We combine ecohydrological observations of sap flow and soil moisture with thermodynamically constrained estimates of atmospheric evaporative demand to infer the dominant controls of forest transpiration in complex terrain. We hypothesize that daily variations in transpiration are dominated by variations in atmospheric demand, while site-specific controls, including limiting soil moisture, act on longer timescales.
We test these hypotheses with data of a measurement setup consisting of five
sites along a valley cross section in Luxembourg. Both hillslopes are covered
by forest dominated by European beech (
Evapotranspiration
Forests are often found in complex topographical settings. Thus, we have to
consider that the first-order physical controls on
Although detailed models of various feedbacks between plant physiology and
the environmental conditions are available
In this study we aim to assess the dominant temporal and spatial controls of
forest transpiration in complex terrain. Therefore, we use the parsimonious
approach of maximum convective power to estimate potential evaporation. The
approach of maximum convective power has so far only been applied for
long-term annual estimates of
We analyze measurements at six different sites along a well-instrumented steep
forested hillslope transect (north-facing vs. south-facing; see
Fig.
Standard meteorological data, global radiation, air temperature, relative
humidity, and wind speed were measured 2 m above ground at all sites. For the
meteorological forcing we used the data from the open grassland site G1, which
is located 240 m to the northwest of the forest site N1; see
Fig.
Measurement setup along a hillslope transect. Captital letters indicate aspect of the sites (N: north-facing, S: south-facing) and the numbering represents the position of the site on the hillslope: upslope (1), midslope (2), and downslope (3).
Our aim is to estimate the potential evaporation from first principles and
with few, independent input data. Therefore we make use of the concept of
thermodynamic limits of convection, which was recently established by
Convection can be thought of as a heat engine, which converts a temperature
gradient into kinetic energy
Land–atmosphere
energy balance scheme for derivation of
atmospheric demand adapted after
Different from the classic Carnot engines, the convective heat engine has
flexible boundary conditions, namely, the temperature gradient
Combining the equilibrium Bowen ratio with the concept of maximum convective
power we obtain an expression for the potential evaporation, herein referred
to as atmospheric demand
We also compare
our results with the well-established FAO Penman–Monteith grass reference
evaporation equation
In complex terrain the incoming radiation is influenced by the slope and the
aspect of the current position
A forest inventory for all sites was done in March 2012. The circumference at breast height of all trees with circumference larger or equal to 4 cm was measured in a 20 m by 20 m plot for each site. Stem basal area was calculated and a total stand basal area was computed for each site.
Leaf area index (LAI) was measured with a LICOR LAI-2200 plant canopy analyzer at all forested sites in two campaigns. The summer campaign was carried out on 11 August 2012 and the winter campaign on 20 March 2014. Here we use the measurements taken with all rings of the LAI-2200. The LAI was averaged from 36 measurements points per site. The difference between summer and winter LAI should reveal the actual leaf area index without stems and topographic shading effects.
The five forested sites are instrumented with multiple sap flow sensors (four
trees at each site, installed between mid-May to November). Heat pulse
sensors (East 30 Sensors, Pullman, Washington 99163 USA) based on the heat
ratio method
The raw measurements obtained every 30 min were quality controlled and
suspect data were filtered before further analysis was performed. At three
larger trees the outermost sensor readings were replaced by the second sensor
depth reading because their annual mean was smaller than the inner sensors,
which indicates a sensor misplacement into the bark of the tree. The sensors
measure the heat pulse velocities at three different radial depths in the
tree. The daily mean sap flux density per tree is obtained by an average of
all readings per depth and day. Units of SFD were converted to
Measurements of sap flux density only provide a relative measure of the
velocity of the ascending xylem sap. To obtain tree water fluxes a
representative xylem area per sensor depth is assumed, which is then
multiplied with the corresponding sap flux density
To upscale to the site level we use the inventory data, which provides the
number of trees in the stand, diameter at breast height (DBH), and species
information. Daily sap flux density per sensor depth was averaged for each
species and tree status (dominant vs. suppressed) for each site. Missing sap
flux density data were filled by linear regression with neighboring sites.
The largest data gaps were filled at sites N2 and S2. Finally, the upscaled daily
stand transpiration was obtained by summing up the product of sap flux
density per depth
As another means to estimate transpiration we use soil moisture measurements.
Soil moisture sensors (Decagon 5TE soil moisture sensors, with an accuracy of
To test if the transpiration estimates are driven by potential atmospheric
demand, we use linear ordinary least squares (OLS) regression with the
transpiration estimates as response variable and
Note that by using time series of daily data, which are shaped by the
seasonal cycle, the assumption of independence of the predictor variables in
the linear regression is not often justified. The effect of serial dependence
generally does not bias the regression coefficients, but reduces the
statistical significance of a regression. Therefore, we estimate the standard
deviation of the regression coefficient (
Daily time series of temperature, global radiation, precipitation, and
site-average soil moisture content for 2013 are shown in
Fig.
Meteorological forcing and average soil moisture at the grassland site (G1) for 2013. A few data gaps were filled with data from nearby grassland sites.
Two independent site-scale transpiration estimates are evaluated in the
following. The first estimate,
Seasonal totals in mm of estimated stand
transpiration
Seasonal totals of
Time series of
evapotranspiration estimates for north-facing hillslope site N1 in the left
panel and south-facing site S1 in the right panel.
Regression statistics for
Site-average
To test if the transpiration estimates are driven by potential atmospheric
demand, we performed a linear regression of the site-average values with
Figure
We also tested if the regression residuals show correlations with other daily
observations. The reported adjusted squared correlation of a linear
regression of the residual with VPD, wind speed, and soil moisture at the site
level is reported in Table
In contrast to the meteorological variables, we found that the residuals are
significantly correlated to the site-average soil moisture content at some
sites.
Figure
By using tree-averaged sap flow density measurements directly we can
assess how strong single trees respond to
The residual regression analysis shows a similar pattern as the site-average
values, with low influence of wind speed and VPD. Site-average soil moisture
content (
Regression statistics of daily
SFD as average per tree and per site as extra row. Column DBH is the
diameter at breast height in centimeters.
Generally, the measurement setup allows one to differentiate between three different levels of aggregation of root water uptake estimates: site-average, per profile, and per depth of the sensor.
Root water uptake per profile is obtained by summing up the estimates of each
sensor. We find that 15 out of 16 profiles show significant slopes
The results show that most of the daily variability in both transpiration
estimates is driven by atmospheric demand. The slope of the linear regression
of
The most obvious factor is the aspect of the sites. While
Site topographic characteristics with
average inclination of each site is given in column “slope angle”. Column,
Another topographic factor influencing the response to atmospheric demand is
the inclination of the sites, where we find that the steeper the site the
lower the slope of the linear regression of SFD to
Apart from the topographic data, the stand structure varies remarkably (see
Table
Observed biometric characteristics of
the five forested sites along the transect. Column names:
Sensitivity to
Plotting
Generally, there are two different physical limitations of atmospheric
evaporative demand, which have been used for modeling
The maximum power-derived estimate of potential evaporation
The derivation of
The dominance of absorbed solar radiation in explaining latent and sensible
heat fluxes was also found by
The derivation of
Another limitation of the approach is the simple linearized scheme for
longwave heat exchange. The description of radiative exchange affects the
maximum power limit, because longwave radiation “competes” with the
convective fluxes to cool the surface
The third limitation is concerned with the spatial representativity of
Hysteresis
of sap flux density (left
Our results demonstrate a strong influence of daily variations in atmospheric
demand on both transpiration estimates. This strong correlation at the daily
timescale may allow us to separate the timescales of atmospheric demand and
plant water limitations, which may become relevant at timescales larger than
1 day. Differences in the slope of the relationship to
Of the many factors that influence transpiration, stand composition and
topography were the most important invariant controls during our measurement
campaign. The measurement transect was placed on a valley cross section to
primarily reveal the influence of hillslope aspect. Our results indicate only
significant effects of aspect and hillslope angle for the sensitivity of SFD to
The biometric measures of stand composition, however, also co-vary with aspect
and hillslope inclination. Here we found a strongly negative linear
relationship of
In addition to the tree size differences, our sites show marked differences
in canopy structure. The open canopy structure may explain the larger
The upscaling procedure integrates both the tree distribution within the
stand and the sap flux density observations to yield the stand transpiration
estimate
Due to low rainfall amounts, soil moisture decreased from July to September
at all sites and all depths. Thus the soil moisture reduction may have
limited transpiration. We captured this effect of soil moisture limitation of
transpiration through the regression of the residuals of the transpiration to
We argue that soil water limitation effects on transpiration could be
topographically enhanced. First, by an aspect that affects the amount of
received solar radiation and thus the atmospheric demand for water. A higher
atmospheric demand increases evaporation from intercepted water and from the
soil, which reduces the amount of precipitation entering the soil. Second,
the hillslope inclination could have enhanced lateral runoff at the steeper
south-facing sites, which reduces the soil water holding capacity
Generally, sap flow observations are not limited by spatial heterogeneity and
complex terrain, which would limit the applicability of micrometeorological
measurements Deriving water fluxes requires extrapolation from the point measurement
at some specific place within the stem to the entire tree. However, sapwood
conductivity can have radial and circumferential differences and
species-specific properties There is a sample bias towards larger trees as the method is more
difficult with very small trees, which would require a different type of
sensor, because the heat ratio method is designed only for lower sap
velocities The inter-comparison of sap flux density measured in different trees is
limited by the fact that xylem characteristics in the estimation of SFD are
required
The advantage of using temporally highly resolved soil moisture readings is
that it allows one to estimate root water uptake without further information on
soil properties Data filtering: the method only applies under conditions with negligible
soil water movement excluding events of infiltration, drainage, capillary
rise, or hydraulic redistribution. These fluxes can have major influences on
the observations of soil moisture and comprise the second term of the right-hand side of Eq. ( Soil heterogeneities, dominant at the hillslopes, can induce large local
variations in soil moisture and may lead to dissimilar / biased
Deep root water uptake in response to drying topsoil may cause root water
uptake below the deepest measurement depth in forest sites as observed e.g.
by
The estimates of site-scale transpiration based on up-scaled sap flow
measurements were of similar magnitudes and correlated well with estimates
derived from soil moisture variations. The seasonal estimates by
The comparison between
We aimed to infer the dominant temporal and spatial controls on forest transpiration along a steep valley cross section through ecohydrological measurements of sap flow and soil moisture and their relation to atmospheric evaporative demand. The estimation of transpiration in space and time for forests in complex terrain is a challenge in its own right. Obtaining transpiration is only possible through indirect observations, whereby each method has its own limitations. Therefore, we used two independent observations to obtain site-scale estimates of transpiration along the hillslope transect. To estimate atmospheric demand, a formulation similar to the well-known Priestley–Taylor equilibrium evaporation concept was employed. The formulation is based on a simplified energy balance representation of the surface–atmospheric system and hypothesizing that convection operates at its upper thermodynamic limit. The formulation does not require empirical parameters and only requires data on the absorbed solar radiation and temperature. We find that at the daily timescale this approach explains most of variability in both transpiration estimates at the site and tree scale. This suggests that atmospheric demand is the dominant control on daily transpiration rates in this temperate forest. Although the well-established FAO Penman–Monteith reference evaporation yields slightly higher correlation and 20–30 % higher values, it requires additional data of net radiation, VPD and wind speed. Thereby both, VPD and wind speed did not add consistently to the explained variance and are also difficult to obtain above forests. While our results demonstrate that thermodynamic limits provide a first-order estimate for potential evaporation, we have to stress that the derivation is based on the simplest possible energy balance representation. Further refinements will probably improve the predictability of surface exchange fluxes.
Despite the prevailing topographic contrasts between the north-facing and the south-facing measurement sites, we find that up-scaled stand transpiration yields rather similar seasonal totals as well as a similar average response to atmospheric demand. This similarity is achieved through a compensation of the low sapwood area with high sap flux densities at the north facing sites, while at the south-facing sites a high sapwood area was accompanied with low sap flux densities. It appears that individual and stand average sap flux densities can vary strongly in heterogeneous terrain in order to compensate for tree size and stand structural differences through tree hydraulic mechanisms. The importance of these stand structural differences on stand transpiration thus masks the potential effects of topographical factors such as aspect and hillslope angle, which are cross correlated. However, during dry periods we find that topographic factors can enhance the response of transpiration to soil water limitation.
Despite unavoidable limitations in estimating stand transpiration and potential evaporation in complex terrain, we find that relating the employed ecohydrological observations to a thermodynamically constrained estimate of atmospheric demand enables important insights in the temporal drivers of transpiration and how they vary at the hillslope scale. First our results highlight the dominance of absorbed solar radiation as the main and independent driver of land–atmosphere exchange. Second, our results suggest an intriguing interplay of tree hydraulics and stand composition, which seemingly leads to transpiration rates close to its physical limits. We conclude that this approach should help us to better understand surface–atmosphere coupling in relation to thermodynamic constraints and how vegetation adapts to these.
We used sap flow sensors based on the heat ratio method
The needles measure heat-pulse velocities at depths of 5, 18, and 30 mm
within the stem. Following the user's manual we assigned for each sensor
depth a representative radius of 15, 25, and 40 mm below the cambium radius
Because tall trees may have a wider active xylem depth than measured by the
inserted sap flow needles
Stem sapwood area was computed using published allometric power-law
relationships of the form
The soil water continuity equation at a point in the soil may be written as
Observed diurnal decline in soil moisture over two sunny days in
summer 2013 to illustrate the approach to estimate daily root water uptake
from diurnal soil moisture variations.
There are, however, periods and locations where soil water fluxes
The data were filtered for (i) precipitation (daily sum
This research contributes to the “Catchments As Organized Systems (CAOS)” research group (FOR 1598) funded by the German Science Foundation (DFG). AH was partially funded by grant SFB 1076 by the German Science Foundation. We thank Conrad Jackisch (KIT) for comments on an earlier draft of the paper. We thank all people involved in the field work. In particular the technical backbone Britta Kattenstroth (GFZ Potsdam), Tatiana Feskova (UFZ – Leipzig), Laurent Pfister and François Iffly (LIST, Luxembourg) and the landowners for giving access to their land. We acknowledge the encouraging and constructive comments of two reviewers, who helped to improve the manuscript.The article processing charges for this open-access publication were covered by the Max Planck Society. Edited by: T. Bogaard