The study site Tharandt DE-Tha (50.96235° N, 13.56529° E, 385 m a.s.l.) is part of the Integrated Carbon Observation System ICOS (https://meta.icos-cp.eu/resources/stations/ES_DE-Tha, last access 23 October 2024) and equipped with a well maintained environmental research structure to provide meteorological, hydrological and ecological measurements. It is located in the Tharandt Forest (60 km2), which is situated in the lower Eastern Ore Mountains about 25 km southwest of the city of Dresden (Germany). The first national monitoring network dedicated to forest-meteorological observations is associated with the Tharandt Forest. The network also happens to be the location with the first reported direct observations of throughfall in the mid-nineteenth century .

The forest at the research site is subject to standard management and is mainly characterized by evergreen conifers. A spruce stand was established in 1887. Today, it consists of 72 % Norway spruce (Picea abies) and 15 % Scots pine (Pinus sylvestris). The remaining canopy is composed of deciduous trees with 10 % European larch (Larix decidua), 1 % birch (Betula spec.) and 2 % other species using data from 1999 as a reference . The more recent stand is described in detail by with a dense canopy (335 trees ha-1), a mean tree height of 31 m and an open trunk space with sparse understory for the year 2008. Continuous in-canopy radiation measurements yielded a leaf area index LAI value of 7.1 around the flux tower for the same year. The general characteristics of the canopy have not changed significantly for 25 years. concluded in a long-term interception study that changes in stand structure, density and LAI remained relatively small and less variable for the period 2008 to 2018. The canopy can be characterized as sufficiently homogeneous for the source area of the throughfall measurements. However, the statistic representation of rainfall partitioning for the footprint of the EC flux measurements by the throughfall collection plots in the vicinity of the tower has not been analyzed in detail so far. Direct flux measurements (including sensible H and latent heat LE) are carried out above the forest canopy in 42 m above ground together with a multitude of meteorological measurements (global and net radiation Rg and Rn, air temperature Tair, relative humidity rH and wind speed u) at various heights of the tower. A detailed summary of the instrumentation and data quality can be found in . The collection of throughfall and gross precipitation is described in detail by . In summary, two large trough systems of 10 m length each and a total area of 3.18 m2 are collecting throughfall with a time resolution of 10 min. The measurements are restricted to periods without frost, typically from April to September. Gross precipitation is measured with a resolution of 10 min about 130 m west of the flux tower in a forest clearing of 50×90 m called Wildacker, which is also the location of the meteorological station. Warm summers with mostly convective precipitation and cold winters with weaker frontal rain or snow are characteristic for the sub-continental climate of the study site. Mean annual temperature is 8.7 °C and mean annual sum of precipitation is 842 mma-1 based on long-term records for the period 1991 to 2020.

All data used in this study refer to the period 2008 to 2010, since a detailed 3D representation of the forest is available as a result of terrestrial laser scans during these years . A map of the study site with vertically integrated PAD (PAI_Local) of the area is shown in Fig. .

The classical canopy water balance WB serves as a reference to quantify interception for the study site DE-Tha (Eq. ). Here, data of gross precipitation Pg measured in a forest clearing was gapfilled and corrected by independent rainfall measurements of daily resolution . Stemflow TS is considered to be negligible for the dominating spruce trees in the research area due to their bark structure and architecture . Forest floor interception EI,FF is difficult to measure as it is very heterogeneous on the small scale. summarize the importance of EI,FF, which is nearly constant throughout the year and accounts on average for 22 % of throughfall. However, evaporation of intercepted water from the litter takes longer than that from the canopy, thus we assume that the forest floor evaporation during an event is negligible. Alternatively, it could be be addressed by additional measurements combined with models, which is beyond the scope of the study. Thus, measurements of free throughfall Tf and drainage TD (above the litter layer of the forest floor) are representing net precipitation Pn, allowing to calculate interception EI,WB from the canopy water balance (WB) as the residual of Pg and Tf. 2Pg=Tf+TD+TS+EI,WB+EI,FF3≈Tf+TD+EI(WB)4≈Pn+EI(WB) EI,WB is analyzed as the sum based on events and no attention is given to the dynamics on a sub-event scale. Only data with liquid rainfall during frost free periods was analyzed and all events with mean temperatures less than 2 °C and minimum temperatures lower than 0 °C were excluded from the analysis.

The conceptual framework after was applied calculating the canopy water balance for the spruce forest dynamically. Two model setups were employed to account for spatial variable vegetation characteristics in the study area. In a basic approach, the whole vegetation stand of the study area was modelled as one big leaf with a mean PAI of 4.65 m2m-2. The second model did describe the horizontal variability of the vegetation with a resolution of 10 m in a gridded domain of x=1140m and y=800m. Both of the models are big leaf models that use no vertical differentiation over the entire height of the vegetation (33 m). The vegetation structure was captured by airborne laser scanning and terrestrial laser scanning (see ). From the work of a vegetation model with a spatial resolution of one cubic meter was available which was integrated to gain the 10 m resolution. The resulting spatially variable PAI_Local of the study domain is presented in Fig.  with an overall PAI of 4.65 m2m-2 and a PAI of 6.54 m2m-2 for the area of the gutter measurements used for the canopy water balance approach. Please note that this values are somewhat smaller than the LAI given in the description of the study site, as they are (i) methodologically different measures and (ii) not related to the same source area. The LAI of 7.1 around the measurement tower refers to the total projected leaf area per unit ground area and is a result of continuous in-canopy radiation measurements during the year 2008. The PAI includes both leaves and woody components and was derived from the above mentioned 3D representation of the forest. Processes and model parameters such as partitioning of precipitation and evaporation components, drainage or canopy storage capacity, are calculated as a function of PAI. Storage depletion is simulated by an exponential drainage approach and by evaporation, which is calculated based on the Penman-Monteith (PM) equation. This results in a water and energy budget for each grid cell depending on the distribution of vegetation (PAI) in the study area. Model structure, parameters and main process equations are explained in detail in Appendix .

The meteorological input included a time series of wind speed u, water vapor pressure vpd and air temperature Tair in 33 m height, as well as net radiation Rn and global radiation Rg in 37 m height. The model simulations were conducted for the period from 2008 to 2010. The resulting events of interception were filtered for liquid rainfall conditions with frost free periods (only events with mean and minimum temperatures higher than 2 and 0 °C, respectively). Time steps between modelled and measured data (EC and 2D approach) were synchronized for comparison. The grid of the 2D simulation results was assigned to the respective footprint areas of the EC measurement and to the area of the throughfall collectors (WB approach). The model performance was evaluated by the coefficient of determination R2, relative absolute error RAE (Eq. ) and Nash-Sutcliffe-Efficiency NSE (Eq. ) for measured (obs) and modelled (mod) throughfall (with μ as the average value). 9RAE=∑(|obs-mod|)∑(|obs-μobs|)10NSE=1-∑(|obs-mod|)2∑(|obs-μobs|)2

The 2D model was evaluated on event basis by canopy interception EI,WB (Eq. ), which is retrieved according to the WB approach described in Sect. . Modelled events were filtered for liquid rainfall conditions (frost free periods), for which the reference measurements of the canopy water balance approach (WB) are reliable. Additionally, only events with footprints fitting inside the model domain were selected. Figure  shows the 2D model results for (i) the location of the throughfall collectors (WB location), (ii) the dynamic flux footprint area (footprint) and the (iii) whole model domain (2D domain). Additionally, the simple big leaf approach for the overall PAI of the grid cells covering the area of the throughfall collectors is depicted in the last panel on the right (big leaf) of Fig. .

For the majority of events, modelled sums of interception evaporation are agreeing very well with the observations EI,WB. The 2D model of the WB location is showing the best agreement with the observed data (NSE = 0.85 and RAE = 0.21), due to matching source areas. However, a view events exceeding evaporation sums of around 8 mm are underestimated by the model, this and the scatter of larger events lead to an overall slope of 0.87. With increasing source areas covering the respective footprints of the EC measurement or the whole model domain, modelled sums of interception evaporation are decreasing, yielding slopes of 0.78 and 0.73, respectively. Due to a higher overall PAI of 6.54 m2m-2 in the WB location, a higher amount of precipitation can be stored on and evaporated from the canopy surface, than for the whole model domain with an overall PAI of 4.65 m2m-2. These results indicate, that the spruce forest of the study area cannot be considered homogeneous and that the WB approach does not reflect the rainfall interception for the wider area around the EC tower.

Modelled evaporation from interception of the simple big leaf approach for the WB location (Fig. , right) agrees only well with observations for events up to 3 mm. This amount corresponds exactly to the storage capacity of the model and the transition from an unsaturated to a saturated canopy leads to an underestimation by the big leaf approach. For events with a precipitation exceeding canopy saturation, modelled throughfall is overestimated leading to underestimated amounts of EI. Results might be improved by adjusting the storage capacity of the model. However, the big leaf model also leads to a higher amount of total interception events (n=302) due to faster drying. In the 2D model approach a variety of grid cells with different PAI is considered, leading to spatially variable storage, throughfall and drainage and finally the interception event ends with the last cell being dry. Unlike the big leaf approach, this reflects more on the process of precipitation routing within the canopy, which leads to a better fit to observed EI.

Table  summarizes the selected interception events of the 2D model shown in Fig.  as average totals over the years 2008 to 2010. On average 50±9 events were evaluated for each year, which do not represent an annual budget. Additionally the results of the independent WB approach (Tf, EI) and the water equivalent of LE from the EC measurement (Etot) are presented. Average annual sums of Tf and EI for the 2D model of the WB location are comparing very well with the independent WB approach. The 2D model shows a slight overestimation for throughfall of only 3 mma-1 for the sums of selected events, which in turn leads to a 3 mma-1 underestimation of EI. As discussed above, the WB approach does not reflect the evaporation conditions of the larger footprint area due to differences in vegetation structure and plant area. Hence, average annual sums of Tf are higher for the respective footprint areas (81.18±9.19 mm), resulting in lower sums of interception evaporation (65.62±7.30 mm).

Due to the high agreement with the WB approach, the physically based 2D model is considered as a good reference for further analyses of evaporation components under interception conditions. Thus, EC-based estimates of Etot are compared to the 2D model estimates of total evaporation for the respective EC footprint areas. The average annual sums of the selected events in Table  demonstrate that evaporation measured by the EC method under interception conditions (35.33±2.19 mm) shows a systematic underestimation with a slope of 0.41 (regression not shown), compared to the 2D model (79.22±9.05 mm). The lower part of Table  shows the fraction of precipitation being stored on the canopy as interception (EI:Pg) and the fraction of precipitation contributing to the total evaporative flux (Etot:Pg). As only a selection of events is taken into account for the analysis, these fractions are not representative as an annual reference. However, modelled and measured EI for the WB location account for 50±4 % and 52±4 % of precipitation. Due to lower amounts of interception for the footprint areas, EI:Pg is lower with a ratio of 45±3 %. Total evaporation measured by the EC method under interception conditions accounts only for 24±2 % of precipitation, which is even below the fractions referring to the interception component only. Modelled Etot of the footprint related areas accounts for 54±5 %, which again indicates that fluxes measured by the EC method are not being well captured under wet conditions.

If the 2D model results are analyzed to estimate the annual water budget of the spruce forest, EI for the whole study domain accounts for 28±3 % and ET for 29±5 % of mean annual precipitation. The interception component EI contributes 49±1 % and transpiration ET 51±1 %, respectively, to modelled total evaporation Etot.

A direct comparison of evaporation by different methods such as eddy covariance EC or canopy water balance WB is not so simple due to different source areas and uncertainties in the respective approaches. The evaluation of the results of both methods presupposes on the one hand similar or homogeneous interception properties, such as meteorological conditions and vegetation characteristics, in the respective source areas. On the other hand, it is assumed that transpiration and evaporation from litter/soil are negligible for saturated conditions or sufficiently closed canopies. Then, measured total evaporation by the EC approach can be substituted by EI. The application of the 2D Rutter model has shown that the classical canopy water balance approach is not statistically representative for the EC footprint area or a larger domain of the investigated spruce forest. The accuracy of the WB approach depends on the structural characteristics of vegetation and on the precipitation regime. Spatially variable Tf and EI, as presented by the model results, require increased sampling efforts than the two throughfall collection gutters. Additionally, reported generally higher relative throughfall sampling errors (up to 40 %) during events with low intensities. suggested to use a scaling factor to compare the different source areas based on the LAI ratio of the average footprint area and the WB location. However, this is not in agreement with the 2D model results for both areas. Modelled evaporation sums of the footprint area are about 0.9 times the amount of the WB location (regression not shown here), while the ratio of the respective PAIs is 0.71 ( used the LAI ratio and arrived at a scaling factor of 0.8).

The model results for the source area of the WB approach agree very well with the observations under frost-free and liquid precipitation conditions. However, some events caused by long (>10 h) or intense precipitation (>10mmh-1) were underestimated by the model and could be further improved by an adjustment of storage parameters or drainage coefficients. Nevertheless, the 2D model was used confidently as a reference for evaporation estimates under liquid interception conditions. An earlier comparison with the EC measurements of latent heat by already demonstrated a systematic underestimation of LEEC, which was also concluded by , , and . When compared for selected events, EC derived evaporation accounts for only 24 % of total precipitation, which is an untypically low proportion for a dense coniferous forest under a temperate climate. Modelled total evaporation for the footprint area accounted on average for 54 % of Pg for the same events. The analysis of an example event emphasized high deviations between the model reference LE2D and LEEC during precipitation and conditions with increased canopy water storage C. These conditions usually coincide with high relative humidity, which can lead to biases due to incorrect low-pass filtering of water vapor especially in closed-path systems . More than 80 % of the data exceeding a relative humidity of 75 % can be attributed to an interception event. Interception conditions prevail on around 55 ± 7 % of all days of the year, of which 21 ± 3 % are with precipitation. Hence, a majority of data is affected by the systematic underestimation effect of LEEC during interception. This applies also to the analyzed period 2008 to 2010, with an above-average annual precipitation sum of 1088 ± 138 mma-1 as compared to the long-term record for the period 1991–2020 with an average annual sum of 842 mma-1.

The unaccounted energy as shown by LER, absolute and relative energy balance residual along bins of rH can be mainly explained by two different phenomena related to dry and wet conditions, respectively. In principle, the following explanation presupposes that systematic measurement errors are already minimized as much as possible in the data processing. Under dry or moderate rH conditions up to 75 %, no LER dependency on humidity was detected. These conditions are generally associated with strong energy fluxes prevalent in daytime convective boundary layers under unstable stratification. Hence, the absolute potential underestimation of LEEC as shown by the differences to LEEB was highest under dry conditions. and concluded, that the absolute median of the residual is greatest under very unstable and unstable conditions. The related systematic error can be explained by insufficient sampling of large-scale coherent eddies through secondary circulations. Assuming scalar similarity, the Bowen ratio of the measured fluxes is equal for large-scale structures, which allows to adjust the underestimated fluxes according to . More recent adjustment methods to correct turbulent EC fluxes for secondary circulations such as proposed by or are also applicable and should be considered for further studies.

For wet conditions with rH exceeding 75 %, a strong non-linear LER dependency on humidity was detected. This LEEC underestimation effect highly coincides with precipitation and interception conditions when water is stored on the canopy. This concerns stable and advective “wet-bulb” conditions. denote conditions of enhanced water vapor transport and low available energy as “pseudo-stable”, since the stability caused by these circumstances does not follow the classic definition of a generally suppressed turbulent transport. The study analyzed EC measurements of LE, EBC and nine correction methods for LEEC (residual and Bowen ratio based approaches) over irrigated vineyards, as well as uncertainties relative to atmospheric conditions. They found a generally larger uncertainty of LE estimates across methods for days and sites with more prevalent daytime pseudo-stable conditions. Hence, solely energy balance based correction methods show strong deviations under various atmospheric conditions , since the reasons for the underestimation of fluxes differ. As a consequence, we extended the energy balance framework in the processing and interpretation of EC data by including the study site's water budget to obtain more reliable latent heat fluxes under wet or interception conditions. The validated 2D Rutter approach served as an independent estimate of LE for interception conditions. Absolute and relative changes in LEEC were in agreement with the findings of . They corrected potential biases of LE caused by incorrect low-pass filtering of water vapor with a data driven machine learning approach. We suggest that a physically based model is preferable to obtain reliable estimates of evaporation on a half-hourly time scale.

Consequently, we combined the two methods addressing different causes for the systematic underestimation of latent heat flux to arrive at a consistent dataset adjusted for dry and wet conditions. The new dataset LEWB yields an average annual increase of total evaporation of 263 ± 26 mma-1. Other than for the solely Bowen ratio based adjustment method, the new approach also shows a strong increase of evaporation for the winter half year, in which pseudo-stable conditions play a major role. estimated evaporation for DE-Tha for the period 1997 to 2020 using the water budget model BROOK90 . They show that in particular the interception component for different model parameter sets is reduced after calibration to the EC flux data adjusted for energy balance closure by a standard Bowen ratio preserving approach. Chapter 3 in states as a common result of several independent comparisons between models and EC measurements that modelled latent heat flux above forest is often overestimated and unlikely to match the (corrected) EC measurement, while short vegetation and cropland is often reasonable well-modelled. A question which arises from these common observations is whether EC measurements of latent heat fluxes for forest ecosystems might be a reasonable reference for the calibration and validation of evaporation models, especially considering the systematically underestimated interception component and the still remaining decreasing relation between LEβ along increasing rH.

estimated long-term total evaporation as the residual of the water balance for the Wernersbach catchment, which is also located in the Tharandt Forest with a similar tree species distribution as the flux tower site DE-Tha. They retrieved an average annual Etot of 709 mma-1 which corresponds to 77 % of precipitation for the period 2000 to 2009. This value is about 71 mma-1 higher than our result after adjusting dry and wet conditions separately for relatively wet years in 2008 to 2010. However, they explained that a difference between 40 and 85 mma-1 could be due to different site conditions. They also compared their findings to the flux measurements of DE-Tha adjusted solely based on the energy balance and concluded, that the differences between the two sites are too large to be explained by different site conditions alone. However, with independent measurements on transpiration and interception as well as roughly estimated soil evaporation and understory evaporation they estimated annual evaporation at DE-Tha and arrived at a value of 631 to 676 mma-1 for 2006 to 2019, which is very close to our adjustment method LEWB with 638 mma-1.

However, extending the energy balance framework by including the water budget in the processing and interpretation of EC data requires either statistically representative throughfall measurements or a reliable canopy water budget model. Detailed information on the vegetation characteristics such as PAI is necessary to match the footprint of the EC measurements and to spatially represent the investigated ecosystem. We demonstrated that our physically-based 2D Rutter model approach can reproduce sums of interception for the source area of independent canopy water budget measurements. Since the 2D model with a closed energy balance agrees very well with canopy water budget measurements, the model results of the EC footprint confidently served as a reference to analyze and adjust EC-based evaporation. However, the model was only validated for liquid rainfall conditions and frost-free periods, since throughfall measurements are only reliable during these conditions. The application of the results to the whole year, especially situations with snowfall, should be further investigated. Firstly, there is a lack of reference data and secondly, the modelling approach does not differentiate between solid and liquid precipitation. We expect that our combined water and energy balance adjustment approach LEWB is still plausible, since snow interception for DE-Tha is estimated less than 2 % if distinguishing these processes . Additionally, a more accurate representation of the precipitation and evaporation distribution could be made possible by considering the vegetation as a volume in a 3D version of the model. The integration of a soil volume could account for vertical soil water movement and storage. A further analysis of the model for a longer study period, also covering dry years or extreme precipitation conditions would be interesting to test the performance of the model. Accurate process modelling will play an important role, given the intensification of rainfall extremes and droughts .