APPENDIX

MSc Thesis Title (1993)

Thesis Abstract

The quantification of evaporative water loss from agricultural and other lands may be accomplished by various means. The Bowen Ratio Energy Balance (BREB) is one method that can be used to provide sub-hourly evaporation estimates required for research, local irrigation scheduling and monitoring of remote sites.

This method of calculating evaporation requires the measurement of the major components of the one-dimensional energy balance equation. The Bowen ratio, defined as the ratio of sensible to latent heat flux densities (Fh / Lv Fw), must also be calculated. It is approximated as the product of the psychrometric constant () and the ratio of the vertical air temperature difference to the water vapour pressure difference. These profile gradients are measured by differential thermometry and psychrometry respectively. To find the amount of available energy, the net irradiance and soil heat flux density energy balance components are measured, while stored canopy and biochemical energy are assumed negligible, as is advection. The vertical flux density of water vapour, LvFw (W m-2), may then be calculated from 20 minute averages of the above measurements. The sensible heat flux density (Fh) is calculated as the remainder of the repartitioned energy.

The BREB method is based on the assumption of similarity between the turbulent exchange coefficients for latent and sensible heat, which has been found to apply only under certain circumstances. The ongoing controversy over this assumption and the history of modifications to correct for advective and other atmospheric conditions are reviewed. A lack of horizontally introduced energy "advection" is another of the requirements of the method's theory, yet some advection is usually present. Under extreme cases the exclusion of advected energy from the energy balance can lead to under-estimations of up to 45% in the calculation of LvFw. Thus both the sensible heat and water vapour types of advection should be assessed and quantified. With extensive uniform upwind fetch, however, local advection cannot occur, and only the infrequent regional advection must be allowed for. A description of the various atmospheric boundary layers in relation to the fetch requirements are given. Sensor height and separation, and the relevant equations are discussed.

An error analysis revealed that the calculated evaporation rate depended most heavily on the net irradiance and the water vapour pressure difference measurements. The overall relative error in the evaporation measurement was expected to be less than 10% during normal day-time conditions. The resolution of the water vapour pressure difference measuring system was found to be a limiting factor of the method. This resolution dictates the minimum height separation of the measuring arms, and the smallest difference measurable.

Good comparisons between two identical Bowen ratio systems located adjacent to one another were found. Further comparison between these and lysimetrically determined daily total evaporation amounts verified the accuracy of the BREB method under the conditions at the experimental site. Little difference was found in comparisons between the open slope and a riparian zone in the same catchment during January.

A method to calculate evaporation using only a generalised exchange coefficient, K, measurements of net irradiance, and a differential air temperature measurement, is tentatively proposed. If the method proves successful, considerably less instrumentation and input will be required, once a K-value has been obtained for a site.

The Bowen ratio energy balance method, as applied, can accurately and continuously measure evaporation from a mountainous catchment, providing the fetch and advection requirements as set out, have been met.

Conclusion

Of the meteorological methods of quantifying evaporative flux density, the Bowen ratio offers the benefits of measuring parameters exclusively above the surface, (although soil heat flux density needs to be quantified below the surface). The advantage of this method is that it requires none of the difficult surface measurements used by other aerodynamic methods. The Bowen ratio has however traditionally only been employed either over short agricultural crops or moderately flat natural terrain. This has been due to the ignorance and difficulty of measuring the extent of the boundary layer within which the gradient measurements must be accomplished. The height of the fully developed boundary layer that is representative of the surface over which it is flowing has been shown to be dependent on both the distance from the start of that new surface and the type of change of surface. Recently the accepted fetch:height ratios have been found to be overly pessimistic, and far more rapid atmospheric adjustments have been found to occur. Thus successful implementation of the method can be expected on far smaller areas with lower fetch requirements.

Due to the formulation of Bowen ratio theory, failure of the system at times of low evaporative flux (due to low available energy near sunrise and sunset) can be expected. Furthermore only evaporation (negative) and not condensation (positive flux densities) can be measured because the method is based on differential air and dew-point temperature thermometry. Dew confounds measurement until it has evaporated from the sensors.

It has been shown only quite recently that the well accepted practice of the use of the assumption of similarity between Kh and Kw under all conditions does not hold. The relative magnitudes of the two exchange coefficients seems to be most different under conditions of sensible heat advection. This results in temperature inversions with the result that the fluxes of two entities are opposite in direction, and the instantaneous fluctuations in air temperature and water vapour pressure do not correspond. (Blad & Verma & Rosenberg, 1974; Warhaft, 1976; Verma & Rosenberg, and Blad 1978; Verma, Rosenberg & Blad, 1978, Motha et al., 1979b and Bertela, 1989).

Neglecting the dependence of and therefore of cp could introduce absolute errors way in excess of the often quoted accuracy of the method. The assumption that the above variables are constants could well have thwarted meaningful conclusions in work in this field if the direction of the errors had happened to coincide.

Towards night condensation of dew on sensors, (thermocouples, air intakes and net radiometer), precludes any meaningful measurement of negative or positive fluxes: that is, evaporation and condensation respectively. This is because the air temperature thermocouples will be measuring the wet bulb temperature and the air around both the intakes will be approaching water vapour saturation). Thus no gradient measurement is possible.

The measured gradients in water vapour pressure and air temperature must, of necessity be larger than the resolution of the individual sensors for meaningful results. If the difference approaches the resolution, the measured differences tend towards zero and random "experimental error" values. Towards the drier periods this implies that the displacement between the measuring arms must be increased to stay above these resolution limits. This measured gradient (difference) should be used as one of the criteria for rejection of periods of calculations of ß, Lv Fw and Fh.

The condensation of dew onto the sensors prevents reasonable measurement often until 10h00 when it has all evaporated, and after dew-fall as early as 16h00. After rain-events similar limitations apply. The loss of data at these low fluxes due to the atmospheric conditions after rain is not as serious as the morning losses of data. This is because the normal cloudless morning evaporative flux usually far exceeds the inter- and post-rain evaporative fluxes, which represent mainly the evaporation of the liquid water remaining from the most recent precipitation and therefore makes little demand on the soil water balance.

These conclusions were all reached without consideration of sensible heat advection and were drawn, presumably, not under potential evaporation, or at least relatively high and unrestricted evaporative conditions. Potential evaporation is defined as the evaporation that would occur from a continuously moist surface with regional characteristics but with an area so small that the fluxes of heat and water vapour have no significant effect on the evaporability of the over passing air (Morton 1971). The evaluation of atmospheric exchange coefficients should be made under conditions that do not confound the measurements. A limited supply of water will decrease the absolute flux density of the entity under consideration, yet its K value will not have changed. This is because the exchange coefficients (or eddy diffusivities), are only dependant on the aerodynamic resistance, eddy size and turbulence or flow properties. Further, they show no apparent dependence on molecular properties such as the mass density and temperature, as is predicted in simple molecular diffusivity theory (Pal Arya 1988). Another limitation of present eddy diffusivity theory is that down-gradient transport is absent in for example, a convective mixed layer where the potential temperature gradient becomes zero. This would imply infinite or even zero values of Kh indicating that K theory becomes invalid in this case. Thus the development of this theory from a molecular basis can go no further, and an alternative approach needs to be applied (Pal Arya 1988).