277 12 Modeling Phosphorus with the Generalized Watershed Loading Functions (GWLF) Model Elliot M. Schneiderman New York City Department of Environmental Protection, Kingston, NY CONTENTS 12.1 History of Model Development 277 12.2 Spatial and Temporal Resolution 279 12.3 Predicting Infiltration and Runoff 279 12.4 Predicting Phosphorus in Runoff 284 12.5 Predicting Phosphorus Leaching 285 12.6 Simulating Management and BMPs 285 12.7 Simulating In-Stream Processes 286 12.8 Example Simulations 287 12.8.1 Use of GWLF to Evaluate BMPs 287 12.8.2 Accuracy of GWLF: Comparison of Simulated to Measured Loads 289 12.8.3 Simulation of Runoff Volumes and Source Areas 292 12.9 Sensitivity Analysis 295 12.10 Availability of Model 295 References 296 12.1 HISTORY OF MODEL DEVELOPMENT The Generalized Watershed Loading Functions (GWLF) model was originally developed at Cornell University by Douglas Haith and associates (Haith and Shoemaker 1987; Haith et al. 1992) as “an engineering compromise between the empiricism of export coefficients and the complexity of chemical simulation models” (Haith et al., 1992, p.1). The GWLF approach conceptualizes the watershed as a system of different land areas — hydrologic response units (HRUs) — that produce surface runoff and erosion and a single groundwater reservoir that supplies base flow. © 2007 by Taylor & Francis Group, LLC 278 Modeling Phosphorus in the Environment Dissolved and suspended substances (i.e., nutrients, sediment) in stream flow are estimated at the watershed outlet by loading functions that empirically relate substance concentrations in runoff, sediment, and base flow to watershed- and HRU-specific characteristics. The strength of this approach lies in its fairly robust hydrologic formulation of a daily water balance and in the ability to adjust loading functions through calibration and for specific watershed conditions to an ever increasing body of knowledge and data on the factors that influence the export of substances in stream flow from a watershed. In addition to the original model there are currently several versions of GWLF in use. ArcView GWLF (AVGWLF) (Evans et al. 2002) was developed by Pennsylvania State Institutes of the Environment for Pennsylvania watersheds. AVGWLF provides a geographic information systems (GIS) interface to GWLF, has a modified sediment algorithm for channel erosion, and incorporates best management practices (BMP) reduction factors. Variable Source Loading Function (VSLF) Model (Schneiderman et al. 2002, 2006) was developed by the New York City Department of Environmental Protection (NYC DEP) for the New York City water supply. VSLF has a modified runoff algorithm to account for saturation-excess runoff; adds optional snowmelt, evapo- transpiration (ET), and groundwater algorithms for tuning hydrologic simulation to varied physiographic settings; modifies the sediment algorithm; adds BMP reduction factors; utilizes Vensim visual modeling software (http://www.vensim.com) for trans- parent viewing of model structure and for viewing tables, graphs, and statistics for all model variables at daily, weekly, monthly, annual, and event time steps; and has built- in model calibration and testing tools. BasinSim (Dai et al. 2000) is a Windows-based version of the original GWLF model developed at Virginia Institute for Marine Science. For research at the Choptank River Basin tributary of Chesapeake Bay, Lee et al. (2000, 2001) and Fisher et al. (2006) converted GWLF to Visual Basic with an ArcView and ArcMap GIS interface and added error analysis and adjustments for nonlinear agricul- tural land-use effects and hydric soils. These versions of GWLF have incorporated various different modifications from the original BASIC program, but all, including the various teaching tool versions, adhere to the basic water balance formulation and loading function philosophy. The various versions of GWLF are commonly used to predict how stream flow and nutrient loads from a watershed are affected by land-use, watershed-manage- ment, and climatic conditions. The U.S. Environmental Protection Agency (EPA) has classified GWLF as a model of mid-range complexity that can be used for developing Total Maximum Daily Load (TMDL) limits for impaired water bodies (U.S. Environmental Protection Agency 1999). GWLF has been applied to the Choptank River Basin tributary of Chesapeake Bay (Lee et al. 2000, 2006), including an application to historical land cover changes (Fisher et al. 2006); the New York City water supply watersheds (New York City Department of Environ- mental Protection 2005; Schneiderman et al. 2002, 2006); and throughout Pennsylvania (http://www.avgwlf.psu.edu). A Web search at the time of this writing shows that a version of GWLF is being used in at least 12 U.S. states — Arizona, Georgia, Illinois, Iowa, Kansas, Michigan, Mississippi, North Carolina, Pennsylvania, New York, Utah, and Virginia — to meet EPA requirements for development of TMDLs. © 2007 by Taylor & Francis Group, LLC Modeling Phosphorus with the GWLF Model 279 12.2 SPATIAL AND TEMPORAL RESOLUTION GWLF has flexibility in the spatial and temporal resolution of model output. The basic time step for the hydrologic water balance calculations is daily, which can be aggregated up to larger time steps. The original GWLF model aggregates hydrologic and water-quality output to a monthly representation, mainly because it does not account for drainage-area-based delays on flood peaks following storms. Daily output from GWLF will generally give too fast a response to rain events because the model computes a daily water balance but does not include routing. VSLF incorporates a time delay for runoff at the watershed outlet using an exponential decay function that can be calibrated. VSLF provides daily, weekly, monthly, annual, and event time step outputs, as desired. Spatial resolution depends on how a GWLF model application is set up. In GWLF the watershed area is divided into HRUs, which are land areas that share a similar hydrologic response to rain or snowmelt events and may not be contiguous. Runoff, erosion, and nutrients associated with runoff and erosion are explicitly tracked for each HRU and can be spatially mapped back to the HRU land areas. Fine resolution division of a watershed into many HRUs can produce model output on a field scale. Water, nutrient, and sediment loads are summed to provide water- shed-scale loading estimates as well. 12.3 PREDICTING INFILTRATION AND RUNOFF Runoff and infiltration are predicted in GWLF using the Soil Conservation Service (SCS) curve number (CN) method (Soil Conservation Service 1972). Daily runoff depth Q is calculated by (12.1) where P (mm) is the depth of rain and snowmelt, I a (mm) is the initial abstraction of rain and snowmelt retained by the watershed prior to the beginning of runoff generation, and S (mm) is a parameter that represents the potential maximum soil water retention when runoff begins. I a is estimated as an empirically derived fraction of available storage (typically assumed to be 0.2 S). Potential soil water retention, S, depends on the moisture status of the soil of the HRU and varies daily between a maximum S max (mm) when the HRU soil is dry and a minimum S min (mm) when the HRU soil is wet. Effective soil water retention for average watershed moisture conditions S avg (mm) is calculated from the SCS CN (CN 2 ): (12.2) CN 2 values can be derived by calibration to base-flow-separated stream flow data (Natural Resources Conservation Service 1997) or from tables compiled by the Q PI PI S = − −+ () () a a 2 S CN avg =− 254 100 1 2 © 2007 by Taylor & Francis Group, LLC 280 Modeling Phosphorus in the Environment U.S. Department of Agriculture (USDA) (Soil Conservation Service 1986) for dif- ferent combinations of land use and soil hydrologic group. Soil hydrologic groups rank soils by their infiltration characteristics, and are used to qualify the propensity of an HRU to generate excess runoff. The upper and lower limits of S are estimated in relation to S avg , based on empirical analysis of rainfall and runoff data for experimental watersheds (Hawkins 1978): S max = 2.381 S avg (12.3) and S min = 0.4348 S avg (12.4) The daily value of S is determined in the original GWLF model by the watershed antecedent moisture (am) condition, determined by the sum of precip- itation occurring during the previous five days (P 5-day ). S is set to S max for the dry condition (P 5-day = 0) and then declines linearly to S avg and S min as P 5-day increases, as given in Figure 12.1. The relationship of S to P 5-day is different for the dormant vs. the growing season. Breakpoint values (from Ogrosky and Mockus 1964) for the dormant and growing season curves, respectively, in Figure 12.1 are am1 = 1.27 FIGURE 12.1 Variation in soil water retention parameter, S, as a function of 5-day antecedent precipitation for growing and dormant seasons. am1 and am2 represent breakpoint values between different antecedent precipitation conditions. 0123456 5-day Antecedent Precipitation (cm) S max S avg S min S dormant am1 am1 am2 am2 growing © 2007 by Taylor & Francis Group, LLC Modeling Phosphorus with the GWLF Model 281 and 3.56 cm, and am2 = 2.79 and 5.33 cm. When snowmelt occurs, it is assumed that the HRU soils are at their wettest condition; hence, S is set to S min , irrespective of P 5-day . An alternative method for calculating S as a direct function of soil moisture content is used in VSLF (Schneiderman et al. 2006). Using the method of Arnold et al. (1998), S varies from storm to storm as (12.5) where SW is the average soil water content (cm 3 /cm 3 ) and w 1 and w 2 are shape coefficients. The shape parameters w 1 and w 2 are calculated by (12.6a) and (12.6b) where FC is the amount of water in the soil at field capacity (cm 3 /cm 3 ) and SAT is the amount of water in the soil when saturated (cm 3 /cm 3 ). When the top layer of the soil is frozen, the available storage is modified by (12.7) where S frz is the available storage adjusted for frozen ground, S is the available storage for a given soil moisture content calculated with Equation 12.5, and R 2frzx is a parameter that adjusts for frozen ground conditions. R 2frzx is set to –0.000826 in the SWAT model but can be calibrated. Stormwater runoff is the primary mechanism for transporting soluble phosphorus (P) from the point where it accumulates on or near the ground surface to the stream and outlet of the watershed. Accurate model predictions of P loads and effects of water- shed management depend on realistic prediction of runoff source areas. GWLF, like many CN-based water-quality models, uses the SCS CN method in a way that implicitly assumes that infiltration excess is the runoff mechanism. Each HRU in a watershed is defined by land use and a hydrologic soil group classification via a CN value that determines runoff response. CN values for different land use and hydrologic soil group combinations are provided in tables compiled by the USDA SS SW SW e wwSW =− + − max 1 12 () w FC SS FC w FC 12 1 = − − +ln / min max w FC SS FC SAT 2 11 = − − − − ln / ln min max 2254. max S SAT SAT FC − − SS RS frz max 2frzx =−[exp( )]1 © 2007 by Taylor & Francis Group, LLC 282 Modeling Phosphorus in the Environment (e.g., Soil Conservation Service 1972, 1986). The hydrologic soil groups used to classify HRUs are based on infiltration characteristics of soils (e.g., Natural Resources Conservation Service 2003) and thus clearly assume infiltration excess as the primary runoff-producing mechanism. The traditional infiltration-excess-based CN method for runoff estimation in GWLF limits the original model’s utility to watersheds where infiltration excess is the dominant runoff-generating mechanism. In humid, well-vegetated areas with shallow soils, such as in the northeastern U.S., infiltration excess does not explain observed storm runoff patterns. On shallow soils characterized by highly permeable topsoil underlain by a dense subsoil or shallow water table, infiltration capacities are generally greater than rainfall intensity, and storm runoff is usually generated by saturation excess on VSAs (Beven 2001; Dunne and Leopold 1978; Needelman et al. 2004; Srinivasan et al. 2002). To improve the accuracy of runoff source area predictions in watersheds where saturation excess is the dominant runoff-generating mechanism, Schneiderman et al. (2006) created a new version of GWLF (VSLF) that simulates runoff from VSAs. In VSLF the watershed is subdivided into wetness index classes by mapping a wetness index (e.g., the topographic index ln a/tan b of the TOPMODEL; Beven and Kirkby 1979) and by defining discrete classes ordered along an axis of increasing available moisture storage. Steenhuis et al. (1995) and Schneiderman et al. (2006) showed that the CN Equation 12.1, when interpreted as representing a saturation excess runoff generation process, gives rise to a characteristic relative soil moisture distribution that is invariant from storm to storm: (12.8) where σ e (mm, effective local moisture storage) is the amount of water that can be stored in the soil at a point location in the watershed when runoff from the watershed begins, S is the average soil water retention parameter for the entire watershed calculated by Equation 12.5 through 12.7, and A s is the fraction of watershed area with lower local moisture storage than the point location. Figure 12.2 shows the relative moisture distribution curve of Equation 12.8 plotted along an axis of increas- ing fraction of watershed with lower local moisture storage. Runoff q (mm) at a given point location in the watershed is simply q = P – I a – s e for P > σ e + I a (12.9) Given the CN-based relative moisture distribution (Equation 12.8), runoff for any point location along the A s fraction of watershed area with lower local moisture storage axis is calculated as (12.10) σ e s SA = − − 1 1 1 () qP A S=− − − ⋅ 1 1 08 () . s © 2007 by Taylor & Francis Group, LLC Modeling Phosphorus with the GWLF Model 283 Runoff q i for a discrete wetness index class, bounded on one side by the fraction of the watershed that has lower local moisture storage, A s,i , and on the other side by the fraction of the watershed that has greater local moisture storage, A s,i+1 , is given by (2.11) Runoff and nutrient loads from each wetness and land-use HRU are tracked separately in the model. A wetness index class may coincide with multiple land uses. Whereas runoff depth within an index class in VSLF will be the same irre- spective of land use, the concentration of pollutant in runoff may vary by both land use and index class. Wetness index classes are thus subdivided by land use to define HRUs with unique combinations of wetness class and land use. In the original GWLF model, runoff is calculated for each defined soil and land use HRU using Equation 12.1. In VSLF, runoff is calculated for each wetness and FIGURE 12.2 Distribution of effective local moisture storage, σ e , normalized to the water- shed average potential soil water retention parameter, S, along an axis of increasing fraction of watershed area with lower local moisture storage, A s . 0 0.2 0.4 0.6 0.8 1 10 9 8 7 6 5 4 3 2 1 0 σ e /S A s qP AA AA i s,i s,i s,i s,i =− ⋅−−− () − − + + 21 1 08 1 1 () . ⋅ S © 2007 by Taylor & Francis Group, LLC 284 Modeling Phosphorus in the Environment land use HRU with Equation 12.11. For the entire watershed, runoff depth Q is the areally weighted sum of runoff depths q i for all discrete wetness and land-use contributing areas: (12.12) Total runoff depth, Q, calculated by this equation is the same as that calculated by Equation 12.1 (Schneiderman et al. 2006), so runoff volume estimates for the watershed as a whole with VSLF are compatible with the original GWLF and other models that use the traditional SCS CN equation. The main hydrological difference is that VSLF distributes storm runoff according to a moisture storage distribution rather than by land use and soil type. This has important implications for predictions of chemical constituents of runoff. 12.4 PREDICTING PHOSPHORUS IN RUNOFF Dissolved P loads in runoff from each HRU are calculated daily in GWLF as the product of simulated runoff and empirically derived HRU-specific nutrient concen- trations. Haith et al. (1992) compiled runoff concentrations for different land uses from the literature for rural land uses. Urban dissolved nutrient concentrations were compiled in the Nationwide Urban Runoff Program (U.S. Environmental Protection Agency 1983). Literature concentration values from these and other sources provide an initial basis for determining these parameters. Runoff concentration data for specific watersheds can be used when available. In the original GWLF, dissolved nutrient concentrations are input as constants, with the exception of agricultural land uses on which winter spreading of manure or fertilizer occurs. For these land uses, seasonal variability in nutrient concentrations is introduced, with elevated concen- trations applied to snowmelt and rain on snow. Use of literature-based concentrations of nutrients in runoff in GWLF presents a number of challenges. Literature-based concentrations generally provide a range of values for a given land use, and the choice of an appropriate value for a given watershed requires an act of judgment. Since the GWLF parameters represent con- centrations in runoff as expressed at the outlet of a watershed, scale differences between study sites on which literature values are based and the watershed being modeled may affect the translation. Even concentration data for runoff in the study watershed may not translate directly to GWLF parameters if the data are sampled at the plot or field scale. Model calibration may be necessary and is recommended where loading data are available. Schneiderman et al. (2002) calibrated nutrient concentrations with a single adjustment factor that was applied to all nutrient con- centrations. In this way the relationships between concentrations associated with different land uses are maintained, as all concentrations shift up or down with the multiplicative factor. In effect, the literature values are used to establish the relative concentrations for different land uses, and calibration establishes the absolute values. QqAA n =− + = ∑ i () s,i s,i i 1 1 © 2007 by Taylor & Francis Group, LLC Modeling Phosphorus with the GWLF Model 285 The use of constant concentrations for nutrients in runoff is deserving of some discussion. On the local plot or field scale, P concentrations would be expected to vary with changes in soil P content in the upper soil layer (Sharpley 1995) or with the timing and intensity of manure or fertilizer applications (Walter et al. 2001). On the watershed scale, however, where the simulation unit (in GWLF and other lumped-parameter HRU models) is the HRU composed of many plots or fields at different stages of fertility and soil P cycles, the temporal variations that exist on the fine scale may cancel out on the broad scale. The New York City Department of Environmental Protection (2005) used the Soil Water Assessment Tool (SWAT) (Bicknell et al. 2001) model, which simulates daily P concentrations in soil and runoff by keeping a mass balance of P, to investigate temporal variation in soil and runoff P concentrations for agricultural land uses in New York City watersheds. The results of an extensive sensitivity analysis suggested that with the exception of agricultural fields that are subject to tillage, predicted soil and runoff P concentrations at a watershed scale were fairly constant. Tilled agricultural fields demonstrated a distinct pattern of reduction of concentrations in runoff (due to mixing of high P upper-layer soil with lower P lower-layer soils) at the time of tillage, followed by a gradual increase in concentrations with time after tillage. VSLF was modified to allow seasonally varying concentrations for cases like this where such variations occur on a watershed scale. 12.5 PREDICTING PHOSPHORUS LEACHING GWLF assumes that the major pathways by which P is exported from a watershed are in runoff from different HRUs and in base flow. GWLF does not predict leaching of P explicitly. In actuality, the importance of P leaching as a pathway for export of P on a watershed scale is uncertain. Observations of elevated P concentrations in base flow in P-enriched watersheds could be considered evidence for transport of leached P from P-saturated soils, but this has not been demonstrated conclusively. Elevated P concentrations in base flow could just as well be caused by high P availability at groundwater discharge sites, including seeps and stream banks. The effects of factors that influence base flow P levels, including leaching of P into shallow groundwater and P entrainment at groundwater discharge zones, is accounted for in GWLF by model and input adjustments to the concentration of P in base flow. In the original GWLF model, the P concentration in base flow was an empirical function of the aerial percentage of active agriculture in the watershed (Figure 12.3). VSLF has an option to allow user input of a base-flow concentration value that is representative of the watershed being studied. 12.6 SIMULATING MANAGEMENT AND BMPS The general approach to simulating management and BMPs with GWLF is to translate the effects of BMPs, either individually or combined, into model parameter adjustments, which are then applied in subsequent scenario runs of the model. For example, hydrologic effects of watershed management and BMPs may be © 2007 by Taylor & Francis Group, LLC 286 Modeling Phosphorus in the Environment expressed through modifications in curve number (affecting runoff), soil water capacity (affecting percolation), melt coefficient (affecting snowmelt), or vegetative cover coefficients (affecting ET). Water-quality effects of BMPs are expressed by modi- fying HRU-specific P concentrations in runoff, P concentration in base flow, point- source concentrations, septic system failure rates, Universal Soil Loss Equation (USLE) parameters that control erosion rates, sediment delivery ratio, and HRU- specific P concentrations in soils. GWLF-VSA and AVGWLF have reduction factors built into the model to streamline the application of BMP effects on model parameters. The reduction factor approach to simulating effects of watershed management is supported by an ever increasing body of knowledge in the literature on the effectiveness of BMPs. Phosphorus removal efficiencies of urban BMPs are mea- sured and compiled for stormwater treatment practices (Winer 2000). Gitau et al. (2005) compiled a database of BMP effectiveness for agricultural BMPs. Gitau and Veith cover the effect of P control BMPs in Chapter 15 of this volume. The USLE methodology (Wischmeier and Smith 1978) provides coefficient values for various management practices. Results of watershed-specific field studies on BMP effec- tiveness can be utilized where available. 12.7 SIMULATING IN-STREAM PROCESSES GWLF simulates in-stream processes as a lumped statistical process where the stream is treated as a single unit. The effect of channel length and physical properties on the timing of base-flow discharge at the outlet of the watershed is treated as a simple exponential time delay that can be calibrated from stream flow data. Though the original GWLF model does not permit a time delay for runoff — runoff at the FIGURE 12.3 Dissolved P concentration in base flow as a function of percent of agricultural land use within a watershed. 0% 20% 40% 60% 80% 100% Percent Agriculture P concentration in baseflow (mg/l) 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 © 2007 by Taylor & Francis Group, LLC [...].. .Modeling Phosphorus with the GWLF Model 287 watershed outlet occurs on the day of precipitation — the VSLF does so by treating runoff delay similarly to base flow In- stream processing of chemical constituents of stream flow is represented minimally in the original GWLF model The timing of P export at the watershed outlet in GWLF is delayed with the exponential time delay of base flow and, in VSLF,... total P during the calibration period (water year 1992), and verification period (water year 1993 to 1996, excluding January 1996) Solid line is the line of perfect fit; dashed line is the regression line; and R2 is the Nash-Sutcliffe model error statistic © 2007 by Taylor & Francis Group, LLC 292 Modeling Phosphorus in the Environment 12. 8.3 SIMULATION OF RUNOFF VOLUMES AND SOURCE AREAS With the development... GWLF Model 295 In contrast, the spatial pattern of runoff predicted by VSLF follows the pattern of the wetness index, with high wetness index areas generating most of the runoff The implications of the runoff generating mechanism for P predictions are visible in Figures 12. 8e and 12. 8f In the original GWLF model all areas of a particular land use generate P equally, as shown in Figure 12. 8e VSLF simulates... method for calculating available moisture storage (Equation 12. 5 through 12. 7) in VSLF greatly improved runoff estimates (Figure 12. 6) Similar analyses for 31 USGS-gaged catchments in the Catskill Mountain region of New York revealed the same pattern (Figure 12. 7) Comparison of runoff predictions for the original GWLF and the VSLF models show that the underlying runoff generating mechanism (in ltration excess... over the 34-year time period under the current land-use conditions with no BMPs and no reductions in wastewater loads; the management scenario represents the watershed loads for the same 34-year time period with all BMPs, septic system upgrades, and WWTP upgrades in effect Using the 34-year meteorologic time series as input to drive the model enabled a comparison of the management scenario with the. .. modeled to base-flow-separated runoff for the West Branch Delaware River at Walton (USGS Gage 01423000) upstream of the Cannonsville reservoir using the uncalibrated original GWLF vs the calibrated VSLF model revealed that the uncalibrated original GWLF model substantially underestimated runoff during both the growing and the dormant season, whereas CN calibration and incorporation of the Arnold et al... 6 8 10 Baseflow-separated event runoff FIGURE 12. 6 Scatterplots (with growing and dormant season bias and Nash-Sutcliffe performance parameters) of base-flow-separated vs -simulated event runoff for West Branch Delaware River at Walton, using the original GWLF model with default CNs vs the GWLFVSLF model with calibrated CNs © 2007 by Taylor & Francis Group, LLC Modeling Phosphorus with the GWLF Model... http://www.vensim.com) AVGWLF is available from the Pennsylvania State Institutes of the Environment (http://www.avgwlf.psu.edu) The software is designed for use in Pennsylvania and application to other states requires code and algorithm changes and the assistance of the software developers BasinSim is available from the Virginia Institute of Marine Science (http://www.vims.edu) These are all noncommercial versions... Weller 2000 Modeling the hydrochemistry of the Choptank River Basin using GWLF and Arc/Info 1: model calibration and validation Biogeochemistry 49:143–173 Lee K.-Y., Fisher T.R., and E.J Rochelle-Newall 2001 Modelling the hydrochemistry of the Choptank River Basin using GWLF and Arc/Info 2: model application Biogeochemistry 56:311–348 Nash, J.E and J.V Sutcliffe 1970 River flow forecasting through conceptual... function relationships simple, the problem of estimating many parameters and the need to determine which subset of a large parameter set has the greatest effect on model output are avoided In the hydrologic submodel, runoff volumes are an exponential function of the CN, whereas runoff timing is determined by a single linear reservoir coefficient (in VSLF) Base flow is determined by a simple recession coefficient, . Development 277 12. 2 Spatial and Temporal Resolution 279 12. 3 Predicting In ltration and Runoff 279 12. 4 Predicting Phosphorus in Runoff 284 12. 5 Predicting Phosphorus Leaching 285 12. 6 Simulating Management. and then declines linearly to S avg and S min as P 5-day increases, as given in Figure 12. 1. The relationship of S to P 5-day is different for the dormant vs. the growing season. Breakpoint. & Francis Group, LLC 290 Modeling Phosphorus in the Environment FIGURE 12. 4 Dissolved P loadings (kg/yr) for baseline and management scenarios including corresponding percent reductions broken