The long-term simulations were previously performed using the coupled Weather Research and Forecasting and the Community Multiscale Air Quality (WRF-CMAQ model; Wong et al., 2012) with WRFv3.4 coupled with CMAQv5.02 driven by internally consistent US emission inventories (Xing et al., 2013) covering the CONUS domain discretized with a grid of 36 km horizontal resolution. Spatial and time-varying chemical lateral boundary conditions were provided by the hemispheric WRF-CMAQ (Mathur et al., 2017) running over the same period (Xing et al., 2015a, b). Interested readers are referred to Gan et al. (2015, 2016) for a detailed description of the settings of the CMAQ model and physical configurations of the WRF model (Table S1 in the Supplement). The performance of the coupled WRF-CMAQ model for major trace gases, aerosol species, and meteorological variables such as ozone (O3), fine particular matter (PM2.5), and aerosol optical depth at both the hemispheric and regional scale has been extensively evaluated in previous studies (Xing et al., 2015a, b; Mathur et al., 2017; Gan et al., 2015, 2016; Astitha et al., 2017; Porter et al., 2017) and has shown skill in simulating the magnitudes and long-term trends of these variables. The dry deposition of each species in the CMAQ model is calculated by multiplying the concentration in the lowest model layer by the dry deposition velocity (Vd). The Vd is calculated as the reciprocal of the sum of the atmospheric aerodynamic resistance (Ra, the resistance to transport through the atmosphere above the surface receptors), quasi-laminar boundary layer (Rb, the resistance to transport across the thin layer of air that is in contact with the surface and varies with the diffusion of the pollutant transported), and surface resistances (Rs, the resistance to the uptake of the pollutant by the surface receptor, typically vegetation or soil).

A previous study using the offline CMAQ model has demonstrated moderate skill simulating WDEP from 2002 to 2006 (Appel et al., 2011). Here we evaluate the coupled WRF-CMAQ model's ability to simulate WDEP of nitrate (TNO3), ammonium (NHx), and sulfate (TS) during 1990–2010 over the US, including both the interannual variability and long-term trends. This is accomplished by comparing the model results with observations from the US NADP (http://nadp.sws.uiuc.edu/ntn/, last access: 21 June 2018), which measures total weekly wet deposition of these species. The deposition is measured by wet-only samples, which are triggered by precipitation. The deposition of sulfate and nitrate are analyzed by ion chromatography and ammonium by flow injection analysis (http://nadp.slh.wisc.edu/educ/sample.aspx, last access: 4 May 2018). We first pair the wet deposition data between the observation and the model results in time and space, and then extract the annual deposition for the sites matching our criteria (at least 18 available years with 75 % annual coverage for each year). Model data during periods of missing observations are not considered in either the statistical evaluation or the trends analysis. By applying the criteria, we use information at 170 of 359 sites, with 141 sites in the eastern US (east of 110∘ W longitude) and 29 sites in the western US (west of 110∘ W longitude). The detailed site information and the number of years of observational data used for the model evaluation can be found in Table S2 and Fig. S1 in the Supplement. In pairing the observed and modeled TNO3 WDEP values (which combines WDEP of NO3- and HNO3), we multiply the model estimated HNO3 WDEP by 0.984 to account for the transformation of HNO3 to NO3- in solution in the measurements. In pairing the observed and modeled NHx WDEP values (which combines WDEP of NH4+ and NH3), we multiply the model estimated NH3 WDEP by 1.06 to account for the transformation of NH3 to NH4+ in the rainwater in the measurements. In pairing the observed and modeled TS WDEP values (which combines WDEP of SO42- and SO2), we multiply the model estimated SO2 WDEP by 1.50 to account for the fact that SO2 will be fully oxidized into SO42- during sampling (Appel et al., 2011).

For the model evaluation, we examine the correlation coefficients (R), mean bias (MB), and the normalized mean bias (NMB):

NMB=∑1N(model-obs)∑1Nobs.

When discussing the model evaluation and deposition trends, we divide the US into 10 ecological regions, following the North America Level I ecoregion definition (https://www.epa.gov/eco-research/ecoregions-north-america, last access: 21 June 2018), including Northern Forests, Northwestern Forested Mountains, Marine West Coast Forest, Eastern Temperate Forests, Great Plains, North American Deserts, Mediterranean California, Southern Semi-arid Highlands, Temperate Sierras, and Tropical Wet Forests (Fig. S1 in the Supplement). For the trend analysis, we focus on the linear trends (Colette et al., 2011; Xing et al., 2015a), in which the linear least square fit method is employed, and significance of trends is examined with a Student t test at the 95 % confidence level (p = 0.05).

Errors in the simulated meteorology and precipitation in particular, can lead to errors in estimating WDEP in the CMAQ model. We follow the previous approach of Appel et al. (2011) to account for biases in modeled precipitation by adjusting the modeled WDEP as Bias adjusted WDmod=PrecipobsPrecipmod×WDmod.

In Eq. (2), WDmod represents the WDEP from the model, Precipobs represents annual or monthly accumulated observed precipitation, and Precipmod represents the corresponding annual or monthly accumulated precipitation from the model.

The US CASTNET provides long-term observations of atmospheric concentrations as well as the dry deposition (https://www.epa.gov/castnet, last access: 7 May 2018). However, the dry deposition values reported are not directly measured, but estimated using the inferential method, pairing the measured air pollutant concentration with a modeled deposition velocity from the MLM model (Meyers et al., 1998). So rather than comparing dry deposition estimates from two models, we choose to evaluate the model's performance in simulating the ambient air concentrations (sulfur dioxide (SO2), sulfate (SO42-), total nitrate (TNO3 = NO3- + HNO3), and ammonium (NH4)). We apply the same criteria in selecting valid observation sites as the NADP/NTN. By doing this, we have chosen 39 valid sites out of total 145 sites. The detailed site information and the number of years of observational data used for the model evaluation can be found in Table S3 in the Supplement.

The coupled WRF-CMAQ model generally overestimates the precipitation throughout US (Fig. 2d, Fig. S2 in the Supplement), consistent with previous findings (Ran et al., 2015). After performing the annual precipitation adjustment for model simulated WDEP, we see that the correlation coefficients (R) are slightly improved relative to using the unadjusted WDEP values (Table 1), increasing from 0.89 to 0.92 for TNO3, from 0.77 to 0.81 for NHx, and from 0.92 to 0.94 for TS (Fig. S3 in the Supplement). There are no significant changes for R when we use the monthly precipitation adjustment compared with the annual precipitation adjustment (Table 1). The model generally underestimates WDEP for both the eastern and western US, except for TS where the model tends to overestimate WDEP in the western US (Figs. 1 and 2). After performing the precipitation adjustment, the NMB values increase for all three species (Table 1). The model exhibited better performance for WDEP in the east than the west, considering both the R and the NMB, largely because of the complex terrain in the western US (Appel et al., 2011).

The 21-year average TNO3 WDEP is highest in the Eastern Temperate Forest region and lowest in the Southern Semi-arid Highlands, as seen from both the observations and model results (Table 2). The model generally underestimates the TNO3 deposition for all the regions with MB values ranging from -1.11 kg ha-1 in the Southern Semi-arid Highlands to -3.73 kg ha-1 in the Tropical Wet Forests, except for the Marine West Coast Forest region where the model overestimates the TNO3 WDEP, with MB values of 0.79 kg ha-1. The correlation coefficients between the model and observations are generally much higher in the eastern US (R larger than 0.80) than in the western US (R less than 0.70). The 21-year average NHx WDEP is also highest in the Eastern Temperate Forest region and lowest in the Southern Semi-arid Highlands (Table 3). The model generally underestimates the NHx WDEP, with MB values ranging from -0.26 kg ha-1 yr-1 in the Northwestern Forested Mountains to -0.81 kg ha-1 in Tropical Wet Forests, and overestimates in the Marine West Coast Forest, with MB of 0.24 kg ha-1. The correlation coefficients between model and observations for NHx WDEP share similar spatial patterns with TNO3 WDEP but have lower R values. The 21-year average TS deposition is highest in the Eastern Temperate Forests region and lowest in the North American Desserts. Similar to TNO3 and NHx, the model underestimates the TS WDEP over most of the regions, but overestimates observed values in the Marine West Coast Forest and Mediterranean California. The R between the model and the observations is generally larger than 0.9 in the eastern US but ranges from 0.46 to 0.79 in the western US.

Clear downward trends are seen for TNO3 and TS WDEP from both the observations and model in Fig. 2a, c, while NHx deposition exhibits much larger interannual fluctuations (Fig. 2b). In Fig. 3 we see much larger decreasing trends for TNO3 and TS WDEP in the eastern US than those in the western US. This is due to the fact that the emission reductions mostly occurred in the eastern US (Xing et al., 2013; Simon et al., 2015), and the model captures this trend very well especially for TNO3 and TS WDEP with R values of 0.94 and 0.95, respectively. A stronger decreasing trend over the Northern Forests and Eastern Temperate Forests regions compared to other regions is observed for both TNO3 and TS WDEP, and the model is also able to capture these very well but a slightly distinctions in the trends for each ecoregion (Tables 2 and 4). We see that the model generally underestimates the magnitude of the decreasing WDEP trends at many sites for TNO3 and TS (Tables 2 and 4), which may be caused by the coarse model resolution (36 km) and uncertainties in the emission inventories. For NHx, we see increasing WDEP trends for most of the sites but the trends are not statistically significant (Table 3).

Compared with Appel et al. (2011), our model results indicate larger bias for WDEP for both the eastern and western US (Table S4 in the Supplement). The NMB increases for all three species in our results from 2002 to 2006 after applying the precipitation adjustment, which was also seen in Appel et al. (2011), except for TS, which Appel et al. (2011) reported decreased bias after the precipitation adjustment. The discrepancies for the model performances between our study and Appel et al. (2011) could be caused by the grid resolutions, in which coarse-resolution models (e.g. 36 km in our study) have more challenges to simulate various chemical and physical processes compared with fine resolution (e.g. 12 km used in Appel et al., 2011). There are numerous differences between the model configuration and versions used in this analysis and those previously used by Appel et al. (2011). Specific model process representation differences between CMAQv5.0 used here and CMAQv4.7 used in Appel et al. (2011) can be found at https://www.epa.gov/cmaq/cmaq-models-0 (last access: 21 June 2018).

To evaluate the model's performance in simulating the DDEP, we compare the model simulated concentration with the observations from CASTNET. Comparisons of annual average simulated concentrations with corresponding measurements at the CASTNET sites show strong correlation for SO2 (R of 0.88), SO4 (0.95), TNO3 (0.94), and NH4 (0.94). Some underestimation for SO4 and overestimation in other species ambient concentrations is noted (Fig. S4 in the Supplement). The model also captures the trends for these species with very high R, but the magnitude of the decreasing trends is underestimated by the model (Fig. S5 in the Supplement).

Table 5 shows that modeled TDEP of TIN, i.e., the sum of TNO3 and NHx, is much higher in the Eastern Temperate Forests than any other ecoregion (regional average of 10.08 and 7.95 kg N ha-1 in 1990 and 2010, respectively), followed by the Northern Forests and Mediterranean California regions. The hotspot for TIN TDEP has shifted from the eastern US in 1990 to the northern central US in 2010, with relative higher values in North Carolina (NC) and Pennsylvania (PA) (Fig. 4). During the period from 1990 to 2010, TIN TDEP has significantly decreased (with p < 0.05 for the standard two-tailed Student's t test) over several ecoregions, including Eastern Temperate Forests, Northern Forests, Mediterranean California, and Marine West Coast Forest (decreasing trend of 0.12, 0.071, 0.038, and 0.017 kg N ha-1 yr-1, respectively) as a result of significant reductions in anthropogenic NOx emissions (Xing et al., 2013). Slightly increasing but not statistically significant trends are estimated in TIN TDEP for the Great Plains and the Tropical Wet Forests while the remaining regions show statistically insignificant decreasing trends (Table 6). We see statistically significant increasing trends of TIN TDEP in eastern NC (larger than 0.2 kg N ha-1 yr-1), which is mainly caused by the increase in NHx TDEP (Fig. 5) arising from increased NH3 emission from hog farming (Xing et al., 2013; Paulot et al., 2014). There are also significant increasing trends of TIN TDEP over Iowa, Minnesota, and South Dakota (larger than 0.04 kg N ha-1 yr-1) because of the increased NHx TDEP related to animal foster and corn plantation (Figs. 4 and 5). In Fig. 5 we see that the TIN TDEP decreasing trends predominantly result from the TNO3 TDEP decreases across the US, with larger decreasing rates in the east than the west. The increasing TIN TDEP trends over the east and central states (such as NC, PA, and Virginia) were caused by the NHx TDEP increases, which in turn arise from increases in NH3 emissions (Paulot et al., 2013).

Similar to TIN TDEP, TDEP of total sulfur (TS), i.e., the sum of SO2 and SO42-, shows a distinct spatial gradient from the east (usually larger than 9 kg S ha-1) compared to the west (lower than 3 kg S ha-1) (Fig. 4). In 1990, the TS was even higher than 30 kg S ha-1 in some states of the central US, such as Indiana, Ohio, PA, and West Virginia. In 2010, TS TDEP is still higher in the east than the west, but TS TDEP in the east has decreased by half (to lower than 15 kg S ha-1) for most regions. From 1990 to 2010, the estimated TS TDEP exhibits significant trends across the US, with decreasing trends generally larger in the east (larger than 0.4 kg S ha-1 yr-1) and lower in the west (less than 0.2 kg S ha-1 yr-1) as a result of SO2 decreases from the passage of the Clean Air Act Amendments of 1990. All the ecoregions experienced statistically significant decreases of TS TDEP over the past 2 decades, which were dominated by the decreases in SO42-, except for the Mediterranean California ecoregion, which showed an insignificant decreasing trend (Table 6). The largest decreasing trend was seen in the Eastern Temperate Forests region (-0.51 kg S ha-1 yr-1), followed by the Northern Forests (-0.23 kg S ha-1 yr-1) and the Great Plains (-0.082 kg S ha-1 yr-1).

Figure 6 shows that the TIN WDEP is higher in the east than the west due to both greater precipitation (Fig. 2d) and higher atmospheric burden of airborne reactive nitrogen in the east (Xing et al., 2013). In addition, estimated TIN WDEP shows widespread significant decreasing trends in the eastern US while trends in the western US generally have smaller magnitudes and often are not statistically significant. The most significant decreasing region is the Eastern Temperate Forests, with an annual decrease of -0.070 kg N ha-1 yr-1, followed by the Northern Forests (-0.037 kg N ha-1 yr-1) and the Great Plains (-0.023 kg N ha-1 yr-1) (Table S5 in the Supplement). The decreasing trends of TIN WDEP are mainly caused by the WDEP of TNO3 (Fig. S6a and Table S5 in the Supplement). There are no significant changes for WDEP of NHx in the majority of the US except for the region Tropical Wet Forests (Fig. S6b), consistent with previous findings (Lajtha and Jones, 2013). TIN DDEP is higher in the eastern US and lower in the northwestern and central US. Significant decreasing trends for the TIN DDEP are seen over the Eastern Temperate Forests (-0.049 kg N ha-1 yr-1), Northern Forests (-0.033 kg N ha-1 yr-1), Mediterranean California (-0.032 kg N ha-1 yr-1), and Marine West Coast Forest regions (-0.022 kg N ha-1 yr-1) (Table S6 in the Supplement). The decreases of TIN DDEP over these regions are dominated by the DDEP of TNO3 (Fig. S6c and Table S6 in the Supplement). In contrast, there are significant increasing trends of TIN DDEP over the Tropical Wet Forests (0.027 kg N ha-1 yr-1), Great Plains (0.026 kg N ha-1 yr-1), and Southern Semi-arid Highlands (0.009 kg N ha-1 yr-1). These increases are caused by the DDEP of NHx (Fig. S6d and Table S6 in the Supplement).

Figure 7 shows a distinct spatial distribution for both the WDEP and DDEP of sulfur, with much higher values in the eastern US in the vicinity and downwind of major sources. Significant decreasing trends are noted for both the wet and dry TS deposition for all the ecoregions except the Marine West Coast Forest and Mediterranean California, where TS WDEP are estimated to increase, though the trend is not statistically significant (Tables S5 and S6 in the Supplement). TS DDEP trends are larger or comparable to TS WDEP trends for the majority of the regions, except for Southern Semi-arid Highlands, Temperate Sierras, and Tropical Wet Forests, where the magnitude of the decreasing trends for DDEP are lower than those for WDEP.

Figure 8a shows that the US domain average TDEP of TIN generally decrease over the past 2 decades, from 5.55 kg N ha yr-1 in 1990 to 5.00 kg N ha yr-1 in 2010. The decrease in TIN TDEP is mainly caused by reductions in TNO3. The TNO3 WDEP is estimated to decrease from 1.26 to 0.76 kg N ha yr-1 and TNO3 DDEP decrease from 1.98 to 1.35 kg N ha yr-1 during the same period. DDEP accounts for large fractions of TDEP for TIN over the entire 1990 to 2010 time period, 58–65 % of TDEP over the US (Fig. S7 in the Supplement). The relative proportions of TNO3 over the TDEP have also changed over the past 2 decades in response to changes in precursor emissions. TNO3 deposition dominates TIN TDEP until the early 2000s. After 2003, however, NHx dominates the TIN TDEP over the US (Fig. S7 in the Supplement). This is consistent with Li et al. (2016), who showed that the US TIN deposition has transitioned from being dominated by TNO3 to NHx as a result of NOx emission reductions and increases of unregulated NH3 emissions. The increasing contributions of NHx to the TIN TDEP can also be seen in Fig. 9, which shows increasing proportions of NHx contributions across larger regions of the CONUS during the 1990 to 2010 period (significant increasing trend (p < 0.05) for the NHx fraction of the total TIN across the US). This has resulted from the significant NOx reduction due to regulations and growth in NH3 emissions (Warner et al., 2017).

Similar to TIN TDEP, the TS TDEP has also decreased, from 6.85 kg S ha-1 yr-1 in 1990 to 3.26 kg S ha-1 yr-1 in 2010 (Fig. 8b), as a result of the decreasing anthropogenic SO2 emissions (Smith et al., 2011; Xing et al., 2013). The TS DDEP dominates the TS TDEP during the first decade, but TS WDEP becomes dominant after the year 2004. The dry sulfur deposition has decreased by 58 % from 1990 to 2010, from 3.65 to 1.55 kg S ha-1 yr-1, while the wet sulfur deposition has decreased by 47 %, from 3.20 to 1.70 kg S ha-1 yr-1, during the same period.