In recent years, the USGS has made frequent use of a computer code called the Soil-Water-Balance (SWB) Model (Westenbroek and others, 2010, 2018) to generate spatial datasets of potential recharge for large geographic areas such as the State of Minnesota (Smith and Westenbroek, 2015) and the glaciated terrain across the northern United States (Trost and others, 2018). The SWB method of recharge estimation calculates potential recharge to groundwater using inputs of precipitation, temperature, land cover, and soil information, and estimates of potential and actual evapotranspiration (ET). The calculations done using this method traditionally have been used in the agricultural sector to estimate crop water demands, but they also can be used to provide estimates of excess soil moisture, which is the source of recharge to groundwater (Westenbroek and others, 2010). Using independent data on recharge for a particular study area, others have calibrated the SWB output for long-term (annual to multiyear average annual) recharge in Minnesota (Smith and Westenbroek, 2015), Rhode Island (Friesz and Stone, 2014), the Lake Michigan Basin (Feinstein and others, 2010), the North Atlantic Coastal Plain (Masterson and others, 2013), the Appalachian Plateau (McCoy and others, 2015), and the USGS glacial aquifers study area (Trost and others, 2018). Long-term base flow from unregulated USGS streamgages has been used by many of these studies to represent spatially averaged watershed recharge as a calibration target dataset for SWB models. A thorough summary of the use of base-flow-derived recharge estimated by various methods of hydrograph separation used as a calibration target dataset for large SWB models is given in Trost and others (2018). For the Maine SWB model, streamflow data from 32 unregulated watersheds were used for the recharge and runoff calibration targets (fig. 1; table 1).

Although the SWB software simulates other components of the overall water budget, including direct runoff and actual ET, few SWB model calibrations to date have used more than observed recharge values to calibrate the model. The SWB model software includes many potential adjustments that control ET and runoff, and the values chosen for these parameters cascade through the calculations to impact potential recharge as well. None of the previous examples of calibrated SWB recharge models reviewed for this study constrained the calibration using ET data, which could result in a nonunique and possibly inappropriate fit of the model parameters. The Maine SWB recharge model presented in this report was calibrated using all available water-balance terms (recharge, direct runoff, and ET), which should result in a more robust and better constrained model. Furthermore, none of the SWB model studies published to date have attempted to quantify the uncertainty in the results, possibly because of the long run times for a large SWB model, but this study conducted a robust calculation of the uncertainty in the modeled potential recharge across the State of Maine.

Land-use data for the Maine SWB model were based on the Maine Land Cover Dataset (MELCD; Maine Office of Geographic Information Systems, 2006; see appendix 1). The MELCD data are based on Landsat Thematic Mapper 5 and 7 imagery from 1999 and 2000 and have a spatial resolution of 5 m. Land-use classes from the MELCD were condensed into 19 categories (table 2; fig. 3). Some modifications to water, wetland areas, and gravel pits were made using the NRCS soils data so that these areas did not conflict between the soil classes and land uses. The resampling to 250- and 500-m grid resolution was done by calculating the most prevalent land use in each larger grid cell. A test was done to determine whether resampling to coarser grid cells changed the overall distribution of land uses in the study area. When the 5-m MELCD data were resampled to 250 and 500 m, the overall percentage of each land use was the same as the original, to within 0.2 percent.

The other two data inputs for SWB (hydrologic soil groups and AWC) were produced for this study using gridded soil survey data from 2016 (NRCS gridded Soil Survey Geographic Database [gSSURGO] data, Soil Survey Staff, 2016). The data format is a raster of soil map-unit keys with a 10-m resolution. The map-unit keys link the raster cells to many attribute tables, including (among others) hydrologic soil groups, drainage classes, soil-unit descriptions, parent material, and AWC. The gridded data were resampled to 250 and 500 m for the Maine SWB model.

The hydrologic soil groups (U.S. Department of Agriculture [USDA], NRCS, 2007) are used in SWB alongside land use to classify the landscape into combinations of land use/vegetation and soil texture that are assumed to transmit water similarly through the rooting zone and unsaturated zone to the water table under the same climatic conditions (Westenbroek and others, 2010). Previous studies using the NRCS hydrologic soil groups as the basis for the soil type data in SWB have generally used the standard seven hydrologic soil groups as defined by the NRCS (A, A/D, B, B/D, C, C/D, and D), where the soils in groups A, B, C, and D range from being able to transmit water very freely (group A soils) to soils that do not transmit water well at all, especially when saturated (group D soils). The groups A/D, B/D, and C/D refer to soils that transmit water differently when saturated and often apply to areas with shallow water tables (wetland areas; USDA, NRCS, 2007).

An initial evaluation of the use of SWB in Maine for this study determined that the group D soils include a range of soil types that ranges, on one end, from tight clay deposits on coastal lowlands to areas that have thin (0–6 in.) soils over exposed bedrock in mountainous areas with high slopes. Because the process of generating runoff and recharge from incoming precipitation in these areas is quite different, the group D soils for Maine were subdivided into three subgroups based on the soil drainage class for each soil unit: “D–Ex” are the D soils that are also excessively drained (primarily shallow soils over bedrock, often steep slopes); “D–SoEx” (somewhat excessively drained D soils) are primarily soils in subdued hilly areas and often are composed of glacial till; “D–Poor” (poorly and somewhat poorly drained D soils) are a group of several poorly drained soil types, including glacial clay deposits, silt loam soils (farmable but not peats), silt-loams, and silty clay loams and silt loams (no plant material or peat mentioned). Some are tidal marshes or upland areas of poor drainage (forested). The nine hydrologic soil groups used in the Maine SWB model are listed in table 3, and their distribution is shown in figure 4.

The model calculates potential recharge based on each cell’s individual land-use class and hydrologic soil group. Considering all the possible combinations of land-use class and hydrologic soil groups in the model area, there are 171 possible categories created by the intersection of these two datasets (table 4). Many of the categories have near zero area across the landscape. The 35 most-abundant categories (named using the format of “land-use class:hydrologic soil group”) together represent 86 percent of the State (fig. 5). Maine is primarily a forested State—13 of the 15 most-abundant categories include mixed, evergreen, deciduous, or wetland forest land-use classes. The other two most abundant categories are scrub/shrub:D–Poor and scrub/shrub:C/D, which largely cover areas in northern and northwestern Maine that were recovering from heavy logging operations in the 1990s. The mixed forest:D–poor, evergreen forest:D–poor, mixed forest:C/D, mixed forest:C, mixed forest:D–SoEx combined account for 37.9 percent of the model area.

The AWC in the soil horizon is defined as the number of inches of water that can be held per foot of soil thickness (see the NRCS Soil Survey Manual [Ditzler and others, 2017] for a complete description of the derivation of these data). The AWC is used by SWB to calculate the maximum amount of soil-water storage that can be held in a model grid cell. SWB calculates the total amount of potential soil moisture storage as the AWC times the rooting zone depth for each model cell, where the rooting zone depths are adjusted for each land-use class:hydrologic soil group category using the SWB lookup table (see the “Lookup Tables and Control File” section below). The available water-capacity grid for Maine (fig. 6) was obtained from the gSSURGO data (Soil Survey Staff, 2016), and modified for areas of missing data (appendix 1).

Although the AWC of the soil, or the amount of water that a soil can hold under saturated conditions, could be thought of as a component of the soil’s hydrologic description, there is not a strong relation between the hydrologic soil groups and the AWC for Maine soils, as illustrated in figure 7. The AWC for hydrologic soil groups A and D–Ex are distinctive in that there is a higher proportion of cells with less than 3 in. of storage per foot than in the other categories, which would be appropriate for very sandy soils (generally describing group A), or thin soil over bedrock (D–Ex). And the amount of water-holding capacity generally increases as the soil group’s capacity to transmit water gets lower, which would be appropriate for finer-grained soils that can hold more water than coarse-grained sandy soils. However, the graphs (fig. 7) illustrate that sometimes the AWC for a soil group does not match the description well—for example, the A/D soil group generally represents wet areas that are poorly drained, and the lack of drainage could increase the amount of water that the soil will hold dramatically as compared to the same soil that has free drainage. The way that SWB calculates infiltration below the rooting depth in a case where the AWC is low does not consider the lack of drainage, however, and could result in more calculated recharge than would otherwise seem reasonable.

The DayMet (version 3) daily climate data from the Oak Ridge National Laboratory (Oak Ridge, Tennessee; Thornton and others, 2018) were the source of the daily minimum and maximum temperature and daily precipitation data used in the Maine SWB model. These data, which are available in the Network Common Data Form (netCDF) format, have a spatial resolution of 1 kilometer. The DayMet data are derived from an algorithm that models daily temperature and precipitation based on ground-surface observations, elevation, and incident solar radiation (Thornton and others, 2018).

Precipitation is a major driver of potential recharge. Typically, the annual precipitation for Maine falls between 40 and 50 in. (fig. 8), with higher amounts at higher elevations and in some of the coastal areas and lower amounts in the rain shadow behind the northern end of the Appalachian Mountains and in northern Maine.

Another source of modeled precipitation data for the Nation are the Parameter-elevation Regressions on Independent Slopes Model (PRISM) data from Oregon State University (PRISM Climate Group, Oregon State University, 2012): annual “normal” precipitation from 1981 to 2010 (fig. 9). These data are available as monthly and annual data, with a spatial resolution of 800 m. These data do not have the spatial or temporal granularity of the DayMet data and cannot be used with the SWB model, but the overall spatial pattern of annual precipitation for Maine should be comparable for both datasets. A gross comparison of the DayMet annual average (fig. 8) and the PRISM data (fig. 9) indicates general agreement in the overall patterns and amounts of annual precipitation, except for the area along the northwestern border with Canada, generally in the area covered by calibration watersheds numbers 2 (St. John River) and 32 (North Branch Penobscot River; and part of 5 [Allagash River]), extending south along the border towards New Hampshire. This discrepancy is assumed to be an artifact of the interpolation method used by DayMet and the available weather stations between Maine and adjacent areas in Canada. Impacts on the modeled SWB potential recharge are discussed in the “Simulated Recharge for Maine, 1990–2015” section.

The Maine SWB model uses two lookup tables to calculate the water balance terms: the primary land-use lookup table, and a second irrigation lookup table, which was used for the ET calculations using the FAO56 ET method (Westenbroek and others, 2018; Allen and others, 1998), which gives much greater control over the ET simulation as compared to the default Thornthwaite-Mather method (Thornthwaite and Mather, 1957. The primary land-use lookup table contains values for runoff curve numbers, maximum daily recharge, and rooting depths for each combination of land-use class and hydrologic soil group in the model (example shown in table 5; see full table, appendix table 1.2). With 19 land-use classes and 9 hydrologic soil groups, the Maine SWB model has 171 different values for each of these categories. Lookup values for interception (if used) vary with land use and growing season and are also included in the SWB land-use lookup table. The irrigation land-use table (see example in table 6; see full table, appendix table 1.3) includes plant growth settings such as crop coefficients (K_cb values for onset of growth, plant maturity, and senescence), growing-season lengths, and bare soil evaporation settings for every land-use class.

PEST’s use of highly parameterized inversion allows for the use of hundreds of model parameters, while not introducing problems of parameter insensitivity and correlation. The primary parameter set for the Maine SWB model consisted of values in the land-use lookup table: 515 parameters for runoff curve numbers, maximum daily recharge, and rooting depths. The interception values were fixed at zero and not used as parameters. The irrigation lookup table accounted for another 28 parameters that controlled the ET calculations: 13 K_cb values and 15 multipliers for bare-soil evaporation applied across sections of the table (543 total parameters; see appendix 2, tables 2.1 and 2.2, available for download at https://doi.org/10.3133/sir20195125, for complete lists).

To reduce the number of parameters from the lookup table evaluated during parameter estimation, a threshold of 0.1 percent of the domain (1,200 model cells) was set so that values for combinations of land-use class and hydrologic soil group that were not widespread in the model (and would provide little value to the overall calibration) were not adjusted during the parameter estimation runs. Initial values for the lookup table were based on pilot calibration exercises for small subset areas of the Maine SWB model. The final parameter estimation runs used 223 adjustable parameters.

SWB model runs and the calibration were performed on a Linux-based operating system, with a Windows 10 emulator, and on a Windows 10 operating system. Parallel processing of the calibration runs was conducted through HTCondor on a dedicated cluster of several hundred computer cores.

PEST uses singular value decomposition during the iteration runs to group parameters into super-parameters, which reduces potential parameter correlation issues that can plague other parameter-estimation procedures.

In total, 3 sets of calibration targets for 32 calibration watersheds (fig. 1; table 1) were used as input to the parameter-estimation runs, which used 13 years of data (2000–12). (The first year [2000] is a model setup year; the actual calibration time period is from 2001 to 2012 [12 years].) A shortened period (as compared to the 1991 to 2015 total time period) for calibration was used for increased overall efficiency and to avoid excessively long calibration run times. The 2000–12 time period was chosen because it includes periods of low flows (2001–3) and periods of high flows (2005 and 2008). The watersheds selected for inclusion in the calibration met the following criteria: flows at the streamgage location represented natural conditions and were unregulated. Four of the watersheds that were used are above the optimal size for hydrograph separation (500 square miles); consequently, the observations from these watersheds were weighted lower than the others. A minimum was not placed on the number of years of streamflow record for the watersheds, which had between 4 and 12 years of record for the calibration.

Parameter estimation refers to the use of software to find the best fit solution of parameter values to reduce the model error, or lack of agreement between the measured and the model simulated values for each observation. The residual (measured value minus the simulated value) for each observation is multiplied by the observation weight, squared (making each value a positive number), and summed (Anderson and others, 2015). The model objective function, or phi (Φ), is the sum of the squared residuals for the model. The combination of parameter values with the lowest possible objective function thus constitutes the best-fit model. The PEST software (Doherty and Hunt, 2010; Doherty, 2004) was used in the calibration of the Maine SWB model. PEST uses information about the model parameters that are set up to run thousands of model runs to find the best fit model. The model runs were controlled and organized using the HTCondor computer cluster at the T.C. Chamberlin computing center at the Wisconsin USGS office.

The modeler controls which parameters will be adjustable during the estimation runs and how much to allow parameters to vary. The upper and lower bounds, within which PEST is allowed to test alternative values, are set for all the parameters in the model. Upper and lower bounds used for the runoff curve numbers, maximum potential recharge, and plant rooting depths used by the SWB lookup table were set using the modeler’s best judgement and values used in other SWB models. Upper and lower bounds for the adjustable parameters for the FAO56 ET lookup table were set after a literature search on the possible ranges of values that would be reasonable for Maine. The complete list of parameters used, whether they were adjustable in the model, and the upper and lower bounds are provided in appendix 2 (tables 2.1 and 2.2).

Initial estimation runs were done that allowed PEST to use the full range of the parameter bound in the best-fit calculations. However, this resulted in some parameters being estimated at their furthest possible limits, not at a most “reasonable” value. PEST allows the modeler to use their knowledge of the system to further reign in the parameter adjustments, so the final values are as close as possible to values the modeler thinks are most reasonable. Tihkonov regularization is a process that can be used in PEST to find the best fit of parameters with a penalty to moving the parameters too far away from a “preferred” value (Anderson and others, 2015). This method prevents highly parameterized models from becoming over-fit, which may result in smaller model error but may not represent reality well (Anderson and others, 2015). The model error of a model using regularization will not be as small as one without but should result in a more parsimonious model. The final Maine SWB runs were done using Tihkonov regularization, after evaluating the parameter values of the initial runs.

The PEST parameter estimation also made use of singular value decomposition (SVD) to reduce the problems that can be introduced in a highly parameterized model of highly correlated parameters and insensitive parameters. SVD groups parameters into super parameters during the estimation runs and uses these super parameters to reduce the correlation and insensitive parameter issues. A more detailed discussion on the use of SVD can be found in Anderson and others (2015).

The model calibration process compared 902 weighted observations of recharge, runoff, and ET to the model output for 2001–12. The model fit for the final calibrated parameters is evaluated by comparing the observed values of recharge, direct runoff, and ET to the model output values. The differences between the observed and simulated values for the 902 observations are the residuals. The overall mean model error (average of all residuals) was 0.39 in. The mean of the absolute value of the residuals, or the mean absolute error (MAE), was 2.32 in. The root mean squared error (RMSE) for the calibrated model overall is 3.14 in. For the recharge observations only, the overall mean model error was 0.03 in., the MAE was 2.64 in., and the RMSE was 3.43 in. The runoff observations are not as well fit: the overall mean model error was 1.06 in., the MAE was 2.75 in., and the RMSE was 3.78 in. The ET observations have a smaller range in values and a smaller range in errors: the RMSE for ET observations was 2.27 in., and the MAE for ET observations was 1.77 in., whereas the mean overall model error for ET was 0.16 in.

Figure 10A illustrates the total model error in graphical form, showing the observed and simulated values, as compared to the 1:1 line and a fitted line that represents the actual mathematical relation between the observed and simulated values. In a perfectly calibrated model that reproduced all observations precisely, all the points would line up with a 1:1 relation between the observed and simulated values. The Nash-Sutcliffe efficiency (NSE) test (Nash and Sutcliffe, 1970) is a normalized statistic that indicates how well the observed versus simulated values fits the 1:1 line (Moriasi and others, 2007; Trost and others, 2018). A Nash-Sutcliffe efficiency value of 1.0 would indicate a perfectly calibrated model; the value for the Maine SWB model is 0.75. The simulated model results line up closely to the 1:1 line, indicating a relatively accurate model where the residuals do not deviate significantly from the line in one direction or another. Figure 10B shows the plot of residuals. The probability plot correlation coefficient (PPCC) test (Helsel and Hirsch, 1992) evaluates the normality of the residuals. The PPCC test for the Maine SWB model indicated a normal distribution of residuals across the 1:1 line (PPCC value=0.98401, probability [p-value] less than 0.0001). In other words, the residuals for the overall model are not very skewed. Another common statistic used to determine the fit of the model is the correlation coefficient squared (r²). The r² value for the simulated versus observed values for the Maine SWB model is 0.76.

The use of Tihkonov regularization, as discussed earlier, prevents an “overfit” model, where a closer model fit is obtained at the expense of keeping parameter values close to the modeler’s judgment of most reasonable values. A larger r² and smaller RMSE could have been obtained without using regularization, but this could have led to model overfitting and unreasonable parameter values.

Considering each type of observation separately (fig. 11) shows that the observations for recharge (fig. 11A, D) fall most closely to the 1:1 line, but the residuals (fig. 11D) are somewhat skewed (the NSE for the recharge observations alone was 0.58, and the PPCC test indicated normality of the residuals, p-value=0.0065). At the high end of observed recharge (more than 25 in/yr) the model underpredicts potential recharge, shown by having a positive residual. At low amounts of observed recharge (less than 15 in/yr), the model overpredicts some of the values, shown by having a negative residual. Between 15 and 25 in/yr, the model does not consistently over- or under-predict the potential recharge. The runoff simulated values have the greatest degree of deviation from the observed values (fig. 11B), and the residuals (fig. 11E) deviate more from the observed values for watersheds and years with high amounts of runoff (NSE=0.52, PPCC indicated normality of the residuals, p-value<0.001). This indicates that the model has difficulty partitioning sufficient water into the runoff part of the water budget when overall runoff is quite high (over 20 in. of observed runoff). The Maine SWB model performs better for runoff when the modeled runoff is less than 20 in/yr.

The ET observations (fig. 11C) are equally balanced across the 1:1 line, but the residuals (fig. 11F) are quite skewed between lower and higher observations (NSE=0.26, PPCC test indicated non-normal residuals at alpha [α]=0.05). The model estimates more ET than the SSEBop observations at the lower range of observed values and too little at the higher range of ET observed values. Comparisons of SSEBop ET estimates to ET flux towers (Reitz and others, 2017; Kim, 2017) have shown that at low ET measurements, the SSEBop method underestimates ET, and at higher ET measurements, the SSEBop method overestimates ET. The estimation bias for the SSEBop method could account for at least some of the skewness in the SWB model results because the errors are in the same direction as they are when comparing actual ET measurements to the SSEBop estimates.

Another graphical approach to evaluating the model performance is a comparison of the observed and simulated three major water-budget components by year for individual watersheds. Six calibration watersheds distributed across the State were selected to illustrate the model performance on a watershed basis (fig. 12). The calibration watersheds, in a clockwise order around the State from north to southwest (fig. 1; table 1), are watersheds 5 (Allagash River; fig. 12A), 31 (Meduxnekeag River; fig. 12B), 14 (Narraguagus River; fig. 12C), 17 (Sheepscot River; fig. 12F), 12 (Little Androscoggin River; fig. 12E), and 8 (Carrabassett River; fig. 12D). All but the Meduxnekeag River watershed have 12 years of complete observations; watershed 31 has more limited recharge and runoff observations, spanning 2004–12. The bars for simulated and observed ET and recharge are just about identical in several years for every watershed. The bars for the observed and simulated runoff are the most unequal, and some watersheds seem to have a consistent bias—in the Allagash River watershed, the modeled runoff is generally higher than observed (and the recharge lower), which could be an artifact of the base flow-separation methods used to calculate the observations (this watershed has a relatively high amount of surface-water storage, and the hydrograph-separation techniques may confuse slow surface-water outflow from lakes and wetlands with groundwater discharge). The Carrabassett River watershed has the opposite—more recharge is modeled than expected, and less runoff, especially during years of high precipitation (2005–6). This watershed has a high proportion of sandy group A soils near its mouth; it is possible that the streamgage does not capture 100 percent of the recharge, and that some may exit the watershed as underflow. Overall, each watershed has its own unique set of circumstances that may help to explain variations in the degree to which the observed values of recharge and runoff agree with the simulated values.

Assuming that the streamgage for each of these calibration watersheds captures all the direct runoff and recharge in the basin (which is a good assumption for most of the watersheds), and that the remaining incoming precipitation becomes ET as estimated by the SSEBop dataset, the total height of the observed bars should equal the total incoming precipitation over the watershed, plus any snow storage that is held over from the previous year. The precipitation totals range from about 35 in/yr in a few watersheds in 2001–2, to about 70 in/yr in 2005 in several watersheds. Similarly, the total height of the simulated bars represents the total input water (DayMet precipitation) plus or minus any changes in soil or snow storage over the watershed. Because of the combination of storage effects and other possible model errors, the total DayMet precipitation does not always agree with the observed

An important measure of the sensitivity of a model to variations in model input parameters (when the true value of the parameter is not known) is a parameter sensitivity analysis. Sensitivity of the model to the parameter values is calculated by PEST as part of the calibration process. The PEST output for the calibration using SVD enables an analysis of the total sensitivity of the model observations, for all the parameter types together, and for just the recharge observations by themselves. Parameter identifiability (Doherty and Hunt, 2009; Anderson and others, 2015) is a type of sensitivity analysis that analyzes the amount of information contained by the observations about each parameter. The calculation of this statistic uses SVD on the matrix expressing the sensitivity of every observation to every parameter. The result is unaffected by parameter correlation, which makes it a better statistic than weighted sensitivities (Doherty and Hunt, 2009).

Considering all the observations together, the model is most sensitive to the K_cb mid-season growth ET parameters (table 7; fig. 13A). This is understandable because these values directly control how much of the total soil moisture is moved by plants into the atmosphere during the height of the growing season and therefore how much is left in the soil to become potential recharge. The runoff curve numbers are the second most sensitive group (table 7; fig. 13A), and these operate at the beginning of the daily calculations to route excess water from the land surface to runoff, directly controlling what is available for plant uptake and potential infiltration.

Because the primary product of this study is the potential recharge to groundwater, a separate identifiability calculation was done for the observations of recharge. The recharge simulations are most sensitive to the runoff curve numbers (table 7; fig. 13B), closely followed by the mid-season K_cb ET parameters and maximum potential infiltration rates. The recharge calculations are more sensitive than the overall model to the maximum potential infiltration rate and rooting depth parameters. This follows from the fact that some of the observations in the overall model, the runoff calculations in particular, do not rely as heavily on these parameters.

As a measure of the uncertainty in the calibrated model 25-year median annual potential recharge grid, a Monte Carlo analysis was performed, using 300 potential realizations of the suite of model parameter values, using the method of Tonkin and Doherty (2009; White and others, 2016; see above section on “Modeling Uncertainty Representation”).

From each of the successful Monte Carlo runs (285 total), the 25-year median grid was calculated. The model fit of each run, as compared to the observation values used during the calibration, also was calculated. Any Monte Carlo run whose model fit fell outside a range of acceptable Φ values was discarded from the final analysis, resulting in 258 model realizations with reasonable combinations of parameter values. The range in Φ values for the “acceptable” runs was from 270 to 360 (the best-fit model from the PEST calibration had a Φ of 318). The model runs with unacceptably low model fit included combinations of model parameter values that produced recharge estimates unlikely to represent actual conditions. Using the remaining 258 model realizations, cell-by-cell statistics were generated, and the standard deviation of all possible values for each grid cell was recorded. As in the best-fit model, each median potential recharge grid was given a screening for anomalously high values before the overall standard deviation grid was calculated.

The resulting grid of standard deviation values (fig. 19) provides a quantitative measure of the uncertainty in the Maine potential recharge grids that is a result of uncertainties in the model parameter values. The overall model uncertainty distribution is graphically shown in figure 20—the average (mean) value for the State is 2.62 in.; the 10th percentile is 1.49 in. and the 90th percentile is 3.78 in. To translate these into an absolute uncertainty of the average recharge, a typical method is to take plus or minus 2 times the standard deviation of a value.

Overall, most of the modeled area has a calculated uncertainty (standard deviation) of 1.5 and 4.0 in. (fig. 20). The uncertainty of the estimated recharge rates for the most abundant land-use class:hydrologic soil group categories in the State have a wide range, from 0.81 to 6.41 in. (table 9). The amount of uncertainty generally is lower for categories with group A or B soils, which are more permeable and well drained. In these areas, the standard deviation from the Monte Carlo runs reflects the fact that few of the parameters that have a high degree of identifiability (fig. 13B) apply to these categories. Several of the categories with more poorly drained soil groups (D–Poor in particular) have much higher standard deviation from the Monte Carlo runs than the other categories, and the values are not directly proportional to the amount of identifiability of the model parameters.

The land-use class:hydrologic soil group categories with the highest average potential recharge, most of which have group A soils and vegetation with relatively shallow root zones such as blueberry barrens, scrub/shrub, pasture/hay, and cultivated crops, also have relatively small amounts of uncertainty relative to the total recharge (fig. 21). The categories with the lowest potential recharge rates, which include land uses with relatively impervious surfaces (roads/runways/bare rock), some wetlands, and forest types with D–Poor soils, have uncertainty values that are much higher in relation to the amount of modeled potential recharge, but some of these uncertainty values are similar in absolute magnitude to the higher-recharge categories.

The standard deviation values can be used to calculate a 95-percent confidence interval around the median potential recharge value. The total 95-percent confidence range is calculated using the standard deviation (σ): minimum=median−(2×σ) and maximum=median+(2×σ). For any area of interest, the 95-percent confidence intervals can be calculated to get an estimate of the overall possible range in the modeled 25-year average potential recharge.

Other factors also contribute to the overall uncertainty in the recharge estimates, but because they are nonvarying components of the model, they cannot be changed to evaluate their contribution to the total uncertainty. These include uncertainty in the DayMet climate data used in the simulation, uncertainty in the soils mapping from NRCS (including the hydrologic soil groups and AWC), and uncertainty in the land-use grid. Some of these other sources of uncertainty that are not specifically quantifiable can be discussed or evaluated in a qualitative manner.

The DayMet data (Thornton and others, 2018) are based on a model that interpolates precipitation and temperature data between climate data-collection points. Across the northwest boundary between Maine and Canada, anomalous values of annual precipitation are likely artifacts of the interpolation methods used between stations in Canada and the United States because these do not appear anywhere else in the State (fig. 8). As discussed in the “Exclusion Zone” section, an exclusion zone was set up to remove those anomalous areas from the final datasets.

Another example of underlying datasets possibly contributing to model error is that land use has changed in some areas of the State since the MELCD data were collected in 1999 and 2000. One particular land-use class, scrub/shrub, is particularly common in the northern and northwestern part of the State where logging in the 1990s produced large areas of clearcuts or patchy clearcuts, which were assigned the scrub/shrub land-use class before trees had a chance to grow back. By the end of the model simulations in 2015, these areas would have likely grown up into young forests, which would change the ET response to precipitation. Although the land use was slowly changing over the 25-year simulation period, which would be reflected in the observations of ET, base flow, and direct runoff, the model is not set up to have parameters that also change with time. Urbanization also increased a small amount during the 25-year simulation time, but this land-use class covers a relatively small percentage of the overall model area.

The other source of data for the model that could contribute uncertainty is the soils data from the NRCS. The mapping of the soil units and assignments of AWC was done originally by county soil staff, and the interpretation of surficial geology and soil classes is not uniform across the State. For example, the hydrologic soil group C/D is described in USDA, NRCS (2007) as having moderately low water transmission rates and a water table less than 60 cm from the surface, which implies that the designation would typically apply to areas with impeded drainage such as wetlands. However, some counties assigned large areas of thin glacial till soils over bedrock in mountainous areas to the C/D hydrologic soil group even if they did not have a shallow water table, whereas in other counties the thin glacial till over bedrock in mountainous areas was assigned to the D hydrologic soil group. Therefore, areas in different parts of the State may not behave very differently (in terms of the observed values of ET, runoff, and base flow), but because the soils are assigned using different criteria the model simulates them quite differently. Another source of possible uncertainty from the NRCS is the AWC data. As discussed earlier, the assignment of the AWC is not always understandable from the point of the hydrologic soil groups (see the “Model Input Data Summary” section) or underlying soil classification, so the accuracy of this dataset is unknown, and the uncertainty contribution to the overall results would be difficult to quantify (but may be important).

The grids of potential annual recharge for Maine are intended to be used to provide first-cut estimates of recharge for geographic areas no smaller than the smallest watersheds used in the calibration of the model—or about 1.5 square miles. It is recommended that the grids be used to calculate an area-wide average potential recharge for any given area of study (as compared to point-specific potential recharge), and an uncertainty around the mean should be calculated from the standard deviation grid at the same time.

One potential use of the Maine SWB potential annual recharge grids would be to create an initial estimate of recharge for an area for which one might want to calculate an overall water budget, such as for a watershed. The suggested application of the data would include the following steps. First, define the watershed boundaries for the study using GIS software or using the Maine StreamStats application (Lombard, 2015; https://streamstats.usgs.gov/ss/). A shapefile of the watershed can be downloaded from StreamStats. Using the datasets from the data release accompanying this report (Nielsen and Westenbroek, 2019), calculate the spatial average (or mean) value for the watershed for each of the potential recharge layers—mean annual, median annual, 25-year minimum, and 25-year maximum. Then, calculate the spatial mean value for the standard deviation layer. Finally, calculate the 95-percent confidence interval on the mean and median using the standard deviation grid: the 95-percent confidence range is calculated using the standard deviation (σ): minimum=median−(2×σ) and maximum=median+(2×σ).

For an example watershed located somewhere in Maine that is 12.4 square miles in area, a list of the results for calculating the mean annual potential recharge could produce the results as listed in table 11. The standard deviation grid is intended for use with the 25-year mean and median potential recharge grids but not for the 25-year minimum or maximum grids.

Areas of no data for the State recharge grids include the White Mountain National Forest and the former Brunswick Naval Air Station, for which areas soils data were not available. In addition, the anomalous DayMet precipitation data (Thornton and others, 2018) were screened out of the final analysis with an exclusion zone in northwestern Maine along the Canadian border (figs. 15–19).

Refer to the “Model Limitations and Assumptions” section for a discussion of the potential use and interpretation limitations of the modeled output. In addition, the mapping of the AWC values does affect the ability of the Maine SWB model to accurately represent the average potential recharge. Users are encouraged to verify that the AWC is in an expected range for the hydrologic soil groups in their area of interest. The AWC and hydrologic soil groups data for this model can be found in the USGS model archive for this model at (https://doi.org/10.5066/P9GRP7DH; Nielsen, 2019).