The measurements considered in this study were conducted at the hydrometeorological research catchment Rietholzbach in northeastern Switzerland (47.38∘ N, 8.99∘ E; 795 m a.s.l.; see Seneviratne et al., 2012 for an overview of the site). The hilly, pre-alpine catchment (elevation range: 682–950 m a.s.l.) drains an area of 3.31 km2 and is a headwater catchment of the Thur river. The region is characterized by a temperate humid climate with a mean air temperature Tair of 7.1 ∘C and ample precipitation P with a mean annual sum of 1438 mm yr-1 (data basis 1976–2015, Fig. 1a and b). Net radiation Rn exhibits a clear seasonal pattern with on average 105 W m-2 in summer and -7 W m-2 in winter (data basis 2000–2015, Fig. 1c). Predominantly weak winds (77 % below 2 m s-1) blow along the east–west orientation of the valley (Fig. 2). Catchment runoff QC is strongly related to subsurface storage (Teuling et al., 2010a) and shows an annual mean of 104 L s-1, which corresponds to 991 mm yr-1. It displays the lowest values in summer and its peak value during snowmelt in March (data basis 1976–2015, Fig. 1d). The conglomerate Nagelfluh, the main parent rock type, originates from the Würm glaciation. The soil type and depth exhibit a high spatial variability. Overall, shallow Regosols dominate on steep slopes, deeper Cambisols are found in flatter areas, and gley soils are located in the vicinity of small creeks. Land use has undergone no major changes since the start of the measurements in late 1975 and is highly related to the topography. On slopes and along creeks, in about one-fourth of the area, forest dominates. Otherwise the area is used as grassland and partially as pasture. The catchment is only sparsely populated.

Most measurements considered in this article are conducted at the site “Büel”, which is located in a grassland area next to the valley bottom in the upper part of the Rietholzbach catchment (see Fig. 2 and https://s.geo.admin.ch/6de2dcf3b5). The ongoing measurements include standard meteorological and hydrological variables such as air temperature, precipitation, air humidity, radiation, soil moisture, runoff, and groundwater level. Evapotranspiration measurements are provided by a lysimeter and an eddy flux tower (see Fig. 2 for an overview on the setup of these measurements). Further details on the relevant instrumentation for this study are given in the following sections. Seneviratne et al. (2012) provided an overview of the characteristics of the catchment and of measurements at the site. For more general information about the catchment we also refer to http://www.iac.ethz.ch/url/rietholzbach.

Lysimetry is a well-established technique to measure evapotranspiration (e.g., Maidment, 1992; Rana and Katerji, 2000; Goss and Ehlers, 2009; Meissner et al., 2010; see also Seneviratne et al., 2012, for a recent overview). Lysimeters are vessels containing a soil column in near-natural condition. Weighing lysimeters allow for the quantitative measurement of water changes within the soil column and thus, in combination with precipitation and lysimeter seepage measurements, also the estimation of evapotranspiration.

Formally, the lysimeter evapotranspiration EL (mm) within a given time interval Δt (here 1 h) is estimated from the initial weight Wt minus the final weight Wt+1 (both in kg), the precipitation P (mm), and lysimeter seepage QL (mm) at the vessel bottom: EL=Wt-Wt+1ρwπr2+P-QL, where ρw stands for the density of water (kg m-3) and r (m) for the radius of the lysimeter. For the comparison with eddy covariance measurements, we derive a parallel time series “EL0” in which EL  is set to 0 during hours with precipitation (P ≥ 0.1 mm, 15.4 % of data), as no reliable data are available from the EC measurements in those cases (see Sect. 2.3).

The Rietholzbach lysimeter has a surface area of 3.1  m2 (radius of 1 m) and a total depth of 2.5 m including a gravel filter layer at the bottom. This size of vessel ensures a higher quality of the measurements (see Seneviratne et al., 2012, and references therein). The lysimeter weight is measured with three load cells and a resolution of 100 g, which corresponds to a water column of approximately 0.03 mm. The surface is covered by grass of similar species composition and treated according to the surrounding grassland (same cutting scheme, but synthetic fertilization instead of slurry; see also Fig. 2). At its installation at the site “Büel” in late 1975, the lysimeter was backfilled with a typical gleyic Cambisol. Seepage at the lysimeter lower boundary is measured by a tipping bucket with a volume of 50 mL, i.e., with a resolution of 0.02 mm (Gurtz et al., 2003). Following the recommendations of the World Meteorological Organization (WMO, 2008), precipitation data were not derived from the lysimeter measurements but were taken from a standard tipping bucket (see Sect. 2.5).

A key requirement for the accurate estimation of local evapotranspiration is the representativeness of the lysimeter for the surrounding area in terms of soil conditions, vegetation composition, and treatment. Major drawbacks are the existence of the vessel and its specific design (Allen et al., 2011; WMO, 2008). At the investigated site, this implies the main following limitations: i.

The lateral water transport is not contributing to the lysimeter water storage dynamics. This point is assessed as being relatively negligible, as the lysimeter is located in a flat area close to the valley bottom and surrounded by a slight and uniform slope. Thus, potential lateral inflow and outflow to the investigated soil volume are assumed to be equal.

Lysimeter data analyzed in this study cover the time period 1 June 2009 to 31 December 2015 (start being restricted by the availability of the EC measurements; see Sect. 2.3). In addition, we refer to the climatological lysimeter time series dating back to 1976 (see Sect. 2.5). Evapotranspiration is calculated in hourly time steps according to Eq. (1) and taking into account the weight changes due to management activities. Missing values in lysimeter weight change Wt - Wt+1 (< 0.1 % of data) are filled by a linear interpolation as the gaps were short and no precipitation occurred. For lysimeter seepage QL missing values (< 0.1 % of data) are filled manually preserving the actual seepage pattern. Evapotranspiration is defined here as an upward flux, i.e., comprising positive values only, as the lysimeter accuracy does not allow one to resolve dew formation. Yet, Eq. (1) can result in negative EL values, because the measurements entering the calculation are based on instruments with differing resolutions, and because they can be biased due to sensor uncertainty. The latter is in particular the case for the precipitation measurements, which are often biased due to an undercatch (e.g., Sevruk, 1982; Adam and Lettenmaier, 2003). Days comprising negative EL are thus treated as described in Jaun (2003) to eliminate such negative values, being consistent with the scheme used for the climatological data series dating back to 1976 (see Sect. 2.5). It takes into account the amount and predominant sign of EL during such days. The method mainly affects the winter period, when it leads to a reduction of the overall amount of positive EL as compared to, e.g., simply setting all negative EL values to 0 (not shown), as the occurrence of negative EL is increased during this season. Based on measured values, a threshold for maximum realistic EL of 0.2 mm h-1 during nighttime (global radiation Rsd < 10 W m-2) and periods with snow cover (albedo α > 0.5) is applied. In addition, a limitation of EL is defined as a function of Rsd. The subsequent gap filling is conducted in two steps: (i) missing nighttime values (0.7 % of data) are set to 0, and (ii) for missing daytime values (0.8 % of data) a linear regression with global radiation Rsd (R2: 0.67) is applied.

The eddy covariance method estimates the vertical mass flux of water vapor (EEC) exchanged by an ecosystem based on fast measurements of vertical wind velocity w (m s-1) and specific humidity q (kg m-3), respectively, on their turbulent fluctuations (denoted by a prime): EEC=w′q′‾. EEC has been measured at the Rietholzbach catchment since late May 2009. The measurements are conducted on a 9 m flux tower, installed at the site “Büel” (see Fig. 2 and https://s.geo.admin.ch/6de2dcf3b5) and equipped on three levels with an ultrasonic anemometer thermometer (sensor type CSAT3, Campbell Scientific Inc., USA; hereafter referred to as “sonic”). On the bottom and top levels, an open-path CO2/H2O infrared gas analyzer (sensor type Li-7500, LI-COR Biosciences, USA; hereafter referred to as “IRGA”) complete the setup. The instruments are operated at 10 Hz and data are saved with a CR3000 data logger (Campbell Scientific Inc., USA). The present study is based on data obtained from the sensors at the lowest level (2 m above ground), as their source area is smallest and closer to the lysimeter (see Fig. 2), and therefore, they experience more homogeneous physical environmental conditions. However, up to 10 % of the measurements are potentially affected by obstacles (trees and a farmhouse) in the area, whereas only 1 % of the measurements within the main wind direction (i.e., from west, see Fig. 2) are potentially influenced (Peter, 2011, based on the footprint model of Kljun et al., 2004). Note that this level is well above the vegetation height (mostly below 15 cm, maximum 40 cm), and clear of the roughness sublayer (estimated three times the canopy height; see Kaimal and Finnigan, 1994; Foken, 2008). In this study we consider data from the time period 1 June 2009 until 31 December 2015.

To enable the comparison with the lysimeter estimates, the statistics were calculated on an hourly time step following the methodology described in, e.g., Lee et al. (2004) or Aubinet et al. (2012). This includes a time lag correction of w and q by maximization of their covariance, the application of the planar fit method after Wilczak et al. (2001) for the coordinate rotation, spectral correction (Moore, 1986), conversion of the buoyancy flux into the sensible heat flux (Schotanus et al., 1983), and correction of density fluctuations (Webb et al., 1980). As open-path IRGAs are not reliably measuring when water is accruing on the optical elements, λEEC is explicitly set to 0 during hours with precipitation (P ≥ 0.1 mm, 15.4 % of the data).

Figure 2 displays the location of the tower with respect to the lysimeter and the radiation measurements, together with the frequency of wind direction and velocity at the location. The horizontal separation distance between sonic volume and IRGA volume amounts to 0.2 m both laterally and longitudinally, with the IRGA being situated west of the sonic (not shown). EC data are masked when the tower and the IRGA are in the upwind direction of the sonic volume (i.e., from 310 to 50∘, red sector) in order to avoid impacts on the measured turbulent fluxes. This is the case for 10.6 % of the data.

Evapotranspiration EEC is related to the surface energy balance as follows: Rn-G=H+λEEC, where Rn refers to the net radiation, G is the surface soil heat flux (see below), H stands for the sensible heat flux, and λEEC stands for the latent heat flux, where λ (J kg-1) is the latent heat of vaporization. Details on the measurements of Rn and G are given in Sect. 2.5. The storage of energy between the surface and the measurement height is neglected in the analyzed measurements as these are performed at 2 m above short grassland (vegetation height mostly below 15 cm, maximum 40 cm). However, it is not negligible for tall vegetation (e.g., Foken et al., 2006). In addition, effects of diurnal storage changes can be averaged out when considering daily instead of hourly energy balances (e.g., Leuning et al., 2012; Anderson and Wang, 2014).

Advective fluxes are also not considered in Eq. (3). This effect can contribute to a non-closure of the surface energy balance (e.g., Leuning et al., 2012, see also below). The vertical component of advection of latent and sensible heat (see e.g., Paw U et al., 2000; Casso-Torralba et al., 2008) can be assessed at the site following the notation of Lee (1998), which is based on the average vertical gradient of moisture or temperature multiplied by the mean vertical wind speed at a specific level. For a quantitative estimate of the horizontal component of advection, measurements are not available at the site and its surroundings. Possible reasons for horizontal advection include slope drainage in complex terrain and heterogeneous land cover (e.g., Katul et al., 2006). Concerning the first reason (slope drainage), the wind from the south-facing valley slope is masked in all analyses as it includes the tower (see above). Concerning the impact of surface heterogeneity, we estimate the potential effect on the energy balance closure by separating the analyses into three wind sectors (i.e., east, west, and south wind directions). While the west sector (i.e., the main wind direction) features homogeneous land cover and horizontal advection should thus not be relevant, the east sector is potentially impacted by a small street and a farmhouse (see Fig. 2).

For the latent heat flux λEEC the same data constraints are applied as for lysimeter evapotranspiration EL, i.e., during nighttime conditions, periods with snow cover, and limitation by Rsd (see Sect. 2.2). Under the present generally humid climate conditions at Rietholzbach, net radiation Rn is the main driver and limiting factor for λEEC (Teuling et al., 2010b; Seneviratne et al., 2012). Thus, gaps in the λEEC time series (31.1 % of data) are filled by a linear regression (R2: 0.90) of these two variables. However, it should be noted that the simple regression with radiation could lead to errors when evapotranspiration is constrained by soil moisture (e.g., Seneviratne et al., 2010). Overall, the relation between the λEEC and the lysimeter time series is not changed by the gap filling (not shown).

As commonly observed with using EC data (e.g., Twine et al., 2000; Wilson et al., 2002; Franssen et al., 2010), the energy balance is not closed at the investigated site (see Sect. 3.2), i.e., the available energy (Rn  - G) is generally higher than the sum of the turbulent fluxes (H + λEEC). This known issue of the EC method is extensively discussed in the literature (e.g., Mahrt, 1998; Foken, 2008; Aubinet et al., 2012; Leuning et al., 2012). It is important to address this issue also in light of the use of EC data for model validation (e.g., Jaeger et al., 2009).

Several approaches can be used to force close the energy balance. Here we apply three different simple approaches to enforce the energy balance closure on an hourly basis, assigning the gap to i.

both H and EEC according to the Bowen ratio β(EEC_BOWEN)

The catchment water balance integrates its components over the entire catchment area over longer time periods. While we focus here on the comparison of the lysimeter and EC evapotranspiration measurements, such catchment water-balance estimates provide an additional reference to evaluate the local-scale techniques. Using this approach, the evapotranspiration EC is estimated as the difference between precipitation P and catchment runoff QC (all in millimeters): EC=P-QC. This approach implies that the change in catchment storage over the given time interval is 0. This assumption generally only holds for long-term averages (≥ 1 year). Although year-to-year variations in storage cannot be fully excluded (e.g., Seneviratne et al., 2012), it can be assumed to yield a reasonable estimate for hydrological years (October to September in Switzerland). In addition, catchment precipitation is estimated here using one precipitation gauge only (thus assumed to be spatially representative). This approach also assumes that all water is leaving the catchment through the discharge gauge at the catchment outlet (see below). Previous analyses suggest that both conditions are reasonably met for the study catchment (Gurtz et al., 2003; Seneviratne et al., 2012).

Precipitation data are taken from the standard tipping bucket (for details see Section 2.5). As the catchment evapotranspiration EC is known to suffer from unrealistic negative values during winter (Lehner et al., 2010), related to high precipitation undercatch during snowfall (up to 60 %, see Gurtz et al., 2003), the precipitation data entering Eq. (4) is corrected for undercatch (based on Gurtz et al. 2003, Table 1 therein). Catchment runoff (QC) is captured at the catchment outlet at the gauge “Rietholz–Mosnang”. This gauge is operated by the FOEN (Federal Office for the Environment, Hydrology Division, Berne, Switzerland). More information on the gauge is available on http://www.hydrodaten.admin.ch/en/2414.html (last access: 21 February 2017).

Precipitation is measured by a standard tipping bucket installed at 1.5 m. Data from parallel measurements with a standard tipping bucket at 0 m and a weighing pluviometer at 1.5 m at the same measurement site are used for quality assessment and gap filling. For remaining gaps, a regression with data from nearby meteorological stations operated by MeteoSwiss is applied.

Net radiation is derived from separate measurements of all four components of the radiation balance (CM21 and CG4, Kipp & Zonen, NL, all ventilated) at a height of 2 m (see Fig. 2).

Soil heat flux is captured with three heat-flux plates (HFP01, Hukseflux, NL) installed at 0.05 m below ground and situated within a 1 m periphery, which are averaged for the analysis. Surface soil heat flux G is determined following Fuchs and Tanner (1968) by calculating the change in heat storage above the sensors. This estimation is performed using the average of three soil temperature sensors (107T, Campbell Scientific Inc., USA) installed at the same locations as the heat-flux plates, as well as soil moisture (TRIME-IT, IMKO GmbH, D) and soil density measurements (Mittelbach et al., 2012). The ensemble of the three different locations for soil heat flux and soil temperature is used to account for the spatial heterogeneity of the soil matrix and thus to obtain surface soil heat-flux data, which are spatially representative for the footprint domain of all other measured components of the energy balance.

Note that soil heat flux was not measured during a 4-month period from July to October 2014 due to a logger failure. This leads to some gaps in the following comparisons due to the fact that the energy gap corrections (i.e., EEC_BOWEN and EEC_E, see Sect. 2.3) cannot be applied for this time period. Apart from this period, the soil heat flux and net radiation time series only hold few and short gaps (< 0.1 % of data), which are filled by a linear interpolation.

All measurements mentioned in Sect. 2 are ongoing. The descriptions refer to the instrumentation for the data since (at least) June 2009. The climatological data series (since 1976) are generally based on varying sensors (types), but have been homogenized over time. More details on the climatological record and respective instrumentation since 1976 can be found in Seneviratne et al. (2012) and in a German-language report (Gurtz et al., 2006).

We first assess how the measurements in the study period compare with the long-term climatology to evaluate if the study period from 1 June 2009 to 31 December 2015 is representative for the mean climatological conditions at the site. Figure 1 displays the average monthly meteorological conditions during the study period compared to the long-term climatology with respect to air temperature Tair, precipitation P, net radiation Rn, catchment runoff QC, lysimeter evapotranspiration EL, and lysimeter seepage QL. The long-term climatological values are derived over the time period 1976–2015, with the exception of net radiation, which has only been measured since 2000 at the site.

Temperature (Fig. 1a) during the study period ranges on average in the upper part of the distribution based on the climatological data series. This is consistent with the recorded long-term increasing temperature trend in Rietholzbach (Seneviratne et al., 2012) and in Switzerland (OcCC, 2008). The variability within the 7 years is similar to the climatology. Precipitation of the study period (Fig. 1b) shows high variability with extreme values in November 2011 (0 mm) and December 2011 (275 mm). Overall, the precipitation data shows that the spring season is often drier and the summer season often wetter in the 7 considered years compared to the long-term climatology. Absolute values and variability for Rn (Fig. 1c) are close to the long-term average. Catchment runoff and lysimeter seepage (Fig. 1d and f) show high variability within the 7 years and compared to the climatological values. QC and QL show a similar behavior (see also Seneviratne et al., 2012). Lysimeter evapotranspiration EL often shows higher summer values (i.e., mostly for June and August) in 2009–2015 compared to the climatology.

Mean precipitation P of a hydrological year sums up to 1598 mm yr-1 (respectively 1446 mm yr-1 when undercatch is not corrected), whereof about 37 % are evaporated as EC and about 63 % leave the catchment as runoff QC (Table 1). All catchment water-balance components show a high year-to-year variability, which is highest for QC with respect to the mean. However, none of the components displays a significant trend over the entire time period (see also Seneviratne et al., 2012, for trends in calendar-year values over the time period 1976–2007). Figure 3 displays the catchment water balance for the hydrological years since 1976/1977. The comparison with the lysimeter-based evapotranspiration EL suggests that in the long-term mean the E / P ratio agrees well with the catchment water-balance approach. The discrepancies between EC and EL on a year-to-year basis are likely due to non-negligible year-to-year variations in terrestrial water storage (soil moisture, groundwater, snow). In fact, the non-equality of (EL + QL) vs. P indicates annual storage variations at the lysimeter, while for EC the change in catchment storage over the given time interval is assumed to be 0 (see Sect. 2.4).

The hydrological year 2009/2010 is one of the wettest hydrological years in terms of precipitation (+14.5 % resp. +18.6 % compared to the average, undercatch-corrected, and uncorrected values), yet the partitioning of P into QC and evapotranspiration (EC and EL) is still close to the long-term average (Table 1). The pattern of the hydrological year 2010/2011, in contrast, is different. Precipitation is lower than average (-9.8 % resp. -6.9 %) for that year, but evapotranspiration (EC and EL) is up to 1.25 times the average, whereas runoff and seepage (QC and QL) display the lowest values of the entire period (-28.8 and -34.2 % respectively compared to the average). It should be noted that the spring 2011 was very dry (e.g., Wolf et al., 2013; Wetter et al., 2014; Whan et al., 2015), which can partly explain these features. Both hydrological years 2009/2010 and 2010/2011 display amongst the highest evapotranspiration values since the beginning of the measurements (EC and EL). The year 2011/12 appears rather normal on the catchment scale, but the lysimeter again shows high EL (+24.8 % compared to the average) and low QL (-18.2 %). This is followed by a wetter year 2012/2013 with higher P (+10.8 % resp. +10.4 %), QC (+23.8 %) and QL (+16.6 %), but lower EC and EL (-11.1 % resp. -3.9 %). The years 2013/2014 and 2014/2015 finally show again lower than average precipitation (up to -10.5 %). For the catchment, this resulted in below normal QC for both years (-12.4 and -14.1 %) and close to normal EC (+4.2 and -2.7 %). The lysimeter on the other hand shows for 2013/2014 slightly enhanced QL (+6.0 %) while EL is close to normal (-4.8 %). For 2014/2015 it experienced a pronounced drying with high EL (+14.7 %) and low QL (-16.8 %), related to the hot and dry summer of that year (e.g., Scherrer et al., 2016). Overall, the study period covers the climatological variability well, including both years with rather extreme conditions as well as years close to average conditions (see Table 1).

The energy balance closure as evaluated from the ordinary least-squares regression between the hourly estimates of the turbulent fluxes (H + λEEC) and the available energy (Rn - G) reaches values of 0.77 for the slope and 18.94 W m-2 for the intercept (R2: 0.94, Fig. 4a; note ideal closure is represented by an intercept of 0 and slope of 1). The ratio of the total amount of the turbulent heat fluxes to available energy amounts to 101.9 %, indicating a surplus of turbulent energy. This is due to mostly slight positive nighttime values of the sum of the turbulent fluxes while available energy displays negative values during night (see Fig. 4b). Ignoring nighttime values (Rsd < 10 W m-2), the closure ratio amounts to 86.4 %; i.e., the sum of the turbulent fluxes H + λEEC is generally lower than the available energy Rn - G. The regression between the daytime hourly estimates reveals a slope of 0.80 and intercept of 10.63 W m-2 (R2: 0.94). All these values are in the range of values reported in literature (e.g., Wilson et al., 2002). Note that the analyses presented here are based on measured data only (i.e., excluding gap-filled data) and masked for precipitation and for wind directions impacted by the tower (see also Sect. 4.2).

Hourly energy balance closure is also compared with daily closure for days where maximally five of the hourly values were gap-filled, which leaves 462 days of valid EC observations (Fig. S1 in the Supplement). The energy balance closure slightly improves on daily timescales: regression slopes increase from 0.76 to 0.84, and R2 from 0.95 to 0.97. The increase of the energy balance closure from hourly to daily timescale hints at an effect of diurnal storage variations on hourly timescale, which tend to get averaged out on daily timescale (see Sect. 2.3).

As mentioned in Sect. 2.3, advective fluxes are not accounted for in the energy balance Eq. (3) and can contribute to the imbalance between the turbulent fluxes and the measured available energy. The estimated amount of vertical advection reveals that the magnitude of vertical advection of latent and sensible heat is small (on average at most around -0.1 W m-2 respectively 0.05 W m-2 at noon; see Fig. S2) compared to the respective average turbulent fluxes (less than 1 %). For horizontal advection, the potential effect on the energy balance closure is estimated by separating the closure analyses into three wind sectors (i.e., east, west, and south wind directions; note that sector north is completely masked due to the presence of the tower in that sector). We focus on daytime here in order to rule out biasing due to the differing distribution of nighttime fluxes among the wind sectors, which are typically small yet can have opposite directions. The results of these analyses reveal that the energy balance closure is rather independent of the wind direction (see Fig. S3). The slope and R2 of the regression analyses are similar for all three wind sectors. This also holds for the daytime ratio of the total amount of the turbulent heat fluxes to available energy, which amounts to 86.5, 86.8, and 82.1 %, respectively, for the east, west, and south sectors. This robustness in the energy balance closure independent of the wind direction (in light of spatial homogeneity in the west sector and the small street and the farmhouse in the east sector; see Sect. 2.3) indicates that horizontal advection is not of great importance at the site.

The mean daily patterns of the energy balance components (Fig. 4b) show that during nighttime H and λEEC often are of similar small magnitude but opposite sign, resulting in slight positive nighttime values of the sum of the turbulent fluxes and an energy balance closure gap equivalent to about the amount Rn - G. The zero crossing of Rn and H occurs at around 07:00 CET when λEEC starts to increase as well. G is delayed by about 2 h. All fluxes have their peak value around 13:00 CET. In the afternoon Rn and H change sign again after 18:00 CET, followed by G. λEEC reaches the nighttime values at around 20:00 CET. Available energy is larger than the turbulent fluxes throughout the day. The energy balance closure gap displays a pronounced daily cycle. During nighttime the closure gap is almost constant at around 25 W m-2 and the largest closure gap is found around noon. The overall daily cycle of the energy closure gap is approximately symmetric around the noon peak, and generally increases with higher fluxes.

Figure S4 displays the daily cycles of surface and 5 cm soil heat fluxes, as well as of soil temperature (see Sect. 2.5). For the latter two, the average based on the three heat-flux plates and the three soil temperature sensors respectively are shown, while the range is based on the data from the three individual sensor locations (and displays the minimum and maximum values, respectively). For the surface soil heat flux, the estimate calculated from the averaged heat-flux plates and temperature sensors is displayed, along with a minimum and maximum estimate based on the individual sensor locations. The effect of the correction based on Fuchs and Tanner (1968) is clearly visible and leads to a shift of the daily cycle of the surface soil heat flux vs. the 5 cm soil heat flux, and to an enhancement of the daily amplitude. The range of the surface soil heat fluxes amounts to 6.7 W m-2 on the average. Especially during nighttime, this amount is substantial compared to the available energy of around -25 W m-2. These results illustrate the spatial heterogeneity of the surface soil heat-flux footprint and underline the importance of employing a set of several soil heat-flux sensors in order to obtain spatial representativeness of the data.

In the following we compare the evapotranspiration estimates on different timescales, from yearly down to hourly timescales. The lysimeter values EL and EL0 are used as reference. The analysis is based on the period 1 June 2009 to 31 December 2015, respectively on the 6 hydrological years therein (i.e., 2009/2010 to 2014/2015). For consistency with EL (see Sect. 2.2), also only the upward fluxes are considered for EEC (i.e., thus based on (neutral to) unstable conditions only). This may result in sums of EEC_H to become higher than the sums of EEC_BOWEN (depending on the distribution of the negative hourly fluxes; see Figs. 5 and 6). Note that the absolute sum of negative EEC amounts to 2.3 % of positive EEC.

Table 2 summarizes the evapotranspiration values of the different methods for the hydrological years 2009/2010 to 2014/2015. The lysimeter estimates (EL) range between 537 and 704 mm yr-1. Setting evapotranspiration to 0 during precipitation events (EL0) allows for a comparison with the estimates of the eddy covariance method and reduces the values remarkably to a range of 521 to 672 mm yr-1 (by up to -8 and -5 % on the average). Except for EEC_E, the eddy covariance estimates show mostly lower values than the lysimeter estimates.

The monthly evolution of EL0 (and EL for comparison) displayed in Fig. 5 displays a pronounced seasonal cycle with highest values in summer and lowest values in winter. EL0 in spring is higher than in autumn. The difference of the monthly EC estimates to EL0 (Figs. 5 and 6) exhibits a seasonal cycle as well, with highest absolute differences in summer when the highest fluxes occur and highest relative differences in winter. The EC estimates mostly underestimate (overestimate) EL0 in summer (spring), while there is no clear tendency during autumn and winter. The EEC_BOWEN estimates based on the daily force closure (see Sect. 2.3) show a consistent temporal evolution but a reduction of EC evapotranspiration compared to the one based on the hourly force closure (see Fig. S5). The underestimation of the EC estimates in summer based on the hourly force closure thus becomes slightly larger, while the rather positive EC bias in winter turns into a predominantly negative bias.

A similar picture results from the analysis of daily (not shown) and hourly evapotranspiration values. Regarding the latter, Fig. 7 displays a scatter plot of hourly values from our reference lysimeter-based evapotranspiration measurement EL0 and from the different EC evapotranspiration estimates for the raw measured data (excluding gaps). Overall, all EC-based estimates appear to underestimate EL0 (slopes of less than 1, and negative biases except for EEC_E), in particular for high values. However, the R2 values are similar for the different EC estimates. In addition, hourly EEC_BOWEN and EL0 is compared for different meteorological conditions and times of the day (see Tables S1–S3 in the Supplement). The agreement between EEC_BOWEN and EL0 (visible in R2 and the relative bias) is worst during nighttime when evapotranspiration is low and less variable (Tables S2 and S3). For the same reason, also low vapor pressure deficit worsens the statistics, as evapotranspiration is also lower in such conditions. Moreover, the statistics during southern wind directions are worse than for the other wind sectors (however, based on much less data). Wind speed, on the other hand, does not seem to have a strong impact on the agreement between EC and lysimeter evapotranspiration, except for the increase in relative bias for low wind speed during western wind directions (Table S1).

The analysis of the hydrological year-based evapotranspiration values derived from the catchment water-balance approach EC and from the lysimeter EL (Fig. 3, Table 1) shows that the considered period with parallel EC and lysimeter measurements is representative and covers the climatological variability at the site well (see also Fig. 1). Despite the scale discrepancy (catchment vs. local scale), EC and EL overall show a similar magnitude of the fluxes. In addition, a previous comparison of the lysimeter seepage and whole-catchment runoff at monthly timescale revealed a high correlation in these measurements (Seneviratne et al., 2012). Based on this, we infer that the local-scale lysimeter measurements are representative for the whole catchment.

The difference between the EC evapotranspiration estimates and the lysimeter evapotranspiration EL0 displays a seasonal dependency with the highest absolute differences in summer, with EEC_BOWEN showing about 10 % lower values during this season (on the monthly timescale). On the other hand, highest relative differences occur in winter (as shown in Figs. 5 and 6). Despite these differences, it is important to note that overall good agreement between the two measurement techniques is achieved.

In terms of instrumental uncertainty of EC measurements, attention was spent on the surface heating effect of the IRGA and its influence on the measured fluxes (e.g., Burba et al., 2008). Reverter et al. (2011) showed that for evaporation fluxes the impact is much smaller than for CO2. The instrument at the site is tilted downwards at an angle of 45∘ in order to minimize the impact on the near-infrared signal by direct solar radiation, as it faces south, and thus to minimize the surface heating effect. This orientation of the IRGA also reduces the accumulation of rainwater on the optical element (see Sect. 2.3). Recently, the accuracy of the vertical wind component w measured with non-orthogonal sonics and the temperature measured by sonics have been under discussion as a potential source of lack of closure. But the different studies disagree on the impact (Loescher et al., 2005; Mauder et al., 2007; Burns et al., 2012; Kochendorfer et al., 2012; Frank et al., 2013; Mauder, 2013), and further investigations are thus needed.

In addition, a drawback of the EC method is the commonly observed closure gap of the energy balance (see Sect. 2.3). The possible underlying reasons are discussed extensively in literature (e.g., Mahrt, 1998; Foken, 2008; Franssen et al., 2010; Aubinet et al., 2012; Leuning et al., 2012). Similar values and daily patterns of the energy balance closure are reported in numerous studies (e.g., Wilson et al., 2002; Franssen et al., 2010) and are also consistent with the data presented in this study. The complex determination of evapotranspiration with the EC method does not allow for a simple error analysis. The closure gap of the energy balance is taken here as an appropriate error estimate assuming an error of less than 5 % in the measurement of the available energy. Thus, the bias in the turbulent fluxes is assumed to be on the order of 5–15 % with a clear daily cycle and higher relative (but smaller absolute) errors during nighttime.

Our analysis also points at another contributor to an overall underestimation of turbulent fluxes by the EC method, namely the lack of reliable latent heat-flux measurements during and following precipitation events. Because of its sensitivity to precipitation, the operation of an open-path IRGA at a rainy site results in a larger fraction of erroneous data in the EEC time series. The assumption is made that EEC is 0 during hours with precipitation (see Sect. 2.3). But the difference between EL and EL0, which reaches up to 8 % (with an underestimation for EL0), shows that this assumption can lead to substantial underestimation of actual evapotranspiration, e.g., because it does not always rain during the entire integration period and it takes a while after a precipitation event until the optical elements are dry again. This is an interesting result for the interpretation of the EC measurements, as EEC is often found to be closer to EL0 than to EL in this study.

Figure 8 shows the energy balance closure analysis as calculated by masking precipitation hours (left part) compared with the same analysis taking into account all hours (i.e., including precipitation hours, right part). As mentioned in Sect. 3.2, the energy closure amounts to 86.4 % (for daytime and masked precipitation) for the measured turbulent fluxes (i.e., no gap correction). For the three applied force-closing methods (see Sect. 2.3) the gap becomes closed per definition. When precipitation hours are included in the analysis, the EC-based energy balance gap becomes larger due to the additional contribution of available energy during these hours (i.e., 81.5 % closure). Applying a correction for the missed latent heat flux during precipitation hours (based on the EL vs. EL0 comparison of Table 2, i.e., increasing latent heat flux by 5 % on the average) results in a closure of 84.4 %. This shows that the amount of underestimation of latent energy during precipitation hours is substantial compared to the overall energy imbalance, contributing about 15 % to the uncorrected gap (cf. 81.5 % vs. 84.4 %). Applying in addition the energy gap correction of the precipitation-masked data (i.e., from Fig. 8, left part) results in closures of 97.1, 97.5, and 97.7 %, respectively. Thus, the additional amount of evapotranspiration during precipitation hours as estimated by the lysimeter corresponds well with the independent measurements of available energy during these periods. It should be noted here that the amount of underestimation of evapotranspiration during precipitation periods scales with the time step used in Eqs. (1) and (2).

The site-specific error in the lysimeter evapotranspiration is discussed in Seneviratne et al. (2012). An overall measurement uncertainty of 5–10 % is assumed, whereas higher errors (20 % or more, e.g., Gurtz et al., 2003) can be assumed during periods of snow cover. In the latter case, also errors in the precipitation measurement (high undercatch under snowfall, e.g., Rasmussen et al., 2012) strongly contribute to errors in EL. While these errors are large in relative terms during the affected months, they are nonetheless only affecting EL when it is at very low values (late autumn, winter, and early spring; see Fig. 1). Hence, they should neither substantially affect the lysimeter evapotranspiration during the growing season nor when aggregated on the yearly timescale.