## 1. Introduction

[2] Evaporation is generally regarded as the most significant loss mechanism from small agricultural reservoirs, lakes and wetlands located in semiarid environments. The most commonly applied model for estimating evaporation from open water bodies is described by Dalton's law [*Dalton*, 1802], which states that the evaporative mass transfer is proportional to the wind speed and the humidity gradient. Later, this was described in mathematical terms as:

where *E* is the evaporative heat flux, *q*_{s} is the specific humidity at the water surface, *q*_{a} is the ambient specific humidity, and *u*_{0} is the upwind wind speed at some reference level. In one-dimensional form, *f* is typically a linear function of *u*_{0} such that:

where *k* is an empirically determined constant. Equation (2) however was found to poorly model small water bodies because there is insufficient fetch for the internal boundary layer that develops as the air flows over the water to reach equilibrium. This two-dimensionality was parameterized within the model by *Harbeck* [1962] who introduced a fetch dependence into the function *f*. On the basis of numerical simulations, *Weisman and Brutsaert* [1973] further adapted the model to account for unstable atmospheric conditions in addition to including the fetch dependence. More recently, *Condie and Webster* [1997], extended (2) to include the effect of a roughness change between the land and water for fetch-limited water bodies using a numerical model similar to that of *Weisman and Brutsaert* [1973].

[3] These models implicitly parameterize the developing internal boundary layer over the water surface through the function *f* in equation (1). The presence of a wind shelter or fringing vegetation at the upwind shoreline however, significantly modifies both the mean and turbulent character of the flow in both the horizontal and vertical directions, rendering this model inaccurate under these conditions. In an effort to improve the efficiency of rural water stores in the agricultural districts of Western Australia, *Hipsey et al.* [2004] investigated the use of wind shelters as tools capable of reducing evaporative losses by developing a two-dimensional (2-D) numerical model that solved the full turbulent equations of motion in addition to conservation equations for heat and moisture. The model was validated against observations from a variety of wind-sheltered agricultural reservoirs, and both the numerical simulations and observed data indicated that evaporation reductions of the order of 20–30% could be achieved using a well-designed windbreak. It was shown that the reduced wind speed and turbulent intensity immediately downwind of a shelter promotes the accumulation of moisture in the air above the water surface and thereby reduces the humidity gradient that drives the evaporative flux. In addition the waviness of the water surface is reduced, resulting in a lower surface roughness and friction velocity, as well as a lower surface area in contact with the atmosphere. Care must be taken however if the purpose of the shelter is to reduce evaporation, because further downwind, wind speeds are still reduced but turbulent intensities are potentially heightened as the flow recovers to its upwind structure. This supports the general theory for modification of microclimate behind windbreaks presented by *McNaughton* [1988], who suggested scalar concentrations (e.g., moisture and heat) are increased in the immediate lee as a result of reduced velocities and dampened turbulent transport, and decreased further downwind in the turbulent wake. For the case of an open water body situated downwind of a wind shelter, we have somewhat of a superposition of this general theory for modification of microclimate and the internal boundary layer that develops in response to the alongwind variation in surface forcing that exists in the absence of any shelter.

[4] The aerodynamic model is an important tool for understanding the behavior of the evolving flow field and microclimate over a water body protected from the wind, however, its complicated nature and long run-times make it impractical for routine water balance investigations or for coupling with hydrodynamic models of the water body. There is therefore a need for an evaporation model similar to (1) that applies to wind-sheltered water bodies and can be used as a simple design tool in water resource studies. It is the aim of this investigation to present a relatively simple model for evaporation from wind-sheltered water bodies. This is achieved by developing a parameterization of the shelter effect that can be used as an index of shelter “efficiency.” The results of the 2-D aerodynamic model presented by *Hipsey et al.* [2004] are used to guide the development of an evaporation model based on (1) and extended to include the shelter parameterization. In accordance with our aim of developing a simple design tool, we then present some simple approximations for the parameters of the evaporation model to reduce the data requirements. Finally, the evaporation model is tested against field data collected from a variety of small, wind-sheltered reservoirs in Western Australia.