Computing Ordinary Least-Squares Parameter Estimates for the National Descriptive Model of Mercury in Fish Techniques and Methods 7-C10 Computing Ordinary Least-Squares Parameter Estimates for the National Descriptive Model of Mercury in Fish Techniques a

For more information on the USGS-the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprod To order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product for the most part is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Abstract A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products ′ X X and ′ X y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce ′ X X and ′ X y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8 p 2 +16 p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software

Scientific Investigations Report 2012-5241

For more information on the USGS-the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprod To order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Suggested citation: Sprague, L.A., and Gronberg, J.M., 2013, Estimated anthropogenic nitrogen and phosphorus inputs to the land surface of the conterminous United States-1992States- , 1997States- , and 2002 where AI i is the total anthropogenic nutrient input to the watershed from years i to n, Fert i is the input from fertilizer from years i to n, Fix i is the input from biological fixation by crops from years i to n (nitrogen only), Atm i is the input from atmospheric deposition from years i to n (nitrogen only), FoodImp i is the input from imported food from years i to n, and FeedImp i is the input from imported feed from years i to n. Over shorter time steps (such as a year), however, livestock waste is not always completely recycled; manure is often used to fertilize crops and pasture in succeeding time steps (for example, Year 2 in Abstract Anthropogenic inputs of nitrogen and phosphorus to each county in the conterminous United States and to the watersheds of 495 surface-water sites studied as part of the U.S. Geological Survey National Water-Quality Assessment Program were quantified for the years 1992, 1997, and 2002. Estimates of inputs of nitrogen and phosphorus from biological fixation by crops (for nitrogen only), human consumption, crop production for human consumption, animal production for human consumption, animal consumption, and crop production for animal consumption for each county are provided in a tabular dataset. These countylevel estimates were allocated to the watersheds of the surfacewater sites to estimate watershed-level inputs from the same sources; these estimates also are provided in a tabular dataset, together with calculated estimates of net import of food and net import of feed and previously published estimates of inputs from atmospheric deposition, fertilizer, and recoverable manure. The previously published inputs are provided for each watershed so that final estimates of total anthropogenic nutrient inputs could be calculated. Estimates of total anthropogenic inputs are presented together with previously published estimates of riverine loads of total nitrogen and total phosphorus for reference