Validation of a coupled δ 2 H n -alkane – δ 18 O sugar paleohygrometer approach based on a climate chamber experiment

. The hydrogen isotope composition of leaf-wax-derived biomarkers, e.g., long-chain n -alkanes ( δ 2 H n -alkane ), is widely applied in paleoclimate. However, a direct reconstruction of the isotope composition of source water based on δ 2 H n -alkane alone is challenging due to the enrichment of heavy isotopes during evaporation. The coupling of δ 2 H n -alkane with δ 18 O of hemicellulose-derived sugars ( δ 18 O sugar ) has the potential to disentangle this limitation and additionally to allow relative humidity reconstructions. Here, we present δ 2 H n -alkane as well as δ 18 O sugar results obtained from leaves of Eucalyptus globulus , Vicia faba , and Brassica oleracea , which grew under controlled conditions. We addressed the questions of (i) whether δ 2 H n -alkane and δ 18 O sugar values allow reconstructions of leaf water isotope composition, (ii) how accurately the reconstructed leaf water isotope composition enables relative humidity (RH) reconstruction, and (iii) whether the coupling of – δ 18 O sugar paleohygrometer approach for paleoclimate and relative humidity reconstructions.


Introduction
Leaf-wax-derived biomarkers such as long-chain n-alkanes and their stable hydrogen isotope composition (δ 2 H n-alkane ) are widely applied in paleoclimatology. Sedimentary δ 2 H n-alkane values correlate with δ 2 H of precipitation (Huang et al., 2004;Mügler et al., 2008;Sachse et al., 2004;Sauer et al., 2001), confirming the high potential of δ 2 H n-alkane to establish δ 2 H records of past precipitation (Hou et al., 2008;Rao et al., 2009;Sachse et al., 2012). However, this interpretation is challenged by heavy-isotope enrichment during evapotranspiration (e.g., Zech et al., 2015). Apart from studies of sedimentary cellulose (Heyng et al., 2014;Wissel et al., 2008), the oxygen stable isotope composition of sugar biomarkers (δ 18 O sugar ) emerged as a complementary paleoclimate proxy during the last decade (Hepp et al., 2015(Hepp et al., , 2017Zech et al., 2013aZech et al., , 2014aZech and Glaser, 2009). The interpretation of the δ 18 O sugar values is comparable to those of δ 2 H n-alkane . When sugars originate primarily from leaf biomass of higher terrestrial plants, they reflect the plant source water (which is often directly linked to the local precipitation) modified by evapotranspirative enrichment of the leaf water Zech et al., 2014a). The coupling of δ 2 H n-alkane with δ 18 O sugar values allows the quantification of the leaf water isotope enrichment and relative air humidity (Zech et al., 2013a). This approach was validated by Tuthorn et al. (2015) by applying it to topsoil samples along a climate transect in Argentina. Accordingly, the biomarker-derived relative air humidity values correlate significantly with actual relative air humidity, highlighting the potential of the δ 2 H n-alkane -δ 18 O sugar paleohygrometer approach.
The coupled approach is based on the observation that the isotope signature of precipitation (δ 2 H precpitation and δ 18 O precpitation ) typically plots near the global meteoric water line (GMWL) in a two-dimensional δ 2 H-δ 18 O diagram. The GMWL is characterized by the equation δ 2 H precipitation = 8 · δ 18 O precipitation + 10 (Craig, 1961;Dansgaard, 1964). In many cases, the local precipitation is directly linked to the source water of plants, which is indeed soil water and shallow groundwater. The isotope composition of xylem water readily reflects these sources (e.g., Dawson, 1993). However, leaf-derived biomarkers reflect the leaf water isotope composition, which is, unlike xylem water, prone to evapotranspiration (e.g., Barbour and Farquhar, 2000;Helliker and Ehleringer, 2002a;Cernusak et al., 2003;Barbour et al., 2004;Cernusak et al., 2005;Feakins and Sessions, 2010;Kahmen et al., 2011;Sachse et al., 2012;Kahmen et al., 2013;Tipple et al., 2013;Lehmann et al., 2017;Liu et al., 2017). During daytime, the leaf water is typically enriched in the heavy isotopes compared to the source water because of evapotranspiration through stomata. Thereby, lighter water isotopes evaporate preferentially, which leads to gradual enrichment of heavier isotopes compared to precipitation. The degree of enrichment by evapotranspiration is mainly controlled by the relative air humidity (RH air ) in the direct surroundings of the plant leaves (e.g., Cernusak et al., 2016). Although the biomarkers reflect the isotope composition of leaf water, there is still a modification of its isotope signature by fractionation during biosynthesis, leading to an offset between leaf water and biomarker isotope compositions. In case the biosynthetic fractionation is known and constant, RH air can be calculated from coupling δ 2 H n-alkane with δ 18 O sugar values.
First applications of this approach for paleoclimatic reconstruction (Hepp et al., 2017(Hepp et al., , 2019Zech et al., 2013a) and climate transect validation studies (Hepp et al., 2020;Lemma et al., 2021;Strobel et al., 2020;Tuthorn et al., 2015) revealed promising results. Furthermore, the stability of the biomarker isotope signals during degradation was studied (Zech et al., 2011(Zech et al., , 2012. In brief, n-alkanes and sugars can be extracted compound-specifically from plants, soils and a wide range of different sediments retaining the isotope signal of intact plant tissues.
The overall aim of this study is to evaluate the δ 2 H n-alkaneδ 18 O sugar paleohygrometer approach by applying it to plant leaf material from three different plants grown in a climate chamber experiment under controlled conditions. More specifically, we addressed the following questions.
i. Which n-alkanes and monosaccharides can be used to obtain δ 2 H n-alkane and δ 18 O sugar results of the leaves grown in our climate chamber experiment, respectively?
ii. How precisely do δ 2 H n-alkane and δ 18 O sugar values allow the reconstruction of δ 2 H leaf water and δ 18 O leaf water , respectively?
iii. How accurately does the leaf water isotope composition reflect RH air ?  (Mayr, 2002). Similar isotope patterns in the three plants could allow the generalization of our results for a wide range of C 3 plants, independent of their habitus. An additional, equally important criterion for the choice of the plants was the resilience of the taxa to the experimental climatic conditions and sufficient growth during the experiments. Air temperature (T air ) was set to 14, 18, 24 and 30 • C and RH air to around 20 %, 30 %, 50 %, and 70 % during the daytime of constant climate conditions (between 11:00 and 16:00 CET) (Fig. 1). During the rest of the day diurnal variations typical for natural conditions were aimed for (for more details see Mayr, 2002). The chambers had a high fresh air supply rate (750 m 3 h −1 ), therefore avoiding an evaporative isotope enrichment in the chambers. Furthermore, uniform irrigation conditions were guaranteed via an automatic irrigation system, which was controlled by tensiometers installed at 9 cm substrate depth. The tank water used for irrigation was sampled periodically (intervals of 1 to 3 d) over the whole experiment and revealed only minor variability in its isotope composition (δ 18 O tank water = −10.7 ± 0.3 ‰ standard deviation (σ ), δ 2 H tank water = −7 ± 1 ‰ σ ). Once a week, soil water (via ceramic cups at 13 cm soil depth) and atmospheric water vapor (via dry ice condensation traps) were sampled (δ 2 H soil water , δ 18 O soil water and δ 2 H atmospheric water vapor , δ 18 O atmospheric water vapor ). Additionally, leaf temperature (T leaf ) was calculated from gas exchange measurements at least once a week (Mayr, 2002).
In order to analyze stable hydrogen and oxygen isotope composition of leaf (δ 2 H leaf water , δ 18 O leaf water ) and stem water, the plants were harvested at the end of the experiment. The vacuum distillation method was used for the extraction of the plant water. It should be noted that stem water is a mixture between phloem and xylem water. Only the latter reflects the isotope composition of soil water. For simplification, stem water is referred to as xylem water in the following (δ 2 H xylem water , δ 18 O xylem water ).
For more details about the experiment, the (plant) water isotope results and gas exchange measurements we refer to the original publication (Mayr, 2002).

Leaf biomarker extraction and compound-specific stable isotope analysis
A total of 24 leaf samples were prepared according to Schäfer et al. (2016) for compound-specific δ 2 H measurements of n-alkanes at the Institute of Geography, Group of Biogeochemistry and Paleoclimate, University of Bern. Microwave extraction with 15 mL dichloromethane (DCM) / methanol (MeOH) at a ratio of 9 : 1 (v : v) at 100 • C for 1 h was conducted. The resulting total lipid extracts were purified and separated using aminopropyl silica gel (Supelco, 45 µm) pipette columns. The hydrocarbon fractions (containing nalkanes) were eluted with n-hexane and cleaned via silvernitrate-coated silica gel pipettes (Supelco, 60-200 mesh) and zeolite (Geokleen Ltd.) columns. The δ 2 H measurements of the dominant n-alkanes (n-C 29 and n-C 31 ) were performed on a GC-2 H-pyrolysis-IRMS system, consisting of an Ag-ilent 7890A gas chromatograph (GC) coupled to an Iso-Prime 100 isotope ratio mass spectrometer (IRMS) via a GC5 pyrolysis-combustion interface operating in pyrolysis mode with a Cr (ChromeHD) reactor at 1000 • C. The compoundspecific δ 2 H values were calibrated against a standard alkane mix (n-C 27 , n-C 29 , n-C 33 ) with known isotope composition (Arndt Schimmelmann, University of Indiana, personal communication, 2008), measured twice every six sample injections. Standard deviation of the triplicate measurements was typically ≤ 5 ‰. The H 3+ factor stayed constant during the measurements. Additionally, the leaf samples were dried and finely ground in preparation for δ 18 O analysis of hemicellulosederived sugars (modified from Zech and Glaser, 2009) at the Institute of Agricultural and Nutritional Sciences, Soil Biogeochemistry, Martin Luther University of Halle-Wittenberg. The hemicellulose sugars were hydrolytically extracted for 4 h at 105 • C using 4M trifluoroacetic acid (Amelung et al., 1996) and purified via XAD-7 and Dowex 50WX8 columns. Prior to the methylboronic acid (MBA) derivatization (4 mg of MBA in 400 µL dry pyridine for 1 h at 60 • C), the cleaned sugars were frozen and freezedried overnight (Gross and Glaser, 2004;Knapp, 1979). Compound-specific δ 18 O measurements were performed on a Trace GC 2000 coupled to a Delta V Advantage IRMS via an 18 O-pyrolysis reactor (GC IsoLink) and a ConFlo IV interface (all devices from Thermo Fisher Scientific, Bremen, Germany). The sample batches were measured along with embedded co-derivatized standard batches, which contained arabinose, fucose, xylose and rhamnose in different concentrations of known δ 18 O value. The δ 18 O values of the standard sugars were determined via temperature conversionelemental analysis-IRMS coupling at the Institute of Plant Sciences, ETH Zurich, Switzerland (Zech and Glaser, 2009). This procedure allows corrections for possible amount dependencies (Zech and Glaser, 2009) and ensures the "principle of identical treatment" (Werner and Brand, 2001). Standard deviations for the triplicate measurements were 0.9 ‰ and 2.2 ‰ (average over all investigated samples) for arabinose and xylose, respectively. We focus on arabinose and xylose in this study because they were (i) the dominant peaks in all chromatograms and (ii) previously found to strongly predominate over fucose (and rhamnose) in terrestrial plants and soils (Hepp et al., 2016).
All δ values are expressed in per mille as isotope ratios (R= 18 O/ 16 O or 2 H/ 1 H) relative to the Vienna Standard Mean Ocean Water (VSMOW) standard in the common delta notation (δ = (R sample − R standard )/R standard ; e.g., Coplen, 2011).
2.3 Framework for coupling δ 2 H n-alkane with δ 18 O sugar results

Deuterium excess of leaf water and relative humidity
The coupled approach is based on the observation that isotope composition of global precipitation plots typically close to the GMWL (δ 2 H precpitation = 8 · δ 18 O precipitation + 10 ‰; Craig, 1961;Fig. 4). The soil water and shallow groundwater, which acts as source water for plants, can often directly be related to the local precipitation. However, especially during daytime, leaf water is typically enriched in heavy isotopes compared to the precipitation due to evapotranspiration through the stomata, therefore plotting to the right of the GMWL ( Fig. 4; e.g., Allison et al., 1985;Bariac et al., 1994;Walker and Brunel, 1990). Under natural climatic conditions, the leaf water reservoir at the evaporative sites is frequently assumed to be in an isotope steady state (Allison et al., 1985;Bariac et al., 1994;Gat et al., 2007;Walker and Brunel, 1990), meaning that isotope composition of transpired water vapor is equal to the isotope composition of the source water utilized by plants during the evapotranspiration process. The Craig-Gordon model (e.g., Flanagan et al., 1991;Roden and Ehleringer, 1999) approximates the isotope processes in leaf water in δ terms (e.g., Barbour et al., 2004): where δ e , δ s and δ a are the hydrogen and oxygen isotope compositions of leaf water at the evaporative sites, source water and atmospheric water vapor, respectively. The equilibrium enrichment (ε * ) is expressed as (1 − 1/α L/V ) × 10 3 , where α L/V is the equilibrium fractionation between liquid and vapor in per mille. The kinetic fractionation parameter (ε k ) describes the water vapor diffusion from intracellular air space through the stomata and the boundary layer into to the atmosphere, and e a /e i is the ratio of the atmospheric to intracellular vapor pressure. In a δ 2 H-δ 18 O diagram, the isotope composition of the leaf water as well as the source water can be described as deuterium excess (d) values by using the equation of Dansgaard (1964), with d = δ 2 H−8·δ 18 O. This allows Eq. (1), in which hydrogen and oxygen isotopes have to be handled in separate equations, to be rewritten as one equation: where d e , d s and d a are the deuterium excess values of leaf water at evaporative sites, source water and atmospheric water vapor, respectively. The kinetic fractionation (ε k ) is typically related to stomata and boundary layer resistances to water flux (Farquhar et al., 1989). We used the kinetic enrichment factor (C k ) instead of ε k to be close to paleostudies where direct measurements of plant physiology are not possible. The kinetic enrichment factor is derived from a more generalized form of the Craig-Gordon model for describing the kinetic isotope enrichment for 2 H and 18 O (C 2 k and C 18 k , respectively) (Craig and Gordon, 1965;Gat and Bowser, 1991). If the plant source water and the local atmospheric water vapor are in isotope equilibrium, the term δ a −δ s in Eq. (1) can be approximated by −ε * . Thus, Eq. (2) can be reduced to The actual atmospheric vapor pressure (e a ) and the leaf vapor pressure (e i ) in kilopascals can be derived from Eqs. (4) and (5) by using T air (Buck, 1981): · RH air (4) When e i is calculated as in Eq. (5), e a /e i represents RH air (ranging between 0 and 1, representing 0 % to 100 % relative humidity). We are aware that the Craig-Gordon model would require T leaf values for calculating e i values. However, the RH reconstruction methodological framework presented is attempted for paleostudies for which the T leaf parameter is probably rather difficult to achieve. However, as can be seen in Fig. 1, leaf temperature is very close to air temperature. With rearranging Eq. (3), an equation is given to derive relative humidity values (Eq. 6): Equilibrium fractionation parameters (ε * 2 and ε * 18 ) can be calculated from empirical equations of Horita and Wesolowski (1994) by using the climate chamber T air values. The kinetic fractionation parameters (C 2 k and C 18 k ) for 2 H and 18 O, respectively, are set to 25.1 ‰ and 28.5 ‰ according to Merlivat (1978), who reported maximum values during the molecular diffusion process of water through a stagnant boundary layer. When using supplementary data of Cernusak et al. (2016), ε k values of broadleaf trees and shrubs over broad climatic conditions can be calculated and are well in the range with the used C 2 k and C 18 k values (23.9±0.9 ‰ and 26.7 ± 1.0 ‰ for ε 2 k and ε 18 k , respectively). If δ 2 H leaf water and δ 18 O leaf water can be reconstructed from the measured δ values of n-alkane and sugar biomarkers, this framework provides a powerful tool to establish relative humidity records from sedimentary archives (Hepp et al., 2017;Zech et al., 2013a).

Isotope composition of plant source water
In a δ 2 H-δ 18 O diagram, the hydrogen and oxygen isotope composition of the plant source water (δ 2 H s and δ 18 O s , respectively) can be reconstructed via the slope of the individual leaf water evapotranspiration lines (LELs; Craig and Gordon, 1965;Gat and Bowser, 1991). The LEL slope (S LEL ) can be derived from Eq. 9: where all variables are defined as in Sect.

Modeling and isotope fractionation calculations
The d e values are modeled using Eq.
(3) and measured RH air as input, which can be compared to the deuterium excess via the measured δ 2 H leaf water and δ 18 O leaf water values. The RH air can be derived from Eq. (6) and compared to the measured ones. In a next step, reconstructed (biomarker-based) deuterium excess leaf water was used as input for Eq. (6) and compared to the measured RH air values. This model represents a simplified approach because δ a − δ s is approximated by −ε * (see Sect. 2.3). In all equations where δ s and d s are needed as input, the measured δ 2 H tank water and δ 18 O tank water were used for calculations. The equilibrium and kinetic fractionation factors were set as described in Sect. 2.3. Model quality was overall assessed by calculating the coefficient of determination R 2 = 1 − (modeled − measured) 2 / (measured − measured mean) 2 and the root mean square error The R 2 is not equal to the r 2 , which provides here the fraction of variance explained by a linear regression between a dependent (y) and an explanatory variable Team, 2015).
The fractionation between the measured leaf biomarkers and leaf water can be described by the following equations (e.g., Coplen, 2011): ε n-alkane/leaf water = δ 2 H n-alkane − δ 2 H leaf water 1 + δ 2 H leaf water /1000 (10) In order to provide a 1σ range bracketing the modeled results and calculations, they were additionally run with values generated by subtracting or adding the individual σ to the average.
All calculations and statistical analysis were realized in R (version 3.2.2; R Core Team, 2015).

Results and discussion
3.1 Compound-specific isotope results

Leaf-wax-derived n-alkanes
The investigated leaf material shows a dominance of the n-C 29 alkane homologue. Such a dominance of n-C 29 in Brassica oleracea and Eucalyptus globulus was also reported by Ali et al. (2005) and Herbin and Robins (1968). Vicia faba leaf samples additionally revealed a high abundance of n-C 31 . This agrees with results from Maffei (1996) and enables a robust determination of compound-specific δ 2 H values for C 29 and C 31 , respectively. The δ 2 H n-alkane values of Vicia faba are therefore calculated as a weighted mean. Figures 2 and 4 illustrate the δ 2 H n-alkane results along with isotope data for leaf, xylem and soil water (the latter were originally published in Mayr, 2002). The δ 2 H n-alkane values ranged from −213 ‰ to −144 ‰ across all three plant species. As revealed by overlapping notches in the respective box plots, there is no statistically significant difference in the median between the three species (Fig. S1a in the Supplement; McGill et al., 1978). Figures S1a and 2 moreover show that the range of δ 2 H n-alkane values is largest for Eucalyptus globulus. However, the low number of samples per plant species prohibits a robust interpretation. The δ 2 H n-alkane values are given in the Supplement.

Hemicellulose-derived sugars
The investigated leaf samples yielded substantially higher amounts of arabinose and xylose compared to fucose and rhamnose. This is in agreement with sugar patterns reported for higher plants (D'Souza et al., 2005;Hepp et al., 2016;Jia et al., 2008;Prietzel et al., 2013;Zech et al., 2012Zech et al., , 2014a and hampers a robust data evaluation of fucose and rhamnose. Therefore, the δ 18 O values were investigated for the pentoses arabinose and xylose and range from 30 ‰ to 47 ‰ and 30 ‰ to 50 ‰ (Fig. 3), respectively. Additionally, the isotope data for leaf, xylem and soil water are shown in Figs. 3 and 4 (originally published in Mayr, 2002). No considerable difference in the δ 18 O values of arabinose and xylose can be seen in the δ 18 O data (r 2 = 0.7, p < 0.001, n = 24). This is in line with the findings of Zech and Glaser (2009) and Zech et al. (2012Zech et al. ( , 2013bZech et al. ( , 2014b) but contradicts slightly more positive δ 18 O arabinose values compared to δ 18 O xylose values reported by Zech et al. (2013a) and Tuthorn et al. (2014). Zech et al. (2013a) and  argue that a biosynthetic fractionation could be the reason for that difference. This is based on the fact that arabinose is biosynthesized via an epimerase from xylose (Altermatt and Neish, 1956;Burget et al., 2003;Harper and Bar-Peled, 2002). Nevertheless, the δ 18 O values of arabinose and xylose were combined here as a weighted mean (as δ 18 O sugar values) for further data interpretation. Overall, the δ 18 O sugar values are not significantly different between the three investigated plant species (Fig. S1b). The δ 18 O sugar values are given in the Supplement.

δ 2 H-δ 18 O diagram
A comparison of compound-specific isotopes of leafhemicellulose-derived sugars and leaf-wax-derived nalkanes with leaf, xylem, soil and tank water (compare Figs. 2, 3 and 4) reveals that soil and xylem water plot close to the tank water. Only a slight heavy-isotope enrichment in the soil and xylem water was observed (see the offset between soil and xylem water compared to the tank water). A larger evaporation effect of these water pools was inhibited by the high fresh air supply to the climate chambers (see Sect. 2.1). Thus, the leaf water shows a clear heavy-isotope enrichment due to evapotranspiration. This enrichment strongly differs between the climate chambers, depending mainly on T and RH conditions. The biomarker results furthermore follow the leaf water with a certain offset, which is ε bio .
3.2 Do n-alkane and sugar biomarkers reflect the isotope composition of leaf water?
3.2.1 δ 2 H n-alkane vs. δ 2 H leaf water The δ 2 H n-alkane data including all plant species reveals a significant correlation with δ 2 H leaf water (r 2 = 0.45 with p < 0.001) (Fig. 5a). A slope of 1.1 and an intercept of −152 ‰ characterize the linear relationship. Since it is well known that measured leaf water is not always equal to the specific water pool in which the n-alkanes were biosynthesized (e.g., Tipple et al., 2015), this could explain the observed rather low r 2 value. The correlation between the δ 2 H n-alkane and δ 2 H leaf water presented here is still well in the range found in the literature. Feakins and Sessions (2010) presented nalkane (C 29 and C 31 ) and leaf water δ 2 H data from typical plant species (excluding grasses) along a southern California aridity gradient, revealing that only δ 2 H of n-C 29 is significantly correlated with leaf water (r 2 = 0.24, p < 0.1,  n = 16, based on the associated supplementary data). Another field dataset from the temperate forest at Brown's Lake Bog, Ohio, USA, revealed significant correlations between δ 2 H of n-C 29 or n-C 31 and leaf water of Prunus serotina, Acer saccharinum, Quercus rubra, Quercus alba, and Ulmus americana (r 2 = 0.49, p < 0.001, n = 38 and r 2 = 0.59, p < 0.001, n = 29, respectively, as derived from the Supplement of Freimuth et al., 2017). Data from a controlled climate chamber experiment using two tree species show a highly significant relationship between δ 2 H of leaf wax nalkanes and leaf water (with C 31 of Betula occidentalis and C 29 of Populus fremontii; r 2 = 0.96, p < 0.001, n = 24, as derived from the Supplement of Tipple et al., 2015).
It seems that each plant type shows a different δ 2 H n-alkaneto-δ 2 H leaf water relation, with the highest slope for Vicia faba and the lowest slope for Brassica oleracea (Fig. 5a) However, we argue that the number of replicates for each plant species is simply too low to interpret this finding robustly. In order to explore possible species-specific effects on the fractionation between the biomarkers and the leaf water in more detail, boxplots of the individual plant species of ε n-alkane/leaf water values are shown in Fig. 5b. Median ε n-alkane/leaf water values are −155 ‰ for Brassica oleracea, −164 ‰ for Eucalyptus globulus and −149 ‰ for Vicia faba, with an overall mean value of −156 ‰ (ranging from −133 ‰ to −192 ‰). The boxplots of ε n-alkane/leaf water reveal that the median of the three investigated plant species can statistically not be distinguished due to overlapping notches. Due to the low sample number from each species, the 95 % confidence interval is larger than the interquar- The measured isotope compositions of leaf water (green squares), xylem water (orange squares), soil water (brown squares), atmospheric water vapor (red squares) and the tank water used for irrigation (blue triangle), which plot very close to the global meteoric water line (GMWL). The deuterium excess with respect to the GMWL is marked as d in per mille. tile range in some cases. However, it seems that at least small species-specific differences cannot be ruled out. Our ε n-alkane/leaf water values well resemble the data from a laboratory study (Kahmen et al., 2011), reporting a median value of −162 ‰ for n-C 25 , n-C 27 and n-C 29 of Populus trichocarpa. Furthermore, they are well comparable to climate chamber data of Betula occidentalis (n-C 31 ) and Populus fremontii (n-C 29 ) from Tipple et al. (2015), reporting a median ε n-alkane/leaf water value of −155 ‰. In addition, field experiments reveal similar median values of −151 ‰ (for n-C 29 ) and −142 ‰(for n-C 31 ) from typical plant species (excluding grasses) from southern California (Feakins and Sessions, 2010) and −144 ‰ (for n-C 29 of the species Prunus serotina, Acer saccharinum, Quercus rubra, Quercus alba and Ulmus americana) from the temperate forest at Brown's Lake Bog, Ohio, USA. The large range in ε xylem water/leaf water values from our study (−192 ‰ to −133 ‰) is also found in different laboratory and field studies (−198 ‰ to −115 ‰, derived from n-C 29 and n-C 31 data from Feakins and Sessions, 2010; Kahmen et al., 2011;Tipple et al., 2015;and Freimuth et al., 2017).
The observed large range in ε n-alkane/leaf water and the rather low r 2 of the relationship between δ 2 H n-alkane and δ 2 H leaf water could point to a more specific water pool being used during biosynthesis rather than bulk leaf water (Sachse et al., 2012;Schmidt et al., 2003). Furthermore, as also nicotinamide adenine dinucleotide phosphate (NADPH) is acting as a hydrogen source during n-alkane biosynthesis, its δ 2 H is clearly more negative than the biosynthetic water pool (Schmidt et al., 2003), further contributing to a weakening of the correlation between δ 2 H n-alkane and δ 2 H leaf water and enlarging the range of ε n-alkane/leaf water . In more detail, alkane synthesis takes place by modifying or expanding fatty acids in the cytosol, while fatty acids are synthesized in the chloroplasts (Schmidt et al., 2003). Thus, the cytosol and chloroplast waters are two hydrogen sources. However hydrogen can additionally be added to the alkanes and fatty acids by NADPH, which originates from different sources (photosynthesis and pentose phosphate cycle; Schmidt et al., 2003). It is therefore challenging to measure directly the water pool from which the alkanes are biosynthesized (Tipple et al., 2015). Moreover, biosynthetic and metabolic pathways in general (Kahmen et al., 2013;Sessions et al., 1999;Zhang et al., 2009), the carbon and energy metabolism of plants more specifically (Cormier et al., 2018), and the number of carbon atoms of the n-alkane chains (Zhou et al., 2010) may have an influence on the fractionation. Our ε n-alkane/leaf water values correlate with T air (Fig. S2a), whereas the correlation with RH air (Fig. S2b) is not significant. This could point to a relationship between ε xylem water/leaf water and plant physiological processes (affecting various plants differently). In summary, the fractionation between leaf water and n-alkanes is strongly influenced by the metabolic pathway of the nalkane biosynthesis including direct hydrogen transfers, exchange reactions and NADPH as a hydrogen source.

δ 18 O sugar vs. δ 18 O leaf water
A highly significant correlation is observed for the correlation between δ 18 O sugar and δ 18 O leaf water (r 2 = 0.84, p < 0.001; Fig. 6a). The regression reveals a slope of 0.74 and an intercept of 30.7 ‰. The observed slope of the δ 18 O sugar vs. δ 18 O leaf water relationship could serve as an indicator of a leaf water (heavy-isotope enrichment) signal transfer damping of approximately 26 %.
The theory behind the signal damping is adopted from the cellulose research (e.g., Barbour and Farquhar, 2000). Barbour and Farquhar (2000) related the extent of the signal damping to the proportion of unenriched source water, which contributes to the local synthesis water pool and to the proportion of exchangeable oxygen during cellulose synthesis. Our damping of 26 % is within the range of values reported for cellulose synthesis in Gossypium hirsutum leaves (between 35 % and 38 %; Barbour and Farquhar, 2000), for Eucalyptus globulus leaf samples (38 %; Cernusak et al., 2005), and for five C 3 and C 4 grasses (25 %; Helliker and Ehleringer, 2002a). Recently, Cheesman and Cernusak (2017) provided damping for leaf cellulose syn- thesis based on plant data grown under the same conditions at Jerusalem Botanical Gardens published by Wang et al. (1998), ranging between 4 % and 100 % with a mean of 49 %, revealing large variations among and between ecological groups (namely conifers, deciduous, evergreen and shrubs). A large range of signal damping associated with leaf cellulose was also reported by Song et al. (2014) for Ricinus communis grown under controlled conditions. A common disadvantage of the abovementioned studies is the absence of direct measurements of the proportion of depleted source water contribution to the local synthesis water (as noticed by Liu et al., 2017), which largely contributes to the extent of the signal damping (Barbour and Farquhar, 2000). However, when transferring cellulose results to pentoses, such as hemicellulose-derived arabinose and xylose, it should be noted that they are biosynthesized via decarboxylation of the carbon at position six (C6) from glucose (Altermatt and Neish, 1956;Burget et al., 2003;Harper and Bar-Peled, 2002). Waterhouse et al. (2013) showed that the oxygen atoms at the C6 position in glucose moieties, used for heterotrophic cellulose synthesis, are strongly affected by the exchange with local water (up to 80 %). Based on these findings, it can be suggested that the influence of the nonenriched source water during the synthesis of leaf hemicelluloses is rather small.
The oxygen isotope composition of leaf sugars (e.g., sucrose and cellulose) is strongly influenced by O exchange processes, which cause more positive δ 18 O values of sugars compared to leaf water (Barbour et al., 2004;Cernusak et al., 2003). Therefore, median ε sugar/leaf water values of +27.0 ‰ for Brassica oleracea, +26.6 ‰ for Eucalyptus globulus and +26.8 ‰ for Vicia faba are observed (Fig. 6b). The overall ε sugar/leaf water average value of the three investigated species is +27.3 ‰ (ranging from +23.0 ‰ to +32.3 ‰). No systematic difference between the individual species is evident. Moreover, the ε sugar/leaf water values do not correlate significantly with T air but significantly with RH air (Fig. S2c and d). A temperature dependence of the ε sugar/leaf water is not supported by this experiment in contrast to results from Sternberg and Ellsworth (2011), where a temperature effect on oxygen fractionation during heterotrophic cellulose biosynthesis is observed. The fractionation observed here between hemicellulose-derived sugars and leaf water, with regard to ε sugar/leaf water values, is well in agreement with the values reported for sucrose (exported from photosynthesizing leaves) and leaf water, which was shown to be +27 ‰ . The cellulose biosynthesis is also associated with an heavy-isotope enrichment of around +27 ‰ compared to the synthesis water as shown in growth experiments (Sternberg et al., 1986;Yakir and DeNiro, 1990). The relatively uniform fractionation is explained via the isotope exchange between the carbonyl oxygens of the organic molecules and the surrounding water (cf. Schmidt et al., 2001). This equilibrium fractionation effect was indeed described earlier by the reversible hydration reaction of acetone in water by Sternberg and DeNiro (1983) to be +28 ‰, +28 ‰ and +26 ‰ at 15, 25 and 35 • C, respectively. However, the observed range of approximately 9 ‰ (Fig. 6b) could indicate that partially not only the oxygen equilibrium fractionation between organic molecules and medium water has to be considered. Presumably, isotope as well as sucrose synthesis gradients within the leaf have to be taken into account when interpreting leaf sugar oxygen isotope compositions and their correlation with leaf water (Lehmann et al., 2017). Lehmann et  11), showing median (thick black line) and interquartile range (IQR) with upper (75 %) and lower (25 %) quartiles and lower and upper whiskers, which are restricted to 1.5 · IQR. Outside the 1.5 · IQR space, the data points are marked with a dot. The notches are extended to ±1.58 · IQR/ √ n by convention and give a 95 % confidence interval for the difference of two medians (McGill et al., 1978). Brassica oleracea, Eucalyptus globulus and Vicia faba samples are shown in red, orange and blue, respectively.
al. (2017) reported a fractionation between sucrose and leaf water of +33.1 ‰. Based on this they proposed a conceptual scheme of how such gradients can lead to discrepancies between the isotope composition of the bulk leaf water and the synthesis water. Thus, the fractionation between carbohydrates and bulk leaf water can exceed the common average of +27 ‰. Also Mayr et al. (2015) found a fractionation between aquatic cellulose δ 18 O and lake water larger than this value of around +29 ‰.

Inter-species variability
The differences observed in ε n-alkane/leaf water (Fig. 5b) and ε sugar/leaf water (Fig. 6b) between the taxa might be explained by different leaf sizes and geometries. Please note that these differences are statistically not significant. We do not know whether this is caused by the rather low sample number of our study (n = 24) or not. Still, the yielded mean biosynthetic fractionation factors over all species are −156 ‰ and +27 ‰ for δ 2 H n-alkanes and δ 18 O sugars , respectively. This is well in agreement with data from the literature (usually −160 ‰ and +27 ‰, respectively).
When reviewing Figs. 2 and 3, we observe differences between chamber 4 and 8 for Eucalyptus globulus, which is mainly related to different sampling time of leaves between the two experiments. Because of the diurnal course of light, which was simulated in each chamber, relative humidity and temperature steady-state conditions prevailed only at 11:00 and 16:00 CET (see Sect. 2.1). While the leaf samples of Eucalyptus globulus from chambers 5 to 8 were sampled during the simulated steady-state daytime conditions, chambers 1 to 4 were sampled after these simulated steady-state day-time conditions due to time restrictions, explaining the deviations in leaf water isotope composition. The sampling time, however, does not influence isotope values of tissue samples, which represent the integrated signal over the entire growing period and do not explain the observed differences in δ 2 H n-alkane . The δ 2 H n-alkane values differ for all plant types, whereas δ 18 O sugar and δ 18 O leaf water do not. The differences in δ 2 H n-alkane are most likely explainable via the fractionation occurring during biosynthesis of n-alkanes, which depends not only on leaf water isotope composition but also on plant physiological factors (e.g., water pressure deficit between air and leaf, transpiration rate, assimilation rate; see discussion in Sect. 3.2.1).

Implications for paleoclimatic reconstructions
The damping of the leaf water oxygen isotope signal caused by the exchange between sugars and water is an important issue, especially in stem, trunk and root tissues. While these tissues hardly produce n-alkanes, (hemi-)celluloses and sugars extracted from such tissues do not show the full leaf water heavy-isotope enrichment because of a partial oxygen exchange with non-enriched stem water (e.g., Zech et al., 2014a). This has to be kept in mind for paleoclimatic reconstructions, especially for the sugars of grasses, which do not record the full leaf water enrichment (e.g., Helliker and Ehleringer, 2002b). In the case of grasses, this signal damping affects n-alkanes, too. However, such uncertainties can be included in the RH reconstruction via assumptions and sensitivity analysis of the used model, thus allowing the quantification of uncertainties in reconstructed RH records as shown by Hepp et al. (2019).

Calculating relative humidity based on measured leaf water
The correlations between leaf-water-based and measured RH air and modeled d e and measured deuterium excess leaf water are illustrated in Fig. 7a and b, respectively. Since the climate chambers had a high fresh air supply (see Sect. 2.1) the variability in the leaf water deuterium excess is predominantly the result of leaf water heavy-isotope enrichment and thus strongly driven by relative humidity. Evidence for the strong control of relative humidity on deuterium excess of leaf water comes from multivariate regression analysis between the measured deuterium excess leaf water values versus RH air and T air . The results reveal that the deuterium excess leaf water significantly correlates with RH air of the climate chambers (p < 0.001), with an r 2 of 0.92. The strong control of RH on the deuterium excess of leaf water is furthermore supported by the significant correlations between calculated versus measured RH air values (Fig. 7a). This is in line with the strong correlation between modeled d e based on T air and measured deuterium excess leaf water values (Fig. 7b).
The modeled d e values show a high agreement with measured deuterium excess of leaf water without being too positive. This could be expected from the literature because the output of the Craig-Gordon-based leaf water enrichment model (e.g., Allison et al., 1985;Barbour et al., 2004;Cernusak et al., 2016;Sect. 2.3) reflects leaf water at the evaporative sites, which should be more positive than the measured bulk leaf water. Especially under low-relative-humidity conditions, the discrepancy between Craig-Gordon model results and the measured values is shown to be more pronounced. This is associated with higher transpiration fluxes and higher isotope heterogeneity within the leaf water due to a non-uniform closure of the stomata (Flanagan et al., 1991;Santrucek et al., 2007). An overestimation of the Craig-Gordon models can hardly be observed here (Fig. 7b). However, based on the accepted leaf water enrichment theory (e.g., Cernusak et al., 2016), higher transpiration rates (e.g., under low-humidity conditions) should still lead to a larger discrepancy between Craig-Gordon-modeled and measured leaf water because the lower the back diffusion of enriched leaf water from the evaporative sites gets, the higher the transpiration flux is.
It should be noted that there is the possibility of building up a more detailed model based on Eq. (2). With this, a model is given to derive d e values with the usage of d a and d s , which can be compared to the measured deuterium excess leaf water values. However, when modeling d e without the simplification δ a − δ s ≈ −ε * , the R 2 results in 0.86, and RMSE equals 13.07 ‰ compared to the presented 0.88 and 12.31 ‰. Furthermore, in Eq. (5) T air can be replaced by T leaf . With this, Eq. (2) results in values based on leaf temperature. This would consider that the Craig-Gordon model requires the temperature of the evaporating surface rather than the air temperature for e i . However, with this model extension the R 2 and the RMSE are 0.55 ‰ and 23.54 ‰, respectively. By rearranging Eq. (2), RH values can be modeled, which can be compared to RH air as well as RH leaf values (e a /e i multiplied by 100 with T leaf ). The respective model characteristics are again lower for the RH leaf case (R 2 = 0.27 and RMSE = 11.84 %) than for the RH air comparison (R 2 = 0.81 and RMSE = 6.56 %). Still Eq. (6) provides better results, as presented in this paragraph (R 2 = 0.84 and RMSE = 6.04 %). This discussion is in line with the differences between T leaf vs. T air and RH leaf vs. RH air conditions in the climate chambers. They reveal the same trends and magnitude, but T leaf is consequently higher than T air along with higher RH leaf values compared to RH air ( Fig. 1; Mayr, 2002). In summary, we therefore argue that the model presented in Eq. (6) (including the simplifications of δ a − δ s ≈ −ε * and using T air in Eq. 5) is able to reconstruct RH air values based on δ 2 H leaf water and δ 18 O leaf water values.

Calculating relative humidity based on reconstructed leaf water
In order to test the proposed paleohygrometer approach, the alkane-and sugar-based (reconstructed) leaf water values were used to calculate RH air . The measured RH air is well reflected by the biomarker-based relative air humidity values (R 2 = 0.54; Fig. 8). Overall, a lower coefficient of determination of the biomarker-based model compared to the leaf-water-based reconstructions (compare black with gray data points in Fig. 8) is observed. This can be attributed to the uncertainties in reconstructed leaf water using δ 2 H n-alkane and δ 18 O sugar data as discussed in Sect. 3.2.1 and 3.2.2. Briefly, the limitations regarding δ 2 H arise from the rather weak relationship between the δ 2 H of the n-alkanes and the leaf water, probably linked with the large range in ε 2 n-alkane/leaf water (Fig. 5b). The applied equation for reconstructing δ 2 H leaf water by using δ 2 H n-alkane using a constant biosynthetic fractionation of −160 ‰ (Eq. 10) was considered to be suitable (Sachse et al., 2012;Sessions et al., 1999). However, this equation also contributes some uncertainty to the final relative humidity reconstruction. With regard to δ 18 O, the relatively large variations in ε sugar/leaf water of 9 ‰ have to be considered (Fig. 6b) because in the δ 18 O leaf water reconstructions a fixed value of +27 ‰ is used (Eq. 11). Such a uniform biosynthetic fractionation is just an approximation of the real, probably more variable values. When biomarkers are used to derive leaf water, the measured bulk leaf water does not capture the isotope value of the water in which the biomarkers are biosynthesized. This could thus partly explain the weaker relationship between measured and calculated RH air . Especially the underestimation of the biomarkerbased RH air values under the 68 % relative humidity condi- Figure 7. Scatterplots illustrating the correlation between (a) modeled (leaf-water-based) and measured air relative humidity (RH air ) and modeled (T air -based) vs. measured leaf water deuterium excess. Black lines indicate the 1 : 1 relationship. R 2 and RMSE are calculated as described in Sect. 2.4, while the RMSE values have the dimensions of the respective variables. Error bars for the measured RH values represent analytical standard deviations (see Mayr, 2002). See Sect. 2.4 for the uncertainties in the calculated and modeled results.
tions as well as the large range in reconstructed RH air values for the 48 %, 49 % and 50 % RH air chambers can be attributed to the leaf water reconstruction uncertainties. It should be mentioned that using Eqs. (7) and (8) to calculate leaf water isotope composition based on the biomarkers via biosynthetic fractionation values implies that the fractionation process in principle can be treated as a single process with a unique source. While this approximation can be questioned (see discussion in Sect. 3.2), the overall correlation between biomarker-based and measured RH air highlights the potential of the approach (Hepp et al., 2017;Tuthorn et al., 2015;Zech et al., 2013a), also for future paleoclimate reconstructions.
3.4 Coupling δ 2 H n-alkane and δ 18 O sugar for δ 2 H source water and δ 18 O source water calculation The second advantage of the proposed coupled δ 2 H n-alkaneδ 18 O sugar approach is a more robust reconstruction of the isotope composition of the source water, which can often be directly linked to the local precipitation signal (Hepp et al., 2015(Hepp et al., , 2017Tuthorn et al., 2015;Zech et al., 2013a). Therefore, we calculated the source water isotope compositions via the slopes of the LELs and the GMWL. In order to show the difference in the approaches using either δ 2 H n-alkane or δ 18 O sugar for source water reconstruction, Fig. 9 depicts (i) the leaf water isotope composition reconstructed from δ 2 H n-alkane and δ 18 O sugar results using the biosynthetic fractionation factors, (ii) the measured δ 2 H leaf water and δ 18 O leaf water values, (iii) the source water isotope composition based on reconstructed leaf water, and (iv) the source water isotope composition based on measured leaf water along with the (v) tank water isotope composition. For δ 2 H, neither the range nor the median of the δ 2 H leaf water is well captured by the alkane-based leaf water values. However, the overlapping notches do not sup- Figure 8. Scatterplot depicting the relationship between modeled (biomarker-based) and measured relative air humidity (RH air ). The black line indicates the 1 : 1 relationship. R 2 and RMSE was calculated as described in Sect. 2.4, while the RMSE values have the dimensions of the respective variables. Error bars for the measured values represent analytical standard deviations (see Mayr, 2002). For uncertainty calculation of the results, see Sect. 2.4. In addition, the leaf-water-based relative air humidity results are shown in light gray for comparison. port a statistical difference in the median values (Fig. 9a). The median is on average 13 ‰ more positive than the measured δ 2 H tank water . A higher agreement between measured and modeled values is observed from leaf-water-based δ 2 H s compared to δ 2 H tank water . The average offset is reduced to 2 ‰, and the range is reduced by approximately 70 ‰ compared to the biomarker-based reconstruction.
For δ 18 O, the sugar-based leaf water values agree with the measured ones regarding the median values, as supported by the largely overlapping notches (Fig. 9b). The range of the reconstructed leaf water is about 6 ‰ lower than for the mea- Figure 9. Boxplots showing the measured leaf water in comparison to the biomarker-based leaf water, source water calculated with biomarker-based leaf water values and source water based on measured leaf water (a: δ 2 H leaf water ; b: δ 18 O leaf water ). Tank water is given as a solid black line in both plots. Source water isotope compositions were calculated via the slopes of the LELs (with either biomarker-based or measured leaf water values) and the GMWL. Boxplots show median (thick black line) and interquartile range (IQR) with upper (75 %) and lower (25 %) quartiles and lower and upper whiskers, which are restricted to 1.5 · IQR. Outside the 1.5 · IQR space, the data points are marked with a dot. The notches are extended to ±1.58 · IQR/ √ n by convention and give a 95 % confidence interval for the difference of two medians (McGill et al., 1978). sured δ 18 O leaf water data. All reconstructed δ 18 O s values, regardless of whether they are biomarker-or leaf-water-based, are comparable to the measured δ 18 O tank water . While the biomarker-based data depict an average offset of 2 ‰, the leaf-water-based values only differ by 0.3 ‰ from the tank water δ 18 O values, referring to the median.
The overall larger range of modeled δ 2 H s and δ 18 O s compared to measured δ 2 H tank water and δ 18 O tank water can be related to uncertainties in S LEL modeling (see equations in Sect. 2.3.2). Bariac et al. (1994) found no agreement between the intersects of modeled LELs with the GMWL and the plant source water. Allison et al. (1985) explained such results with changing environmental conditions, leading to various LELs with a locus line not necessarily passing the δ 2 H s and δ 18 O s data point, in a system that approaches rapidly new steady-state conditions. However, when a larger isotope range of source water is used in the studies, leaf water seems to be a good tracer for source water changes when a Craig-Gordon model is applied (Benettin et al., 2021;Bush et al., 2017).

Conclusions
The climate chamber results suggest that leaf-wax-derived nalkane and hemicellulose-derived sugar biomarkers are valuable δ 2 H leaf water and δ 18 O leaf water recorders, respectively.
The coupling of δ 2 H n-alkane and δ 18 O sugar by using a simplified Craig-Gordon equation allows moreover a more robust RH air reconstruction of the chambers in which the plants were grown compared to single isotopes. With regard to the research questions, we conclude the following: i. n-C 29 predominated and occurred at abundances suitable for compound-specific δ 2 H measurements in the leaf samples from all investigated species (Eucalyptus globulus, Vicia faba var. minor and Brassica oleracea var. medullosa). For Vicia faba, additionally n-C 31 could be evaluated robustly. δ 18 O sugar values could be obtained for the hemicellulose-derived monosaccharides arabinose and xylose.
iii. RH air can be derived robustly by using the measured leaf water isotope composition (δ 2 H leaf water and δ 18 O leaf water ) and a rearranged Craig-Gordon model (R 2 = 0.84; p < 0.001; RMSE = 6 %).
iv. Biomarker-based and measured RH air correlation with R 2 of 0.54 (p < 0.001) and RMSE of 10 % highlights the great potential of the coupled δ 2 H n-alkane -δ 18 O sugar paleohygrometer approach for reliable relative humidity reconstructions. Uncertainties regarding relative humidity reconstructions via biomarker-based leaf water isotope composition arose from leaf water reconstructions and model uncertainties, as shown in (ii) and (iii).
v. The coupled δ 2 H-δ 18 O approach enables a better back calculation of the plant source water compared to single isotopes. Reconstructed source water isotope composition (δ 2 H s , δ 18 O s ) is in the range of the measured tank water (δ 2 H tank water , δ 18 O tank water ). However, modeled δ 2 H s and δ 18 O s showed a clearly larger range compared to δ 2 H tank water and δ 18 O tank water . The uncertainties for source water determination are thus considerably higher compared to the relative humidity reconstructions.
Data availability. The temperature, relative humidity, leaf water δ 2 H and δ 18 O, xylem water δ 2 H and δ 18 O, soil water δ 2 H and δ 18 O, the tank water δ 2 H and δ 18 O, and the atmospheric water vapor δ 2 H and δ 18 O data are available from Mayr (2002). The δ 2 H n-alkane and δ 18 O sugar data are available in the Supplement.
Author contributions. JH, MZ and CM wrote the paper; CM was responsible for the climate chamber experiment together with WS and provided the leaf samples and the data; MZ and RZ were responsible for compound-specific isotope analysis on the biomarkers; JH, MT and IKS did laboratory work and data evaluation of the biomarker compound-specific isotope analysis; BG, DJ, KR and all co-authors contributed to the discussion and commented on the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
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Acknowledgements. We would like to thank Marcel Bliedtner and Jana Zech (both from the University of Bern) for help during lipid biomarker and δ 2 H n-alkane analysis. We thank Marianne Benesch (Martin Luther University of Halle-Wittenberg) and Maria Schaarschmidt (University of Bayreuth) for laboratory assistance during sugar biomarker and δ 18 O sugar analysis. We also acknowledge Natalie Orlowski (University of Freiburg), Marco Mar-ius Lehmann (Swiss Federal Institute WSL, Birmensdorf) and Lorenz Wüthrich (University of Bern) for helpful discussions. We are very grateful for the constructive discussion on an earlier version of this paper as a preprint at Biogeosciences. We cordially thank Helge Niemann and the two anonymous reviewers for the great editorial support and their constructive and encouraging reviews. Involvement of Kazimierz Rozanski was supported by the Polish Ministry of Science and Higher Education. Johannes Hepp greatly acknowledges the support given by the German Federal Environmental Foundation. The experiment carried out by Christoph Mayr was gratefully supported by the HGF project "Natural climate variations from 10 000 years to the present". The experiments were possible due to the assistance of Jana This open-access publication was funded by the University of Bayreuth.
Review statement. This paper was edited by Helge Niemann and reviewed by two anonymous referees.