Diffuse phosphorus models in the United States and europe: their usages, scales, and uncertainties

Watershed-scale spatial prediction of agricultural land phosphorus mass balance and soil phosphorus metrics: A bottom-up approach

Analysis of nutrient balance at the watershed scale, including for phosphorus (P), is typically accomplished using aggregate input datasets, resulting in an inability to capture the variability of P status across the study region. This study presents a set of methods to predict and visualize partial P mass balance, soil P saturation ratio (PSR), and soil test P for agricultural parcels across a watershed in the Lake Champlain Basin (Vermont, USA) using granular, field-level data. K-means cluster analyses were used to group agricultural parcels by soil texture, average slope, and crop type. Using a set of parcels accounting for ∼21% of the watershed's agricultural land and having known soil test and nutrient management parameters, predictions of partial P mass balance, PSR, and soil test P for agricultural land across the watershed were made by cluster, incorporating uncertainty. This resulted in an average partial P balance of 5.5 ± 0.2 kg P ha-1 year-1 and an average PSR of 0.0399 ± 0.0002. Furthermore, approximately 30% of agricultural land had predicted soil test P values above optimum levels. Results were used to visualize areas with high P loss potential. Such data and visualizations can inform watershed P modeling and assist practitioners in nutrient management decision making. These techniques can also serve as a framework for bottom-up modeling of nutrient mass balance and soil metrics in other regions.

A reconnaissance survey of channel bank particulate phosphorus concentrations, controls and estimated contributions to riverine loads across England

Channel banks can contribute a significant proportion of fine-grained (<63 μm) sediment to rivers, thereby also contributing to riverine total particulate phosphorus loads. Improving water quality through better agricultural practices alone can be difficult since the contributions from non-agricultural sources, including channel banks, can generate a 'spatial mismatch' between the efficacy of best management applied on farms and the likelihood of meeting environmental objectives. Our study undertook a reconnaissance survey (n = 76 sites each with 3 profiles sampled) to determine the total phosphorus (TP) concentrations of channel banks across England and to determine if TP content can be predicted using readily accessible secondary data. TP concentrations in adjacent field topsoils, local soil soil type/texture and geological parent material were examined as potential predictors of bank TP. Carbon and nitrogen content were also analysed to explore the impacts of organic matter content on measured TP concentrations. The results suggest that channel bank TP concentrations are primarily controlled by parent material rather than P additions to adjacent topsoils through fertilizer and organic matter inputs, but significant local variability in concentrations prevents the prediction of bank TP content using mapped soil type or geology. A median TP concentration of 873 mg kg-1 was calculated for the middle section of the sampled channel bank profiles, with a 25th percentile of 675 mg kg-1, and 75th percentile of 1159 mg kg-1. Using these concentrations and, in comparison with previously published estimates, the estimated number of inland WFD waterbodies in England for which channel bank erosion contributes >20% of the riverine total PP load increased from 15 to 25 (corresponding range of 17-35 using the 25th and 75th percentiles of measured TP concentrations). Collectively, these 25 waterbodies account for 0.2% of the total inland WFD waterbody area comprising England.

Random forest-based modeling of stream nutrients at national level in a data-scarce region

Nutrient runoff from agricultural production is one of the main causes of water quality deterioration in river systems and coastal waters. Water quality modeling can be used for gaining insight into water quality issues in order to implement effective mitigation efforts. Process-based nutrient models are very complex, requiring a lot of input parameters and computationally expensive calibration. Recently, ML approaches have shown to achieve an accuracy comparable to the process-based models and even outperform them when describing nonlinear relationships. We used observations from 242 Estonian catchments, amounting to 469 yearly TN and 470 TP measurements covering the period 2016-2020 to train random forest (RF) models for predicting annual N and P concentrations. We used a total of 82 predictor variables, including land cover, soil, climate and topography parameters and applied a feature selection strategy to reduce the number of dependent features in the models. The SHAP method was used for deriving the most relevant predictors. The performance of our models is comparable to previous process-based models used in the Baltic region with the TN and TP model having an R² score of 0.83 and 0.52, respectively. However, as input data used in our models is easier to obtain, the models offer superior applicability in areas, where data availability is insufficient for process-based approaches. Therefore, the models enable to give a robust estimation for nutrient losses at national level and allows to capture the spatial variability of the nutrient runoff which in turn enables to provide decision-making support for regional water management plans.

Updates to the Annual P Loss Estimator (APLE) model

The Annual P Loss Estimator (APLE) is a spreadsheet-based model developed for predicting annual field-scale P loss in surface runoff and changes in soil test P. This empirically based model was designed for use by those without significant modeling experience. However, a significant limitation with the model is that it does not calculate runoff. Moreover, APLE is deterministic and thus predicts a single value for a given set of inputs, thereby ignoring any uncertainties associated with model inputs. Here, we describe modifications to APLE that allow users to estimate runoff using the Curve Number method. Using Monte Carlo simulations, the updated version of APLE also provides users the ability to account for model input uncertainties in estimating model prediction errors. We provide examples of using the revised version of APLE (ver. 3.0) for calculating P loss from two fields in Mississippi over a 4-yr period and calculating the change in Mehlich-3 P concentrations over a 9-yr period at three locations in Maryland following cessation of P application. Both examples demonstrate that incorporating estimates of uncertainties in both measured data and model predictions provides modelers with a more realistic understanding of the model's performance.

Sensitivity and uncertainty analysis for predicted soil test phosphorus using the Annual Phosphorus Loss Estimator model

In this study we conducted a sensitivity and uncertainty analysis using the Annual P Loss Estimator (APLE) model focusing on model predictions of soil test phosphorus (STP). We calculated and evaluated the sensitivity coefficients of predicted STP and changes in STP using 1- and 10-yr simulations with and without P application. We also compared two methods for estimating prediction uncertainties: first-order variance approximation (FOVA) and Monte Carlo simulation (MCS). Finally, we compared uncertainties in APLE-predicted STP with uncertainties in measured STP collected from multiple sites in Maryland under different manuring and cropping treatments. Results from our sensitivity analysis showed that predicted STP and changes in STP for 1-yr simulations without P inputs were most sensitive to initial STP, whereas model STP predictions were most sensitive to manure and fertilizer application rates when sensitivity analyses included P inputs. For the 10-yr simulations without P application inputs, the range in sensitivity coefficients for crop uptake and precipitation were much greater than for the 1-yr simulations. Prediction uncertainties from FOVA were comparable to those from MCS for model input uncertainties up to 50%. Using FOVA to calculate APLE STP prediction uncertainties using the Maryland data set, the mean measured STP for nearly all site years fell within the 95% confidence intervals of the STP prediction uncertainties. Our results provide users of APLE insight into what model inputs require the most careful measurement when using the model to predict changes in STP under conditions of P drawdown (i.e., no P application) or P buildup.

Estimating dissolved phosphorus losses from legacy sources in pastures: The limits of soil tests and small-scale rainfall simulators

A legacy of using P fertilizers on grazed pastures has been enhanced soil fertility and an associated increased risk of P loss in runoff. Rainfall simulation has been extensively used to develop relationships between soil test P (STP) and dissolved P (DP) in runoff as part of modeling efforts scrutinizing the impact of legacy P. This review examines the applicability of rainfall simulation to draw inferences related to legacy P. Using available literature, we propose a mixing layer model with chemical transfer to describe DP mobilization from pasture soils where readily available P in the mixing layer is rapidly exhausted and contact time controls DP concentrations responsible for subsequent DP mobilization. That conceptual model was shown to be consistent with field monitoring data and then used to assess the likely effect of rainfall simulation protocols on DP mobilization, highlighting the influence of soil preparation, scale and measurement duration, and, most important, hydrology that can facilitate the physical transport of P into and out of surface flow. We conclude that rainfall simulation experimental protocols can have severe limitations for developing relationships between DP in runoff and STP that are subsequently used to estimate legacy P contributions to downstream water resources.

Modeling of phosphorus loss from field to watershed: A review

Phosphorus (P) losses from nonpoint sources into surface water resources through surface runoff and tile drainage play a significant role in eutrophication. Accordingly, the number of studies involving the modeling of agricultural P losses, the uncertainties of such models, and the best management practices (BMPs) supported by the modeling of hypothetical P loss reduction scenarios has increased significantly around the world. Many improvements have been made to these models: separate manure P pools, variable source areas allowing the determination of critical source areas of P loss, analyses of modeling uncertainties, and understanding of legacy P. However, several elements are still missing or have yet to be sufficiently addressed: the incorporation of preferential flow into models, the modification of P sorption-desorption processes considering recent research data (e.g., pedotransfer functions for labile, active, or stable P, along with P sorption coefficients), BMP parameterization, and scale-up issues, as well as stakeholder-scientist and experimentalist-modeler interactions. The accuracy of P loss modeling can be improved by (a) incorporating dynamic P sorption-desorption processes and new P subroutines for direct P loss from manure, fertilizer, and dung, (b) modeling preferential flow, connectivity between field and adjacent water bodies, and P in-stream processes, (c) including an assessment of model uncertainty, (d) integrating field and watershed models for BMP calibration and scaling field results up to larger areas, and (e) building a holistic interaction between stakeholders, experimentalists, and modelers.

Modification of the MONERIS Nutrient Emission Model for a Lowland Country (Hungary) to Support River Basin Management Planning in the Danube River Basin

The contamination of waters with nutrients, especially nitrogen and phosphorus originating from various diffuse and point sources, has become a worldwide issue in recent decades. Due to the complexity of the processes involved, watershed models are gaining an increasing role in their analysis. The goal set by the EU Water Framework Directive (to reach “good status” of all water bodies) requires spatially detailed information on the fate of contaminants. In this study, the watershed nutrient model MONERIS was applied to the Hungarian part of the Danube River Basin. The spatial resolution was 1078 water bodies (mean area of 86 km2); two subsequent 4 year periods (2009–2012 and 2013–2016) were modeled. Various elements/parameters of the model were adjusted and tested against surface and subsurface water quality measurements conducted all over the country, namely (i) the water balance equations (surface and subsurface runoff), (ii) the nitrogen retention parameters of the subsurface pathways (excluding tile drainage), (iii) the shallow groundwater phosphorus concentrations, and (iv) the surface water retention parameters. The study revealed that (i) digital-filter-based separation of surface and subsurface runoff yielded different values of these components, but this change did not influence nutrient loads significantly; (ii) shallow groundwater phosphorus concentrations in the sandy soils of Hungary differ from those of the MONERIS default values; (iii) a significant change of the phosphorus in-stream retention parameters was needed to approach measured in-stream phosphorus load values. Local emissions and pathways were analyzed and compared with previous model results.

Phosphorus and the Chesapeake Bay: Lingering Issues and Emerging Concerns for Agriculture

Hennig Brandt's discovery of phosphorus (P) occurred during the early European colonization of the Chesapeake Bay region. Today, P, an essential nutrient on land and water alike, is one of the principal threats to the health of the bay. Despite widespread implementation of best management practices across the Chesapeake Bay watershed following the implementation in 2010 of a total maximum daily load (TMDL) to improve the health of the bay, P load reductions across the bay's 166,000-km watershed have been uneven, and dissolved P loads have increased in a number of the bay's tributaries. As the midpoint of the 15-yr TMDL process has now passed, some of the more stubborn sources of P must now be tackled. For nonpoint agricultural sources, strategies that not only address particulate P but also mitigate dissolved P losses are essential. Lingering concerns include legacy P stored in soils and reservoir sediments, mitigation of P in artificial drainage and stormwater from hotspots and converted farmland, manure management and animal heavy use areas, and critical source areas of P in agricultural landscapes. While opportunities exist to curtail transport of all forms of P, greater attention is required toward adapting P management to new hydrologic regimes and transport pathways imposed by climate change.

Development of PLEAD: A Database Containing Event-based Runoff Phosphorus Loadings from Agricultural Fields

Computer models are commonly used for predicting risks of runoff P loss from agricultural fields by enabling simulation of various management practices and climatic scenarios. For P loss models to be useful tools, however, they must accurately predict P loss for a wide range of climatic, physiographic, and land management conditions. A complicating factor in developing and evaluating P loss models is the relative scarcity of available measured field data that adequately capture P losses before and after implementing management practices in a variety of physiographic settings. Here, we describe the development of the P Loss in runoff Events from Agricultural fields Database (PLEAD)-a compilation of event-based, field-scale dissolved and/or total P loss runoff loadings from agricultural fields collected at various research sites located in the US Heartland and southern United States. The database also includes runoff and erosion rates; soil-test P; tillage practices; planting and harvesting rates and practices; fertilizer application rate, method, and timing; manure application rate, method, and timing; and livestock grazing density and timing. In total, >1800 individual runoff events-ranging in duration from 0.4 to 97 h-have been included in the database. Event runoff P losses ranged from <0.05 to 1.3 and 3.0 kg P ha for dissolved and total P, respectively. The data contained in this database have been used in multiple research studies to address important modeling questions relevant to P management planning. We provide these data to encourage additional studies by other researchers. The PLEAD database is available at .

Developing a non-point source P loss indicator in R and its parameter uncertainty assessment using GLUE: a case study in northern China

Uncertainty analysis is an important prerequisite for model application. However, the existing phosphorus (P) loss indexes or indicators were rarely evaluated. This study applied generalized likelihood uncertainty estimation (GLUE) method to assess the uncertainty of parameters and modeling outputs of a non-point source (NPS) P indicator constructed in R language. And the influences of subjective choices of likelihood formulation and acceptability threshold of GLUE on model outputs were also detected. The results indicated the following. (1) Parameters RegR₂, RegSDR₂, PlossDP_fer, PlossDP_man, DPDR, and DPR were highly sensitive to overall TP simulation and their value ranges could be reduced by GLUE. (2) Nash efficiency likelihood (L₁) seemed to present better ability in accentuating high likelihood value simulations than the exponential function (L₂) did. (3) The combined likelihood integrating the criteria of multiple outputs acted better than single likelihood in model uncertainty assessment in terms of reducing the uncertainty band widths and assuring the fitting goodness of whole model outputs. (4) A value of 0.55 appeared to be a modest choice of threshold value to balance the interests between high modeling efficiency and high bracketing efficiency. Results of this study could provide (1) an option to conduct NPS modeling under one single computer platform, (2) important references to the parameter setting for NPS model development in similar regions, (3) useful suggestions for the application of GLUE method in studies with different emphases according to research interests, and (4) important insights into the watershed P management in similar regions.

Modeling Phosphorus Losses through Surface Runoff and Subsurface Drainage Using ICECREAM

Modeling soil phosphorus (P) losses by surface and subsurface flow pathways is essential in developing successful strategies for P pollution control. We used the ICECREAM model to simultaneously simulate P losses in surface and subsurface flow, as well as to assess effectiveness of field practices in reducing P losses. Monitoring data from a mineral-P-fertilized clay loam field in southwestern Ontario, Canada, were used for calibration and validation. After careful adjustment of model parameters, ICECREAM was shown to satisfactorily simulate all major processes of surface and subsurface P losses. When the calibrated model was used to assess tillage and fertilizer management scenarios, results point to a 10% reduction in total P losses by shifting autumn tillage to spring, and a 25.4% reduction in total P losses by injecting fertilizer rather than broadcasting. Although the ICECREAM model was effective in simulating surface and subsurface P losses when thoroughly calibrated, further testing is needed to confirm these results with manure P application. As illustrated here, successful use of simulation models requires careful verification of model routines and comprehensive calibration to ensure that site-specific processes are accurately represented.

Simulation of targeted pollutant-mitigation-strategies to reduce nitrate and sediment hotspots in agricultural watershed

About 50% of U.S. water pollution problems are caused by non-point source (NPS) pollution, primarily sediment and nutrients from agricultural areas, despite the widespread implementation of agricultural Best Management Practices (BMPs). However, the effectiveness of implementation strategies and type of BMPs at watershed scale are still not well understood. In this study, the Soil and Water Assessment Tool (SWAT) ecohydrological model was used to assess the effectiveness of pollutant mitigation strategies in the Raccoon River watershed (RRW) in west-central Iowa, USA. We analyzed fourteen management scenarios based on systematic combinations of five strategies: fertilizer/manure management, changing row-crop land to perennial grass, vegetative filter strips, cover crops and shallower tile drainage systems, specifically aimed at reducing nitrate and total suspended sediment yields from hotspot areas in the RRW. Moreover, we assessed implications of climate change on management practices, and the impacts of management practices on water availability, row crop yield, and total agricultural production. Our results indicate that sufficient reduction of nitrate load may require either implementation of multiple management practices (38.5% with current setup) or conversion of extensive areas into perennial grass (up to 49.7%) to meet and maintain the drinking water standard. However, climate change may undermine the effectiveness of management practices, especially late in the 21st century, cutting the reduction by up to 65% for nitrate and more for sediment loads. Further, though our approach is targeted, it resulted in a slight decrease (~5%) in watershed average crop yield and hence an overall reduction in total crop production, mainly due to the conversion of row-crop lands to perennial grass. Such yield reductions could be quite spatially heterogeneously distributed (0 to 40%).

Comparing an Annual and a Daily Time-Step Model for Predicting Field-Scale Phosphorus Loss

A wide range of mathematical models are available for predicting phosphorus (P) losses from agricultural fields, ranging from simple, empirically based annual time-step models to more complex, process-based daily time-step models. In this study, we compare field-scale P-loss predictions between the Annual P Loss Estimator (APLE), an empirically based annual time-step model, and the Texas Best Management Practice Evaluation Tool (TBET), a process-based daily time-step model based on the Soil and Water Assessment Tool. We first compared predictions of field-scale P loss from both models using field and land management data collected from 11 research sites throughout the southern United States. We then compared predictions of P loss from both models with measured P-loss data from these sites. We observed a strong and statistically significant ( < 0.001) correlation in both dissolved (ρ = 0.92) and particulate (ρ = 0.87) P loss between the two models; however, APLE predicted, on average, 44% greater dissolved P loss, whereas TBET predicted, on average, 105% greater particulate P loss for the conditions simulated in our study. When we compared model predictions with measured P-loss data, neither model consistently outperformed the other, indicating that more complex models do not necessarily produce better predictions of field-scale P loss. Our results also highlight limitations with both models and the need for continued efforts to improve their accuracy.

Assessing Coastal Plain Risk Indices for Subsurface Phosphorus Loss

Phosphorus (P) Index evaluations are critical to advancing nutrient management planning in the United States. However, most assessments until now have focused on the risks of P losses in surface runoff. In artificially drained agroecosystems of the Atlantic Coastal Plain, subsurface flow is the predominant mode of P transport, but its representation in most P Indices is often inadequate. We explored methods to evaluate the subsurface P risk routines of five P Indices from Delaware, Maryland (two), Virginia, and North Carolina using available water quality and soils datasets. Relationships between subsurface P risk scores and published dissolved P loads in leachate (Delaware, Maryland, and North Carolina) and ditch drainage (Maryland) were directionally correct and often statistically significant, yet the brevity of the observation periods (weeks to several years) and the limited number of sampling locations precluded a more robust assessment of each P Index. Given the paucity of measured P loss data, we then showed that soil water extractable P concentrations at depths corresponding with the seasonal high water table (WEP) could serve as a realistic proxy for subsurface P losses in ditch drainage. The associations between WEP and subsurface P risk ratings reasonably mirrored those obtained with sparser water quality data. As such, WEP is seen as a valuable metric that offers interim insight into the directionality of subsurface P risk scores when water quality data are inaccessible. In the long term, improved monitoring and modeling of subsurface P losses clearly should enhance the rigor of future P Index appraisals.

Revised Method and Outcomes for Estimating Soil Phosphorus Losses from Agricultural Land in the Chesapeake Bay Watershed Model

Current restoration efforts for the Chesapeake Bay watershed mandate a timeline for reducing the load of nutrients and sediment into receiving waters. The Chesapeake Bay watershed model (WSM) has been used for two decades to simulate hydrology and nutrient and sediment transport; however, spatial limitations of the WSM preclude edge-of-field scale representation of phosphorus (P) losses. Rather, the WSM relies on literature-derived, county-scale rates of P loss (targets) for simulated land uses. An independent field-scale modeling tool, Annual Phosphorus Loss Estimator (APLE), was used as an alternative to the current WSM approach. Identical assumptions of county-level acreage, soil properties, nutrient management practices, and transport factors from the WSM were used as inputs to APLE. Incorporation of APLE P-loss estimates resulted in greater estimated total P loss and a revised spatial pattern of P loss compared with the WSM's original targets. Subsequently, APLE's revised estimates for P loss were substituted into the WSM and resulted in improved WSM calibration performance at up to 79% of tributary monitoring stations. The incorporation of APLE into the WSM will improve its ability to assess P loss and the impact of field management on Chesapeake Bay water quality.

Evaluation of the TBET Model for Potential Improvement of Southern P Indices

Due to a shortage of available phosphorus (P)-loss datasets, simulated data from an accurate quantitative P transport model could be used to evaluate a P Index. The objective of this study was to compare predictions from the Texas Best Management Practice Evaluation Tool (TBET) against measured P-loss data to determine whether the model could be used to improve P Indices in the southern region. Measured P-loss data from field-scale study sites in Arkansas, Georgia, and North Carolina were used to assess the accuracy of TBET for predicting field-scale loss of P. We found that event-based predictions using an uncalibrated model were generally poor. Calibration improved runoff predictions and produced scatterplot regression lines that had slopes near one and intercepts near zero. However, TBET predictions of runoff met the performance criteria (Nash-Sutcliffe efficiency ≥ 0.3, percent bias ≤ 35%, and mean absolute error ≤ 10 mm) in only one out of six comparisons: North Carolina during calibration. Sediment predictions were imprecise, and dissolved P predictions underestimated measured losses. In North Carolina, total P-loss predictions were reasonably accurate because TBET did a slightly better job of predicting sediment losses from cultivated land. In Arkansas and Georgia, where the experimental sites were in forage production, the underprediction of dissolved P led directly to the underpredictions of total P. We conclude that TBET cannot be used to improve southern P Indices, but a curve number approach could be incorporated into P Indices to improve runoff predictions.

Improved Simulation of Edaphic and Manure Phosphorus Loss in SWAT

Watershed models such as the Soil Water Assessment Tool (SWAT) and the Agricultural Policy Environmental EXtender (APEX) are widely used to assess the fate and transport of agricultural nutrient management practices on soluble and particulate phosphorus (P) loss in runoff. Soil P-cycling routines used in SWAT2012 revision 586, however, do not simulate the short-term effects of applying a concentrated source of soluble P, such as manure, to the soil surface where it is most vulnerable to runoff. We added a new set of soil P routines to SWAT2012 revision 586 to simulate surface-applied manure at field and subwatershed scales within Mahantango Creek watershed in south-central Pennsylvania. We corroborated the new P routines and standard P routines in two versions of SWAT (conventional SWAT, and a topographically driven variation called TopoSWAT) for a total of four modeling "treatments". All modeling treatments included 5 yr of measured data under field-specific, historical management information. Short-term "wash off" processes resulting from precipitation immediately following surface application of manures were captured with the new P routine whereas the standard routines resulted in losses regardless of manure application. The new routines improved sensitivity to key factors in nutrient management (i.e., timing, rate, method, and form of P application). Only the new P routines indicated decreases in soluble P losses for dairy manure applications at 1, 5, and 10 d before a storm event. The new P routines also resulted in more variable P losses when applying manure versus commercial fertilizer and represented increases in total P losses, as compared with standard P routines, with rate increases in dairy manure application (56,000 to 84,000 L ha). The new P routines exhibited greater than 50% variation among proportions of organic, particulate, and soluble P corresponding to spreading method. In contrast, proportions of P forms under the standard P routines varied less than 20%. Results suggest similar revisions to other agroecosystem watershed models would be appropriate.

Applicability of models to predict phosphorus losses in drained fields: a review

Most phosphorus (P) modeling studies of water quality have focused on surface runoff loses. However, a growing number of experimental studies have shown that P losses can occur in drainage water from artificially drained fields. In this review, we assess the applicability of nine models to predict this type of P loss. A model of P movement in artificially drained systems will likely need to account for the partitioning of water and P into runoff, macropore flow, and matrix flow. Within the soil profile, sorption and desorption of dissolved P and filtering of particulate P will be important. Eight models are reviewed (ADAPT, APEX, DRAINMOD, HSPF, HYDRUS, ICECREAMDB, PLEASE, and SWAT) along with P Indexes. Few of the models are designed to address P loss in drainage waters. Although the SWAT model has been used extensively for modeling P loss in runoff and includes tile drain flow, P losses are not simulated in tile drain flow. ADAPT, HSPF, and most P Indexes do not simulate flow to tiles or drains. DRAINMOD simulates drains but does not simulate P. The ICECREAMDB model from Sweden is an exception in that it is designed specifically for P losses in drainage water. This model seems to be a promising, parsimonious approach in simulating critical processes, but it needs to be tested. Field experiments using a nested, paired research design are needed to improve P models for artificially drained fields. Regardless of the model used, it is imperative that uncertainty in model predictions be assessed.

Using fuzzy logic analysis for siting decisions of infiltration trenches for highway runoff control

Determining optimal locations for best management practices (BMPs), including their field considerations and limitations, plays an important role for effective stormwater management. However, these issues have been often overlooked in modeling studies that focused on downstream water quality benefits. This study illustrates the methodology of locating infiltration trenches at suitable locations from spatial overlay analyses which combine multiple layers that address different aspects of field application into a composite map. Using seven thematic layers for each analysis, fuzzy logic was employed to develop a site suitability map for infiltration trenches, whereas the DRASTIC method was used to produce a groundwater vulnerability map on the island of Oahu, Hawaii, USA. In addition, the analytic hierarchy process (AHP), one of the most popular overlay analyses, was used for comparison to fuzzy logic. The results showed that the AHP and fuzzy logic methods developed significantly different index maps in terms of best locations and suitability scores. Specifically, the AHP method provided a maximum level of site suitability due to its inherent aggregation approach of all input layers in a linear equation. The most eligible areas in locating infiltration trenches were determined from the superposition of the site suitability and groundwater vulnerability maps using the fuzzy AND operator. The resulting map successfully balanced qualification criteria for a low risk of groundwater contamination and the best BMP site selection. The results of the sensitivity analysis showed that the suitability scores were strongly affected by the algorithms embedded in fuzzy logic; therefore, caution is recommended with their use in overlay analysis. Accordingly, this study demonstrates that the fuzzy logic analysis can not only be used to improve spatial decision quality along with other overlay approaches, but also is combined with general water quality models for initial and refined searches for the best locations of BMPs at the sub-basin level.

Measurement and modeling of phosphorous transport in shallow groundwater environments

Leaching of phosphorus (P) from agricultural soils, especially those that are sandy, is adversely impacting P-limited ecosystems like Florida's Everglades. A more developed understanding of P and water management strategies and their effects on P leaching is needed to achieve reductions in subsurface P losses, especially from intensively managed dual cropping systems under plastic mulch in shallow water regions. We compared the effects of conservation P and water management strategies with traditional practices on P transport to groundwater. A 3-year experiment was conducted on hydrologically isolated plots with plastic-mulched successive cropping systems to compare high (HEI) and soil test based recommended (REI) external input (water and fertilizer P) systems with traditional sub-irrigation (seepage), and REI with a potential water conservation subsurface drip irrigation system (REI-SD) with regard to groundwater P concentrations above and below the low conductivity spodic horizon (Bh). The REI treatments had higher available storage for rainfall and P than HEI. Use of both REI systems (REI=2098μg/L and REI-SD=2048μg/L) reduced groundwater P concentrations above the Bh horizon by 33% compared to HEI (3090μg/L), and results were significant at the 0.05 level. Although the subsurface drip system saved water, it did not offer any groundwater quality (P) benefit. Mixing and dilution of influent P below the low conductivity Bh horizon between treatments and with the regional groundwater system resulted in no significant differences in groundwater P concentration below the Bh horizon. Groundwater P concentrations from this study were higher than reported elsewhere due to low soil P storage capacity (SPSC), high hydraulic conductivity of sandy soils, and a high water table beneath crop beds. The HEI system leached more P due to ferilizer P in excess of SPSC and used higher irrigation volumes compared with REI systems. Despite a 40% difference in the average amount of added fertilizer P between HEI (187kg P2O5/ha) and REI (124kg P2O5/ha), soil Mehlich 1 P (M1P) values were similar for both systems while they received Pinput. Soil M1P for REI and REI-SD increased to a maximum of 55mg/kg while they received Pinput, and then gradually decreased after Pinput ceased. However, M1P for HEI increased steadily to a maximum of 145mg/kg by the end of the study with continued Pinput. Mehlich-1 P measured six years after the study still showed relatively high levels of P, a legacy effect of Pinput. The main factors influencing groundwater P concentration varied by seasons. During fall with frequent rainfall, the concentrations were influenced mainly by M1P and Pinput, and highlight a need for greater focus on Pinput management (vs. water management) during this season. However, during the dry period of spring, a greater focus on irrigation management is required since depth to water table and rainfall also become contributing factors. Three multivariate models (r(2)=0.67 to 0.93), for spring, fall, and annual periods, were developed for predicting groundwater P concentrations for a wide range of water and P inputs (0 to 191kg P2O5/ha of Pinput). The uniqueness of these models is that they use readily available hydrologic (rainfall and water table depth), management (Pinput), and soil (M1P) data commonly monitored by growers when managing water and nutrient inputs on agricultural landscapes. The development of similar models may not be necessary for other agro-ecosystems in similar regions since long-term data collected in these regions may be applied, with verification, to the models presented here.

Bayesian uncertainty assessment of a semi-distributed integrated catchment model of phosphorus transport

Process-based models of nutrient transport are often used as tools for management of eutrophic waters, as decision makers need to judge the potential effects of alternative remediation measures, under current conditions and with future land use and climate change. All modelling exercises entail uncertainty arising from various sources, such as the input data, selection of parameter values and the choice of model itself. Here we perform Bayesian uncertainty assessment of an integrated catchment model of phosphorus (INCA-P). We use an auto-calibration procedure and an algorithm for including parametric uncertainty to simulate phosphorus transport in a Norwegian lowland river basin. Two future scenarios were defined to exemplify the importance of parametric uncertainty in generating predictions. While a worst case scenario yielded a robust prediction of increased loading of phosphorus, a best case scenario only gave rise to a reduction in load with probability 0.78, highlighting the importance of taking parametric uncertainty into account in process-based catchment scale modelling of possible remediation scenarios. Estimates of uncertainty can be included in information provided to decision makers, thus making a stronger scientific basis for sound decisions to manage water resources.

Three-dimensional lake water quality modeling: sensitivity and uncertainty analyses

Two sensitivity and uncertainty analysis methods are applied to a three-dimensional coupled hydrodynamic-ecological model (ELCOM-CAEDYM) of a morphologically complex lake. The primary goals of the analyses are to increase confidence in the model predictions, identify influential model parameters, quantify the uncertainty of model prediction, and explore the spatial and temporal variabilities of model predictions. The influence of model parameters on four model-predicted variables (model output) and the contributions of each of the model-predicted variables to the total variations in model output are presented. The contributions of predicted water temperature, dissolved oxygen, total phosphorus, and algal biomass contributed 3, 13, 26, and 58% of total model output variance, respectively. The fraction of variance resulting from model parameter uncertainty was calculated by two methods and used for evaluation and ranking of the most influential model parameters. Nine out of the top 10 parameters identified by each method agreed, but their ranks were different. Spatial and temporal changes of model uncertainty were investigated and visualized. Model uncertainty appeared to be concentrated around specific water depths and dates that corresponded to significant storm events. The results suggest that spatial and temporal variations in the predicted water quality variables are sensitive to the hydrodynamics of physical perturbations such as those caused by stream inflows generated by storm events. The sensitivity and uncertainty analyses identified the mineralization of dissolved organic carbon, sediment phosphorus release rate, algal metabolic loss rate, internal phosphorus concentration, and phosphorus uptake rate as the most influential model parameters.

Sensitivity and uncertainty analysis for the annual phosphorus loss estimator model

Models are often used to predict phosphorus (P) loss from agricultural fields. Although it is commonly recognized that model predictions are inherently uncertain, few studies have addressed prediction uncertainties using P loss models. In this study we assessed the effect of model input error on predictions of annual P loss by the Annual P Loss Estimator (APLE) model. Our objectives were (i) to conduct a sensitivity analyses for all APLE input variables to determine which variables the model is most sensitive to, (ii) to determine whether the relatively easy-to-implement first-order approximation (FOA) method provides accurate estimates of model prediction uncertainties by comparing results with the more accurate Monte Carlo simulation (MCS) method, and (iii) to evaluate the performance of the APLE model against measured P loss data when uncertainties in model predictions and measured data are included. Our results showed that for low to moderate uncertainties in APLE input variables, the FOA method yields reasonable estimates of model prediction uncertainties, although for cases where manure solid content is between 14 and 17%, the FOA method may not be as accurate as the MCS method due to a discontinuity in the manure P loss component of APLE at a manure solid content of 15%. The estimated uncertainties in APLE predictions based on assumed errors in the input variables ranged from ±2 to 64% of the predicted value. Results from this study highlight the importance of including reasonable estimates of model uncertainty when using models to predict P loss.

Using a phosphorus loss model to evaluate and improve phosphorus indices

In most states, the phosphorus (P) index (PI) is the adopted strategy for assessing a field's vulnerability to P loss; however, many state PIs have not been rigorously evaluated against measured P loss data to determine how well the PI assigns P loss risk-a major reason being the lack of field data available for such an analysis. Given the lack of P loss data available for PI evaluation, our goal was to demonstrate how a P loss model can be used to evaluate and revise a PI using the Pennsylvania (PA) PI as an example. Our first objective was to compare two different formulations-multiplicative and component-for calculating a PI. Our second objective was to evaluate whether output from a P loss model can be used to improve PI weighting by calculating weights for modified versions of the PA PI from model-generated P loss data. Our results indicate that several potential limitations exist with the original multiplicative index formulation and that a component formulation is more consistent with how P loss is calculated with P loss models and generally provides more accurate estimates of P loss. Moreover, using the PI weights calculated from the model-generated data noticeably improved the correlation between PI values and a large and diverse measured P loss data set. The approach we use here can be used with any P loss model and PI and thus can serve as a guide to assist states in evaluating and modifying their PI.

Simulating soil phosphorus dynamics for a phosphorus loss quantification tool

Pollution of fresh waters by agricultural phosphorus (P) is a water quality concern. Because soils can contribute significantly to P loss in runoff, it is important to assess how management affects soil P status over time, which is often done with models. Our objective was to describe and validate soil P dynamics in the Annual P Loss Estimator (APLE) model. APLE is a user-friendly spreadsheet model that simulates P loss in runoff and soil P dynamics over 10 yr for a given set of runoff, erosion, and management conditions. For soil P dynamics, APLE simulates two layers in the topsoil, each with three inorganic P pools and one organic P pool. It simulates P additions to soil from manure and fertilizer, distribution among pools, mixing between layers due to tillage and bioturbation, leaching between and out of layers, crop P removal, and loss by surface runoff and erosion. We used soil P data from 25 published studies to validate APLE's soil P processes. Our results show that APLE reliably simulated soil P dynamics for a wide range of soil properties, soil depths, P application sources and rates, durations, soil P contents, and management practices. We validated APLE specifically for situations where soil P was increasing from excessive P inputs, where soil P was decreasing due to greater outputs than inputs, and where soil P stratification occurred in no-till and pasture soils. Successful simulations demonstrate APLE's potential to be applied to major management scenarios related to soil P loss in runoff and erosion.

A Monte Carlo approach to the inverse problem of diffuse pollution risk in agricultural catchments

The hydrological and biogeochemical processes that operate in catchments influence the ecological quality of freshwater systems through delivery of fine sediment, nutrients and organic matter. Most models that seek to characterise the delivery of diffuse pollutants from land to water are reductionist. The multitude of processes that are parameterised in such models to ensure generic applicability make them complex and difficult to test on available data. Here, we outline an alternative--data-driven--inverse approach. We apply SCIMAP, a parsimonious risk based model that has an explicit treatment of hydrological connectivity. We take a bayesian approach to the inverse problem of determining the risk that must be assigned to different land uses in a catchment in order to explain the spatial patterns of measured in-stream nutrient concentrations. We apply the model to identify the key sources of nitrogen (N) and phosphorus (P) diffuse pollution risk in eleven UK catchments covering a range of landscapes. The model results show that: 1) some land use generates a consistently high or low risk of diffuse nutrient pollution; but 2) the risks associated with different land uses vary both between catchments and between nutrients; and 3) that the dominant sources of P and N risk in the catchment are often a function of the spatial configuration of land uses. Taken on a case-by-case basis, this type of inverse approach may be used to help prioritise the focus of interventions to reduce diffuse pollution risk for freshwater ecosystems.

Predicting stream N and P concentrations from loads and catchment characteristics at regional scale: a concentration ratio method

We used a concentration ratio method to predict yearly and summer averages of stream total nitrogen, nitrate and total phosphorus concentrations at a regional scale. The ratio of the median daily concentration on the flow weighted annual concentration was used. This ratio characterizes the concentration dynamics of a catchment. We took advantage of the commonly used budget type models applied at a regional scale to relate concentrations to loads instead of directly to land uses, as has previously been done. The relationship was modeled with Boosted Regression Trees using catchment and stream characteristics along with loads and flows obtained from the SPARROW budget model. The ratio modeling approach was compared to a direct approach for concentration prediction, and also to a simple method where the mean ratio was used. The modeling performances of the ratio models were overall satisfying (r2 of 49% to 78%), and a better choice than the two other methods tested. This ratio modeling approach is based on a steady state assumption and largely ignores temporal dynamics. As such, this modeling technique does not replace the more physically-based techniques, but allows for hybrid approaches for improved spatial interpolations. This method could be used to predict effectively the impact (at equilibrium) of land use change and management scenarios on water quality at a regional scale.

International phosphorus workshop: diffuse phosphorus loss to surface water bodies--risk assessment, mitigation options, and ecological effects in river basins

Agriculture is a major source of P to the aquatic environment in many countries. Although efforts have been made to improve the P utilization in agricultural production, which is reflected in modestly declining P surpluses in many countries, increasing agricultural P surpluses are still observed in some countries. The IPW5 Special Submission included in this issue addresses and discusses four key topics that emerged from the workshop: (i) managing agricultural P losses-effectiveness, uncertainties, and costs; (ii) P modeling at different scales; (iii) functioning of riparian buffers; (iv) ecological responses to P loadings and impacts of climate change. Each of these four topics interacts with each other as well as with the four tiers of the P Transfer Continuum (Source, Mobilization, Transport, and Ecological Effects). In this review paper we highlight the main outcomes of the workshop and the special collection of eight papers. Moreover, we identify the main gaps in our knowledge and future research directions on P, which are linked to important issues such as addressing scale effects, improved P models with the ability to quantify uncertainty, the linking of P losses with ecological effects, and climate change.