radiation depends on indices that correct for the effects of cloud

Clearness | K_{T} | Rs | Rns | Rnl_{ } | Rn_{measured} | |||
---|---|---|---|---|---|---|---|---|

Rn | Rn_{BRUNT} | Rn_{FAO-24W} | Rn_{FAO-24D} | Rn_{FAO-56} | ||||

Clear sky | 0.83 | 20.13 | 15.50 | −7.65 | −7.51 | −5.04 | −4.66 | 10.25 |

Scattered clouds | 0.60 | 17.50 | 13.48 | −4.48 | −4.36 | −3.03 | −2.39 | 10.44 |

Broken clouds | 0.46 | 13.41 | 10.33 | −2.62 | −2.55 | −1.78 | −1.40 | 7.28 |

Overcast | 0.26 | 7.50 | 5.77 | −1.29 | −1.26 | −0.87 | −0.02 | 3.05 |

K_{T}, clearness index, Rs, global solar radiation; Rns, net shortwave radiation; Rnl, net longwave radiation, Rn, net radiation.

cover and pressure of water vapor. In the Rn_{BRUNT}, Rn_{FAO}_{-24W} and Rn_{FAO}_{-24D} models, net longwave radiation has the same effect as cloud cover, changing only the indices that correct for pressure of water vapor in the air, which decreases the size of its effect, the index values being 0.47 for Equation (5), compared with 0.31 for Equation (6) and 0.20 for Equation (7).

Under conditions of clear sky, scattered clouds and broken clouds, the Rn_{estimated} values obtained with the Rn_{FAO}_{-24D} and Rn_{FAO}_{-56} models were comparable to the Rn_{measured}. Under overcast conditions, none of the models employed was able to adequately represent the Rn_{measured} or the ET obtained therefrom (_{estimated} depends on the proportional contribution of net shortwave radiation and net longwave radiation. Under overcast conditions, the net longwave radiation share corresponded to only 15% - 22% of that of net shortwave radiation, which affected the estimation of Rn, because the net shortwave radiation was more prominent. Under conditions of clear sky, the net longwave radiation share corresponded to 30% - 49% of the net shortwave radiation share, having an even greater effect on the estimation of Rn (

According to the coefficient of determination, index of agreement, MAE and efficiency values, the best estimates of ET were obtained via the Rn_{FAO-24D} model, followed by the models Rn_{FAO-56}, Rn_{FAO-24W}, Rn_{BRUNT} and Rn_{Rs}. The Rn_{estimated} obtained with the Rn_{FAO-24D} and Rn_{FAO-56} models more closely approximated the Rn_{measured} than did that obtained with the other models. Despite the similarity of the equations applied in the Rn_{FAO-24D} and Rn_{FAO-56} models, which differ only in the effect of cloud cover, there were significant differences between the two models. The Rn_{FAO-56} model underestimated the cloud cover, thereby increasing the estimated ET.

Under conditions of clear sky, scattered clouds and broken clouds, the Rn_{estimated} values obtained with the Rn_{FAO-24D} and Rn_{FAO-56} models were comparable to the Rn_{measured} value. As cloud cover decreases, the net longwave radiation balance becomes more negative and therefore has a greater effect on the calculation of the Rn_{estimated}, bringing it into closer proximity with the Rn_{measured}.

The Rn is the meteorological element that has the greatest influence on ET and can cause significant errors in the estimation of ET when not correctly measured or estimated.

This study received financial support from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, São Paulo Research Foundation; Grant No. 05/59535-4).