Before considering evaporation suppression from covered reservoirs, we first quantify fluxes from the uncovered reservoir as the reference state. The quantification of the temperature profile within the water body is the key to defining surface heat fluxes and thus radiative energy storage into the reservoir. For simplicity, we employed a one-dimensional energy balance equation with subsurface radiation absorption and diffusive heat transfer including molecular and eddy thermal diffusivity to describe the vertical temperature profile in a reservoir according to the following (Dake and Harleman, 1969; Vercauteren et al., 2011): ∂Tw∂t=∂∂zαT,w+Dw∂Tw∂z+Q(z,t)ρwcw, where Tw is water temperature at depth z, αT,w is molecular thermal diffusion, Dw is eddy thermal diffusivity, and ρw and cw are density and specific heat of water, respectively. The heat source Q accounts for the absorption of radiative flux within the water body and is a function of depth (light attenuation) and time (diurnal or seasonal variation of incoming radiation) (Dake and Harleman, 1969): Q(z,t)=η(1-β)(1-αw)Rs(t)e-ηz, where β is the absorption coefficient of incoming solar radiation (Rs) at the water surface, αw is water surface albedo and η is the light attenuation coefficient that is affected by the total suspended solids, dissolved organic matter and chlorophyll (Lee and Rast, 1997). For example, η increases with increasing water turbidity. Alternatively, the heat source term can be quantified based on the dependence of light attenuation on wavelength (Rabl and Nielsen, 1975; Vercauteren et al., 2011). Among different formulations for eddy thermal diffusivity that governs heat transfer within the water body (McCormick and Scavia, 1981; Malacic, 1991; Vlasov and Kelley, 2014), we opt for the analytical representation based on Henderson-Seller (1985), which describes Dw as a function of depth, density and friction velocity at the surface (that is a function of wind speed over the reservoir). Dw=kus*zP0exp⁡(-k*z)[1+37Ri2]-1, where k is von Karman's constant, P0 is the neutral value of turbulent Prandtl number, and us* is the friction velocity at the water surface that is characterized based on friction velocity of the air flow at the surface (ua*): us*=ρaρwua*, with air density ρa. The parameter k* is a function of latitude (ϕ) and wind speed (U) (Henderson-Seller, 1985): k*=6.6sin⁡ϕU-1.84. Ri is the Richardson number defined as (Henderson-Seller, 1985) Ri=-1+1+40N2k2z2/(us*2exp⁡(-2k*z))1/220, with buoyancy frequency N: N2=-gρw∂ρw∂z. The bottom boundary condition in deep reservoirs is often considered as a constant temperature or zero heat flux. In shallow reservoirs, one must consider the energy balance at the reservoir bottom and heat exchange with soil profile beneath. Hence, in a shallow reservoir with depth D, the energy balance at the bottom and related heat flux are expressed as follows: ρwcw(αT,w+Dw)∂Tw∂zz=D=(1-β)(1-αw)Rs,D(t)+ksZ(TsZ-TD), where ks is the effective thermal conductivity of the soil layer beneath the reservoir, Rs,D is the shortwave radiation intercepted at the bottom of reservoir, TD is the bottom temperature of the reservoir (assumed similar to the water temperature at z=D Incropera and DeWitt, 2001), and TsZ is a linearized soil temperature at thermal decay depth Z (Shahraeeni and Or, 2011; Aminzadeh and Or, 2014). The water surface energy exchange expressed in terms of radiative, sensible and latent heat fluxes governs the surface boundary condition for Eq. (1): ρwcwαT,w∂Tw∂zz=0=β(1-αw)Rs(t)+σ(εaTa4-εwTws4)+ha(Ta-Tws)-DaLδ(Cs(Tws)-Ca), where αw is water surface albedo, σ is the Stefan–Boltzmann constant, εa and εw are atmospheric and water surface emissivity, respectively, Tws is water surface temperature, Ta is the air temperature, ha is the sensible heat flux coefficient (see below), Da is the vapor diffusion coefficient in air, L is the latent heat of vaporization, δ is the thickness of the air boundary layer that is a function of wind speed (Haghighi and Or, 2013), Cs is saturated vapor concentration at the water surface and Ca is the vapor concentration in air mass above the boundary layer. The dependency of saturated vapor concentration on the water surface temperature (Eq. 8) through the Clausius–Clapeyron relation highlights the potential nonlinear evaporation enhancement with surface warming (Aminzadeh and Or, 2014). Note that evaporative flux (driven by vapor concentration gradient) could alternatively be represented in terms of specific humidity. The sensible heat flux coefficient ha is quantified as follows (Gaikovich, 2000; Aminzadeh and Or, 2014; Haghighi and Or, 2015a): ha=kaδ, in which ka is the air thermal conductivity.

Often, an unstable temperature profile develops in the water column where a cold water layer may form above a warmer layer due to subsurface radiation absorption; such conditions trigger convective mixing in natural reservoirs. Typically, mixing processes in the water body may require complex and higher dimensional modeling of flows; however, for simplicity, we opted for the 1-D mixing approach of Dake and Harleman (1969) that results in a uniform temperature within a mixed layer of water while conserving energy (see Fig. 2): ∫0hm(Tw-Tm)dz=0, where Tm and hm are temperature and vertical thickness of the surface mixed layer, respectively. The solution of Eq. (1) results in a vertical temperature profile, an important ingredient for quantifying surface heat fluxes including evaporative loss from the reservoir (and for updating the mixed layer temperature).

The inflows and outflows of water in a reservoir may alter the heat storage of the water body, especially in multiuse reservoirs (e.g., water release for electrical energy production in dams). The net advected heat into the reservoir is characterized by the volume-weighted heat content of water inflows and outflows (Moreo and Swancar, 2013): QV=∑iρwcwVi(Ti-T‾)-∑eρwcwVe(Te-T‾), where QV is the rate of change in heat content due to the changes in water budget of the reservoir; Vi and Ti and Ve and Te are the rates and mean temperatures of inflows and outflows, respectively, and T‾ is the mean temperature of the reservoir. The parameter QV can be considered in terms of a heat source or sink (e.g., similar to the radiation absorption) to investigate the effect of heat advection due to water exchanges on the energy balance and thus temperature profile in a reservoir.

We have neglected lateral conductive heat transfer in the reservoir, assuming that the side area of the reservoir is small relative to its surface area (reflecting conditions in many shallow reservoirs where surface fluxes and subsurface radiation absorption dominate). This simplifying assumption enables focus on a simple 1-D model for quantification of the vertical temperature profile and thus surface heat fluxes from uncovered and covered shallow water bodies.

The use of floating cover elements, which aimed to suppress evaporative losses, also modifies interactions of the reservoir surface with overlying air flow and thus wind-driven subsurface mixing patterns. The interception of radiative flux by the cover surface decreases radiation penetration into the water body, shifting the energy partitioning to the cover surface. To simplify the analyses, we consider the energy balance of a reservoir covered by floating Styrofoam discs (similar to the laboratory experiments described in Sect. 3.2). A covered reservoir surface (Fig. 3a and b) is represented by a unit cell comprised of a floating disc surrounded by water gaps whereby the ratio of cover area to the total unit cell area defines the surface coverage (Fig. 3c). We thus modify the surface boundary condition of the reservoir while retaining a simple 1-D formulation and considering energy exchanges with the airflow and floating elements: ρwcwαT,w∂Tw∂zz=0=fw(β(1-αw)Rs(t)+σ(εaTa4-εwTws4)+ha(Ta-Tws)-φDaLδe(Cs(Tws)-Ca))+fcqc, where fw and fc are the areal fractions of free and covered surface, respectively (fw=1-fc), and δe represents an effective air boundary layer thickness over the partially covered reservoir. The parameter φ accounts for the aerodynamic enhancement of vapor flux from relatively small water gaps in comparison with the thickness of the viscous sublayer (Assouline et al., 2011). Hence, the reduction of vapor diffusion resistance from individual gaps (governed by the combined effect of gap size ag, boundary layer thickness and lateral spacing) would enhance vapor diffusion and result in values of φ≥1 that are defined as follows (Schlünder, 1988; Haghighi et al., 2013): φ=1fw+agδefwππ4fw-1. Note that in this expression it was assumed that ag has a circular shape. This expression becomes effective for gap sizes much smaller than the boundary layer thickness.

Due to the strong lateral mixing induced by air flow at the reservoir surface (relative to the scale of water gaps), we assume a uniform horizontal temperature at the water surface that is defined based on the heat exchanges with air and conductive flux between floating elements and water surface (qc) via Eq. (12). Hence, the energy balance equation of the floating disc in the unit cell is used to quantify temperature distribution of the cover and thus the conductive heat exchange with water: 1αT,c∂Tc∂t=1r∂∂rr∂Tc∂r+∂2Tc∂h2, in which Tc is cover temperature at radial coordinate r and thickness h, and αT,c is molecular thermal diffusivity of cover material. The boundary condition at the surface and periphery of discs in contact with air flow is governed by radiative and sensible heat fluxes. For the bottom of the disc in contact with water surface we assume that the temperature is equal to the water temperature. Simultaneous solution of Eqs. (1) and (14) with associated boundary condition (Eq. 12) enables quantification of temperature profiles in water body and floating elements that are linked via conductive heat flux (qc).

The air flow friction velocity (ua*) and the effective thickness of the viscous sublayer over the partially covered reservoir (δe) are determined using the analyses of Haghighi and Or (2015b) for evaporating porous surfaces covered with bluff body obstacles obtained based on the theory of drag partitioning over rough surfaces (Shao and Yang, 2008; Nepf, 2012) (see Appendix A for details).

In summary, the effect of floating elements on the energy balance of the reservoir and thus surface fluxes is seen by considering (1) the energy balance of the water column that now receives less radiative energy in the presence of covers, (2) the energy balance of the cover and its thermal exchanges with water column, and (3) the heat and mass exchanges at the surface of unit cell (comprised of floating cover and water gap) with overlying air flow.

The energy balance Eqs. (1) and (14) were solved numerically using the finite difference method (forward time–central space scheme). The modeling results of vertical temperature profile and surface heat fluxes for the uncovered water reservoir were assessed primarily by using water temperatures and surface fluxes (radiative, evaporative and sensible heat fluxes) measured at Lake Mead, USA (Moreo and Swancar, 2013). The model evaluation for the uncovered water body serves as a “reference state” for studying the effects of partial cover on heat storage and energy balance of large water reservoirs. We have used hourly meteorological data from Lake Mead (air temperature and humidity, wind speed, and solar radiation) obtained from March 2010 to February 2011 to reproduce the evolution of water temperature profiles and associated heat fluxes. The thermal and radiative properties of the lake used in the model are listed in Table 1.

In the absence of “reservoir-scale” data for model validation of a covered reservoir (e.g., potential data sets from Ivanhoe Los Angeles reservoir are not yet publically available), we designed a series of experimental studies of evaporation suppression from a small water basin covered with floating discs at laboratory scale (Fig. 4). The main purpose was to systematically vary external forcing (wind, radiation and combination) towards gaining new insights into energy partitioning at the surface of covered water bodies (the full scope of the laboratory study will be reported elsewhere). A subset of these laboratory experiments was used to provide a preliminary evaluation of the model for covered surfaces to improve understanding of reservoir-scale modeling results.

A square-shaped water reservoir of 1.44 m2 area and 0.16 m depth (mounted on a balance to measure mass loss) was covered with Styrofoam discs of 0.2 m diameter and 0.02 m thickness. The black or white colored discs covered 91 % of the water surface. Wind velocities controlled using an upstream wind tunnel and shortwave radiation by four Xenon light sources were used independently and in combination to create different evaporative forcing (i.e., wind, radiation and wind+radiation). The resulting evaporation rates were determined by measuring the mass of the water basin. The air temperature, relative humidity and wind velocity were also monitored above the covered surfaces. An infrared camera (FLIR SC6000, USA) recorded the surface temperature of the covered reservoir with a spatial resolution of 0.8 mm. We conducted a series of experiments in which external boundary conditions (forcing) such as constant wind (∼2.3 m s-1) without radiation, radiation (∼350 W m-2) without wind, and a combination of radiation and wind were maintained for 2 days to permit equilibration and convergence to steady-state conditions. Similar series of conditions were applied to basin covered with white or black floating discs and to the same uncovered basin.

The model was used to evaluate a hypothetical covered reservoir using meteorological variables obtained from the European Fluxes Database Cluster (http://www.europe-fluxdata.eu/home, last access: 28 February 2017), with covers that resemble those used in the laboratory experiments. We have used half-hourly meteorological data including air temperature, relative humidity, wind speed and radiation for Majadas (Spain) representing conditions in a dry region with significant atmospheric evaporative demand for the water year from 1 March 2004 to 1 March 2005. The model was used to study potential effects of floating disc-shaped elements (diameter of 0.2 m and thickness of 0.02 m) on heat fluxes and water temperature profiles within the hypothetical reservoir with a depth of 10 m. The vertical simulation domain was comprised of 626 equally spaced grid points at 0.016 m spacing. Initially, the reservoir was assumed to have a uniform vertical temperature of 11 ∘C with zero heat exchange at the bottom boundary. Details of the floating cover thermal and radiative properties are presented in Table 1.

We first assessed the modeling results of water temperatures and surface fluxes for the uncovered reservoir considering the Lake Mead data. Model estimates of mean monthly temperature profiles were compared with measured water temperature profiles in Lake Mead as depicted in Fig. 5. The comparison illustrates that the model was able to capture the temperature dynamics in the lake reasonably well (with slight underestimation in late summer). The measured and simulated fluxes are summarized in Table 2, showing relative errors of 27 % and 13 % between modeled and measured annual values for net radiation (Rn) and evaporation (LE) fluxes, respectively. Given the simplifying assumptions, the model overestimated the sensible heat flux (H) reported by Moreo and Swancar (2013) based on the Bowen ratio method with associated energy closure considerations (Foken, 2008; Kalma et al., 2008).

The evaporation rates from the laboratory basin were obtained directly from a digital balance, whereas the surface temperature dynamics were recorded by IR thermography as depicted in Figs. 6 and 7, respectively. Surprisingly, the evaporation measurements in Fig. 6a show that, irrespective of the type of external forcing (wind and radiation) or the color of the floating discs, the resulting evaporation rate from covered water surfaces was about 20 % of the uncovered surface. The corresponding evaporation suppression efficiency of 80 % is less than the cover fraction of 91 %. This reduced efficiency is attributed partially to the increased surface temperature of the water between the discs compared to the uncovered water reservoir (shown in Fig. 7). Subsequently we have used the laboratory forcing (wind, radiation, air temperature and humidity) in the model to describe the evaporative losses and capture temperature dynamics over the surface of uncovered and covered water basins. Despite the small size of the basin (and scale mismatch with the reservoir-scale model), the simulations were in good agreement with evaporative mass loss rates (Fig. 6b) and IR surface measurements (Fig. 7). This limited experimental evidence highlighted the potential applicability of the model for quantifying evaporation suppression and predicting dynamics of surface temperature that are in the core of energy partitioning over covered water bodies.

The theoretical results supported by laboratory measurements clearly demonstrated that the main effect of floating covers on evaporation suppression and energy partitioning was concentrated at the surface and thus upheld the focus on the top boundary condition for the full reservoir-scale model reported in this study. Nevertheless, we note that these experiments may not reflect influences of temperature profiles, heat storage, mixing and ground flux that could potentially affect water temperature and, in turn, the top boundary of the reservoir.

Model predictions for the evolution of mean daily temperature profile of uncovered and covered reservoir using white and black Styrofoam discs in a (hypothetical) reservoir with depth of 10 m are depicted in Fig. 8. The stable temperature profile and slow heat uptake during spring results in a gradual temperature increase, especially in the uncovered reservoir. As expected, the highest water temperature of the uncovered reservoir occurs during summer, with a warm layer of water at top of the reservoir whose temperature decreases monotonically to the bottom. However, the onset of convective thermal mixings in fall and low radiative flux rapidly yield an almost uniform temperature profile in winter and the beginning of spring. The reservoir was then assumed to be covered by Styrofoam discs with diameter of 0.2 m and thickness of 0.02 m providing a surface coverage of 0.91 (maximum packing of discs). Due to the geometry of floating elements and their density on the surface (cover areal fraction), the effective thickness of air boundary layer over the covered surface was calculated similar to the thickness of the boundary layer over the uncovered water reservoir (Appendix A).

The mean daily temperature profiles of the reservoir covered with white and black discs depicted in Fig. 8 clearly demonstrate that covering the surface with floating elements yields a much colder reservoir. Surprisingly, despite large differences in the surface albedo of black and white discs (see Table 1) and thus different cover surface temperatures (Fig. 9), the resulting water temperature profile did not vary much between reservoirs covered with these two types of floating discs.

In the following, we investigate the effect of surface coverage and cover properties on the evolution of surface heat fluxes.

The physically based model describes various effects of floating element placement on the energy budget and surface fluxes of water reservoirs as well as the great potential for suppressing evaporative losses using such a simple method. Our modeling results demonstrated that covering the surface with modular floating elements yields a colder reservoir relative to the uncovered scenario due to the interception of incoming radiative flux by the cover surface shifting the energy partitioning to the reservoir surface. Despite significant difference in the surface albedo of black and white discs, the water temperature profile of the covered reservoir was similar. We attribute this to the strong thermal insulation of the Styrofoam elements that effectively decoupled the top surface of the covers (that may attain different temperatures based on color) from the temperature and fluxes on the water surface.

In other words, the low thermal diffusivity of Styrofoam discs resulted in negligible heat conduction to the water body, whereas the intercepted radiative flux on the cover surfaces (especially the black) results in a considerable increase in cover temperature (Fig. 9a) with higher sensible heat and long wave radiate exchange. In contrast with expectation, the radiative properties of the floating covers did not affect the water surface temperature, and the use of thermally insulating covers leaks only small amounts of heat to the water (Fig. 9b) that mildly influences the evaporative flux from covered reservoir (Fig. 10c). These results have been confirmed in laboratory experiments for the basin covered with white or black discs where the evaporative fluxes from the covered surface were 20 % of the uncovered surface regardless of the cover color and forcing (see Fig. 6a).

The reduction of evaporating area on the surface of covered reservoirs primarily suppresses evaporative loss from the water body. Considering the 1-D modeling of vapor flux in the present study, the decrease in evaporative loss is expected to be equal to the covered area fraction. However, the evaporation ratio larger than the uncovered areal fraction (0.09) in Fig. 12 is attributed to the higher water surface temperature in gaps between floating elements relative to the uncovered water surface as illustrated in Fig. 9b. An interesting feedback mechanism may play a role in the evaporation suppression efficiency where high evaporative fluxes from uncovered water reservoirs may result in more surface temperature depression and thus lower saturated vapor concentration relative to the vapor concentration at the surface of water gaps over partially covered reservoirs. In addition, conductive heat fluxes from cover elements to the water surface could potentially contribute to an increase in water surface temperature depending on thermal properties of the cover material. The higher gap temperature relative to the uncovered water obtained from the modeling was also observed in laboratory experiments (Fig. 7a) supporting the nonlinearity of evaporation suppression from partially covered reservoirs.

Although we assumed that air temperature and humidity (obtained from European Fluxes Database for the numerical experiment) are the same over uncovered and partially covered reservoirs, it is important to note that the higher sensible heat flux over the covered reservoir could locally increase air temperature in contact with water gaps that, in turn, enhances evaporative loss from covered reservoir and decreases evaporation suppression efficiency. In addition to the physical considerations of the energy balance and evaporation suppression in covered reservoirs, further investigations including the ecological aspects and cost efficiency discussed below are needed to provide a comprehensive assessment for application of floating covers.

Reservoirs may serve multiple functions, including the support of various ecosystems; hence, the introduction of opaque floating covers to suppress evaporation may alter water temperature, light penetration and gas exchange, all of which affect the life in the reservoir. The full consideration of ecological targets is beyond the scope of this study; clearly certain parameters could be included in the cover design and management to limit adverse impacts on the ecology of the water body (in some cases, a cover may suppress toxic algal blooms in a reservoir). For example, here we consider effects of floating covers on gas exchange across the air–water interface as a function of uncovered fraction (fw). The oxygen transfer at the surface of reservoir (Fs,O2) is expressed as follows (Stefan et al., 1995; Schladow et al., 2002): Fs,O2=fwks,O2(Ce,O2-Cw,O2), where ks,O2 is the oxygen transfer coefficient, and Ce,O2 and Cw,O2 are equilibrium oxygen concentration and oxygen concentration in the surface layer, respectively. The dissolved oxygen in the water body is consumed by aerobic organisms (e.g., fish and aquatic microorganisms) and affects various chemical reactions in a reservoir (Stefan et al., 1995). The mechanical sheltering impact of surface covers that dampens wind-driven mixing at the surface may affect air–water oxygen exchange and transport in the water column, yielding a stratified oxygen profile in the reservoir. Although the interception of radiative flux by the cover surface decreases subsurface radiation absorption and results in a colder reservoir that may enhance oxygen solubility in water (Wilkinson et al., 2015), the reduction of radiation absorption limits convective mixing driven by unstable temperature profiles and intensifies a stratified oxygen distribution. Moreover, the photosynthesis by aquatic plants and microorganisms in darker and colder reservoirs covered with floating elements decreases, which then affects the oxygen budget according to the oxygen transfer equation (Stefan et al., 1995): ∂C∂t=∂∂zαO2+Dw∂C∂z+PO2-RO2, where C is oxygen concentration at time t and depth z, αO2 is molecular oxygen diffusion, and PO2 and RO2 are oxygen production by photosynthesis and consumption due to biological activities within the water body, respectively. In summary, exchange rates and oxygen production and concentration in a reservoir are strongly dependent on water temperature, radiative flux, transport processes and nutrients that are likely to be influenced by surface coverage. Note that ecological considerations of covered reservoirs are not limited to aquatic organisms and additional aspects including accessibility of birds and wildlife should also be investigated. Such ecological objectives become part of the reservoir cover design, and evaporation suppression must be balanced by ecological and also economic constraints, as is discussed next.

The significant reduction in evaporative loss from the reservoir could be gauged by direct economic impact in terms of the cost of alternate source of water, where available. The economic efficiency of evaporation suppression depends on the costs of construction (Pc, USD m-2), annual maintenance of covers (Pm, USD m-2 yr-1), alternate water cost (w, USD m-3), annual evaporation from the uncovered reservoir surface (E, m yr-1) and evaporation suppression efficiency of floating covers (ε) (Cooley, 1983; Assouline et al., 2011). Assuming a life span of Y years for the floating elements, the economic efficiency per unit area of reservoir (ζ, USD m-2) is estimated as follows: ζ=Y(εwE-Pm)-Pc. We thus calculate ζ for the hypothetical reservoir presented in Sect. 3.3 with annual evaporative losses for uncovered surface E=1.6 m yr-1 (see Table 3) and estimated cover efficiency ε=0.8. Considering water price w=1 USD m-3 (e.g., seawater reverse osmosis costs are in the range of 0.5 to 3 USD m-3 Gilau and Small, 2008; Guler et al., 2015) floating cover cost Pc=5 USD m-2 (based on commercially available HDPE floating balls) and cover maintenance cost Pm=0.1 USD m-2 yr-1, the economic efficiency of such floating elements for a period of 5 years is ∼1 USD m-2. Hence, for a reservoir with 100×100 m2 surface area, water costs savings equivalent to USD 10 000 are feasible for a 5-years operation (along with 64 000 m3 of water protected from evaporation).

Tacit in this standard estimate is availability of an alternate water source (e.g., desalinated water), whereas in many regions in the world with poor infrastructure and acute water shortages, the value of evaporation suppression may transcend such estimates and the real measure could be expressed in terms of livestock supported by the additional water or avoidance of crop failure. A recent study by Haghighi et al. (2018) has chosen to focus on the water footprint associated with the production of HDPE floating elements as a factor in the water-saving potential of evaporation suppression by this method. The analysis seems to overlook that the ecological and economic values of water saving are not geographically uniform (unlike atmospheric CO2 footprints); hence, water savings in an arid region with no water source alternatives may not be directly linked with the water footprint of floating elements produced in another (potentially water-rich) region. Water scarcity and droughts may exacerbate water shortage problems and transboundary (or regional) conflicts over shared water resources. Some of these political challenges could be alleviated by promotion of efficient local storage using cost-effective evaporation loss mitigation measures (such as floating covers).

Many aspects of the hydrodynamics and turbulent conditions associated with atmospheric stability over the evaporating reservoir surface were not explicitly addressed in the present study. In a recent study of soil surface evaporation, Haghighi and Or (2015c) have linked effects of different stability conditions in the Monin–Obukhov similarity (MOST) atmospheric turbulent profiles with the surface boundary layer approach used in the present work. The study offered corrections for adjusting the viscous sublayer and thus the effects of atmospheric stability conditions on heat and vapor exchange with surfaces. Elements of the analyses of Haghighi and Or (2015c) could be incorporated into the modeling of surface–atmosphere exchanges over partially covered water reservoirs. Such an analysis would be warranted once we resolve important aspects of the effects of floating elements on features of the viscous sublayer over the partially covered surface. At present, the effects of floating element shapes and cover density on surface shear stresses (in the air and in the water body), impacts of inflows–outflows, bottom topography and breaking waves have not been implemented and are expected to affect surface condition and subsurface turbulent mixing and thus modify effective eddy diffusivity. Moreover, the model parametrization should consider the depth dependency of eddy thermal diffusivity and the effect of reservoir depth on largest thermal eddies that could develop in the water body. The availability of data from covered ponds and larger reservoirs would provide the impetus to systematically address these important ingredients and improve the predictive framework for application of modular covers in controlling evaporative losses from water bodies.

As mentioned above, the simple 1-D energy and mass flux model has tacitly neglected lateral conductive fluxes between the water body and sides of the reservoir, which was deemed a reasonable approximation for shallow reservoirs and where floating elements dominate surface fluxes. Energy balance errors incurred due to lateral heat fluxes in small reservoirs (e.g., agricultural ponds) warrant special studies (motivated by measurements) to improve energy closure and provide reliable estimates of surface fluxes and evaporation suppression efficiency.