Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 12 5 2008 10.5194/hess-12-1229-2008 http://www.hydrol-earth-syst-sci.net/12/1229/2008/ http://www.hydrol-earth-syst-sci.net/12/1229/2008/hess-12-1229-2008.html http://www.hydrol-earth-syst-sci.net/12/1229/2008/hess-12-1229-2008.pdf 1229 1239 2008-10-15 Incorporating landscape characteristics in a distance metric for interpolating between observations of stream water chemistry S. W. Lyon steve.lyon@natgeo.su.se J. Seibert A. J. Lembo T. S. Steenhuis M. T. Walter Physical Geography and Quaternary Geology, Stockholm University, Stockholm, Sweden Geography and Geosciences, Salisbury University, Salisbury MD, USA Biological and Environmental Engineering, Cornell University, Ithaca NY, USA Spatial patterns of water chemistry along stream networks can be quantified using synoptic or "snapshot" sampling. The basic idea is to sample stream water at many points over a relatively short period of time. Even for intense sampling campaigns, the number of sample points is limited and interpolation methods, like kriging, are commonly used to produce continuous maps of water chemistry based on the point observations from the synoptic sampling. Interpolated concentrations are influenced heavily by how distance between points along the stream network is defined. In this study, we investigate different ways to define distance and test these based on data from a snapshot sampling campaign in a 37-km² watershed in the Catskill Mountains region (New York State). Three distance definitions (or metrics) were compared: Euclidean or straight-line distance, in-stream distance, and in-stream distance adjusted according characteristics of the local contributing area, i.e., an adjusted in-stream distance. Using the adjusted distance metric resulted in a lower cross-validation error of the interpolated concentrations, i.e., a better agreement of kriging results with measurements, than the other distance definitions. The adjusted distance metric can also be used in an exploratory manner to test which landscape characteristics are most influential for the spatial patterns of stream water chemistry and, thus, to target future investigations to gain process-based understanding of in-stream chemistry dynamics. Alexander, R. B., Smith, R. A., and Schwarz, G. E.: Effect of stream channel size on the delivery of nitrogen to the Gulf of Mexico, Nature, 403, 758–761, 2000. Alexander, R. B., Johnes, P.J., Boyer, E. W., and Smith, R. A.: A comparison of methods for estimating the riverine export of nitrogen from large watersheds, Biogeochemistry, 57–58, 295–339, 2002. Alexander, R. B., Smith, R. A., and Schwarz, G. E.: Estimates of diffuse phosphorus sources in surface waters of the United States using a spatially referenced watershed model, Water Sci. Technol., 49(3), 1–10, 2004. Bailly, J.-S., Monestiez, P., and Lagacherie, P.: Modelling spatial variability along drainage networks with geostatistics, Math. Geol., 38, 515–539, 2006. Bernhardt, E. S., Likens, G. E., Buso, D. C., and Driscoll, C. T.: In-stream uptake dampens effects of major forest disturbance on watershed nitrogen export, P. Natl. Acad. Sci. USA, 100(18), 10 304–10 308, 2003. Beven, K. J. and Kirkby, M. J.: A physically based, variable contributing area model of basin hydrology, Hydrol. Sci. B., 24, 3–69, 1979. Burns, D. A., McHale, M. R., Driscoll, C. T., and Roy, K. M.: Response of surface water chemistry to reduced levels of acid precipitation: comparison of trends in two regions of NewYork, USA, Hydrol. Process, 20, 1611–1627, 2006. Chokmani, K. and Ouarda, T. B. M. J.: Physiographical space-based kriging for regional flood frequency estimation at ungauged sites, Water Resour. Res., 40, W12514, doi:10.1029/2003WR002983, 2004. Christakos, G.: Modern spatiotemporal geostatistics, Oxford University Press, New York, 2000. Closs, G., Downes, B., and Boulton, A.: Freshwater Ecology, Blackwell Science Ltd, Malden, MA, USA, 2004. Cressie, N.: Fitting models by weighted least squares, J. Math. Geol., 17(5), 563–586, 1985. Cressie, N.: Statistics for spatial data, John Wiley & Sons, Inc., New York, 1991. Cressie, N., Frey, J., Harch, B., and Smith, M.: Spatial prediction on a river network, Journal of Agricultural, Biological, and Environmental Statistics, 11(2), 127–150, 2006. Dent, C. L. and Grimm, N. B.: Spatial heterogeneity of stream water nutrient concentrations over sucessional time, Ecology, 80, 2283–2298, 1999. Fausch, K. D., Torgersen, C. E., Baxter, C. V., and Li, H. W.: Landscapes to riverscapes: briding the gap between research and conservation of stream fishes, Bioscience, 52(6), 483–498, 2002. Foran, J., Brosnan, T., Connor, M., Delfino, J., Depinto, J., Dickson, K., Humphrey, H., Novotny, V., Smith, R., Sobsey, M., and Stehman, S.: A framework for comprehensive, integrated, watershed monitoring in New York City, Environ. Monit. Assess., 62, 147–167, 2000. Ganio, L. M., Torgersen, C. E., and Gresswell, R. E.: A geostatistical approach for describing spatial pattern in stream networks, Front. Ecol. Environ., 3(3), 138–144, 2005. Gardner, B., Sullivan, P. J., and Lembo, A. J.: Predicting stream temperatures: geostatistical model comparison using alternative distance metrics, Canadian Journal of Fish and Aquatic Sciences, 60, 344–351, 2003. Gottschalk, L.: Correlation and covariance of runoff, Stoch. Hydrol. Hydraul., 7, 85–101, 1993a. Gottschalk, L.: Interpolation of runoff applying objective methods, Stoch. Hydrol. Hydraul., 7, 269–281, 1993b. Grayson, R. B., Gippel, C. J., Finlayson, B. L., and Hart, B. T.: Catchment-wide impacts on water quality: the use of "snapshot" sampling during stable flow, J. Hydrol., 199, 121–134, 1997. Legleiter, C. J., Lawrence, R. L., Fonstad, M. S., Marcus, W. A., and Aspinall, R.: Fluvial response a decade after wildfire in the northern Yellowstone ecosystem: A spatially explicit analysis, Geomorphology, 54, 119–136, 2003. Little, L. S., Edwards, D., and Porter, D. E.: Kriging in estuaries: as the crow flies, or as the fish swims?, J. Exp. Mar. Biol. Ecol., 213, 1–11, 1997. Lyon, S. W., McHale, M. R., Walter, M. T., and Steenhuis, T. S.: The impact of runoff generation mechanisms on the location of critical source areas, J. Am. Water Resour. As., 42(2), 793–804, 2006. McHale, M. R., Cirmo, C. P., Mitchell, M. J., and McDonnell, J. J.: Wetland nitrogen dynamics in an Adirondack forested watershed, Hydrol. Processes, 18, 1853–1870, 2004. Monestiez, P., Bailly, J.-S., Lagacherie, P., and Voltz, M.: Geostatistical modeling of spatial processes on directed trees: Application to fluvisol extent, Geoderma, 128, 179–191, 2005. Peterson, E. E., Merton, A. A., Theobald, D. M., and Urquhart, N. S.: Patterns of spatial autocorrelation in stream water chemistry, Environ. Monit. Assess., 121, 571–596, 2006. Peterson, E. E., Theobald, D. M., and Ver Hoef, J. M.: Geostatistical modeling on stream networks: developing valid covariance matrices based on hydrological distance and stream flow, Freshwater Biol., 52, 267–279, 2007. Preston, S. D. and Brakebill, J. W.: Application of spatially referenced regression modeling for the evaluation of total nitrogen loading in the Chesapeake Bay watershed, US Geological Survey Water Resources Investigations Report, 99–4054, 1999. Salvia, M., Iffly, J. F., Vander Borght, P., Sary, M., and Hoffmann, L.: Application of the "snapshot" methodology to a basin-wide analysis of phosphorus and nitrogen at stable low flow, Hydrobiologia, 410, 97–102, 1999. Sauquet, E., Gottschalk, L., and Leblois, E.: Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme, Hydrol. Sci. J., 45, 799–815, 2000. Seibert, J. and McGlynn, B. L: A new triangular multiple flow-direction algorithm for computing upslope areas from gridded digital elevation models, Water Resour. Res., 43, W04501, doi:10.1029/2006WR005128, 2007. Skøien, J. O., Merz R., and Blöschl G.: Top-kriging – geostatistics on stream networks, Hydrol. Earth Syst. Sci., 10, 277–287, 2006. Skøien, J. O. and Blöschl, G.: Spatiotemporal topological kriging of runoff time series, Water Resour. Res., 43, W09419, doi:10.1029/2006WR005760, 2007. Smith, R. A., Schwarz, G. E., and Alexander, R. B.: Regional interpretation of water-quality monitoring data, Water Resour. Res., 33(12), 2781–2798, 1997. Tetzlaff, D., Soulsby, C., Bacon, P. J., Youngson, A. F., Gibbins, C., and Malcolm, I. A.: Connectivity between landscapes and riverscapes – a unifying theme in integrating hydrology and ecology in catchment science?, Hydrol. Processes, 21, 1385–1389, 2007. Torgersen, C. E., Gresswell, R. E., and Bateman, D. S.: Pattern detection in stream networks: quantifying spatial variability in fish distribution, Proceedings of the Second Annual International Symposium on GIS/Spatial Analyses in Fishery and Aquatic Sciences, Fishery GIS Research Group, Saitama, Japan, 2004. Tripler, C., Kaushall, S. S., Likens, G. E., and Walter, M. T.: Environmental change and the role of potassium in forested ecosystems, Ecol. Lett., 9, 451–466, 2007. US Department of Agriculture – Natural Resources Conservation Serivce (USDA-NRCS): Soil Survey Geographic (SSURGO) database for Delaware County, New York, http://www.ncgc.nrcs.usda.gov/products/datasets/ssurgo/, accessed in: 1 August 2005, 2000. US Geological Survey (USGS): Standards for digital elevation models, Department of the Interior – USGS, Reston, VA, available at http://data.geocomm.com/catalog/US/ 61061/546/index.html, accessed in: 1 January 2002, 1992. Ver Hoef, J. M., Peterson, E., and Theobald, D.: Spatial statistical models that use flow and stream distance, Environ. Ecol. Stat., 13, 449–464. 2006. Wayland, K. G., Long, D. T., Hyndman, D. W., Pijanowski, B. C., Woodhams, S. M., and Haack, S. K.: Identifying relationships between baseflow geochemistry and land use with synoptic sampling and R-mode factor analysis, J. Environ. Qual., 32, 180–190, 2003. Williams, M., Hopkinson, C., Rastetter, E., Vallino, J., and Claessens, L.:, Relationships of land use and stream solute concentrations in the Ipswich River basin, Northeastern US, Water, Air, and Soil Pollution, 161, 1–4, 55–74, 2005. Yuan, L. L.: Using spatial interpolation to estimate stressor levels in unsampled streams, Environ. Monit. Assess. 94, 23–28, 2004.