Parameterizing the effect of a wind shelter on evaporation from small water bodies



[1] The potential use of windbreaks to reduce evaporation from small agricultural reservoirs motivated the development of a simple evaporation model that includes the effect of wind shelters. The shelter effect is parameterized by averaging the integral of the horizontal velocity deficit curve over the length of the water body. This parameterization, termed the “shelter index,” ranges between 0 and 1, representing no shelter to complete shelter, respectively. The results of a two-dimensional aerodynamic model that solves the disturbed flow field and evolving microclimate over the water body guided the development of a Dalton-type evaporation model, modified to include the shelter parameterization. The modified Dalton expression summarized the results of the aerodynamic model to a high degree of accuracy (R2 = 0.988). Because the shelter parameterization requires knowledge of the horizontal velocity profile, an approximation of the shelter index that can easily be estimated from physical windbreak characteristics (height, porosity) is presented. In addition, a simple approximation based exclusively on upwind meteorological information is presented for estimation of surface humidity. The evaporation model using the approximations for the shelter index and surface humidity showed excellent agreement (R2 = 0.875) with measured evaporation data from a variety of small wind-sheltered water bodies at two sites in the agricultural districts of Western Australia. The evaporation model and approximations have the advantage of requiring only routinely available meteorological information and information on windbreak physical characteristics that can be estimated a priori. It is therefore an excellent design tool for water resource managers to evaluate the efficiency of a wind shelter in reducing evaporation or for coupling with hydrodynamic models.

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:

equation image

where E is the evaporative heat flux, qs is the specific humidity at the water surface, qa is the ambient specific humidity, and u0 is the upwind wind speed at some reference level. In one-dimensional form, f is typically a linear function of u0 such that:

equation image

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.

2. Data Collection

[5] A comprehensive field experiment that measured boundary-layer evolution over a variety of wind-sheltered water bodies was conducted at two sites in the agricultural districts of southern Western Australia. The first site was located at Corrigin (117°48′E, 32°12′S) on a cereal and sheep farm that experiences a long-term mean annual rainfall of 375 mm and an average class-A pan evaporation rate of 2100 mm/year. The second site was located at Katanning (117°30′E, 33°45′S), 200 km south of Corrigin and 350 km southeast of Perth, with a mean annual rainfall of 450 mm and an average class-A pan evaporation rate of 1800 mm/year. The field trial conducted at Corrigin ran between 9 September 2000 and 24 November 2000, and the Katanning trial ran between 26 November 2000 and 9 January 2001. The period between October and March is typically hot and dry due to the easterly and north-easterly winds bringing air across the desert. This period is of most interest from a water conservation perspective because of the excessive evaporation rates.

[6] Three water bodies at each field location were chosen for experimentation, and were subject to different degrees of sheltering from the wind. The chosen dams were typical square prismoidal earth dams with water surface areas of approximately 3600 m2 (water body length, XW = 60 m), and maximum depths ranging between 4 and 6 m. The dams at both sites are surrounded on three or four sides by solid earth banks that rise to a height of 1.5 m. Each of the three water bodies on each of the sites was chosen specifically to minimize differences between shape and size, as well as upwind topography and land-use differences, so that the approaching flow and water body dynamics were similar in all cases. The three reservoirs at each site are differentiated as follows (Figure 1): (1) bank only (BO) is mostly unprotected from the wind except for some small protection provided by an earthen bank (XW/HBO = 40, where HBO is the height of the upwind bank); (2) artificial barrier (AB) is similar to BO but with a 2.5 m shade cloth barrier (30% porosity) erected on two sides aligned to catch the warm, dry summer winds (XW/HAB = 15 where HAB is the height of the upwind bank plus the height of the barrier), and (3) natural shelterbelt (NS) is the water body was located downwind of a natural tree shelterbelt with optical porosity of approximately 50% and a height of 7.5 m and 15 m for Katanning (XW/HNS = 8) and Corrigin (XW/HNS = 4), respectively.

Figure 1.

Field schematic showing the three experimental scenarios: i, bank only (BO); ii, artificial barrier (AB); iii, natural shelter (NS).

[7] The monitoring equipment installed at each dam consisted of an upwind station measuring wind speed and direction, air temperature, humidity and solar radiation (at 2 m), plus three floating platforms distributed across the water surface. The floating platforms measured the temperature of the surface waters and supported a 2 m high mast with cup anemometers at 0.5 m and 2.0 m. One or two of the platforms during each of the trials also measured air temperature and relative humidity at a height of 0.5 m.

[8] Evaporation was estimated from each water body using a water balance approach. The change in depth of the reservoirs was measured using a vented and temperature compensated pressure sensor placed on the reservoir floor, and depth evolution was disaggregated into seepage and evaporation components by identifying periods of little or no evaporation, and then assuming losses were solely attributable to leakage (stock were excluded during these periods). The seepage rate was considered a Darcy flux, linearly related to the measured pressure head, so that the seepage rate was calculated as a function of time. The corrected depth trace was used to estimate daily evaporative volumes.

[9] The data from the field experiment was primarily used to validate the performance of the aerodynamic model [Hipsey et al., 2004]. In this paper, we use diurnal averages of the upwind meteorology (wind speed, air temperature and humidity), water surface temperature and evaporation to evaluate the performance of the evaporation model (section 7).

3. Background on the Aerodynamic Model

[10] A detailed description and validation of the 2-D aerodynamic model, and the results of the simulations used in this investigation, is presented by Hipsey et al. [2004] and so only a brief outline is presented here. The modified flow fields brought about by the presence of a wind shelter are modelled using the turbulent Navier-Stokes equations modified to include parameterizations for the interaction between the air and the solid elements of the obstacle [Wang and Takle, 1995]:

equation image
equation image
equation image

where u and w are mean velocities in the x and z directions, u′ and w′ are their respective fluctuating components and p is dynamic pressure. Because we are only concerned with the shallow atmospheric surface layer, equation (4) is nonhydrostatic but accounts for thermally induced changes in density through the first term on the right hand side; here, equation image is the local temperature departure from the reference temperature, T0. The last term on each of the momentum equations represents the drag force imposed on the flow as it passes through the shelter, where CD is the drag coefficient for unit plant area density, A is the plant area density and U = equation image is the mean wind speed. The Reynolds stress terms are estimated using a KEl closure model that approximates the stress terms using the prognostic equations for turbulent kinetic energy, E, and mixing length, l, as described by Mellor and Yamada [1982].

[11] The presence of the water body is accommodated within the model by specifying different upwind and downwind surface roughness values (zo1 and zo2 respectively). In addition to estimating the flow fields, the model solves the evolving temperature and humidity fields about the obstacle, and based on the friction velocity and surface temperature and moisture scales, predicts the along-wind evolution of the kinematic heat fluxes over the water surface.

[12] The aerodynamic model was validated against two days of boundary-layer data collected during the field experiment at both the Corrigin and Katanning sites. For each of the three experimental scenarios (BO, AB, and NS), three-hourly integrations of the measured forcing data (upwind wind speed, air temperature, relative humidity and water surface temperature) were used to drive the model. In addition, a hypothetical “no shelter” scenario was simulated and was forced using the data from the BO scenario. In this paper, we use the areally averaged evaporative heat flux results from these simulations to guide the development of the simple evaporation model (section 5). To illustrate the model's performance, two days of the three hourly simulations were integrated and compared to water balance measurements (Figure 2).

Figure 2.

Comparison of the diurnally and areally averaged evaporation estimates from the water balance data and model simulations for the three shelter scenarios. Each point refers to a 2-day period for the Corrigin (solid symbols, 14–15 November 2000) or Katanning (open symbols, 27–28 November 2000) trial. Taken from Hipsey et al. [2004] (with kind permission of Kluwer Academic Publishers).

4. Parameterization of the Shelter Effect

[13] There is an extensive body of literature on horizontal wind speed evolution behind windbreaks, examining results from numerous field trials, wind-tunnel experiments and complex numerical analyses. These results describe a situation where the horizontal velocity slightly decreases immediately upwind of the shelter, slows considerably throughout the quiet zone immediately leeward of the barrier, and then recovers further downwind in the wake zone. Relative to the upwind flow, the quiet zone has reduced wind speeds and calm conditions, whereas the wake zone is characterized by recovering (but still reduced) wind speeds and potentially enhanced turbulence. The horizontal extent of the shelter effect is a linear function of the windbreak height, H, and the magnitude of the maximum velocity reduction typically depends on the porosity of the barrier.

[14] The most comprehensive parameterization of shelter effectiveness in modifying the mean wind field, is to integrate the velocity deficit, (1 − û), where û = u/u0, between the wind shelter and far downwind where the shelter no longer exerts any influence, and then integrate this result between the ground and, say, z = H. Fortunately, the vertical profiles of wind speed downwind of a windbreak are typically similar if z is scaled by H and u is scaled u0, and so it is only necessary to integrate over the x-direction for a given value of z/H. This integral has been termed the “shelter index” [Jensen, 1961], described as:

equation image

where ξ = x/H. The definition of the shelter index can be disaggregated to include the relative contributions of the quiet and wake zones:

equation image

where ξq is the normalized distance to the end of the quiet zone. Both the quiet and wake zones have distinct properties with regard to the turbulent transport processes that influence the downwind momentum, temperature and moisture fields, and so it is important to understand the relative influence of Squiet and Swake on the value of S. However, if it is possible to perform the integration between the windbreak and far downwind where the shelter has no influence, then the ratio Squiet/Swake is approximately constant, irrespective of windbreak porosity, atmospheric stability or the upwind surface roughness, because of the universal form of the velocity deficit curve. In other words, the relative contributions of the quiet and wake zones are always similar, and S is therefore an excellent indicator of the overall effectiveness of a windbreak. For this application however, we are only concerned with the shelter effect as experienced by the water body, and not the entire shelter effect created by the windbreak. We therefore only integrate across the water surface; but this introduces site-specific variability in the ratio Squiet/Swake. For example, a large water body located mostly in the wake zone could have a higher value of the shelter index than a small water body located entirely within the wake zone despite the smaller water bodies' better protection. It is therefore prudent to average the integrated velocity deficit over the length of the water body, XW, to give a revised shelter index (Figure 3):

equation image

where ξs = xs/H is the distance between the shelter and the near-shore line scaled by barrier height, and ξW = (XW + xs)/H is the distance between the wind shelter and the far shoreline scaled by barrier height. The use of SW over S signifies that (8) no longer measures the overall efficiency of the wind shelter, but instead is a measure of the average shelter efficiency experienced by the water body. The averaging process indirectly removes site to site variation of Squiet/Swake as a result of the asymmetric nature of û(ξ); the quiet zone is always weighted more heavily than the wake zone.

Figure 3.

Schematic of the shelter index parameterization (equation (9)). Not to scale.

[15] Ideally, SW should tend to zero as it approaches the no-shelter limit, and one as shelter efficiency reaches a maximum. This is the case for typical windbreak applications where the upwind and downwind surface roughness (zo1 and zo2 respectively) values are equal, and where there is no horizontal gradients in surface temperature or humidity. Where along-wind variation of surface forcing does exist, the value of SW does not tend to zero at the no-shelter limit. For example, even where no wind shelter is present, the roughness change experienced by the air as it flows from land to water results in an internal boundary layer that develops as the air accelerates over the smoother water surface. Under this scenario, equation (8) suggests that SW < 0, and we must therefore consider the effect of any wind shelter relative to this value, denoted S0. For convenience, the definition of SW is corrected by S0 so that as the no-shelter limit is approached, SW → 0:

equation image

This definition is therefore consistent for the case where along-wind variation in surface forcing exists (i.e., local advection) or where upwind and downwind conditions are equal. Indeed, the value of S0 is a function of the magnitude of the horizontal gradients, such that S0 → 0 as (zo1, Ts1, qs1) → (zo2, Ts2, qs2) where 1 and 2 denote upwind and downwind conditions respectively.

5. Development of an Evaporation Model

[16] An analysis of variables that influence evaporation from a water body yields:

equation image

where qs is the areally averaged surface humidity of the water body, qa is the upwind humidity of the air, and we specify u as a function of x for some reference height (z = 2 m is used in this study). For this analysis, the water body fetch, XW, and upwind roughness, zo1, are approximately constant, and so we remove them. If we normalize by the humidity gradient, and specify that u(x) = f(u0,SW), then:

equation image

an expression similar to (1). As indicated by Hipsey et al. [2004], we would expect evaporation to be maximum when there is no shelter (i.e., SW = 0), and to decrease as shelter effectiveness increases:

equation image

where a weak power law dependence is introduced through the constant η, and ksk so that as SW → 0 the model will tend to equation (2). By substituting equation (12) into equation (11), the resultant expression for evaporation becomes:

equation image

[17] The results of the 2-D aerodynamic model simulations are used to evaluate the parameters η and ks. Figure 4a shows the diurnally and areally averaged evaporation from these simulations normalized by the daily averages of the humidity gradient and upwind wind speed as a function of the scale (1 − equation image), where the overbar is used to indicate a daily average. The shelter index, SW, was calculated for each simulation by numerically integrating the velocity deficit curve according to equation (9) at z = 1.6 m. Although it would have been more consistent to estimate SW at z = 2 m (i.e., the height at which u0 is specified), the small nature of these water bodies, and compatability of the grids used in the aerodynamic model meant that is was more appropriate to focus closer to the water. Note that the diurnal average of the shelter index is used to eliminate daily variability in the horizontal velocity profile caused by changes in atmospheric stability (although we emphasize that this variability is small). By averaging the shelter index in this way, we get the approximately neutral value, and in doing so get an index that is mostly constant for a particular windbreak configuration, i.e., an index specific to the wind shelter and not the ambient environmental conditions. S0 was similarly calculated for the same forcing conditions by assuming a smooth transition between the land and water.

Figure 4.

(a) Normalized diurnal evaporative heat flux estimates from the aerodynamic model as a function of (1 − equation image) showing the line of best fit. (b) performance of the evaporation model (equation (13)) against the evaporation predictions from the 3-hourly aerodynamic model simulations.

[18] The best fit using a least squares regression was given by ks = 8820 and η = 0.47, yielding R2 = 0.892. Using these parameters, an excellent agreement between the evaporation model and the results of the three-hourly simulations from the aerodynamic model was achieved (Figure 4b) as expected since the parameters were chosen to fit the daily averages. Note that under unstable conditions, typical of these small water bodies, the dominant evaporative process will change from forced to free convection as the extent of shelter is increased, limiting the applicability of (13). As a result, it is expected that the data points in Figure 4a would not continue along the trend line as (1 − equation image) falls below 0.2, but instead begin to asymptote. Therefore, where free convection dominates (either low wind conditions or high shelter efficiency), it would be more appropriate to use a model such as that presented by Ryan et al. [1974], where f(u0) in (1) is replaced with a function of the virtual temperature gradient between the water surface and the overlying air, fTv). However, it is emphasized that for all practical purposes, shelter efficiencies above 0.8 are unlikely.

6. Practical Application

[19] The abstract nature of the shelter index, requires that the numerical model be run to predict the horizontal velocity profile, û(ξ), so that equation (9) may be evaluated. The simplified evaporation model, equation (13), therefore depends on the output of the aerodynamic model and hence fails in its objective of being a simple design tool. There is therefore a need for a simple approximation of SW to reduce our dependance on the aerodynamic model. In addition, for typical water balance investigations in remote agricultural locations, it is unlikely that surface water temperature information will be available. We therefore also present an approximation for the surface humidity, qs, based on routinely available meteorological information.

6.1. Approximation of the Shelter Index

[20] To model the downwind velocity recovery we adopt an expression originally used by Seginer [1975] and Borrelli et al. [1989] and later extended by Schwartz et al. [1995]:

equation image

valid only for ξ ≥ ξmin. In equation (14), cd is an empirically determined decay constant and ξmin is the downwind location where the minimum value of the velocity profile, ûmin, occurs. The distance between the shelter and ξmin does not necessarily constitute the quiet zone. Schwartz et al. [1995], estimated ξquiet, the distance to the end of the quiet zone, from wind-tunnel results:

equation image

implying that equation (14) is capable of predicting wind speeds in a section of the quiet zone and through the entire wake zone. Of course, this becomes problematic where a portion of the water body lies upwind of ξmin. Fortunately, the universal nature of û(ξ) enabled us to estimate SW numerically between ξs and ξW and between ξmin and ξW. A comparison of these two methods (R2 = 0.98) yields a proportionality constant, denoted cq, of 1.1. Note that cq was estimated by assuming the distance to the leeward shoreline ξs = 2. Substituting equation (14) into equation (9) and introducing the constant cq yields an approximation for the shelter index:

equation image

Table 1 presents estimates of both the numerical and approximated shelter index for the various shelter scenarios, in addition to the parameters used in equation (16). The data indicate that the approximation reproduces the values from the aerodynamic model to a high degree of accuracy. We now systematically review estimation methods for the parameters ξmin, ûmin and cd so that we may reduce our dependance on the numerical model completely.

Table 1. Comparison of Numerical and Approximated Shelter Index Values and the Parameters Used in Equation (16) for the BO, AB, and NS Shelter Scenarios
SiteScenarioHeight, mAerodynamic ModelaApproximation
ξminûmincdcqequation imageequation imageError
  • a

    The aerodynamic model data was estimated from results at z = 1.6 m.

  • b

    The no shelter simulations were identical to the BO simulations (i.e., upwind and surface forcing) except for the absence of the earthen bank. The negative shelter index reflects the development of the internal boundary layer, i.e., S0.

  • c

    As û(ξ) may exceed 1 for the BO scenario, we were not able to estimate a numerical value of cd. A value of −0.25 was assumed for equation image calculation, as this gave the best results.

  • d

    The value of cq for the BO scenario was set to 1.0 because its nonporous nature results in ξmin ≤ 1. This implies the entire water body is situated downwind of ξmin and so no correction is necessary.

 no shelterb0.0    −0.08  

[21] Schwartz et al. [1995] presented a regression between cd and the upwind roughness, zo1, based on a combination of field and wind-tunnel data taken at z/H ≈ 0.2:

equation image

implying that the velocity recovery downwind is heightened in proportion to the ambient turbulent intensity. The data points used in the analysis ranged between 100 < H/zo1 < 1000, slightly above the values of the AB scenario (HAB/zo1 ≈ 50). Nonetheless, extrapolation of equation (17) to this value yields cdAB = −0.127, significantly lower than the average values suggested by the numerical model (−0.19 and −0.15 for Corrigin and Katanning AB scenarios respectively). The large cd values can be attributed to the roughness change, which dampens the shelter effect by encouraging enhanced acceleration over the smoother water surface. The results from the Corrigin NS simulations however, agree well with equation (17) because XW is relatively low compared to HNS, and so the roughness change is not felt as strongly by the recovering momentum field. Therefore application of equation (17) is only warranted for design assessments where XW/H ≤ 5, otherwise we recommend a higher value such as those presented here to account for the roughness change. Indeed, for equation (16) to accurately appproximate the shelter index for the BO scenarios, cd = −0.25 was required to produce the best results. We also note that at night when Richardson number above the water is indicative of unstable conditions (i.e., cool air overlying warmer water), the decay coefficient is further increased. This agrees with the findings of Seginer [1975] who suggested that the shelter effect (and hence cd) is reduced during ambient instability. For the purposes of estimating the diurnal evaporation volume however, the neutral value is adopted as representative of the daily average.

[22] The value of the minimum velocity, ûmin, was found to be a function of porosity, ϕ, by Schwartz et al. [1995]:

equation image

where α is an empirically determined constant, ranging from 0.86 for 2-D fence windbreaks to 1.5 for “three-dimensional” shelterbelts. A similar relationship was found by Borrelli et al. [1989], who instead used a second order polynomial. Equation (18) makes sense physically because more porous shelters exert a smaller drag force on the wind and therefore have less of a retarding influence. The location at which the minimum velocity occurs, ξmin, is a linear function of windbreak height, ξmin ≈ 3H.

[23] By taking advantage of these formulations, equation image can be calculated a priori from physical windbreak characteristics and the surrounding land-use; cd varies with the upwind roughness length according to equation (17), ûmin is a function of porosity as given by equation (18) and ξmin depends on the height of the wind shelter. This therefore satisfies our overall objective of developing a simple design tool that can be easily applied to water balance investigations or hydrodynamic models.

6.2. Approximation of Surface Humidity

[24] The response of the surface layer of a water body to meteorological forcing is not straightforward and we emphasize that the approximation presented here is only intended where no other field or modeling information exists. The relationship we present is qualitatively similar to that presented by Condie and Webster [1997], with some modifications to reflect the field data collected as part of the field trial and the added complication of wind sheltering:

equation image

where a1, a2 and a3 are constants, equation image is the diurnally averaged solar radiation flux (W m−2), equation image is the diurnally averaged air temperature (°C), and equation image is the diurnally averaged upwind wind speed (m s−1) at a height of 2 m. The constants and exponents were determined empirically from all available (areally averaged) data collected during the field trial (Figure 5). Equation (19) reflects the fact that surface water temperatures increase in proportion to solar heating and the ambient air temperature, and decrease with increasing wind speed as a result of increased evaporative cooling. The influence of the shelter effect on surface temperatures is captured by modifying the upwind wind speed according to the shelter index. In effect, a high level of wind protection reduces the wind speed experienced by the water body and therefore decreases evaporative cooling. It is noted here that the increase in surface water temperatures due to decreased evaporative cooling is small. The role that wind shelters play in shading, and therefore cooling the water surface has not been incorporated here, as for the scenarios presented this was not considered as having a significant impact, although if sufficient data existed, it could be incorporated into equation (19) by scaling ϕs with a function of equation image.

Figure 5.

A comparison of the diurnally and areally averaged surface humidity field data and an empirical scale formulated from diurnal averages of routinely available meteorological data.

[25] The response of water temperatures to surface forcing is slow, and so equation (19) can only be safely applied on a diurnal timescale. For design purposes and water balance investigations this is deemed adequate and the benefits of predicting qs using only upwind meteorological conditions are significant, but at finer timescales direct measurements or more accurate model simulations are required.

7. Performance Against Observed Data

[26] Finally, the evaporation model is tested against observed data collected as part of the Corrigin and Katanning field trials (Figure 6). The field data was collected as part of the same trial used to estimate the model parameters, but the data presented for this test (57 days for Corrigin and 42 days for Katanning) was not included. For comparative purposes, the present evaporation model which corrects for the effect of wind sheltering, (equation (13)), is shown alongside the standard evaporation model (equation (2)). In addition, the results of equation (13) using the approximated shelter index, equation image, and approximated surface humidity, equation image are presented. For a more detailed look at the performance of the models for the individual sites, refer to Table 2.

Figure 6.

Performance of evaporation models against measured data, Ē, for (a) standard evaporation model with no shelter parameterization (equation (2)), (b) evaporation model including shelter index parameterization (equation (13)), and (c) same as Figure 6b but using approximations for the shelter index (equation (16)) and surface humidity (equation (19)). The constants were specified according to the regression in Figure 4b, k = ks = 8820 and η = 0.47.

Table 2. Statistical Comparison of Evaporation Models and the Daily Field Data Shown in Figure 6a
  • a

    Evaporation models are equations (2), (13), and (13) with the approximations for surface humidity (equation (19)) and the shelter index (equation (16)).

  • b

    Based on 57 days of data.

  • c

    Based on 42 days of data.

  • d

    RMS: root mean square error (W m−2).

  • e

    Slope of regression line between field and model data, fixed at (0,0).

Equation (2)RMSd21.535.075.625.949.078.2
Equation (2)R20.8460.8490.7060.9100.8290.778
Equation (2)slopee0.9470.8040.5340.9300.8210.680
Equation (13)RMSd20.
Equation (13)R20.8460.8490.7060.9100.8290.778
Equation (13)slopee1.011.020.9580.9961.130.971
Equation (13) (with approximations)RMSd22.925.022.526.119.130.6
Equation (13) (with approximations)R20.8010.7480.6670.8470.9060.699
Equation (13) (with approximations)slopee0.9701.011.040.9891.011.09

[27] Equation (2) consistently over-predicts the evaporation, particularly for the AB and NS scenarios, and is unable to account for much of the scatter (R2 = 0.727). Including the influence of the wind shelter through equation image significantly improved predictive capacity and considerably reduced scatter (R2 = 0.884). Much of the scatter in this diagram is inherent in the field data as an artifact of the water balance methodology used to estimate evaporation.

[28] Substituting the approximated values of the shelter index and surface humidity into equation (13) did not significantly reduce the accuracy of the model (R2 = 0.875). The high error bounds seen in the surface humidity approximation had only a marginal effect on the overall performance of the evaporation model, indicating little sensitivity to this parameter. As indicated in Table 2, it did generally cause a moderate increase in scatter. Importantly, by taking advantage of the approximations, the data requirements of the model have been significantly reduced with only little compromise of accuracy. Indeed, where daily predictions are adequate, we have an accurate model of evaporation from wind-sheltered water bodies that is based on routinely measured meteorological quantities and windbreak physical characteristics.

8. Conclusions

[29] It has been shown previously using complicated numerical analyses that sheltering a water body from the wind can significantly reduce evaporation [Hipsey et al., 2004]. For this reason, the application of windbreaks upwind of agricultural reservoirs is potentially a cost-effective and sustainable strategy to improve the efficiency of water storages in semiarid climates. It was the aim of this paper to present a relatively simple evaporation model for small water bodies that parameterizes the influence of a wind shelter and can be used as a design tool for water resource managers or for coupling with hydrodynamic models of the water body.

[30] The efficiency of a windbreak at modifying the downwind microclimate was parameterized by averaging the integral of the velocity deficit curve over the length of the water body. The resultant “shelter index” ranges between 0 and 1 representing no shelter through to complete shelter respectively. Using the shelter index, a modified Dalton expression for evaporation, (equation (13)), was developed, and found to successfully summarize the results of the complex 2-D aerodynamic model for a range of different shelter scenarios.

[31] To further simplify the data requirements of the shelter parameterization, an approximation for the shelter index that is based on windbreak physical characteristics such as height and porosity was developed (equation (16)). The approximation reproduced the numerically calculated values to a high degree of accuracy. Additionally, for applications where no surface water temperature information is available, and where shading is not important, a simple empirical expression for estimating surface humidity (equation (19)) that is based exclusively on upwind meteorological information and the shelter index was developed. Therefore daily evaporation volumes can be estimated from wind-sheltered water bodies according to daily averages of the routinely available data (air temperature, humidity, wind speed and solar radiation) together with design information including the upwind surface roughness, and windbreak height and porosity.

[32] Excellent agreement was found between the model and evaporation data collected from a variety of wind-sheltered agricultural reservoirs in semiarid Western Australia. The model could safely be applied to similar sized reservoirs, lakes or wetlands situated downwind of either engineered wind shelters or natural fringing vegetation.


[33] We are grateful for the financial support provided by the Water Corporation of Western Australia and Office of Water Regulation. This is Centre for Water Research reference ED1768MH. We would also like to thank the reviewers for their many helpful comments.