The full water balance for a given hydrologic unit can be generally expressed as Iin-Iout = ΔS, where Iin and Iout represent the hydrologic inflows and outflows to some control volume, and ΔS is the change in water storage within the control volume. More specifically, the full water budget for a watershed under natural (non-anthropogenic) conditions can be written as 1Prain+Psnow+Rin-Rout+Qin-Qout-ETveg-Edir=ΔSsoil+ΔSsurf+ΔSgw+ΔSsnow.

In Eq. (), inflows to the watershed are precipitation in the form of rain or snow (Prain,Psnow), surface runoff entering the basin from upstream areas (Rin), or subsurface influx (Qin). Water may leave the watershed in the form of surface runoff (Rout), evapotranspiration from transpiration (ETveg) or evaporation from bare surfaces (Edir), or as groundwater flux to downstream basins (Qout) or deeper reservoirs (Qrecharge). These fluxes have a net impact on yield increases or decreases in sources of basin water storage, such as soil and groundwater reservoirs (ΔSsoil and ΔSgw), surface water ponding (ΔSsurf), or storage as snow water equivalent (ΔSsnow). Components in Eq. () are typically expressed as units of equivalent water height or volume per unit of time. This description of the water budget equation (Eq. ) is illustrated in Fig. 1a, and it may be amended to incorporate other components particular to a watershed; these could include anthropogenic fluxes and storage like irrigation, dam storage or pumping, or they could be unique traits of the basin such as fractured flow, lacustrine groundwater discharge, or seawater intrusion. Equation () may also be simplified by lumping precipitation, evapotranspiration, and storage components and also by ignoring surface and subsurface inputs external to watershed divides, which, for large enough control volumes, will be negligible (Fig. 1b). The water balance may then be simply expressed as 2P-ET-R=ΔS for precipitation P, evapotranspiration ET, surface runoff R, and total change in all storage sources ΔS.

In this study, the complete water balance (Eq. , Fig. 1a) is modeled using ParFlow–CLM (Kollet and Maxwell, 2006; Maxwell and Miller, 2005), an integrated groundwater–surface water model which uses the mixed form of the Richards equation to simulate three-dimensional variably saturated flow. The Richards equation is given as 3SsS(ψp)δψpδt+ϕδS(ψp)δt=Δ⋅-Ks(x)kr(ψp)⋅∇(ψp-z)+qs for specific storage Ss (L-1), relative saturation S (–), pressure head ψp (L), saturated hydraulic conductivity tensor Ks (LT-1), relative permeability kr (–), and porosity of the medium ϕ (–) at depth z (L) and time t (T). In Eq. (), relative permeability varies with pressure head through time based on relationships established by van Genuchten (1980), and qs is a source–sink term (T-1). A free-surface overland-flow boundary condition for continuity of pressure and flux applies to the groundwater flux term across the land surface and subsurface interface. The kinematic wave approximation of the momentum equation is used to solve overland flow, which is a function of ponded depth given by Manning's equation: 4v=S0nψ2/3, where n is the Manning roughness coefficient (LT-1/3) and ψ is the ponding depth (surface pressure head) (L). Note that the friction slope S0 (–) in Eq. () is used to approximate the bed slope (–) in the kinematic wave approximation.

ParFlow is coupled with the Common Land Model (CLM) (Dai et al., 2003), a land surface model which balances energy and calculates evapotranspiration at the land surface, in order to simulate the coupled water and energy budgets. CLM requires atmospheric conditions (precipitation, temperature, specific humidity, wind speed, and longwave and shortwave radiation) in order to provide hourly partitioning of net radiation into sensible, latent, and ground heat. Shown in Eq. (), CLM calculates direct evaporation from the ground using the gradient between specific humidity at the ground surface qg (MM-1) and at a reference height qa (MM-1), along with air density ρa (ML-3), atmospheric resistance rd (TL-1), and a soil resistance term β (–). 5ETdir=-βρaqa-qgrd

To calculate actual transpiration, CLM adjusts potential transpiration by stomatal and aerodynamic resistance terms as follows. 6ETpot=ρaLAI+SAIrb(qf-qc)7ETveg=ETpot×LdrbLAILAI,sunrb+rs,sun+LAI,sharb+rs,sha

Potential transpiration (Eq. ) is a function of leaf and stem area index LAI and SAI (–), boundary layer resistance rb (TL-1), air density ρa (ML-3), and the gradient of specific humidity between foliage and canopy qf-qc (MM-1). Transpiration (Eq. ) only occurs from the dry fraction of the canopy (Ld) and further depends on stomatal resistance rs (TL-1). In Eq. (), the sunlit (sun) and shaded (sha) fractions of the dry canopy are separately defined with their own LAI and stomatal resistance values. Note that the leaf and stem area index and stomatal resistance terms are parameterized by plant functional types and defined per cell, without fractional vegetation, and for a single canopy layer. For a further explanation of ET calculations in ParFlow–CLM, see Jefferson et al. (2017).

The PFCONUSv1 model represents the first integrated groundwater–surface water model employed at the continental scale at hyper-resolution (1 km). A full description of the model configuration and inputs can be found in Maxwell et al. (2015) and Maxwell and Condon (2016), but a brief summary is given below.

Spanning roughly 6.3 millionkm2 at 1 km lateral grid spacing, the PFCONUSv1 model encompasses the majority of eight major river basins in the United States at high resolution, including the Ohio, Missouri, Arkansas, Mississippi, and Colorado River basins. The model is composed of 3442 cells in the x (east–west) direction and 1888 cells in the y direction (north–south). Its five vertical layers of variable thickness provide a cumulative vertical depth of 102 m. From the top, soil layers are 0.1, 0.3, 0.6, and 1 m, respectively. Topographic slopes were calculated using the Barnes et al. (2016) algorithm, applied to the HydroSHEDS (Hydrological data and maps SHuttle Elevation Derivatives at multiple Scales; Lehner et al., 2008) digital elevation model, to guarantee a connected drainage network. Vegetation classes for characterization of plant functional parameters were provided by the IGBP land cover classifications and the USGS land cover dataset. Distributed, heterogeneous soil parameters, including saturated hydraulic conductivity, porosity, and van Genuchten parameters, were assigned to spatial soil units described by the Soil Survey Geographic database (SSURGO). Geologic units for the bottom 100 m thick layer of the PFCONUSv1 model were developed from the Gleeson et al. (2011) national permeability map. Estimates from Gleeson et al. (2011) were adjusted using the e-folding relationship described in Fan et al. (2013), which accounts for topographic complexity, and variance in permeability was also reduced. No-flow boundary conditions were imposed at the bottom of the model domain (assuming impermeable bedrock) and on the sides. Note that with a model depth of just over 100 m, the model may more appropriately be considered a shallow aquifer storage model. Deeper ΔS contributions are not resolved, which may not represent deeper hydrologic flow paths of thick and expansive aquifers such as the Ogallala, the saturated thickness of which can exceed 300 m (McGuire et al., 2012); however, as Maxwell et al. (2015) explain, the current model thickness and vertical discretization are limited not by computational expense but by data availability, with a lack of detailed depth-to-bedrock and aquifer thickness estimates at meaningful resolution.

Initial conditions were provided by an intensive spin-up process. First, a steady-state ParFlow groundwater configuration was run continuously without CLM; this model was forced by an average surface recharge flux derived from Maurer et al. (2002) and run continuously until the difference between outflow and recharge rates was less than 3 % of total water storage change. A full description of this steady-state model and its performance can be found in Maxwell et al. (2015). Second, and using the initial condition provided by the steady-state model, a transient system was simulated with the fully coupled ParFlow–CLM for water year 1985, the most climatologically average water year within the past 30 years. As described in Maxwell and Condon (2016), atmospheric forcing was bilinearly interpolated from the North American Land Data Assimilation System Phase 2 (NLDAS-2) (Cosgrove, 2003; Xia et al., 2012a, b) For spin-up purposes, the transient simulation was run continuously for 4 years of repeated 1985 atmospheric forcing to provide an initial condition for the simulation in this study. Thus, the initial condition provided here represents pressure head, soil moisture, and surface energy balance conditions that would be present during the most climatologically average water year in recent history. Since the model does not incorporate anthropogenic abstractions in the form of pumping, injections, irrigation, or surface water diversions and dam storage, the initial conditions provided also represent a pre-development scenario.

For this study, PFCONUSv1 was run for modern-day water years using initial conditions provided by the transient spin-up process described above. The simulation here was run at hourly temporal resolution for water years 2003 through 2006. Atmospheric forcing originated from the 12 km NLDAS-2 product (Xia et al., 2012a, b); however, finer-resolution products were blended in where available and elevation effects were incorporated to produce higher-resolution, more physically realistic meteorological variables. Such products included the 4 km Stage IV and Stage II radar and gauge products and Level 2 shortwave radiation from the GOES Surface and Insolation Products (GSIP). These adjustments to the 12 km NLDAS data and the finer-resolution products are described, for example, in Pan et al. (2016) and include the following: gap-filling and daily rescaling procedure to ensure the Stage IV hourly data match daily totals from NLDAS-2; adjustments to timing for the GSIP Level 2 data based on solar angles; and elevation-dependent downscaling of 12 km NLDAS-2 products, such as hydrostatic effects for atmospheric pressure and lapse rates for specific humidity, air temperature, and longwave radiation. The final atmospheric variables were interpolated using bilinear interpolation to the 1 km PFCONUSv1 grid.

An important consideration when attempting high-resolution integrated models of this kind is of course the computational demand. ParFlow–CLM solves the globally implicit solutions to nonlinear and coupled equations in Eq. () through Eq. () with a Newton–Krylov parallel solver (Jones and Woodward, 2001); the associated significant computational challenge is tackled with a multigrid preconditioner and highly scaled parallel efficiency (Kollet et al., 2010; Reed M. Maxwell, 2013; Osei-Kuffuor et al., 2014). The simulations presented here were run on 3456 processors distributed to 72 and 48 units in the x and y directions, respectively, on the Cheyenne high-performance computing system managed by the National Center for Atmospheric Research (NCAR) Computational and Information Systems Lab. Required core hours for a single water year averaged over 300 000 core hours for this processor topology; however, the scaled parallel efficiency even at this decomposition is over 60 %. The hourly outputs generated over 11 TB of information per water year, while the required storage for the interpolated atmospheric forcing alone was over 3 TB per water year.

Simulated runoff, evapotranspiration, and sources of storage change from the PFCONUSv1 model were compared against available point-scale measurements and coarse-resolution remote sensing products in order to identify locations of relatively better or worse performance, major sources of model bias, and regions most in need of improvement. Table 1 provides a summary of all data products compared to PFCONUSv1 outputs. It is important to note here that while we use absolute error metrics common to calibrated models developed specifically for prediction, calibration of the PFCONUSv1 model is not a goal of this study, nor is it feasible given the computational demands posed by such a highly parallelized platform. Rather, the intent is to evaluate the model's ability to demonstrate realistic behavior, to identify regions, times, and sources of uncertainty, and to prioritize areas of improvement for future model development.

Performance metrics for evaluating PFCONUSv1 include percent annual bias or total annual bias, Spearman rank correlation coefficient, and the ratio of root mean squared error to the standard deviation of observations (RSR). While these were not calculated for all validation datasets and the temporal resolution at which they were evaluated differed between datasets (e.g., daily, weekly, or monthly), they are each used at some point in our analysis, so we define them here.

As a measure of average magnitude accuracy with an optimal value of 0, percent bias is given by 8PBIAS=∑i=1nSi-Oi∑i=1nOi⋅100, where Si and Oi are simulated and observed values. Percent bias in PFCONUSv1 outputs was calculated using daily observations in Eq. () such that days during which observations were unavailable were excluded for both simulated and observed annual totals. Percent bias is an effective metric for evaluating long-term mean values, but it cannot be used to evaluate timing or shorter temporal events; further, if the model underpredicts and overpredicts with similar magnitudes, PBIAS can be deceivingly low.

For these reasons, we also calculate for each stream gauge Spearman's rank correlation coefficient, or Spearman's ρ, given by Eq. (). 9ρ=1-6∑i=1ndi2n(n2-1)

Unlike the coefficient of determination R2, which describes the degree of collinearity between the data, Spearman's ρ independently ranks the simulated and observed values, with di in Eq. () being the difference in ranks for a given value i, and n is the number of values in the series. Unlike other metrics describing temporal correlation, such as R2 or Nash–Sutcliffe efficiency, ρ is less restrictive; it does not assume linearity and instead tests for monotonic correlation. The optimal value for ρ is 1, and the cutoff for good performance is likely analogous to that of R2, which varies in the literature but is generally around 0.6.

A final performance metric, the RMSE–observation standard deviation ratio (RSR), is also provided. RSR is given by Eq. () and describes root mean squared error (RMSE) relative to the standard deviation of the observations. 10RSR=RMSESt.  Dev.  Obs.=∑i=1nOi-Si2∑i=1n(Oi-O‾)2

In Eq. (), O‾ is the mean of observations. While RSR is less widely used than PBIAS and ρ, its benefit lies in its normalization of the common error index statistic RMSE; the ratio describes error relative to natural variability in the true system such that an RSR of 1 suggests that the mean daily error is equal to 1 standard deviation of observed values and thus comparable to what we may expect from noise or intra-annual variability. An RSR value of 0 is optimal, while values under 0.5 (RMSE is less than half of the standard deviation of observations) are considered to be excellent (Moriasi et al., 2007).

Together, performance metrics (Eq.  through Eq. ) are quantitative indicators of model realism, representing a model's ability to capture long-term states (PBIAS) and timing (ρ), as well as its error relative to expected system variability (RSR). However, many other statistical criteria are popular (Waseem et al., 2017), and the target values used to indicate unacceptable, acceptable, or excellent performance can vary because criteria for evaluation necessarily depend upon model purpose (i.e., a regional surface water model that has been well calibrated for operational forecasting will represent spatiotemporal patterns of streamflow with higher accuracy than a continental-scale land surface model can plausibly achieve). Further, performance is expected to decrease with increasingly higher temporal resolution: for instance, criteria may be more lenient across all error metrics when moving from monthly to daily timescales at the watershed scale (Moriasi et al., 2015) as well as from seasonal to monthly timescales at the global scale (Krysanova et al., 2020). As a physically based, high-resolution (spatially and temporally), and uncalibrated continental-scale model, a primary purpose of the PFCONUS, and others like it (Gleeson et al., 2021), is to understand process interactions between groundwater, surface water, and ecohydrological fluxes. In this study, a PFCONUS-simulated water balance component in Eq. () is generally judged to be excellent for this purpose with the following measures: RSR < 0.6, ρ > 0.7, or |PBIAS| < 20 %. Locations that indicate unacceptable or poor performance are those with RSR < 1.2, |PBIAS| < 75 %, and ρ > 0.5. However, error metrics are reported with the primary goal of intercomparison across locations (interpretation of metrics should be paired with visual inspection of spatial patterns and time series provided) or, where discussed, relative to the performance of other continental-scale hydrologic or land surface models. Gleeson et al. (2021) caution against the use of model evaluation to indicate a “finished” product and instead recommend open-ended evaluation and model improvement. Metrics (Eq.  through Eq. ) are therefore used to identify where future development of PFCONUS can be focused to improve upon timing, volume, and variability of fluxes. Performance metrics reported in this study are also supplemented by plots of probability of exceedance or non-exceedance where appropriate (see Figs. S1 through S8 in the Supplement), which should help regional-scale modelers identify relative performance of major basins at various thresholds. Since there are many other commonly used performance metrics particular to streamflow, we also report Nash–Sutcliffe efficiency and Kling–Gupta efficiency for simulated flows at USGS gauges (Fig. S9 in the Supplement) (Gupta et al., 2009).

The ability to accurately simulate overland flow at the major basin or continental scale and above has for several years been a topic of much interest in the hydrologic community. Continental or global streamflow estimates could be coupled to general circulation models to provide predictions of surface water resource vulnerability to climate change (e.g., Koirala et al., 2014); large-scale runoff models could additionally provide flood forecasts to regions lacking developed surface water monitoring networks (Kauffeldt et al., 2016). While integrated groundwater–surface water modeling is computationally demanding, results from PFCONUSv1 represent a rare opportunity to evaluate streamflow performance (1) because the integrated system platform resolves shallow aquifer, vadose zone, and surface water transfer, and (2) streams form naturally as surface water is routed by topography without requiring pre-defined stream reaches.

PFCONUSv1 streamflow R was evaluated against 2392 USGS stream gauges which are well distributed across the United States. We analyze model performance using percent bias, Spearman rank correlation, and RSR. However, Gleeson et al. (2021) suggest that while the use of error metrics and direct comparison of observations with simulated values are valuable for evaluation, they should be supplemented with hydrologically meaningful diagnostic signatures to better understand system dynamics. Further, PBIAS can be sensitive to precipitation provided by the interpolated NLDAS atmospheric forcing product. Since P is an input to the PFCONUSv1 rather than a model result, runoff ratio (RR=RP) was also calculated to extract model performance independent of precipitation bias and to better represent a diagnostic measurement of watershed response to rainfall. RR measures the amount of precipitation partitioned to runoff, with lower RR values generally indicating a greater portion of precipitation lost to infiltration or evapotranspiration. “True” runoff ratios were estimated by first identifying all GHCND precipitation gauges upstream of a USGS stream gauge. The mean annual precipitation was then calculated and applied over the drainage area defined by the Geospatial Attributes of Gages for Evaluating Streamflow (GAGES-II) dataset (Falcone, 2002). RR is equal to the ratio of total USGS gauge flow to GHCND precipitation. A similar process was done for simulated RR using NLDAS-interpolated precipitation, simulated flow at the gauge cell, and model drainage area from the input digital elevation model derived from HydroSHEDS. Note that while the interpolated NLDAS precipitation, unlike the GHCND gauge network, is continuous in space, only modeled cells which matched the nearest-neighbor GHCND gauge network were used to estimate upstream precipitation in order to create as controlled a comparison as possible. Runoff ratios were not calculated for USGS stream gauges with fewer than three upstream GHCND precipitation gauges.

Observed total annual flow during the simulation period is shown in Fig. 3a; annual streamflow varies by several orders of magnitude across US major basins, with higher flows in the east and the Pacific Northwest and the lowest flows in the Great Plains. Runoff ratios are generally highest in the east; the majority of the arid west exhibits RR of less than 0.1, with the exception of topographically complex regions and headwater watersheds of the Rocky Mountains (Fig. 3c).

PFCONUSv1 reproduces point-scale annual flows across the United States with a median annual PBIAS of 7.7 % and with 25th and 75th percentiles of -26.2 % and 77.4 %, respectively (Fig. 3b). Shown in Fig. 3e and f, the 25th, 50th, and 75th percentiles for daily Spearman's ρ are 0.42, 0.65, and 0.76, while the same for RSR are 0.86, 1.2, and 2.5. The median PFCONUSv1 minus USGS difference in RR is 0.016 (Fig. 3d), which corresponds to a mean percent bias in runoff ratio of 8.3 %. The PFCONUSv1 model simulates observed streamflow with RSR < 0.6, ρ > 0.7, and |PBIAS| < 20 % at 54 gauges (approximately 2 % of available sites). An additional 97 locations (4 % of gauges) exhibit RSR < 0.7, ρ > 0.65, and |PBIAS| < 30 %. An additional 382 locations (15.7 % of gauges) show RSR < 1, ρ > 0.6, and |PBIAS| < 50 %. And, finally, an additional 268 gauges (11 % of gauges) show RSR < 1.2, ρ > 0.5, and |PBIAS| < 75 %. As has been shown in previous literature (Waseem et al., 2017), different performance metrics do not always indicate the same closeness of fit: while 2099 gauges (86 % of the dataset) show either RSR < 1.2, |PBIAS| < 75 %, or ρ > 0.5, only 801 gauges (34 % of all gauges) fit all those criteria.

Streamflow performance varies widely across major basins. For instance, median PBIAS, ρ, and RSR for the Ohio River Basin are -7.8 %, 0.79, and 0.84, respectively, and the median of simulated RR values is within 6 % of the median estimate of RR = 0.42 from observations. Simulated flows in the Tennessee River Basin also appropriately simulate observed flows: mean PBIAS, ρ, and RSR are -11.9 %, 0.69, and 0.89, respectively; 60 % of the gauges in the basin perform with RSR < 1.2, ρ > 0.5, and |PBIAS| < 75 %, and observed and simulated mean RR values are 0.49 and 0.53, respectively, for a percent bias in RR of 9 %. Conversely, the majority of the upper Missouri River Basin shows weak timing performance (median ρ of 0.49) and higher overall bias: the median PBIAS for Missouri is 65 % and median RSR is 2.2, indicating that the majority of Missouri gauges exhibit daily RMSE that is twice the volume of expected daily variability. The Great Plains region is certainly the region with the worst streamflow performance: PFCONUSv1 percent bias in the majority of these gauges is greater than 300 %, and in some cases, simulated flow is greater than 10 times the volume observed. While the mean difference in runoff ratio in this region is only 0.04, this is on average 4 times larger than RR estimated from observations. Results in Fig. 3 therefore suggest that in the arid Great Plains region, a very small change in runoff ratio can result in dramatic error in streamflow bias, and the PFCONUSv1 struggles to capture low flows in this region. There is evidence that continental-scale hydrologic models commonly share this struggle to capture streamflow dynamics in the Great Plains region. The first phase of the Continental Hydrologic Intercomparison Project has shown that a NOAA US National Water Model configuration of WRF-Hydro shares the same streamflow performance category (poor hydrograph shape and/or timing and high bias) as PFCONUSv1, run for the single water year 1985, at many gauges in the Great Plains region (Tijerina et al., 2021). While the intercomparison project is in its infancy and this comparison was primarily proof-of-concept, such results may stress the importance of representing groundwater abstractions and irrigation over the Ogallala in continental-scale hydrologic models.

Note that in Fig. 3, no filtering was done for these metrics in order to eliminate gauges with incorrect drainage area from topographic processing discrepancies, nor have we removed sites proximate to dams, influenced by nearby pumping or irrigation, or affected by bias in atmospheric forcing. As an example of PFCONUSv1 performance in ideal conditions, we show in Fig. 4 selected examples of individual gauge comparisons for each major basin in the PFCONUSv1 domain. Gauges chosen for Fig. 4 were those that tended to be minimally impacted by bias from anthropogenic effects or by errors in basin delineation by topographic processing. Such gauge attributes were determined based on geospatial stream properties obtained from the Geospatial Attributes of Gages for Evaluating Streamflow (Gages-II) dataset (Falcone, 2002), as well as the National Hydrography Dataset (see the supplemental information in Maxwell and Condon, 2016, for a detailed description of geospatial stream gauge attributes). Streamflow time series examples in Fig. 4 include gauges with the following properties: (1) represented greater than 300 km2 of upstream drainage area, (2) PFCONUSv1 drainage area differed from actual drainage area by less than 20 %, (3) total dam storage was less than 3 % of total annual flow for the closest upstream dam, (4) total withdrawals for the previous 5 years were less than 3 % of total annual flow, (5) total irrigated area in 2002 constituted no more than 15 % of the total drainage area, and (6) upstream area Spearman's ρ for precipitation performance must be greater than 0.5. The examples in Fig. 4 therefore represent naturalized gauges with minimal bias in a priori inputs, low anthropogenic impact, and good performance potential. We also compared domain-wide PFCONUSv1 performance at reference gauges identified by Maxwell et al. (2015) (locations with the least human influence and best representing “natural” ecohydrologic conditions) with non-reference gauges. As a whole, PFCONUSv1 performed better at reference locations regardless of the error metric used (Fig. S1). However, the difference in performance between reference and non-reference locations varies considerably between basins (Figs. S4 and S5). The Pacific Northwest, Missouri, Lower Colorado, and Arkansas–Red–White basins exhibit much greater performance at reference gauges across all error metrics, while other basins show mixed signals or poorer performance at reference gauges (Figs. S1 and S2), indicating sources of bias other than anthropogenic effects.

Evapotranspiration is a major component of the water balance, accounting for roughly 60 % partitioning of land precipitation into the atmosphere annually (Oki and Kanae, 2006); however, it is also widely considered to be an incredibly difficult value to constrain (Senay et al., 2013; Velpuri et al., 2013; Xu and Singh, 2005) and is often estimated simply as the residual of other components of the water balance. Unlike streamflow and precipitation, direct point measurement methodologies are limited, costly, and difficult to maintain. Direct estimates can be inferred from sap flux measurements; lysimeters, which weigh plant and soil mass to track temporal fluctuations in water storage; or chemical tracers, such as deuterium (Wilson et al., 2001). Currently, the method which likely provides the most defensible direct measurements of ET is the eddy flux or eddy correlation method. Eddy flux towers relate observed turbulent heat fluxes at the surface (latent and sensible heat) to the covariance between instantaneous fluctuations of vertical wind speed, humidity, and temperature (Baldocchi, 2003; Swinbank, 1951). The PFCONUSv1-simulated daily ET was compared to observations from 30 eddy covariance towers managed by the FLUXNET mission. Locations of these sites and their relative performance are shown in Fig. 5, along with time series examples from three FLUXNET sites with complete observations during the entire observation period.

Results in Fig. 5 demonstrate the ability of the PFCONUSv1 model to simulate daily and seasonal ET across difference climatic zones. The mean 25th, 50th, and 75th percentiles for PFCONUSv1-simulated daily ET PBIAS are 3 %, 26 %, and 55 %, respectively. Given that remote sensing estimates regularly exhibit uncertainty of 50 %–60 % for point-scale ET estimates, or > 20 % uncertainty in ET at the basin scale (Velpuri et al., 2013), PFCONUSv1 ET results are promising, especially for an uncalibrated model. For daily time series, 25th, 50th, and 75th percentiles are 0.6, 0.72, and 0.81 for ρ and 0.69, 0.92, and 1.33 for RSR, respectively. Because the metric is an indicator of monotonic agreement, the high overall Spearman's ρ values are particularly telling because ρ is sensitive not only to seasonal trends which dominate the time series variance but also the influential day-to-day (sub-seasonal) noise. Out of 30 FLUXNET sites with observations during the simulation time period, the PFCONUSv1 model performs with RSR < 1.2, |PBIAS| < 75 %, or ρ > 0.5 at 19 locations (63 % of locations); at 29 out of 30 sites, the PFCONUSv1-simulated ET fits one of these criteria.

The spatial discontinuity of FLUXNET certainly limits ET performance evaluation across the remaining PFCONUSv1 model domain. Eddy covariance ET estimates are applicable within the fetch of the prevailing winds, which is generally on the order of ∼ 1 km radius surrounding towers (Wilson et al., 2001), and statistical interpolation is generally not recommended without considerable parameterization of atmospheric and vegetative conditions to inform upscaling (Jung et al., 2009).

To evaluate performance at larger spatial scales, the PFCONUSv1 model has also been compared to the MOD16A2 and SSEBop algorithms for MODIS thermal imagery processing. These data, along with PFCONUSv1, have been aggregated to HUC8 spatial scale and monthly temporal resolution to help reduce uncertainty associated with cloud cover in the 8 d product. Cumulative annual evapotranspiration for MOD16A2, SSEBop, and PFCONUSv1 are shown in Fig. 6a–c. Both MOD16A2 and SSEBop algorithms should be considered evapotranspiration modeling techniques produced from remote sensing observations rather than observations themselves. However, regions where PFCONUSv1 comparisons to the MOD16A2 and SSEBop agree establish greater confidence in the model's bias or timing of ET estimates. We have therefore used PBIAS, ρ, and RSR error metrics, with PFCONUSv1 monthly ET observations as simulated and MODIS datasets as observed values. Multiple studies to date have compared MOD16A2 and SSEBop performance over a range of geophysical characteristics, vegetative types, and aridity indices by comparing to Penman–Monteith-based estimates (Knipper et al., 2016), lysimetric observations (Senay et al., 2014), FLUXNET observations or upscaled information from FLUXNET sites, and vegetative indices (Senay et al., 2013; Velpuri et al., 2013), with results showing good general agreement and within ∼ 50 % error for annual ET totals at point observations. Despite its considerably more simplistic approach for estimating ET from MODIS thermal land imaging, SSEBop performs nearly as well as or, in the case of the western US, better than MOD16A2 (Velpuri et al., 2013). Therefore, we also show MOD16A2 performance relative to SSEBop for reference (Fig. 6c, f, i, l, and o), where Oi observations are MOD16A2 and Si observations are MOD16A2 monthly ET (Eqs. 8 and 10).

PFCONUSv1 shows similar overall agreement with MOD16A2 and SSEBop algorithms in annual ET, with differences within ± 30 mm across the domain. All products provide similar spatial signatures of ET, with overall higher ET in the southwest and the lowest ET in the Great Basin and Colorado River basins. PFCONUSv1 estimates tend to agree more with SSEBop with regards to timing and residual variation, and they are more similar to MOD16A2 with regards to PBIAS (particularly in the western United States) (Fig. 6). The 50th percentiles for PFCONUSv1 PBIAS against MOD16A2 and SSEBop are 7.5 % and 8 %, respectively; 25th and 75th percentiles of PBIAS are -4.4 % and 24 % for MOD16A2 and -4.4 % and 35 % for SSEBop. In several regions, PFCONUSv1 shows similar comparisons with both MODIS products. For instance, in the Upper Mississippi, both products suggest that PFCONUSv1 overpredicts ET in the north and underpredicts in the south, and both products suggest PFCONUSv1 underpredicts ET in the Rocky Mountain headwaters and across most of the Ohio River Basin (Fig. 6d and e). The approximately 30 % underestimation of ET in the CO headwaters further agrees with the PFCONUSv1 performance relative to FLUXNET observations at the Niwot Ridge site in Colorado. However, most of the Missouri and the Arkansas–Red–White basins show opposite behavior between PFCONUSv1-MOD16A2 and PFCONUSv1-SSEBop comparisons; in these regions, we can be less certain of model bias as described by remote sensing of ET. Broadly, across the western US, PFCONUSv1 shows better agreement with MOD16A2 with regards to ET magnitude (PBIAS) because SSEBop estimates negligible ET in the Basin and Range region (Fig. 6e); however, PFCONUSv1 shows dramatically better performance relative to SSEBop in terms of Spearman's ρ and RSR (Fig. 6g and h). The 25th, 50th, and 75th percentiles of ρ are 0.38, 0.85, and 0.92 for monthly PFCONUSv1 compared to MOD16A2; the quantiles for PFCONUSv1 compared to SSEBop are 0.85, 0.91, and 0.93. Similarly, 25th, 50th, and 75th percentiles of RSR are 0.41, 0.85, and 2.2 for performance relative to MOD16A2 and 0.38, 0.47, and 0.62 for performance relative to SSEBop.

Despite differences between PFCONUSv1 comparisons to the two MODIS algorithms, results shown in Fig. 6 suggest that PFCONUSv1 appropriately estimates the magnitude and temporal progression of ET compared to the performance of other LSMs. In a study comparing LSM-based recharge estimates in the western United States, Niraula et al. (2017) showed that the LSMs Mosaic, VIC, and Noah simulated spatially distributed ET with 0.87, 0.77, and 0.75 Pearson's correlation relative to MODIS. Pearson's correlations between PFCONUSv1 and MOD16A2, and between PFCONUSv1 and SSEBop, are 0.9 and 0.95, respectively, which motivates future comparisons of PFCONUSv1 performance relative to other LSMs. However, it is important to again note that MODIS ET estimates are themselves models, and as such they are susceptible to epistemic errors in input data (e.g., inaccuracies in leaf area index or other parameterizations), measurement and remote sensing errors (e.g., cloud cover), and other uncertainties.

Terrestrial water storage represents all components of the water balance stored on and below the Earth's surface. As such, total storage S is an aggregate of water stored on land in surface water bodies or in the canopy, as well as snow water equivalent, soil moisture in the vadose zone, and shallow or deep saturated aquifer storage. Estimates of overall S could simply involve measuring and combining individual components, but these calculations (1) require highly developed monitoring networks and an impressive amount of in situ observations and (2) can have large margins of error if not all of the assorted hydrological stores are accurately resolved (Troch et al., 2007). The most common method for S estimation calculates storage as a remainder of other water balance terms: P, ET, and R in Eq. (), (e.g., Rodell et al., 2011; Tang et al., 2010).

Recent advances in remote sensing have granted hydrologists an estimate of changes to total S, without partitioning out storage sources, by measuring fluctuations of Earth's gravity fields as a proxy for mass change. Since water represents the greatest fluctuation of terrestrial mass, gravity anomalies can be translated to variability in S. The newly available GRACE twin satellite mission provides approximately monthly values of total water storage at the global scale and at coarse (> 105 km2) resolution (e.g., Strassberg et al., 2009). Storage anomaly estimates are based on K-band microwave measurements of the distance between the two low-flying satellites, which varies as a function of gravity field fluctuations (as well as atmospheric, oceanic, and solid Earth tides, which must be corrected to resolve the global water budget; Dahle et al., 2019).

The PFCONUSv1 total water storage anomalies (calculated as a sum of all simulated surface and subsurface hydrologic stores) were compared to five monthly gravity field solutions: the RL06 spherical harmonic solutions provided by JPL, GFZ, and CSR, as well as the mascon solutions JPLm and CSRm. Figure 7 shows seasonal storage amplitude in space and basin-aggregate storage change through time by comparing PFCONUSv1 and GRACE solutions for six major river basins. Some basins have been left out due to incompleteness in the model domain or due to size: the basis function for GRACE solutions is generally on the order of 300 000 km2 such that storage anomaly estimates for smaller basins (e.g., the Tennessee River Basin) are not well resolved.

Seasonal storage amplitude represents the average peak-to-peak storage gain or loss over the course of a water year, and it is therefore a depiction of seasonality or intra-annual S signal. The GRACE solution shown in Fig. 7 is the JPL mascon solution provided at 0.5∘ resolution, and amplitude for other GRACE products shows similar spatial signals; however, note that mascon solutions are calculated given a 3∘ equal-area basis function and subsequently downscaled using forward modeling techniques to account for leakage errors (Wiese et al., 2016). GRACE mascons are not independent of each other, and uncertainty increases dramatically with decreasing basin size. However, qualitative comparisons between GRACE and PFCONUSv1 amplitude indicate several regions of agreement for high or low seasonality. Topographic highs in the Rocky Mountains, where the snow water equivalent signal likely dominates overall storage variance and is entirely seasonally dependent, show high amplitude for both PFCONUSv1 and GRACE (Fig. 7a and b). The Upper and Lower Colorado River basins, in particular, show very similar spatial patterns for overall amplitude. Another area of agreement is the comparably high amplitude in the Lower Mississippi River basin. In both GRACE and PFCONUSv1, the Arkansas–Red–White region sees higher seasonality of total water storage in the east and lower in the west; the locations of highest amplitude for both GRACE and our model lie in the Pacific Northwest region. However, broadly speaking the PFCONUSv1 amplitude is lower than GRACE for the majority of the domain and particularly in the east. Other continental- or global-scale land surface models have also underpredicted seasonal storage amplitude across global river basins relative to GRACE; for example, the WaterGAP (Water Global Assessment and Prognosis) hydrologic model consistently underpredicted amplitude for most of the global land area (Döll et al., 2014), and a validation of four LSMs and global hydrologic models found that the numerical models reproduced GRACE storage signals only to a very limited degree (Zhang et al., 2017). However, LSM tendency for GRACE mismatch is likely attributed to insufficient groundwater representation, which is not as likely to be the cause for PFCONUSv1 and GRACE disparities.

Temporal progression of storage was calculated with the area-weighted mean of the Colorado, Arkansas, Ohio, Missouri, and Upper Mississippi River basins (Fig. 7c–h). Uncertainty (shaded regions) shown indicates the leakage error associated with downscaling 3∘ basis functions to 0.5∘ solutions for the JPL mascon product. We show only the JPLm uncertainty, simply because uncertainty estimates for the RL06 products were not yet available at the time of this analysis. The CSR mascon product is suggested to have an error of approximately 2 cm that is more or less constant through time and space.

The PFCONUSv1 model shows good agreement in the timing storage anomalies for most basins, with Spearman's ρ rank correlation ranging from 0.43 to 0.94 relative to the mean of all GRACE solutions: individual ρ values for major basins are 0.43 (Missouri), 0.63 (Upper Colorado), 0.76 (Pacific Northwest), 0.79 (Great Basin), 0.81 (Lower Colorado), 0.86 (Upper Mississippi), 0.88 (Ohio), and 0.93 (Arkansas–Red–White). However, correlation is not necessarily the best predictor of adequate model performance; for instance, the Upper Mississippi has the third-highest ρ value out of six major basins, but more than 80 % of the total anomaly time series lies within the uncertainty bars provided for the JPLm product. Further, several discrepancies exist between PFCONUSv1 and GRACE trends and amplitude. For example, despite its monotonic agreement with GRACE storage amplitude for the Ohio River Basin, the PFCONUSv1 model simulates a seasonal storage amplitude that is, on average, more than 30 % lower than what GRACE observes. The Upper Colorado River basin captures seasonal timing, but the overall storage gain over the simulation period is roughly 3 times that of what GRACE observes.

Differences between the PFCONUSv1 and GRACE storage water anomaly estimates can come from various sources: (1) model error and uncertainty in PFCONUSv1 model parameters and configuration, error and uncertainty associated with GRACE measurement error, or error associated with the intensive post-processing and filtering on the raw spherical harmonic GRACE solutions; (2) hydrologic stores unaccounted for in the PFCONUSv1 model, such as deep (> 100 m) aquifer storage; or (3) anthropogenic impacts, particularly from groundwater withdrawals from municipal and agricultural aquifer depletions (Chen et al., 2016).

Total water storage anomalies were also validated based on their partitioned components: ΔSgw, ΔSsoil, and ΔSsnow. First, PFCONUSv1 water table depth (WTD) was compared to USGS well observations across the United States in Sect. 3.4.1. As discussed below, WTD does not necessarily translate to ΔSgw, but it is still a very informative hydrologic state. PFCONUSv1 soil moisture was compared to a combined active/passive remote sensing product in Sect. 3.4.2, and PFCONUSv1 snow water equivalent was compared to snow telemetry measurements in Sect. 3.4.3.

Major biases exist in preprocessing of PFCONUSv1 meteorological forcing and topography, which are peripheral to but act simultaneously with all other sources of bias (Table 2). In this way, isolating the effects of a single bias source can be challenging. Streamflow itself is sensitive to errors in drainage area, topographic relief, and precipitation or temperature bias, and the errors in surface and subsurface moisture flux can propagate downstream to impact moisture availability and evapotranspiration in areas remote from the original bias source.

Plenty of sources of uncertainty can contribute to biases not discussed in Sect. 4.1 (Table 2). We have chosen to address meteorological forcing and topographic processing errors above simply because they are somewhat readily quantifiable, while parameter values and other epistemic uncertainties, such as simplification or scaling of model physics, are poorly constrained or simply unknown. Other biases include population of model parameter fields.

While we do not discuss model parameter uncertainty, such as conductivity, porosity, van Genuchten parameters, Manning's surface roughness, land and vegetation parameters, or model horizontal and vertical discretization, these are also areas for improvement. For example, Maxwell et al. (2015) show that national geologic and soil parameter datasets are prone to errors via political boundaries, such as state lines, and the PFCONUSv1 model oversimplifies deeper geology, with a 100 m vertically homogenous layer.

However, as mentioned above, these fields are poorly constrained at the continental scale, and simulations are necessarily limited by availability of appropriate distributed products. Model parameter population is often addressed through calibration, but population of parameter fields becomes increasingly difficult as resolution increases and calibration becomes more computationally demanding. Future model iterations may need to take advantage of methods that allow transfer of parameters (e.g., conductivity) from coarse-resolution, efficient models to high-resolution ones (Foster and Maxwell, 2019). Model discretization is another concern. Coarsening of vertical and lateral resolution is a necessity at the continental scale, but aggregating to ∼ 1 km resolution certainly comes with inherent uncertainties and loss of information. DEMs in particular will lose topographic drivers with scale (Wu et al., 2008), resulting in loss of relief; on the other hand, coarse-resolution cells could result in inappropriately steep pressure gradients as a function of Richards' equation parameterization and pressure-dependent permeability (Maxwell and Condon, 2016), and suitable vertical length scales for Richards' equations generally do not exceed several meters (Or et al., 2015). This calls into question the scalability of model physics; as Beven and Cloke (2012) rightly point out, whether or not governing partial differential equations will scale linearly is a concern. However, the current governing equations for PFCONUSv1 are simply the best currently known representation of hydrologic processes at this scale.

Finally, process representation is certainly a concern. Transient anthropogenic modules, such as urban hydrology models, pumping and injections, or surface water diversions, are currently possible but add to computational demand and require detailed historical data on water use with temporal and spatial coverage simply not yet available. As a naturalized model, the PFCONUSv1 simulations presented here will necessarily overpredict water tables and baseflow in regions where extractions are apparent. For instance, Maxwell and Condon (2016, supplemental information) show streamflow examples at the Lees Ferry USGS gauge, where timing and volume of streamflow are entirely governed by dam hydraulics. Condon and Maxwell (2019) show that incorporating a century of groundwater depletion across the PFCONUSv1 domain considerably decreases streamflow, with sensitivity to pumping concentrating downstream; more specifically, they found that long-term depletions over the High Plains aquifer resulted in a swap of discharging to recharging groundwater. However, naturalized continental models with high fidelity in non-anthropogenic settings could be used to estimate impact from human influence simply by examining the difference between observed and simulated conditions.