Methods
Each ecosystem service was quantified and mapped by using empirical estimates and spatially explicit model for the terrestrial landscape of the Yahara Watershed for 2006. Crop production (expected annual crop yield, bu per yr) Crop yield was estimated for the four major crop types (corn, soybean, winter wheat and oats) that account for 98.5 percent of the cultivated land in the watershed by overlaying maps of crop types and soil-specific crop yield estimates. The spatial distribution of each crop was obtained from the 2006 Cropland Data Layer (CDL) from the National Agricultural Statistics Service (NASS) and soil productivity data were extracted from Soil Survey Geographic (SSURGO) database. Crop and soil data were converted to 30 m resolution and the two maps were overlain to estimate crop yield in each cell. For each crop-soil combination, crop area was multiplied by the estimated yield per unit area. Estimates for each crop type were summed to map estimated crop yield for 2006. Pasture production (expected annual forage yield, animal-unit-month per year ) As for crop production, forage yield was estimated by overlaying the distribution of all forage crops (alfalfa, hay and pasture/grass) and soil specific yield estimates. The spatial distribution of each forage crop was also derived from 2006 CDL, and rescaled to 30 m grid prior to calculation. The SSURGO soil productivity layer provided estimates of potential annual yield per unit area for each forage crop. Overlay analyses were performed for each forage-soil combination, as done for crops, and summed to obtain the total expected forage yield in the watershed for 2006. Freshwater supply (annual groundwater recharge, cm per year) . Groundwater recharge was quantified and mapped using the modified Thornthwaite-Mather Soil-Water-Balance (SWB) model. SWB is a deterministic, physically based and quasi three-dimensional model that accounts for precipitation, evaporation, interception, surface runoff, soil moisture storage and snowmelt. Groundwater recharge was calculated on a grid cell basis at a daily step with the following mass balance equation<p align="center">Recharge= (precipitation + snowmelt + inflow) –<p align="center">(interception + outflow + evapotranspiration) – delta soil moisture<p align="center"> We ran the model for three years (2004 to 2006) at 30m resolution, with the first two years as spin up of antecedent conditions (e.g. soil moisture and snow cover) that influence groundwater recharge for the focal year of 2006. Carbon storage (metric tons<sup> </sup>per ha) We estimated the amount of carbon stored in each 30 m cell in the Yahara Watershed by summing four major carbon pools: aboveground biomass, belowground biomass, soil carbon and deadwood/litter. Our quantification for each pool was based mainly on carbon estimates from the IPCC tier-I approach and other published field studies of carbon density and was estimated by land-use/cover type.Groundwater quality (probability of groundwater nitrate concentration greater than 3.0 mg per liter, unitless 0 to1) Groundwater nitrate data were obtained from Groundwater Retrieve Network (GRN), Wisconsin Department of Natural Resources (DNR). A total of 528 shallow groundwater well (well depth less than the depth from surface to Eau Claire shale) nitrate samples collected in 2006 were used for our study. We performed kriging analysis to interpolate the spatial distribution of the probability of groundwater nitrate concentration greater than 3 mg<sup> </sup>per liter. We mapped the interpolation results at a 30m spatial resolution using Geostatistical Analyst extension in ArcGIS (ESRI). In this map, areas with lower probability values provided more groundwater quality service, and vice versa. Surface water quality (annual phosphorus loading, kg per hectare). We adapted a spatially explicit, scenario-driven modeling tool, Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) to simulate discharge of nonpoint-source phosphorus. A grid cells phosphorus contribution was quantified as a function of water yield index, land use/cover, export coefficient, and downslope retention ability with the following equation:Expx = ALVx * sum of the products from y=x+1 to X for (1-Ey)where ALVx is the adjusted phosphorus export from pixel x , Ey is the filtration efficiency of each downstream pixel y , and X represents phosphorus transport route from where it originated to the downstream water bodies. Filtration efficiency was assigned by cover type: natural vegetation was assigned a high value, semi-natural vegetation an intermediate value, and developed or impervious covers were assigned low values. We ran the model for 2006 and mapped estimated phosphorus loading across the watershed. The ecosystem service of providing high quality surface water was the inverse of phosphorus loading. Therefore, areas with lower phosphorus loading values delivered more surface water quality, and areas with higher phosphorus loading values supplied less surface water quality.Soil retention (annual sediment yield, metric tons per hectare). We quantified annual sediment yield as the (inverse) indicator for soil retention by using the Modified Universal Soil Loss Equation (MUSLE). MUSLE is a storm event based model that estimates sediment yield as a function of runoff factor, soil erodibility, geomorphology, land use/cover and land management. Specifically, a grid cells contribution of sediment for a given storm event is calculated as:Sed= 11.8*(Q*q<sub>p</sub>)<sup>0.56</sup> * K * LS * C * Pwhere Sed represents the amount of sediment that is transported downstream network (metric tons), Q is the surface runoff volume (m<sup>3</sup>), q<sub>p </sub>is the peak flow rate (cubic meters per s), K is soil erodibility which is based on organic matter content, soil texture, permeability and profiles, LS is combined slope and steepness factor, and C* P is the product of plant cover and its associated management practice factor. We used the ArcSWAT interface of the Soil and Water Assessment Tool (SWAT) to perform all the simulations. We ran this model at a daily time step from 2004 to 2006, with the first two years as spin up , then mapped total sediment yield for 2006 across the watershed. Similar to surface water quality, the ecosystem service of soil retention was the inverse of sediment yield. In this map, areas with lower sediment yield provided more of this service, and areas with higher sediment yield delivered less. Flood regulation (flooding regulation capacity, unitless, 0 to 100) We used the capacity assessment approach to quantify the flood regulation service based on four hydrological parameters: interception, infiltration, surface runoff and peak flow. We first applied the Kinematic Runoff and Erosion (KINEROS) model to derive estimates of three parameters (infiltration, surface runoff and peak flow) for six sampled sub basins in this watershed. KINEROS is an event-oriented, physically based, distribution model that simulates interception, infiltration, surface runoff and erosion at sub-basin scales. In each simulation, a sub basin was first divided into smaller hydrological units. For the given pre-defined storm event, the model then calculated the amount of infiltration, surface runoff and peak flow for each unit. Second, we classified these estimates into 10 discrete capacity classes with range from 0 to 10 (0 indicates no capacity and 10 indicates the highest capacity) and united units with the same capacity values and overlaid with land cover map. Third, we calculated the distribution of all land use/cover classes within every spatial unit (with a particular capacity). We then assigned each land use/cover a capacity parameter based on its dominance (in percentage) within all capacity classes. As a result, every land use/cover was assigned a 0 to 10 capacity value for infiltration, surface runoff and peak flow. This procedure was repeated for six sub basins, and derived capacity values were averaged by cover type. We applied the same procedure to soil data and derived averaged capacity values for each soil type with the same set of three parameters. In addition, we obtained interceptions from published studies for each land use/cover and standardized to the same 0 to 10 range. Finally, the flood regulation capacity (FRC) for each 30m cell was calculated with the equation below:FRC= for each land use and land cover class the sum of (interception + infilitration + runoff + peakflow) + for each soil class the sum of (infiltration + runoff + peakflow).To simplify interpretation, we rescaled original flood regulation capacity values to a range of 0 to100, with 0 representing the lowest regulation capacity and 100 the highest. Forest recreation (recreation score, unitless, 0 to 100). We quantified the forest recreation service as a function of the amount of forest habitat, recreational opportunities provided, proximity to population center, and accessibility of the area for each 30m grid cell with the equation below:FRSi= Ai * sum of (Oppti + Popi + Roadi)where FRS is forest recreation score, A is the area of forest habitat, Oppt represents the recreation opportunities, Pop is the proximity to population centers, and Road stands for the distance to major roads. To simplify interpretation, we rescaled the original forest recreation score (ranging from 0 to 5200) to a range of 0 to 100, with 0 representing no forest recreation service and 100 representing highest service. Several assumptions were made for this assessment approach. Larger areas and places with more recreational opportunities would provide more recreational service, areas near large population centers would be visited and used more than remote areas, and proximity to major roads would increase access and thus recreational use of an area. Hunting recreation (recreation score, unitless 0 to100) We applied the same procedure used for forest recreation to quantify hunting service. Due to limited access to information regarding private land used for hunting, we only included public lands, mainly state parks, for this assessment. The hunting recreation service was estimated as a function of the extent of wildlife areas open for hunting, the number of game species, proximity to population center, and accessibility for each 30m grid cell with the following equation:<br />HRSi= Ai * sum of (Spei + Popi + Roadi)where HRS is hunting recreation score, A is the area of public wild areas open for hunting and fishing, Spe represents the number of game species, Pop stands for the proximity to population centers, and Road is the distance to major roads. To simplify interpretation, we rescaled the original hunting recreation score (ranging from 0 to 28000) to a range of 0 to100, with 0 representing no hunting recreation service and 100 representing highest service. Similar assumptions were made for this assessment. Larger areas and places with more game species would support more hunting, and areas closer to large population centers would be used more than remote areas. Finally, proximity to major roads would increase access and use of an area.
