Geografisk Tidsskrift, Bind 88 (1988)Estimation of the surface energy balance in the Sahelian zone of Western AfricaHenrik Søgaard Side 108
Søgaard, Henrik:
Estimation of the surface energy balance in the
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,
Henrik Søgaard,
associate professor, Institute of Geography,
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 STUDIESThe
climatological energy balance can be considered to
1. The radiation
balance, Rn, 2. The sensible
heat transfer, Qh, to and from the atmosphere,
3. The latent
heat of evaporation/condensation, Qe, 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 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
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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 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 Vertical transfer of sensible heatDuring 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 ![]() Fig. 1. The climatological profile mast located at Markoye. The numbers refer to the separate sensors discussed in the text. Side 110
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 ![]() Table 1. Monthly mean rainfall and standard deviation, Markoye 1955-86. ![]() (2) where Cp is heat
capacity for air: 1005 J/kg K 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 (3) ![]() filtering of the
Ri-data has been necessary before further
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. 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 turbulenceFor incorporating
the atmospheric stability, the gradient ![]() (4) where g is the
acceleration of gravity 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 which by
integrating leads to the logarithmic wind profile.
Based on the
Monin-Obukhov theory the influence of Side 111
![]() Fig. 2. Diurnal variation in wind speed (u2 - ul) and air temperature (T - Tl) differences between the two levels, 8.5 and 2 m, respectively. The data are from the 20 January 1987. incorporating a
non-dimensional function of z/L, denoted ![]() (9) combining the
equations (3) and (9), and applying the ![]() (10) dividing by
equation (2) gives ![]() Fig. 3. Diurnal variation in Richardson Number on 20 January and 2 July 1987. The January-data have been filtered through a low-pass filter. ESTIMATING SCALING TEMPERATURE AND FRICTION VELOCITYUnder unstable conditionsThe 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
![]() (12) Simple comparison
between (11) and (12) shows ![]() (13) and, more
important, -Cp p u*/Qh having the dimension
![]() (14) ![]() O6) where ![]() (\~i\
![]() and The
non-dimensional temperature gradient (ph can, according
![]() (18) As shown by
Paulson (1970), the following expression is ![]() <19) Side 112
![]() Fig. 4. Diurnal variation in the major energy balance parameters throughout 20 January 1987. where ![]() Under atmospheric
instability, Qh can now be derived ![]() Fig. 5. Diurnal variation in the major energy balance parameters throughout 2 July 1987. Sensible heat flux in stable airIn the
Businger-Dyer formulation, (j) h and (pm are equal
(20) ![]() By integrating
the expression between the two levels the ![]() (21) and analogous for
the wind: ![]() (22) Under stable
conditions Qh can now be derived from DIURNAL VARIATION IN ENERGY BALANCE COMPONENTSThe 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 daysFor
intercomparison the procedure has been applied on
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![]() Fig. 6. Variation in daily values in the major energy balance parameters during the first part of the rainy season 1987. Positive values in Qh, ET, Qs are shown downward, negative values upward. 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
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![]() Table 2. The major energy balance components, Markoye Ranch 1987 One of the main
objectives of the present study has been 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). Side 114
![]() Fig. 7. The difference between evapotranspiration and net radiation as function of midday temperature difference between surface and air. Daily values from Markoye Ranch 25 June - 9 July 1987. In a study based
on data from Sahel, England et al. ![]() (23) where c is a sensible
heat transfer coefficient. 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 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. ![]() Fig. 8. The difference between evapotranspiration and net radiation as function of midday surface temperature. Daily values from Markoye Ranch 25 June - 9 July 1987. 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. forApplicability 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 Linear regression
on the points given in table 2, leads to (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
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![]() Fig. 9. The difference between evapotranspiration and net global radiation as function of midday surface temperature. Daily values from Markoye Ranch 25 June - 9 July 1987. 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). CONCLUSIONIt 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 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. ACKNOWLEDGMENTSThe 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. ReferencesBusinger, J.
A., Wyngaard, J. C., Izumi, Y. & Bradley, E. F.
C.N.E.S,
I.N.R.A, 1.R.A.T., I.S.R.A. & D.M.N. (1987): Suivi
du Cochemé, J.
& Franquin, P. (1967): An agroclimatology survey of
Deacon, D. L.
(1969): Physical Processes Near the Surface of the
Dyer, A. J.
(1974): A review of flux-profile relationships.
Boundary-Layer 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.
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
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. |