Søgaard, Henrik: Estimation of the surface energy balance in the
Sahelian zone of Western Africa. Geografisk Tidsskrift 88: 108-115.
1988.

In studies of desertification in the Sahelian zone of Western Africa an improved knowledge of the water and surface energy balance is recognized to be oj_'major importance. Based on micro-climatological measurements collected during an ongoing field study in the northern part of Burkina Faso, a number of methods for deriving surface energy balance are examined. It is found that for the actual case, with profile measurements restricted to two levels above the surface, exact values of the sensible heat flux can accurately be obtained by applying non-dimensional gradients based on the Monin-Obukhov turbulence theory. Utilization of the results for deriving actual evapotranspiration from standard observations is demonstrated, and the paper finally discusses applicability of the results in satellite remote sensing.

Keywords: Climatology, Energy balance, Sahel, Desertification,
Actual evapotranspiration. Sensible heat flux.

Henrik Søgaard, associate professor, Institute of Geography,
University of Copenhagen, Øster Voldgade l O, DK-1350 Copenhagen

As an integrated part of the EEC-sponsored project: "Characterisation par les techniques de télédétection de la dynamique de la desertification å la périphérie du Sahara", a Danish remote sensing project on desertification was initiated in 1987 aiming at the development of algorithms for deriving agro-climatological parameters and vegetation indicators from satellite data. The intention was that these algorithms should be designed for use in a microcomputer-based image processing system. During a parallel phase of the project this low cost image processing system was developed on a microcomputer with a worldwide distribution net. For a further discussion of the image processing system reference is made to Rasmussen et al. (1987).

As most of the existing algorithms for deriving the surface energy balance from satellite were developed and calibrated in other climatic regions and their transferability to the Sahelian zone was not known beforehand, it was decided to conduct a field experiment in a typical part of the area. This was found in the Oudalan province in the northern part of Burkina Faso, approx. 16° N, 0° W., a region with a yearly rainfall of less than 400 mm. A proper climatological description of the region is found in Cochemé and Franquin (1967).

West of Markoye town an automatic agro-climatological station was established within an area designated to the governmental cattle-breeding station called Markoye Ranch. The location of the mast is indicated on fig. 1, and as seen, the mast is surrounded by single acacia-like trees, while the surface is covered by grass and small bushes.

During the rainy season 1987 comprehensive field studies were conducted on both climate and vegetation. The present paper only considers the climatic aspect of the field survey; further details for the rest of the field program are found in Rasmussen et al. (1987).

METHODOLOGY FOR ENERGY BALANCE STUDIES

The climatological energy balance can be considered to
consist of the following four major terms:

1. The radiation balance, Rn,

2. The sensible heat transfer, Qh, to and from the

atmosphere,

3. The latent heat of evaporation/condensation, Qe,
4. The soil heat flux, Qs.

In short, the energy balance equation shows how the available surplus of radiation energy is used at the surface. As all other energy terms, e.g. the consumption by photosynthesis, numerically are of much less importance, the energy balance can be formulated as follows:

(1)

The three right-hand components (Qh, Qe, Qs) are regarded
as positive when energy is directed away from the
surface toward either atmosphere or soil.

As the field measurements are conducted in a remote area without power supply, it has been necessary to design an equipment which could automatically measure the basic parameters with a minimum of maintenance. The central unit is an Aanderaa datalogger with interchangeable storing unit with a capacity of 65,000 10-bits words.

On the mast 10 of the 12 sensors mounted on two cross bars placed 2.25 m and 8.5m above soil surface, while two resistance thermometers are buried respectively 1 and 10 cm below the surface. In each level are measured temperature, wind speed and humidity. The sensor-system is constructed by the Norwegian company Aanderaa. During field campaigns all of the sensors are scanned every 10 min.

Two Aanderaa pyrradiometers directed upward and downward, respectively, have been applied for estimating the global radiation and the reflected global radiation. In situ both instruments were calibrated against a standard Kipp and Zonen solarimeter.

The thermal infra-red radiation was derived from surfacetemperature
recordings utilizing the Stenfan-Bolzmanequation.
During field campaigns the surface brightnesstemperature

nesstemperaturewas measured by use of a Raytek IR-thermometer, and in the rest of the period it was calculated from soil temperature multiplied by the estimatedemissivity of 0.95.

The atmospheric counter radiation has been calculated
by the Brunt equation, with locally adjusted coefficients
(Rasmussenetal. 1987).

The soil heat flux was in some periods recorded by a heat flux plate and the derived thermal conductivity has been used for flux calculation from the recorded soil temperature

As recording of the Rn and Qs-terms is relatively
straightforward, the two remaining terms, namely Qh and
Qe, call for most attention.

Vertical transfer of sensible heat

During daytime the Sahelian environment experiences a vigorous heat load on the surface due to solar radiation. Most of the absorbed energy is distributed to the bottomnear air layers by radiation and eddy diffusion. The heating of the air implies a reduction in density which in turn generates a convective circulation. This heat convection, together with the mechanical induced turbulence due to the wind action, is the mechanism for the upward transfer of sensible heat and the downward transfer of momentum.

In the night-time the temperature profile is inverted, there is no heat convection, and even the mechanical turbulence is suppressed due to the dynamic stability of the atmosphere.

The linking between atmospheric stability and wind structure is demonstrated in fig. 2., which shows the vertical differences in wind speed and temperature on 20 January. This day was found, to be typical for the dry season with light wind, mean 2 m/s and mean temperature around 35°C.

During daytime the vertical temperature difference is fairly constant, corresponding to a temperature gradient, dT/dz, of only -4°C/100 m, which is close to the superadiabatic temperature gradient. The well developed turbulence implies very small vertical differences in speed within the boundary layer. Opposite throughout the night when there occur temperature inversions up to 20°C/100 m, the wind speed can nearly double between the two levels.

Most effectively the influence of the turbulence on heat flux can be analyzed by the eddy correlation technique. This method requires both power and computing facility, which are unavailable in the region, so this method was rejected. Instead it was decided to utilize 2-level profile measurements for the atmospheric fluxes. From the discussionin relation to fig. 2 it was clear, however, that standard algorithms assuming near neutral stability could hardly be used. This will be exemplified by inspection of one of the most applied of these equations, namely, the

Thornthwaite-Holzman formula for deriving sensible heat flux, Deacon (1969). In this formula the flux is obtained by multiplying the gradients in wind speed by gradients in temperature. As demonstrated in fig. 2 this procedure implies systematic errors with overestimation at night and severe underestimation during daytime.

Returning instead to the fundamental expression, the
sensible heat transfer can in accordance with molecular
diffusion theory be formulated as

(2)

where

Cp is heat capacity for air: 1005 J/kg K
p is air density of the air (^=1.25 kg/m3)
Kh is the eddy viscosity (m2/s)
d 9/dz is the vertical potential temperature gradient.
0 ~T+z 0.01 (dry adiabatic temperature gradient).

Having the dimension square-meter per second, Kh may be inferred as the product of eddy size and eddy velocity. This implies, however, that Kh increases non-linearly with the distance from the surface. The Kh dependency on atmospheric stability, wind speed and elevation makes a substitution of Kh absolutely necessary for practical use. This will be discussed below.

Similar to equation (2), the flux of momentum, denoted
T can be found from

(3)

filtering of the Ri-data has been necessary before further
processing. Even after filtering distinct fluctuations are
observed.

In the beginning rainy season, 2 July, the Ri-fluctuation is diminished to a level that makes filtering excessive. It is characteristic that with nearly the same radiation heat load the instability is very much less in July than in January. It is further worth noticing that in the dry season there seems to exist an upper Ri-limit of approximately 0.25. The existence of an upper Ri-limit, has been discussed by Businger (1971), who points at a number of 0.21, while 0.25 appears in a recent paper by Panopsky and Dutton( 1984).

The application of the Ri in the transfer theory is, however, difficult, as Ri depends on the distance from the surface. The Monin-Obukhov mixing Length (L) defined below, is appropriate alternative, as z/L is essentially independent of height.

(5)

where

k is von Karman constant = 0.4.
u* is friction velocity.

In the present case with its restricted number of vertical observations, it is impossible, however, to determine the mixing length directly. Instead, the Ri-z/L-relation formulated by Businger and Dyer (1974) has been applied:

(6)

Characteristics of atmospheric turbulence

For incorporating the atmospheric stability, the gradient
Richardson number, defined below, can be applied.

(4)

where

g is the acceleration of gravity
T is mean temperature, K
du/dz is the vertical wind speed gradient

Fig. 3 shows the diurnal variation in Ri during the two selected days of study, namely the 20 January and the 2 July. In the dry season there are strong oscillations in Ri during daytime, numbers go from oto -10, and a low-pass

(7)

Implementation of the turbulence theory

It is well-known that under neutral stability, i.e. strong wind and cloudy conditions, the mechanical turbulence will dominate, and here the wind shear (du/dz) can be found as

(to
W

which by integrating leads to the logarithmic wind profile.

Based on the Monin-Obukhov theory the influence of
thermal structure on the wind shear can be formulated by

incorporating a non-dimensional function of z/L, denoted
(pm

(9)

combining the equations (3) and (9), and applying the
definition u*2 = Tip , one obtains

(10)

dividing by equation (2) gives

ESTIMATING SCALING TEMPERATURE AND FRICTION VELOCITY

Under unstable conditions

The relation between z/L and (pm has been formulated in a number of empirical studies during the last twenty years. The one presented below, which is denoted the Businger-Dyer formula, is by far the most widespread, however. For other expressions reference is made to Panofsky and Dutton (1984).

(15)

(11)

comparison with the following equation defining the nondimensional
temperature gradient in accordance with
equation (9):

(12)

Simple comparison between (11) and (12) shows

(13)

and, more important, -Cp p u*/Qh having the dimension
temperature, are assigned the scaling temperature, T*;
consequently Qh can now be estimated from:

(14)

O6)

where

(\~i\
<17>

and

The non-dimensional temperature gradient (ph can, according
to Businger and Dyer, be devised as:

(18)

As shown by Paulson (1970), the following expression is
obtained by integration from level zl to level z2:

<19)

where

Under atmospheric instability, Qh can now be derived
from equation (14) after solving (16) and (19) for T* and
u* respectively.

Sensible heat flux in stable air

In the Businger-Dyer formulation, (j) h and (pm are equal
under atmospheric stability:

(20)

By integrating the expression between the two levels the
ratio temperature difference divided by scaling temperature
is obtained as:

(21)

and analogous for the wind:

(22)

Under stable conditions Qh can now be derived from
equation (14) after solving (21) and (22) for T* and u*
respectively.

DIURNAL VARIATION IN ENERGY BALANCE COMPONENTS

The algorithms given above have been assembled in an interactive Pascal computer program, which runs on the same computer system as used for the image processing mentioned in the introduction. To illustrate the results the variation in each of the parameters is given below for the same two days as shown in fig. 3 (20 January and 2 July) exemplifying the dry and wet season respectively. As 3 of the 4 terms in the balance equation are determined, the last term Qe may be found by simple arithmetic.

In fig. 4 is shown the variation in net radiation, sensible heat flux, the soil heat flux and the latent heat flux. Besides Rn, which is largely mirroring the solar radiation, the sensible heat flux is by far the most important term. In the night the sensible heat flux is directed toward the ground. It is remarkable, however, that due to the laminar flow at night the strong temperature gradient considered in fig. 2 gives only rise to a limited flux of about 10 W/m².

In fig. 5 is likewise shown the energy balance on 2 July. It is remarkable that the evaporation accounts for most of the energy consumption in the morning, while this term is reduced in the afternoon, when the soil surface becomes dry, and the soil water transfer cannot keep up with the available energy.

The energy balance on different days

For intercomparison the procedure has been applied on
all data set from the rainy season given in table 2. The
individual terms are summarized over alO hours period

from 7h to 17h. The results have been compared to results derived using the Bowen-ratio approach, and at several occasions it is found that the Bowen-ratio method gives evaporation results which are out of the range between zero and potential evapotranspiration.

Furthermore Bowen-ratio cannot be applied in dry season when there is no measurable water vapor gradient. Consequently it has been decided to estimate Qh from the approach outlined above, while the Qe term is simply found as a residual from the energy equation.

It should be noted that a rather similar procedure has

recently been applied by a French group studying agroclimatology
in Senegal (C.N.R.S et al., 1987).

For comparison with evapotranspiration (ET) all the components original calculated in MJ/day have been recalculated to mm of evaporation by dividing with the latent heat of vaporization (2.47 MJ/m²); consequently Qe is renamed to ET.

In fig. 6 is shown the variation in the same components during the first part of the rainy season. The effect of the two rainfall events, 24-25 June and 1-2 July, can be easily distinguished. During the next few days the soil surface dries out and and QH increases. It should be noticed that due to cooling effect of the evaporation on 25 June the soil temperature gradient is directed upward supplying the surface with additional energy.

Application of the results for Qh

One of the main objectives of the present study has been
to elaborate a procedure for estimating actual evapotranspiration
from field observations.

The data in table 2 has accordingly been examined in order to know whether Qe or Qh can be obtained from less comprehensive data set, (e.g. standard meteorological observations and/or satellite data).

In a study based on data from Sahel, England et al.
(1983) have proposed the following simple algorithm for
deriving heat flux

(23)

where

c is a sensible heat transfer coefficient.
Ts is the surface temperature at 14 h local time.
Ta is the air temperature 2m above surface at 14 h.

Obviously the c-factor depends on atmospheric stability and wind speed. On basis of the collected wind speed data, which show very little variation in daily mean values, it seems justified to include the wind speed contribution in the "constant".

On the other hand it has been found that the atmospheric stability, and thus heat transfer ability, varies from the dry to the wet season. As the state in the growing season is of major importance, the expression is further examined for only the wet season.

An analysis of the data presented in table 2 shows a
significant correlation between Qh and (Ts - Ta) in the
first 15 days of the rainy season 1987 (r = 0.6).

As the thermal turbulence in the air strongly depends on the heat transport from the soil surface, it is further assumed that the constant c is mainly a function of the surface temperature, so the air temperature can be ignored in equation (23). This hypothesis is supported by the data in table 2 as the correlation coefficients between Qh and temperature is improved to 0.7 when Qh is expressed as a linear function of Ts only.

Even though some deviations occur, it seems reasonable to assume that for the rainy season in this region the daily sensible heat flux can be estimated from midday soil surface temperatures.

for

Applicability estimating evapotranspiration The sensible heat flux is, however, of little practical use compared to the last term of the equation namely actual evapotranspiration. By a further elaboration of equation (1) and (23) it may be assumed that the actual evapotranspiration, ET, can be found as

(24)

where the right-hand term covers combined sensible heat
flux and soil heat flux.

Linear regression on the points given in table 2, leads to
the following relationship, shown in fig. 7:

(25)

By this approach, adopted from B. Seguin (1983), it is notable that the determined slope coefficient is practically identical with the coefficients given in the quoted studies and later confirmed in the most recent papers (Vidal, 1987).

As it was the case with the sensible heat flux the degree of
statistical significance is even improved by utilizing a

linear equation on Ts only, cfr. fig. 8.

A further inspection of the data reveals that the deficit in daily thermal infrared radiation is highly correlated with surface temperature, and it is thus rational to reduce the equation even further by substituting the absorbed global radiation (Sn) for the net radiation. This leads to the following expression:

(26)

The function is shown in fig. 9, and it is remarkable that the significant correlation is retained (-0.92), and that ET can be derived from standard observations by applying equation (26).

CONCLUSION

It has been found when applying the Monin-Obukhov theory with a number of adjustments proposed in particular by Businger and Dyer it is possible to derive consistent data on the sensible heat flux from 2-level measurements on wind speed and air temperature in the Sahelian zone of Western Africa.

The collected data support most clearly the linear model approach for deriving evapotranspiration from radiation combined with midday surface- and air temperatures. The slope of this linear function is found to be equal to what is found in studies conducted in regions with subtropical

Further reduction of the model parameters shows that
the actual evaporation can be estimated from data directly
rectlyavailable from satellite observations, namely surface
temperature and absorbed global radiation.

Due to the agreement with the quoted studies, it seems, justified to conclude that the results support the view that actual evapotranspiration in this part of Sahel can be monitored directly by using satellite data even though the general validation is not, yet, completed.

ACKNOWLEDGMENTS

The present work has been funded by EEC, DGVIII, to whom the author wishes to express his gratitude. Thanks is due to Anette Reenberg, Søren Kristensen and Carsten E. Hansen for kind assistance during the field work in Burkina Faso.

References

Businger, J. A., Wyngaard, J. C., Izumi, Y. & Bradley, E. F.
(1971): Flux profile relationships in atmospheric surface layer.
J. Atm. Sci. Vol. 28, p. 181-189.

C.N.E.S, I.N.R.A, 1.R.A.T., I.S.R.A. & D.M.N. (1987): Suivi du
bilan hydrique å l'aide de la télédétection par satellite. Application
au Senegal. Rapport Final.

Cochemé, J. & Franquin, P. (1967): An agroclimatology survey of
semiarid areas in Africa south of the Sahara. WMO Techn.
Note 86.

Deacon, D. L. (1969): Physical Processes Near the Surface of the
Earth. In World Survey of Climatology, Vol 2, p. 39-103.

Dyer, A. J. (1974): A review of flux-profile relationships. Boundary-Layer
Meteorol. Vol. 7, p. 363-372.

England, C. E., Gombeer, R., Hechinger, E., Herschy, R. W., Rosema, A. & Stroosnijder, L. (1983): The Group Agromet Monitoring Project: Application of Meteosat Data for Rainfall, Evaporation, Soil-Moisture and Plant-Growth Monitoring in Africa. ESA Journ. Vol. 7, p. 169-188.

Panofsky, H. A. &Dutton, J. A. (1984): Atmospheric Turbulence.
Models and Methods for Engineering Applications. John Wiley
& Sons, New York, 1984.

Rasmussen, K., Folving, S., Holm, J. & Søgaard, H. (1987): Microcomputer oriented methodologies for deriving agro-climatological parameters and vegetation indicators from satellite data. Final Report, internal CEC-report.

Seguin, B. & Itier, B. (1983): Using Midday Temperature to
Estimate Daily Evaporation from Satellite Thermal IR data.
Int. Journ. Rem. Sens. Vol. 4, p. 371-383.

Vidal, A., Ken, Y., Lagouarde, J. P. & Seguin, B. (1987): Télédétection et bilan hydrique: utilisation combinée d'un modele agrométéorologique et des données de FIR thermique satellite NOAA-AVHRR. Agr. Met. Vol. 39, p. 155-176.