_{1}

^{*}

Calculation of open water evaporation is important for hydrology, industry, agriculture, environment, and other fields. The available methods of calculating evaporation are based on field or laboratory experiments and should not be used for scale-up to open water evaporation for similitude relationships cannot be correctly obtained. The methods are thus unjustified scientifically. In addition, surface evaporation is not a local phenomenon that is a function of independent meteorological parameters. These are in fact dependent parameters, and the solar energy exchanged with the surface of the earth is the only independent variable for open water evaporation. Contrary to the existing methods, meteorological records and measurements are therefore not required. Many parts of the world do not have full or partial records available. For these, the available methods are likely not to be useful. In addition, future meteorological records or measurements cannot be made available for evaporation projection in a warming world. This may well place a limit on using the existing methods. The work presented in this manuscript reveals a new understanding of evaporation as a climate parameter instead and can be calculated as such. Minimal to no meteorological records or measurements may be required. The advantages of the proposed method are scientific justification, simplicity, accuracy, versatility, low to virtually no cost, and can be used to map present and future evaporation in a short period of time.

Evaporation applications by solar energy are characterized by low cost, and solar evaporation pans have been used to produce salt, minerals, and chemicals for a long time [

The importance of determining present and future evaporation and the time and costs required for preparing meteorological records motivated this submission. Open water evaporation is not the same as class A or test pan evaporation. While these vary with local ambient conditions, open water evaporation is a climate parameter. It varies with the solar energy exchanged with the surface of the earth as this work indicates. Its variability during the year is caused mostly by variation in the earth’s axial tilt with the motion of the earth around the sun. This motion is an established knowledge and can be used as basis for evaporation calculation. Because world average surface temperature and evaporation are measured, they can be used as pilot data. The latitude at which the world average values manifest can be determined. Similitude relationships can then be established between the latitudes, and open water evaporation can be scaled-up and obtained. Minimal to no meteorological variables are necessary. Scale-up from laboratory and pilot data are scientific methodologies widely used in the chemical and other industries.

The objective of this manuscript is to derive the equation of open water evaporation utilizing the physics of the earth and scale-up methodologies, calculate evaporation for sample locations, and compare the calculated evaporation with observations. The calculated evaporation is found to be in agreement with observations. This offers an inexpensive way of mapping present and future evaporation cost effectively in a short period of time, which has merit at the societal level.

Reference [

Meteorological stations use class A evaporation or equivalent pan. In the industry, it is common to install larger-diameter test evaporation pans having two meters in diameter and approximately 60 cm deep. For these pans, the recommended coefficient for scale-up to open water evaporation is between 0.6 and 0.7 [

The calculated evaporation or factors are valid for the specific site or location in consideration, which renders these methods expensive and impractical for mapping evaporation, especially in a warming world. Reference [

Clearly, the existing methods assume that evaporation as a mathematical function and the meteorological parameters as independent parameters of the function. This may be true for cooling towers and other industrial applications but not for surface evaporation of the earth. Evaporation is a heat transfer phenomenon, and in the absence of variation in the heat exchanged with the surface, surface evaporation remains unchanged regardless of the values of wind speed, relative humidity, or surface temperature. In reality, evaporation and the meteorological parameters are dependent parameters; they depend on the heat exchanged with the surface, which is the only independent parameter. This heat exchanged varies with the motion of the earth around the sun. Because the motion of the earth is known, meteorological record is not required for calculating surface evaporation.

Unlike the existing methods, open water evaporation is calculated by knowing the physics of the earth and the available data relative to world average surface temperature and evaporation. These can be used as pilot data. The scale-up from laboratory and pilot data using similitude is a scientific method that is widely used for complex applications. Most of the commercial complexes presently operating in the world have been designed based on scale-up procedures. Chemical engineering reference [

Evaporation data for validation are gathered to subject the proposed procedure to a vigorous test. Sample locations of the world have been selected such that they have considerably different geographic and climatic conditions. The Dead Sea, 31˚N, Jordan, is the lowest location on the surface. The related evaporation is obtained from an engineering study conducted by [

The main concept is that annual average evaporation at the surface of the earth is measured; it is equal to annual precipitation. Therefore, if a mathematical equation correlating evaporation at a given location and annual average evaporation can be established, then meteorological records and measurements are unnecessary. The mathematical correlation is summarized in equation (21). The equation is derived based on the physics of the earth and representative scale-up of the measured world average surface temperature and evaporation. Validation of the equation is presented under results. Derivation of the equation is divided into three stages. Stage one covers basic thermodynamics of the earth, stage two utilizes Beer-Lambert Law equation to model radiative energy exchanged with the atmosphere, and the third and last stage applies energy exchange relationships between the atmosphere and the surface of the earth.

The earth’s subsystems that exchange solar radiation include atmosphere, surface water, and land. Land has a small thermal capacity and can be neglected. While the solar energy exchanged with surface water is thermal, or enthalpy, in nature, the energy exchanged with the atmosphere is thermal and potential energy. When the atmosphere absorbs solar heat, it rises against gravity and expands into the surrounding outer space that has negligible mass and pressure. Air expansion ceases at equilibrium. Seasonal variations affect this equilibrium because the distance between the earth and the sun varies. The axial tilt of the earth alters the energy exchanged with the geographic northern and southern hemispheres. Therefore, thermodynamic transformations must result from the motion of the earth around the sun, and the atmosphere and surface water must exchange energy with seasonal variations. Surface evaporation varies as a consequence.

Because the surrounding outer space has negligible mass, the potential energy and enthalpy of the atmosphere cannot be exchanged with outer space. Only radiation may be exchanged with outer space. Therefore, variation in the energy of the atmosphere can only be exchanged with the surface and the following must be valid:

Δ E a + Δ Q s = 0 (1)

E e = E a + Q s = C 1 (2)

where

E a = Energy of the atmosphere (enthalpy and potential energy), J.

Q s = Surface energy (enthalpy or heat), J.

E e = Energy of the atmosphere and surface combined, J.

C 1 = Constant of integration, J.

The solar energy absorbed by the atmosphere and surface, E e , is equal to the latent heat of surface evaporation based on observations: At the conclusion of a full revolution of the earth around the sun, variation in the energy of the surface and atmosphere are negligible for it is a repeatable cycle. The only observed change is water evaporation and its subsequent condensation as precipitation. Therefore

E e = E L v (3)

where

E e = Annual rate of solar heat absorbed by the atmosphere and surface, J∙yr^{−1}.

E = Annual rate of surface evaporation, which is equal to precipitation, kg∙yr^{−1}.

L v = Latent heat of water evaporation, 2.46 × 10^{6} J∙kg^{−1}.

The solar energy absorbed, E e , can be calculated. It is approximately equal to the latent heat of condensing 2.61 × 365 = 953 mm of rain annually [

E e = 953 mm × 1.0 kg ⋅ mm − 1 ⋅ yr − 1 ⋅ m − 2 × 5.1 × 10 14 m 2 × 2.46 × 10 6 J ⋅ kg − 1 = 1.20 × 10 24 J ⋅ yr − 1 (4)

where 5.1 × 10^{14} is the total surface area of the earth measured in m^{2}.

The solar heat absorbed by the earth raises the atmosphere (air and clouds) to its current position and maintains present average surface temperature. The energy absorbed by the atmosphere is enthalpy and potential energy, whereas the surface gains solar energy as heat. Because the temperature of the sun is considerably greater than the temperature of the earth, radiation from the earth to the sun may be neglected. The net incident solar radiation may thus be assumed to be absorbed by the side of the earth’s sphere facing the sun. The other side radiates heat to outer space. Using Beer-Lambert Law equation, the radiative energy absorbed by the atmosphere and surface are

E a r = ( 1 − f ) I A c [ 1 − e − τ ] (5)

Q s = ( 1 − f ) I A c [ e − τ ] − ε A s σ T s 4 / 2 (6)

τ = a Z t (7)

where

E a r = Rate of radiative solar energy absorbed by the atmosphere, W.

Q s = Rate of radiative solar energy absorbed by the surface, W.

f = A factor that accounts for the reflected solar energy by the earth, dimensionless.

I = Solar Constant, 1.368 × 10^{3} W∙m^{−2}.

A c = Earth’s circle area as viewed from the sun, π ( R e + Z ) 2 ≈ 1.28 × 10 14 m 2 .

τ = Average optical depth of the atmosphere, dimensionless.

ε = Emissivity of the surface, dimensionless, approximately equal to unity.

A s = Earth’s surface area, 4 π R e 2 ≈ 5.1 × 10 14 m 2 .

σ = Stefan-Boltzmann Constant, 5.67 × 10^{−8}, W∙m^{−2}∙K^{−4}.

T_{s} = Surface temperature, K.

a = Absorption coefficient of solar radiation by the atmosphere (air and clouds), km^{−1}.

Z t = Average distance traveled by solar radiation in the atmosphere, km.

R_{e} = Earth’s radius, 6.38 × 10^{6} m.

The radiative energy absorbed by the atmosphere, E a r , can be determined from data available. It is approximately equal to one third of the total solar energy absorbed by the atmosphere and surface, E e , based on [^{16} W). The measured value of the factor, f , is approximately equal to 0.30 [_{s} = 286.70 K.

Z t = ( 1 / π ) ∫ − π / 2 + π / 2 Z n ( θ ) d θ (8)

where θ is arbitrary latitude and Z n ( θ ) is the distance traveled by sunrays in the atmosphere at noon for the arbitrary latitude

Z n ( θ ) = ( R e + Z ) cos ( ψ ) − R e cos ( θ ) (9)

where Z is the height of the atmosphere, approximately equal to the average height of the mesopause, 96 km [

Z t ( θ ) = ( 1 / π ) ∫ − π / 2 + π / 2 Z ( ф ) d ф (10)

where

Z ( ф ) = [ R e cos ( θ ) + Z n ( θ ) ] cos ( α ) − R e cos ( θ ) cos ( ф ) (11)

In ^{−1}, which can be reasonably used for all other latitudes. The optical depth of the atmosphere for other latitudes is then determined by multiplying Z t ( θ ) by 0.00048, they are presented in

From Equations (5) and (6)

Δ Q s = − Δ E a r = − ( 1 − f ) I A c e − τ Δ τ (12)

Not considered in Equation (12) is variation in the radiation term ( ε A s σ T s 4 / 2 ) of Equation (6). The reason is that, unlike solid surfaces, surface water has negligible thermal conductivity, and the value of this term is controlled by convention heat transfer of surface water. The convection heat transfer coefficient does not vary tangibly with the observed surface temperature variation, and variation in this radiation term may be neglected. Equation (12) indicates that variation in the optical depth of the atmosphere induces a thermodynamic transformation where energy is exchanged between the atmosphere and surface. For the scenario where energy is transferred from the cold atmosphere to the warm surface, the external energy required is available; it is equal to the variation in the potential energy of the atmosphere and the laws of thermodynamics are thus satisfied. For a given latitude, θ, the solar heat exchanged with the surface follows based on Equation (12):

Latitude, degrees | Z t , km | Z t ( θ ) , km | Optical depth | Solar energy absorbed by atm., W∙m^{−2} | Solar energy to surface, W∙m^{−2} |
---|---|---|---|---|---|

0 | 96.0 | 223.2 | 0.107 | 97.3 | 860.3 |

5 | 96.4 | 223.9 | 0.107 | 97.6 | 860.0 |

10 | 97.5 | 225.8 | 0.108 | 98.4 | 859.2 |

15 | 99.3 | 228.8 | 0.110 | 99.6 | 858.0 |

20 | 102.1 | 233.5 | 0.112 | 101.5 | 856.1 |

25 | 105.8 | 239.6 | 0.115 | 104.0 | 853.6 |

30 | 110.6 | 247.4 | 0.119 | 107.2 | 850.4 |

35 | 116.8 | 257.3 | 0.124 | 111.3 | 846.3 |

40 | 124.7 | 269.7 | 0.129 | 116.3 | 841.3 |

45 | 134.8 | 285.0 | 0.137 | 122.4 | 835.2 |

50 | 147.8 | 304.1 | 0.146 | 130.1 | 827.5 |

55 | 164.9 | 328.3 | 0.158 | 139.6 | 818.0 |

60 | 187.9 | 359.1 | 0.172 | 151.6 | 806.0 |

65 | 219.9 | 399.5 | 0.192 | 167.1 | 790.5 |

70 | 266.5 | 454.0 | 0.218 | 187.5 | 770.1 |

75 | 338.9 | 530.6 | 0.255 | 215.3 | 742.3 |

80 | 461.0 | 644.3 | 0.309 | 254.7 | 702.9 |

85 | 686.0 | 823.1 | 0.395 | 312.5 | 645.1 |

90 | 1110.1 | 1110.1 | 0.533 | 395.6 | 562.0 |

Δ Q s ( θ ) = − ( 1 − f ) I A c ( θ ) e − τ ( θ ) Δ τ ( θ ) (13)

where Δ Q s ( θ ) is variation in the rate of energy exchanged with the surface at the latitude in consideration, W; A c ( θ ) is the surface area perpendicular to solar radiation, m^{2}; τ ( θ ) is the average optical depth of the atmospheric at the latitude in consideration, dimensionless; and θ is latitude in degrees. Because variation in the total rate of energy exchanged with the surface, Δ Q s , is known, then variation in the rate of energy exchanged with the surface at any latitude, Δ Q s ( θ ) , can be calculated from Equations (12) and (13)

Δ Q s ( θ ) = Δ Q s × [ Δ τ ( θ ) / Δ τ ] e − [ τ ( θ ) − τ ] × A c ( θ ) / A c (14)

Seasonal variation occurs infinitesimally with time and the height of the atmosphere varies infinitesimally as well. The distance traveled by solar radiation is variable and the optical depth of the atmosphere varies as a consequence. Because the diameter of the atmosphere is large, its circumference can be assumed to be a straight line in a small area. Similarities between triangles following small variation in the height of the atmosphere, ^{2} and double integrated with respect to θ and ф, in a similar fashion to Equations (8) and (10). Keeping in mind that the functions and variables are separable, the result of the double integration is Δ Z t ( θ ) / Z t ( θ ) ≈ Δ Z t / Z t . If the numerators and denominators are multiplied by the absorption coefficient of solar radiation, a , then Δ τ ( θ ) / τ ( θ ) ≈ Δ τ / τ , Δ τ ( θ ) / Δ τ ≈ τ ( θ ) / τ , and Equation (14) simplifies

Δ Q s ( θ ) = Δ Q s × [ τ ( θ ) / τ ] e − [ τ ( θ ) − τ ] × A c ( θ ) / A c (15)

Variation in the rate of energy exchanged with the surface at a given latitude, Δ Q s ( θ ) , can be used to calculate latitude temperature change

Δ T s ( θ ) = Δ Q s ( θ ) / [ M ( θ ) C p a ] (16)

M ( θ ) = E ( θ ) / [ W s ( θ ) − W t ( θ ) ] (17)

where

Δ T s ( θ ) = Variation in latitude surface temperature, K.

M ( θ ) = Latitude flow rate of the circulated dry air, kg∙yr^{−1}.

C p a = Specific heat of air, J∙kg^{−1}∙K^{−1}.

E ( θ ) = Latitude rate of surface evaporation, kg∙yr^{−1}.

W s ( θ ) = Latitude water vapor mixing ratio, kg water per kg dry air.

W t ( θ ) = Latitude water vapor mixing ratio at the tropopause, 0.0 kg water per kg dry air.

Equations (15), (16), and (17) yield

E ( θ ) = [ Δ T s / Δ T s ( θ ) ] × [ τ ( θ ) / τ ] e − [ τ ( θ ) − τ ] × E × W s ( θ ) / W s × A c ( θ ) / A c (18)

where E is a known surface water evaporation at a known latitude, and the measured world average precipitation of the entire surface of the earth will be used for E; ΔT_{s} is variation in the world average surface temperature, K; and W_{s} is the world average water vapor mixing ratio, kg water per kg dry air. These world average meteorological parameters are measured or available and can thus be used as pilot data for scale-up. Therefore evaporation at any latitude can be determined by measuring or calculating latitude surface temperature, T_{s}(θ). The rest of the variables are known from the motion of the earth around the sun and

The solution of Equation (18) requires obtaining the latitude at which world average surface temperature and evaporation occur. This latitude can be determined by computing the average optical depth for a hemisphere τ h

τ h = ( 1 / A h ) ∫ 0 A h τ ( θ ) d A h (19)

where A h is surface area of half hemisphere ( π R e 2 ) that observes solar radiation. Equation (19) can be simplified for finite element analysis

τ h = ∑ θ = 0 θ = θ f τ ( θ ) cos ( θ ) d θ (20)

The upper limit of the summation, θ f , is the latitude where surface water exists. It is approximately equal to 70 degrees. Thereafter, the surface is assumed to be covered with Arctic and Antarctic ice. Integration of Equation (20) yields to τ h = 0.128 based on

Equation (18) gives latitude surface evaporation, E(θ), if the angle θ and surface temperature change, ΔT_{s}(θ), of the latitude in consideration are known. On the other hand, the world average values of E, ΔT_{s}, and W_{s} are a result of solar energy exchanged. If the solar radiation is imagined to cease, surface air temperature approaches zero absolute. At steady state when surface evaporation, E, is equal to the observed average value, variation of surface air temperature, ΔT_{s}, measures average surface temperature rise with respect to zero absolute. The ratio, ΔT_{s}/ΔT_{s}(θ), can thus be replaced by T_{s}/T_{s}(θ), where the values of the temperature are in degrees Kelvin. The ratio W_{s}(θ)/W_{s} is reasonably equal to the ratio of absolute humidity at saturation. This ratio can be determined if T_{s}(θ) is known, for the average surface temperature T_{s} is available. The world average evaporation, E, calculated at 40˚ latitude is available in the literature; it is equal to the annual precipitation, about 953 mm annually [

E ( θ ) = [ { T s ( 40 ) + 273.2 } / { T s ( θ ) + 273.2 } ] × [ τ ( θ ) / τ ( 40 ) ] e − [ τ ( θ ) − τ ( 40 ) ] × ( 953 / 365 ) × [ W s ( θ ) / W s ( 40 ) ] × [ cos ( θ ) / cos ( 40 ) ] (21)

In Equation (21), the ratio A_{c}(θ)/A_{c}(40) is replaced with its equivalent cos(θ)/cos(40). The values of T_{s} and T_{s}(θ) are now in ˚C. Open water evaporation, E(θ), is in mm∙day^{−1}.

Calculation steps of open water evaporation follow: Step one: given day of the year, d , where January 1^{st} is day 1, calculate the declination angle, δ , in degrees, δ = sin − 1 [ sin ( 23.5 ∘ ) sin { ( 360 / 365 ) ( d − 81 ) } ] . Step two: calculate the instantaneous latitude θ = geographic latitude-δ. In the southern hemisphere the geographic latitude is negative. Step three: read from ^{−1}. On monthly basis, use for, d , average day of the month for simplicity and multiply by the number of days of the month in consideration. For annual evaporation multiply average daily evaporation by 365. Justification for using the pilot data for average surface temperature, T_{s}(40), is explained under the Discussion section. Example:

Lake Okanagan, Canada, average evaporation for the month of October: d = 288.5; number of days = 31; latitude = 49.5˚N; T_{s}(40) = 14.9˚C; declination angle = −9.8˚; θ = 49.5 + 9.8 = 59.3˚N; T_{s}(θ) = 10.2˚C, Kelowna; from _{s}(θ)/W_{s}(40) = 0.71; E(θ) = 1.6 mm∙day^{−1}; E(θ) = 1.6 × 31 = 50 mm for October. Observed open water evaporation is unavailable, observed class A pan evaporation is 70 mm; estimated pan coefficient = 50/70 = 0.71. Similarly, brine evaporation can be calculated by knowing the total dissolved solids. These reduce vapor pressure, which can be obtained and W_{s}(θ) determined. Evaporation from brine can be calculated following the same procedure. Calculation of monthly evaporation for sample locations is presented in

Evaporation calculation and projection in a warming world are important at the societal level. Presently, there are no low cost and accurate methods at the same time for calculating evaporation. Background Information and Data sections present examples where calculation of evaporation with accuracy is determined. It is complex and requires substantial resources. The inconveniences and limitations of the present methods are inherent to considering surface evaporation as a function of ambient conditions. Meteorological data and measurements are thus required. The work presented in this manuscript reveals that evaporation is a function of the solar heat exchanged with the surface, and can be addressed as a

Description/ Location | Dead Sea, Jordan | Melbourne, Australia | Lake IJssel, Netherlands | |||||
---|---|---|---|---|---|---|---|---|

Specific gravity 1.00 | Specific gravity 1.26 | Specific gravity 1.00 | Specific gravity 1.00 | |||||

Calculated | Observed | Calculated | Observed | Calculated | Observed | Calculated | Observed | |

January | 2.56 | 3.24 | 1.34 | 1.34 | 5.56 | 6.45 | 0.66 | 0.36 |

February | 3.05 | 3.86 | 1.62 | 1.73 | 5.39 | 5.36 | 0.81 | 0.55 |

March | 4.02 | 4.97 | 2.17 | 2.35 | 4.58 | 4.84 | 1.17 | 0.94 |

April | 5.27 | 7.12 | 2.89 | 3.98 | 3.33 | 2.67 | 1.59 | 2.00 |

May | 6.93 | 8.95 | 3.87 | 5.12 | 2.46 | 1.71 | 2.02 | 2.97 |

June | 8.68 | 10.12 | 4.90 | 6.07 | 1.94 | 1.00 | 2.61 | 3.45 |

July | 9.92 | 10.10 | 5.65 | 6.07 | 1.91 | 1.61 | 2.67 | 3.05 |

August | 9.63 | 10.19 | 5.48 | 5.70 | 2.32 | 1.94 | 2.79 | 2.58 |

September | 8.19 | 8.71 | 4.63 | 4.68 | 2.94 | 2.67 | 2.22 | 1.66 |

October | 5.87 | 6.68 | 3.26 | 3.35 | 3.63 | 4.03 | 1.71 | 0.92 |

November | 3.52 | 4.84 | 1.90 | 2.16 | 4.29 | 5.83 | 0.89 | 0.55 |

December | 2.74 | 3.48 | 1.46 | 1.47 | 4.88 | 5.65 | 0.63 | 0.35 |

Annual | 5.87 | 6.87 | 3.26 | 3.67 | 3.60 | 3.65 | 1.65 | 1.62 |

climate parameter instead. No meteorological records are thus required. This is a major difference between the methods that can yield to a low cost and reasonably accurate methodology for calculating evaporation. Additionally, the proposed method can be used to project evaporation with climate change, whereas the existing methods cannot.

Unlike the existing methods of calculating evaporation, the method used in this work adheres to the scale-up methodologies. All latitudes are in fact circular, and those in consideration between 0˚ and 70˚ are similar in having atmosphere, surface water, land, outer space, solar radiation, and gravity. They are smaller earths and can be scaled-up from one another. Therefore, dimensionless scale-up groups are derived and used in Equation (21). By far the most complex similitude relationship to establish is the geographic one. Land albedo, elevation, and thermal properties can be different. Theoretical and empirical relationships are available in the literature, example [_{s}(θ), and the temperature of a similar pilot geographic location, T_{s}(40˚), are the only requirements.

The measured pilot temperature values of T_{s}(40˚) for geographic similarity are average surface temperatures at approximate latitude of 40˚ as determined under Results. At this latitude, the world average precipitation is also measured and it is equal to the world average evaporation, E, used in Equation (21). Although the measured world average precipitation is equal to average evaporation, they are not necessarily equal at a given latitude. For instance, in arid locations precipitation is negligible but evaporation is high. The evaporation calculated by Equation (21) is a “potential” evaporation of an imaginary water body having constant water inventory at the location in consideration.

Because average surface temperature is used as pilot data for evaporation scale-up, selection of this temperature, T_{s}(40), in Equation (21) is important. This selection is based on “geographic” similarities with the locations where evaporation calculation is desired. If the location is close to sea water, Sea Surface Mean Temperature of 16.1˚C should be used for average surface temperature T_{s}(40). If the location is in remote area inland where sea water has minimal to no effect, Land Surface Mean Temperature of 8.5˚C should be used instead. The selection is based on the weighted average surface temperatures reported by [

Evaporation varies with weather departure from average conditions, and evaporation departure can be calculated with this method, including maximum and minimum daily evaporation. However, the long-term average evaporation varies with the seasons. As a result, monthly evaporation maps are prepared around the world, which suggests that evaporation is a climate parameter based on observations as well.

It should be noted that Equation (21) does not account for the impact of variation in the distance between the earth and the sun because it is small compared with the effect of the earth’s axial tilt. On an annual basis, the calculated evaporation by Equation (21) does not require correction for distance variation. However, correction is required on a monthly basis. The correction is +3.8% for December and −3.8% for June. A linear interpolation may be used for the months in between. This correction is based on a maximum total variation in the solar constant of about 7.5% with respect to its average value according to [^{−1}.

Finally, the values used for the pilot average surface temperature T_{s}(40) in the calculations are only those mentioned under the Discussion section. They are limited and discrete values. If the values can be interpolated or extrapolated based on geography or other considerations, open water evaporation could be calculated practically accurately. As of now, using such a procedure cannot be justified based on the available literature. Therefore, room for improvement exists.

Thanks to the team of the Journal of Water Resources and Protection for their review and comments. It is gratefully acknowledged for handling the manuscript. The time and effort of those who contributed directly or indirectly to this work are appreciated.

The authors declare no conflicts of interest regarding the publication of this paper.

Swedan, N.H. (2018) Calculation of Open Water Evaporation as a Climate Parameter. Journal of Water Resource and Protection, 10, 762-779. https://doi.org/10.4236/jwarp.2018.108043