Spatiotemporal Characteristics of the Association between AOD and PM over the California Central Valley

: Many air pollution health e ﬀ ects studies rely on exposure estimates of particulate matter (PM) concentrations derived from remote sensing observations of aerosol optical depth (AOD). Simple but robust calibration models between AOD and PM are therefore important for generating reliable PM exposures. We conduct an in-depth examination of the spatial and temporal characteristics of the AOD-PM 2.5 relationship by leveraging data from the Distributed Regional Aerosol Gridded Observation Networks (DRAGON) ﬁeld campaign where eight NASA Aerosol Robotic Network (AERONET) sites were co-located with EPA Air Quality System (AQS) monitoring sites in California’s Central Valley from November 2012 to April 2013. With this spatiotemporally rich data we found that linear calibration models (R 2 = 0.35, RMSE = 10.38 µ g / m 3 ) were signiﬁcantly improved when spatial (R 2 = 0.45, RMSE = 9.54 µ g / m 3 ), temporal (R 2 = 0.62, RMSE = 8.30 µ g / m 3 ), and spatiotemporal (R 2 = 0.65, RMSE = 7.58 µ g / m 3 ) functions were included. As a use-case we applied the best spatiotemporal model to convert space-borne MultiAngle Imaging Spectroradiometer (MISR) AOD observations to predict PM 2.5 over the region (R 2 = 0.60, RMSE = 8.42 µ g / m 3 ). Our results imply that simple AERONET AOD-PM 2.5 calibrations are robust and can be reliably applied to space-borne AOD observations, resulting in PM 2.5 prediction surfaces for use in downstream applications.


Introduction
The use of remotely sensed Aerosol Optical Depth (AOD) for estimating concentrations of ground monitored fine particulate matter (PM 2.5 ) has been well established in many applications, e.g., [1][2][3][4][5][6][7][8][9]. The motivation for incorporating AOD as an explanatory variable in PM estimation models lies in the physical principles underlying the basic relationships between AOD and airborne particle concentrations [10]. Further lending to its appeal, satellite observations of AOD provide spatial coverage that far surpasses point measurements of ground-level PM. The 4.4 km resolution Multiangle Imaging Spectroradiometer (MISR) AOD product, which has the spectral and angular features that enable the characterization of aerosol size and type, is suitable to address this issue. The only caveat is that its temporal coverage is not daily; MISR has a weekly recurrence, therefore, information on the aerosol type and size cannot capture the day to day variation in air quality [11]. The new 4.4 km MISR aerosol product has been used in a number of previous air quality studies [2,[12][13][14]
In order to comply with MISR AOD we used a quadratic log-log interpolation to calculate AOD at 550 nm (Equation (1); [31,32]), which required availability of AOD in at least 3 wavelengths using the 870 nm, 675 nm, 500 nm, and 440 nm bands for each day-station pair. The coefficients were extracted by solving a three-way equation system in order to calculate AOD at 550nm (a detailed example can be found in Appendix A): log(AODwaveI)ij ~ b0ij + b1ij * log(waveI) + b2ij * log(waveI) 2 ; I = 1, ..., 3 (1) where AODwaveI = 1,…,3 is the AOD in a known wavelength I = 1, …, 3 at site i and day j, and b0, b1, and b2, are the coefficients derived from the interpolation using AOD in known wavelengths. Applying these coefficients to Equation (1) using waveI = 550 will reveal AOD at 550 nm for each site i and day j. AOD and its spectral dependence can be expressed approximately as a power law relationship, where the Ångstrom exponent equals the log ratio between the ratio of two AOD values and the ratio   Figure 1) and had available data during the campaign time period.
In order to comply with MISR AOD we used a quadratic log-log interpolation to calculate AOD at 550 nm (Equation (1); [31,32]), which required availability of AOD in at least 3 wavelengths using the 870 nm, 675 nm, 500 nm, and 440 nm bands for each day-station pair. The coefficients were extracted by solving a three-way equation system in order to calculate AOD at 550nm (a detailed example can be found in Appendix A): log(AODwave I ) ij~b 0 ij + b1 ij * log(wave I ) + b2 ij * log(wave I ) 2 ; I = 1, ..., 3 where AODwave I = 1, . . . ,3 is the AOD in a known wavelength I = 1, . . . , 3 at site i and day j, and b 0 , b 1 , and b 2 , are the coefficients derived from the interpolation using AOD in known wavelengths. Applying these coefficients to Equation (1) using wave I = 550 will reveal AOD at 550 nm for each site i and day j. AOD and its spectral dependence can be expressed approximately as a power law relationship, where the Ångstrom exponent equals the log ratio between the ratio of two AOD values and the ratio of two wavelengths, respectively. If the Ångstrom exponent is known, AOD at one wavelength can also be calculated from AOD at another wavelength [31]. However, when the AOD is measured at three or more wavelengths in different spectral regions, the wavelength dependence of the Ångstrom exponent can be better described by a second order polynomial empirical relationship between the logarithmic AOD and logarithmic wavelengths. The second order coefficient accounts for the curvature in the log (AODwave I ) and log (wave I ) relationship. Ignoring the second-order approximation sometimes introduces significant errors [32].

PM 2.5 EPA Data
Daily PM 2.5 concentrations, measured by EPA Federal Reference Method (FRM) gravimetric monitors, were collected by EPA AQS monitors and the data were obtained from https://aqs.epa.gov/ aqsweb/airdata/download_files.html. The data were processed to remove negative concentrations. For our analysis, we average AERONET AOD to match the daily FRM PM 2.5 temporal resolution resulting in a complete AOD-PM dataset for the DRAGON campaign that includes a total of 301 co-located daily observations. Three sites in the Central Valley have long-term AERONET-AQS co-locations (Fresno and Bakersfield same locations as the DRAGON campaign; Modesto not included in the DRAGON campaign but in the region). This dataset includes a total of 3806 co-located daily observations starting in 2002.

MISR Data
The MISR instrument onboard NASA's Terra Satellite has been collecting data with nine camera angles and 4 spectral channels since early 2000. The most recent version 23 (V23) of the aerosol retrieval algorithm was recently processed at 4.4 km [33] using high-resolution (275 m) MISR observations and includes additional improvements for retrievals over dark water [34]. The MISR V23 aerosol product has been shown to have a better sampling than the previous V22 version and demonstrated improved performance at high AOD values. The MISR V23 is also better able to resolve spatial gradients in AOD for a wide range of aerosol loadings [25], and therefore suitable for evaluation of AOD spatial variability for variety of aerosol conditions. In addition to AOD, the V23 aerosol product includes MISR component-particle optical properties covering size, shape, and absorption properties. For this study we focus on total AOD, retrieved at 550 nm, matching available MISR overpasses with the daily AOD and PM 2.5 at the coincident DRAGON sites as done in other MISR satellite AOD-PM 2.5 studies [2]. For these matches we examined the relationships between AERONET and MISR AOD as well as AQS PM 2.5 and MISR AOD.

Stage 1:
The main goal of this study is to develop and evaluate regression-based calibration models using only AERONET AOD and AQS PM 2.5 concentrations. After calibration, the models are then applied to convert MISR AOD to PM 2.5 (Stage 2). We start with a simple linear regression (Equation (2)), referred to as a baseline model: where PM is the daily PM 2.5 concentration, α and β are the model intercept and slope, respectively, AOD is the daily AERONET AOD at 550 nm, and ε is the prediction error in µg/m 3 . The marginal correlation between remotely sensed AOD and PM2.5 concentrations in the baseline model, motivated the development of other models. We then developed a set of Generalized Additive Models (GAMs) to model non-parametric functions of AOD and the spatial and temporal components of the data, and to examine their roles in the calibration [2]. Additive models are used to construct a regression model of smooth functions of the independent variables, where the linear relationship between the variables and the response are replaced by a functional relationship [35,36] Building on the baseline model, we added a cubic regression smoothing spline (f ) on AERONET AOD (Model 1; Equation (3)); a spatiotemporal model with a tensor product spline (f s,t (x,y,t)) of space and time (Model 2; Equation (4)); a spatiotemporal model with a cubic spline (f ) for space and functions of time, which is broken down into three components using a cubic regression spline (f t1 ) on date (t 1 ), and indicator categorial functions (I t2 and I t3 ) for month (t 2 ; used only with long-term AQS-based models) and day of the week (t 3 ), respectively (Model 3; Equation (5)); a temporal only model (Model 4; Equation (6)); and a spatial only model with a 2-D tensor product spline (f s ) of space (geographic coordinates, x,y) that captures spatial patterns of the measurements (Model 5; Equation (7)).
Stage 2: The second step was to demonstrate how well the calibration models predict PM 2.5 when applied to satellite-based AOD. We used MISR AOD observations (550 nm) from 4.4 km pixels coincident with each DRAGON site. The calibration, validation, and evaluation processes are detailed in Figure 2.
Model 5: PMs = α + f(AOD) + fs(x,y) + εs (7) Stage 2: The second step was to demonstrate how well the calibration models predict PM2.5 when applied to satellite-based AOD. We used MISR AOD observations (550 nm) from 4.4 km pixels coincident with each DRAGON site. The calibration, validation, and evaluation processes are detailed in Figure 2.

Model Evaluation
The results from all Stage 1 and 2 models are presented based on leave-one-site-out cross-validation (LOSO CV), where R 2 , Root Mean Square Error (RMSE), and Mean Absolute Bias (MAB) represent the statistics based on observed (from left out site) versus predicted (from model on remaining sites) data. Bias is defined as the estimate of the systematic error, here we use the absolute bias, determined as the difference between the monitored PM 2.5 and the modeled PM 2.5 concentrations. The bias will provide an estimate to the models' direction, namely, if they are overestimating or underestimating the PM 2.5 concentrations in the study area in general and between the sites.
To better understand the contribution of the temporal component of the models, we leveraged three long-term co-located AQS-AERONET sites in Bakersfield, Fresno, and Modesto with available data from 2002 to the present. To these data we re-fit the baseline model and Models 1, 2, and 4, with Model 2 having tensor product for the temporal components only (date, month, day of the week). The spatial component was not able to fit with only 3 sites.
To better understand the contribution of the spatial component of the models, we examined the spatial distribution of the residuals from the best fitting DRAGON model to see if there was any pattern. We also applied the long-term models from Bakersfield and Fresno to each DRAGON site to determine the feasibility of using a calibration model from one site spatially over a larger domain. These models were evaluated by comparing the observed DRAGON data to the predictions from the two long-term AQS-AERONET models.

Results
Stage 1: Site-specific summary statistics of DRAGON AERONET AOD and PM 2.5 concentrations, ordered by their Spearman correlations, are detailed in Table 1. Mean AOD did not vary widely by site (0.10 in Madera City and Tranquility to 0.14 in Porterville); mean PM 2.5 exhibited spatial variability, primarily from east to west (13. Applying the non-linear GAM (Model 1) modestly improved the Baseline linear model (Table 2; Figure 3) where the R 2 increased by 5% and RMSE decreased by 0.45 µg/m 3 . The inclusion of a spatiotemporal tensor product (Model 2) further improved the model fit, increasing the R 2 from 0.40 to 0.65, and lowering RMSE from 9.93 µg/m 3 to 7.62 µg/m 3 ( Table 2). Separating the spatial and temporal basis functions within the same model (Model 3) results in the same R 2 (0.65) but slightly lower RMSE

Stage 2:
The number of coincident MISR AOD pixels over the DRAGON sites was only N = 38 due to MISR's near-weekly orbit. Applying the calibration models to MISR AOD yielded similar model evaluation statistics (Table 2). For example, the linear (baseline model) regression between PM2.5 and AERONET AOD had R 2 = 0.35 and RMSE = 10.38 μg/m 3 (N = 301); when applied to MISR, AOD yielded R 2 = 0.37 and RMSE = 10.60 μg/m 3 (N = 38) (Table 2, Figure 3). Model 3, the best performing calibration, also performed best on the MISR observations (R 2 = 0.60; RMSE = 8.42 μg/m 3 ), improving the baseline model by 80% (Table 2, Figure 4). Similarly, the temporal products were found to be the main contributor (Model 4) in the model evaluation on MISR data. With AOD, the temporal terms explained approximately 61% of the variation in PM2.5, while AOD with spatial terms explained only 44% of the variation. While the AERONET-based calibration models have a negligible bias, the MISR-based estimations seem to marginally underestimate the PM2.5 concentrations for all models (e.g., negative MAB ~ −1.3 μg/m 3 ; Table 2).

Stage 2:
The number of coincident MISR AOD pixels over the DRAGON sites was only N = 38 due to MISR's near-weekly orbit. Applying the calibration models to MISR AOD yielded similar model evaluation statistics (Table 2). For example, the linear (baseline model) regression between PM 2.5 and AERONET AOD had R 2 = 0.35 and RMSE = 10.38 µg/m 3 (N = 301); when applied to MISR, AOD yielded R 2 = 0.37 and RMSE = 10.60 µg/m 3 (N = 38) (Table 2, Figure 3). Model 3, the best performing calibration, also performed best on the MISR observations (R 2 = 0.60; RMSE = 8.42 µg/m 3 ), improving the baseline model by 80% (Table 2, Figure 4). Similarly, the temporal products were found to be the main contributor (Model 4) in the model evaluation on MISR data. With AOD, the temporal terms explained approximately 61% of the variation in PM 2.5 , while AOD with spatial terms explained only 44% of the variation. While the AERONET-based calibration models have a negligible bias, the MISR-based estimations seem to marginally underestimate the PM 2.5 concentrations for all models (e.g., negative MAB~−1.3 µg/m 3 ; Table 2).       Model Evaluation: Spatial analyses of the per-site RMSE from the DRAGON AERONET-PM 2.5 calibration models show high values with a strong spatial trend based on the baseline linear model (Figure 6, left) that are significantly improved when spatiotemporal Model 3 is applied (Figure 6, right). The overall improvement in the total RMSE for all stations is 27% ranging from a 7% decrease in Porterville site to a 41% decrease in the Fresno site.
Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 16 ( Figure 6, left) that are significantly improved when spatiotemporal Model 3 is applied (Figure 6, right). The overall improvement in the total RMSE for all stations is 27% ranging from a 7% decrease in Porterville site to a 41% decrease in the Fresno site.
(a) (b) We also ran the Baseline model, Model 1 (GAM w/AOD), Model 2 only with a temporal tensor product, and Model 4 (GAM w/separate temporal products) on each DRAGON site and examined the R 2 and RMSE (Figure 7a,b). The results clearly demonstrate that the GAM models with the temporal predictors are doing better for each station. The single site models were also applied to the DRAGON-MISR data and showed relatively constant results for the linear baseline model, yet the temporal predictors change by site with a high error in Porterville (Figure 7c  We also ran the Baseline model, Model 1 (GAM w/AOD), Model 2 only with a temporal tensor product, and Model 4 (GAM w/separate temporal products) on each DRAGON site and examined the R 2 and RMSE (Figure 7a,b). The results clearly demonstrate that the GAM models with the temporal predictors are doing better for each station. The single site models were also applied to the DRAGON-MISR data and showed relatively constant results for the linear baseline model, yet the temporal predictors change by site with a high error in Porterville (Figure 7c Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 16 ( Figure 6, left) that are significantly improved when spatiotemporal Model 3 is applied (Figure 6, right). The overall improvement in the total RMSE for all stations is 27% ranging from a 7% decrease in Porterville site to a 41% decrease in the Fresno site.
(a) (b) We also ran the Baseline model, Model 1 (GAM w/AOD), Model 2 only with a temporal tensor product, and Model 4 (GAM w/separate temporal products) on each DRAGON site and examined the R 2 and RMSE (Figure 7a,b). The results clearly demonstrate that the GAM models with the temporal predictors are doing better for each station. The single site models were also applied to the DRAGON-MISR data and showed relatively constant results for the linear baseline model, yet the temporal predictors change by site with a high error in Porterville (Figure 7c  There was a total of 3806 available co-located AOD-PM2.5 observations at the long-term (2002present) AERONET-AQS sites in Fresno, Bakersfield, and Modesto ( Figure 1; Table 3). The Fresno site had the most data and the highest correlation coefficient between AOD and PM2.5 (R = 0.47). Table 3. Summary statistics between AOD and PM2.5 at long-term co-located AERONET-AQS sites. To the combined data from the 3 sites, re-fitting the Baseline model and Models 1, 2, and 4 shows, not unexpectedly, that on the long-term data the GAM model incorporating only temporal products (Model 4) had the best results in both AERONET-PM2.5 calibration model (R 2 = 0.61; RMSE = 8.6 μg/m 3 ) and MISR-based evaluation (R 2 = 0.38; RMSE = 11.22 μg/m 3 ). However, the Stage 2 MISR application of the calibration model was not as good as we saw with the spatiotemporal Model 3 above, and the improvement of Model 4 from the Baseline model was comparatively low ranging from R 2 = 0.34 to R 2 = 0.38 based on Model 4 ( Figure 8).

Site Name Number of obs. Correlation Coefficient (R)
To test the feasibility of using one calibration model to predict PM2.5 over the larger Central Valley region, we calibrated the Baseline model and Model 4 at the long term AERONET-AQS PM2.5 sites in Fresno and Bakersfield (that were part of the DRAGON network) separately, and evaluated the model on MISR data (at all DRAGON sites). The estimated evaluation error was spatially examined by distance from the AQS site locations (Figure 9). There was a total of 3806 available co-located AOD-PM 2.5 observations at the long-term (2002-present) AERONET-AQS sites in Fresno, Bakersfield, and Modesto ( Figure 1; Table 3). The Fresno site had the most data and the highest correlation coefficient between AOD and PM 2.5 (R = 0.47). Table 3. Summary statistics between AOD and PM 2.5 at long-term co-located AERONET-AQS sites. To the combined data from the 3 sites, re-fitting the Baseline model and Models 1, 2, and 4 shows, not unexpectedly, that on the long-term data the GAM model incorporating only temporal products (Model 4) had the best results in both AERONET-PM 2.5 calibration model (R 2 = 0.61; RMSE = 8.6 µg/m 3 ) and MISR-based evaluation (R 2 = 0.38; RMSE = 11.22 µg/m 3 ). However, the Stage 2 MISR application of the calibration model was not as good as we saw with the spatiotemporal Model 3 above, and the improvement of Model 4 from the Baseline model was comparatively low ranging from R 2 = 0.34 to R 2 = 0.38 based on Model 4 ( Figure 8).

Site
To test the feasibility of using one calibration model to predict PM 2.5 over the larger Central Valley region, we calibrated the Baseline model and Model 4 at the long term AERONET-AQS PM 2.5 sites in Fresno and Bakersfield (that were part of the DRAGON network) separately, and evaluated the model on MISR data (at all DRAGON sites). The estimated evaluation error was spatially examined by distance from the AQS site locations (Figure 9). Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 16 (a) (b)  Except for the Tranquility site, there is a clear reduction in the prediction error between the linear regression ( Figure 9, upper panel) and Model 4 ( Figure 9, center panel) even when calibrating the model on data from only one long-term site. No significant differences are seen in Model 4 results between the models calibrated on two different long-term AQS stations, Fresno, and Bakersfield, and applied to all DRAGON sites (Figure 9; center panel).

Discussion
In this study, we examined the contribution of both spatial (locations of sites) and temporal (date, month, day of the week) components in the prediction of PM 2.5 concentrations, based solely on remotely sensed AOD measured at AERONET sites in Central Valley, CA. We found a strong effect of the spatial and temporal predictors in all examined models and datasets, indicating that linear models with AOD as the only predictor are not capable of capturing complex dependencies in AOD-PM relationships. More sophisticated statistical models are therefore needed to explain the relationships in time and in space. Similar approaches have been taken in studies of the association between satellite AOD and PM 2.5, including Sorek-Hamer et al. [37] who reported that both Multivariate Adaptive Regression Splines (MARS) and GAM models were more efficient than a linear regression in retrieving PM 2.5 concentrations from different satellite aerosol products. Strawa et al. [38] showed that GAM resulted in an improved correlation coefficient, particularly capturing hourly PM 2.5 exceedances that were not seen in the simple linear regression model. Franklin et al. [2] found that spatiotemporal tensor products of space and time best characterized the associations between MISR AOD in small, medium and large fractions to predict PM 2.5 and PM 10 concentrations, respectively.
Similarly, we found by leveraging the DRAGON data, which provides rich spatial and temporal information on both AOD and PM 2.5 , that including spatiotemporal functions in a regression model resulted in a far better calibration between AOD and PM 2.5 than a simple linear regression (R 2 0.65 vs. 0.35; RMSE 7.58 vs. 10.38 µg/m 3 ). Importantly, our results indicate that temporal functions are the largest contributors to the performance of AOD-PM 2.5 calibration models; that is, the temporal component of the spatiotemporal calibration models played a stronger role in the model improvement than the spatial component alone. Applying the DRAGON-AERONET spatiotemporal calibration models to MISR AOD data revealed good results with R 2 and RMSE values that were better than those seen in other studies [2,12]. However, one limitation is that due to the nature of the daily PM 2.5 data available at the DRAGON sites, we were not able to look at associations specifically at the MISR overpass time.
Leveraging the longer time series at the Fresno and Bakersfield sites showed promising results for the AERONET-AQS calibration model (R 2 = 0.61; RMSE = 8.6 µg/m 3 ), again indicating the functional temporal components contributed significantly to the models over a simple AOD model alone. However, when these calibration models were evaluated on MISR data, the R 2 was far lower (0.38) and RMSE higher (10.73 µg/m 3 ). It did not matter what site was used in developing the calibration model, as evidenced by nearly identical RMSE when either the Fresno or the Bakersfield site was applied to MISR data. With this limited dataset we were able to show that although spatial variability exists, the temporal predictors strongly contribute to the explained variance, but using one site for AOD-PM 2.5 calibration is likely to be more useful for predicting over small (local) regions as long as the site-specific characteristics are well characterized in the model.
Having a spatially and temporally calibrated AOD-PM 2.5 model is shown to be the best approach when subsequently applying it to convert satellite-observed AOD over a larger region. With separate spatial and temporal components in one model (Model 3) fit on the DRAGON data we could capture the spatial trends in PM 2.5 levels over the Central Valley, CA ( Figure 5). These results imply that simple AERONET AOD-PM 2.5 calibrations with both spatial and temporal components are robust and can be reliably applied to space-borne AOD observations, resulting in PM 2.5 prediction surfaces for use in downstream applications. An important consideration of our results is that if applied to different regions of the world there will be different topological and meteorological conditions that may alter the magnitude and strength of the AOD-PM 2.5 association. To address this issue, studies have incorporated random effects to distinguish a nested geographical hierarchy [39] where regions or countries (e.g., Brazil) are nested within super-regions (e.g., Latin America and Caribbean) to allow for multi-scale heterogeneity in the spatiotemporally adjusted AOD-PM association. Following these results, since they apply to a certain study area during a limited period of observations, future research will examine the application of the spatiotemporal characteristics on different AERONET AOD-PM co-locations where available, in other parts of the U.S. and globally, and apply more sophisticated machine learning methods incorporating additional variables, e.g. meteorology, traffic, according to the MAIA modeling scheme.
The results from this study demonstrate the use of AERONET aerosol products for modeling exposure estimates as a proxy for satellite-based PM 2.5 estimations. The upcoming MAIA mission will be capable of characterizing aerosol sizes, compositions and quantities. One of the main objectives of MAIA is to provide researchers with modeled PM estimates that can be used in health studies in order to better understand associations between air quality and health outcomes. The results of this study help to inform and support the MAIA algorithm development process.

Conclusions
The primary objective of this study was to develop spatiotemporal models that link aerosol optical properties obtained from AERONET to co-located ground-level PM 2.5 mass concentrations obtained from the EPA national monitoring networks, and then apply the calibration models to convert MISR AOD to PM 2.5 maps. By focusing primarily on the DRAGON field campaign in California's Central Valley we were able to characterize spatial dependencies and the strong contribution of temporal predictors to the AOD-PM 2.5 association. The linear correlation between AERONET AOD and PM 2.5 from different co-located sites had a wide range with relatively high correlations, with a strong dependency on the site. Leveraging spatial and temporal effects in a non-linear model resulted in a better fit R 2 = 0.65 and improved RMSE = 7.58 µg/m 3 . Finally, applying the DRAGON AERONET-based calibrated model to MISR AOD is reliable with predicted vs. observed PM 2.5 R 2 = 0.65 and RMSE = 7.99 µg/m 3 . Using only temporal dependencies from a longer time series at one site (Fresno) resulted in poorer results but can still be applied to predict PM 2.5 from MISR relatively well. Our results point out the value in spatially dense campaigns such as DRAGON and imply that AERONET AOD in addition to spatial and temporal information can be utilized for calibrating AOD-PM models with cautious on the site-specific effects.