Distribution of small seasonal reservoirs in semi-arid regions and associated evaporative losses

To quantify the size and density of small water reservoirs and estimate associated evaporative losses, we selected regions where water is seasonally scarce, yet rainfall is predictably sufficient to fill water reservoirs. Our study focuses on semi-arid regions (prone to high evaporation losses) where seasonal rainfall (800 mm > mean annual precipitation (MAP) > 300 mm) as delineated in figure 1(f). The mean annual aridity index (ratio of precipitation to potential evapotranspiration) AI < 0.5 [34, 35] was estimated from 1950 to 2000, and MAP > 300 mm for the record from 1979 to 2013 [36]. We filtered out regions that preclude the use of reservoirs, such as forests, urban areas, wetlands, and mountains using consistent global land cover (300 m pixel size) ESA products [37].

Within this region (called semi-arid water storage region, SAWS), we selected 10 specific ‘areas of interest’ (AOI) where—(i) different forms of agriculture are taking place, and (ii) water storage could be practiced. The 10 AOI cover a range of socio-economic states, agricultural practices, and infrastructure potential conditions (for assessing alternate water sources and evaporation suppression value) across five continents focusing on USA, Brazil, Spain, Italy, Morocco, Nigeria, India, Myanmar, China, and Australia as representative countries.

The AOI is overlain by a 10 × 10 km grid with 10% of grid cells (a grid cell is denoted in the following as a ‘mask’—see SI, figure S1 is available online at stacks.iop.org/ERC/2/061002/mmedia) randomly chosen to quantify water reservoir size and spatial density from the relevant Sentinel-2 satellite imagery within each mask (the sampling percentage choice of 10% of the AOI is explained in SI– figure S2). The Satellite captures 13 different wavelength bands (443 nm–2190 nm) with pixel size of 10–60 meters (depending on wavelength; see SI, table S1). As we show in more detail in Supplementary Information file (figure S9), the reflectance (measured by satellite) in the infrared range is much smaller compared to soil and vegetation and can reasonably distinguish water bodies.

We used imagery acquired at the end of the wet season (see SI, figure S6 for the distinction between wet and dry seasons) assuming that most reservoirs are water filled—this is marked as time T₀. Another image for the same area is acquired 90 days later in the dry season (T_val) to provide quality check and avoid randomly inundated lands (only areas also classified as ‘water’ after 90 days are considered as water reservoirs). To classify water reservoirs, inundated agricultural land (e.g., rice) and vegetation, we have used two indices; Normalized Difference Water Index NDWI (positive for water areas but negative for other surfaces), and Normalized Difference Vegetation Index NDVI (positive for vegetation) that were computed at T₀ and T_val. Region-specific thresholds were defined for NDWI and NDVI to extract binary images for vegetation and initial water bodies (see SI, section 1 and figure S1).

Results of previous inventories of large reservoirs and natural lakes [38] show that the frequency-size distribution follows a power-law. As presented in figure 2(b), a power-law distribution was fitted for our data of small water reservoirs (5 size classes) truncating areas above 100 000 m² (0.1 km²) and those below 300 m² as well to reduce the bias that can be introduced to the fitted power-law exponent (decrease in the absolute value of β) with the detection failure of reservoirs at the satellite imagery cell limit (100–200 m²). We bin the frequency of reservoirs that fall in 5 size classes since the reservoirs have irregular shapes and might not be filled to top at time of image acquisition; hence the exact area of the reservoir could have some discrepancies particularly because a rather conservative NDWI threshold is applied. The power-law is determined by computing the probability density function (pdf) for the reservoir sizes extracted from the masks:

$$\begin{eqnarray}&&pdf\left(A\right)=K\cdot {A}^{\beta }\end{eqnarray} \tag{ 1 }$$

with reservoir area A, coefficient K and power-law exponent β. To estimate the total storage in the SAWS (AOI in addition to blue area in figure 1(f)), we first aggregated all water reservoirs from the different AOIs by continent (note that in the remaining text ‘Oceania’ is referred to as ‘Australia’ due to the lack of SAWS in other parts of that geographic region), then derived power-laws for each continent (see SI—table S2) scaled for reservoir density per km² and size. The differences reflect effects of climate and anthropogenic practices in different regions of the world since abundance of natural lakes in semi-arid regions is marginal [23].

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To estimate number and volume of reservoirs, we assign a representative size to each of the five size classes (‘bins’) that were used to determine the power-law (see figure 2(b)). The estimated number of reservoirs within a size class of areas ΔA defined by maximum a_max and minimum area a_min was then calculated as:

$$\begin{eqnarray}&&{N}_{{a}_{\min }\lt A\leqslant {a}_{\max }}=M\cdot K\cdot {A}^{\beta }\cdot {\rm{\Delta }}A\end{eqnarray} \tag{ 2 }$$

with area M of SAWS per continent in km² and the area A in m² representative for the size class defined by:

$$\begin{eqnarray}&&A={10}^{0.5(Log\left({a}_{\max }\right)+Log\left({a}_{\min }\right))}\end{eqnarray} \tag{ 3 }$$

Studies have shown that reservoir volume is related to its surface area by power function whose parameters may vary spatially [24, 39]. We synthesized several reported power-laws linking reservoir area and volume into a representative relation which includes the regional differences (see SI, section 2). The relation enables estimation of the stored water volume (V, m³) from observed reservoir area (A, m²) (see SI, figure S3) using:

$$\begin{eqnarray}&&V=0.38\,{A}^{1.173}\end{eqnarray} \tag{ 4 }$$

To estimate the water storage per SAWS for each continent, we estimate the volume of reservoirs within a size class of representative area A with density N simply as:

$$\begin{eqnarray}&&{V}_{{a}_{\min }\lt A\leqslant {a}_{\max }}=0.38\cdot N\cdot {A}^{1.173}\end{eqnarray} \tag{ 5 }$$

We estimate small reservoir numbers and storage capacity in semi-arid regions (about 27 million km²—21% of the Earth land surface). The number and areas of small water reservoirs were estimated by spatial sampling of 4770 masks (each covering 100 km²) randomly distributed over 10% of the representative AOI (red regions in figure 1(f)). The spatial density of small reservoirs varied across regions (SI, table S3) with highest density of 420 reservoirs in a sampling mask in South Asia (India). The lowest average spatial density per country was 5 small reservoirs per 100 km² in Nigeria, and the highest was in Myanmar with 40 small reservoirs per 100 km². The probability density function of reservoir sizes obtained for size classes between 0.0003 and 0.1 km² in SAWS of each continent followed a power-law (see equation (1) in section 2) with similar exponents near 1.5 irrespective of climate and population density, as depicted in figure 2. Additional information on the sensitivity of the power-law coefficients to the sampling procedure and reservoir extraction accuracy are provided in SI—figures S2 and S4, respectively. The number and area of small water reservoirs for the entire SAWS of each continent were deduced from the estimated power-laws as represented in figure 2(b), and water storage volumes from area-volume relations (see equation (4) in section 2). The median small-reservoir size was ∼1 400 m² with Australia tending to have smaller reservoirs, and the largest in Africa and America. As reported in table 1, we estimated 2.9 million small reservoirs globally in the SAWS with an estimated total water surface area of 17 800 km² and seasonal storage of 37 km³.

We examined the potential of extending power-law distributions of size-densities for large reservoirs from other studies to recover the small-reservoir results of this study. For a direct comparison, we first estimated power-law relations for the size distribution of large lakes or reservoirs (Hydrolakes and GRanD) restricted to the SAWS in each continent [19, 27]. The extrapolated estimates using large water bodies relations exhibited significant discrepancies with the direct estimates of small reservoirs size-density (see SI, figure S5(a) and table S2). In addition, we found that the approach proposed by Downing et al [23] for estimating farm ponds from the area of farmlands (within administrative boundaries; e.g. cities) and mean annual precipitation tends to overestimate reservoirs coverage as shown in SI (figure S5(c)) for an example in entire SAWS of India. The discrepancy could be attributed to the climatic differences as their field surveys were conducted primarily in humid regions of the USA. Finally, we assessed whether the size-density distribution of small reservoirs in SAWS, primarily in the USA, was similar to that obtained for natural lakes and reservoirs of same size range in humid northern regions. The resulting size-frequency distribution of natural lakes with areas between 0.0003 and 0.1 km² delineated from Sentinel-2 imagery followed a power-law with an exponent of 1.2 (see SI, figure S5(b)) and was significantly lower than exponent of 1.8 for water reservoirs in semi-arid regions. The total water surface area per 100 km² for natural small lakes was 25% less than for small water reservoirs in semi-arid regions. These results suggest that resulting small-reservoir size distributions carry signatures of anthropogenic construction practices and differences in climatic conditions.

Water losses from small reservoirs in semi-arid regions are attributed primarily to evaporation [40]. Seepage losses are negligible considering that on-farm ponds are often lined by low-permeability clay liners, plastic sheets or sprayed concrete [2, 41]. An objective of this study was to capitalize on the estimated small-reservoir distribution to assess the efficacy of methods for suppressing evaporation in their regional context. We thus estimate the regional evaporation demand considering regional climate and seasonal storage.

While direct measurements of open water evaporation are scarce in semi-arid regions, Penman-Monteith equation (see SI, section 2.2) was proven to provide relatively good estimates for evaporation from open water showing low sensitivity to parameter variations compared to other methods [12, 40, 42, 43]. The evaporative budget (ET*) from free water surfaces of small reservoirs was computed for each region by subtracting the mean monthly precipitation (P) from the cumulative monthly evaporation (ET_o) computed with standard FAO application of the Penman-Monteith method [44] reported in CGIAR dataset [34] (see SI, figure S6(B)) [35]. The estimates focused on the dry period, when evaporative rates are highest and reservoir inflows are negligible. The global precipitation dataset Chelsa [36] was used to identify the dry period for each region within the prescribed SAWS. The months with rainfall values lower than 30% of the maximum monthly precipitation for the northern and southern hemispheres were considered as ‘dry season’ (for equatorial regions the threshold was 50%; see SI—figure S6(A)).

For the computation of the volume losses, we considered a unified geometry for the reservoirs (see SI, section 2.2 and figure S3). During the dry season, the diminishing water depth and shrinking evaporating surface area are calculated based on this unified geometry. The results in figure 3 show that estimated evaporative losses (i) may amount up to 75% of stored water during the dry season, and (ii) vary with regional climate. Note that these estimates represents the upper bound of losses since it neglect the withdrawal of water for water use. When the sum of evaporation and withdrawal during the wet season is larger than the stored volume, the fraction of evaporation to stored volume is slightly different (especially for sizes >3000 m²). This is discussed in Supplementary Information file (section 3.1 and table S5).

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The fraction of estimated evaporative water losses ranges from 5%–10% in northern latitudes to 75% in the Sahel region and in Australia due to the reception of higher solar radiation in the latter regions. In terms of absolute volumetric water losses (see SI, figure S7), the highest losses were in America and Asia due to high reservoir densities (figure 2(a)). The estimated losses amount to about 38% (13.8 km³) of the storage during the dry season in the SAWS, while globally the evaporative budget of large dams and artificial reservoirs accounts for only 5% of total storage as reported by Aquastat [45]. Hence, the need for evaporation protection for seasonal small reservoirs in semi-arid regions is acute and should be given attention as discussed in next sub-section.

Cheap floating cover elements could be a simple and scalable solution for suppressing evaporative losses from the many small reservoirs that serve largely rural populations in semi-arid regions. Results from recent studies have shown that across a wide range of climatic conditions, such covers suppress between 70 and 85% of the evaporation relative to uncovered water surfaces [33, 46]. Floating covers reduce the exposed water surface, increase the effective boundary layer over the surface, and shift radiation and heat exchange from the water surface to the top surfaces of the covers [33, 46]. The packing of floating spheres or discs permit light penetration and gas exchange through the 9% uncovered area (gaps formed between the elements), thus permitting ecological functions (we report preliminary results from an ongoing field experiment in SI—section 3 and figure S8). Attractive features of this technologically simple evaporation suppression method are (i) the relatively low cost (SI—section 4), and (ii) the scalability to various reservoir sizes, particularly suitable for small on-farm reservoirs.

The cover effectiveness is influenced by atmospheric conditions [46], but for simplicity we have used a constant evaporation suppression efficiency of 80% over the dry season as specified by Aminzadeh et al [33] for Styrofoam disks. In figure 4, we add regional context by presenting savings percentage for each country of SAWS and highlighting social information about the population and agricultural land areas in each continent. Figure 4 reveals that the highest suppression potential is in the Sahel region. However, such ranking may differ considering the economic value of an alternative water source (see SI—section 4). For example, the rank of Australia in the list of suppression potential may decline considering seawater desalination price (due to proximity of SAWS region to the coast and the generally flat topography, the transport of desalinated water may be cheaper than buying floating covers).

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