1 Core ideas

  • Hydrus-2D/3D was used to generate nomographs for solar farm stormwater runoff

  • Nomographs were built into an easy-to-use Excel spreadsheet-based solar farm runoff model

  • Design storm depth, soil texture, depth and bulk density had a large impact on solar farm runoff

  • Low impact vegetative surface cover had a moderate impact on solar farm runoff

  • Solar array size, spacing and orientation on the landscape had a small impact on runoff

2 Introduction

Solar energy has recently become the most economical form of electricity generation in the US [1]. Due to a push for increased reliance on renewable energy sources combined with the cost-efficiency of solar energy, photovoltaic (PV) electricity generating installations have had an increasing role in the US electrical grid and are expected to expand drastically in the years to come [2]. Empirical data regarding the impact of PV installations on stormwater runoff is limited [3], and approaches for estimating their hydrologic impact vary widely across the country. In the worst case, ground mounted solar facilities are often mis-represented as completely impervious surfaces, which implies runoff responses like those from rooftops or paved surfaces. This ignores the disconnected impervious nature of these facilities, in which runoff from solar arrays enters pervious areas between arrays where infiltration can occur.

Low impact development (LID) strategies attempt to utilize natural and engineered infiltration techniques to control stormwater [4]. LID approaches in relation to PV systems are often associated with rooftop solar installations, such as reduction of impervious surfaces and implementation of native or site-appropriate vegetation [4]. Studies on green roofs, where vegetation is introduced to impervious building rooftops, show both modeled [5] and measured [6] reductions in stormwater generation. Several recent studies shift focus from rooftop solar and explore the impact of ground-mounted PV installations on local hydrology and stormwater [7,8,9,10]. Walston et al. (2021) looked specifically at native vegetation management practices at ground-mounted PV installations and their impact on ecosystem services. They found that native vegetation at solar installations increase pollinator supply, carbon storage potential, and sediment and water retention [11].

The Photovoltaic Stormwater Management Research and Testing (PV-SMaRT) project provided funding to the University of Minnesota by DOE-SETO to develop research-based, PV-specific tools to estimate how low impact management practices at ground-mounted PV sites impact stormwater runoff. A previously published PV-SMaRT funded paper [12] described how a numerical hydrologic model (Hydrus-2D/3D) was field-calibrated and validated against soil moisture measurements at five commercial PV solar farms with perennial vegetation located in Colorado, Georgia, Minnesota, New York and Oregon. These sites were chosen to represent a wide variety of soil factors and climatic regimes to determine their impacts on stormwater runoff. Complex factors unique to PV installations were considered in this hydrologic modeling such as rainfall interception by solar panels, generation of concentrated runoff at a drip-edge, and the subsequent infiltration of drip-edge runoff downslope in a pervious area having a wide range of surface conditions, as well as in a pervious area beneath the adjacent downslope row of solar arrays that are themselves impervious to rainfall. These factors are currently ignored by other stormwater models commonly applied at solar farms, which either assume that the entire facility is either pervious or impervious, or that it has a level of imperviousness that is calculated by averaging the area of arrays and the area of pervious surfaces between arrays [13, 14].

The objective of the current paper was to extend the previously developed PV-SMaRT Hydrus-2D/3D stormwater runoff model [12] for ground-mounted PV installations by developing a user-friendly spreadsheet-based calculator that can rapidly evaluate pre- and post-construction site conditions at ground-mounted PV installations and their impacts on stormwater runoff. This objective is achieved by using results from nearly 1,000 simulations of the numerical Hydrus-2D/3D model to develop exponential regression equations relating soil texture, soil bulk density, and soil depth to a runoff CN. This regression is further supplemented with results from field test sites in the PV-SMaRT project to account for panel width and spacing (ground-to-cover ratio) as well as orientation along the slope of the landscape. Finally, slope and ground cover (bare soil, row crop, perennial vegetation, etc.) are incorporated into the calculator using extensively studied relationships from the literature [15,16,17].

3 Methods

A numerical hydrologic model was developed from the PV-SMaRT study [12] simulating stormwater runoff at ground mounted solar PV facilities using Hydrus-2D/3D software [18]. This model simulates water flow in variably saturated soils based on the van Genuchten hydraulic conductivity equation [19] and can calculate infiltration through a soil profile as well as expected overland runoff. The Hydrus-2D/3D model was chosen to simulate soil moisture and stormwater runoff at PV facilities because of its ability to accurately represent soil hydrologic processes and account for multiple upper boundary conditions. These boundary conditions include incident precipitation that occurs in the area between solar panels, an area with potentially zero precipitation that impacts the ground underneath a panel in the absence of wind, and an area of concentrated precipitation that represents panel runoff accumulating and falling on the ground at the downslope panel edge. The model can also route overland runoff underneath subsequent downslope arrays and account for infiltration under the panel (Fig. 1). Nodal spacing of model domains was approximately 5 cm vertically and between 5 and 50 cm for horizontal nodes. Higher nodal densities were used where the upper boundary condition transitioned from no precipitation (under panel) to concentrated precipitation (drip edge runoff) to incident precipitation between panels in attempt to accurately quantify this transition. A three-panel domain created originally for the five PV-SMaRT field-test sites produced satisfactory results (RMSE values for soil moisture content ranging from 0.023 to 0.038), while preserving the likelihood of convergence for the Hydrus model [12].

Fig. 1
figure 1

Hydrus-2D/3D representation of a drip edge runoff, b incident precipitation, c surface and lateral soil moisture migration under downslope panel, and d overland runoff

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Initial analysis of the PV-SMaRT study modeling results determined that design storm size, soil bulk density, and soil profile depth had the largest impact on resultant runoff amounts [12]; therefore, these were the initial variables that received focus in model simulations used to develop the user-friendly spreadsheet-based PV runoff calculator. Twelve soil textures were simulated with associated default van Genuchten soil hydraulic properties. For each of the twelve major soil textures, simulations included 5 design storms, variable soil profile depths of 50, 100, and 150 cm, and bulk density values of 1.0, 1.2, 1.35, 1.5, and 1.7 g/cm3. 24-h design storms were initially chosen based on common hydrologic design considerations and consisted of 2-year (8.9 cm), 10-year (10.2 cm), and 100-year (15.2 cm) return frequencies obtained from the NOAA Precipitation Data Server [20]. These specific values represented the most common intensities among the five PV-SMaRT sites, and 24-h storms were simulated based on NOAA Atlas 14 synthetic rainfall distributions [21]. Some soils with high infiltration rates (coarse textures, low bulk densities, deep profiles, etc.) occasionally yielded zero runoff for these design storms, thus storms of 20 and 25 cm were added to ensure runoff would be initiated for most simulations in order to inform subsequent curve number regressions.

Runoff values were recorded for each of the combinations of twelve soil textures, five bulk densities, three profile depths, and five design storms yielding a database of nearly 1,000 combinations of rainfall and runoff. Elhakeem and Papanicolaou (2009) used exponential regression to translate rainfall and runoff measurements from small rainfall simulator plots in six Iowa counties into a runoff CN [22]. A similar approach was used here; rainfall and runoff combinations for simulated solar farms were translated into curve numbers for every combination of texture, bulk density and profile depth based on the NRCS curve number method standard equation [23]:

$$Q=\frac{{\left(P-{I}_{a}\right)}^{2}}{\left(P-{I}_{a}+S\right)} for\; P>{I}_{a}$$

\(Q\) = Runoff (mm)\(P\) = Precipitation (mm)\(S\) = Soil moisture retention after runoff begins (mm)\({I}_{a}\)= Initial abstraction (mm) where \({I}_{a}\)= 0.2 \(S\)Curve Number (\(CN\)) is then determined as:

$$CN=\frac{\text{25,400}}{S+254}$$

3.1 Soil texture and bulk density

The resultant database included a CN value for every soil texture, bulk density, and profile depth combination. For a given soil texture, variations in bulk density produced the largest changes in predicted runoff, relative to variations in other site-specific factors. A relationship between CN and bulk density was determined for each soil texture using exponential regression:

$$CN=a*{b}^{x}$$

\(CN\) = Curve Number\(x\) = Bulk Density (g/cm3)

An excel spreadsheet was utilized to store the resultant database of regression coefficients, which was then used as a lookup table to calculate a baseline CN for any user-defined soil texture and bulk density combination. The allowable range of bulk density values within the calculator is between 1 and 1.8 g/cm3.

3.2 Soil profile depth

Depth to an impermeable layer, or soil profile depth, was the next most important variable identified in driving expected runoff rates and CN values in the original PV-SMaRT publication [12]. As depth to an impermeable layer increased in simulations, CN values and runoff decreased in Hydrus simulations. For most soil textures, changes in runoff became negligible at depths greater than approximately 100 to 150 cm. Soil profile depth had a larger impact on runoff CN for coarser-textured soils with higher infiltration rates; heavier-textured soils were limited more by surface infiltration rates, and depths greater than 100 cm yielded little change in runoff CN. The CN regression relationship with bulk density described in the previous section was thus developed for each soil texture at two different depths: 50 cm and either 100 or 150 cm (depending on which depth limited CN). CN value for a user-specified profile depth is then determined by linear interpolation between the shallower and deeper bulk density regression. CN interpolations were constrained by the deeper profile curve for each soil texture, so CN values would not change when profile depth exceeded the CN-limited depth. The allowable range of profile depth values within the calculator ranges between 30 and 150 cm.

3.3 Ground cover

Soil texture, soil bulk density, and soil depth create a baseline CN value in the calculator for any user-defined combination within the allowable input range. Other data input parameters are then accounted for by modifying this baseline CN. Abundant research has been completed on the impact of ground cover on runoff CN [15]. NRCS lookup tables, commonly known as TR-55 tables, were utilized to account for ground cover effects other than the perennial vegetation studied at PV-SMaRT solar farm sites. Pasture/grassland in fair condition (50–75% ground cover, not heavily grazed) was chosen from the TR-55 tables as the baseline ground cover to approximate these plantings. Deviation of TR-55 CN values from this condition were then used to calculate a CN modifier for different ground cover conditions. TR-55 lookup tables also rely on hydrologic soil group to provide accurate CN estimates. Each soil texture was simulated within the calculator for low, medium, and high bulk density values as determined from chapter 3 of the NRCS Soil Survey Manual relating texture and bulk density classes [24]. This yielded a relation for each texture and bulk density combination to an expected value of saturated hydraulic conductivity. Resultant values of saturated hydraulic conductivity were then used to infer soil hydrologic group from chapter 7 of the National Engineering Handbook [25], so a relationship between CN and soil hydrologic group could be estimated (Table 1). Baseline CN is then used within the calculator to approximate hydrologic soil group and provide a modifier unique to a given hydrologic soil group and ground cover combination.

Table 1 Baseline Curve Number (CN) translation to a Hydrologic soil group for determining ground cover CN modifier
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3.4 Panel presence, width and spacing

As determined in the first PV-SMaRT publication [12], changes in panel size and spacing had a smaller impact on runoff than changes in bulk density and soil depth; to explore this factor in detail would compound the number of simulations already approaching 1,000 and would require far more data processing than the scope of this research requires. These factors are instead accounted for by modifying the baseline CN based on existing PV-SMaRT Hydrus-2D/3D simulation results. All Hydrus simulations in the calculator were run with 3 m (10 foot) panels spaced at 7.6 m (25 feet) on center. This was used as the baseline condition within the calculator, and CN modifiers change baseline CNs according to their deviation from these conditions. Panels were assumed to be at a 45-degree angle in simulations, a common condition observed in the original PV-SMaRT study sites, to simulate high precipitation interception and subsequent panel runoff. Multiple angles are not directly accommodated within the calculator, but panel width and panel spacing were accommodated by converting to a ground-to-cover ratio. This ratio is calculated by dividing the horizontal ground distance with no panel covering by the horizontal distance covered by a panel at a 45-degree tilt. It is analogous to a permeable-to-impermeable ratio as viewed from above. Ground-to-cover ratios for the PV-SMaRT sites ranged from as low as 1:1 (equal amounts of permeable to impermeable area) to 4.5:1. Panel spacings with a ground-to-cover ratio less than 1:1 would cause shading on adjacent panel rows and would theoretically be avoided except for extreme slope conditions; spacings with very high ratios would also be theoretically avoided since they would start to diminish potential electricity generation at a PV site. Ground to cover ratios were simulated at PV-SMaRT solar farm sites ranging from 1:1 to 7:1 to obtain a relationship between runoff and panel spacing.

Additional Hydrus simulations were run for each soil texture with all panels removed from the model domain and the upper boundary condition set to incident precipitation. Resultant runoff CN values from these simulations were then compared to simulations in the presence of solar panels to create a CN modifier to account for panel presence within the calculator.

3.5 Panel orientation

Baseline Hydrus simulations were run for solar arrays installed either along the contours of the landscape or parallel to the local slope. This allowed for panel runoff to be routed and infiltrated both between solar panels and beneath the subsequent downslope panels. It is possible to have panel installations that are perpendicular to local slope, or positioned up and down slope, where runoff accumulates in a concentrated area at the drip edge and flows downslope between panels (no infiltration underneath panels). Additional Hydrus simulations were conducted to capture this condition for each soil texture. Simulations were created using drip edge runoff amounts that accumulate in a concentrated area as opposed to infiltrating beneath downslope panels. Data from measurements of drip edge runoff relative to incident precipitation at the PV-SMaRT solar study sites determined that runoff from a 3 m (10 foot) fixed panel was approximately 10 times the incident precipitation rate on average [12], so this value was used in Hydrus simulations with panels oriented up and down slope.

3.6 Slope

Slope at PV-SMaRT solar farm study sites varied between 1.5 and 5%. A recent publication [26] outlines two common methods of slope adjustment on CN, namely the Sharpley-Williams method and the Huang method, both allowing for consideration of a greater range in slopes than those occurring at the relatively flat PV-SMaRT study sites. Both methods are used within the spreadsheet runoff calculator tool, and the greater slope-adjusted CN of the two is used when slopes are more than 10% to provide the most conservative slope-modified runoff estimate.

3.7 Final calculator considerations

Certain combinations of the baseline variables for soil texture, bulk density, and depth can combine with other CN modifiers to produce CN values slightly outside the theoretical range of possible CN values. In these uncommon instances, the calculator restricts the final CN value to be within the theoretical bounds of the curve number method, namely 30 for the lower threshold and 100 for the upper threshold.

The steps used in the present paper for the Hydrus-2D/3D pre-processing simulations that were used to generate nomographs, and the subsequent steps used in the easily used solar farm Excel-based runoff calculator are depicted in Fig. 2. Baseline CN nomographs are generated using Hydrus-2D/3D simulations based on a wide range in values for soil characteristics such as soil texture, soil depth and bulk density. The baseline Hydrus-2D/3D generated CN value nomographs are then modified by taking into account adjustments for ground cover, slope, and solar array characteristics to generate a set of final runoff CN nomographs. These nomographs are then incorporated into an easy to use Excel-based solar farm runoff calculator. The user then inputs site-specific data (soil texture, soil depth, soil bulk density, ground cover condition, slope, solar array characteristics and desired 24-h storm depth for a desired return frequency storm) for the solar farm of interest into the solar farm calculator. Nomographs within the solar farm calculator use these inputs to generate a site-specific runoff CN value and stormwater depth runoff estimate.

Fig. 2
figure 2

Workflow diagram describing the Hydrus-2D/3D pre-processing steps to generate runoff curve number nomographs that are incorporated into an easy-to-use solar farm Excel-based stormwater calculator (shaded portion of diagram) with all inputs and the allowable data input ranges for numerical factors as well as variable options if they are categorical factors

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4 Results

4.1 Soil texture and bulk density

Soil texture and bulk density have a very large influence on CN and expected runoff (Fig. 3). When soil profile depth and bulk density is held at a constant (50 cm and 1.4 g/cm3), CNs range from a low of 43 (Loamy Sands) to a high of 85 (Clay Loam). For a 25.4 cm (10 in) 24-h precipitation event, these CNs translate into expected runoff values of 6.76 cm for Loamy Sands (2.66 in) to 20.60 cm for Clay Loams (8.11 in), an increase of 13.84 cm (5.45 in) in runoff. Bulk density was found to be a significant driver of CN and runoff amongst the variables analyzed in the first PV-SMaRT publication [12]. For a medium textured soil (Sandy Clay) held at a constant 50 cm profile depth, bulk density yields a CN of 58 at its lowest (1.0 g/cm3) and 89 at its highest end of the bulk density range (1.8 g/cm3). These CN values would yield a range of expected runoff from the above storm of 11.61 cm (4.57 in) for an uncompacted loose soil to 22.12 cm (8.71 in) for a compacted dense soil, an increase in 10.52 cm (4.14 in). Preventing or mitigating soil compaction during and after solar facility construction through traffic/vegetation management practices as well as decompacting soil after construction could be highly effective practices to reduce runoff. Native bulk densities should also be considered during the siting phase of potential PV projects to determine runoff implications of different site selections.

Fig. 3
figure 3

Relationship of bulk density and Curve Number (CN) for selected soil textures held at a constant 50 cm profile depth

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4.2 Soil profile depth

Depth to an impermeable layer was found to be the next most sensitive parameter affecting solar farm runoff. When soil texture and bulk density are held constant (Clay Loam and 1.4 g/cm3), soil depth differences yield CN values ranging from 62 for depths greater than 100 cm, and as high as 94 for depths shallower than 30 cm. For a 25.4 cm (10 in) 24-h precipitation event, these CN values translate into expected runoff values of 13.2 cm (5.2 in) for the deeper profile and 23.6 cm (9.3 in) for the shallower profile, an increase of 10.4 cm (4.1 in). When evaluating a very coarse textured soil such as a Sand, these CN values range from 30 (soil depth > 150 cm) to 74 (soil depth < 30 cm). For the above precipitation event, this translates to a range of 2.5 cm (1.0 in) of runoff for the deep profile to 17.3 cm (6.8 in) of runoff for the shallow profile, an increase of 14.8 cm (5.8 in). Figure 4 illustrates the relationship between profile depth and bulk density changes for selected soil textures. Cut and fill construction techniques that remove topsoil would typically increase expected runoff and should be minimized. Soil profile depth should also be considered during the site selection phase of a project to identify sites with deeper soils that could reduce potential runoff.

Fig. 4
figure 4

Relationship between bulk density, soil profile depth, and Curve Number (CN) value for selected soil textures and depths in parentheses

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4.3 Baseline curve number values

The runoff calculator computes a baseline CN with user-input of soil texture, bulk density, and soil depth. This allows for a wide range of site-specific soil characteristics to be represented within the calculator which were directly informed by HYDRUS-2D/3D model results. Figure 5 displays good agreement between actual HYDRUS-2D/3D model results and the exponential regression nomographs in the solar farm runoff calculator for a silt loam soil across a range of bulk densities and multiple soil profile depths. Once the baseline CN is established with soil characteristics, the calculator then allows for further adjustment to baseline CN values by accommodating specific choices for ground cover, ground surface slope, and panel size, spacing and orientation.

Fig. 5
figure 5

Comparison of runoff Curve Number (CN) values generated by HYDRUS-2D/3D modeling results and the PV-SMaRT solar farm runoff calculator CN values and resulting regression curves for a silt soil texture as affected by soil bulk density at multiple soil profile depths

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4.4 Ground cover

Ground covers considered in the calculator include bare soil, gravel, row crops (with multiple management considerations), turf grass, newly established pollinator, forest, and mature prairie. Table 2 provides the percent change in CN for each ground cover condition and soil hydrologic group with respect to the baseline ground cover of newly established perennials. CN values increase from baseline values by as much as 57% if low impact practices such as perennial cover are converted to bare soil for hydrologic group A soils, implying a much larger expected runoff amount without low impact cover. Ground cover should be an important consideration of PV installations both during site selection and post-construction management of a site. Conversion of low impact ground cover (forest/mature prairie) to high impact ground cover (gravel/bare soil) should be avoided. Establishment of moderately low impact ground covers, such as newly established perennial cover, could reduce stormwater runoff in comparison with a higher impact ground cover (row crop/turf grass).

Table 2 Percent change in Curve Number (CN) values for multiple ground cover types relative to the baseline ground cover of “Newly Established Perennial Cover”
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4.5 Panel presence, width and spacing

The addition of panels and their respective size and spacing had less of an impact on resultant curve numbers (Fig. 6) than the baseline CN inputs of soil texture, bulk density, and soil depth. When adding solar panels to a landscape with typical bulk density and profile depth values (1.4 g/cm3 and 50 cm), average CN values for all soil textures increase. This increase ranges from an average across all soil textures of 3.7 points for widely set panels (ground-to-cover ratio of 4:1) to 7.7 points for narrowly spaced panels (ground-to-cover ratio of 1:1). For example, simulating a 25.4 cm (10 in) 24-h storm over a medium textured Sandy Clay with no panels present yields an expected runoff value of 13.9 cm (5.5 in). When adding solar panels for a Sandy Clay soil with a range in ground-to-cover ratios, predicted runoff increases from 15.7 cm (6.2 in) with wide panel spacing to 17.0 cm (6.7 in) with narrow panel spacing. This translates to a 14% increase in runoff for widely spaced panels and a 23% increase in runoff for narrowly spaced panels. Wider panel spacings allow for a larger area between arrays where low impact vegetative plantings can mitigate runoff. The runoff calculator can quickly be used to indicate how runoff from a baseline condition having no solar panels compares with runoff from a post-construction condition with solar panels installed with various panel widths and array spacings.

Fig. 6
figure 6

Relationship of panel presence and absence as well as multiple panel spacings with resultant Curve Number (CN) values

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4.6 Panel orientation

The orientation of panel arrays with respect to the local slope of the landscape had a moderate impact on CNs. When converting panel arrays that follow the landscape contours (parallel to slope) to panel arrays that are installed up and down the slope (perpendicular to slope), resultant CN values increase for every soil texture. The average increase in CN value from a baseline condition of a 50 cm soil depth and a bulk density of 1.4 g/cm3 is 8.2 points. For example, a Clay soil with the above baseline soil conditions and panels parallel to slope has a CN of 72.1 with expected runoff from a 25.4 cm (10 in) 24-h storm of 16.5 cm (6.5 in). When panel arrays are oriented up and down the landscape slope, CN increases to 78.9 and expected runoff increases to 18.7 cm (7.4 in), an increase of 2.2 cm (0.9 in). Orienting panel arrays along topographic contours results in lower runoff than arrays installed perpendicular to slope, because concentrated flow is reduced and vegetation between arrays is able to more efficiently infiltrate runoff.

4.7 Slope

Slope did not make a significant difference in CN and runoff values for the relatively flat PV-SMaRT study sites; however, research suggests CN modification for steeper slopes. When comparing relatively flat slopes of 5% (baseline condition in the calculator) to a steeper landscape of 20%, CN value increases for every soil texture in the calculator. When comparing all soil textures with the baseline condition of 50 cm profile depth and 1.4 g/cm3 bulk density, the average CN increase is 3.6 points when slope increases from 5 to 20%. For example, a Clay soil with the above baseline soil conditions and a 5% slope has a CN of 72.1 with expected runoff from a 25.4 cm (10 in) 24-h storm of 16.51 cm (6.5 in). When slope is increased to 20%, CN increases to 76.0 and expected runoff increases to 18.0 cm (7.0 in) an increase of 1.5 cm (0.5 in).

4.8 Discussion

The runoff calculator is intended to accurately reflect the impacts of varying several site characteristics by providing nearly instantaneous estimates of associated runoff given the disconnected impervious nature of solar facilities. It summarizes a multitude of research findings on complex design considerations into a very straightforward tool that can be used by even novice users. The runoff calculator can be used for both assessing site suitability in the pre-construction stage of a proposed project and for evaluating potential runoff impacts in the post-construction period with and without low impact development practices. By providing rapid estimates of expected runoff change for numerous site characteristic combinations, users can evaluate different management considerations to select site design and management practices that minimize runoff using green design principles. This approach can help avoid elevated costs to mitigate stormwater runoff associated with installation of expensive water retention structures. For sites with heterogenous characteristics (multiple slope classes, two unique soil types, etc.), runoff CN values can be generated for each sub-region of a solar farm and area-weighted to provide better runoff estimates. CN values generated in the PV-SMaRT runoff calculator can also be used as inputs for conventional stormwater modeling approaches with models such as the US EPA’s Stormwater Management Model (SWMM) or HydroCAD.

4.9 Case study

The PV-SMaRT solar farm runoff calculator described above is a spreadsheet-based approach for estimating the impact of soil texture, soil depth, soil bulk density, slope, ground cover characteristics, and solar array design characteristics on stormwater curve number values and stormwater runoff for a specified 24-h design storm depth. A case study based on comparing a coarse soil (Sandy Loam) and a fine soil (Clay) illustrates how each variable within the runoff calculator can affect resultant CN values for both soil textures. Figures 7 and 8 display a set of typical baseline site condition input variables (blue fields) for these two soil textures. For baseline conditions, CN for the coarse soil is 42.0; while CN increases to 71.2 when changing only soil texture to a fine-textured Clay soil. For a 25.4 cm (10 in) 24-h storm, these CN values generate runoff depths of 6.3 cm (2.5 in) and 16.2 cm (6.4 in), respectively, on the Sandy Loam and Clay soils.

Fig. 7
figure 7

Case study example of baseline runoff calculator inputs (blue fields) and runoff curve number and runoff outputs (maroon fields) for a coarse-textured soil

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Fig. 8
figure 8

Case study example of baseline runoff calculator inputs (blue fields) and runoff curve number and runoff outputs (maroon fields) for a fine-textured soil

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Table 3 represents the above baseline conditions shown in Figs. 7 and 8 for both soil textures in the “Mid CN Condition” columns. The impact of changes in each individual variable are also evaluated for their effect on CN values in the columns labeled lower and higher CN condition. For example, when the Sandy Loam is changed from a typical bulk density of 1.4 g/cm3 to a compacted bulk density of 1.8 g/cm3, CN value increases drastically by 39.2 points from the baseline CN value to 81.2. Preventing and mitigating soil compaction is key to reducing runoff from solar farms. When soil depth decreases to 30 cm for the Sandy Loam, CN value increases dramatically by 37.8 points to 79.8. When baseline vegetation condition of “Newly Established Pollinator” is changed to a “Bare Soil” condition, the Sandy Loam CN value increases by 24.1 points to 66.1, showing the benefits of perennial vegetation between arrays on runoff mitigation. When panel spacing is decreased from 7.6 m to 4.6 m, CN shows a smaller increase of only 1.2 points to 43.2. The magnitude of CN value changes from baseline (mid CN condition) for the lower and higher CN condition scenarios are smaller with the Clay soil texture than the Sandy Loam texture (Table 3). This is particularly true for changes in soil depth and vegetative cover.

Table 3 Effect of input variables within the runoff calculator with low, typical, and high values on resultant Curve Number (CN) values as simulated on a coarse- (Sandy Loam) and a fine-textured soil (Clay)
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The case study with two soil textures illustrates how widely runoff CN values can vary depending on specific combinations of site-characteristics. Runoff is affected most by soil texture, soil bulk density, and soil profile depth. Soil compaction can be avoided by controlling vehicle traffic on wet soils and by minimizing landscape grading during construction activities. Runoff mitigation is enhanced if site selection focuses on avoiding locations with fine-textured, shallow soils. Ground cover has a moderate impact on runoff, and low impact perennial vegetation plantings are particularly beneficial for runoff mitigation and reductions in soil bulk density. Panel presence, spacing, width and orientation have an impact on runoff, but play a smaller role than soil bulk density and vegetation characteristics.

5 Conclusions

A user-friendly spreadsheet-based runoff CN calculator for ground mounted solar PV facilities was developed based on regression curves representing nearly 1,000 Hydrus 2D/3D simulations run for different soil textures, soil depths, soil bulk densities and design storms. User inputs include soil texture, soil depth, soil bulk density, vegetative cover, presence or absence of solar arrays, panel spacing, panel width and orientation, and slope. The runoff calculator quickly estimates CN values for pre- and post-construction scenarios, including low impact development practices such as avoidance of compacted soils, perennial vegetation plantings, and wider array spacings. Users can input a 24-h design storm depth of interest and the calculator will estimate expected depth of runoff. Solar farm stormwater depths can range from values typical of completely impervious surfaces to no runoff, depending on the specific combination of soil texture, soil depth, bulk density, vegetation type, array spacing and orientation.

This runoff calculator can provide accurate and nearly instantaneous runoff estimates to novice users to inform both site-suitability decisions as well as construction management and installation choices. This tool can provide financial savings by promoting low impact development practices that reduce the need for costly runoff mitigation structures. If applied with thoughtful consideration, it also has the potential to encourage low impact development principles on the ever-increasing area of utility scale ground-mounted PV installations that will be installed in the years to come; this will minimize the impact of this landuse change on overland runoff and associated surface water quantity and quality issues. If low impact design considerations are prioritized during installation of ground-mounted PV operations, this tool could significantly reduce runoff volume from commercial solar PV sites and provide a net benefit in water quality when converting from certain high impact pre-existing landuse conditions.