Effect of stream channel size on the delivery of nitrogen 

to the Gulf of Mexico 

Richard B. Alexander, Richard A. Smith, & Gregory E. Schwarz 

U.S. Geological Survey, 413 National Center, Reston, Virginia 20192, USA 

Published in Nature, Vol. 403, 17 February 2000, pp. 758-761 

An increase in the flux of nitrogen from the Mississippi River during the latter half of the twentieth 

century has caused eutrophication and chronic seasonal hypoxia in the shallow waters of the 

Louisiana shelf in the northern Gulf of Mexico1-5. This has led to reductions in species diversity, 

mortality of benthic communities, and stress in fishery resources4

. There is evidence for a 

predominantly anthropogenic origin of the increased nitrogen flux2,5-7, but the location of the most 

significant sources in the Mississippi basin responsible for the delivery of nitrogen to the Gulf of 

Mexico have not been clearly identified, because the parameters influencing nitrogen-loss rates in 

rivers are not well known. Here, we present an analysis of data from 374 US monitoring stations, 

including 123 along the six largest tributaries to the Mississippi, that shows a rapid decline in the 

average first-order rate of nitrogen loss with channel size—from 0.45 day-1 in small streams to 0.005 

day-1 in the Mississippi River. Using stream depth as an explanatory variable, our estimates of 

nitrogen-loss rates agreed with values from earlier studies. We conclude that the proximity of 

sources to large streams and rivers is an important determinant of nitrogen delivery to the estuary in 

the Mississippi basin, and possibly also in other large river basins. 

 The problem of tracing nitrogen through large watersheds stems from the difficulty of establishing a 

spatially continuous mass balance between three rate variables: the in-stream flux of nitrogen, the rate of 

nitrogen supply from atmospheric and terrestrial sources, and the rate of removal due to denitrification and 

storage on the landscape and in stream channels. Much of the controlled study of supply and removal 

processes has taken place in relatively small watersheds6

 where landscape and channel conditions are less 

variable. Few measurements of nitrogen loss rates are available for the relatively heterogeneous basins 

typical of large river channels. Moreover, the reported range of nitrogen loss rates for stream and river 

channels exceeds two orders of magnitude, and few explanations for this large variability have emerged. 

Although various physical and chemical properties of rivers6,8-13 are known to influence nitrogen loss rates, 

including oxygen concentrations, the organic content of benthic sediments, channel depth, water travel time 

(that is, water residence time), and streamflow, little has been reported about how loss rates vary over a 

range of river sizes. In the absence of systematic knowledge of nitrogen loss rates in channels, no accepted 

method has emerged for predicting nitrogen transport over long channel distances. Thus, recent efforts7,14 

to identify the location and types of sources in the Mississippi River basin responsible for nitrogen entering 

coastal waters have met with only limited success. 

 We used a recently developed mass-balance method12 (SPARROW—SPAtially-Referenced Regression 

On Watershed attributes) to estimate nitrogen flux through the interior watersheds of the Mississippi basin, 

refining the technique to more precisely quantify nitrogen transport in large channels such as those in the 

Mississippi River and its major tributaries. The regression model and the compilation of the spatial 

watershed data on nitrogen source inputs, physical characteristics of the landscape, and attributes of the 

digital stream network have been previously described12 (see Supplementary Information). The method 

correlates observations of stream nitrogen flux (that is, the response variable) with spatially referenced 

explanatory data on nitrogen source inputs (for example, fertilizer use, atmospheric deposition) and factors 

controlling nitrogen transport in watersheds, including physical characteristics of the landscape (for 

example, soil permeability) and aquatic systems (for example, channel size, water velocity). The structural 
 2

form of the model, which contains separate landscape and stream parameters, provides empirical estimates 

of the rates of terrestrial and in-stream removal of nitrogen (see table 1). The response variable in the 

spatial regression model is mean stream nitrogen flux computed from water-column measurements of total 

nitrogen (TN; sum of nitrate-nitrite and kjeldahl nitrogen—ammonia plus organic nitrogen) in filtered 

samples and daily flow measurements15 at 374 river locations in the United States. These monitoring 

locations include a subset of 123 stations in the watersheds of six major tributaries to the Mississippi River 

(Fig.1). The mean flux estimates at all stations are adjusted to reflect 1987 nitrogen inputs and long-term 

mean flow conditions, based on the records of concentration and flow for the period 1978 to 1992. Source 

inputs for 1987 are representative of average inputs over at least the past two decades (see Supplementary 

Information). 

 The regression results show that the mean first-order rate of total nitrogen loss (fraction of nitrogen 

removed per unit water travel time) is inversely related to channel size, and spans nearly two orders of 

magnitude (Table 1) over the range of rivers studied. To reliably estimate the functional form over the 

wide range of river sizes, channel size is defined according to four discrete streamflow classes. Benthic 

denitrification, a biologically-mediated process, is expected to be the prominent loss process quantified by 

the empirical in-stream loss rates, but the long-term physical storage and release of particulate nitrogen on 

flood plains and in reservoirs16,17 may also be reflected by the rate coefficients. The inverse relation 

between in-stream nitrogen loss and channel size is probably explained by the influence of channel depth 

(that is, water stage) on particulate nitrogen settling times and the supply of nitrate for denitrification10,18. 

The supply of nitrate to benthic sediments is controlled by the direct diffusion of nitrate nitrogen in the 

water column6,8,10,18, the nitrification of ammonia supplied by mineralized organic nitrogen8,19, and the 

exchange of nitrogen-enriched stream water in the hyporheic zone20-22. Channel depth is a measure of the 

volume of stream water available for processing by a unit area of benthic sediment. Thus, nitrogen removal 

via denitrification and settling generally decreases in deeper channels where less contact and exchange of 

stream waters occurs with the benthic sediment. A previous study6

 described the percentage aquatic nitrate 

loss as a declining function of the ratio of depth to water travel time, but did not express nitrogen loss as a 

rate, and thus did not separate the effect of depth from travel time. 

 We plotted the empirically derived SPARROW loss rates vs. mean stream depth in Fig. 2 based on an 

empirical transformation of stream flow. We compared these estimates of in-stream loss with the available 

literature estimates6,8,11,13,23-28 for the larger temperate watersheds for which estimates of water travel time 

could be obtained. The travel time of water in streams governs the time of exposure of stream nitrogen to 

removal processes, including the settling of organic particulate nitrogen, exchange of ground and surface 

waters (i.e., hyporheic flow)20-22, and nitrate diffusion to the benthic sediment8,18,19. Few empirical studies 

of in-stream nitrogen removal are available, and even fewer studies report estimates for total nitrogen and 

large rivers as analysed in this study. The available literature estimates of percentage nitrogen removal 

were re-expressed as a loss rate per unit water travel time and plotted as a function of depth. The 

transformed rates agree reasonably well with the magnitude and declining monotonic pattern of the 

SPARROW rates of in-stream loss over a wide range of channel depths (Fig. 2). Similar agreement was 

also found for in-stream loss rates plotted as a function of stream flow. These findings provide limited 

confirmation of the validity of the SPARROW rates of nitrogen loss. Moreover, the findings demonstrate 

the consistency of the literature loss estimates over a considerable range of river sizes when nitrogen loss is 

expressed as a rate (per unit water travel time) and plotted as a function of depth. In Fig. 2, the greatest 

agreement in loss rates appears in the larger rivers deeper than one metre, where the literature rates show 

the least variability and are within a factor of two of the SPARROW rates. For depths above four metres, 

relatively close agreement is found in the rates of nitrogen loss in the freshwater tidal reaches of the 

Potomac and Delaware8

 (0.003 and 0.006 per day, respectively) and the SPARROW rate of 0.005 per day. 

In rivers with mean depths less than one metre, greater variability generally exists among the literature and 

SPARROW rates. This may be explained by the greater influence of benthic processes (and variations in 

benthic conditions, such as the organic content and degree of oxidation of sediments) on nitrogen loss in 

shallow streams. 

 Figure 2 indicates that the first-order rate of nitrogen removal in streams (that is, k in Table 1) declines 

rapidly with increasing channel size as in-stream loss processes become progressively less effective with 

increases in channel depth. At the basin scale, depth and water velocity increase (as water travel time per 
 3

unit channel length decreases) in a downstream direction29. Each of these changes in stream attributes 

contributes to a decrease in stream nitrogen loss per unit channel length. In the Mississippi basin, the 

decrease in nitrogen loss per unit length due to increases in depth is approximately three times greater than 

the decrease in loss per unit length due to increases in velocity (see Supplementary Information). To assess 

the total effect of changes in the first-order loss rate and water velocity on nitrogen delivery to the Gulf of 

Mexico from interior river locations in the Mississippi basin, we applied the rate coefficients in Table 1 to 

river network data on channel size and water travel time. We quantified the percentage of the nitrogen 

export from each of the outlets of 742 interior watersheds in the Mississippi basin that is delivered by 

streams to the Gulf (Fig. 3; see Supplementary Information for the absolute quantities of nitrogen delivered 

by source). On the basis of this analysis, we find that the region of high nitrogen delivery to the Gulf is 

dendritic in shape and extends far upstream along the major tributaries in the eastern and central portions of 

the basin (for example, Ohio, Tennessee, Lower Missouri, Lower Arkansas and Upper Mississippi rivers). 

Despite the long water travel times, many watersheds located on large rivers more than 2,500 kilometres 

from the Gulf deliver significantly larger fractions of their exported nitrogen (some more than 90%) to 

coastal waters than watersheds located on smaller streams less than a few hundred kilometres from the 

Gulf. In addition, the dendritic pattern of nitrogen transport leads to widely varying delivery percentages in 

each of the major regional drainages of the Mississippi basin, ranging from more than 90% from 

watersheds on the largest rivers to substantially less than 40% from watersheds on small streams (see Table 

3 in Supplementary Information). This wide variation is evident despite similarities of the distances of 

interior watersheds from the Gulf of Mexico within each regional drainage. Nitrogen deliveries from many 

arid watersheds in the more distant drainages of the western Mississippi basin (that is, the western portions 

of the Missouri and Arkansas/Red regions) are uniformly small because of the effect of the typically 

shallow rivers with high nitrogen-loss rates and the lengthy water travel times to the Gulf. 

 We conclude that, because the nitrogen loss rate in streams declines rapidly with increasing channel size, 

knowledge of the length of time that surface waters are transported through channels of varying size can 

help to predict the quantities of nitrogen delivered from interior locations to coastal waters. Despite 

uncertainty in the rate of nitrogen loss in stream channels of a given size, the evidence of a large, 

systematic decline in the rate of nitrogen removal from small streams to large rivers has important 

implications for nutrient management in the Mississippi river basin, and more generally, in large coastal 

watersheds. The delivery of nitrogen to coastal systems from point and diffuse sources is not a simple 

function of the distance of these sources from coastal waters. Instead, the proximity of sources to large 

streams and rivers, as measured by the length of time that surface waters travel through smaller tributaries, 

is a major determinant of their downstream transport to marine systems. Information on the rates of 

nitrogen delivery to coastal waters may assist in evaluations of efficient nutrient control strategies, 

including efforts to identify the most significant watersheds and sources contributing to riverine exports of 

nitrogen to coastal ecosystems. 

Received 27 July; accepted 22 December 1999. 

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11. Behrendt, H., Inventories of point and diffuse sources and estimated nutrient loads—a comparison for different river basins in 

central Europe, Wat. Sci. Tech. 33, 99-107 (1996). 

12. Smith, R.A., G.E. Schwarz & R.B. Alexander, Regional interpretation of water-quality monitoring data, Wat. Resour. Res. 33, 

2781-2798 (1997). 

13. Preston, S.D. & J.W. Brakebill, Application of Spatially Referenced Regression Modeling for the Evaluation of Total Nitrogen 

Loading in the Chesapeake Bay Watershed (U.S. Geological Survey Water Resources Investigations Report 99-4054, Baltimore, 

Maryland, 1999). 

14. Brezonik, P.L. et al., Effects of reducing nutrient loads to surface waters within the Mississippi River Basin and the Gulf of 

Mexico (Report of Task Group 4 to the White House Committee on Environment and Natural Resources, Hypoxia Work Group) 

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15. Alexander, R.B., Slack, J.R., Ludtke, A.S., Fitzgerald, K.K. & T.L. Schertz, Data from selected U.S. Geological Survey national 

stream water quality monitoring networks, Wat. Resour. Res. 34, 2401-2405 (1998). 

16. Johnston, C.A., G.D. Bubenzer, G.B. Lee, F.W. Madison & J.R. McHenry, Nutrient trapping by sediment deposition in a 

seasonally flooded lakeside wetland, J.Environ. Qual. 13, 283-290 (1984). 

17. Billen, G., S. Dessery, C. Lancelot & M. Meybeck, Seasonal and inter-annual variations of nitrogen diagenesis in the sediments 

of a recently impounded basin, Biogeochemistry. 8, 73-100 (1989). 

18. Baker, L.A. & P.L. Brezonik, Dynamic model of internal alkalinity generation: calibration and application to precipitationdominated lakes, Wat. Resour. Res. 24, 65-74 (1988). 

19. Novotny, V., and H. Olem, Water Quality: Prevention, Identification, and Management of Diffuse Pollution (Van Nostrand 

Reinhold, New York, 1994). 

20. McMahon, P.B., & J.K. Bohlke, Denitrification and mixing in a stream-aquifer system: effects on nitrate loading to surface

water, J. Hydrol., 186, 105-128 (1996). 

21. Triska, F.J., Duff, J.H., & R.J. Avanzino, Patterns of hydrological exchange and nutrient transformation in the hyporheic zone of 

a gravel-bottom stream: examining terrestrial-aquatic linkages, Freshwat. Biol., 29, 259-274 (1993). 

22. Harvey, J.W., Wagner, B.J., & K.E. Bencala, Evaluating the reliability of the stream tracer approach to characterize streamsubsurface water exchange, Water Resour. Res., 32, 2441-2451 (1996). 

23. Hill, A., Denitrification in the nitrogen budget of a river ecosystem, Nature 281, 291-292 (1979). 

24. Hill, A., Nitrate-nitrogen flux and utilization in a stream ecosystem during low summer flows, Can. Geogr. XXV, 225-239 

(1981) 

25. Sjodin, A.L., Lewis, W.M., Jr. & J.F. Saunders, III, Denitrification as a component of the nitrogen budget for a large plains river, 

Biogeochemistry 39, 327-342 (1997). 

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27. Billen, G., Lancelog, C. & M. Meybeck, N, P, and Si Retention Along Aquatic Continuum from Land to Ocean, In Ocean 

Margin Processes in Global Change, (eds. Mantoura, R.F.C., Martin, J.M. & Wollast R.) 19-44 (Wiley, 1991). 

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(Texas Natural Resource Conservation Commission, IS 87-04, Austin, Texas, 1987). 

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Geological Survey Professional Paper 252, Reston, Virginia, 1953). 

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Virginia, 1987). 

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from the London editorial office of Nature. 

Acknowledgements 

We thank J. Bohlke, D. Goolsby, R. Hirsch, S. Seitzinger, and N. Rabalais for comments on the manuscript. Also S. 

Seitzinger and R. Stiles assisted in obtaining published data from watershed studies of nitrogen loss. M. Ierardi 

assisted in preparing the figures. 

Correspondence and requests for materials should be addressed to R.B.A. (e-mail: ralex@usgs.gov). 
 5

Table 1 SPARROW spatial regression model coefficients for total nitrogen 

Model Parameters Coefficient 

Units 

Bootstrap 

Coefficient 

Lower 90% 

CI 

Upper 90% 

CI 

Nitrogen source, β 

 Point sources dimensionless 0.394 0.094 0.639 

 Fertilizer application dimensionless 1.37 0.605 2.34 

 Livestock waste production dimensionless 0.903 0.012 1.97 

 Atmospheric deposition dimensionless 4.78 1.84 8.21 

 Nonagricultural land kg ha-1 yr-1 18.6 6.18 29.3 

Land-to-water loss coefficient, α 

 Temperature oF-1 0.017 0.009 0.023 

 Soil permeability hr. cm-1 0.036 0.024 0.049 

 Drainage area per stream length km-1 0.043 0.017 0.063 

In-stream loss rate coefficient, k 

 k1 (Q < 28.3 m3 s-1) day-1 0.455 0.344 0.579 

 k2 (28.3 m3 s-1 < Q < 283 m3 s-1) day-1 0.118 0.063 0.176 

 k3 (283 m3 s-1 < Q < 850 m3 s-1) day-1 0.051 0.007 0.092 

 k4 (Q > 850 m3 s-1) day-1 0.005 0.000 0.019 

Coefficients are estimated in a spatial non-linear least-squares regression of stream nitrogen flux at 374 monitoring locations on 

watershed characteristics, based on a robust bootstrap estimation procedure12 (r-squared=0.881; MSE=0.435; see Supplementary 

Information for explanation of the SPARROW model and coefficients). The nonpoint-source coefficients (β) multiplied by an 

exponential land-to-water delivery function (i.e., e-αz , where z is a vector of land-to-water loss factors; for example, temperature) 

quantify the proportion of available nitrogen mass delivered to rivers as a function of the specified source inputs and landscape 

characteristics. The land-to-water delivery function is equal to one for point-source inputs. The rate coefficients (k) quantify the firstorder rate of in-stream nitrogen loss per unit of water travel time (for example, k4=0.5% removal of nitrogen per day of water travel 

time). The regression residuals provide acceptable adherence to model assumptions. In-stream loss rates are fit separately for 

stream reaches with mean stream flow (Q) corresponding to the indicated intervals. Nitrogen loss rates (for example, k4) were 

estimated according to a continuous function of streamflow in preliminary analyses; however, a discrete functional form defined by 

separate stream flow classes provides the most accurate fit to the observational data for the extreme river sizes; the uppermost 

class has great significance to large rivers in the Mississippi basin. Model predictions of flux are typically within 32% of the 

observed values based on the median of station values (interquartile range from 15 – 61%). A validation of the model predictions 

through comparisons with an independent data set of 68 monitoring stations in the Chesapeake Bay watershed in the eastern 

United States provided reasonable confirmation that the predictions are relatively unbiased (model predictions are typically within 

39% of the observed values with an interquartile range from 19 – 82%), and that the residuals accurately describe the unexplained 

variability in the model from which confidence intervals (CI) are developed.
Nitrogen delivered (%)

0 to 20

20 to 30

30 to 50

50 to 80

80 to 90

> 90

Figure 3 Percentage of the nitrogen export from interior watersheds delivered to the Gulf.

Approximately equally sized interior watersheds, ranging from about 2,400 to 4,900 km2

(mean is 3,900 km2), are systematically defined according to the hydrologic cataloging unit

classification30. The delivery percentage is the fraction of the nitrogen exported from

inland watersheds that remains after in-stream transport to the Gulf, and is computed as

[exp(-k't)100], where k' is a vector of SPARROW estimates of in-stream nitrogen loss for

four stream sizes (Table 1), and t is a vector of mean water travel times from each

watershed outlet to the Gulf for each of the four stream sizes. The water travel times from

locations above the diversion from the Lower Mississippi river to the Atchafalaya river are

computed as the flow-weighted mean of the travel time (2.4 days) for each pathway to the

Gulf. See the Supplementary Information for regional estimates of the delivery percentages and the absolute quantities of nitrogen delivered by source.

6

 Watershed

Ohio / Tennessee

Upper Mississippi

Central Mississippi

Missouri

White / Arkansas

Lower Mississippi

Monitoring stations

Major rivers

Figure 1 River monitoring stations and major regional watersheds in the Mississippi

river basin.
Figure 2 Nitrogen-loss rate in relation to stream channel depth. Stream flow is empirically

transformed by regressing observations of mean depth on mean stream flow, on the basis

of data from a study of stream morphology and hydraulics at 112 river locations in the

United States29 (stream depth and flow are monotonically related according to D =

0.2612S0.3966, where D is mean stream depth in metres and S is mean stream flow in

m3s-1; R2=0.83). Literature estimates of in-stream nitrogen loss, L (expressed as a fraction

of external inputs), are re-expressed as a loss rate (per unit water travel time), R, according

to R = -t

-1 ln(1 - L), where t is the water time of travel and ln is the natural logarithm. Loss rates

are reported for the following nitrogen forms: total nitrogen (TN), nitrate-nitrogen (NO3),

and dissolved inorganic nitrogen (DIN). SPARROW refers to the mean nitrogen-loss rates

estimated in this analysis. CB SPARROW refers to mean estimates separately derived for

streams of the Chesapeake Bay watershed over depths of 0.5 to 4 m (ref. 13). Water travel

times were estimated for the Rhine, Elbe and Warnow11 rivers from river network data12 for

watersheds in the northeastern quadrant of the United States, based on a regression of the

mean water travel time, T, from headwater reaches to the outlet reach of each watershed in

units of days on total drainage area, A, in units of square kilometres (R2=0.88, T=-0.0065 +

0.2642A0.3). The mean time of travel for watershed streams is computed as one half of T.

These estimates assume similar hydraulic properties and drainage density for the European

and US watersheds. Channel depths for data from the Rhine river

27 and the European

watersheds11 were determined from the empirical transformation of stream flow given above.

The graphed range of loss rates for nitrate, based on a synthesis of denitrification measurements from selected watersheds in North America6, is computed as the ratio of mass transfer

coefficients (representing the height of the water column from which nitrate is removed per

unit time) to mean depth.

0.4 1 10

Mean stream depth (m)

In-stream loss rate (per day)

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

SPARROW Mean, U.S. Rivers (TN)

SPARROW 90% Confidence Interval

CB SPARROW (TN)

Howarth Synthesis (NO3) 

Delaware R. (DIN)

Potomac R. (TN)

Rhine R., Elbe R., Warnow R. (DIN)

Rhine R.

S. Platte R. (NO3)

Neversink R. (NO3)

Duffin Ck. (TN)

San Antonio R. (TN)

13

11

6

8

27

25

26

23, 24

8

28

7