Dependency of Evaporation and Class A Pan Coefficient on Meteorological Parameters
Ethiopia Environment and Forest Research Institute, Bahir Dar Environment and Forest Research Center, Ethiopia
Submission: March 16, 2020; Published: April 14, 2020
*Corresponding author: Antensay Mekoya, Ethiopia Environment and Forest Research Institute, Bahir Dar Environment and Forest Research Center, P.O. Box: 2128 Bahir Dar, Ethiopia
How to cite this article: Antensay M. Dependency of Evaporation and Class A Pan Coefficient on Meteorological Parameters. Int J Environ Sci Nat Res.
2020; 24(2): 556134. DOI: 10.19080/IJESNR.2020.24.556134
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, ETo was calculated according to Food and Agricultural Organization-Penman Monteith method. The results showed that the evaporatin schemes were mainly driven by solar radiation (R2 ≥ 0.69, RMSE ≤ 0.76mm d-1) and vapor pressure deficit (R2 ≥ 0.53, RMSE ≤ 0.92mm d-1). The effect of wind speed at 2m in deriving the evaporation schemes was negligibly small (R2 < 0.12). An equation is derived for estimation of Ep from measured meteorological parameters alone which makes this study special. In another scenario, Class A pan coefficient (Kp) which is the ratio of ETo and Ep had shown good correlation with Ep only (R2 = 0.50, RMSE = 0.19, n = 1483). The correlation of Kp with ETo, shortwave radiation, wind speed at 2m, vapor pressure deficit, relative air humidity, and air temperature was too low (R2 < 0.1).
Keywords: Class A pan evaporation; Class A pan coefficient; Solar radiation; Vapor pressure deficit; Air temperature; Relative air humidity; Wind speed; Reference evapotranspiration; Potential evapotranspiration; Summer half-year; Tharandt
Abbreviations: Ep: Class A Pan evaporation; Kp: Class A Pan Coefficient; PET: potential evapotranspiration; ETo: reference evapotranspiration; SHY: summer half-year which is the time from april to september; PETs: PET estimated according to Haude, Wendling, and Penman; Rn: net solar radiation; Rs: solar or shortwave or incoming radiation; u2: 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-
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.  p.698; also refer Moderow et al.  and Wang & Dickinson . Vapor pressure deficit (i.e., air humidity and air temperature) is also one of the meteorological parameters which affect evaporation or evapotranspiration . The rate at which molecules leave water depends on the vapor pressure of the water (ew) and the rate at which molecules enter the air depends on the vapor pressure of the air (ea) above the water surface. Thus, the rate of evaporation depends on the difference between them called vapor pressure deficit (VPD); i.e., VPD = ew–ea. Therefore, evaporation is proportional to (ew – ea) and continuous until ew = ea. 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 ETo estimated according to FAO56-PM method on wind speed at 2m (u2), VPD, and shortwave and net solar radiation (Rs & Rn) 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 (Ep) with u2, VPD, and Rs & Rn as well as with air temperature and with relative air humidity was also investigated (n = 1709).
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 (Ep) is calculated
as described in Mekoya et al. . PET estimated using three
a) Haude (2005) as cited in Weiß ;
b) Wendling (1991) as cited in Wendling ; and
c) Penman (1963) as cited in ASCE-EWRI .
ETo is estimated according to Allen et al.  (FAO56-PM). Net
radiation (Rn) (in MJ m-2 d-1) is also calculated as described in Allen
et al. .
For the analyses, measured shortwave radiation in MJ m-2
d-1 at 3m above ground (Rs) was used. At Tharandt over the ten
years (2004 to 2013) the average, extreme maximum and extreme
minimum values of net radiation (Rn) were 8.87, 26.83 and 0.10MJ
m-2 d-1; whereas its corresponding values of Rs were 6.19, 15.87
and -0.96MJ m-2 d-1, respectively.
Saturation vapor pressure (es) in kPa is calculated as given
Where, T is air temperature (in °C).
To get saturation vapor pressure (es) in hPa using T2pm, Eq. 1
is modified as
Relative humidity in % (RH) expresses the degree of saturation
of the air as a ratio of the actual (ea) to the saturation (es) vapor
pressure at the same temperature.
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 (u2) in m s-1 is
calculated as given below.
Where uz 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 (u2) 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
u2, VPD, Rs and Rn was evaluated using a linear regression model
where values of Pearson’s correlation coefficient (r), R2, RMSE,
and p-value (at 95% confidence interval or at 0.05 significant
level) were used for assessing the fit of the regression model.
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 u2. Generally PET schemes, ETo, and Ep had shown
significantly poor dependency with u2. The dependency was nonsignificant
(p-value > 0.05) only in the case of PET estimated
according to Haude7. Moreover, PETs, ETo and Ep increased with
increasing wind speed at 2m for u2 ≤ 1 m s-1 and slightly decreased
with increasing values of u2 for u2 > 1 m s-1, where in all cases R2
was less than 0.1 (not shown).
The dependency of PETs and ETo with vapor pressure deficit
was high (R2 ≥0.78; RMSE ≤ 0.62 mm d-1) and significant (p-value <
2.2∙10-16 < 0.05); the dependency in the case of Ep was also ‘slightly
strong’ (R2 = 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 (R2 = 0.98; RMSE = 0.23mm d-1) and significant.
Note that PET according to Haude is calculated by multiplying
calibrated factor and VPD.
Figure 6 & 7 show that the dependency of PETs and ETo on
shortwave or solar radiation was high (R2 ≥ 0.89). The dependency
of Ep on Rs was also a bit high (R2 = 0.69; RMSE = 0.76mm d-1).
The dependency was extremely high in the case of Penman
and Wendling PETs (R2≥0.98). The dependency of evaporation
schemes on net solar radiation was very high and significant
particularly in the case of ETo, 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 ETo and Ep 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 Ep (see Table 3 & 4). The intercorrelation between
ETo, PET according to Wendling, and PET according to Penman
was very high (r > 0.9).
The Pearson’s correlation coefficient (r), R2, RMSE, the slope
(a), the y-intercept (b), and an accuracy factor ‘F’ = 2(R2 +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). Ep can be estimated
with good accuracy from ETo, Rn, Kp, and VPD as given below,
where y is replaced by Ep and x is replaced by ETo, Rn, Kp, VPD, Rs,
Tmax, RHmin, RH and T.
However, the calculation of ETo, Rn, Kp and VPD is not a simple
task as it requires many parameters to be fulfilled. In contrast,
estimation of Ep using only measured meteorological parameters
such as Rs, Tmax, RHmin, RH, and T which can be easily obtained from
meteorological offices on request has been desired and are given
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 (Ep) in mm d-1 can be estimated with good accuracy
from Rs, Tmax, and RHmin as [1.86 (0.2 Rs - 0.33) + 0.82 (0.16 Tmax -
0.86) + 0.56 (5.01 – 0.05 RHmin)]/(1.86 + 0.82 + 0.56) ≈ (0.4 Rs +
0.13 Tmax - 0.03 RHmin + 1.5)/3.24 (see Eq. 15)
Where, Epd 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 (Tmax) in oC, and daily minimum
relative air humidity (RHmin) in %.
Class A pan coefficient (Kp) is the ratio of ETo and Ep. Its
correlation with meteorological variables such as solar radiations
(Rs and Rn), vapor pressure deficit (VPD), wind speed at 2m (u2),
relative air humidity (RH) and air temperature (T) was too low
(R2 < 0.1). Also, the correlation between Kp and ETo was too low
(R2 = 0.1; RMSE = 0.26). However, its correlation with Ep for Ep ≥1
mm d-1 was relatively ‘good’ (R2 = 0.50; RMSE = 0.19; n = 1483; see
On the basis of the result of the linear regression model, for
Tharandt site and places with similar climatic and or topographic
characteristic with Tharandt, a rough estimate of summer halfyear
daily values of Kp can be estimated from measured Ep (for 1
≤ Ep ≤ 7.2 mm d-1); range = [0.388, 1.38] (see Eq. 16).
Where Kp is Class A pan coefficient and Epd is derived Class A
pan evaporation in mm d-1.
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 (u2) was not uniform. For u2≤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 u2,
whereas, for u2 > 1m s-1, they slightly decreased with increasing
values of u2. 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 u2 > 1 m s-1 and for u2 ≤ 1 m s-1) on evaporation schemes
is not clear. It might happen due to the influence of the nearby
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 (Ep) 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 Ep alone with
good accuracy. Also, at Tharandt, for the summer half-year Ep
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
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
First of all, I do praise GOD and GOD’s Mother above all. I
particularly thank Virgin Mary’s or ‘Tsadiqane Mariam’ (‘ፃድቃኔ
ማርያም’) monastery of Ethiopia. Next, I thank Technische
Universität Dresden, Faculty of Environmental Sciences, Institute
of Hydrology and Meteorology, Chair of Meteorology for providing
me all the data used for the study. I also thank DAAD, the National
Meteorology Agency of Ethiopia (NMA), and the Ethiopian
Meteorology Society for giving me financial support during my
master’s study. Very special thanks to my official supervisors Prof.
Dr. Christian Bernhofer and Dr. Uta Moderow for their excellent
supervision during my master thesis (finished in 2017). I am
also grateful to my friend Mr. Abebe Guadie and my lecturer Mr.
Endalkachew Bekele; they supported me in the publication of my
previous research article. Last but not least, I would like to thank
my wife and my family and friends for their crucial support and
for sharing love and happiness.
All data used during the study were provided by a third
party. Direct requests for these materials may be made to the
provider as indicated in the Acknowledgements. Also, all models
or code generated or used during the study are available from the
corresponding author by request.
Ertek A (2011) Importance of pan evaporation for irrigation scheduling and proper use of crop-pan coefficient (Kcp), crop coefficient (Kc) and pan coefficient (Kp).African Journal of Agricultural Research 6(32): 6706-6718.
Wendling U (1991) Schätzmethoden der Verdunstung landwirtschaftlicher Bestände nach den Ansätzen von Penman und Turc. = ‘Estimating evaporation in crop stands according to Penman and Turc formulas.’ (in German, with English summary). Arch.Acker- PflanzenbauBodenkd 35: 251-257.
ASCE-EWRI (2002)The ASCE Standardized Reference Evapotranspiration Equation Appendices A-F. Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers (ASCE) Standardized Reference Evapotranspiration Task Committee (TC).
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrig and Drain, Paper No. 56, Food and Agricultural Organization of the United Nations, Rome, Italy.