The water balance and chemistry of lakes with little or no surface inflow can be substantially impacted by the spatial pattern of lacustrine groundwater discharge (LGD) and corresponding fluxes of nutrient or pollutant inputs across the groundwater-surface water interface [Loeb and Goldman, 1979; Enell, 1982]. The quantification of groundwater-borne loads requires the determination of both, water fluxes and concentrations of relevant compounds in groundwater discharge. Due to the spatial heterogeneity of exchange fluxes at the sediment-water interface, the determination of groundwater discharge and its chemical load is often a challenge. This study focuses on the identification and quantification of groundwater discharge and its spatial pattern.
1.1. Spatial Patterns of Seepage Fluxes
 Exchange fluxes between groundwater and surface water are controlled (i) by hydraulic head gradients between aquifer and lake as the driving force and (ii) by the spatial distribution of hydraulic conductivity of sediments at the aquifer-lake interface. Spatial variability in drivers (hydraulic head gradients) and controls (hydraulic conductivity) of exchange fluxes determine patterns of lacustrine groundwater discharge (LGD). Significant spatial heterogeneity of seepage fluxes has been revealed by a number of experimental studies [e.g., Kishel and Gerla, 2002; Kidmose et al., 2011; Cherkauer and Nader, 1989; Lautz and Ribaudo, 2012]. For example, Kishel and Gerla  identified significant horizontal and vertical heterogeneity of flow directions and fluxes within a densely spaced grid of piezometers (every 2 m in a 10 × 10 m domain). Lautz and Ribaudo  used flux rates from heat transport modeling based on time series and streambed temperatures to develop an upscaling approach for a 30 m stream reach.
 For homogenous isotropic aquifers, LGD has been found to concentrate in a narrow band close to the shore [McBride and Pfannkuch, 1975]. As a consequence, shallow groundwater usually discharges close to the shore whereas smaller fluxes of deeper groundwater discharge more offshore [McBride and Pfannkuch, 1975; Frape and Patterson, 1981]. Increased seepage rates at nearshore areas may also result from the spatial distribution of fine-grained, low-permeability muddy sediments in a lake. The depth of the muddy sediment is usually largest in the central parts of a lake and decreases toward the shore. Wave action can resuspend light, freshly deposited material from shallow areas while material that settled in deeper parts of a lake is less affected. Thus, hydraulic conductivities of shoreline sediments are usually higher than of sediments from deeper lake sections [Kishel and Gerla, 2002; McBride and Pfannkuch, 1975; Krabbenhoft et al., 1990b]. The fact that highest seepage rates usually occur in near vicinity to the shore is convenient for the experimental determination of seepage rates as measurements can be conducted in the shallowest and most accessible parts of the lake. In many lakes, this means that seepage measurements can be conducted by wading, rather than from boats or by diving [Shaw et al., 1990].
 The spatial patterns of seepage rates in their relation to shore distances have been studied by direct measurements with seepage meters [Lee, 1977; Brock et al., 1982; Harvey et al., 2000] and by the application of numerical models [e.g., Pfannkuch and Winter, 1984; Shaw and Prepas, 1990; Schafran and Driscoll, 1993]. However, the identification of spatial patterns and quantification of seepage fluxes across aquifer-lake interfaces is a major challenge. Quantitative approaches either treated an entire lake as a lumped system, and therefore estimations lacked detailed information on spatial patterns [Brock et al., 1982; Krabbenhoft et al., 1994; Harvey et al., 2000] or were based on point measurements, i.e., point estimates of local fluxes [Lee, 1977]. As point observations are representative for the specific local conditions and processes only, a large number of labor-intensive measurements is required and an extrapolation of these observations to the entire lake encompasses high uncertainty. Hence, current studies of lake water balances and nutrient budgets often lack adequate information of spatial patterns of seepage fluxes across the aquifer-lake interface, which critically limits the representativeness of results.
1.2. Quantitative Methods for Estimating Seepage Flow
 Recent years have seen the development and application of a wide range of approaches for monitoring and quantifying LGD. Net exchange of groundwater has been estimated by identifying and solving the different components of the water balance equation [Brock et al., 1982; Belanger et al., 1985; Harvey et al., 2000]. Furthermore, mass balances of stable isotopes [Krabbenhoft et al., 1994] or conservative chemical tracers such as chloride [Krabbenhoft and Webster, 1995] have been used to quantify LGD. However, all mass balance approaches integrated spatial heterogeneities and temporal variability of the flow field and thus, did not provide spatially detailed information of exchange flow patterns [Krabbenhoft et al., 1990a].
 In contrast to the aforementioned lumped approaches for entire lakes, seepage meters that are deployed at the sediment-water interface for measuring water fluxes over a specified area of the lake bed [Lee, 1977; Kalbus et al., 2006] provide a possibility for direct monitoring of small-scale exchange fluxes between groundwater and surface water [Rosenberry, 2005]. Further indirect methods for quantifying LGD rates are based on Darcy's law and require detailed observations of pressure head gradients (e.g., in piezometers) and hydraulic conductivity of the local aquifer [Stauffer, 1985; Kishel and Gerla, 2002]. Sediment depth profiles of temperature [Schmidt et al., 2006; Stonestrom and Constantz, 2003; Anibas et al., 2009; Meinikmann et al., 2013] or conservative ions [Mortimer et al., 1999; Schuster et al., 2003] at the sediment-water interface have been successfully analyzed for indirect determination of water fluxes at the groundwater-surface water interface. However, the application of these methods is subject to certain assumptions (see sections 2.2.2 and 4.1) and requires the existence of distinct differences in the respective characteristics of the groundwater and surface water end-members. If end-member characteristics are distinctive, fluxes can be calculated from the curvature of the observed gradient at the sediment-water interface. Dampening and phase shifts of diurnal temperature oscillations can be used if time series of temperature profiles are available [e.g., Hatch et al., 2006, Constanz, 2008]. Despite some problems in using temperature as a tracer arising from diurnal signal propagation during snapshot sampling or retardation effects (since temperature is not a conservative tracer) these methods have been successfully applied for the quantification of 1-D vertical fluxes at the groundwater-stream interface [Hatch et al., 2006; Hannah et al., 2009; Krause et al., 2011; Meinikmann et al., 2013].
1.3. Fiber-Optic Temperature Sensing
 Recent developments in fiber-optical sensor technologies provide a novel and robust methodology for investigating spatial patterns of exchange fluxes between groundwater and surface water by Fiber-Optic Distributed Temperature Sensing (FO-DTS) [Selker et al., 2006a, 2006b; Tyler et al., 2009; Krause et al., 2012]. Based on the differences in groundwater and surface water temperatures, spatial patterns of groundwater discharge can be identified by tracing temperature anomalies at the sediment-water interface. Temperatures can be traced along fiber-optic cables of several kilometers length with currently 0.3–4 m spatial resolution and measurement precision of 0.05–0.1°C for sampling intervals of 30 s [Selker et al., 2006a; Hausner et al., 2011; Van de Giesen et al., 2012]. In contrast to the aforementioned methodologies, FO-DTS is useful for spatially detailed measurements at larger scales, and therefore has the potential to provide temperature information for tracing LGD with high spatial resolution at scales exceeding previous detailed investigations of local flow. FO-DTS has successfully been applied for qualitative identification of complex of groundwater upwelling patterns in streams [Slater et al., 2010; Mwakanyamale et al., 2012], wetlands [Lowry et al., 2007], and coastal zones [Henderson et al., 2009]. Hence, spatially detailed FO-DTS observations may provide an adequate measure to upscale detailed point observations or provide an efficient screening tool for identifying locations for detailed analyses of groundwater upwelling. The upscaling approach based on DTS data described in this study is novel as here DTS data are related to lacustrine groundwater discharge determined by both temperature profile gradients and vertical hydraulic gradients and thus allows for the quantification of flux rates. This is an important improvement of DTS application beyond simply visualizing the spatial pattern of groundwater discharge.
 The objective of the present study is to test whether FO-DTS-based upscaling of point measurements of lacustrine groundwater discharge rates is an adequate and feasible approach to represent the spatial heterogeneity of LGD rates. A transect of piezometers for determination of vertical hydraulic gradients is therefore combined with a manually measured grid of vertical temperature profiles and a FO-DTS survey of temperatures at the lake-aquifer interface. Obtaining a large data set of temperature profiles or vertical hydraulic gradients (VHG) is time consuming and tedious and hence often limits the spatial extent and resolution of experimental studies. We therefore derived and tested two upscaling methodologies based on information from a single transect of either temperature profile or VHG-derived LGD estimations. The two transfer functions combined this information with FO-DTS temperature measurements to identify detailed 2-D patterns of LGD rates at a larger scale. These DTS-based upscaling approaches were compared to a very simple 1-D-upscaling approach based on the assumption of exponential decline of LGD with distance to the shore.