Everything you need to know about SPARROW

Visit the national USGS SPARROW website for an overview of SPARROW modeling.

SPARROW Modeling Techniques

USGS scientists developed SPARROW (Smith and others, 1997) to:

• Utilize monitoring data and watershed information to better explain the factors that affect water quality
• Examine the statistical significance of contaminant sources, environmental factors, and transport processes in explaining predicted contaminant loads
• Provide a statistical basis for estimating stream loads in unmonitored locations

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The model estimates contaminant concentrations, fluxes (or “mass,” which is the product of concentration and streamflow), and yields in streams (mass of nutrients entering a stream per acre of land), and evaluates the contributions of selected contaminant sources and watershed properties that control transport throughout large river networks. It empirically estimates the origin and fate of contaminants in streams and receiving bodies, and quantifies uncertainties in these estimates based on coefficient error and unexplained variability in the observed data.

The SPARROW model builds on actual stream monitoring by using spatially comprehensive geospatial data in a calibrated SPARROW model to predict water-quality conditions at unmonitored stream locations (see illustration below). The geospatial data sets describe fertilizer and manure applications, atmospheric deposition to the land surface and urban sources. The model predictions are illustrated through detailed maps that provide information about contaminant loadings and source contributions at multiple scales for specific stream reaches, basins, or other geographic areas.

SPARROW methods and selected results for watersheds across the U.S. are presented by Smith and others, 1997. The theory, model documentation, and illustrated user application of SPARROW can be found in the online USGS methods report, The SPARROW Surface Water-Quality Model: Theory, Application and User Documentation by G.E. Schwarz, A.B. Hoos, R.B. Alexander, and R.A. Smith. 

How are stream load measurements used in SPARROW?

Stream loading information is used for calibration of SPARROW models and is thus one of the most important types of data for them. To maximize the accuracy and precision of the SPARROW model calibration, it is important to have a set of load measurements that are representative of the area being considered and that are available in sufficient quantity to capture the variability that occurs in that area. For these reasons, significant effort is expended on finding loading data from throughout the modeled watersheds (and even nearby watersheds). This effort often requires the integration of data from a variety of sources including federal, state and local water-quality management agencies.

To develop stream loading information, water-quality data are compiled from as many sites as possible in the area of interest. Water-discharge information from stream gages is also compiled and gage locations are matched to water-quality monitoring sites so that discharge data can be associated with the water-quality concentration data. Statistical procedures are used to estimate annual stream loads based on discharge-concentration relations and temporal variations such as trends (Schwarzand others, 2006). In most cases, a long-term discharge record is used and the load estimates are “de-trended” to estimate the stream load that would occur under current water-quality conditions, conditioned on long-term average discharge conditions. This de-trending procedure removes spatial variation that would be due to weather patterns and helps to focus the model purely on the spatial patterns of the environmental factors that affect water quality.

What types of data are used for prediction in SPARROW models?

SPARROW modeling requires the integration of many types of geospatial data for use as explanatory variables which are considered as either constituent sources or delivery factors. Sources might include certain land types such as urban area, or known contaminant sources such as sewage treatment plants. Delivery terms can include any basin characteristic that may be associated with natural attenuation. For example, denitrification is often associated with certain soil characteristics and the spatial pattern of those soil characteristics is often related to that of constituent loads. In some cases delivery terms might also be associated with enhanced delivery. For example, high basin slope might cause more rapid flows which could increase the delivery of constituents. Delivery is also influenced by the water time of travel in streams, which can be estimated from published USGS time-of-travel studies (e.g., Reed and Stuckey, 2001). Examples of some geospatial data sets used to develop explanatory variables in past SPARROW models are listed below.

Contaminant Source Data Sets for:

• Agriculture




• NASS




• Permit Compliance System (PCS)




• Sewered Population




• Atmospheric Deposition




• NRI




• CENSUS




• Land area

Contaminant Delivery Data Sets:

• SSURGO




• STATSGO




• National Soil Survey




• PRISM




• NCDC

What water-quality constituent sources are considered in SPARROW models?

Many environmental factors have been identified as sources in SPARROW models. Among those are point sources as defined by data sets describing actual locations of dischargers such as sewage treatment plant or data sets describing population or urban area as surrogates for point sources. Agricultural sources have also been identified in a variety of forms including:

1. Agricultural land as defined using land use / land cover data
2. Estimates of fertilizer application
3. Estimates of manure generation
4. Estimates of nutrients applied to specific crops.

Other sources identified using SPARROW models include atmospheric deposition, urban land and natural sources, such as from mining areas. In all cases, these data sets are continually improved and those improvements are incorporated in SPARROW models as they occur.

Any of these constituent sources or others can be potentially included in a SPARROW model, provided the geospatial data are available to describe it and spatial patterns in the source can be successfully correlated with those in the measurements of stream loading of that constituent.

Because SPARROW is based on mass balance, sources must be available for all parts of the region to determine their overall importance. Thus, some data sets that provide detailed information for only a fraction of the model area would not be useful in a SPARROW model because the same information would not be available everywhere. For example, detailed estimates of agricultural inputs of nitrogen collected by one state may not be useful for a model covering the entire country because the data would be missing in the other states.

The successful correlation of a source with stream loading measurements (and its inclusion in a SPARROW model as a statistically significant source) is dependent upon whether

The source is sufficiently large to make an important contribution to the overall mass balance in the stream network, and (b) the spatial variability in that source as described by the geospatial datasets is sufficiently large. Both of these conditions are required for SPARROW to identify a source as statistically significant—i.e., find that the spatial patterns in a source are correlated with those in stream water quality.

How are watershed characteristics used in SPARROW models?

In the same way that SPARROW identifies the relative importance of contaminant sources to streams, it also estimates the importance of landscape factors in the delivery of those contaminants to streams. SPARROW imposes mass balance constraints on all estimates of contaminant loading. Thus all sources must be balanced by environmental attenuation processes (losses) in order to estimate the measurements of stream loading with minimal error. For example, nutrients originating from agricultural land may be lost through denitrification as they are transported from the land surface through shallow ground water to streams. Soil permeability may enhance denitrification and so the spatial distribution of the value of soil permeability may be related to contaminant loading downstream.

Any landscape characteristic could be evaluated as a potential loss factor for delivery of contaminants to streams. Landscape characteristics can only be statistically identified as important if they vary sufficiently across the modeled area and can be distinguished in their magnitude from the spatial variability in other landscape characteristics that are equally important. For example, soil permeability and soil organic matter would not both be identified as statistically important if they were related to the same underlying attenuation process (e.g. - denitrification) and occurred in the same spatial pattern.

Many landscape characteristics have been identified as important attenuation factors in SPARROW models. Examples include soils characteristics such as soil permeability, climatic factors such as long-term average temperature and precipitation, physiographic characteristics such as slope and topography, and drainage patterns such as stream density and artificial drainage. New data sets continue to be developed and thus create opportunities for evaluating new potential loss factors in SPARROW models.

What is the spatial framework underlying SPARROW models?

SPARROW is designed to describe the spatial patterns in water quality and the factors that affect it. This is accomplished by linking water-quality monitoring sites to a digital stream network that describes the spatial linkages between sites (upstream or downstream). Digital stream networks provide information on streams throughout a region and usually break streams into segments (reaches) that vary in size depending upon the scale of the data set. Drainage boundaries are established for each stream reach and these boundaries are used to identify the contributing drainage areas to stream reaches. Geographic data bases describing watershed characteristics such as land use are linked with the drainage areas to quantify the amount of each factor contributing to conditions in each stream reach. Thus the digital stream reach and associated drainage areas provide a spatial framework that allows the integration of data collected at water-quality monitoring sites with data describing upstream watershed characteristics.

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Stream Reach Networks: Two digital stream networks have been used predominantly in SPARROW models to date (see graphic below). The first is referred to as the U.S. Environmental Protection Agency Enhanced Reach File 1 or ERF1 (Alexander and others, 1999). This data set extends over the continental United States and includes approximately 62,000 stream reaches at the scale of 1:500K. The second digital stream network used in SPARROW models is known as the National Hydrography Dataset (NHD) (U.S. Geological Survey, 1999). However, a newer enhanced version known as NHDPlus is now available that includes many stream reach attributes that were not available with the original NHD data set. Like ERF1, NHD (and NHDPlus) extends over the continental United States. However, NHD was designed to include much more spatial detail and includes 2.6 million stream reaches at the scale of 1:100K.

How are landscape characteristics and monitoring data linked to the spatial framework in SPARROW models?

SPARROW provides a predictive tool that integrates many types of data. Calibration data are derived from water-quality monitoring information at sites located throughout a study area. Those data are associated with reaches in a digital stream network to define spatial relations among the monitoring sites and among their drainage areas. Detailed geospatial data bases are then linked with the stream network drainage areas to define the basin characteristics in all of the areas that drain to monitoring locations and to all individual stream reaches. Once the linkages are developed, all of these types of data are combined in one data base that is used for model development.

The figure below provides a small example and illustration of the spatial framework that forms the basis of SPARROW as described above.

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Within each contributing area, environmental factors that affect water quality are quantified using spatially-detailed geographic information. Environmental factors can include a wide range of sources such as sewage treatment plants, urban area or agricultural land. Environmental factors can also include characteristics that are related to natural attenuation (losses) of contaminants through processes such as denitrification or sequestration. Examples of such environmental factors include soil permeability or geologic characteristics. A second type of loss accounted for in SPARROW is that which occurs during transit through stream channels. Instream losses are estimated by comparing upstream load measurements to those downstream. Contaminant loads coming from upstream as well as those from intervening stream reaches are balanced against the measured downstream load to estimate the amount of instream loss. In this way, mass-balance provides the fundamental basis of SPARROW.

What is a base year and why is it used in SPARROW models? 

In general, the SPARROW model predictions of nutrient sources and loads reflect long-term mean annual nutrient conditions in streams. A statistical procedure is used to ensure that the model predictions reflect long-term hydrologic and water-quality variability during a consistent time period, which produces robust model predictions of nutrient sources and transport processes. The model predictions of the mean annual load for the calibrated model are standardized to a single year referred to as the “base year” to give an estimate of the mean nutrient load that would have occurred in streams during that year if mean annual flow conditions had prevailed.

The designated base year for a SPARROW model is usually chosen to ensure consistency with other ancillary data used in the model, including nutrient-source data, land use, climate, stream networks, etc. Land-cover data (USGS National Land Cover Data or NLCD) are only available for specific years, typically at 5 year intervals. These are complemented by agricultural statistics on animal nutrients and crop land area and production, which are only reported every 5 years. County based estimates of the nutrient content in animal manure, from the U.S. Department of Agriculture (USDA), are also reported for only specific periodic years.

How are long-term discharge and water-quality data integrated to calculate an annual stream load?

The SPARROW model uses the mean annual load (mass per unit time, expressed, for example, as kilograms per year) at each stream monitoring station to calibrate the model.  The mean annual load is computed using USGS load estimation methods; for details, see the SPARROW model documentation. 

In brief, these load estimation methods combine regularly collected nutrient measurements at the monitoring stations with daily streamflow values, typically from the previous 30-year period. This approach yields more accurate estimates of the long-term mean annual load than can be obtained by using the individual contaminant measurements alone.  The mean annual contaminant load is also standardized to a single time referred to as the “base year”, which is the designated time period for comparing contemporaneously spatial variability in water-quality loads and contaminant sources in the SPARROW model. Standardizing provides an estimate of the mean contaminant load that would have occurred in the designated base year if mean annual flow conditions had prevailed.  The use of standardized loads in the SPARROW model gives more robust estimates of contaminant sources and transport processes as compared to an approach based solely on using the water-quality records during any single year or short multi-year periods.  The standardization procedure accounts for differences in station record lengths and sample sizes and ensures that the nutrient loads are representative of long-term hydrologic and water-quality variability. This emphasis on long-term mean conditions enhances the capability of the model to estimate the major sources and watershed processes that affect the long-term supply, transport, and fate of nutrients in watersheds.

How are temporal variations in rainfall and hydrology accounted in SPARROW models?

Actual water-quality load measurements show large year-to-year variations, driven largely by year-to-year variations in weather and flow conditions. For example, USGS long-term monitoring of water quality and streamflow show that the amount of nitrogen increased since the late 1960s; and that the amount was low during the drought in the late 1980s but high during the flood of 1993, even though the amount of nitrogen applied to fields in the basin was not significantly different (see Fact Sheet 135-00).  In addition, year-to-year variations in the mean-annual nitrogen load can range over as much as two orders of magnitude at monitoring stations, although the annual variations more typically range from 20-40 percent of the long-term mean annual load.

Year-to-year variations, such as these, and within-year variations in contaminant concentration and streamflow are accounted for in a step prior to SPARROW spatial modeling.  This prior step is critical to obtain stream contaminant loads for calibrating the SPARROW model that are representative of the long-term mean hydrologic and water-quality conditions at each monitoring station. SPARROW has the objective of explaining spatial differences in contaminant loads that are related to the intrinsic factors that control the mean rates of nutrient supply and transport, rather than the factors that explain more extreme hydrologic conditions during any particular year or years at a location. The SPARROW predictions of mean nutrient load include the effects of spatial variations in mean climatic (precipitation, temperature) and streamflow conditions.  This emphasis on long-term mean conditions enhances the capability of the spatial model to estimate the major contaminant sources, including land uses and human activities, and natural processes that affect the long-term supply, transport, and fate of nutrients in watersheds.

Can the SPARROW model be used to evaluate trends in stream contaminant loads?

Past SPARROW models have been developed to describe mean annual water-quality loads for a specified base year and have not been used to describe trend or changes over time in stream loads. However, on-going research is focused on developing SPARROW models of decadal and seasonal changes in stream loads. Models of decadal changes will assume that sources, processes, and stream loads are in steady state during each modeled 10-year period. Therefore, these models provide an opportunity to assess how much of the change in stream loads results from changes in contaminant inputs from various sources (e.g., wastewater treatment discharges, fertilizer application) vs. how much arises from underlying changes in processes and human activities that may alter the rates of contaminant delivery to streams (e.g., agricultural conservation practices, soil nutrient mineralization).

SPARROW Modeling: Prediction and Uncertainty

What metrics do SPARROW models predict?

SPARROW models are developed using mass balance constraints to quantify the relation between stream constituent load (the mass of the constituent being transported by the stream) and the sources and losses of mass in watersheds. Thus the models are inherently designed to predict load (mass per time) for all stream reaches in the modeling region. However, the predictions of stream load can be modified to provide a variety of water-quality metrics that can support various types of assessments.

The SPARROW prediction metrics include constituent yields, concentrations, and source contributions to stream loads:

(a) Constituent yields:

The constituent yield (mass per unit area per time) is calculated as the stream load divided by the contributing drainage area. Measures of yield are useful for water-quality managers to determine the relative contribution of contaminants from different parts of a large drainage area. Contaminant loading typically increases with stream drainage area, making it difficult to compare loads among different sized streams. Yield gives a measure of stream load that is normalized for drainage size, and thus, provides a reliable metric for determining which drainages export the largest amount of contaminant load independent of their size.

SPARROW models provide predictions of “total”, “incremental”, and “delivered” yields, based on corresponding measures of load. These measures provide management-relevant information about the sources and fate of contaminants for a range of spatial scales. The “total” yield describes the load per unit area that is delivered to the downstream end of a reach from sources throughout the entire drainage above the reach (i.e., calculated as the total load delivered to the end of the reach, divided by the total upstream drainage area associated with the reach). By contrast, the “incremental” yield describes the load per unit area delivered to the downstream end of a reach exclusively from sources in the land area that drains directly to the reach without passing through another reach (i.e., the "incremental" drainage area). Thus, the incremental yield is independent of contaminant contributions from the drainage areas of upstream reaches, and measures relatively "local" sources of contaminants that enter a single stream reach.

Finally, the “delivered” yield is useful to describe the downstream fate of the contaminant load per unit area for a given stream reach. This metric is especially useful for quantifying the contaminant load contribution of watersheds (based on either the total or incremental drainage area) to downstream receiving waters, such as reservoirs or sensitive coastal estuaries. The delivered yield accounts for the natural attenuation of contaminants in streams and reservoirs (e.g., long-term storage; denitrification) during transport from a given stream reach to downstream receiving waters. The delivered yield is calculated by multiplying the “total” or “incremental” yield of a stream reach by the SPARROW model estimate of the "delivery fraction", which describes the proportion of the contaminant load that is not attenuated or removed by natural processes during downstream transport. There are many examples of the use of SPARROW delivered yields to identify watersheds that have the largest contributing loads to coastal waters, including for the Mississippi River Basin, Chesapeake Bay, and New England watersheds.

(b) Constituent concentrations:

Concentration is determined in SPARROW by dividing the load predictions by long-term average flow in each stream reach. Concentration measures are most useful for understanding the suitability of water for use by aquatic organisms and humans (e.g., water contact, drinking-water supplies), and depend critically upon the volume of water flowing in streams. It is important to note that SPARROW predictions of concentration are flow-weighted estimates. These estimates may differ from time-weighted estimates of water-quality concentrations, which the USEPA and the States often use to assess whether regulatory standards are met (additional information is available from USGS studies of time-weighted concentrations; e.g., Effects of nutrient enrichment in streams; Stream nutrient concentrations; Trends in nutrient enrichment of streams).

(c) Source contributions to stream loads:

Water-quality managers also have a need to determine the contributions of contaminants in streams that originate from various types of sources in watersheds. SPARROW provides estimates of the major sources of contaminants to streams, including municipal point sources and urban and agricultural diffuse sources. The model predictions of source contributions in streams may be expressed as loads, yields, or in relative terms as percentages of the stream load. In addition, the source contributions may be reported for the “total” or “incremental” drainage areas associated with stream reaches. Collectively, this highly informative set of model predictions can be used to assess the “local” and regional contributions of major contaminant sources to both inland streams and coastal waters.

How does spatial scale affect SPARROW model predictions?

SPARROW models are generally designed to be “scale independent”, meaning that the model predictions are considered to be valid across a wide range of spatial scales, corresponding approximately to the scale of the geospatial data used to calibrate the model. Typically, the models can be used to simulate water-quality conditions over scales ranging from single stream reach catchments (ranging from a few square kilometers to tens of square kilometers) up to the size of large watersheds and river basins that span thousands of square kilometers. Thus, SPARROW models are flexible and can be used to perform various types of assessments that span a range of basin sizes.

There are, however, scale-related limitations to using the model for water-quality management. These include:

1. Increased uncertainty at locations and scales that differ from those of the existing monitoring data used for model calibration
2. The possibility of differing model results for models developed at different scales

In the first case, SPARROW predictions may potentially have higher uncertainty for drainage basin sizes smaller or larger than those of the stream monitoring sites used to calibrate the model. One of the challenges for SPARROW, as well as for any watershed model, is the difficulty of obtaining a large sample of monitoring sites from small catchments, where environmental conditions and corresponding stream water quality can vary considerably. Because of the heterogeneity of conditions at small scales and limited monitoring resources, fewer stream monitoring data are available over these spatial scales. For the national SPARROW models, the monitored drainage basin sizes range from several hundred square kilometers to considerably more than 1,000 square kilometers, whereas the more current regional SPARROW models typically have many more monitoring sites located in smaller watersheds (newer national versions of the SPARROW model that are under development will make use of these more detailed monitoring data). In the SAGT (South Atlantic-Gulf Tennessee) SPARROW total nitrogen model, for example (Hoos and McMahon, 2009), the monitored drainage basins range in size from 15 to 28,000 square kilometers (interquartile range from 230 to 1,600 square kilometers). However, it’s important to recognize that in both the national and regional models, the incremental drainage areas (i.e., areas located between nested monitoring sites), which are generally smaller than the areas reflected in the size distribution of the total drainages for the monitoring sites, provide additional fine-scale information that assist with the estimation of nutrient supply and transport processes in model calibrations.

Increased uncertainties can also arise for model predictions at smaller spatial scales because some of the data sets used to calibrate SPARROW models are reported for larger areas than the drainage areas for which model predictions are computed or where monitoring occurs. For example, county-level reporting (interquartile range = 1,000 to 2,500 square kilometers) is common for many of the governmental agricultural data bases (e.g., fertilizer application, animal wastes), although the spatial accuracy of the county-level data are frequently improved through the use of land use data (e.g., 30-m or 1-km resolution) in SPARROW modeling to spatially refine the location of agricultural activities within counties.

SPARROW provides a tool for integrating available water-resource information across a range of spatial scales. The confidence intervals reported for the SPARROW model predictions (i.e., loads, yields, source shares) incorporate the observed variability in the model performance over the range of the calibration data, and thus, provide a reliable measure of the statistical uncertainties in the reported predictions. At spatial scales (typically small catchments) that differ from those reflected by the geospatial data used to calibrate the model, the uncertainty of the model predictions is potentially larger than the reported uncertainties. Because of the wide range of variability in streamwater-quality conditions at small spatial scales, there are no established guidelines or rules as to the magnitude of the uncertainties in SPARROW predictions when the model is applied outside of the calibration range. Nevertheless, the monitoring data and geospatial data used for calibration can provide an approximate guide as to the spatial limits of the model predictions. Thus, it is recommended that users of the model recognize that the reported uncertainty measures provide only approximate estimates of the reliability of the predictions in cases where the model is applied beyond the calibration range.

A second scale-related limitation of SPARROW predictions is that models calibrated for different but overlapping spatial areas may not provide identical predictions of mean conditions (e.g., load, yield, source shares) for a given watershed, even if that watershed is a subset of the larger drainage area included in one of the models. This may be explained by differences in the calibration data, which can display different ranges of variability in environmental conditions over different spatial extents. Such differences can cause the estimated model parameters and predictions to differ among SPARROW models. The effects of environmental processes and properties on stream water quality conditions may also differ in their importance over different spatial scales, especially in relation to the long-term mean annual conditions reflected in SPARROW models. For example, the long-term mean annual temperature may be important in explaining the variation in mean annual nutrient delivery across the United States or within a large region of the United States; this may correspond to differences in the response of water quality to the broad differences in temperatures in one state (e.g., North Carolina) as compared to those in another (Wyoming). However, temperature may explain little of the variation in nutrient delivery within any single state because of the small spatial variability in mean annual temperatures. In such cases, a regional SPARROW model can provide a broader, and more accurate, perspective on the factors affecting spatial variability in long-term mean annual stream water-quality conditions than a small-scale spatial model can provide. In general, results from a regional model can be applied within a specific sub-region (e.g., State) with the same limitations of uncertainty that hold throughout the larger model extent (e.g., as reflected by the confidence intervals on predictions), unless certain local environmental conditions and human activities that are known to affect water quality conditions in that sub-region are not represented in the regional model, or unless the spatial structure in the pattern of residuals (i.e., prediction errors) in that sub-region suggest that some factor(s) affecting water quality are not represented in the regional model. Thus, it is important for users of the model results to recognize these limitations and to select the results from SPARROW models that are representative of the spatial scales for their management applications.

What causes uncertainty in SPARROW models?

All models, including SPARROW, are imperfect representations of reality and therefore have uncertainty associated with them. There are many reasons for that uncertainty including:

1. Limitations in the supporting stream monitoring and geospatial data
2. Limitations in the understanding of the environmental processes affecting water quality
3. Limitations of the modeling approach in representing the environmental processes accurately

It is difficult to precisely quantify the amount of uncertainty related to the latter two items. However, uncertainty caused by limitations in the underlying data sets is understood and is being continually improved.

One important cause of uncertainty is the limitation in the number of monitoring sites available for model calibration. As in any statistical model, uncertainty in SPARROW models decreases as the number of sites available for calibration increases. In the case of SPARROW, the number of calibration sites is defined by the number of sites with sufficient water quality and discharge data for calculating a constituent load. Historically, the number of sites represented in federal, state and local agency monitoring programs has vacillated. However, recently the number of sites with sufficient monitoring data has begun to decline. Such declines should be expected to cause greater uncertainty in all environmental models, including SPARROW.

Uncertainty in SPARROW models is also determined by the quality of the geospatial data available for building explanatory variable data. Many of the data sets from which important variables are derived are only available at a relatively coarse scale, such as for counties. To develop predictor data from such data sets, the values must be distributed to the smaller scale of stream reach drainages. This results in predictor data that have spatial uncertainty, although that uncertainty is generally reflected in the model errors through the calibration process.

How is uncertainty accounted for in SPARROW models?

Uncertainty is always present in environmental models such as SPARROW. Uncertainty can be caused by many factors, but it is often related to limitations in the quantity and quality of the supporting data sets. These limitations are unavoidable because of the magnitude of the effort and the lack of resources available to support more extensive data base development. For example, water-quality measurements cannot be collected at all times at the monitored stream locations. Thus, there are intrinsic measurement uncertainties in describing stream water-quality loads from the monitoring data that are used to calibrate the SPARROW model.

Like all statistical models, SPARROW models are developed through a calibration process in which parameter values are estimated to minimize uncertainty in predicting stream constituent loads. This is achieved through a statistical algorithm called non-linear least squares in which parameter values are estimated to minimize the squared difference between the measured and predicted loads. Uncertainty is quantified as the residual error in load prediction that cannot be accounted for through parameter adjustment. The overall uncertainty in the model is quantified through a number of statistical diagnostics. However, the most common measure of uncertainty is referred to as the “mean square error” which is simply the average of the squared differences between the measured and predicted loads.

How can SPARROW model uncertainty be used to better understand the factors affecting water quality?

SPARROW models are designed to account for the spatial variability in stream water-quality monitoring data by relating them to spatially defined environmental factors. Uncertainty in the models is quantified by the differences between measured and modeled estimates of stream load, commonly referred to as residuals. The calibration process is designed to minimize those differences. Measures of uncertainty are used to assess the quality of the fit of the model and are used to estimate the margin of error in the prediction of loads, concentrations, yields, and source contributions.

Spatial patterns of high or low residuals that may be observed in maps may potentially reveal important environmental factors that may not be accounted for in the model. For example, a SPARROW model could consistently overestimate nitrogen loads in a specific part of a model region. Those large residuals may reveal a spatial pattern that coincides with a watershed characteristic that may be associated with them. In the case of nitrogen, for example, large residuals could occur where denitrification is important. Denitrification could be enhanced in areas with specific soil or geologic characteristics such as high soil permeability. The pattern in model residuals may indicate that inclusion of such explanatory variables is important. Thus the visualization of maps of spatial patterns in SPARROW model uncertainty are commonly used to investigate (and account for in subsequent model calibrations) environmental factors that may be related to important underlying processes affecting water quality.

SPARROW Modeling: Implications for Management and Monitoring

How can SPARROW models be used to guide the planning of future monitoring programs?

SPARROW models are statistical in nature and their uncertainty is often a function of both the quality and number of data available for calibration. For SPARROW models, calibration data consist of load estimates at monitoring sites. Inaccurate or imprecise load measurements at monitoring sites will create uncertainty in the models as will fewer monitoring sites. Where uncertainty is associated with large prediction errors, additional or refined monitoring can potentially be implemented to reduce the uncertainty. In a more general sense, compiling data for a SPARROW calibration may reveal limitations in the available monitoring load data. This information could help agencies make their monitoring programs more efficient.

SPARROW models are atypical in the realm of water-quality modeling in that they are capable of assisting with the interpretation of the data collected at a network of monitoring sites (Smith and others, 1997). Once a SPARROW model has been constructed for a monitoring network, some commonality exists between the objectives of monitoring and those of SPARROW modeling. It then becomes logical to consider using the model to choose sampling locations that simultaneously optimize monitoring and modeling objectives.

To design an optimal monitoring network, it is necessary to first clearly define the monitoring objective(s). A SPARROW model can then serve as the infrastructure of an algorithm for optimizing network design. For example, McMahon and others (2003) proposed using a SPARROW model to locate new monitoring to ensure the most accurate model-based predictions of the exceedence of a stream water-quality criterion. For this objective, it makes sense to collect data at stream locations where the model prediction of exceedence is both very close to the threshold value and highly uncertain (rather than focusing on stream locations where the prediction exceeds the threshold value very frequently or rarely). SPARROW models are able to provide quantitative information on model prediction uncertainty for each stream reach and, thus, indicate where additional sampling would best support an objective. Objectives may also address other aspects of model uncertainty.

How can findings be used by decision makers and stakeholders?

SPARROW modeling and interpretations of model findings advance our understanding of the spatial differences in pollution sources and the environmental and hydrologic processes that control their transport and delivery to downstream waters. The findings have important relevance to policy making and management related to water-quality concerns. Model predictions and related information can help States, Federal agencies, and other stakeholders identify the nutrient contributions to streams from pollution sources and upstream drainages (e.g., sub-watersheds, States).

One application of SPARROW results that can assist with improved understanding of stream nutrient loads and sources is their use in Total Maximum Daily Load (TMDL) assessments, especially in watersheds where little or limited stream monitoring data have been collected. For example, SPARROW results for the New England region were used previously in a TMDL assessment of nitrogen loadings from the Connecticut River to the Long-Island Sound to address concerns over seasonal coastal hypoxia and the location of contributing watershed sources. In this example, SPARROW provided information (Moore and others, 2004) about the delivery of nitrogen to the Sound from point and nonpoint nitrogen sources (e.g., atmospheric deposition, municipal wastewater) from upstream watersheds in four states and sub-basins of the Connecticut River Basin.

SPARROW also provides information that can be used to target upstream watersheds where the implementation of management strategies might be expected to result in more efficient reductions of nutrient loads in downstream water bodies per unit of effort expended upstream. These watersheds include those where the SPARROW predictions of “delivered yield”, the nutrient mass per unit area delivered to downstream waters, are high. Watersheds with high delivered yields typically have large nutrient contributions from point and/or nonpoint sources; these watersheds also efficiently deliver nutrients to downstream waters because generally smaller quantities of nutrients are removed during transport on land and in water as compared to those for watersheds with low delivered yields. This type of SPARROW information has been used by States and federal agencies to identify upstream watersheds that should receive priority management. For example, the Maryland Department of Natural Resources is using SPARROW estimates of the delivered yield (and associated source shares for agriculture, atmospheric deposition, etc.) to assist with targeting nutrient reduction efforts in the Chesapeake Bay watersheds.

The Kansas Department of Health and Environment has also used SPARROW predictions of nutrient delivery to the Gulf of Mexico to identify intra-state watersheds that should receive high priority for nutrient management. This is part of the efforts by the state of Kansas to mitigate the effects of nutrient over-enrichment and eutrophication in state and coastal waters of the Gulf of Mexico (see “Kansas Nutrient Reduction Plan,” 2004).

In addition, the USDA recently recommended the use of SPARROW results together with other information on nutrient sources to target the placement of conservation practices in 12 states in the Mississippi River Basin in an effort to control the downstream delivery of nutrients to the Gulf of Mexico (e.g., see USDA Healthy Watershed Initiative (2009)).

The SPARROW predictions of stream loads and nutrient sources and transport can also provide broad-scale information in support of regional assessments of nutrient sources in coastal and inland waters. For example, SPARROW results were used previously by NOAA to assist with assessments of the susceptibility of estuaries in the conterminous United States to nutrient enrichment (NOAA National Eutrophication Survey, 1999). The USDA Natural Resources Conservation Service (NRCS) has also used SPARROW to inform the calibration and verification of their applications of agricultural watershed models as part of assessments of the national water-quality effects of conservation practices in the Conservation Evaluation and Assessment Program (CEAP).

SPARROW predictions can also inform policy makers on issues of nutrient management and nutrient criteria setting. In 2009, a National Research Council panel cited SPARROW as an important information tool that can assist in identifying priority drainage basins for targeting management and nutrient control efforts in the Mississippi River Basin. SPARROW findings have also increased the understanding of the influence of headwaters on downstream water quality (e.g., Alexander and others, 2007), which has contributed to improved understanding of federal Clean Water Act jurisdiction and guidance to USEPA regions and U.S. Army Corps of Engineer Districts (e.g., see reference to the Journal of American Water Resources Association featured collection on Headwaters Hydrology.

What are the implications of SPARROW results for modeling and monitoring?

Development of hydrologic and water-quality models has progressed significantly over the last 20 years, resulting in improved broad-based assessments of water-quality conditions and improved the understanding of key factors and processes that affect water quality, such as land use, chemical sources of contamination, natural landscape features, and hydrologic transport.

1. Success of the SPARROW model approach depends on: Accurate and spatially detailed information about the watershed including information about cropping patterns, urban populations, point source discharges, and animal manure management
2. Spatially extensive long-term water-quality data, coupled with streamflow data
3. Continuing research and application of models that explicitly consider land and water processes and the way that they determine the downstream movement of pollutants

Unfortunately, water-quality monitoring by Federal and State agencies has declined remarkably. For example, during 1975-1980, when monitoring was at its peak, the number of locations in the U.S. where the USGS collected nutrient data suitable for use in studies such as the SPARROW model or for long-term trend analysis was about 4,500. In contrast, the number we have today is only about 1,900 stations, a decline of about 60 percent.

In addition to water-quality monitoring, much of the spatial ancillary data needed to interpret the water-quality data are lacking, including better information on point source discharges, use of chemicals, land-use changes, water use, land-management practices, conservation efforts, geomorphology and stream networks, and geologic settings. Currently, we face data limitations regarding ancillary information needed for model support, including that for point sources, agricultural applications and practices, and changes in land-management practices (including, for example, on best management and conservation efforts).

We must continue to integrate long-term, on-the-ground monitoring with predictive tools to assure relevant representation of the physical, chemical, and biological processes in the models, coupled with powerful statistical techniques to estimate the importance of various factors used in the models. Continued monitoring and data collection will reduce the overall uncertainty of model predictions and estimates. In turn, uncertainty analyses associated with each prediction will help to guide future monitoring and data-collection needs.

SPARROW Modeling in the South Atlantic-Gulf Tennessee Region

At what scales are results from the SAGT SPARROW model applicable in Florida?

It has been suggested that the South Atlantic-Gulf Tennessee (SAGT)-SPARROW total nitrogen model is a regional model, and is not calibrated for Florida. SPARROW models are generally designed to be scale independent and are considered to be valid across a wide range of spatial scales, corresponding approximately to the scale of the geospatial data used to calibrate the model. Typically, SPARROW models can be used to simulate water-quality conditions over scales ranging from single stream reach catchments (ranging from a few square kilometers to tens of square kilometers) up to the size of large watersheds and river basins that span thousands of square kilometers. Thus, SPARROW models are flexible and can be used to perform various types of assessments that span a range of basin sizes.

Regional scale geospatial data, developed along watershed boundaries, were used to calibrate the SAGT-SPARROW total nitrogen model (Hoos and McMahon, 2009). The ability of the model to accurately predict loadings at small spatial scales is limited by the degree of spatial resolution in the geospatial datasets. Some of these geospatial datasets, such as inputs from fertilizer use and livestock, are resolved only to the county level, although the spatial accuracy of the county-level data was enhanced for the SAGT SPARROW total nitrogen model through the use of detailed land use data (USGS National Land Cover Data set) to spatially refine the location of agricultural activities within counties. Nevertheless, because the average county size in the SAGT SPARROW model domain is 1425 km₂, we have suggested extra caution in interpreting nitrogen source terms for reaches where the watershed size is approximately that size or smaller. The SAGT-SPARROW predictions of total nitrogen load and source shares can therefore be used to assess water-quality conditions in terminal reaches for watersheds contributing to, for example, Choctawhatchee Bay or Charlotte Harbor (watershed drainage area = 13,496 and 8,134 km₂, respectively), but should be used with caution to assess conditions in terminal reaches for watersheds contributing to, for example, Sarasota Bay (653 km₂).

The SAGT-SPARROW total nitrogen model was calibrated to fit observed nutrient flux measurements at 321 monitoring sites, ranging in size from 15 to 28,000 square kilometers (interquartile range from 230 to 1,600 square kilometers). No spatial structure was observed in the model residuals that indicates that the model performed any better or worse in Florida compared to the other States or watersheds in the SAGT model domain.

The geology in some parts of Florida favors an exchange of water and nitrogen between surface water and groundwater. Is SPARROW valid in these areas?

As discussed in Hoos and McMahon (2009), the SPARROW approach of explaining instream loads based on watershed attributes has limitations for stream reaches for which the actual hydrologic boundaries do not correspond with the apparent watershed determined from surface topography. This may occur in certain river basins in northern and central Florida where flow exchange with the underlying regional aquifer contributes substantial nitrogen influx to and outflux from the surface-water basins. Model predictions are presented for river basins identified with this concern (Oklawaha, Crystal, Lower Sante Fe, Lower Suwanee, St. Marks, and Chipola River basins) but may be less reliable due to this unmodeled flux component. In addition, accuracy of SPARROW model predictions for the St. Johns River and Indian River basin may be affected by inadequate representation of the hydrologic network by the ERF1_2 digital segmented network used in the model.