A COMPARISON OF PICHfi ATMOMETERS WITH

CONVENTIONAL ESTIMATES OF THE VENTILATION TERM OF

THE PENMAN MODEL

RICHARD BELL0

Department of Geography, York Universily, North York, Canada, M3J lP3

(Received in final form 15 September, 1989)

Abstract. When shielded from the sun and exposed to the ambient wind regime, PichC atmometers accurately reproduce estimates of the ventilation term of the Penman model using conventional psychrometry and anemometry. Results show that 98% of the variability in conventional estimates are accounted for by the variability in the atmometers when a square-root dependence on wind speed is incorporated into calculations of the evaporative flux from the atmometers. The potential for using a fairly simple instrument for the spatial extension of latent heat flux estimates from freely evaporating surfaces is discussed.

1. Introduction

In the field, the study of spatial variations in energy budgets, or basin-scale or regional-scale processes comes at great expense. For most, the ability to replicate micrometeorological stations over an entire drainage basin, for example, is limited and as a consequence the majority of studies suffice in reporting results from a single location. Simple, yet effective instrumentation would increase the basis for a better understanding of processes in environments which are neither infinite nor homogeneous.

Devices which purport to measure surface evaporation, like evaporimeters, atmometers or pans have seen a long history of development (Brutsaert, 1982). Although they possess the advantages of being relatively inexpensive and of inte- grating the flux over time, few replicate the environments they are supposed to represent and are unreliable for the estimation of the surface latent heat flux (Monteith, 1981).

The PichC atmometer consists of a water-filled graduated glass burette. When suspended in an inverted position, a filter paper, fixed by a brass clip, supports the water column which continually moistens the filter. A small hole in the basal clip admits air to replace evaporated water (Figure 1).

Stanhill (1962) was apparently the first to note that although the PichC at- mometer does not record surface evaporation, it does respond to the drying power of the air. When suitably shielded from the sun, the instrument responds to both increases in wind speed and vapour pressure deficit. Since these same two variables are responsible for variations in the ventilation term of Penman’s (1948) model, the potential exists that the instrument could replace psychrometers and anemometers normally required for estimation of the ventilation term. Although Stanhill showed

Boundary-Layer Meteorology 51: 159-167, 1990. 0 1990 Kluwer Academic Publishers. Printed in the Netherlands.

160 RICHARD l3ELLO

Fig. 1. Pichk atmometer showing radiation shield.

a correlation between Picht evaporation in a Stevenson screen and the ventilation term, the results were not conclusive.

Thorn et al. (1981) analysed the energy balance of the Piche atmometer inside a Stevenson screen and compared PichC estimates to conventional estimates of the ventilation term. Their results indicate two principal sources of error. First, a correction factor is required to account for the change in turbulent regime caused by the Stevenson screen. Second, accurate Piche evaporation will only be attained

PICHt ATMOMETERS AN” THE VENTILATION TERM OF THE PENMAN MODEL 161

if the filter paper is at the same wet-bulb temperature as the muslin wicks used in psychrometers. This is difficult to attain in reality, since the temperature of the water column in contact with the evaporating surface will lag behind ambient air temperature changes. Also, any differences in the radiation imbalance between sensors and surroundings could create discrepancies between PichC and psychro- meter evaporation values.

The present study examines the performance of shielded PichC atmometers when exposed to the ambient wind regime with the objective of providing routine estimates of the ventilation term of the Penman model.

2. Theory

The evaporation from a freely evaporating surface is given by Penman (1948) as

QE = [WS + r)l<Q* - QG) + wpf(u)(e.sV) - eW + ~1, (1)

where QE is the latent heat flux, Q* is the net radiation, QG is the ground heat flux, S is the slope of the saturation vapour pressure versus temperature curve at the mean wet-bulb temperature, y is the psychrometric constant, p is the air density, c, is the specific heat of air at constant pressure, e, is the saturation vapour pressure at dry-bulb temperature, T, e is the actual vapour pressure and f(u) is a function of wind speed. The original empirical relationship of Penman was linearly dependent on wind speed at 2 m. As Thorn and Oliver (1977) have shown, the original wind speed coefficients of Penman apply under a moderate range of atmospheric stabilities and surface roughnesses. The second term of (1) is referred to as the ventilation term and will be represented here by P,..

P, can also be expressed in terms of an aerodynamic resistance as

Pv = (wJrJ(ex(T) - eY(S + ~1, (2)

where r, = (ln(zlzO))*/(z#) = u,/u*~ under neutral conditions, and U* is the fric- tion velocity, k is von Karman’s constant and z. is the surface roughness. If we define a surface drag coefficient as C DZ = u**/~f, then substitution into (2) yields

Pv = wpC~,4es(T) - e>/(S + ~1, (3)

The linear dependence of the ventilation term on wind speed is shown explicitly in (3). Although the derivation depends on the assumption of a log profile in neutral conditions, Bradley (1971) has shown CoZ to be valid below heights of 1 m from conditions ranging from strong instability to slight stability. This follows from the dominance of mechanically generated turbulence over buoyancy effects in the zone closest to the earth’s surface (Deacon and Swinbank, 1958). The slope of the saturation vapour pressure curve can be approximated by S = (e,(T) - e,(T,)I(T - T,,,), where T,,, is the wet-bulb temperature. Substituting into (3) and setting D, = (T - T,,,), results in

(4)

162 RICHARD BELL0

in which the linear dependence of the ventilation term on wet-bulb depression is shown explicitly.

The evaporation from the surface of a PichC atmometer is given by

QEpi = (pCJ~)Cp&i(Uz)(epi - e>, (5) where the subscript pi refers to PichC and Cpi is an evaporative exchange coef- ficient for the atmometer. Assuming the filter paper is saturated at the wet-bulb temperature, and substituting the psychrometric equation into (5), it follows that

Q~pi = ~pCpi.fpi(~z)~z. (6)

Combining (4) and (6);

Pv = Q,,iC,,u,l(C,if,i(uz>>. (7)

If fpi(Ui) is also a linear function of wind speed, then it follows from (7) that P,, can be estimated by applying a constant to PichC evaporation if measurements are taken within, say, the lowest meter of the atmosphere.

3. Methods

The construction of the PichC atmometers used in this study differs slightly from those commercially available. The outside diameter of the glass tube and metal clip are 15 and 19.3 mm, respectively. Three filter diameters of 30, 42.5 and 55 mm were compared. Initial analysis indicated that atmometer evaporation was directly proportional (24%) to the total exposed filter surface. The middle size was used in all subsequent measurements since it provided increased measurement resol- ution compared with the smallest size, and maintained its structural integrity whereas the largest did not.

Each atmometer was fitted with a 75-mm-diameter polished aluminum disc to reduce solar heating. The shield rests snugly around the glass tube, supported by the metal clip about 15 mm above the evaporating surface (Figure 1). Two at- mometers were suspended from cross-arms on a mast so that the evaporating surfaces were 0.5 and 1.0 m above the ground surface.

At the same heights were mounted shielded and aspirated thermocouple psych- rometers and new Gill #12102 three-cup anemometers. Signals were recorded every 10 s on a Campbell CR7 datalogger for hourly average dry- and wet-bulb temperatures and wind speed.

Atmometer water levels were normally recorded twice daily in early morning and near dusk. A recording resolution of 0.1 mL corresponds to 1.25% of an 8 mL drop on a moderate evaporation day. The decrease in the water column was converted into energy units per unit area evaporating surface over the measure- ment interval. For 42.5 mm filters, a constant of 1.046 x lo6 J m-* mL-’ was ap- plied. The coefficients subsequently derived are thus directly comparable to the ground latent heat flux and independent of the filter sizes used in other experi- ments.

PICHe ATMOMETERS AND THE VENTILATION TERhl OF THE PENMAN MODEL 163

The time of manual readings rarely corresponded exactly to an hour’s end. Fractional hours of P, were calculated from the datalogger output on a simple time-proportioned basis for the beginning and ending hours of each measurement period.

Measurements were taken over a lichen-dominated peat plateau. Normally water is not freely available over this surface and evaporation is sub-potential (Rouse and Bello, 1985). Therefore, Piche evaporation is compared with P,! = P,ICD, = pcpuzD, in the analysis which follows.

The study extended from mid-June to mid-August, 1985. Eighty-one measure- ment periods comprised mostly half-days and occasionally full days when manual readings were taken only once. During this time, the Piche atmometers at both levels functioned adequately. Wind speeds ranged from calm to 10 m s-r, averag- ing 4.5 m ss’. Temperatures ranged from freezing to 35°C and wet-bulb depre- ssions from zero to 12 “C.

Data were excluded from the analysis when (i) wet-bulb wicks dried out or (ii) atmometers were found empty. The latter resulted from the instruments swaying and striking the support mast during periods of high winds. Evaporating surfaces never dried out otherwise. The filter paper discoloured after several days when local pond water was used. Filter paper was replaced each time an atmometer was refilled.

4. Results

Figure 2 shows the relationship between QEr,l and Pl, for the 0.5 and 1.0 m measurement levels. Least-squares fit for both relationships is good with about 91% of the variability in PichC evaporation explained by P:.. However, regression formulae differ despite identical instrumentation at both levels.

Some of the scatter in the relationships results from including data from 14 rainfall events. During these episodes, rain, which accumulated in psychrometer shields and on anemometer cups, might be expected to affect estimates of P,‘.. Also, some rain would seep past the atmometer radiation shields and accumulate on the filter paper to be evaporated before the water column would commence to drop following the rain. Nevertheless, the removal of rain-event data might misrepresent the potential accuracy of the atmometer under actual field conditions, which argues for their inclusion.

The thermal lag effect noted by Thorn et al. (1981) manifested itself as a nocturnal accumulation of condensate in the top, empty portion, of the glass tube. Apparently, a vapour pressure gradient induced by the warmer temperature of the water compared with that of the exposed glass was sufficient to produce this flux. Returning these droplets of water to the water column indicated that the error in reading was never more than 0.1 mL, however.

An analysis of the residuals derived from Figure 2 was conducted to identify causal mechanisms for the observed errors. The variables tested included incoming

164 RICHARD BELL0

12

1C

2

0

,-

I-

O

o50cm n=81 . .

Y q 2.4 x106t 7.01 x 1O-3X

r*= 0.91 0 0 . .

0 . 0.

.

. 0

0 l . .

l o 0

e” “’

.

0

0 .

0

.

l lOOcm n=81

Y=3.07 x 105t6.51 x 1O-3X

r*=0.92

0.5 1.0 1.5 2

P((J mm2 X 10’1

Fig. 2. Relationship between half-day estimates of PI and QE,,i at two levels.

short-wave radiation, net radiation, temperature and wet-bulb depression. The results indicate that none of the above factors contributed to significant errors in the Piche atmometer as employed.

The linear relationships were tested with the alternate measurement level as an independent data source. The comparison of measured versus predicted values of PJ yielded poor agreement with root-mean-square errors of 21 and 25% of mean P: values for the 0.5 and 1.0 measurement levels, respectively.

The foregoing analysis indicates that the coefficients in (7) cannot be adequuLely represented by a single constant corresponding to the slope regression coefficient. Thorn et al. (1981) suggest, from laminar drag considerations about flat discs, for example, that Piche evaporation should be proportional to the square root of the

PICHE ATMOMETERS AND THE VENTILATION TERM OF THE PENMAN MODEL 165

wind speed. Their data however, did not show such a relationship when the atmometer was located inside a Stevenson screen.

To test the possibility that the screen might be unduly interfering with the turbulent regime, half-day estimates based on hourly values of P:/u~'~ were derived and compared with QEPi. The intercepts are very similar with values of -2.2 x

and -1.8 x lo5 for the lower and upper levels, respectively. Also, the slope coefficients are virtually identical with corresponding values of 0.0135 and 0.0134. Coefficients of determination are 0.99 and 0.98, respectively. The very small and negative intercepts are presumably the result of rain accumulation on the filter papers. Ignoring the intercepts and using the mean value of (C,,if,i(U;))-’ =

2.0

1.5 - m 0

;; c*l

k

2 1.0

z

t;l E .- +- UY 01

->

CL 0.5

. (0 9’ I-

l cm

. 0 :go

b Q !

0

. . . :“o

0 50 cm n=81 r*= 0.97 rmse = 6.3 x 10'

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00 .

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0 .

I-

0

0100 cm n=81 r* = 0.96 rmse = 8.2 x10'

0 I I I 0 0.5 1.0 1.5 0

P: measured (J mm2 X 10’1

Fig. 3. Relationship between measured and estimated P{. using the wind-run to derive the square root of the mean wind speed.

166 RICHARD BELL0

74.07~~“~ to scale both values of Q Epi, satisfactory results are obtained between measured and estimated P:. The square-root dependence of the PichC coefficient on wind speed removes most of the scatter shown in Figure 2 and provides a single relationship for all instruments. Root-mean-square errors of 10 and 11% of the mean values for the two levels, respectively, compare favourably with those associ- ated with other field measurements.

The practicality of employing the Piche atmometer as an operational research instrument is compromised if a companion datalogger is required to measure hourly wind speeds. Figure 3 illustrates that high accuracy is retained for estimates less than or equal to 24 hr if the wind-run is used to derive the square root of mean wind speed over the measurement period. Root-mean-square errors increase only marginally to 12 and 13% of the mean values for the two levels. This suggests that a totalizing anemometer in tandem with the atmometer are capable of accurately representing Pi in a field setting.

5. Discussion

The thermodynamic effect of evaporating water from a wick on an enclosed thermometer is well established. This study suggests that the quantity of water producing the thermodynamic effect is equally well founded in physics. The advan- tage of the PichC atmometer is its simplicity, portability and cost. Constructed at under Can$30, with the most primitive of radiation shields, it provides acceptable estimates of the ventilation term of Penman’s model. For those routinely involved in field psychrometry, the fact that the evaporating surface never dries out could also be perceived to be an advantage.

Rather than being viewed as a time-wasting anachronism made redundant by the versatility of Penman-type formulae, the atmometer holds the potential for extending evaporation estimates. At a scale of several kilometers, say, the evapor- ation from surfaces where water is freely available is likely to vary spatially more as a result of changes in the drying power of the air than from energy availability. The information required to produce such regional estimates is more easily ac- quired with atmometers. Improvements in design which would serve to reduce errors even further would therefore seem to be warranted.

6. Conclusions

Estimates from shielded PichC atmometers exposed to the ambient wind regime are in good agreement with conventional estimates of the ventilation term of Penman’s model. When combined with anemometers that record the wind-run, they provide a satisfactory measure of the drying power of the air.

167

Acknowledgements

The project was funded by the Natural Sciences and Engineering Research Council of Canada and through a research grant from the Faculty of Arts, York University. The assistance of D. Joiner, T. Papakyriakou and J. Smith are gratefully acknowl- edged as is the Department of Indian and Northern Affairs for the support of these individuals through the Northern Scientific Training Programme. Logistical support was provided by the Churchill Northern Studies Centre.

References

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