Evaporation in hydrology and meteorology

ISSN-0169-6246

July 1990

Evaporation in Hydrology

and Meteorology

Comm unicat io nofthe Departmentof

SanitaryEnginee ring and Water Management Ir.

T

.

Brandsma

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R~~P

.lft

WMG-Gez

. echnology

Facultyof Civil Engineering

Department of SanitaryEng ineering andWat er Management

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Evaporation in Hydrology and Meteorology

Theo

Brandsrna

Ju

ly

23, 1990

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.-Mededeling nr. 34

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Contents

1 Introduction 1

2 Theory 2

2.1 Factors governing evaporation . 2 2.2 Planetary boundary layer

.

. .

3 2.3 Mathematica! description of

evaporation . . . 4 3 Methods for determining

evapora-tion 5 3.1 Budget methods

....

.

5 3.2 Budget-profile methods 6 3.3 Combination methods 8 4 Applications in literature 9 5 Special conditions 12

6 Difliculties in determining

evapo-ration 14

7 Discussion 14

Technisc he

Universiteit

Delft

Faculteit

CiTG

Bibliotheek Civiele Techn

iek

Evaporation in Hydrology and Meteorology

Theo Brandsma

July 23, 1990

Abstract

In this paper the role of evaporation in hydrology and meteorology is discussed, with the emphasis on hydrology. The basic theory of evaporation is given and methods to determine evaporation are presented. Some applications of evaporation stud-ies in literature are given in order to illustrate the theory. Further, special conditions in evaporation

are considered, fol1owed by a fotmulation of the difficulties in determiningevaporation, The last part of the paper gives a short discussion about evaporation model development.

1

Introduction

Evaporation can be defined as the energy eon-suming phase transition from liquid to vapor, while in the reverse process,condensation, the same amount of energy is set free. In this, evaporation is the eonneeting link between the water budget and the energy budget.

For evaporation from saturated surfaces, of-ten a distinction is made between evaporation

from the soil and transpiration by plants, to-gether denoted as evapotranspiration. How-ever, in many cases this distinction is rather artifieial, therefore, in this paper, the term evaporationisused for both processes. A fur-ther distinction can be made between poten-tial and actual evaporation. Potenpoten-tial evapo-ration is the evapoevapo-ration occurring when there are no limitations in water supply,i.e., the

sur-face is always saturated. The actual evapora-tion is the evaporaevapora-tion experieneed in reality, and is always a fraction of the potential evapo-ration. One other term is often used, namely, the open water evaporation. The open wa-ter evaporation is the evaporation from a lake with a limited water depth.

Evaporation is an important factor both in hydrology and meteorology. On the one hand, in hydrology, evaporation plays an important role in the determination of, e.g.,the quantity of water to add to the soil to keep the transpi-ration near its maximum, or the predietion of the maximum outflow from a reservoir. In me-teorology, on the other hand, one needs evap-oration estimates for weather foreeasting.

Usually the evaporation models, used in

hy-drology, use the overlying air as an indepen-dent boundary condition, while in the same way, the weather forecasting or elimate mod-els, use the surface proeesses as an indepen-dent boundary condition. This is not cor-rect. Therefore, attempts should be made to develop an integral approach, a eoupling between hydrologie and meteorologie models. Such a coupling should comprise a detailed deseription of the soil-plant-atrnosphere pro-cesses. The recent eall for macroseale hydro-logie models as an integral part of c1imate modelling, wil! probably stimulate the devel-opment of coupled soil-atmosphere models.

At present there are no operational meth-ods for measuring or adequate forecasting the

actual evaporation. Hydrologists, e.g.,use

es-timates of potential evaporation as a function of calculated evaporation from shallow water surfaces, together with model calibration, to account for actual evaporation in hydrologie simulation. The uncertainties in these esti-mates can amount to several tens of percents. In many watersheds, the uncertainty in evap-oration estimates equals or exceeds even the total amount of water one wants to extract.

The remaining part of this paper will give a summary of the evaporation theory together with a brief review of the most widely used methods for estimating evaporation. Further, some applications of these models in litera-ture are given, followed by a discussion about some special conditions in evaporation stud-ies. In the last part the most important dif-ficulties encountered in determining evapora-tion are presented.

2

Theory

2.1

Factors governmg

evapora-tion

Evaporation from saturated surfaces is deter-mined mainly by energy supply, to evaporate the water, and by the ability of the atmo-sphere to transport the vapor away from the surface. However, in many cases the surface is not saturated and factors, describing the prop-erties of the surface and vegetation, become also important. The most important factors are stated as follows. .

1. Meteorologica1 factors. Weather fac-tors like temperature, humidity, incoming radiation, wind speed and atmospheric stability are the most important meteoro-logical factors. Since solar radiation is an

important factor, evaporation also varies with latitude, season, time of the day and sky conditions.

2. Time-dependent surface properties. These are factors like roughness, stom-ata! resistance, colour and external wet-ness. The rate of evaporation of a sat-urated soil surface is approximately the same as that from an adjacent water sur-face of the same temperature. As the soil begins to dry, evaporation decreases and its temperature raises to maintain the energy balance. Eventually, evapora-tion virtually ceases, since there is no ef-fective mechanism for transporting water from appreciable depths. Thus the rate of evaporation from soil surfaces is lim-ited by the availability of water.

3. Properties of the surface on the weather side. These properties are of-ten combined into the term adveetion.

They are time-dependent, e.g., due to changes in wind direction, which causes air to flow over different adjacent surfaces.

Today no model exists containing all the vari-ables mentioned .

From the three factors, mentioned above, it can be derived that the actual evaporation at any given time and at any given location, is usually quit different from the climatologi-cal mean. The deviation from this mean can be characterized by a cyclic or periodic be-haviour, namely with a daily and with a sea-sonal time scale.

The conditions under which evaporation takes place range between two extreme con-ditions. Penman (1956) denoted these condi-tions 'mid-ocean' and 'mid-desert' condicondi-tions. The first is the state in which evaporation takes place from a limited water area, in the midst of an infinite area of the same kind of surface. The second is the state in which a reservoir, or an other evaporating surface, is surrounded by an infinite plane from which no evaporation can take place. At the 'mid-ocean' extreme the size of the area studied is of no

importance, but under 'mid-desert' conditions the size may be very important.

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...

,

...

,

1::1 IS .Utt~ITJ 21 TI.. aIG.n

-•

.u...

..

0 + r T " " " " " " " " -o 100 h

,-,

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Figure 1: The diurnal variation of the PBL height h, Dots indicate observations of h with an acoustic recorder, squares are estimates of hobtained from temperature profiles. The in-dicated line is based on model calculations.

(From de Bruin and Holtslag in Evaporation and Weather, 1987).

for weather forecasting and cIimate studies. In such models the dynamics and thermodynam-ies of the atmosphere are described very de-tailed, but the surface processes are generally treated as independent boundary conditions.

The transport between the surface and the lowest millimeters of air is governed by molec-ular conduction of heat,molecular diffusionof tracers, and molecular viscous transfer of mo-mentum. Once in the air, turbulence takes over to transport momentum, heat and other constituents to greater depths in the atmo-sphere. Usually an effective turbulent flux is defined which is the sum of molecular and tur-bulent fluxes.

2.2

Planetary boundary layer

The planetary boundary layer (PBL) can be defined as that part of the troposphere (the lower part of the atmosphere), that is directly influenced by the presence of the earth's sur-face and to sursur-face forcings with a time scale of about an hour or less (StuIl, 1988).

The earth's surface is the lower boundary to the PBL. Transport processes at th is bound

-ary modify the lowest 100 to 3000 m of the atmosphere, creating the PBL.The daily cy-cIe of warming and cooIing the earth's surface and the roughness of the surface, are the driv-ing forces behind the existence of the PBL.

Generally the flow of air within the PBL is turbulent. The turbulent state of the PBL ap-pears to be primarily determined by the wind speed,surface roughness and the surface fluxes of sensible heat and water vapor. On the one hand, if the PBL is heated from below, i.e.,the vertical surface flux density of sensible heat, H, is positive, the PBL is unstably stratified. Then relatively warm, and thus less dense, air is near the surface, whereas at greater height the air is cooler and thus more dense. This state occurs during daytime. On the other hand, the PBL is stabie if H

<

0, i.e., the surface is cooling. At last, ifH is small and wind speed is large the PBL is neutrally strat-ified. It is obvious that evaporation plays an important role,especially in the diurnal vari-ation of the PBL height. An example of this variatien is given in figure1.

Besides influence on stability and height of the PBL, evaporation also plays an important role in the formation of fog, clouds and precipi-tation. In spite of the fact that meteorologists recognize the importance of water vapor for atmospheric processes, evaporation is hardly ever described properly in models developed

2.3

Mathematical description of

evaporation

The evaporation at the surface of the earth is a one-dimensional process. However, in reality, evaporation is governed by a three-dimensional process,namely,turbulence in the air. This turbulence influences the evapora-tion by advecevapora-tion of heat and water to or from the surface.

Brutsaert (1982), among ethers, showed that the reality is very complex. When consid-ering only the transport of water vapor in the air, the following conservation equation must be solved

8q

at

+

(v.Vq)

=

"v

V2 q (1)

where

q

is specific humidity, v

=

iu+jv+kwis

the velocity of the air and

"v

is the molecular diffusivity of water vapor in the air .

In practice equation 1 is not directly appli-cable, since the flow of the atmosphere is al-most invariably turbulent. This means that the description of the velocity field and also the content of water vapor, at any given point in time and space, is practically impossible,

and can only be accomplished in statistical sense.

The simplest and probably most important statistic is the mean, also known as the first moment. This mean can be obtained as fol-lows. First decomposing the dependent vari-ables into a mean and a turbulent fluctuation, namely

u

=

u+u',

v

=

ïï+v', w

=

üi+w'

and

q

=

q+q'.

Then,after applying time-averaging

over a suitable period and using equation 1, one obtains Oq _8q _Oq _Oq {)

-8t +u

_8x

+v

_8y

+w

_8z

=-[8x(u'q')

8 - -

8

-+-(v'q')

+

-(w'q')]

+

"v

V2q

(2)

8y

8z

The terms on the left-hand side represent the rate of change in mean specific humidity,ob

-served when following the mean motion of the air. The cross correlations on the right-hand side may be called Reynolds fluxes, and they represent the diffusive flux components due to turbulent motion. The last term is the conver-gence of the transfer rate by molecular diffu-sion.

To solve equations 1 and 2 information is needed on the flow field. This requirement ne-cessitates the introduetion of additional tions; these are an equation of state, and equa-tions of conservation of bulk air mass, of mo-mentum and of energy. Within these four equations there are four unknowns, namely: temperature, density,pressure and velocity of the air, 50the velocity field can be solved.

The equations are not easy to solve. For instance, equation 2, for the mean quantities, contains second order moments which are not known. Therefore, an additional equation for the second order moments is needed. Simi-Iarly, the equation for the second order mo-ments contains third order momo-ments, and 50

on. Therefore, there are always more un-knowns than equations.This problem of hav-ing always more unknowns than equations is known as the problcm of closure. Actually, daily experience show. thAteven the mean mo-tion of the atmospbereinvolvesphenomena of considerable compleany. lIence it seems an al-most hopelesswk,ladescn be this mean mo-tion and the distnbuuo n of the mean specific humidity by the solutlOn ol a number of par-tial differenpar-tial eqU&1wn., cven if the closure problem did not c.uat.

Fortunately, howc vrr. It IS possible to

sim-plify the general problem Iorrnulated by the conservation equAtlOlU cocs idera bly, and still obtain some very n"&lIIn&ful results. This is accomplished, /irat. Ly considering the at-mosphere neerest tbc surface as a steady boundary layer, &DJM"Cond, by application of similarity princrples la dcscribe the turbu-lence. Theapplicatsonolsimilarity principles

The budget methods are mathematically the simplest methods, however, in practice there are several problems with the application of these methods.

The methods for determining evaporation are divided in three categories, the budget meth-ods, budget-profile methods and combination methods. In some cases, however, there is an overlap between these categories.

Budget methods

Methods for

determin-ing evaporation

3.1

The above considerations about the three-dimensional flow in the atmosphere show that this problem, even for meteorologists, is a very complicated one. This explains why, till now, hydrologists did not include the three-dimensional flow in their evaporation modeis, and meteorologists treat evaporation at the earth's surface as an independent boundary condition.

and semi-empirical turbulence theory allevi-

3

ates the closure problem, since it aIlows the substitution of second and higher order rno-ments of turbulent fluctuations by terms con-taining only mean and lower order variables,

respectively.

The water budget method This method can be stated mathematically as

dS

(P-E)A+I-O=

dt

(3)

The energy budget method The energy budget method, applied to the earth's surface, can be stated mathematically as

where Pis the rate of precipitation, E is rate of evaporation,Ais the surface area, I is sur-face and groundwater inflow rate,0 is surface and groundwater outflow rate,

*

is the rate of change of water storage. Them~thodis sim-ple in theory but application rarely produces reliable results, since all errors in measuring precipitation, infiow, outfiow and change in storage are refiected directly in the computed evaporation. Besides, this method is inappli-cable to predict evaporation in the design of planned water storage or irrigation engineer-ing projects. This explains, why it is usually necessary to determine evaporation indepen-dently from the water budget, on the basis of meteorologie al data.

(4)

Q*

=

H +>'E+G

As outlined by Wartena (1974), the hydrol-ogists is confronted with the foIlowing prob-Iem. From a physical viewpoint local instan-taneous evaporation is weIl defined, but inte-gration with respect to time and place, in or-der to arrive at evaporation rates for extended periods and areas,as required in hydrology, is generally impossible, Therefore, only charac-teristic values are used. These characcharac-teristic values are based on values of, e.g., tempera-ture and humidity, averaged with respect to time and place.

In hydrology three approaches are used to obtain evaporation values. The first approach is based on energy budget or water budget con-siderations. The second approach is based on energy budget-profile considerations. And the third approach is a combined approach,based on the energy budget-profile method and an aerodynamic method. To use these methods one has to simplify the real problem by us-ing similarity considerations and parameteri-zations. In section 3 the most important evap-oration modeis, based on these methods, are elaborated.

J ' N A M J J A S O N D .. _ .1

(6)

\

\G

/

~/

J r M A M J J A S O " a

Figure 2: Example of the mean annual cycle of net radiation QO, sensible and latent heat fluxes Hand AE, and the soil heat flux Gin: (A) water with a depth of 5 m; and (B) in water with a depth of 15 m (From De Bruin, 1982).

.. w..'

3.2

Budget-profile methods

The budget-profile methods are in general based upon the energy budget, and measure-ments of the vertical humidity and tempera-ture profiles in the atmosphere. Four methods are treated in this subsection.

Energy budget/Bowen ratio method The Bowen ratio,

/3,

is defined as the ratio of sensible and latent heat fluxes at the surface

H

/3

==

>'E

(5)

and

where QO is net radiation which can be mea-sured directly or can be calculated using equa-tion 5,His sensible heat flux,>'Eis latent heat flux (evaporation), Gis the soil heat flux, K

is the short wave and Lis the long wave radi-ation, the arrow

!

denotes incoming and the arrow

i

denotes outgoing radiation.

In general QO can be determined and G can be estimated (G ~ 0 when considering daily over land evaporation values),so the problem is reduced to finding the ratio H / >'E.In sub-sectien 3.2, methods for determining this ratio are presented. In figure 2 an example is given of the mean annual cycle of the components in the energy budget.

Instrumental methods Two instrumental methods should also be mentioned in this con-text. The first is the evaporation pan. The evaporation pan is a pan shaped instrument filled with water. The pan evaporation is de-termined by measuring the quantity of water lost by evaporation. Subsequently,open water evaporation is determined by applying a so-called pan coefficient, Although there may be some criticism on the theoretical foundation of this method, in practice the pan coefficient is quite consistent and does not vary excessively from region to region and from season to sea-son.

The second method is the lysimeter. The lysimeter is a box in the ground filled with the same soil and covered with the same vegeta-tion as the surrounding environment. Evapo-ration in the box is determined with the water budget method. The lysimeter can give good estimates of actual evaporation. Continuity with the environment, to be able to neglect advection,is an important condition.

Combination of the energy budget and the Bowen ratio, equation 4 and 6, gives for the latent flux and sensible heat flux, >'Eand H respeetively

latent heat,sensible heat, momenturn or any other admixture from eovarianees. Over a uni-form surface under steady state conditions, the surface fluxesE andH can be estimated from

where'Yis the psychometrie constant,T_oisthe surface temperature,T2is the air temperature at 2 m, eo is the water vapor pressure at the surface and e2 isthe water vapor pressure at 2m.

The energy budget method eombined with the Bowen ratio can thus give reliable esti-mates of>'Eand H, if the neeessary temper-ature and humidity parameters can be mea-sured.

Itis now assumed that >'Eisproportional to the vertieal humidity gradient, an H is pro-portional to the vertieal temperature gradi-ent, and similarity prineiples ean be applied to both profiles. Then,O ean be determined from profile data of specific humidity and tem-perature in the atmosphere near the ground. No measurements of atmospherie turbulenee or mean wind speed are required. When,O issmall, the method may be less susceptible.

The Bowen ratio ean then be expressed as

(10)

(11)

Priestley and Taylur wcthod Based on energy principles&lidprofi lerncthods, Priest-ley and Taylor (19;2)developcd the following equation for evapor auo a, -hieh is applieable to both saturated lAnd&liJ waLer surfaces respeetively, where E is the evaporation rate at the surface, pis the density of the air, cp

is the specific heat of the air,

w',

s'

,

and 8' are the deviation from the mean vertieal wind-speed, humidity and potenrial température re-speetively.

In practice the fluxEis determined by mea-suring the fluetuations w' and q' and then eomputing the cross-correlation over a suit-able averaging period (about half an hour), and similarly forH.

In theory the method is good, but in prae-tice the method will not be broadly applied beeause of the complieated , and thus expen-sive, instruments needed. The method re-quires fast response meaauring instrurnents for wind speed and humidity parameters. Hydrol-ogists do not use thia mrthod,however, micro meteorologists do uae lt.

(8)

(9) (7) >'E

=

Q" -

G

1+.0

H

=

'o(Q" -

G)

1+.0

Eddy eorrelation method Strietly speak-ing this method is not a budget-profile method but a transport method, However, profile methods are the approximation of the eddy eorrelation method, therefore this method is given here.

Equations for the mean constitute the basis for the eddy correlation method. This method consists of determining the turbulent fluxes of

>'E

=

a- '- (Q" - G) (12)

, ~.,

where cr is the Praf'1l l lor y Taylor parameter and s is the slope ol rhe saturation specific humidity-ternperature cur ve , Priestley and Taylor applied cqua lioll 12 to several situa-tions above land and &hove sca and found an average value of a

=

I ::6as the overall mean with a range of 0.26.

Makkink method Makkink (1957) pro-posed a simplified method for evaporation dur

-ing summer conditions in The Netherlands

It should be noted that the equation according to Makkink must be used in the erop factor method, which is dealt with in section 3.3.

(13)

3.3

Combination methods

Penman method Penman (1948) derived the fol1owing equation for evaporation and he verified it for open water,bare soil and grass The combination methods consist of a com-bination of the energy budget-profile method and the aerodynamic method, the method was first introduced by Penman (1948). Aerody-namic methods usuaily consist of empirical re-lations including a function of windspeed.

>'E

=

sQ·

+

r>'Ea ₍₁₄₎

s+-r

where >'Ea

=

f(

u)[e,

(Ta) -

eal

is the dry-ing power of the air, f(u)is a wind function,

e,(Ta ) is the saturation water vapor pressure

at Ta(air temperature) and ea is the water

vapor pressure at screen height.

The main reason for Pen man to develop this equation was to eliminate the surface tempera-ture, which is very difficult to measure indeed. Measurements are needed for sunshine dura-tion, temperature,relative humidity and wind-speed. They are needed at only one height.

Although the Pen man method is adequate for many conditions, in many cases the necessary input data are lacking. Then one can use sim-plified versions ofwhich the Priestley and Tay-lor and Makkink are weil known examples.

Just like the method of Makkink the Pen-man method is used to obtain values of open water evaporation (Eo). The erop factor method is applied to Eo to obtain potential

evap ora tion from a cropped surfaceaccording

to whereClandC2are constants andJ(!is the in-coming short wave radiation which is observed directly on a routine base at several stations in The Netherlands. Makkink assumed that G

=

0 (good approximation for wet grass-land) and that C2 accounted for aerodynamic

effects. For summer conditions in The Nether-landsC2~O.

De Bruin (in Wartena et al., 1981) corn-pared the Makkink method with several other methods, among others the Penman method. He found a good agreement between the Pen-man method and the method of Makkink for summertime open water evaporation val-ues. The Makkink method appeared to have such advantages, that the Royal Netherlands Meteorological Institute (KNMI) decided to use this methodinst ead of Penman's method, starting from the first of April 1987.

The main reason to look for an other for-mula for the determination of open water evaporation was the fact that from Penman's equation, which was used before April 1987, several versions exists,which caused a tremen-dous confusion. The main advantages of the method of Makkink are (De Bruin, in Evapo-ration and Weather,1987)

• lts behaviour is very similar to that of Penman'smethod.

• It is remarkably simpie: it requires only air temperature and global radietion as input. Bothcan be measured directly and very accurately.

• Under dry conditions Makkinks formula appears to have an even better

whereEpis potential evaporation and fisthe erop factor which depends on erop type and season.

Penman-Monteith method Using the same physics as Penman, Monteith (1965) de-rived a formula that gives the evaporation from a dry vegetated surface

s(Q· - G) +pCp

#->'E

=

.

(16)

s+r(I+~)

where D

=

e.(Ta ) - ea , cp is specific heat of

air at constant pressure,ra is aerodynamie re-sistanee and r. is eanopy or surface resistanee.

The Penman-Monteith equation is defined for a dry erop eompletely shading the ground.

Irthe erop is eovered with a thin water layer,

r. beeomes zero and the original Penman for-mula is obtained. So equation 16 deter mines also the evaporation from a fully wetted erop.

However, the behaviour of the formula be

-tween dry and wet erop conditions is not clear.

For eropped surfaces it appeared th at the erop factor method is very crude. For more accurate ealculations the Penman-Monteith method ean be reeommended.

4

Applications

In

litera-ture

In this section some applications of evapora-tion methods are given, most of whieh are de-seribed in the previous chapter. The applica

-tions are meant to give some insight in the use, possibilities and limitations of the methods.

De Bruin and Keyman (1979) applied the Priestley-Taylor method to the fermer Lake Flevo in the Netherlands. The lake had an area of 460 km2 _{and an average depth of}

3 m. Daily values of evaporation in the period

April-October 1967 are determined with the energy budget/Bowen ratio method (which are eonsidered to be the true values of evapora-tion) and are compared with corresponding estimated values obtained by the Priestley-Taylor method.

The Priestley-Taylor method appeared to give quite satisfactory results at a

=

1.26 (the value which Priesley and Taylor found), using 24 hour periods in summertime.

Using three hourly estimates of tempera-ture and humidity the diurnal variation of the Bowen ratio, {J, is studied. As an example the results for July 1967 are givenin figure 3.

It can be seen from figure 3 that a has a pronounced diurnal variation, with minimum early in the day and maximum in the late af

-ternoon. The variatien of a is due to the vari-ation of{J.In turn, the variatien in{Jis mainly due to variatien in To - T2 because qo - q2 is nearly constant.

Besides a diurnal variatien ofa also a sea-sonal variat ien of a is found. For the period April-October 1967 this variation is given in figure 4. Figure 4 shows a pronounced seasonal variatien of a, with a differing only slightly from 1.26 in the period May-September but in April and Octobera is about 1.50. This is as-cribed to the fact that in summertime>'Eis large and in spring and autumn >'Eis small, then the relative errors will be large.

De Bruin (in Wartena et al., 1981) com-pared 4 methods for determining evapora-tion in The Netherlands. The methods com-prised the Penman method, the Priestley-Taylor method, the Makkink method, and the Thom-Oliver method. (the Thom-Oliver method was not considered to be of major im-portance and is therefore not induded in this paper). The cornparison was made for an ex-tremely dry year and two more or less normal years,for the period May-September and with

111..---,

11 10 u ~ 11 UI Cl: :;)

!ë "

Cl:

~

11 UI

..

1.611--""'--...--'----'---'~-'---...- - t ex:

t

u

.•.,...

-'-

...,u

I~-~-~-~--- ~'·I IJ oe: S~ AU JN A~ MA

Figure 4: The seasonal variation ofa. (From De Bruin and Keyman, 1979).

IDI~-~-~----~-~-~----l o .J

..

!ë

Cl:.1 Z

~

.1 lil

" , . - - - ,

~., -~~:~~~:_~

.

.

-

....

/ - _

..

-._-_

....

-~

"

~O

)-.. n Ö i 11 :;) ~ 11 ~10 CJI•.•.-·-···-···'··

···-···-le

,l-~---r:----:"O:--~---::'=--::-::~

VI 000 )()O 100 Klo IJOO I~ 1100 1100 1400 TIME (METI

Figure 3: Diurnal variation of the parameter a, the Bowen ratio

P,

surface water temper-ature Ta, depth averaged water temperature

Tw , air temperatureT2and specific humidity

q2over Lake Flevo in July 1967. (From De Bruin and Keyman, 1979).

the restrietion to grassland.

The method of Makkink was found to be a very attractive alternative for the Penman method, when it is believed that the latter

gives the right evaporation values. As noted in section 3 this led to the introduetion of the Makkink method at the Royal Netherlands Meteorological Institute.

Omar and EI-Bakry (1981) applied the en-ergy budgetfBowen ratio method and an aero-dynamic method to Lake Nasser to obtain monthly values of evaporation. Lake Nasser has an area of 5000 km2 and an average depth of about 25 m (maximum dep th is about 90 m). The energy budget/Bowen ratio method was adapted for heat advected by the water into or out of the lake. For the aerody-namic method use was made of the empirical formulaEB

=

0.1296U2(eo - e2)where EB is the rate of evaporation according to the aero-dynamic method and U2 is the wind speed at

2 m height. Measurements were used from the period 1970-1971.

There appeared to be a good agreement be-tween both methods,therefore the calculation

.J F' M A M J J A S 0 N 0

MONTH

.Figure 5: Annual variatien of the budget terms at the surface of lake Nasser: A is

ad-vected heat by the water, >"Eis lake evapora-tion (Erom Omar and El-Bakry, 1981).

28 24 20 '>. 0 16 "'0 N

'e

12

....

~ 8 w 4 ~ cc .... ·0 w <:l

9

-4 CD -8

~

-12 ~'--. Q* ..., "

/

/:

Il~:~\\"

i \ '"" i \

~

.1

-,

J! ' \ ---- ---- , ' ." , °°. t \ , ' "'---"'~"~1C'--r...::." /<l ;'~ ........ ',---~... .',' '\"

'--ti-

\ _

of sensible and latent heat during daytime. The first method is the Penman-Monteith method and the second is a modification of the Priestley-Taylor method. This modified Priestley-Taylor method uses net radiation,air

temperature and an indication of the mois-ture condition at the surface. Both methods are compared on the basis of hourly micro-meteorological data above short grass, ob-tained at Cabauw in The Netherlands during the summer of 1977. The results refer to pre-dominantly unstable and advection free condi-tions and to a short grass cover.

It appeared th at the modified Priesyley-Taylor method has approximately the same skill as the more complete, but also more corn-plicated, method of Penman-Monteith. Th~

led to the conclusion that for many practi-cal problems, the modified Priestley-Taylor method must be preferred. It was also found that the soil heat flux is about

iö

of the net radiation, G~0.1Q·.

of the mean lake evaporation was made with the arithmetical mean of the two methods, Figure 5 shows the annual variatien of the budget terrns at the surface of the lake. It can be noted from figure 5 that evaporation is mainly driven by radiation,

Q.,

and, to a less extent, by sensible heat flux; H. The effect of the heat stored in the lake (G),has been nearly canceIled by the net heat advected into the lake(A).

On the average, evaporation is ab out 13% higher than net radiation. This can be as-cribed to the effects of adveetion of dry air and water. The average annual Iake evaporation is about 7.4 mm/day. For a one year period, this is equal to 11% of the lake's water content.

De Bruin and Holtslag (1982) compared two methods for determining the surface fluxes

De Bruin (1982) considers a model suitable for the determination of the température and the water balance of a weIl mixed water reser-voir.The model has a sound and clear physical basis and it uses only standard meteorological data. Because bodies of water with a depth of about 10 m, very often are mixed naturally by wind, the model can be of great practical interest. The model is verified by using the en -tire annual cycles of two relatively small water reservoirs, of different depths, in the south-western part of the Netherlands. Calculations have been catried out for the period 1971-1976. The mean annual cycle of the energy bal-ance for a lake of 5 mand a lake of 15 m is given in figure 2 of section 3.1. It is seen that in both cases the net radiation is almost in phase with the noon solar elevation, while it is only slightly dependent on water depth. The influence of the water depth on the ether terms

tion will not give the right result when applied to these problems.

(~

(a)

Figure 7: Typical variation of terms of the surface energy balanee for (a) daytime over land; (b) nighttime over land; (c) oasis effect of warm dry air adveetion over a moist sur-face; and (d) daytime over see with no advec-tion. Arrow sizes indicate relative magnitude. (From Stull, 1988).

The normal situation is the determination of evaporation during the day, thenQ. is di-rected downward because there is more down-ward radiation entering the surface layer than it leaving upward. The latent and sensible heat flux, >'Eand H respective1y, are directed upward because of vapor and heat transport upward from the surface. This is illustrated in figure 7a for a land surface. In this figure the relative magnitudes of the different compo-nents are given by the arrow sizes. An example of the absolute values of the diurnal variation of the terms in the energy balance is given in figure8.

5

Special conditions

of the energy balanee is more pronounced,

es-pecially the influence on the heat storage term G. This is due to the fact th at in spring and early summer solar energy is stored in the rel-atively cold water. For weU mixed bodies of water the amount of stored energy is prop or-tional to the water depth. The mean value ofG over several years is zero. Therefore,the heat stored in spring and early summer will be released later in the year. Thisreleased energy will enhance the evaporation and the sensible heat flux. Thisexplains qualatively why there is a phase shift between evaporation and net radiation, and why this ph ase shift increases with water depth,

The course ofTw (mean temperature of the waterin the reservoir) is simulated rather weil by the model. Figure 6 gives an example of the reservoir named Petrusplaat, for the year 1976.

.

:Ioe

2~

.

:1

1O~

:i

'I

0J@

• .;;:,.J.-riF;:;-T,';'"M:;-r-,A-:-"1ir;'_M":'ö"J"'-'TJ'lrA:-TI--:s::-r1-=0-"1N~i-=D::-t"'

Figure 6: A comparison between the rnea

-sured and computed water temperature of Petrusplaat (15 m deep) in 1976 (dashed line

=

observed;solid line

=

computed). (From De Bruin, 1982).

Evaporation under special conditions almost always deals with the storage of energy and tq.eadveetion of energy and water. In this section some of these conditions are consid-ered. Most methods for determining

evapora-At night over land, when >'Eis very small and even negative as can be seen in figure 8, the situation is totally changed. Net radiation,

Q*,is often directed upward because ofthe net upward long wave radiative cooling to space.

is not always water vapor in the air. In the Netherlands 60 to 80% of the annual dew is evaporated soil moisture by distillation (Wartena, 1989). Further, the format ion of dew is strongly dependent on wind speed (De Bruin and Holtslag, 1987). When windspeed is large evaporation will occur also during the night.

It is clear from the preceding conaidera-tions, that the determination of evaporation during nighttime conditions is a complicated task which cannot be solved by using routine weather data.

Another special condition.denoted oasis ef-fect, is illustrated in figure 7c. Imagine warm dry air flowing over a cool moist oasis. There is st rong evaporation from the moist ground and plants into the air,resulting in latent cooling that keeps the oasis at a pleasant temperature. However, this upward latent heat flux is op-posed by a downward sensible heat flux from the warm air to the cool ground. Thus

>'E

is directed upward while

Q'

and Hare directed downward. When considering only these three terms, it is seen th at the latent heat flux can be greater in magnitude than the solar heat-ing, because of the additional energy, H, that is extracted from warm air by evaporation.

Figure 7d gives an example of the ocean en-ergy budget. The ocean energy budget be-haves differently from the land budget because turbulence in the water can efficiently trans-port heat away from the surface and distribute it deeper in the water. Also the heat capacity of water is about 4000 times larger than that of the air, meaning th at a lot of heat can be absorbed into the water with little tempera-ture change. Thus the diurnal cycle of radia-tion is almest completely balanced by a corre-sponding diurnal variation of energy transport

into the sea, In addition, the nearly constant

15 11 2t 24 T• • t O l l T l -Q. H 0 0 0 o 0

....

.-..

..

-.00+--,.---,...-_.----.---,.-...,..---.---1 o

Figure 8: The observed diurnal variation of the components in the surface energy balance at Cabauw on a eloudless day in summertime (May 31,1978). (From De Bruin and Holtslag, 1987).

The sensible heat flux, H,is directed down-ward because of a downdown-ward heat flux from the air. Dew or frost formation also make the latent heat flux,

>'E

,

directed downward. Con-duction of heat from the warm ground up to the cooler surface makes Gdirected upward. This is illustrated in figure 7b. It should be noted that the absolute values in figure 7b are small compared to the ones in figure 7a. Dew formation will take place when the dew-point temperature is higher than the surface minimum temperature. The formation of dew makes the determination of evaporation diffi-cult because the surface will behave as an open water surface until the dew is evaporated. In winter when the relevant temperature differ-ences are likelyto be small and unequal, there may be more condensation on the surface.

It should be noted th at the souree of dew

100 IW/.'I 100 '00 .00 100 0 0

sea surface temperature with time, results in a nearly constant heat and moisture flux and associated slow tempora! changes in air tem-perature and humidity.

As the ocean is always moving, the absorp-tion of energy at one piace can give enhanced evaporation at an other place. Contrary, the release of energy at one place can give reduced evaporation at an other place, This is caused by the adveetion of heat by gulf streams and other large scale eddies in the ocean. Con-sequently, to predict evaporation over ocean waters one needs coupled ocean-atmosphere modeIs.

are too complicated to be accounted for by a few parameters only.

For cases where potentialevaporation data are used for calculation of the real (actua!) evaporation, the following difficulties and ori-gins of discrepancies can be stated:

• Inaccuraciesin the model.

• Neglecting advective influences. For a square parcel of, e.g.,1 ha th is can cause errors of 20% under extreme conditionsin

humid zones, and up to 40 or 50% in arid zones.

• Use of weather data measured above other surface covers.

• Water is not always available without lim-itation.

• Derivation of the potential evaporation for crops based on results obtainedfor a standard erop, e.g.,grass.

• A deep water body, e.g, an ocean, can store and release large amounts of energy and thus act like a flee wheel. As aresuit the cycle of available energy for evapora-tion may lag several months behind the solar input cycle.

6

Difliculties in determin-

All but the last itemized points were stated by

ing evaporation

Wartena (1974).

Evaporation from an irrigated field in an arid elimate can lead to strongly enhanced evaporation. The ratio of act ual to potential evaporation can be larger than 1 because of advection. There is a parallel between this ex

-ample and the oasis ex-ample.

The last example mentioned here is evapo-ration from a forest. Evaporation from a for-est requires a special approach because of the great aerodynamicroughness of a forest and the large fraction of intercepted water. It is obvious that these factors dep end largely on the type of forest and the prevailing weather conditions.

Discussion

• The theory is one dimensionaI.

• The vegetation layer. In reality the ex -change processes in the vegetation layer The main difficulties arisingfrom the deterrni-nation of evaporation are statedin this section.

7

In this paper the role of evaporation in hy-drology and meteorology was discussed with the emphasis on hydrology. The basic theory was reviewed and methods for the determina-tion of evaporadetermina-tion were elaborated. Some ap-plications of evaporation studies in literature were given followed by a discussion on special Two general limitations of the present day

conditions and difficultiesin determining evap-oration.

Frorn the discussionin this paper it is clear that evaporation is still a complicated subject.

Most of the theory, needed for a better

trest-ment of evaporation, is available. However, this theory inc1udes complicated three dimen-sional turbulent flow of airinthe atmosphere and complicated soil-plant-atmosphere inter-actions. Therefore, this process has not been modelled successfully up till now. At present, hydrologists and meteorologists are still using simp Ie one dimensional evaporation models for operational purposes. As these methods give estimates of evaporation with reasonable

at-curacy, it is not likely that complicated soil-atmosphere models, for evaporation purposes, will be developed within the near future.

An area of interest isin the recent c1imate studies. Attempts are now bcing made to in-corporate large scale hydrological models in elimate models using satellite data. In these studies evaporation will not be an independent boundary condition,but it will be an integral part of both modeis. Itshould be noted how-ever, that the farmer, who needs daily evapo-ration values, can do nothing with the results of such a coupled large scale model.

References

Brutsaert, W., Euaporation into the Atmo-sphere, D.Reidel Publishing Company, The Netherlands, 1982.

De Bruin, H.A.R., Temperature and Energy Balance of a Water Reservoir Determined From Standard Weather Data of a Land Station,

Jour-nal of Hydrology, 59, 261-214, 1982.

De Bruin, H.A.R.,and A.A.M.Holtslag, A Sim-ple Parameterisation of the Surface Fluxes of Sen

-sible and Latent Heat During Daytime Compared with the Penman-Monteith Concept, Journalof Applied Meteorology,21(11),1610-1620,1982.

De Bruin, H.A.R.,and A.A.M.Holtslag,

Inter-actions with the Planetary Boundary Layer,ElJap

-oration and Weather, Proceedinç« and

Informa-tion, No. 39, TNO Committee on Hydrological Research, the Netherlands, 1981.

De Bruin, H.A.R., and J.Q. Keyman, The Priestley-Taylor Model Applied to a Large Shal-low Lake in The Netherlands, Joumal of Applied Meteorology, 18, 898-903, 1919.

Malckink, G.F.,Testing the Penman formula by means of Lysimeters, Iourn, Int. of Water Eng.,

11,211-288,1957.

Monteith, J.L., Evaporation and Environment,

Proc. Symp. Soc. Erp.Biol.,19,205-234,1965. Omar, M.H., and M.M. EI-Baltry, Estimation of Evaporation From the Lake of the Aswan High Dam (Lalte Nasser) Ba.sed on Measurements over the Lake, Agricultural Meteorology, 23, 293-308, 1981.

Penman, H.L.,Natural Evaporation Irom Open Water Bare Soil and Grass,Proc. Roy.Soc.

Lon-don, A193,120-145.

Penman, H.L., Evaporation: An Introductory Survey,Neth. Joum.of Agrie.Sci., .,9-29,1956.

Priesley, C.H.B.,and R.J .Taylor, On the A&-sessment of Surface Heat Flux and Evaporation Using Large-scale Parameters, Monthly Weather

RelJiew,100(2), 81-92, 1912.

StuII, R.B.,An Introduction to BoundaryLal/er

Meteorology, Kluwer Academie Publishers, The Netherlands, 1988.

Wartena, L., Basic Difficulties in Predicting Evaporation, Journal ofllydrologl/, 23, 159-111,

1914.

Wartena, L.,etal., Enoporation in Re/ationto Hl/drologl/,TNO Committee on Hydrological Re-search, No. 28, The Netherlands, 1981.

.

.

MEDEDELING VAN DE VAKGROEP GEZOND8EIDSTECHNIEK EN WATERBEllEERSING

In de serie "Mededeling van de Vakgroep Gezondheidstechniek en Waterbeheersing" zijn tot nu toe de volgende publlcaties verschenen:

1. Siebers. H.II.: Patterns and varlablllty oCphosphate and heavy metals in sedlments oCtwo shallow lakcs.

2. Fllpse, M.J. en van der lIeIde, J.: Ontwikkellngen met betrekkIng tot vaste aCvalstoCfen ex art. 4, 17. 26. 26 van de ACvaistoCCenwet In perIode van ca. 1980 tot1985.

3. Kop, J.II.:Plan vorming voor de drinkwatervoorzienIng. (Cebruarl 1986) 4. Blanken. J.G. den en Hoogh, M.P.A.J. de: Modellen voor deslnCectIe van

gezuiverd aCvaiwater met chloor en ozon.

5. Kop, J.Il.:Het probleem van de wederzijdse afstemming van de beiangen van drinkwatervoorziening en mllleubescherming bij de plannlng voor de winnIng van zoet grondwater. (augustus 1986)

6. Dockelman, R.H. en de NIet, H.: Het berekenen van modelkrommen voor Geo-elektrische metingen.

7. Vos, W.L., Donze, M. and Dulteveld, H.: On the reClectance spectrumoCalgae In water: the nature oCthe peak at 700 nm and lts shlCt with varylng algal concentratIon.

8. Smlt, D., van Marneren, II.J. en Veldkamp, R.G.: De zuurstoChuishouding van de Utrechtse Vecht.

9. Van der lIelde, J.: Kinetische modellen voor ontwerp en beheer van actieC-sllb-installaties deei 1 en 2. (Cebruari 1987)

10. Boulan, R.P., M. Donze en SJ.P. Klapwljk: FosCaatbalans van de polder Reeuwijk en een aantal deelgebieden.

11. De Groot, C.P.M. en A.N. van Dreemen:Ontspanningsflotatie en de bereiding van drInkwater.

12. Den Blanken, J.G. en M.P.A.J. de 8oogh: Modeivorming voor verwijdering van indicatororganismen in het actieC-sllbproces.

13. K.K. l.Ushra and A.N. van Dreemen: Gravei-bed flocculation. 14. VlIs, E. van der:De flltratletheorle. (maart 1988)

15. Koreman, E.A. en A.N. van Dreemen: Toepassing van het vriesdooiproces bij de ontwatering van coaguiatiesllh.

16. Ganzevles, P.P.G., J.H. Kop en R. Ywema: Materiaaikeuze aCvaiwater-leidingen. (Juni 1988)

.

.

18. Den manken. J.G. en N.P.A.J. de lIoogh: Modelvorming voor een goede

procesregellng van de desinfectie met chloor c.q, ozon aan de hand van Instelbare en/of direct meetbare variabelen. (augustus 1988)

19. Noppeney, R.N.: De Invloed van stagnantezonesop dispersie.

20. Noppeney, R.N.: Gevoellgheidsonderzoek Alarmmodel RIJn; De invioedslengte van samenvloellngen bIJ dispersie. (november 1988)

21. Noppeney. R.N.: De verspreiding van olle op rivieren benaderd met het Taylor-model.

22. Noppeney. R.N.: De invloed van near-field processen op een far-field dispersie beschrijving.

23. Ellen, T. van: De invloed van afvoerfiuctuatles op de verspreiding van een verontreinigingsgolf. Uunl 1989)

24. manken. J.G. den: Afscheidssymposium prof.ir. A.C.J. Koot.

25. Hooykaas, L.J., Donza, M. en Sj.P. Klapwijk : Fosfaatbaians van de polder Reeuwijk en de Reeuwijkse plassen. Uanuari 1989)

26. Verwoerdt, P. en NazIJk, A. van: De één-dimensionale dispersievergelijking van Taylor bIJ een opdeling van de rivier in vakken. (maart 1989)

27. NazIJk. A. van: Gevoellgheidsonderzoek Alarmmodel Rijn; eindrapportage. (mei 1989)

28. manken. J.G. den en Hoogh, M.P.A.J. de: Desinfectie van behandeld afval-water met chloor: vergelijking van eenpunts- en tweopuntsdosering;

deel I: Tekst. bijlage A. B en C. deel 2: Bijlage D. E. F en G. (mei 1989)

29A. Verstappen, G.G.C.: Gedrag van organische mlcro-v.rontrelnlgingen in rivieren. Uull 1989)

29B. Mooren. J.J.M. en lIeide, J. van der: Leaching of he.vy .t.is from thermally decontamlnated soUs. (maart 1989)

30. NIeuwstad, Th.J., Wortel, N.C., Bout, F.N. van

d..

.n Altlng. 8.J.: Een vergelijking tussen ladingsgewijze en continue zulverlnc v.n afvalwater. Uuni 1989)

31. Kramer. J.P., Wouters•.J.W. en J.l1. Kop: Dynasand P'Uu.U•.Uull 1989) 32. NIeuwstad, Th.J.: Treatment of munlcipal ....t •••ter In a pllot-scale