meteorological and soil factors affecting evaporation from fallow soil

551.573 METEOROLOGICAL AND SOIL FACTORS AFFECTING

EVAPORATION FROM FALLOW SOIL

By H. L. PENMAN, M.Sc.. Ph.D., A.1nst.P.

(Communicated by Dr. B. A. KEEN, D.Sc., F.Inst.P., F.R.S.) [Manuscript received July 1, 19401

SUMMARY Using the conception of natural periods, for which the difference

between rainfall and drainage can be equated to the evaporation, the mean daily rates of evaporation from a block of fallow soil a t Rothamsted are examined for 94 periods varying in length from 13 to 45 days. In seeking correlations with single daily meteorological observations two types of treatment are employed. ( I ) The year is considered in three seasons of four months each-sumnier, winter and two equinoctial pairs of months-and it is shown that an almost complete description of evaporation can be obtained in terms of rainfall only, the nature of the correlation varying from season to season. (2) A general treatment is attempted in physical terms, considering evaporation as due to diffusion across a non- turbulent boundary layer whose thickness is determined by wind velocity, the soil surface being assumed to be continuously a t IOO per cent R.H. The general agreement between observed and predicted values is very good in winter. The summer data are shown to lie between the theoretical limits imposed by the assumptions of (i) continuous IOO per cent R.H. a t the surface, and (ii) a steady retreat of the ICO per cent R.H. layer into the soil, i.e., no upward movement of liquid during the evaporation process. The considerable scatter in the data is attributed partly to the inadequacy of single daily meteorological observations but chiefly to the lack of knowledge of the conditions existing at the soil surface.

The data on which this survey is based are the q.00 h. meteorological readings a t Rothamsted and the daily totals of rainfall and drainage as recorded by the I/I,OOO acre gauges installed by Lawes and Gilbert in 1870. The soil of the drain gauges is in its natural undisturbed state, fallow and uncultivated. Since 1870 there have been several papers dealing with different aspects of the drainage data and these are discussed in a general survey of the records (Penman and Schofield, 1941) ; a brief recapitulation of the relevant parts of this survey will serve as a basis for the present account.

One of the main objectives was the establishment of the conditions under which the difference between the total rainfall and the total drainage of a selected period-generally defined as the " deficit " of the period-can be equated to the evaporation which has occurred in that period. The conditions are satisfied for a " natural " period, which is the interval between the cessations of two falls of rain that cause drainage, the total drainage being

401

402 H. L. PENMAN

measured between the two cessations of percolation. Hence the drainage period is slightly out of phase with the rainfall period owing to the time taken for complete discharge, and for accurate demarcation of natural periods it is essential that each fall of rain shall be followed by at least one rainless day. This does not always occur, and for greater convenience in observation the prac- tical natural period is taken as the interval between two cessations of drainage, or between two well-marked drainage minima. This introduces two end errors which tend to annul each other and the resultant error is no greater than that involved in taking one day as the unit of time. No actual natural periods were examined- that is one of the present objects-but the conception was applied to consider how far arbitrary periods could be regarded as approxi- mating to natural periods. Satisfactory arbitrary periods were considered and the conclusions drawn from them were:-

(a) Civil Years. Annual evaporation (1881-1934) is nearly constant, increasing slightly with annual rainfall ;

( b ) Half Years. (i) Winter (0ct.-March inclusive) evaporation is constant and independent of rainfall. There is some scatter in the data which is not due to variation in mean air temperature;

(ii) Summer (April-Sept. inclusive) evaporation is about twice as great as that for winter and shows marked dependence on summer rainfall. The mean curve for the data .is approximately parabolic with unit slope near the origin. Part of the small scatter in the data is attributed to the effects of rainfall distribution in summer seasons ;

( c ) Long period mean monthly totals. The twelve so-year means are uniquely dependent upon the " evaporating power " of the air, which is, in effect, the mean saturation deficit in mm. of mercury. A similar plot against mean air temperature yields a loop with spring values about 50 per cent greater than autumn values at the same mean temperature. The winter data agree with estimates made for evaporation from an open water surface, but the summer values fall below the open water curve, and are nearly constant.

Individual calendar months were rejected as unsuitable for the following reasons :-

( I ) Rain or snow falling near the end of one month may con- tribute to the drainage of the nest, i.e., the measured monthly deficits are over- and under-estimates of the evaporations in the respective months ;

( 2 ) The evaporation occurring during a rainless period a t the end of one calendar month will be included in the deficit of the next, i.e., the evaporations will be under- and over-estimated respectively ;

(3) In case ( 2 ) a further source of error arises when correlations are made. The deficit of the second month is due to the evaporation of the second month and part of the first ; for correlation purposes the meteorological conditions should be averaged over the same period and not over the second month only.

In a statistical note following the general survey, Sahni (1941) examined short natural periods of two to thirteen days in June, July and August, and concluded that a cubic regression on rainfall

EVAPORATION FROM FALLOW SOIL 403

accounted for most of the variance in evaporation, the residual variance being non-significantly correlated with mean wind velocity and relative humidity, the signs of the coefficients being a s expected.

The purposes of the present account are:- (i) to extend the examination of evaporation to longer natural

periods in all seasons of the years; (ii) to attempt to obtain greater precision in evaluating the

" evaporating power '' of the air so that a physical inter- pretation rather than an empirical statistical correlation can be employed ;

(iii) to see how far single daily meteorological observations can be used to estimate the evaporating power; and

(iv) in the light of the deficiencies thereby exposed, to indicate what supplementary observations may be needed.

SEASONAL EVAPORATION AND RAISFALL

Ninety-four natural periods varying in length from thirteen to forty-five days and covering the years 1927-1939 have been con-

FIG. 1.-Dependence of seasonal evaporation on rainfall.

sidered. The mean. daily rates of evaporation are shown in Fig. I plotted against the mean daily rainfall. To show seasonal effects the year has been split into three groups of four months and to avoid confusion only two sets of data are plotted. They are summer (May-Aug. inclusive) and winter (Nov.-Feb. inclusive). The points for periods falling in the equinoctial pairs of months overlap those for the summer and winter periods. The dotted curve is that obtained by Sahni for shorter summer periods, and, considering the almost four-fold extrapolation, the agreement is good. The main features of the figure correspond to those noted above ( b , (i) and (ii)) for half-years. The winter data show no obvious dependence on rainfall ; the summer data show a positive correlation with rainfall, the values asymptotically approaching the line

404 H. L. PENMAN

of unit slope near the origin. No points can lie above this line because for a natural period the deficit cannot exceed the rainfall.

'The causes of the scatter of the points will be considered later. The curves show that if one is prepared to regard the year as built up of two or three seasons,. the main features of evaporation can be interpreted in terms of regressions on seasonal rainfall alone, with a different regression for each season. To unify the data some factor allowing for seasonal variation in evaporation at constant rainfall is needed. The obvious choice is mean air temperature, and while the analysis of Crowther (1930) showed that mean seasonal temperature varied in phase with seasonal evaporation, that of Koshal (1934), confirmed by Sahni, showed that variations in mean air temperature were quite ineffective in accounting for intra-seasonal fluctuations such as are represented in the scatter of the points of Fig. I .

It was the need for some other seasonal factor which led Penman and Schofield to attempt an approximate explanation in terms of the physical factors involved, and in the following section this approximate treatment is amplified.

EVAPORATING POWER

The process of evaporation is regarded as due to molecular diffusion of water vapour across a non-turbulent boundary layer immediately above the soil surface, the thickness of which is determined by the wind velocity, into a turbulent atmosphere where the diffused vapour is carried away. The movement of water to the soil surface may be as liquid or vapour. In the former case, if the supply is sufficiently rapid, the surface may be kept at 100 per cent R.H. and evaporation will proceed at a rate which is dependent only on air conditions. In the latter case, where the saturated layer is below the surface, the soil itself will impose a resistance to vapour movement and the rate of evaporation will be correspondingly reduced, and will be dependent on both soil and air conditions. 'The evaporating power is taken to correspond to the first case and in attempting a quantitative estimate the following assumptions are made :-

(i) The surface of the soil is kept at 100 per cent R.H.; (ii) The soil surface temperature has the same value as the

(iii) The daily mean for each is given by the mean of maximum

(iv) The mean daily humidity is given by the q.00 h. reading ; (v) Mixing of diffused water vapour is so complete in the

turbulent layer that the R.H. immediately above the boundary layer is given by the value in the screen ;

(vi) The thickness of the boundary layer is determined by the wind velocity estimated from the Beaufort reading at 9.00 h. The rate of evaporation per unit area is then given by

air temperature in the screen ;

and minimum air temperatures ;

D (pl - p,)i7Cm 1 cc. vapour per second,


where D is the coefficient of diffusion of water vapour into air =.024 cm.z/sec. at IoOC.

p , - p , is the partial pressure drop across the boundary layer = ( I - R.H.) x saturation V.P. a t air temperature.

1 is the thickness of the boundary layer=&/V cm. where V is the wind velocity in cm./sec. (see e.g. Brunt, 1934).

The mean Beaufort figure for the 94 periods is 2.00 , which has been taken as equivalent t o 240 cm./sec. Hence the mean value of 1 is 0 2 5 cm., and making the necessary conversion of units, the mean daily rate of evaporation becomes

3.48 x I O - ~ x ( p , - p , ) x Blz.00 in. per day where (p , -p , ) is in mm. of mercury and B is the mean Beaufort number for the period examined.

CORRECTION OF OBSERVED EVAPORATION FOR R.\IXFALL

The evaporating power is serving a double function. In the first place, it is being used to distinguish the members of the family of curves which could be drawn for different seasons as in Fig. I ; in the second, when the assumptions of the preceding section are satisfied it is being used to give an estimate of the actual evaporation. A prion' we know that in summer the first of these assumptions will only be reasonable for a short time after a fall of rain and the evaporating power will represent the upper limit of possible evaporation.

In using evaporating power as a parameter distinguishing the seasonal regressions on rainfall it is necessary to standardise the rainfall conditions, and in the absence of any formal guide it is proposed that the observed evaporation be corrected to that for a rainfall of 0.08 in. per day. The correction factors have been obtained from the regression equations of Koshal connecting monthly drainage and monthly rainfall. Recast, these fall into the form

R-D=a+bR! , or A (R-D)=bARt, where AR' is the deviation from' the mean rainfall. The constant b varies cyclically throughout the year from a December minimum of 0 0 1 5 t o a July maximum of 0.50. In the absence of a diagram showing the measured evaporation before correction the general effect can be seen by comparing Figs. I and 2 . In the former, the range of summer data is from 0 0 2 6 to 0100 in. evaporated per day ; in the latter, the range of the same data, corrected, is 0038 to 0og1 in. per day. The correction has little effect on equinoctial data and' practically none on winter data.

The results plotted in Fig. 2 are for all the available data, the three types of season being distinguished. Again temporarily ignoring the scatter, we can follow the seasonal changes in evaporation and note that for a considerable part of the year the points lie near the line of unit slope, confirming the inference from the earlier study that for the period October to March the evaporation from fallow soil is the same as would occur from an open water surface under the same meteorological conditions. .4s anticipated, the summer points lie below the line of unit slope, indicating that

This is a fifty year mean value.

406 H. L. PENMAN

under the more severe drying conditions the supply of water to the soil surface has not been sufficiently rapid to keep the surface at 100 per cent R.1-I.

,

0

I I 5 10

&&A&& E ~ a p r a G q &vu- o f R > ( * p e % ~ d )

FIG. 2.-SeasonaI evaporation from fallow soil (Rothamsted).

EVAPORATION IN THE ABSENCE OF LIQUID MOVEMENT TO THE SURFACE

The evaporating power of the air sets an upper limit to seasonal evaporation. A lower limit can be found by assuming that soil effects exert their maximum influence, and in the following very approximate treatment an estimate of the order of magnitude is made. It is assumed that no liquid movement upward occurs and that the layer at 100 per cent R.H. retreats within the soil as the evaporation proceeds. The process is then doubly hindered ; (u) by resistance in the soil, and ( b ) by resistance in the boundary layer. The impedance of the soil (2,) is given by

Z , = x / o 6 6 S D A (Penman, 1940) where z is the depth of the layer at IOO per cent R.H. ;

S is the fractional pore-space of the soil; D is the coefficient of diffusion into air; A is the area of cross-section; 0.66 is an experimentally determined constant.

For the air, 2,=1/0.4 as before, and the instantaneous rate of evaporation becomes

( p , - p , ) / 7 6 0 (2, + 2,) cc. vapour per sec. As evaporation proceeds the value of x increases, i.e., the

instantaneous rate decreases. 'Taking S as 0.5 and using the mean value of Z(0.25 cm.) and, integrating the equation set up, we obtain

0126 E2+1.04 E-3.48 P = o


where E = total evaporation in units of O O I in. in i days ;

i.e., E l r is the mean daily rate of evaporation for a period of i days.

In a natural period the soil may be re-wetted several times by rain. W e assume that the effective number of such re-wettings is given by the number of days on which the precipitation exceeds the mean daily evaporation for the period and that the value of r is obtained by dividing the number of days in the period by the number of such " wet " days. Table I shows the seasonal variation of r and p , - p,, the means being taken by months, so that for each month a value of P is known and the twelve solutions of the quadratic can be found. From these the mean daily evaporations follow and they are plotted on Fig. 2 against the corresponding values for zero soil impedance. The actual points are not shown as they lie on a fairly smooth curve, a result not implicit in the analysis.

P=product of 7 and ( p , - p 2 ) ;

TABLE I Month hfean r Mean ( p , - p , ) P E Evaporation Evaporating power

(daysi (mm.) per day (in.) of air (in. per day) I I . 8 j 0 5 7 I'Oj 2 5 1'3j x 10-1 2'00 XIO-' 2 2.3 0'77 I 75 3'8 1.65 2'70

1'28 6 2 2'30 4'50 7-53 2 80 600

3 2'7 2.6

5 2'95 2'22 6 jj 9 6 3'2j 7'75 6 3.85 3'02 11.60 13'7 3.55 106J 7 3'3 2.08 6 8 j 9.8 3.00 7'30 8 3.1 2'22 6 . 8 j 9.8 3'1.5 7'75 9 28 1.60 4 ' jo 7.5 2'70 5.60 I0 2'7 1.10 2.95 5.6 2'0 j 3-85 11. 1 '6j 062 1'00 2'4j I'jO 2'1 j I 2 1 9 0'53 I 00 2'4j 1'30 I .8j

There are so many assumptions involved in the derivation of the curve that it can only be claimed as representing the order of the daily evaporation to be anticipated in the absence of liquid movement to the surface. Except near the origin it lies below the observed points, and this is still true of the data before the rainfall correction is applied.

CAUSES OF SCATTER IN DATA

( a ) General The main sources of error lie in the approximate nature of

the estimates of evaporating power. Accepting the mean of maximum and minimum air temperatures as the daily mean air temperature, it will not in general represent the mean soil.surface temperature. The error in winter may easily amount to 0 5 O C . or more, which will cause an error of 07 x IO-? in. per day in the estimated evaporating power. Accepting this amount of tolerance on either side of the line of unit slope, most of the scatter can be taken up. In summer the effect of radiation will be to raise the soil surface temperature above the air temperature and the soil mean will generally be greater than the air mean. The evaporating power of the air will thus be an under-estimate of the potential

408 H. L. PENMAN

evaporation from the soil surface, but as the evaporation is also dependent upon soil conditions large variations in air conditions may have little effect on the observed evaporation. In the inter- mediate seasons cooling of the surface by evaporation and heating by radiation may again cause differences in mean temperatures sufficient to account for much of the scatter of the points.

The og.00 h. readings of humidity will not be the same as the daily means; the error will not be the same in all seasons, but in magnitude it is probably not as important as that due to temperature.

The wind data must be similarly criticised. For precision anemometer readings should be used. The Beaufort readings have been used here for three reasons.

(i) The rain-gauge enclosure is t mile away from the wind

(ii) The enclosure is somewhat sheltered to the south and

(iii) The drain-gauges have a stone coping 10 cm. high which

These last two reasons considerably reduce the accuracy of the estimate of the thickness of the boundary layer, and the scatter of the points in Fig. 2 is little worsened by using the mean value of I for all points. In view of the uncertainty, points with mean Beaufort numbers less than 1.3 or greater than 3.0 have been queried ; these may be legitimately disregarded in making the com- parison between observed and predicted values of daily rates of evaporation.

( b ) Particular (i) Winter. Many winter periods include snow falIs. Drifting

may cause unequal distribution so that the recorded " rainfall '' is not always a true measure of the actual precipitation on the surface of the drain-gauge. Frost may hold up drainage near the end of a natural period thus leading to an error in the estimation of the evaporation.

The main cause of the summer scatter probably arises from differences in rainfall distribution in time. A fall of 0.8 in. of rain in one day rarely fails to produce drainage; the same amount spread over 10 days in summer is generally completely evaporated, and the more often the soil is rewetted the greater is the amount of summer evaporation. In general this means that the greater the total summer rainfall the greater will be the summer evaporation (Fig. I ) , but in periods of equal totals and with other factors equal there will be variations in summer evaporation depending upon rainfall distribution. The most favourable case will be that in which the showers fall at intervals frequent enough to keep the soil surface wet; the observed points will then lie on the line of unit slope. An extreme case of formal interest is that in which rain falls continuously. Presumably no evaporation could occur and the curve of Fig. I would meet the rainfall axis a t the

recorder on the laboratory roof.

west by a belt of trees 30 yards away.

will act as a wind break.

(ii) Summer.

appropriate yalue of the mean daily rainfall.


I ~ S C U S S I O X AND CONCLUSIOSS

This section follows the order of the points outlined on p. 403 above :-

(i) The results of this survey show that the main points established by Penman and Schofield for long arbitrary periods approxi- mating to natural periods also hold for natural periods. A series of seasonal empirical relationships between evaporation and rainfall can be established (Fig. I). In winter the water supply from below is sufficiently rapid to keep the soil surface a t 100 per cent R.H. ; the rate of removal is slow and the frequency of re-wetting by rain is high, particularly in November, December and January (Table I). Consequently, further winter rain has no effect on the surface humidity and hence none on the evaporation rate, so that winter evaporation depends only on the evaporating power of the boundary layer and is independent of total rainfall. The main cause of variance is the relative fluctuations of soil and air temperatures. In summer the upward movement between showers is not sufficient to maintain saturation a t the surface and part of the resistance to evaporation is now due to the soil. Although some upward movement does take place the maintenance of summer evaporation is very dependent on re-wettings by rain, and, as Table I shows, these are less frequent than in winter. Hence we find that summer evaporation is markedly dependent on rainfall and on the way in which that rainfall is distributed in time; also that a s the evaporating power of the air increases, the observed values depart more and more from the theoretical and begin t o approach the values which they would have if soil resistance was a t its maximum. From this obvious importance of soil factors in midsummer it is apparent that attempts to correlate summer evaporation with air conditions only will lead to results which may be seriously mis- interpreted. .

(ii) and (iii) The physical concepts used in deriving the evaporating power could doubtless be made more precise, but the greatest gain would follow from increased precision in the measurement of the quantities used to evaluate the evaporating power. If the suggested reasons for the scatter are accepted a s reasonable we may regard the physical basis as adequate, i.e., it is possible to obtain a value of the potential evaporating power of the air from first principles involving no empirical correlations. Fig. 2

shows that the observed rate of evaporation for a considerable part of the year is of the same order as the evaporating power, the departures from expectation being randomly distributed about the line of unit slope, a very satisfactory result. For the warmer part of the year the potential evaporating power of the air ceases to be a measure of rate of evaporation owing to the increased importance of soil factors. The position of the dotted curve of Fig. 2 confirms the anticipation that in practice there is some movement of liquid and some movement as vapour when surface evaporation is in progress. I t is not yet possible to give a quantitative account of the balance between these two types of response to a moisture gradient and i t is hoped that further

4 10 H. L. PENMAN

evaporation studies will throw some light on this important problem in soil physics.

The inadequacy of single daily meteorological, observations has been shown in discussing scatter. The chief sources of scatter are thought to be the non-equality of soil and air temperatures, the crude estimate of wind, and the effect of rainfall distribution. The last might be allowed for statistically and it may be that in this case some empiricism will be necessary; an alternative is suggested in the following section. Of the other two factors, the first arises because we have imposed a property on the maximum and minimum air temperature readings which is unreasonable ; their mean cannot be expected to give the soil surface mean and the way out of this difficulty is obvious. The estimation of wind remains as a difficulty. The present use of the rainfall and drainage records was probably not envisaged when the site of the gauges was chosen, and under other conditions it would be possible to ensure that wind-breaks formed by trees were non-existent. The coping cannot be omitted as it is needed to prevent run-off and the washing away of surface soil, and it appears that to decrease the wind error we must introduce errors in estimation of the drainage. An effective compromise may be possible and we cannot say that the existing conditions, in the absence of the trees, are the best possible.

(iv) With this reservation the necessary improvements in observations are obvious. The substitution of daily means, taken from continuous records, for og.00 h. readings would bring extra precision. The soil measurement chiefly needed is that of the actual water vapour pressure a t the soil surface, to be compared with that 0 2 5 cm. above the surface. The difficulty is apparent; but if overcome, the measurement would enable evaporation in all seasons to be predicted. Failing this, the less difficult alternative is to measure the soil surface temperature from which exact pre- diction will be possible in winter, but empirical corrections for rainfall will be needed in summer.

ACKNOWLEDGMENT The task of selecting natural periods and totalling up the

rainfall, drainage, temperature and relative humidity for each was performed by Mr. P. Sahni, M.Sc., in the course of collecting data for his survey (referred to in the text). Having access to this material has considerably reduced the amount of computation involved in preparing the present account and my grateful thanks are offered to him for this valuable assistance.

REFERENCES Brunt, D. 1934 Physical and Dynamical Meteorology, p. 262.

Camb. U. Press. Crowther, E. M. 1930 Proc. Roy. SOC. B., 107, 1. Koshal, R. S. 1934 J . Ag+ic. Sci., 24, 105. Penman, H. L. 1940 J . Agric. Sci., 30, 437. Penman, H. L., and 1941 J . Agric. Sci., 31.

Sahni, P. 1941 J . Agric. Sci., 31. Schofield, R . K.

meteorological and soil factors affecting evaporation from fallow soil

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