An evaluation of grassland evapotranspiration

Agricultural Me teorology, 11 ( 1973 ) 373 - 383 © Elsevier Scientific Publishing Company, Amsterdam- Printed in The Netherlands

AN EVALUATION OF GRASSLAND EVAPOTRANSPIRATION LAWRENCE C. NKEMDIRIM and PAUL F. HALEY Department of Geography, University of Calgary, Calgary, Alta. (Canada) (Accepted for publication September 14, 1972)

ABSTRACT Nkemdirim, L. C. and Haley, P. F., 1973. An evaluation of grassland evapotranspiration. Agric. Meteorol., 11 : 373-383.

Evapotranspiration in a grassland area was estimated by the energy balance method and by the Penman combination model. An equation of the form A = P(ln D)a was obtained for estimating actual evapotranspiration when the potential rate and the number of days following a period of significant wetting is known. Evapotranspiration declined from the potential rate as soil moisture decreased. The Bowen ratio was used to indicate evaporative stress as the summer advanced. The ratio showed a strong negative correlation with rainfall. INTRODUCTION A number of methods are available to hydrologists and climatologists for calculating evaporative moisture loss. Two of the best known methods are the energy budget approach and the Penman combination model. The energy budget approach The energy budget is represented by the equation: R =LE+H+G

(1)

where R is the net radiation; L E is the water vapour flux; H is the sensible heat flux and G is the soil heat flux. The net radiation can be measured with an all-wave net radiometer and the soil heat flux can be determined by the use of the Fourier heat conduction equation given by: G = Gz +

pc

dz

(2)

where G is the heat flux through the surface; Gz the heat flux across a reference depth z; pc is the heat capacity and OT/at at the time temperature gradient between the surface and the reference depth z. Nkemdirim and Yamashita (1972)have dealt with the problem of evaluating eq.2 and indicated that provided soil moisture is measured continuously the

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L.C. NKEMDIRIMAND P. F. HALEY

G term can be calculated with comparative ease. The determination of the soil heat flux allows the combined water vapour flux and sensible heat fluxes to be treated as a residual energy. Thus:

R - G = L E +H

(3)

Bowen (1926) developed the ratio: H L--E = 13

(4)

as a simple method of assigning correct values to the two fluxes. He found that by taking measurements of the temperature of the evaporating surface and the temperature and humidity of the over-lying air, the gradients AT/Axz and Aq/2xz can be found. Based on the assumption that the rate of transfer of heat and water vapour is equal at low levels in the atmosphere, 13may be calculated by the equation: 14 _ Cp a r

13-LE

L ~q

(5)

where Cp is the specific heat of air at constant pressure;L the latent heat of vapourization and ~T/Oq the ratio of the temperature and specific humidity gradients at two levels. It can then be shown that:

R-G LE - 1 +/3

(6)

and:

R-G H = 1 +1/~

(7)

In spite of the shortcomings of the method discussed by Deacon et al. (1958) the method has been used successfully by Mukammal et al. (1966), Storr et al. (1970) and Nkemdirim and Yamashita (1972) to determine evapotranspiration. Budyko (1956) and Chang (1965), among others, have shown that where water supply is unlimited the bulk of the available energy is used in the evaporation process.

The Penman model Penman (1948) considered the difficulty of obtaining adequate data for the use of the Bowen ratio as a tool for estimating evaporation. He suggested that the estimation could be facilitated by employing humidity and temperature measurements taken at only one level (2 m) and replacing the inter-height differences in humidity by a statement which reflects the vapour pressure deficit. This second modification altered the evaporation problem in a substantial way in that what is being estimated is the water vapour content. This is the socalled potential evapotranspiration which defines the upper limit of evaporation under the

EVALUATION OF GRASSLAND EVAPOTRANSPIRATION

375

existing atmospheric condition. It can be readily seen, therefore, that the potential evapotranspiration is a function of atmospheric characteristics. It follows that if water is available in unlimited quantities over a surface, the potential evapotranspiration is equa~ to the actual evapotranspiration. Under this circumstance, the Penman and Bowen models should yield similar results. On the other hand, when water is restrictive, the actual evapotranspiration should be less than the potential. Operationally, the difference between potential and actual evapotranspiration is a measure of water need and, m agriculture, this difference has to be supplied through irrigation if optimal plant development is desired. The question as to what point in time marked departure in potential rate becomes evident has been discussed by Budyko (1956) who, quoting from work carried out by Alpatev in Russia, suggested that evaporation from field crops is close to potential value when soil moisture is not lower than 70-80% of field capacity. Marlatt et al. (1961) concluded from field experiments with beans planted in sandy loam soil that evaporation will proceed at potential rate until about 84 mm of water per metre depth of soil (below field capacity) has been withdrawn. Denmead and Shaw (1962) maintained that the transpiration rates do not start to decrease until the soil moisture is near permanent wilting point. They concluded from evidence available to them that plant wilting begins as soon as the evaporation rate starts to decrease from its potential value rather than at the permanent wilting point. Sellers (1965) thought that evapotranspiration rates would decrease linearly with decreasing soil moisture. This paper examines three aspects of the evapotranspiration question: (1) the seasonal variation in the Bowen ratio; (2) the relationship between actual and potential evapotranspiration; and (3) the relationship between transpiration rates and soil moisture.

METHOD The method used for evaluating actual evapotranspiration was the energy balance method and involved the use of the Bowen ratio calculated on an hourly basis. The parameters for calculating the ratio - inter-height differences in temperature and specific humidity, net radiation and soil heat flux - were measured. Temperature and humidity were both measured at 0.5 and 2 m. The soil heat flux was determined from eq.2. The Penman model was used for evaluating potential evapotranspiration. Soil moisture was measured with a neutron probe calibrated under field conditions. A twin-tank lysimeter was used to check the accuracy of the Penman modeh All measurements were taken in the University Weather Research Station experimental farm. A fetch ratio of better than 10:1 was maintained on the site. The soil depth is approximately 3 m. It is slightly basic and of the black chernozem variety. The organic matter ranged from 3 to 11% in the first 50 cm depth. At this level moisture volume fraction at field capacity was estimated at 30%; 10% represented permanent wilting point. The natural vegetation over the site was prairie grass.

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L.C. NKEMDIRIM AND P. F. HALE¥

The experiment was conducted from about mid-June to mid-August, 1971. The general weather condition and soil moisture are given in Fig.1. A fairly wet and cool early summer was followed by a dry, hot late season. 25

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Bowen ratio and actual evapotranspiration It has been pointed out that the Bowen ratio represents the sharing of the residual energy between sensible heat transfer to the atmosphere and latent heat. When moisture is unrestricted in its supply, almost all the available energy is used up in the evapotranspiration process and the Bowen ratio should approach zero. Thus, it could be rightly said that values of the ratio close to zero in daytime represent conditions in which evapotranspiration is at or near the potential rate. Conversely, high values of the ratio are typical of days when the actual evapotranspiration is less than the potential since the bulk of the residual energy is beingused for direct heating of the atmosphere. Examination of Fig.3 and the precipitation portion of Fig. 1 reveals the negative correlation between the ratio and wet days. Fig.2 shows the frequency of the daytime Bowen ratio throughout the period investigated. If the arbitrary ratio of 0.2* is used *The value 0.2is not quite so arbitrary. Chang (1965) and Budyko's (1956) work seem to suggest that this is probably a good cut-off point. Moreover, lysimeter and Penman model values indicated that this cut-off point is not unreasonable.

EVALUATION OF GRASSLAND EVAPOTRANSPIRATION

377

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Fig.2. The frequency of hourly Bowen ratios. as a cut-off point for potential evapotranspiration, it was estimated that on approximately 65% of the period maximum transpiration was taking place. Very high values of/3 were uncommon throughout the season. Fig.3 shows the daily distribution of the ratio. The superimposed smooth curve shows a gradually rising trend with advancing season. Viewed in conjunction with the soil moisture pattern (Fig. 1), the correspondence of the trend with increasing soil-moisture stress becomes evident. The trend also corresponds to drought conditions. The Bowen ratio could, therefore, be used as a measure of either soil-moisture stress or as an index of evaporative stress since it relates directly to the availability of evaporative water. It is to be noted that irregularity in pattern is directly linked to irregular surface wetting.

Comparison of actual to potential evapotranspiration Potential evapotranspiration calculated through the Penman model was checked against lysimeter readings. The figures were in close agreement except when the prairie

378

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grass surrounding the lysimeter showed signs of dormancy. At those times, the lysimeter values exceeded those obtained through the model. Inhomogeneity of surface conditions resulting in oasis effect was held responsible for the discrepancy. Fig.4 shows that for most of June and early July the paths followed by actual and potential evapotranspiration were similar but late in the season the directions ran

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opposite each other. The season was clearly divisible into 2; namely, a wet (Period 1) and a dry (Period 2) period. The mean values of actual and potential evapotranspiration and other relevant information are contained in Table I.

EVALUATION OF GRASSLAND EVAPOTRANSPIRATION

379

TABLE I Periods of evapotranspiration Evapotranspiration

Potential Actual

Period I (40 days)

Period 2 (12 days)

mean value (mm)

standard number of deviation rain days

mean value (mm)

standard number of deviation rain days

3.09 2.79

0.78 0.78

4.45 2.00

0.52 0.77

13 13

0 0

A plot of actual against potential evapotranspiration (Fig.5) showed two distinct clusters separated by an intermediate area. On examination, the upper cluster represented points obtained for days in which a storm event was recorded and up to three days after the event, while the lower cluster represented points several days after a significant storm event. While the relationship between the two factors was close to 1 : 1 for the 70 •

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Fig.5. Actual evapotranspiration vs. potential evapotranspiration. upper cluster, actual evapotranspiration was only 45% or less of the potential for the lower points. If a line were drawn through the origin o f the co-ordinate system to each point, actual evapotranspiration could be expressed in terms of the tangent of the angle a separating the point and the potential evapotranspiration axis and potential evapotranspiration. Thus, in the schematic diagram below (Fig.6):

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L.C. NKEMDIRIM AND P. F. ttALEY

Actual Evapotransplratlon (P,A)

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Potential Evapot ranspiration

Fig.6. Schematic representation of the relationship between daytime actual and potential evapotranspiration. A = P tan a

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It can be seen that the larger the departure from potential evapotranspiration, the smaller the angle. The tangent of a can be described as an evaporative stress index. It can also be used as an index representing the resistance of the surface to moisture withdrawal from it. The indexes calculated in Table II were used as the basis for Fig.7 and the response of the stress to storm events is readily discernible. Exploiting this response, the size of the index TABLE II Evaporative stress index Date

Index

Date

Index

June 25 July 1 July 4 July 12 July 17 July 18 July 19

0.824 0.740 0.613 0.795 0.700 0.687 0.543

July 25 July 28 July 30 July 31 Aug. 1 Aug. 11

0.781 0.933 0.810 0.754 0.570 0.566

was then related to the number of days, D, elapsing since the last significant wetting (rainfall of 5 mm or more). The relationship was expressed by the equation: tan a = (In D) -°'lT°s

{9)

Substituting for tan c~ in eq.8 we have: A = P[(in D)-°'lT°S l

(10)

Eq. 10 is made operational if the potential evapotranspiration and the D are known. A test of the formula showed agreement with "observed" values to 95%.

EVALUATION OF GRASSLAND EVAPOTRANSPIRATION

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Actual evapotranspiration and soil moisture The soil is the main source of moisture for many plants, and transpiration is one way in which the soil moisture is depleted. The level at which soil moisture evapotranspiration falls off significantly from the potential rate is an issue which has been referred to earlier. Soil moisture was monitored regularly with a neutron probe. Part of Fig.1 shows its distribution during the field season, and its size depended on rainfall since no irrigation was applied to the plot. The maximum soil-moisture volume fraction monitored was about 20%, 10% below field capacity. Fig.8 shows the ratio Ea/Ep, where Ea is the actual potential evapotranspiration and Ep the potential. It is clear that evapotranspiration proceeds at, or dose to, the potential rate at moisture volume of 18%. Thus, for 1 m layer of soil whose field capacity is 30%, it is possible for 120 mm of moisture to be withdrawn before pronounced departure from potential rates becomes evident. The change of transpiration rate with soil moisture is demonstrably non-linear, but follows an almost exponential curve. With soil moisture below 11%, the actual evapotranspiration remains virtually unchanged. The grass surface must assume dormancy at this stage, and any water lost must be directly from the soil surface. CONCLUSION This paper has shown that the Bowen ratio could be used as a measure of climatic stress. An evaporative stress index can be determined as a function of number of days following a significant wetting of the surface. This in turn forms a basis for determining

382

L.C. NKEMDIRIM AND P. F. HALEY

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actual evapotranspiration when potential evapotranspiration is known. Soil moisture as low as 18% by volume can support evapotranspiration in grassland at the potential rate. ACKNOWLEDGEMENTS

The research presented in this paper was partially supported by the National Research Council of Canada and the Department of Geography, The University of Calgary. REFERENCES Bowen, I. S., 1926. The ratio of heat-losses by conduction and evaporation from any water surface. Phys. Rev., 27: 779-787. Budyko, M. I., 1956. The Heat Balance of the Earth's Surface (translated from Russian, N. A. Stepanova U.S. Dep. Agric., Washington, D.C.

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Chang, J., 1973. On the study of evapotranspiration and water balance. Erdkunde, 19: 141-150. Deacon, E. L., Priestly, C. B. and Swinbank, W. C., 1958. Evaporation and the water balance. In: Climatology, Reviews of Research. UNESCO, pp.9-34. Paris. Denmead, O. T. and Shaw, R. H., 1962. Availability of soil water to plants as affected by soil-moisture content and meteorological conditions. Agron. J., 54: 385-390. Marlatt, W. E., Havens, A. V., Willits, N. A. and Brill, G. D., 1961. A comparison of computed and measured soil moisture under snap beans. J. Geophys. Res., 66: 535-541. Mukammal, E. I., King, K. M. and Cork, H. F., 1966. A comparison of aerodynamic and energy budget techniques in estimating evapotranspiration from a cornfield. Arch. Meteorol. Geophys. Bioklimatol., Ser. A, pp.384-395. Nkemdirim, L. C. and Yamashita, S., 1972. Energy balance over prairie grass. Can. J. Plant Sci., 52: 215-225. Penman, H. L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. (London) Ser. A., 193: 120-145. Sellers, W. D., 1965. Physical Climatology. Univ. of Chicago Press, Chicago, I11., 272 pp. Storr, D., Tomlain, J., Cork, H. F. and Munn, R. E., 1970. An energy budget study above the forest canopy at Marmot Creek, Alberta, 1967. Water Resour. Res., 6(3): 705-716.