INTRODUCTION
Evapotranspiration (ET) is one of the most important components in the natural water cycle whose precise determination is essential for water balance, irrigation, water supply planning and water resources management purposes. Actual evapotranspiration from a given vegetated surface is the product of grass reference evapotranspiration (ET_{0}) and a given coefficient for the special vegetative cover. Reference evapotranspiration is directly measured by a weighing lysimeter or indirectly estimated from either meteorological data or from pan evaporation. There are around 50 different methods used to estimate reference evapotranspiration, all of which often yield different results due to varying assumptions and meteorological data used in them (Grismer et al., 2002). It should also be mentioned that evaporation pan has had the highest ranking in most studies carried out to compare various methods of estimating ET_{0 }(Raghuwanshi and Wallender (1998).
Class A evaporation pan is widely used due to its simplicity and ease of data interpretation and has come to be known as the most precise and accurate measure of reference evapotranspiration in humid areas (Irmak et al., 2002). Although evaporation intensity from Class A evaporation pan is different from the evapotranspiration intensity from vegetated surfaces due to climatic differences affecting evaporating surfaces and also due to differences in their locations, a number of studies have shown a high correlation between these two intensities (Doorenbos and Pruitt, 1975). A pan coefficient (K_{p}) is used to relate the two intensities as follows:
Based on the conditions of the vegetative cover and the location where the
evaporation pan is installed, Doorenbos and Pruitt (1977) proposed two tables
to determine K_{p}. One table belongs to the situation where the evaporation
pan is located amid the vegetative cover and the other belongs to the conditions
where the pan is installed on arid land but the vegetative cover is at a given
distance. In these Tables, pan coefficient depends on distance of the vegetative
cover from the evaporation pan (F), wind speed (U) and Relative Humidity (RH).
The values for F are presented quantitatively but those of U and RH are presented
as classifications in the Tables. At the time of proposing these Tables, no
computers were available but later on when computers and data loggers were developed
and when electronic data transmission became possible, automatic conversion
of E_{pan} to ET_{0} and the elimination of search operations
became possible (Snyder, 1992). These developments led to other advances by
researchers who used statistical regression methods to develop linear and nonlinear
polynomials or combinations thereof in lieu of the original Tables (Allen and
Pruitt 1991; Cuenca 1989; Snyder 1992). These equations are functions of F,
U and RH.
Doorenbos and Pruitt’s Tables for determining K_{p }were based on ET_{0} measurements using large weighing lysimeters in which grass had been grown up to a height of 7 to 15 cm (Snyder et al., 2005). More recently, however, definition of ET_{0} has changed from evaporation from a grass cover as described above to the evapotranspiration estimated from PenmanMonteith equation with grass assumed to have a fixed height of 12cm, a bulk stomatal resistance of 70 s/m^{–1} and an aerodynamic resistance of U_{2}/208 in which U_{2} is the wind speed at 2meter height from ground surface (Snyder et al., 2005). FAO recommended the above equation as the standard equation for determining ET_{0} and assessment of other estimation methods (Allen et al., 1998). Thus, the abovementioned tables and equations derived thereof do not comply with new standards and, hence, it essential to develop new equations based on ETPM equation for conversion of E_{pan} to ET_{0}.
Evaporation pans used in Iran are typically installed on barren land without standard vegetative cover. Some of the pans belonging to the Meteorological Organization of Iran are installed at airports. This state of affairs requires a study on the correlation between E_{pan} and ET_{0} measured by these stations and the development of a model for converting E_{pan} to ET_{0} using pan evaporation data, wind speed and air humidity. The present study aims to achieve these objectives.
MATERIALS AND METHODS
Sources of data: The data required for the purposes of the present study
were collected from 10 meteorological stations of the Iranian Meteorological
Organization in Khuzestan Province. The data covered a period of 10 years from
1990 to 2000 and included daily pan evaporation as well as the data required
for the ETPM equation (maximum and minimum air temperature, relative humidity,
sunshine hours and wind speed). The days with inadequate data were removed from
the records. The heights measured in the study are 2m (for air temperature and
relative humidity) and 10m (for wind speed) above ground surface. To convert
wind speed to a height of 2m, the logarithmic wind profile was used (Allen et
al., 1998). Table 1 presents stations, station codes,
height above sea level, average minimum and maximum daily temperatures, relative
humidity and wind speed observed over the study years. It is seen that parameter
averages for these stations do not have very significant differences.
Table 1: 
Average
annual values measured at study meteorological stations 

The average maximum and minimum annual temperatures vary from 33.5 to 35.8
and 17.0 to 22.4°C, respectively, the highest belonging to Aghajari and
the lowest to Safiabad. Average relative humidity varies from 31.2 to 42.9%
and average wind speed varies from 0.8 to 2.8 m sec^{–1}. Figure
1 shows the spatial distribution of the stations used in this study. These
stations cover most of the farmland in central and southern Khuzestan.
PenmanMonteith equation: The ETPM equation recommended by FAO as the standard method of estimating ET_{0} and comparison of other methods was used in this study as a variable in developing a model of converting E_{pan} to ET_{0}. The Equation is as follows:
where, ET_{0} is grass reference evapotranspiration (mm/day); T_{a}, air temperature (°C); U_{2}, wind speed at 2m height (m see^{–1}); R_{n}, net radiation flux at ground surface (MJ/m^{2}/day); e_{s}e_{a}, saturation vapor pressure deficit (kPa); Δ slope vapor pressure curve (kPa/°C); and γ is a psychrometric constant [kPa/°C]. The relations proposed by Allen et al. (1998) have been used to determine the values for R_{n}, e_{s}e_{a}, Δ and γ.
E_{pan} to ET_{0} conversion equations: Three first, second and third order correlation models were studied for E_{pan} to ET_{0 }conversion. Pan evaporation, wind speed and relative humidity were used as independent variables and grass reference evapotranspiration estimated from ET_PM Equation was used as the dependent variable. The first order model was derived from linear regression of the following independent variables:

Fig. 1: 
Location
of the study meteorological stations in Khuzestan Province 
where, ET_PAN is the evapotranspiration calculated from the above relation
based on E_{pan}, U and RH data and b, b_{1} and b_{3}
are coefficients. The second order model was derived from regressions of second
and third powers and the third order model was derived from the regressions
of the first through to the third powers of the above independent variables.
These equations have a general form along the following lines:
where, F_{i} is the dependent variable obtained from regression of the first to third powers of the variables E_{pan}, U and RH; and n is the number of variables in the second and third order models with values of 9 and 19, respectively.
RESULTS
Grass reference evapotranspiration was estimated for all the stations used
in this study using Eq. (2) and the results were compared
with the evaporation pan measured values (Fig. 2). It is shown
in this Figure that despite the nonstandard conditions of the evaporation pan
locations in the study stations, a high linear correlation holds between ET_PM
and E_{pan} (R^{2} = 0.77). This is due to identical effects
of air temperature and solar radiation on both reference evapotranspiration
and pan evaporation.

Fig. 2: 
Dispersion
and statistical results from reference evapotranspiration values obtained
form PenmanMantieth method versus those from the proposed model 
Table 2: 
Variables
and coefficients of the third order reference evapotranspiration model 

Table 3: 
Statistical
results from E_{pan} to ET_{0} conversion models 

The coefficient obtained (0.77) indicates that the combination of air temperature
and solar radiation alone account for 77% of the evaporation process taking
place. This observation means that factors other than temperature and solar
radiation must also be included when developing a reference evapotranspiration
model based on evaporation pan data. In this study, we also included wind speed
and relative humidity.
Using SPSS, the coefficients for first, second and third order models were estimated. Those input variables which were not significant at 0.05 were eliminated from the model (second and third order models) using the stepbystep method. The effect was reduction input variables to 5 for the second order model and to 12 in the case of the third order model. Table 2 presents the coefficients for the third order model. The results from the first and second order models were as follows:
The statistical results obtained from the as one models are presented in Table
3. The it is seen (Table 3) that the second and third
order models yield better results compared to the first order model but no significant
differences are observed between the second and third order models. Therefore,
the second order model with fewer variables is recommended as the one superior
to others for E_{pan} to ET_{0 }conversion in Khuzestan region.
The determination coefficient for this model is 0.93 and its root mean square
error is 0.9 mm day^{–1}. The application of this model to all study
stations yielded almost identical results such that the determination coefficient
in all cases varied from 0.89 to 0.95, correlation slope passing through the
intercept of coordinates varied between 0.86 and 1.01 and root mean square error
ranged between 0.7 to 1.1 mm day^{–1}.
CONCLUSIONS
In the present study, pan evaporation values from meteorological stations without vegetative cover in khuzestan Province were compared with results from PenmanMonteith grass reference evapotranspiration. The results showed that despite the differences in conditions between the pan evaporation and reference evapotranspiration, a high correlation holds between these types of evaporation (R^{2} = 0.77) and that if other effective parameters are introduced into polynomial correlation models, improved estimations of reference evapotranspiration will be possible on the basis of pan evaporation data. For this purpose, three first, second and third order polynomials were studied with pan evaporation, wind speed and air humidity as the main variables. The second and third order models showed higher accuracy levels but regarding the fact that the two models yielded almost similar results, the second order model was recommended for the conditions in Khuzestan on the grounds that this model required fewer input variables.
ACKNOWLEDGMENT
The authors would like to express their thanks to Tehran University for their support for this study.