Class A pan coefficients ( Kp ) to estimate daily reference evapotranspiration ( ETo )

The Class A pan coefficient (Kp) has been used to convert pan evaporation (ECA) to grass-reference evapotranspiration (ETo), an important component in water management of irrigated crops. There are several methods to determine Kp values, using wind speed, relative humidity and fetch length and conditions. This paper analyses the following methods to estimate Kp values: Doorenbos & Pruitt (1977); Cuenca (1989); Snyder (1992); Pereira et al. (1995); Raghuwanshi & Wallender (1998); and FAO/56 (Allen et al., 1998). The estimated and the observed values of Kp, obtained from the relationship between ETo measured in a weighing lysimeter and ECA measured in a Class A pan, were compared by regression analysis. The same routine was adopted to evaluate ETo estimates with different Kp values. The results showed that all methods to estimate Kp did not predict it well, with low correlation (R2 < 0.2), which resulted in estimates of ETo with high dispersion (R2 < 0.8). The best Kp methods to estimate ETo were Pereira et al. (1995) and Cuenca (1989), both presenting high efficiency. The use of an arbitrary and constant Kp (0.71) to estimate ETo, produced the same precision and accuracy as the estimates of Kp based on Pereira and Cuenca methods. This fixed value is a practical and simple option to convert ECA into ETo, but this value must be calibrated for each place under different climatic conditions.

Revista Brasileira de Engenharia Agrícola e Ambiental, v.7, n. 1, p.111-115, 2003 Campina Grande, PB, DEAg/UFCG -http://www.agriambi.com.br Paulo C. Sentelhas 1 & Marcos V. Folegatti 2 1 ESALQ/USP -Setor de Agrometeorologia, Departamento de Ciências Exatas.CP 9, CEP 13418-900, Piracicaba, SP.Fone: (19) 3429-4283.E-mail: pcsentel@esalq.usp.br(Foto) 2 ESALQ/USP.CP 9, CEP 13418-900, Piracicaba, SP.Fone: (19) 3429-4217.E-mail: mvfolega@esalq.uso.brAbstr Abstr Abstr Abstr Abstract: act: act: act: act: The Class A pan coefficient (Kp) has been used to convert pan evaporation (ECA) to grass-reference evapotranspiration (ETo), an important component in water management of irrigated crops.There are several methods to determine Kp values, using wind speed, relative humidity and fetch length and conditions.This paper analyses the following methods to estimate Kp values: Doorenbos & Pruitt (1977); Cuenca (1989); Snyder (1992); Pereira et al. (1995); Raghuwanshi & Wallender (1998); and FAO/56 (Allen et al., 1998).The estimated and the observed values of Kp, obtained from the relationship between ETo measured in a weighing lysimeter and ECA measured in a Class A pan, were compared by regression analysis.The same routine was adopted to evaluate ETo estimates with different Kp values.The results showed that all methods to estimate Kp did not predict it well, with low correlation (R 2 < 0.2), which resulted in estimates of ETo with high dispersion (R 2 < 0.8).The best Kp methods to estimate ETo were Pereira et al. (1995) and Cuenca (1989), both presenting high efficiency.The use of an arbitrary and constant Kp (0.71) to estimate ETo, produced the same precision and accuracy as the estimates of Kp based on Pereira and Cuenca methods.This fixed value is a practical and simple option to convert ECA into ETo, but this value must be calibrated for each place under different climatic conditions.

INTRODUCTION
Reference evapotranspiration (ETo) is an essential component for use in water supply planning and irrigation scheduling (Snyder, 1992) since the crop evapotranspiration (ETc) is estimated by ETo multiplied by the crop coefficient (Kc).One common method to estimate ETo is converting the class A pan evaporation (ECA) into ETo by using a pan coefficient (Kp), which varies depending on the site and the weather conditions as showed by Doorenbos & Pruitt (1977) and Allen et al. (1998).
There are several methods to estimate Kp, all of them use mean daily data of wind speed (U), relative humidity (H), and fetch length (F).Doorenbos & Pruitt (1977) reported a table with Kp values ranging from 0.40 to 0.85, depending on these variables and the ground cover type surrounding the pan.
However, with modern automatic weather stations and computer facilities, it is convenient to automate ECA to ETo conversions using equations (Snyder, 1992).In order to solve this problem, Cuenca (1989) suggested a polynomial equation to predict Kp values from U, H, and F. According to Snyder (1992) the equation proposed by Cuenca is complex, and in some cases the output is quite different from the original data found in Doorenbos & Pruitt's table (Doorenbos & Pruitt, 1977).Then, Snyder (1992) presented another equation to predict Kp using the same variables in a multiple linear regression.Subsequently, Pereira et al. (1995)  In the FAO/56 Bulletin, Allen et al. (1998) presented another regression equation derived from Doorenbos & Pruitt's table, but they mentioned that the use of that equation may not be sufficient to consider all local environmental factors influencing Kp and that local adjustment may be required, making an appropriate calibration of ECA against ETo measured by a lysimeter or computed with the Penman-Monteith method, as presented by Conceição (2002).
Although there are several methods to estimate Kp, few are the papers that evaluated their precision and accuracy under Brazilian climatic conditions.Most of the methods have shown that Kp value is highly dependent on surrounding conditions and is determined by U, H and F. According to Pereira et al. (1995), fetch distance (F) is extremely difficult to estimate as it varies continuously as the field dries down, and only a guess can be given for any given day.The same authors considered another problem with the application of the Doorenbos & Pruitt's table: the first class of the daily wind speed, which is up to 175 km d -1 , is too high for most of the Brazilian tropical climates.According to Villa Nova et al. (1996) determination of Kp is the greatest problem in converting ECA into ETo and from this to crop evapotranspiration (ETc).
Based on the above discussion, the objective of this paper was to evaluate different methods used to predict Kp values and their influence on the daily estimates of ETo.In addition, we tested a constant value of Kp as a simple and practical option to convert ECA into ETo.

MATERIAL AND METHODS
In order to evaluate the different methods used to predict Kp values, data consisting of temperature (T), relative humidity (H), and wind speed at 2 m (U), from an automatic weather station located at ESALQ, University of São Paulo, Piracicaba, SP, Brazil (latitude: 22 o 42' S; longitude: 47 o 38' W; altitude: 546 m) were used (Table 1).Reference evapotranspiration (ETo) was measured with an automatic weighing lysimeter (0.65 m depth; 1.20 m length; 0.85 m width) covered with Paspalum notatum L. The grass was clipped whenever necessary to keep its height between 0.08 and 0.15 m, as suggested by FAO (Smith, 1991) to obtain the proper ETo, during 112 days from December 1995 to December 1996.On the other days there were operational difficulties with this kind of lysimeter because of high intensity rainfall and wind which resulted in uncertainties and errors as described by Pereira et al. (2002).Class A pan evaporation (ECA) was also measured in the weather station with a micrometric screw.
T -mean air temperature; H -mean relative humidity; U -mean wind speed at 2 m above the surface; n -effective hours of sunshine; SR -incoming solar radiation; R -rainfall  where s = the slope of the vapour pressure curve at the daily average air temperature; γ = the psychrometric coefficient; and r c /r a = the relationship between the grass canopy resistance to the water vapour diffusion (r c ) and the resistance offered by the air layer to exchange water vapour from the evaporating surface (r a ) given by an empiric relation with the wind speed, suggested by Allen et al. (1989) and adopted by FAO (Smith, 1991;Allen et al., 1998): where X 1 = ln of the fetch distance (F) in m; X 2 , X 3 , and X 4 = wind speed categories of 175-425, 425-700, and >700 km d -1 , respectively, and were assigned values of one or zero depending upon their occurrence (a zero value for these variables represented a wind speed < 175 km d -1 ); X 3 and X 4 = relative humidity categories of 40-70% and >70%, respectively (a zero value for these variables represent a relative humidity < 40%).
f) FAO/56 (Allen et al., 1998) Kp = 0.108 -0.0286U + 0.0422 ln (F) + 0.1434 ln (H) --0.000631 [ln (F)] 2 ln (H) g) Constant Kp: this value was determined for Piracicaba, SP, Brazil, by the relationship between ETo and ECA with data from December 1995 to December 1996, during 112 days, and tested with independent data obtained in the same conditions described above, from January 1997 to October 1997, during 123 days.
To evaluate the performance of the Kp methods in daily ETo estimates, using the Class A pan method (ETo = ECA .Kp), several performance criteria were used including regression analysis, agreement index (D), mean absolute error (MAE), maximum absolute error (MAXE), and efficiency (EF), as suggested by Willmott et al. (1985) and Zacharias et al. (1996).These criteria are defined as:

EF
where O i = observed value; E i = estimated value; and O = mean observed values.

RESULTS AND DISCUSSION
Figure 1 shows the relationship between Kp estimated by Doorenbos & Pruit's table and the Eqs. 1, 2, 3, 5, and 6 and the calculated values (Kp = ETo/ECA).It can be seen that Kp predicted by all methods remained between 0.6 and 0.9 while the calculated values varied from 0.4 to 1.0.In general, all methods did not predict Kp values very well, with low correlation (R 2 < 0.2).Pereira et al. (1995) found similar results evaluating their method (Eq.3).This performance is explained, in part by the fact that most of these methods were developed based on the values presented by Doorenbos & Pruitt (1977).
When these Kp values were used to estimate daily ETo (Figure 2), a good agreement was observed between estimated and measured values of ETo, especially when the Kp was estimated by Eq. 1 and Eq. 3. ETo estimated with Kp from Doorenbos & Pruit's table and Eqs. 2, 5 and 6 presented, in general, an overestimation between 4 and 12%.However, the R 2 values, which indicate the precision of the estimates, varied between 0.69 and 0.77, which is a consequence of the poor accuracy and precision of the Kp methods.Similar results were found by Conceição (2002) when studying monthly ETo estimated by Class A and Penman-Monteith methods.
Table 2 presents the statistical analysis of ETo estimates using different Kp methods.The best Kp equations to convert ECA into ETo were Eq. 3, and Eq. 1.With these methods, the relationship between measured and estimated ETo showed high accuracy and good precision: Pereira's method (b = 0.9926, D = 0.937, R 2 = 0.7647 and EF = 0.756); Cuenca's method (b = 1.014,D = 0.927, R 2 = 0.7219 and EF = 0.723).The other methods presented a bad performance, mainly when ECA was converted in ETo by the use of Kp obtained from Doorenbos & Pruitt's table and Snyder's equation (Eq.2).In these cases, the relationship between measured and estimated ETo showed an overestimation of 7 and 12%, respectively, and low efficiency (EF < 0.6).
When a constant value of Kp (0.71), determined locally (Figure 3), was used to estimate daily ETo, the same precision and accuracy in relation to the ETo estimated with Kp from proposed a model for the Kp which was based on the relationship between ETo and ECA, both estimated by Penman-Monteith equation, adopting a maximum Kp value equal to 0.85.After that, Raghuwanshi & Wallender (1998) suggested a new equation to estimate Kp using categorical (Yes = 1; No = 0) and quantitative variables based on U, H, and F. The predicted Kp obtained by the authors showed better fit than Cuenca's or Snyder's equations in relation to the data from Doorenbos & Pruitt's table.

Table 1 .
Monthly climatic conditions during the experimental period, in Piracicaba, state of São Paulo, Brazil, from December 1995 to December 1996