Dependency of Evaporation and Class A Pan Coefficient on Meteorological Parameters

The relation of evaporation deriving meteorological parameters particularly wind speed, solar radiation and vapor pressure deficit with evaporation schemes namely Class A pan evaporation (Ep), potential evapotranspiration (PET) and reference evapotranspiration (ETo) at Tharandt, Germany for the summer half-year of 2004-2013 was investigated. PET was calculated using three methods: 1. Haude (2005), 2. Wendling (1991), 3. Penman (1963); whereas, ET o was calculated according to Food and Agricultural Organization-Penman Monteith method. The results showed that the evaporatin schemes were mainly driven by solar radiation (R 2 ≥ 0.69, RMSE ≤ 0.76mm d -1 ) and vapor pressure deficit (R 2 ≥ 0.53, RMSE ≤ 0.92mm d -1 ). The effect of wind speed at 2m in deriving the evaporation schemes was negligibly small (R 2 < 0.12). An equation is derived for estimation of E p from measured meteorological parameters alone which makes this study special. In another scenario, Class A pan coefficient (K p ) which is the ratio of ET o and E p had shown good correlation with E p only (R 2 = 0.50, RMSE = 0.19, n = 1483). The correlation of K p with ET o , shortwave radiation, wind speed at 2m, vapor pressure deficit, relative air humidity, and air temperature was too low (R 2 < 0.1). Haude, Wendling, and Penman; n solar radiation; s : solar or shortwave or incoming radiation; u 2 : wind speed at 2m; VPD: vapor pressure deficit; RH: relative air humidity; T: air temperature; Haude7: PET calculated according to Haude in which 17 values which were greater than 7mm d -1 are replaced by 7mm d -1


Introduction
Evaporation does not take place at a constant rate as its rate naturally depends on meteorological, geographical, and topographical factors. The principal meteorological parameters affecting evapotranspiration are solar radiation, air temperature, relative air humidity and wind speed (Trajković and Živković (2009) as cited in Isikwue BC et al. [1] p.698; also refer Moderow et al. [2] and Wang & Dickinson [3]. Vapor pressure deficit (i.e., air humidity and air temperature) is also one of the meteorological parameters which affect evaporation or evapotranspiration [4]. The rate at which molecules leave water depends on the vapor pressure of the water (e w ) and the rate at which molecules enter the air depends on the vapor pressure of the air (e a ) above the water surface. Thus, the rate of evaporation depends on the difference between them called vapor pressure deficit (VPD); i.e., VPD = e w -e a . Therefore, evaporation is proportional to (e w -e a ) and continuous until e w = e a . Similarly, evaporation is proportional to the difference between actual humidity and the saturated humidity at a given temperature.
In this article, the dependency of the methods of estimation of PET estimated according to Haude (Haude7), Wendling and Penman and ET o estimated according to FAO56-PM method on wind speed at 2m (u 2 ), VPD, and shortwave and net solar radiation (R s & R n ) at Tharandt from 2004 to 2013 for the summer half-year (n = 1830) was investigated. The summer half-year dependency of Class A pan evaporation (E p ) with u 2 , VPD, and R s & R n as well as with air temperature and with relative air humidity was also investigated (n = 1709).

Data and Methodology
The study area was Tharandt, Germany (altitude: 220 m a.s.l, latitude: 50°58'42.06" N, longitude: 13°34'52.69" E). Ten years (01.01.2004 to 31.12.2013) daily and ten minutes data of Tharandt meteorological station was the basis of the data set. The meteorological parameters and measurement devices used for the study are presented in Table 1. The pan used for measurement of pan evaporation is the World Meteorological Organization (WMO) standard Class A pan evaporimeter (see Figure 1). Class A pan evaporation (E p ) is calculated as described in Mekoya et al. [6]. PET estimated using three methods Penman (1963) as cited in ASCE-EWRI [9].
ET o is estimated according to Allen et al. [10] (FAO56-PM). Net radiation (R n ) (in MJ m -2 d -1 ) is also calculated as described in Allen et al. [10].

International Journal of Environmental Sciences & Natural Resources
For the analyses, measured shortwave radiation in MJ m -2 d -1 at 3m above ground (R s ) was used. At Tharandt over the ten years (2004 to 2013) the average, extreme maximum and extreme minimum values of net radiation (R n ) were 8.87, 26.83 and 0.10MJ m -2 d -1 ; whereas its corresponding values of R s were 6.19, 15.87 and -0.96MJ m -2 d -1 , respectively.
Saturation vapor pressure (e s ) in kPa is calculated as given below.
To get saturation vapor pressure (e s ) in hPa using T 2pm , Eq. 1 is modified as Relative humidity in % (RH) expresses the degree of saturation of the air as a ratio of the actual (e a ) to the saturation (e s ) vapor pressure at the same temperature. 100. ; [1] (2) a s e RH e = Modifying Eq. 2 and replacing RH with RH 2pm , we have: Generally, daily vapor pressure deficit (VPD) in kPa was calculated using Eq. 1 and Eq. 2. However, in the case of PET according to Haude, VPD in hPa was calculated using Eq. 1a and Eq. 3. Daily wind speed at 2 m above ground (u 2 ) in m s -1 is calculated as given below. Where u z is measured wind speed at z m above the ground surface (in m s -1 ), and z is height of measurement above the ground surface (in m).
Daily wind speed at 2m above ground (u 2 ) in m s -1 is used as calculated in Eq. 4 (except for PET according to Wendling which uses Eq. 5).
Finally, the degree of dependency of evaporation schemes on u 2 , VPD, R s and R n was evaluated using a linear regression model where values of Pearson's correlation coefficient (r), R 2 , RMSE, and p-value (at 95% confidence interval or at 0.05 significant level) were used for assessing the fit of the regression model.

Evaporation schemes and meteorological parameters
The dependency of evaporation schemes on wind speed Figure 2 shows the dependency of potential evaporation schemes namely PET according to Haude, Haude7, Wendling and Penman with wind speed at 2m. Similarly, Figure 3 shows the dependency of reference evapotranspiration and Class A pan evaporation with u 2 . Generally PET schemes, ET o , and E p had shown significantly poor dependency with u 2 . The dependency was nonsignificant (p-value > 0.05) only in the case of PET estimated according to Haude7. Moreover, PETs, ET o and E p increased with increasing wind speed at 2m for u 2 ≤ 1 m s -1 and slightly decreased with increasing values of u 2 for u 2 > 1 m s -1 , where in all cases R 2 was less than 0.1 (not shown).  The dependency of evaporation schemes on vapor pressure deficit

International Journal of Environmental Sciences & Natural Resources
The dependency of PETs and ET o with vapor pressure deficit was high (R 2 ≥0.78; RMSE ≤ 0.62 mm d -1 ) and significant (p-value < 2.2•10 -16 < 0.05); the dependency in the case of E p was also 'slightly strong' (R 2 = 0.53; RMSE = 0.93mm d -1 ) and significant (see Figure 4 & 5). Particulary in the case of PET according to Haude it was extremely high (R 2 = 0.98; RMSE = 0.23mm d -1 ) and significant. Note that PET according to Haude is calculated by multiplying calibrated factor and VPD.  The dependency was extremely high in the case of Penman and Wendling PETs (R 2 ≥0.98). The dependency of evaporation schemes on net solar radiation was very high and significant particularly in the case of ET o , and PET according to Wendling and Penman (see Table 2).  The relation between the evaporation schemes with maximum air temperature are presented in Figure 8 & 9. Generally, the correlation of the evaporation schemes with air temperature (not shown) was lower as compared to their correlation with maximum air temperature. A significant positive correlation (r ≥ 0.6) was observed between all evaporation schemes and maximum air temperature. Also, the relation of air humidity with the evaporation schemes is presented in Table 3, the corresponding graph for ET o and E p is presented in Figure 10. For minimum relative air humidity and relative air humidity a significant good negative correlation (r ≤ -0.7) was observed with all evaporation schemes except E p (see Table 3 & 4). The intercorrelation between ET o , PET according to Wendling, and PET according to Penman was very high (r > 0.9).

Derivation of equations for estimation of Class A pan evaporation
The Pearson's correlation coefficient (r), R 2 , RMSE, the slope (a), the y-intercept (b), and an accuracy factor 'F' = 2(R 2 +1-RMSE) of the linear regression model ('y = ax + b') described before are summarized in Table 4. F ranges from negative values to 4. Negative values of F indicate no accuracy and F = 4 indicates perfect alignment of model prediction or simulated or estimated data (y) and simulator or measured data (x). E p can be estimated with good accuracy from ET o , R n , K p , and VPD as given below, where y is replaced by E p and x is replaced by ET o , R n , K p , VPD, R s , T max , RH min , RH and T. 0.47 (9 VPD + However, the calculation of ET o , R n , K p and VPD is not a simple task as it requires many parameters to be fulfilled. In contrast, estimation of E p using only measured meteorological parameters such as R s , T max , RH min , RH, and T which can be easily obtained from meteorological offices on request has been desired and are given below. Comparatively relative air humidity (RH) and air temperature (T) have lower values of accuracy factor (F). Therefore, using weighted average of F and Eq. 10, Eq. 11 and Eq. 12, Class A pan evaporation (E p ) in mm d -1 can be estimated with good accuracy from Rs, T max , and RH min as Where, E pd is Class A pan evaporations in mm d -1 derived from measured solar or shortwave radiation (Rs) in MJ m -2 d -1 , daily maximum air temperature (T max ) in o C, and daily minimum relative air humidity (RH min ) in %.

Class A pan coefficient and meteorological parameters
Class A pan coefficient (K p ) is the ratio of ET o and E p . Its correlation with meteorological variables such as solar radiations (R s and R n ), vapor pressure deficit (VPD), wind speed at 2m (u 2 ), relative air humidity (RH) and air temperature (T) was too low (R 2 < 0.1). Also, the correlation between K p and ET o was too low (R 2 = 0.1; RMSE = 0.26). However, its correlation with E p for E p ≥1 mm d -1 was relatively 'good' (R 2 = 0.50; RMSE = 0.19; n = 1483; see Figure 12).

Conclusion
At Tharandt for the summer half-year from 2004 to 2013 evaporation was mainly driven by solar radiation and vapor pressure deficit. The correlation between air temperature and relative air humidity with evaporation schemes was also good. Sunshine duration, which is not considered in this study, might also have good correlation with evaporation schemes. The effect of wind in deriving evaporation was negligibly too low. Moreover, the effect of wind speed at 2m (u 2 ) was not uniform. For u 2 ≤1 m s -1 , the evaporation schemes namely Class A pan evaporation, reference evaporation and potential evaporation (PET) according to Haude, Wendling and Penman increased with increasing values of u 2 , whereas, for u 2 > 1m s -1 , they slightly decreased with increasing values of u 2 . Note however that the cause for the negligibly too low effect of wind speed at 2m on evaporation schemes might have resulted due to topography of the study site. Because Tharandt station is located at the bottom of a 'V-shaped' valley in which there is a high shelter effect that could have an impact at least on the wind and sunshine duration. The non-uniform effect of wind speed (for u 2 > 1 m s -1 and for u 2 ≤ 1 m s -1 ) on evaporation schemes is not clear. It might happen due to the influence of the nearby Weißeritz river.
The correlation between Class A pan coefficient and meteorological parameters such as solar radiation, vapor pressure deficit, wind speed at 2m, relative air humidity, air temperature and reference evapotranspiration was too low. However, its correlation with Class A pan evaporatin (E p ) was comparatively good. Thus, for Tharandt site and places with similar climatic and topographic characteristics with Tharandt, Class A pan coefficient can be estimated from E p alone with good accuracy. Also, at Tharandt, for the summer half-year E p can be estimated from reference evapotranspiration, net solar radiation, Class A pan coefficient, vapor pressure deficit, solar or shorwave radiation, maximum air temperature, minimum relative air humidity, relative air humidity, and air temperature with very good accuracy. Particularly, the estimation of Class A pan evaporation merely based on measured solar radiation, maximum air temperature and minimum relative humidity makes this study special. Inclusion of actual sunshine duration hours which might improve the accuracy of the estimation of Class A pan evaporation is recommended.
The results of this study can be used for other parts of the world; however, only after proper validation because for instance unlike the case in Tharandt, in other parts of the world, the contribution of wind speed in deriving evaporation (evapotranspiration) maybe even higher than vapor pressure deficit. Note also that the equations developed in this study are based on ten years of climate data of a single station. Therefore, the results of this article shall be evaluated again using at least thirty years of climate data from multiple stations, if available, as ten years may not be enough to draw a generalized and strong conclusion. Last but not least, the knowledge obtained from this study may be used for evaporation related study in Tharandt and in areas with similar climatic conditions with Tharandt which can serve for decision makers to take appropriate measures in various agriculture, water and forestry sectors. Because summer half-year evaporation and precipitation amounts were almost equal, this study can also be implemented in warmer areas of the world with some modifications.