Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Phosphorus loss assessment tools: a review of underlying concepts and applicability in cold climates


Identifying critical source areas (CSAs) of a watershed by phosphorus (P) loss assessment tools is essential for optimal placement of beneficial management practices (BMPs) to address diffuse P pollution. However, lack of significant progress in tackling diffuse P pollution could be, in part, associated with inefficacy of P loss assessment tools for accurately identifying CSAs. Phosphorus loss assessment tools have been developed to simulate P loss from the landscape where runoff is mainly driven by rainfall events. Therefore, they may underperform in cold climates where the land is often frozen during winter and runoff is dominated by snowmelt. This paper (i) reviews the strengths and weaknesses of current P loss assessment tools and their underlying assumptions in simulating soil P dynamics and P transfer to runoff, and (ii) highlights a number of challenges associated with modeling P transfer from agricultural land to surface waters in cold climates. Current P loss assessment tools do not appear to fully represent hydrological and biogeochemical processes responsible for P loss from CSAs, particularly in cold climates. Effort should be made to develop P loss assessment tools that are capable of considering P dynamics through the landscape as a result of abiotic perturbations that are common in cold climates, predicting runoff and P movement over frozen/partially frozen soils, and considering material-P connectivity between landscape and surface waters. Evaluating P loss assessment tools with water quality data is necessary to ensure such modifications result in improved identification of CSAs.


Phosphorus (P) export from agricultural land has been identified as a primary cause of water quality impairment as P plays an important role in freshwater eutrophication (Schindler et al. 2012; Watson et al. 2016). Eutrophication poses several consequences to aquatic ecosystems, such as increased frequency of harmful planktonic and benthic algal blooms and hypoxia, reductions in water transparency and aquatic biodiversity, and increased costs of drinking water treatment (Sharpley et al. 2003a; Smith and Schindler 2009; Watson et al. 2016). Despite the development and implementation of a wide range of beneficial management practices (BMPs) to reduce P export, little or no significant improvement in water quality has been reported for some of the world’s largest freshwater resources including the Great Lakes of North America (Schindler et al. 2012; Sharpley et al. 2015; Watson et al. 2016). Lack of progress in reducing diffuse P pollution could be, in part, associated with inappropriate placement or selection of BMPs within agricultural watersheds, the lag time in water quality response to BMPs, climate variability, and inadequate P management regulations or landowners’ commitment (Sharpley et al. 2013).

Past research has shown disproportionate losses of P from certain areas of a watershed known as critical source areas (CSAs) where large P sources could coincide with hydrological flows across small portions of the watershed (Ghebremichael et al. 2010; Li et al. 2017). For example, Ghebremichael et al. (2010) found that 80% of the total P loss from the Rock River watershed in Vermont, USA is generated from only 24% of the watershed area. Identifying such CSAs or “hotspots” in a watershed by P loss assessment tools is essential for optimal placement of BMPs to address P pollution that can lead to eutrophication (Kleinman et al. 2011a).

Several approaches ranging from simple, easy-to-use P indices (e.g., the Pennsylvania P index (Weld et al. 2002); the Kentucky P index (Bolster 2011)) to complex process-based models (e.g., the soil and water assessment tool (SWAT) (Arnold et al. 1998); the annualized agricultural non-point source pollution (AnnAGNPS) (Bosch et al. 1998)) have been developed assuming runoff is generated primarily through rainfall-runoff events, as is the case in most warm temperate climates, but these tools have also been used in cold climates. The term “cold climates” used throughout this paper refers to the regions with prolonged periods of average daily temperatures below zero degrees Celsius during winter where a greater proportion of runoff is generated during snowmelt than rainfall events (e.g., Northern US states, Canada, Northern Europe). However, the lack of evidence for downstream water quality improvement where P loss assessment tools have been used to place BMPs leads us to consider whether or not these tools have failed to accurately delineate CSAs.

Failure to accurately identify CSAs could be associated with inability of P loss assessment tools to fully account for the hydrological and biogeochemical processes responsible for P loss, particularly in cold climates. Phosphorus loss assessment tools have been modified and extensively used worldwide to simulate P loss from the landscape (e.g., Beaulieu et al. 2006; Bechmann et al. 2007; Collick et al. 2016; Das et al. 2008; Easton et al. 2008; Li et al. 2015; Li et al. 2017; Niraula et al. 2013; Reid 2011), and efforts have been made to revise some of the empirically based equations and/or their underlying assumptions (e.g., Collick et al. 2016; Bolster and Vadas 2018; Mekonnen et al. 2017; Vadas and White 2010; Vadas et al. 2013). However, there is little information in the literature on the effectiveness of P loss assessment tools for simulating P loss during snowmelt runoff events; neither is there any thorough review regarding applicability of the underlying concepts of P loss assessment tools in cold climates. This manuscript (i) reviews the strengths and weaknesses of current P loss assessment tools and their underlying concepts in delineating CSAs of agricultural watersheds, and (ii) highlights a number of challenges associated with modeling P transfer from agricultural land to surface waters in cold climates. The manuscript was structured to describe how soil P dynamics and runoff contributing areas are simulated by P loss assessment tools in agricultural watersheds.

Simulating soil P dynamics in agricultural watersheds by P loss assessment tools

Process-based P loss assessment tools

Commonly used process–based tools, such as SWAT and AnnAGNPS, use the conceptual P model of Jones et al. (1984), which was originally developed for the erosion productivity impact calculator (EPIC) model (Williams et al. 1984) to simulate the processes responsible for soil P dynamics. Jones et al. (1984) conceptualized P cycling in soils by dividing soil total P into the inorganic (labile, active, and stable) and organic (fresh and stable/humic) P pools. However, these P routines and their underlying assumptions may not be applicable beyond a narrow range of soils, climates, and nutrient management practices (Vadas and White 2010; Vadas et al. 2013; Bolster and Vadas 2018).

For example, according to Jones et al. (1984) the stable inorganic P pool is initialized from the active P and is thought to be fourfold of the size of active P pool. However, the validity of this assumption for many soils has been recently challenged by Bolster and Vadas (2018). Research by Yuan et al. (2005) showed that the AnnAGNPS model failed to simulate dissolved P loss from a watershed in the USA, and concluded that this was likely due to simplistic assumptions made by Jones et al. (1984) regarding soil P processes. The original P routines of Jones et al. (1984) are based on inorganic P addition to soil over 6-month incubation studies (Sharpley et al. 1984, 1989), which cannot accurately simulate incidental P losses (water extractable P) and/or P dynamics associated with land application of manure/biosolids (Vadas et al. 2005; Collick et al. 2016). Collick et al. (2016) revised P routines of SWAT to consider P loss associated with application of manure to soil surface, but the revisions are not part of the publicly available version of SWAT and similar revisions for other process-based tools (e.g., AnnAGNPS) are still required.

An important parameter used in P routines of process-based tools to initialize soil P pools is P sorption capacity parameter (PSP) which represents the mass of P in soil solution once a relative equilibrium between solution P and active P pools is established. Sharpley et al. (1984, 1989) proposed equations to determine PSP based on physicochemical properties of soils that were subjected to three drying-wetting cycles over 6-month incubation studies. However, Vadas and White (2010) reported underestimation of soil total P pool by SWAT, partly due to overestimation of PSP values by equations proposed by Sharpley et al. (1984, 1989). Furthermore, unlike AnnAGNPS that calculates daily PSP values based on soil properties, SWAT and EPIC use a constant PSP value during the entire model simulation which may inaccurately predict soil P pools, particularly labile P pool (Vadas et al. 2013). Using accurate PSP of the soils is essential to predict the risk of P loss by these tools.

This highlights the crucial need for updating P routines of the process-based tools, and PSP values in particular, to accurately simulate soil P dynamics in agricultural watersheds. A significant research gap is a lack of effort to examine P routines of the Jones et al. (1984) and the underlying assumptions for cold climates. Importantly, in the method proposed by Sharpley et al. (1984, 1989) for determining PSP of USA soils, the soils were subjected only to three drying-wetting cycles during 6-month incubation studies. Consequently, the resulting PSP values could be invalid for soils in cold climates that undergo several freezing-thawing cycles, in addition to drying-rewetting cycles.

Hypothetically, soil P processes in cold climates are different from those processes in more temperate climates because in cold climates the soils often experience substantial abiotic perturbations. Frequent abiotic perturbations can potentially affect physical and biological properties of the soils, and consequently the mass of P loss in runoff (Blackwell et al. 2010; Vaz et al. 1994; Wall et al. 1988). During freezing, for example, water in soil pores requires more space as it expands to form ice crystals. This would apply pressure on soil pore walls resulting in disruption of soil aggregates, increased soil erodibility, and subsequent particulate P loss to runoff (Lehrsch et al. 1991; Wall et al. 1988). Freezing-thawing and/or drying-rewetting cycles can solubilize P from the soil microbial biomass through bacterial cell lysis, thereby increasing dissolved P loss to runoff (Blackwell et al. 2010). Furthermore, research has also shown that freezing-thawing cycles can significantly increase P release from plant residues depending on the freezing intensity, plant type, the moisture content of plant residue, the number of freeze-thaw cycles, and the level of interactions between soil and plant residue (Cober et al. 2018, 2019; Bechmann et al. 2005; Elliott 2013). Considering the effect of freezing-thawing cycles on partitioning between soil P pools and P movement through the landscape is of great importance.

Empirical P loss assessment tools

Unlike process-based tools, empirical P loss assessment tools (i.e., P indices) do not attempt to model soil P dynamics to predict P loss in runoff. These tools are simplified to operate with a limited number of input parameters, so that they can practically be used by landowners or consultants rather than researchers and represent the annual risk of P loss rather than a calculated amount for each runoff event. Several P indices estimate the inherent risk of dissolved P losses from a field by multiplying agronomic soil P test value (e.g., Olsen extractable P concentration) by an extraction coefficient and runoff potential. Particulate P loss is also determined by multiplying the quantity of soil loss by mean P concentration in sediments (e.g., Reid 2011). Thus, the annual risk of P loss predicted by P indices largely depends on P concentration in soil/sediments.

The dynamic soil/sediment P status at CSAs is the balance of the amount of P applied to these areas, the mass of P removed by runoff and/or vegetation, and the mass of P deposited in these areas by runoff from upslope (Page et al. 2005). However, P indices ignore variations in soil P status with season and abiotic perturbations because they rely on a single P concentration value of soil/sediment. In cold climates for example, the potential of P loss to runoff from frozen/partially frozen soils during winter or early spring is assumed to be the same as P loss from soils to runoff in summer/fall, even though it may not be due to seasonal differences in soil microbial activity as well as the level of interactions between applied fertilizer/manure and soil. Since the time scale of P indices is annual, using a single P extraction coefficient may be adequate to predict the potential of P loss to runoff. However, if this coefficient is derived from growing season conditions and is actually quite different under winter conditions, the accuracy of this coefficient is called into question.

Phosphorus indices generally consider inherent and applied soil P sources separately to describe soil P dynamics and to identify areas with greater risk of P loss (e.g., Weld et al. 2002; Andersen and Kronvang 2006; Reid 2011). This separation approach to some extent overlooks the interaction between these sources and assumes applied P (manure and/or fertilizer) as a large P source with a short-term impact on water quality compared with inherent soil P which could be a small P source but with a continuous, long-term impact on downstream water quality (Kleinman et al. 2011a, b).

Simulating runoff contributing areas to P loss by P loss assessment tools

Understanding hydrological processes governing runoff generation and movement within agricultural watersheds is critical for identifying CSAs. However, identifying the location of runoff generating areas in agricultural watersheds and their hydrological connections to surface waters is very challenging. Table 1 presents some of the P loss assessment tools and their approach for predicting runoff contributing areas and hydrological connectivity to surface waters. Since there is an overlap between some of the empirical and process-based P loss assessment tools in their approach for predicting runoff contributing areas, both of these tools were discussed in this section. The following sections describe various approaches used by current P loss assessment tools to predict runoff contributing areas of an agricultural watershed.

Table 1 Some of the P loss assessment tools and their approach for simulating runoff contributing areas to P loss in various climates

Proximity to surface water approach

Many empirical P loss assessment tools rely on a predetermined distance from surface water as runoff contributing areas to P loss during rainfall or snowmelt events. This is associated with the general assumption and informal field observations that areas close to surface waters have a higher potential for P loss (e.g., Gburek et al. 2000; Sharpley et al. 2003b; Andersen and Kronvang 2006; Williams et al. 2017). For example, the Ontario P index assumes that runoff contributing areas of a field are limited to areas located within 50 and 150 m from surface water during growing and non-growing season, respectively (Reid 2011). This simplistic assumption regarding runoff contributing areas overlooks the effects of topography, event type (rainfall vs. snowmelt) and subsurface drainage on runoff generation, channelization, and hydrological connectivity of surface runoff (Thomas et al. 2016). For example, topography can aggregate diffuse shallow flows into concentrated flows leading to runoff with a high flow rate that can transfer P from a longer distance within a field from the surface water (Reid 2011; Habibiandehkordi et al. 2017). In cold climates, the majority of runoff and P loss generally occurs during spring-snowmelt events (e.g., Hansen et al. 2000; Glozier et al. 2006; Little et al. 2007) when the land is still frozen and soil infiltration is minimal. Our informal field observations in Manitoba and Ontario, Canada show that snowmelt runoff can be initiated from areas well beyond 150 m from surface waters. The proximity to surface water approach is also questionable where artificial drainage system or tile drains are present as these features can facilitate subsurface P transfer to water bodies from a greater distance from surface water (Reid et al. 2012).

Topographic index approach

Past research has shown strong relationships between saturation-excess runoff contributing areas of a watershed and soil moisture patterns (e.g., Walter et al. 2000; Cheng et al. 2014). The topographic index (TI) proposed by Kirkby (1975) is widely used to predict such areas within a watershed with potential of saturation-excess runoff by taking into account the relationship between the upslope contributing area (α), and the local surface slope angle (β) as ln(α/tan β) (Beven 2001; Endreny and Wood 2003). Endreny and Wood (2003) used the topographic index (TI) to identify CSAs of P loss in the New York’s West Branch River watershed. However, the steady state assumption of TI does not address variations in the size of runoff contributing areas by season. The assumption also ignores the presence of artificial tile drains and/or bedrock topography that can alter saturation-excess runoff contributing areas (Beven 1997; Page et al. 2005; Freer et al. 2002).

Buchanan et al. (2013) proposed the travel-time P index (TTPI) that also relies on TI approach to determine saturation-excess runoff areas, but it considers hydrological connectivity based on the runoff travel time (Table 1). The travel-time between each saturation-excess runoff generating area and a receiving stream is determined from the depth of overland flow and the downslope flow conditions (Buchanan et al. 2013). However, both TI and TTPI values vary with digital elevation model (DEM) resolution (Quinn et al. 1991, 1995; Valeo and Moin 2000), and high-resolution DEM may not be available for many regions.

The TI approach also ignores the potential of P transfer from CSAs to surface waters through infiltration-excess runoff process, although this process can occur frequently in cold climates. In cold climates, soil infiltration is minimal when the ground is frozen in winter, thereby infiltration-excess runoff could occur even under medium intensity rainfall events. Despite recent efforts to optimize formulation of TI, for example by using a fine resolution (3 m) DEM and the multiple triangular slope algorithm to compute slope, the TI approach at its very best appeared to be capable of explaining only 60% of soil moisture patterns (i.e., saturation-excess runoff contributing areas) of agricultural landscapes in south-central New York, USA. where saturation-excess is the dominant runoff process (Buchanan et al. 2014).

Curve Number and Green and Ampt approaches

Several process-based P loss assessment tools such as SWAT, the generalized watershed loading function (GWLF) model (Haith and Shoemaker 1987), and AnnAGNPS use the Natural Resources Conservation Service’s Curve Number (CN) (USDA-SCS 1972) or Green and Ampt (Green and Ampt 1911) equations to predict runoff contributing areas, assuming that runoff is generated only through infiltration-excess process (Table 1).

Consequently, these tools are unable to capture runoff contributing areas where saturation-excess is the dominant runoff generating process. For example, runoff generated from shallow permeable soils above a restricting layer and runoff over frozen/partially frozen soils are not well quantified using these models (Agnew et al. 2006; Easton et al. 2008). Effort has been made to reconceptualize the GWLF and SWAT models to account for the areas with potential of saturation-excess runoff (Easton et al. 2008; Schneiderman et al. 2007). For example, the modified version of SWAT known as the SWAT-VSA appears to be promising in representing the timing, quantity, and spatial distribution of surface runoff contributing areas compared with the traditional SWAT model (Collick et al. 2015; Easton et al. 2008), but its performance yet to be evaluated in cold climates.

Considering hydrological connectivity by P loss assessment tools

Currently, neither empirical nor process-based P loss assessment tools can reliably consider hydrological connectivity between the landscape and surface water during runoff events. As mentioned earlier, empirical tools only consider areas close to streams/rivers as hydrologically connected areas to surface waters. The process-based tools assume that hydrologic response units (HRUs) or grid cells contribute equally to runoff generation and P loss and are not capable of simulating hydrological connectivity between discrete units of the landscape (Gassman et al. 2007). Generally, hydrological connectivity refers to the transfer of water from one part of the landscape to another that can lead to some watershed runoff response (Bracken and Croke 2007). This hydrological connectivity definition does not consider the physical and biogeochemical processes affecting the fate of P being transferred across hydrologically connected landscapes (Oldham et al. 2013). Therefore, we adopted and modified the "material connectivity" definition of Oldham et al. (2013) to a definition of material-P connectivity as the ability of P to transfer between landscape and receiving waters while subject to physical and biogeochemical processing. Although significant research has been undertaken to identify CSAs of P loss in agricultural watersheds over decades, our knowledge about material-P connectivity, particularly in cold climates is still in its infancy.

Understanding how material-P connectivity between landscape positions and surface waters develops and changes over time would ultimately lead to improving P loss assessment tools for accurately predicting CSAs in cold climates. In the Canadian prairies, for example, the presence of a large number of landscape depressions known as “prairie potholes” resulted from the glacial recession can significantly affect runoff generation and material-P connectivity (Casson et al. 2019; Hayashi et al. 2003; Wilson et al. 2019). Prairie potholes can intercept surface runoff, promote infiltration and deposition of particulate P, and provide an opportunity for biogeochemical removal from or release of P to surface runoff. During rainfall or snowmelt events, prairie potholes can be connected to drainage networks through fill-and-spill process (Leibowitz et al. 2016), and material-P connectivity between landscape and surface water may occur. The balance between the rate of P transport into the potholes, the rate of particulate P deposition, and the rate of P removal or release to surface runoff through biogeochemical processes (e.g., sorption to soil, reductive-dissolution of Al/Fe/Ca/Mg-bound P under reduced condition) will determine the material-P connectivity between the landscape and surface water. Mekonnen et al. (2016) developed a new version of SWAT, known as SWAT with probability distributed landscape depression (SWAT-PDLD), which is capable of simulating runoff in landscapes with numerous landscape depressions. However, neither the SWAT-PDLD nor other P loss assessment tools consider P retention or remobilization within landscape depressions.

An important step to develop a working model of material-P connectivity is explicitly identifying runoff contributing areas under seasonally varying weather conditions. Electrical resistance sensors appear to be a promising tool for recording the time of runoff initiation, identifying surface runoff contributing areas, and their connections to surface waters (Masselink et al. 2017; Moody and Martin 2015). High-resolution soil moisture measurements along with runoff and stream water chemistry analyses during rainfall and/or snowmelt events may reveal how hydrological connectivity affects nutrients export from land to water bodies (Ocampo et al. 2006; Stieglitz et al. 2003). Research has shown that the lack of hydrological connectivity between landscape components can lead to deposition of P-enriched sediments at specific locations within an agricultural field where they can be further transferred to surface waters by subsequent runoff events (Buda et al. 2009). Therefore, frequent and detailed soil sampling, as an indirect evidence, could reveal information for modeling purposes regarding material-P connectivity for the specific climate, soil, and topographical conditions.

Summary and further research needs

Accurate identification of CSAs in agricultural watersheds using P loss assessment tools is needed to ensure cost-effective implementation of BMPs to reduce the risk of P transfer from land to water bodies. Current P management strategies in cold climates rely on the output of P loss assessment tools which may not fully represent hydrological and biogeochemical processes responsible for P loss in these regions. The concepts discussed in this paper should be used as a starting point for the modification and reconceptualization of P loss assessment tools for accurately identifying CSAs in cold climates.

Like many P indices, process-based P loss assessment tools also appear to have limited ability in accurately predicting P loss from the landscape, particularly in cold climates where runoff is mainly driven by snowmelt. This could be, in part, associated with the snowmelt hydrology component of these tools which cannot fully consider runoff over frozen land, intermittent snow melting process (i.e., when snow melts due to short-term warm temperature and refreezes before runoff reaches to surface water), and infiltration into partially frozen soils (see for example, Wang and Melesse 2005; Das et al. 2008; Lévesque et al. 2008). Improving the snowmelt hydrology component of process-based tools is necessary to accurately predict P loss from the landscape in cold climates.

There is lack of information in the literature on the ability of P routines of process-based tools to accurately initialize the quantity of soil P pools in cold climates; neither is there any attempt to update the equations used to estimate PSP values from soil properties in cold climates. In cold climates, the soils undergo several freezing-thawing and drying-rewetting cycles which could affect the quantity of soil P pools and subsequently the potential of P loss to runoff. Further research is needed to understand the quantity of soil P pools and the interactions between soil P biomass and P concentration in runoff for soils that experience substantial abiotic stresses.

There is a crucial need for developing P loss assessment tools capable of considering the magnitude, duration, and frequency of material-P connectivity between the landscape and surface waters under different conditions of topography, soil texture and chemistry, and management in cold climates. To develop such P loss assessment tools, techniques should be used to identify and quantify parts of the landscape that generate both surface and subsurface runoff under seasonally varying weather conditions. Furthermore, P loss assessment tools need to be improved to consider P retention or remobilizations as runoff moves through the landscape during rainfall and snowmelt runoff events.

Finally, while the process-based P loss assessment tools may better describe runoff and P loss from the landscape compared with empirical tools, they are complex and require a wide range of inputs that may not be readily available. Further, complex tools do not necessarily provide better information regarding runoff and P loss than simple P index approaches under diverse soil, climate and topography. Recent findings in the USA show that many P indices could provide information comparable with the complex, data-intensive process-based models (Osmond et al. 2017) which could be also the case in cold climates. This may be associated with the lack of frequent water quality data for model calibration. Such uncertainties associated with model parameters can result in equifinality, where combinations of input parameters by different models may lead to equally good fit to observations (Beven 2006). Regardless, evaluating P loss assessment tools with water quality monitoring data is crucial to assess whether changes in the structure and formulations of these tools result in improved delineation of CSAs in cold climates.



Beneficial management practices


Critical source areas




  1. Agnew LJ, Lyon S, Gérard-Marchant P, Collins VB, Lembo AJ, Steenhuis TS, Walter MT (2006) Identifying hydrologically sensitive areas: bridging the gap between science and application. J Environ Manag 78(1):63–76

  2. Andersen HE, Kronvang B (2006) Modifying and evaluating a P index for Denmark. Water Air Soil Pollut 174(1-4):341–353

  3. Arnold JG, Srinivasan R, Muttiah RS, Williams JR (1998) Large area hydrologic modeling and assessment part I: model development. JAWRA J Am Water Resour Assoc 34(1):73–89

  4. Beven K (1997) TOPMODEL: a critique. Hydrol Process 11(9):1069–1085

  5. Beven KJ (2001) Rainfall-runoff modelling- the primer. Wiley, Chichester, UK

  6. Beaulieu L, Gallichand J, Duchemin M, Parent LE (2006) Sensitivity analysis of a phosphorus index for Quebec. Can Biosyst Eng 48:1

  7. Bechmann ME, Kleinman PJ, Sharpley AN, Saporito LS (2005) Freeze–thaw effects on phosphorus loss in runoff from manured and catch-cropped soils. J Environ Qual 34(6):2301–2309

  8. Bechmann ME, Stålnacke P, Kværnø SH (2007) Testing the Norwegian phosphorus index at the field and subcatchment scale. Agric Ecosyst Environ 120(2-4):117–128

  9. Beven K (2006) A manifesto for the equifinality thesis. J Hydrol 320(1-2):18–36

  10. Blackwell MSA, Brookes PC, de La Fuente-Martinez N, Gordon H, Murray PJ, Snars KE, Williams JK, Bol R, Haygarth PM (2010) Phosphorus solubilization and potential transfer to surface waters from the soil microbial biomass following drying–rewetting and freezing–thawing. Adv Agron 106:1–35

  11. Bolster CH (2011) A critical evaluation of the Kentucky phosphorus index. J Kentucky Acad Sci 72(1):46–59

  12. Bolster CH, Vadas PA (2018) Comparison of two methods for calculating the P sorption capacity parameter in soils. Soil Sci Soc Am J 82(2):493–501

  13. Bosch DD, Theurer FD, Bingner RL, Felton G, Chaubey I (1998) Evaluation of the AnnAGNPS water quality model. ASAE Paper No. 98–2195.

  14. Bracken LJ, Croke J (2007) The concept of hydrological connectivity and its contribution to understanding runoff-dominated geomorphic systems. Hydrol Process 21(13):1749–1763

  15. Buchanan BP, Archibald JA, Easton ZM, Shaw SB, Schneider RL, Walter MT (2013) A phosphorus index that combines critical source areas and transport pathways using a travel time approach. J Hydrol 486:123–135

  16. Buchanan BP, Fleming M, Schneider RL, Richards BK, Archibald J, Qiu Z, Walter MT (2014) Evaluating topographic wetness indices across central New York agricultural landscapes. Hydrol Earth Syst Sci 18(8):3279–3299

  17. Buda AR, Kleinman PJ, Srinivasan MS, Bryant RB, Feyereisen G. W (2009) Effects of hydrology and field management on phosphorus transport in surface runoff. J Environ Qual 38(6):2273-2284

  18. Casson NJ, Wilson HF, Higgins SM (2019) Hydrological and seasonal controls of phosphorus in Northern Great Plains agricultural streams. J Environ Qual 48:978–987

  19. Cheng X, Shaw SB, Marjerison RD, Yearick CD, DeGloria SD, Walter MT (2014) Improving risk estimates of runoff producing areas: formulating variable source areas as a bivariate process. J Environ Manag 137:146–156

  20. Cober JR, Macrae ML, Van Eerd LL (2018) Nutrient release from living and terminated cover crops under variable freeze–thaw cycles. Agron J 110(3):1036–1045

  21. Cober JR, Macrae ML, Van Eerd LL (2019) Winter phosphorus release from cover crops and linkages with runoff chemistry. J Environ Qual 48:907–914

  22. Collick AS, Fuka DR, Kleinman PJ, Buda AR, Weld JL, White MJ, Veith TL, Bryant RB, Bolster CH, Easton ZM (2015) Predicting phosphorus dynamics in complex terrains using a variable source area hydrology model. Hydrol Process 29(4):588–601

  23. Collick AS, Veith TL, Fuka DR, Kleinman PJ, Buda AR, Weld JL, Bryant RB, Vadas PA, White MJ, Harmel RD, Easton ZM (2016) Improved simulation of edaphic and manure phosphorus loss in SWAT. J Environ Qual 45(4):1215–1225

  24. Das S, Rudra RP, Gharabaghi B, Gebremeskel S, Goel PK, Dickinson WT (2008) Applicability of AnnAGNPS for Ontario conditions. Can Biosyst Eng 50

  25. Easton ZM, Fuka DR, Walter MT, Cowan DM, Schneiderman EM, Steenhuis TS (2008) Re-conceptualizing the soil and water assessment tool (SWAT) model to predict runoff from variable source areas. J Hydrol 348(3-4):279–291

  26. Elliott J (2013) Evaluating the potential contribution of vegetation as a nutrient source in snowmelt runoff. Can J Soil Sci 93(4):435–443

  27. Endreny TA, Wood EF (2003) Watershed weighting of export coefficients to map critical phosphorous loading areas. JAWRA J Am Water Resour Assoc 39(1):165–181

  28. Freer J, McDonnell JJ, Beven KJ, Peters NE, Burns DA, Hooper RP, Aulenbach B, Kendall C (2002) The role of bedrock topography on subsurface storm flow. Water Resour Res 38(12):5–1

  29. Gassman PW, Reyes MR, Green CH, Arnold JG (2007) The soil and water assessment tool: historical development, applications, and future research directions. Trans ASABE 50(4):1211–1250

  30. Gburek WJ, Sharpley AN, Heathwaite L, Folmar GJ (2000) Phosphorus management at the watershed scale: a modification of the phosphorus index. J Environ Qual 29(1):130–144

  31. Ghebremichael LT, Veith TL, Watzin MC (2010) Determination of critical source areas for phosphorus loss: Lake Champlain basin, Vermont. Trans ASABE 53(5):1595–1604

  32. Glozier NE, Elliott JA, Holliday B, Yarotski J, Harker B (2006) Water quality characteristics and trends in a small agricultural watershed: South Tobacco Creek, Manitoba, 1992–2001. Environment Canada, Ottawa, ON

  33. Green WH, Ampt GA (1911) Studies on soil physics, 1.The flow of air and water through soils. J Agric Sci 4(1):11–24

  34. Habibiandehkordi R, Lobb DA, Sheppard SC, Flaten DN, Owens PN (2017) Uncertainties in vegetated buffer strip function in controlling phosphorus export from agricultural land in the Canadian prairies. Environ Sci Pollut Res 24(22):18372–18382

  35. Haith DA, Shoemaker LL (1987) Generalized watershed loading functions for stream flow nutrients. JAWRA J Am Water Resour Assoc 23(3):471–478

  36. Hansen NC, Gupta SC, Moncrief JF (2000) Snowmelt runoff, sediment, and phosphorus losses under three different tillage systems. Soil Tillage Res 57(1-2):93–100

  37. Hayashi M, van der Kamp G, Schmidt R (2003) Focused infiltration of snowmelt water in partially frozen soil under small depressions. J Hydrol 270(3-4):214–229

  38. Jones CA, Cole CV, Sharpley AN, Williams JR (1984) A simplified soil and plant phosphorus model: I. Documentation 1. Soil Sci Soc Am J 48(4):800–805

  39. Kirkby MJ (1975) Hydrograph modeling strategies. In: Peel R, Chisholm M, Haggett P (eds) Progress in human and physical geography. Heinemann, London, pp 69–90

  40. Kleinman P, Sharpley A, Buda A, McDowell R, Allen A (2011a) Soil controls of phosphorus in runoff: management barriers and opportunities. Can J Soil Sci 91(3):329–338

  41. Kleinman PJ, Sharpley AN, McDowell RW, Flaten DN, Buda AR, Tao L, Bergstrom L, Zhu Q (2011b) Managing agricultural phosphorus for water quality protection: principles for progress. Plant Soil 349(1-2):169–182

  42. Lehrsch GA, Sojka RE, Carter DL, Jolley PM (1991) Freezing effects on aggregate stability affected by texture, mineralogy, and organic matter. Soil Sci Soc Am J 55(5):1401–1406

  43. Leibowitz SG, Mushet DM, Newton WE (2016) Intermittent surface water connectivity: fill and spill vs. fill and merge dynamics. Wetlands 36(2):323–342

  44. Levesque E, Anctil F, Van Griensven ANN, Beauchamp N (2008) Evaluation of streamflow simulation by SWAT model for two small watersheds under snowmelt and rainfall. Hydrol Sci J 53(5):961–976

  45. Li Z, Luo C, Xi Q, Li H, Pan J, Zhou Q, Xiong Z (2015) Assessment of the AnnAGNPS model in simulating runoff and nutrients in a typical small watershed in the Taihu Lake basin, China. Catena 133:349–361

  46. Li S, Zhang L, Liu H, Loáiciga HA, Zhai L, Zhuang Y, Lei Q, Hu W, Li W, Feng Q, Du Y (2017) Evaluating the risk of phosphorus loss with a distributed watershed model featuring zero-order mobilization and first-order delivery. Sci Total Environ 609:563–576

  47. Little JL, Nolan SC, Casson JP, Olson BM (2007) Relationships between soil and runoff phosphorus in small Alberta watersheds. J Environ Qual 36(5):1289–1300

  48. Masselink RJ, Heckmann T, Temme AJ, Anders NS, Gooren H, Keesstra SD (2017) A network theory approach for a better understanding of overland flow connectivity. Hydrol Process 31(1):207–220

  49. Mekonnen BA, Mazurek KA, Putz G (2016) Incorporating landscape depression heterogeneity into the soil and water assessment tool (SWAT) using a probability distribution. Hydrol Process 30(13):2373–2389

  50. Mekonnen BA, Mazurek KA, Putz G (2017) Modeling of nutrient export and effects of management practices in a cold-climate prairie watershed: Assiniboine River watershed, Canada. Agric. Water Manage 180:235–251

  51. Moody JA, Martin RG (2015) Measurements of the initiation of post-wildfire runoff during rainstorms using in situ overland flow detectors. Earth Surf Process Landf 40(8):1043–1056

  52. Niraula R, Kalin L, Srivastava P, Anderson CJ (2013) Identifying critical source areas of nonpoint source pollution with SWAT and GWLF. Ecol Model 268:123–133

  53. Ocampo CJ, Sivapalan M, Oldham C (2006) Hydrological connectivity of upland-riparian zones in agricultural watersheds: implications for runoff generation and nitrate transport. J Hydrol 331(3-4):643–658

  54. Oldham CE, Farrow DE, Peiffer S (2013) A generalized Damkohler number for classifying material processing in hydrological systems. Hydrol Earth Syst Sci 17(3):1133–1148

  55. Osmond D, Bolster C, Sharpley A, Cabrera M, Feagley S, Forsberg A, Mitchell C, Mylavarapu R, Oldham JL, Radcliffe DE, Ramirez-Avila JJ, Storm DE, Walker F, Zhang H (2017) Southern Phosphorus Indices, water quality data, and modeling (APEX, APLE, and TBET) results: a comparison. J Environ Qual 46(6):1296–1305

  56. Page T, Haygarth PM, Beven KJ, Joynes A, Butler T, Keeler C, Freer J, Owens PN, Wood GA (2005) Spatial variability of soil phosphorus in relation to the topographic index and critical source areas. J Environ Qual 34(6):2263–2277

  57. Quinn PFBJ, Beven K, Chevallier P, Planchon O (1991) The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models. Hydrol Process 5(1):59–79

  58. Quinn PF, Beven KJ, Lamb R (1995) The in (a/tan/β) index: How to calculate it and how to use it within the topmodel framework. Hydrol Process 9(2):161–182

  59. Reid DK (2011) A modified Ontario P index as a tool for on-farm phosphorus management. Can J Soil Sci 91(3):455–466

  60. Reid DK, Ball B, Zhang TQ (2012) Accounting for the risks of phosphorus losses through tile drains in a phosphorus index. J Environ Qual 41(6):1720–1729

  61. Schindler DW, Hecky RE, McCullough GK (2012) The rapid eutrophication of Lake Winnipeg: greening under global change. J Great Lakes Res 38:6–13

  62. Schneiderman EM, Steenhuis TS, Thongs DJ, Easton ZM, Zion MS, Neal AL, Neal AL, Mendoza GF, Todd Walter M (2007) Incorporating variable source area hydrology into a curve-number-based watershed model. Hydrol Process 21(25):3420–3430

  63. Sharpley AN, Jones CA, Gray C, Cole CV (1984) A simplified soil and plant phosphorus model: II. Prediction of labile, organic, and sorbed phosphorus1. Soil Sci Soc Am J 48(4):805–809

  64. Sharpley AN, Singh U, Uehara G, Kimble J (1989) Modeling soil and plant phosphorus dynamics in calcareous and highly weathered soils. Soil Sci Soc Am J 53(1):153–158

  65. Sharpley AN, Daniel T, Sims T, Lemunyon J, Stevens R, Parry R (2003a) Agricultural phosphorus and eutrophication, 2nd ed. U.S. Department of Agriculture, Agricultural Research Service, ARS–149, 44 pp.

  66. Sharpley AN, Weld JL, Beegle DB, Kleinman PJ, Gburek WJ, Moore PA, Mullins G (2003b) Development of phosphorus indices for nutrient management planning strategies in the United States. J Soil Water Conserv 58(3):137–152

  67. Sharpley A, Jarvie HP, Buda A, May L, Spears B, Kleinman P (2013) Phosphorus legacy: overcoming the effects of past management practices to mitigate future water quality impairment. J Environ Qual 42(5):1308–1326

  68. Sharpley AN, Bergström L, Aronsson H, Bechmann M, Bolster CH, Börling K, Djodjic F, Jarvie HP, Schoumans OF, Stamm C, Tonderski KS, Ule´n B, Uusitalo R, Withers PJA (2015) Future agriculture with minimized phosphorus losses to waters: research needs and direction. Ambio 44(2):163-179

  69. Smith VH, Schindler DW (2009) Eutrophication science: where do we go from here? Trends Ecol Evol 24(4):201–207

  70. Stieglitz M, Shaman J, McNamara J, Engel V, Shanley J, Kling GW (2003) An approach to understanding hydrologic connectivity on the hillslope and the implications for nutrient transport. Glob Biogeochem Cycles 17(4)

  71. Thomas IA, Mellander PE, Murphy PNC, Fenton O, Shine O, Djodjic F, Dunlop P, Jordan P (2016) A sub-field scale critical source area index for legacy phosphorus management using high resolution data. Agric Ecosyst Environ 233:238–252

  72. USDA-SCS (Soil Conservation Service) (1972) National engineering handbook, Part 630 Hydrology, Section 4, Chapter 10

  73. Vadas PA, Haggard BE, Gburek WJ (2005) Predicting dissolved phosphorus in runoff from manured field plots. J Environ Qual 34(4):1347–1353

  74. Vadas PA, White MJ (2010) Validating soil phosphorus routines in the SWAT model. Trans ASABE 53(5):1469–1476

  75. Vadas PA, Bolster CH, Good LW (2013) Critical evaluation of models used to study agricultural phosphorus and water quality. Soil Use Manag 29(s1):36–44

  76. Valeo C, Moin SMA (2000) Grid-resolution effects on a model for integrating urban and rural areas. Hydrol Process 14(14):2505–2525

  77. Vaz MR, Edwards AC, Shand CA, Cresser MS (1994) Changes in the chemistry of soil solution and acetic-acid extractable P following different types of freeze/thaw episodes. Eur J Soil Sci 45(3):353–359

  78. Wall GJ, Dickinson WT, Rudra RP, Coote DR (1988) Seasonal soil erodibility variation in southwestern Ontario. Can J Soil Sci 68(2):417–424

  79. Walter MT, Walter MF, Brooks ES, Steenhuis TS, Boll J, Weiler K (2000) Hydrologically sensitive areas: Variable source area hydrology implications for water quality risk assessment. J Soil Water Conserv 55(3):277–284

  80. Wang X, Melesse AM (2005) Evaluation of the swat models snowmelt hydrology in a northwestern minnesota watershed. Transactions of the ASAE 48 (4):1359–1376

  81. Watson SB, Miller C, Arhonditsis G, Boyer GL, Carmichael W, Charlton MN, Confesor R, Depew DC, Ho¨o¨k TO, Ludsin SA, Matisoff G, SP ME, Murray MW, Richards RP, Rao YR, Steffen MM, Wilhelm SW (2016) The re-eutrophication of Lake Erie: Harmful algal blooms and hypoxia. Harmful Algae 56:44–66

  82. Weld JL, Parsons RL, Beegle DB, Sharpley AN, Gburek WJ, Clouser WR (2002) Evaluation of phosphorus-based nutrient management strategies in Pennsylvania. J Soil Water Conserv 57(6):448–454

  83. Williams JR, Jones CA, Dyke PT (1984) The EPIC model and its application. In: Proc. Int. Symp. on minimum data sets for agrotechnology transfer, March 21– 26, 1983. ICRISAT Center, India.

  84. Williams MR, King KW, LaBarge GA, Confesor RB, Fausey NR (2017) Edge-of-field evaluation of the Ohio phosphorus risk index. J Environ Qual 46(6):1306–1313

  85. Wilson HF, Casson NJ, Glenn AJ, Badiou P, Boychuk L (2019) Landscape controls on nutrient export during snowmelt and an extreme rainfall runoff event in northern agricultural watersheds. J Environ Qual 48:841–849

  86. Yuan Y, Bingner RL, Theurer FD, Rebich RA, Moore PA (2005) Phosphorus component in AnnAGNPS. Trans ASAE 48(6):2145–2154

Download references


The authors would like to thank the Ministry of the Environment, Conservation and Parks of Ontario for financial support of the manuscript.

Author information

Correspondence to Reza Habibiandehkordi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible editor: Philippe Garrigues

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Habibiandehkordi, R., Reid, D.K., Goel, P.K. et al. Phosphorus loss assessment tools: a review of underlying concepts and applicability in cold climates. Environ Sci Pollut Res 27, 3794–3802 (2020).

Download citation


  • Cold climates
  • Critical source areas
  • Phosphorus loss assessment tools
  • Runoff
  • Water quality