Effects of Sampling Interval on Spatial Patterns and Statistics of ...

Effects of Sampling Interval on Spatial Patterns and Statistics of Watershed Nitrogen Concentration Shuo-sheng “Derek” Wu1 Department of Geography, Geology, and Planning, Missouri State University, 901 South National Avenue, Springfield, Missouri 65897

E. Lynn Usery and Michael P. Finn Center of Excellence for Geospatial Information Science, U.S. Geological Survey, 1400 Independence Road, Rolla, Missouri 65401

David D. Bosch Southeast Watershed Research Laboratory, Agricultural Research Service, U.S. Department of Agriculture, 2375 Rainwater Road, Tifton, Georgia 31794

Abstract: This study investigates how spatial patterns and statistics of a 30 m resolution, model-simulated, watershed nitrogen concentration surface change with sampling intervals from 30 m to 600 m for every 30 m increase for the Little River Watershed (Georgia, USA). The results indicate that the mean, standard deviation, and variogram sills do not have consistent trends with increasing sampling intervals, whereas the variogram ranges remain constant. A sampling interval smaller than or equal to 90 m is necessary to build a representative variogram. The interpolation accuracy, clustering level, and total hot spot areas show decreasing trends approximating a logarithmic function. The trends correspond to the nitrogen variogram and start to level at a sampling interval of 360 m, which is therefore regarded as a critical spatial scale of the Little River Watershed.

INTRODUCTION Environmental scientists often need to take a water quality sampling survey in a watershed to examine pollutant concentration levels that are critical to human health. The purpose of this study is to investigate how sampling intervals affect the spatial patterns and statistics of watershed nitrogen concentration. Our approach is to systematically take samples at incremental intervals from a model-simulated watershed nitrogen surface and compare the analyses from different sampling intervals. This approach allows us to efficiently take multiple sample sets and conduct analysis. 1Corresponding

author; email: [email protected]

172 GIScience & Remote Sensing, 2009, 46, No. 2, p. 172–186. DOI: 10.2747/1548-1603.46.2.172 Copyright © 2009 by Bellwether Publishing, Ltd. All rights reserved.

WATERSHED NITROGEN CONCENTRATION

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We used the Agricultural Non-Point Source (AGNPS) pollution model to simulate watershed nitrogen concentration. The AGNPS pollution model was developed by the U.S. Department of Agriculture to estimate sediment and nutrient yields from agricultural activities in agricultural watersheds (Young et al., 1989; Panuska et al., 1991). This model is a distributed, cell-by-cell, event-based model that predicts surface runoff, sediment yield, and nutrient loading of phosphorus, nitrogen, and chemical oxygen demand on the basis of 22 input parameters derived from soil, land cover, and elevation data (Young et al., 1994, 1995). This study examined the clustering level and hot spot pattern of watershed nitrogen concentration using spatial statistics. Spatial statistics was developed to analyze the spatial patterns of geographic variables and is commonly used to study vectorbased socioeconomic data (ESRI, 2005). In this study, we used spatial statistics to examine the cell-based modeling outputs of nitrogen nutrient loading. Watershed nitrogen concentration varies geographically and is, therefore, appropriate for study using spatial statistics. Particularly, spatial statistics allows us to visually examine statistically significant high-nitrogen clusters (termed hot spots), which can provide insights into where to mitigate the impact of agricultural activities on water quality. The results have implications for watershed management and resources planning. Sampling-interval effects on clustering and hot spot analyses also are of interest to watershed researchers and managers. In the following sections, we first review past studies of sampling-interval effects on spatial analysis of geographic variables. Then we describe our study area, data source, and methodology. The computation of spatial statistics is particularly elaborated in detail. Lastly, we discuss important findings and methodological limitations of this study before concluding with some future research directions. LITERATURE REVIEW Scientists often need to take regular samples of environmental variables to model natural processes (Morris, 1999; Litaor et al., 2002; Tian et al., 2002) or as a preliminary effort for optimizing a subsequent sampling scheme (Van Groenigen et al., 1997; Simbahan and Dobermann, 2006). Nevertheless, analysis based on different sampling intervals may produce different results. Researchers have studied the effects of sampling intervals on spatial analysis of various variables. For example, Li (1992), Gong et al. (2000), Aguilar et al. (2005), and Chaplot et al. (2006) examined how the accuracy of digital elevation models varies with sampling interval. Oliver and Frogbrook (1998), Bourennane and King (2000), and Frogbrook and Oliver (2000) tested how different sampling intervals effect the interpolation accuracy of various soil variables. Western and Blöschl (1999), Oline and Grant (2002), Sobieraj et al. (2004), and Iqbal et al. (2005) investigated the effect of sampling interval on spatial patterns and statistics of soil properties. The common conclusion from these studies is that there is a tradeoff between sampling interval and analysis accuracy. Ultimately, the optimal sampling interval is dependent on the purpose of the study and the available resources. Although geostatisticians have proposed a theoretical framework to determine the optimal sampling interval based on preliminary samples and geostatistics (Curran and Atkinson, 1998), the effects of sampling interval of a particular variable on a certain analysis at a specific study area are still uncertain unless empirically

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Fig 1. The Little River Watershed, Georgia, USA.

tested. Yet an empirical test of the effects of sampling interval is rarely done due to the intensive work of taking samples at multiple intervals. Our approach to investigate sampling-interval effect is to take samples from model-simulated digital raster data. Using model-simulated digital raster data allows us to efficiently take multiple sets of sample points, conduct various types of analysis using the sample sets, and compare the analysis results from different sampling intervals. Particularly, this study investigates the effects of sampling interval on clustering and hot spot analyses of watershed nitrogen concentration. Clustering analysis helps determine whether the overall level of nitrogen concentration in a watershed is statistically significant, while hot spot analysis allows one to locate statistically significant high-nitrogen clusters (ESRI, 2005). The results of clustering analysis can be used to prioritize watersheds for pollution management, while the results of hot spot analysis can be used to locate areas in a watershed that have critical needs for clean-up treatment. STUDY AREA AND DATA SOURCE Our study area is the Little River Watershed, Georgia, USA, approximately 12 km wide and 35 km long, with an area of 334 km2 (Fig. 1). The Little River Watershed is one of the experimental watersheds for the U. S. Department of Agriculture (USDA) Agricultural Research Service (ARS) Southeast Watershed Research Laboratory (SEWRL). The primary goal of SEWRL is to “develop an improved understanding of basic hydrologic and water quality processes on Coastal Plain watersheds and evaluate the effects of agricultural management practices on the region’s natural resources and environment” (Bosch et al., 2007). The fundamental dataset used for sampling analysis is a 30 m resolution raster surface of watershed nitrogen concentration, which is generated from the AGNPS pollution model based on 22 input parameters derived from soil, elevation, and land cover data of 30 m resolution (Usery et al., 2004). The 30 m elevation dataset comes from the USGS National Elevation Dataset (NED) (USGS, 2006). The 30 m land cover dataset is based on the USGS National Land Cover Database (NLCD) (USGS, 2007). The 30 m soil dataset originates from the USDA Digital Soil Geographic Databases (USDA, 2006), which was in vector polygon format and was converted to a 30 m raster to match the land cover and elevation datasets.


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Fig. 2. An illustration of the sampling scheme.

METHODOLOGY To investigate the effect of sampling interval on spatial analysis, we first took 20 sets of point samples at 30 m to 600 m intervals for every 30 m increase from the AGNPS-simulated 30 m resolution nitrogen surface. Figure 2 illustrates this approach. We then calculated the mean, standard deviation, variogram sill, variogram range, interpolation accuracy, clustering level, and hot spot pattern based on the samples. Lastly, we examined how these statistics changed with sampling intervals. A variogram is a graph of semivariance against lag. Semivariance is calculated as half the average of the squared difference between paired sample values separated by a certain distance called lag. The mathematical equation of semivariance, g(h), at a certain lag, h, can be expressed as:

1 g ( h ) = --------2Nh

N

∑ ( z1 – zi + h )

(1)

i=1

where Nh is the number of paired samples separated by lag h, and zi and zi+h are the values of the pair of samples separated by lag h. A variogram indicates the extent of spatial autocorrelation across space and is a fundamental tool for geostatistical interpolation. For example, Figure 3 illustrates a simple variogram. We can see that as the lag increases, the semivariance becomes larger. At a certain distance called range, the semivariance stabilizes at a value called sill. The range represents the limit of spatial dependence and indicates the distance over which variable values would be similar. Spatial interpolation based on geostatistics is optimal in the sense that the estimation

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Fig. 3. An illustration of the variogram.

variance is minimized under the assumption of stationarity (Burrough and McDonnell, 1998). Geostatistical interpolation is a popular approach for interpolation of geographical variables. Therefore we study the effect of sampling interval on the variogram of watershed nitrogen. In the comparison of the interpolation accuracy from different sampling intervals, we use the natural neighbor algorithm (Boissonnat and Cazals, 2001) instead of geostatistics for interpolation because our samples are considerably dense relative to the size of the Little River Watershed. The natural neighbor algorithm is a simple and robust interpolation algorithm that is sufficient to meet our need for interpolation. We interpolated 19 nitrogen surfaces of 30 m resolution from the point samples at 60 m to 600 m intervals (Fig. 4). The interpolated surfaces were then compared with the original 30 m nitrogen surface to calculate the root mean square error (RMSE) and the total absolute error (TAE). We computed the global Moran’s index to represent the overall clustering level of nitrogen concentration in the watershed. The global Moran’s index (I) is calculated as follows (see Wong and Lee, 2005): n

∑ ∑ Wij ( Xi – X ) ( Xj – X )

i j I = ------------------------------------------------------------------2 W ij ( X j – X )

∑∑ ∑ i

j

(2)

i

where Xi is the nitrogen value for the ith cell, X is the mean nitrogen of the watershed, Xj is the nitrogen value for the jth cell, Wij is a weight parameter for the pair of cells i and j to represent proximity relations, and n is the number of cells in the watershed. The equation basically tests if near cells have more similar values than distant cells do. The sum of cross-products in the equation will be positive if neighboring cells have relatively similar values; the value of I will be greater than 0, indicating similar values are clustered. On the other hand, the sum of the cross-products in the equation will be negative if neighboring cells have relatively dissimilar values; the value of I will be less than 0, indicating similar values are dispersed. If some neighboring cells have similar values and some do not, and there are roughly as many cell


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Fig. 4. Original and selected 30 m resolution interpolated nitrogen surfaces based on certain sampling intervals.

pairs with positive cross-products as there are with negative cross-products, the result of summing the cross-products will be close to 0, indicating a random distribution. For the purpose of comparing different sampling intervals, we used a cutoff neighborhood distance to define the weight function in calculating the global Moran’s index. Cell pairs within this distance were assigned a weight of 1 and all other pairs were assigned a weight of 0. This neighborhood distance can be regarded as the scope of spatial interaction and can be determined from the variogram analysis, using the variogram range as the neighborhood distance. We calculated the variogram of watershed nitrogen concentration and determined the variogram range on the basis of the first semivariance peak, which is approximately 900 m. A distance of 900 m was then used as a cutoff neighborhood distance to calculate the global Moran’s index. We computed the Z score of the global Moran’s index to compare the clustering level from different sampling intervals. The Z score indicates the level that the local clustering is significantly different from a random distribution. It is therefore appropriate to compare cluster and hot spot statistics between different sample datasets using the corresponding Z scores. We computed the local Getis-Ord statistic for each cell for studying hot spots of nitrogen concentration. The local G statistic (Gi) for the ith cell is calculated as the sum of nitrogen values in its neighborhood divided by the sum of nitrogen values in the entire watershed (Getis and Ord, 1992):

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∑ Wij Xj

j G i = --------------------- , j may equal i, Xj

∑

(3)

j

where Xj is the nitrogen value for the jth cell, and Wij is a weight parameter for the pair of cells i and j to represent proximity relations. A cell with high Gi indicates cells in its neighborhood have relatively high nitrogen values. Conversely, a cell with low Gi indicates cells in its neighborhood have relatively low nitrogen values. A Gi near 0 indicates no apparent concentration of high or low values in the neighborhood of the target cell. This occurs when the surrounding cell values are close to the mean, or when the target cell is surrounded by a mix of high- and low-nitrogen values. We used the same cutoff neighborhood-distance parameter of 900 m in calculating the global Moran’s index to calculate the local G statistic. Furthermore, the Z score of the Gi was computed to indicate the level that a high- or low-nitrogen concentration is significantly different from a random distribution (Ord and Getis, 1995). As with the Gi value itself, a group of cells with high Z scores indicates a cluster of cells with high nitrogen values, and vice versa; a Z score near 0 indicates no cluster of either high or low values. We compared nitrogen hot spot patterns for different sampling intervals based on the Z score of the Gi of 1.96 and above, which indicates a 95 percent confidence interval and represents high statistical significance (Fig. 5). The total hot spot areas within the watershed were also compared for different sampling intervals. RESULTS The mean and the standard deviation of nitrogen concentration do not have consistent trends with increasing sampling intervals (Figs. 6A and 6B). The results indicate that the mean and the standard deviation from higher sampling densities are not necessarily more accurate. Nevertheless, the trends appear to fluctuate more at larger sampling intervals. Therefore, we consider the statistics from smaller sampling intervals to be more robust and reliable. For the variograms at different sampling intervals, the sill does not consistently increase or decrease with increasing sampling intervals, whereas the range remains similar at approximately 900 m (Figs. 7 and 8). Because the smallest lag available for computing the semivariance of a variogram is the respective sampling interval, e.g., the 30 m lag for the 30 m sampling interval, large sampling intervals do not allow representative variograms to be constructed when the variogram range is relatively small. In addition, smaller sampling intervals produce a larger numbers of samples that generally yield more reliable estimates of the semivariance. For the above reasons, geostatistical interpolation based on higher sampling densities is preferred to achieve higher accuracy. For the Little River Watershed, a sampling interval smaller than or equal to 90 m appears to be necessary to build a reliable variogram model (Fig. 9). The RMSE and the TAE for interpolation both have an increasing trend with increasing sampling intervals (Figs. 10 and 11). The trend is similar to the variogram of the 30 m nitrogen at equivalent lag distances (Fig. 9). Furthermore, the trend


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Fig. 5. Selected hot spot patterns based on different sampling intervals.

approximates a logarithmic function that starts to level at a sampling interval of approximately 360 m, showing that interpolation based on a sampling interval of 360 m and larger will be similar. It indicates that using a large sampling interval for cost effectiveness may be preferred if a sampling survey cannot be taken at a sampling interval smaller than 360 m. The overall clustering level indicated by the global Moran’s index Z score has a decreasing trend with increasing sampling intervals (Fig. 12). At a sampling interval of 510 m, the Z score is 2.27, indicating that high-nitrogen patches in the watershed are clustered with a high degree of statistical significance (a Z score of 2.33 indicates a 98 percent confidence interval; a Z score of 1.96 indicates a 95 percent confidence interval; a Z score of 1.65 indicates a 90 percent confidence interval). At the 540 m sampling interval, the Z score is 1.12, indicating that high-nitrogen patches in the watershed are clustered with a relatively lower degree of statistical significance. The implication for watershed scientists is that they can use sample data at a large sampling interval up to 510 m to derive reliable clustering statistics of nitrogen concentration for the Little River Watershed. Observing hot spot maps from different sampling intervals (Fig. 5), we see that the nitrogen hot spots correspond to high-nitrogen patches in the original nitrogen map (Fig. 4). As the sizes of hot spots decrease with increasing sampling intervals, small hot spots disappear, which is consistent with the decreasing trend of the overall

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Fig. 6. The mean (A) and the standard deviation (B) of nitrogen concentration from 30 m to 600 m sampling intervals.

clustering level (Fig. 12). In addition, the total hot spot area in the watershed shows a decreasing trend with increasing sampling intervals (Fig. 13). The trend starts to level at a sampling interval of approximately 360 m, indicating that a majority of highvalue nitrogen clusters are of a size smaller than 360 m. The limit of sampling interval for hot spot analysis corresponds with that for clustering analysis. DISCUSSION The nitrogen interpolation accuracy, overall clustering level, and total hot spot area have similar trends that start to level at a sampling interval of 360 m. The sampling interval of 360 m appears to be a critical point beyond which interpolation errors become stable and clustering statistics become constant. At a corresponding variogram lag of 360 m, the semivariance of nitrogen concentration also becomes similar. We may interpret that 360 m is a critical spatial scale for the Little River Watershed and many important watershed processes relevant to nitrogen concentration are occurred within this spatial scale. Researchers would need to take sampling intervals smaller than 360 m to study those watershed processes in the watershed.


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Fig. 7. Variograms from 30 m to 600 m sampling intervals.

Fig. 8. Scatterplot showing the variation in semivariance with sampling interval in Figure 7.

To study the effects of sampling interval, we used the AGNPS pollution model to generate a simulated 30 m nitrogen surface to take incremental samples. A limitation of this approach is the potential error of the AGNPS pollution model and the subsequent error in spatial analysis using the model output. This study used the Little River Watershed as a case area to study the effects of sampling interval. Future research may study other watersheds of different sizes and characteristics and compare the results. The trends of watershed statistics with changing sampling intervals may be similar but the observed critical sampling intervals are likely to be different depending on the characteristic spatial scale of the corresponding watershed.

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Fig. 9. Variograms from 30 m to 150 m sampling intervals.

Fig. 10. The trend of the root mean square error (RMSE) with sampling interval.

Fig. 11. The trend of the total absolute error (TAE) with sampling interval.

This research studied the effects of sampling interval using a model-simulated watershed nitrogen surface. Future studies may adopt the same approach to study other watershed modeling outputs, such as surface runoff, sediment yield, and


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Fig. 12. The trend of clustering levels with sampling interval.

Fig. 13. The trend of total hot spot areas with sampling interval.

nutrient loadings of phosphorous and chemical oxygen demand. Comparing analysis results of these pollution variables may provide insights of pollution mechanism and hydrological processes in the watershed. CONCLUSIONS This study has investigated how spatial patterns and statistics of the nitrogen concentration in the Little River Watershed change with sampling interval, by taking incremental samples at 30 m to 600 m intervals for every 30 m increase from a AGNPS-simulated, 30 m resolution nitrogen surface. The results indicate that the mean and standard deviation do not change consistently with sampling interval, whereas the estimates are more robust and reliable at small sampling intervals. Variogram sills do not have consistent trends with changing sampling intervals, whereas variogram ranges remain roughly the same. A sampling interval smaller than or equal to 90 m is needed to construct a reliable variogram for geostatistical interpolation. The nitrogen interpolation error, overall clustering level, and total hot spot area have comparable trends with increasing sampling intervals that approximate a logarithmic

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function. The trends also correspond with the nitrogen variogram at equivalent lag distance. A sampling interval of 360 m appears to be a critical point at which the trends start to level and the analysis results become similar. This is because most high-value nitrogen patches in the watershed are at a spatial scale smaller than 360 m. Measuring the clustering level of watershed nitrogen concentration and distinguishing statistically significant high-value nitrogen clusters provide insights for watershed contamination management and resources planning. Studying the effects of sampling interval on spatial analysis of watershed nitrogen concentration helps scientists choose optimal sampling intervals for cost benefits. Discovering the trends of spatial statistics with sampling interval also help researchers identify critical spatial scales of important watershed processes. REFERENCES Aguilar, F. J., Aguera, F., Aguilar, M. A., and F. Carvajal, 2005, “Effects of Terrain Morphology, Sampling Density, and Interpolation Methods on Grid DEM Accuracy,” Photogrammetric Engineering and Remote Sensing, 71(7):805–816. Boissonnat, J. D. and F. Cazals, 2001, “Natural Neighbor Coordinates of Points on a Surface,” Computational Geometry-Theory and Applications, 19(2-3):155–173. Bosch, D. D., Sheridan, J. M., Lowrance, R. R., Hubbard, R. K., Strickland, T. C., Feyereisen, G. W., and D. G. Sullivan, 2007, “Little River Experimental Watershed Database,” Water Resources Research, 43(9), Art. No. W09470. Bourennane, H. and D. King, 2000, “Impact of the Sampling Density of the Primary Variable and Precision of the Auxiliary Variable on the Estimation of Soil Properties using Kriging with an External Drift,” in Proceedings of International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences (Accuracy 2000), Heuvelink, G. B. M. and M. J. P. M. Lemmems (Eds.), Amsterdam, The Netherlands: Delft University Press, 67–74. Burrough, P. A. and R. McDonnell, 1998, Principles of Geographical Information Systems, New York, NY: Oxford University Press, 356 p. Chaplot, V., Darboux, F., Bourennane, H., Leguedois, S., Silvera, N., and K. Phachomphon, 2006, “Accuracy of Interpolation Techniques for the Derivation of Digital Elevation Models in Relation to Landform Types and Data Density,” Geomorphology, 77(1-2):126–141. Curran, P. J. and P. M. Atkinson, 1998, “Geostatistics and Remote Sensing,” Progress in Physical Geography, 22(1):61–78. ESRI, 2005, The ESRI Guide to GIS Analysis, Volume 2: Spatial Measurements and Statistics, Redlands, CA: ESRI Press, 252 p. Frogbrook, Z. L. and M. A. Oliver, 2000, “The Effects of Sampling on the Accuracy of Predictions of Soil Properties in Precision Agriculture,” in Proceedings of International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences (Accuracy 2000), Heuvelink, G. B. M. and M. J. P. M. Lemmems (Eds.), Amsterdam, The Netherlands: Delft University Press, 225– 232. Getis, A. and J. K. Ord, 1992, “The Analysis of Spatial Association by use of Distance Statistics,” Geographical Analysis, 24(3):189–206.


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