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Dead in the Water: Methodology

April 10, 2006

Our model used fertilizer nitrogen inputs (lb N/acre/yr), population/acre, animal waste inputs (lb N/acre/yr) and atmospheric nitrate deposition (lb nitrate-N/acre/yr) for the years 1990 — 2003. We applied model coefficients to data on fertilizer use, population, and animal waste inputs for the comprehensive list of watersheds in the MRB for the years 1990-2003. We then generated estimates of the portion of the total modeled load contributed by each factor as lb/acre, multiplying this value by the number of acres in a watershed to generate a total load. We multiplied the modeled total nitrate flux by the delivery efficiency value from the SPARROW model (Alexander et al. 2000a). Like the SPARROW model, our model estimates the contribution of each watershed to nitrogen flux, independent of upstream sources. The sum of these watershed contributions was compared to the measured spring nitrate flux at USGS monitoring stations located at St. Francisville, LA on the Mississippi River and Melville, LA on the Atchafalaya River.

Spatial framework of the analysis

Watershed delineation

The Mississippi River Basin is defined for hydrological purposes as being comprised of 848 interconnected smaller watersheds. Each watershed is, by definition, an area of land that channels runoff to a single river or stream. The drainage area associated with a particular water quality monitoring site may be comprised of one, many, or the majority of the 848 watersheds, as is the case for the main monitoring stations located just above where the Mississippi and Atchafalaya Rivers drain into the Gulf of Mexico.

Our model was calibrated using a set of 27 non-overlapping drainage areas, three of which contained smaller drainages nested within them, for a total of thirty sites, and 208 individual site/year combinations. All sites chosen had data collected for a minimum of four years in 1990-2002. The mean drainage area was 12,682 square miles and the median was 12,449 square miles; the largest was 23,481 and the smallest 3,960 square miles.

We delineated site drainages in ArcMap (ESRI 2005) using the National Hydrography Dataset from USGS and the USGS Enhanced River Reach database (version 2).

Inputs to the analysis

Spring nitrate flux

We used data in USGS's searchable online National Water Information System (NWIS), for surface water nitrate for 1989 to the present. We focused on spring nitrate flux, selecting water quality monitoring sites where data had been collected for at least two months between February and June, in at least four years between 1990-2003. We averaged measurements that were conducted on the same day. Nitrate concentration data were multiplied by stream discharge data, after which concentrations and total flux were time-and flow-weighted.

Fertilizer calculated from USDA Planted Acres Database

Fertilizer inputs were estimated by multiplying the number of acres of each crop at the county level by that crop's fertilization rate (as lb N/acre). Acres of crops were estimated with the "Planted Acres" database for 1990-2002 from USDA, which provides yearly information on acres planted to 692 crops at the county level, for every state. We estimated fertilizer application rates with USDA data by state and year for major crops, and used data available online from the Fertilizer Institute and an FAO report (FAO, 2002) where USDA data were not available. Planted acreages were multiplied by fertilizer application rates to estimate total pounds of fertilizer nitrogen applied in each county. To obtain watershed-level estimates of fertilizer use, we used ARC GIS to overlay a map of counties on a map of watersheds. We multiplied total county fertilizer by the proportion of a county that lay within a watershed, summing the values for all polygons that comprised each watershed.

Calculated fertilizer application rates were checked against a 1990-2003 database of fertilizer sales by county (AAPFCO 2002). Data are for tons of N, P, and K sold as farm and non-farm fertilizer in counties in the United States, with two reporting periods per year. We recompiled data for a "fertilizer year" by merging data from the July-December reporting period of one year with the January-June reporting period of the following year. We used linear regression to assess the relationship between fertilizer use estimated with the USDA planted acres database and actual fertilizer sales, by county, within states. Because the fertilizer sales data are not complete for every state in every year and some states do not break shipments out by county, the comparison did not include every state and every year. However, it did include all years' data for Corn Belt states with the highest fertilizer use, and data from other important agricultural states. For states where we could subtract out "non-agricultural" fertilizer from the fertilizer sales database, our estimates of fertilizer nitrogen use still tended to be lower than actual sales. For Illinois, fertilizer sold exceeded our estimates by about 10 percent (N = 1424, R2 = 0.78); for Indiana, sales exceeded estimates by about 17 percent (N = 1287, R2 = 0.56); and in Missouri, sales also exceeded estimates by about 17 percent (N = 1561, R2 = 0.76).

To calculate the cost of fertilizer nitrogen lost to runoff in the MRB each year, we multiplied the yearly average cost of fertilizer nitrogen by the portion of the modeled nitrate-nitrogen flux that is derived from fertilizer runoff. We calculated an average yearly cost for fertilizer nitrogen by multiplying the amount of each type of fertilizer sold in the MRB from the fertilizer sales database by its respective cost (ERS 2005), summing that dollar figure and dividing it by the total mass of fertilizer nitrogen. Fertilizer prices for 2005 were obtained from the September 2005 "Green Markets Dealer Report" (IOMA, 2005), a newsletter that reports market trends in the fertilizer industry.

Atmospheric N deposition

We acquired raster data on nitrate deposition rates from the National Atmospheric Deposition Program (NADP) website for 1994-2003, and point data for 1990-1993, which we interpolated using ARC GIS Spatial Analyst (version 9.1; ESRI, 2005). We then used Spatial Analyst to calculate mean deposition values on a watershed basis for each year.

Population and N from human waste

Tract-level population data from the Bureau of the Census were aggregated to the watershed level for the census years 1990 and 2000, and we used linear interpolation to estimate population for intervening years. We extended existing trends for the years 2000-2003, setting watershed population levels at zero for negative totals. The error in the model associated with these estimations should be extremely small, since sparsely populated watersheds are few, and occur only in the dry western part of the MRB. To estimate the contribution from municipal point sources, we used a database of total nitrogen outflows from 32,000 municipal sewage facilities in 1980 (available on the SPARROW website; Gianessi and Peskin 1984). These data were provided at the county level, so we re-expressed the data on a watershed basis and estimated a per-capita value for waste nitrogen for the sites in our analysis. We assumed that nitrate comprises about 75 percent of the total nitrogen in municipal waste outflows (Mueller and Helsel 1996; Twichell et al. 2002).

Animal waste

Data on numbers of beef cows, milk cows, sheep, hogs, and poultry were compiled at the county level from National Agricultural Statistics Service (NASS) historical agricultural census data for 1987, 1992, 1997 and 2002. Since the agricultural census is conducted every five years, we estimated values for intervening years using linear interpolation. In the 2002 census, there were some counties where the government has blocked publication of agricultural data because the number of farms is very small. In these cases, we estimated the number of animals in each category by multiplying the county's 1997 total by the percent change in animal numbers that occurred at the state level (where the total consists of the sum for all counties), and added this to the 1997 total. Animal numbers were multiplied by waste output and N content of waste. We followed the protocol used in the SPARROW model to calculate animal waste inputs as N, checking for consistency of values from Smil (2001).


Precipitation and runoff are major determinants of the amount of N conveyed to surface waters. We multiplied all N inputs to the model with a runoff term derived from a USGS dataset (Dave Wolock, pers. comm.) in which runoff data are available by watershed and month. We downloaded data for the months of February through June for 1990-2002, and generated a single average spring runoff value for each site's drainage by summing the average runoff value over those months in the watersheds that comprised each site's total drainage, then dividing that sum by the total number of acres in the drainage.

Delivery efficiency

Denitrification is a major influence on the amount of N that actually reaches the Gulf. The SPARROW model demonstrated that the "delivery efficiency" of large rivers far exceeds that of small streams, where a major portion of N inputs may be denitrified, and that inclusion of this term significantly improves model predictions (Alexander et al. 2000a). The set of downloadable delivery efficiency terms does not include terms for watersheds in the Arkansas/Red River basin, thus we estimated these values based on their basin attributes and values for nearby watersheds. The Red River drains into the Atchafalaya, but nitrogen flux from this source is small, compared to the nitrogen in the Atchafalaya that is derived from the Mississippi's diversion at the Old River Control Structure (Goolsby et al. 2001).

Agricultural subsidies

Farm subsidy data were provided from the Environmental Working Group subsidy database (EWG 2004), which is based on data acquired from USDA. Data were compiled at the zip code level, allowing a high degree of resolution in summing subsidy totals within watersheds. Data were compiled as agricultural support payments and conservation payments. Conservation payments primarily included money allocated under the Conservation Reserve Program (CRP), Wetlands Reserve Program (WRP), and the Environmental Quality Incentive Program (EQIP). We estimated subsidy allocation at the watershed level by mapping the zip codes associated with subsidy payments into watersheds and summing by watershed. For cases where subsidy checks were sent to zip codes other than that where the crops were actually grown, we allocated subsidies to counties, and then distributed the subsidy amount in the watershed according to the proportion of the county contained therein.

Assumptions behind the model

There were several assumptions behind the way we structured the model. All nitrogen inputs to the landscape were included in the model on a per acre basis, as if inputs were spread evenly over the landscape, even if inputs occur at discrete points. Fertilizer inputs were included as if a whole year's worth of applications had been applied, with the model finding the coefficient that best describes what portion is then found as nitrate-N in rivers and streams. Animal waste inputs were modeled similarly, with the understanding that some portion of manure is spread like fertilizer, while some other portion accumulates in waste piles and lagoons. We assumed that the majority of atmospheric ammonium deposition has been volatilized from agricultural sources such as fertilized fields and animal waste, and is largely redeposited locally (Ferm 1998). Therefore, we did not include atmospheric ammonium deposition in the model, using only atmospheric nitrate deposition, which is assumed to result mostly from fossil fuel combustion (NADP 2000). Atmospheric nitrate deposition was modeled as the mean annual deposition rate for each watershed. To estimate the contribution from municipal point sources, we regressed total nitrogen outflow from 32,000 facilities against county-level population (data available on the SPARROW website; Gianessi and Peskin 1984), then applied that per-capita estimate to our model, assuming that nitrate comprises about 75 percent of total nitrogen (Mueller and Helsel 1996).

We did not include mineralization of native soil nitrogen as a term in the model, although some other models have done so (Burkart and James 1999, Goolsby et al. 1999). Recent documentation of nitrogen fluxes from forested watersheds of the US indicates nitrogen losses are extremely low where soils remain undisturbed (Lewis 2002), and in our own dataset, nitrate flux was generally found to be low where fertilized agriculture was not a factor. Mineralization of native soil nitrogen in agricultural soils that have been worked for a number of years is likely to be low, since the greatest conversion of organic to inorganic forms usually occurs in the years immediately following disturbance, then tapers off as soil reserves are depleted (Mann 1986, Knops and Tilman 2000, Schils et al. 2002). Additionally, soil mineralization in agricultural soils is likely to occur in areas where fertilization has occurred, making the two inputs indistinguishable (Goolsby et al. 1999). Decomposition of crop residues likely contributes significantly to soil inorganic nitrogen pools, but nitrogen inputs from this source represent fertilizer inputs from past years, which the model does not include.

Structure of the model

Modeled estimates of spring nitrate flux are variable year to year, due mostly to differences in the timing and location of precipitation and runoff. Nevertheless, there is a certain core area of intensively cropped land that consistently contributes to aquatic nitrate loading. For the final version of the model to be used in mapping, we averaged inputs and modeled estimates of nitrate flux for 1995-2002, years for which we had both model output data, and data on agricultural support payments. We ranked watersheds by their average nitrate flux (lb N acre-1 day-1 for the March-June period) over these years in descending order, and summed the flux for each watershed as a whole. Summing the farmed acres in the watersheds with the highest flux allowed us to identify the areas of the MRB that are the largest sources of nitrate to the Gulf.

The model's form was as follows, and had an R2 = 0.84:

Model flux_ac = average_runoff * (fert*(lbfert_ac)2.13 + anim*(animN_ac)) + dep*ndep_ac + pop*(pop_ac)

fert = 9.5379 x 10-6
anim = 2.089 x 10-4
dep = 3.935 x 10-4
pop = 1.44 x 10-2

Units were as follows (all inputs were modeled as if they were spread evenly over the watershed):

  • flux_ac: pounds nitrate-nitrogen leaving the watershed, per acre, per day
  • average_runoff: average daily runoff per acre for the watershed, in millimeters
  • lbfert_ac: pounds fertilizer nitrogen applied in the watershed, per acre, per year
  • animN_ac: pounds nitrogen produced in the watershed as animal waste, per acre, per year
  • ndep_ac: pounds nitrate-nitrogen deposited per acre in the watershed, per year
  • pop_ac: number of persons in the watershed, per acre

The response of nitrate flux to fertilizer inputs on a watershed basis was nonlinear, with a threshold around 30 lb N/acre at which aquatic nitrate flux abruptly becomes higher. Expressing fertilizer use as the proportion of the watershed under fertilized agriculture, the threshold occurs between 30-40 percent. The relationship between fertilizer inputs and nitrate flux is best described with a strongly nonlinear term in the model, and explains why certain watersheds so disproportionately contribute to total nitrate flux. However, it should be noted that the watersheds with the highest values for fertilizer inputs and agricultural intensity also tend to be watersheds where a significant portion of agricultural fields are tile-drained (USDA 1987, cited in David et al. 1997). Tile drainage quickly removes water from surface soils, which reduces opportunities for nitrate to be assimilated by soil microorganisms, or lost to denitrification. The extent to which tile drainage contributes to the apparent threshold effect of fertilizer inputs on nitrate flux is unknown. If nitrate flux were a simple linear function of fertilizer inputs, the fertilizer term's exponent would be one or greater. In any case, however, the magnitude of the exponent does not affect the relative ranking of watersheds in terms of their contribution of fertilizer runoff to the Gulf.