2.3.1 Microlysimeters

For direct measurements of soil evaporation (E_lys), four microlysimeters were installed at a number of locations around the EC-station (one in each cardinal direction) at the beginning of every observation period. In order to obtain an undisturbed soil monolith for each microlysimeter, an SDR-35 polyvinyl chloride (PVC) collar with an inner diameter of 0.2 m, a wall thickness of 0.005 m, and a depth of 0.11 m was pushed carefully into the ground. Afterwards the collar including the soil column was retrieved, its outside was cleaned, and the bottom of each lysimeter was sealed with an acrylic glass disc, which prevented percolation and capillary rise from or into the microlysimeter. The microlysimeters were then weighed initially and returned to their original positions. We made sure that the lysimeters were levelled with the soil surface, their walls were fully surrounded by soil, and that the crop was affected and destroyed as little as possible, so that the general conditions and characteristics of the field site could still be maintained (e.g., regarding heat flux, shading). All four microlysimeters were subsequently collected, cleaned, weighed, and distributed again every 60 or 90 min. A scale with a precision of 0.1 g (equivalent to 0.00318 mm evaporation) was used. The scale was enclosed in a box to avoid wind effects during the measurements. Finally, the measured weight differences were converted to the standard units of the surface energy balance (W m⁻²) by means of the lysimeters surface area, the time periods between weighing, and the latent heat of vaporization (Quade et al., 2019).

2.3.2 Soil CO₂ flux chambers

Soil respiration (R_s) was observed with an automated soil CO₂ gas flux system (Li-8100, Li-Cor Inc. Biosciences, Lincoln, Nebraska, USA), connected to four long-term soil flux chambers. The chambers were installed close to the EC-station (one in each cardinal direction) on top of PVC soil collars with a diameter of 0.2 m and a total height of 0.07 m, from which 0.05 m was inserted into the soil. Each chamber was closed at 30 min intervals for 90 s during flux measurements, while CO₂, water vapour concentration, and chamber headspace temperature were recorded at a sampling rate of 1 Hz. The CO₂ concentration was standardized to dry air and a constant temperature to eliminate effects of changes in air density and water vapour dilution during closure time. R_s was subsequently calculated by adjusting a linear regression fit to the final 60 s of the measurement before reopening.

2.3.3 Leaf-level measurements

Leaf gas exchange was measured using a Li-Cor LI-6400XT portable photosynthesis system with a 6400-02B LED light source. Leaf-level measurements included instantaneous stomatal conductance to water vapour (g_sw) and photosynthesis (A_leaf), maximum light-saturated photosynthesis (A_max) is the maximal primary productivity under high light conditions, CO₂-response curves, and light-response curves. Measurements of g_sw and A_leaf were performed during the three IOPs, starting at sunrise and ending when measurements of g_sw indicated that stomata had nearly closed (g_sw<0.05 mol m⁻² s⁻¹). For measurements of g_sw and A_leaf, tillers were picked randomly in the field and immediately mounted in the leaf chamber for measurements. Initial tests showed no difference in g_sw between excised and attached tillers. Settings of leaf chamber photosynthetically active radiation (PAR) and CO₂ followed the diurnal variability measured in the field. For comparison with other observations, measurements of g_sw and A_leaf were binned and averaged at 30 min intervals. A_max was measured during the three IOPs, as well as on 8 May between 10:00 and 12:00 UTC. For measurements of A_max, the light intensity (PAR) was set to 1500 µmol m⁻² s⁻¹ and the leaf was equilibrated under a reference CO₂ concentration of 450 µmol CO₂ mol⁻¹ air. CO₂ response curves were measured during IOP 1 and IOP 3, prescribing CO₂ concentrations in the following order: 0, 50, 100, 150, 250, 350, 450, 600, 800, and 1200 µmolCO₂ mol⁻¹ air. All CO₂-response curves were measured using a light intensity (PAR) of 1500 µmol m⁻² s⁻¹. Light-response curves were measured on IOP 1 only and used a reference CO₂ concentration of 450 µmol CO₂ mol⁻¹ air. PAR values were changed in the following order: 0, 25, 50, 100, 200, 400, 800, 1200, and 1500 µmol m⁻² s⁻¹. The stomatal conductance to water vapour (g_sw mol m⁻² s⁻¹) of the curves that relate A and PAR (A–PAR) in between 0 and 200 µmol m⁻² s⁻¹ for the three repetitive experiments within the PAR range were (average and standard deviation in brackets): 0.49 (0.13), 0.12 (0.02), and 0.34 (0.06). Leaves were allowed to equilibrate to leaf chamber conditions in terms of gas exchange (approximately 1–2 min) but not in terms of stomatal aperture. For all measurements, leaf chamber temperature was set between 20 and 25 ^∘C. Relative humidity in the leaf chamber was set between 60 % and 75 %. Measurements of A_max, CO₂-response curves and light-response curves were performed on attached tillers.

2.3.4 Sap flow

Sap flow in wheat tillers was measured with the heat balance method (Sakuratani 1981; Baker and van Bavel, 1987). A total of 24 tillers were selected at random, diameters measured with an electronic calliper, and SGA3-type sap-flow sensors installed at the lowest possible internodes following the procedure recommended by the manufacturer (Dynamax, 2007, 2017). Sensors were connected with electrically shielded wire to AM 16/32 multiplexers controlled and scanned by CR1000 data loggers (Campbell Scientific, Logan, Utah, USA). Energy supply to the stem heaters was carefully regulated to the highest permissible level in order to obtain a strong heat signal. We employed the dual voltage regulators (Dynamax AVRDC) which were parts of wired measurement, control, and extension units assembled and tested by the heat balance sensor manufacturer (Flow32 1K A and B models, Dynamax Inc., Houston, Texas, USA). Data were processed according to the calculation procedure of Dynamax (2007) with adaptations to wheat (Langensiepen et al., 2014) to obtain reliable data on the convective stem heat flow generated by sap flow. Here we take the evolution of the tiller densities from 480 tillers per square metre (IOP 1 and IOP 2) to 370 tillers per square metre (IOP 3) into account.

2.3.5 Profiling elevator

Vertical profiles H₂O and CO₂ expressed as mole fractions χH₂O and χCO₂ (mole of substance per mole of moist air), temperature (T_air,p) and wind speed (u_p) from the soil surface to the surface layer above the crop canopy were measured with a portable elevator system. The elevator moved continuously up and down the measuring sensors attached to an extension arm over a total profile height of 2 m. A sampling tube connected to a differential gas analyser (LI-7000, Li-Cor Inc. Biosciences, Lincoln, Nebraska, USA) collected χH₂O and χCO₂ at a frequency of 20 Hz. T_air,p and u_p were measured at the same frequency by a ventilated fine-wire thermocouple (FW3, Campbell Scientific, Logan, Utah, USA) and a hot-wire anemometer (8455-075-1, TSI, Shoreview, Minnesota, USA). All measurements were duplicated as a continuous fixed-height measurement at the top of the profile. During the data post-processing, the temporal and vertical resolution of the mean profiles was set to a time-averaging block of 30 min with a vertical resolution of 0.025 m. Time delays in each variable with respect to the position caused by response times of the sensors, electronic delays, and the tube transport of the gas samples were adjusted by a hysteresis minimization algorithm. Detailed information on the profile measurement setup and the processing of the data profile is given in Ney and Graf (2018). The measured concentration profiles were then used to determine the vertical source profiles of H₂O and CO₂, with the aim of providing an independent, non-invasive partitioning between above-ground net primary production (NPP) and R_s or evaporation (E) and transpiration (Tr_p). To estimate source profiles and flux partitioning, we used an analytical dispersion Lagrangian technique introduced by Warland and Thurtell (2000) and further developed by Santos et al. (2011). Other than in the above-mentioned literature, a simple optimization method (Nelder and Mead, 1965) was used to fit four parameters: soil source, canopy source, and shape parameters p and q of a beta distribution, which describes the vertical source distribution within the canopy.

2.3.6 Scintillometer

The receiver of a displaced-beam laser scintillometer, hereafter referred to as DBLS (SLS-20, Scintec, Rottenburg, Germany), was placed 9 m southeast of the EC station (Fig. 1). The scintillometer measurements height was 1.95 m a.g.l. The path length towards the instrument transmitter was 86.8 m. It was pointed along a transect from northwest to southeast. The DBLS measures the scintillation intensity of two displaced laser beams (wavelength of 670 nm and separation distance of ∼2.7 mm). The structure parameter of temperature ($C_T^{\mathrm{2}}$) and dissipation rate of turbulent kinetic energy (ε) are determined from the log variance of one beam and log covariance between the beams. The general equation that links the scintillometer measurements to fluxes is given by

where F_x is defined as the turbulent flux of the transported variable x, $C_x^{\mathrm{2}}$ is the structure function parameter of x, and K_x represents the turbulent exchange coefficient that links F_x to $C_x^{\mathrm{2}}$. K_x is a function of the friction velocity, u_*, and the Obukhov length, L. Finally, ρ is the air density, and z is the measurement height above the surface. For the sensible heat flux H=F_T, x represents temperature (T) and appropriate constants need to be added to convert Eq. (1) to energy fluxes. H, u_*, and L are solved iteratively as a function of the DBLS-measured $C_T^{\mathrm{2}}$ and ε (Thiermann, 1992; Hartogensis et al., 2002). The Monin–Obukhov Similarity Theory (MOST) functions that define K_x were taken from Kooijmans and Hartogensis (2015). For our purpose, however, the exact shape of the MOST functions is of minor importance as we are primarily interested in the dynamic temporal behaviour of the fluxes rather than an accurate description of their quantitative values. We are aware that advective contributions can lead to the violation of MOST. However, advection did not influence our measurements for two reasons. First, the scintillometer transmitter and receiver are far enough from the edges of the CloudRoots field given the height of the sensor (1.95 m), the wind speed and direction during the IOPs, and the stability conditions. All of these mean that the footprints are small enough to fit within the field. The typical footprint length (90 % footprint contribution) for the 3 IOPs yields IOP 1 (85 m), IOP 2 (30 m), and IOP 3 (75 m). Second, the scintillometer has a path weighting function that is at its maximum in the middle of the path and near-zero at the transmitter and receiver positions, i.e. the major contribution occurs at the farthest point of the field edge.

The added value of DBLS fluxes over the traditional EC method is that they converge to statistically stable flux estimates at much shorter flux averaging times of 1 min or less, while the EC technique typically requires flux averaging times of 10 to 30 min (Hartogensis et al 2002; van Kesteren et al., 2013b). The essence behind this is that the flux estimate is based on structure parameters that are defined in the inertial range of the turbulent spectrum. As such, the flux estimates rely on a limited range of the turbulent scales that contribute to the flux rather than all of them as is the case with the EC method.

We also adopted the combination technique introduced by van Kesteren et al. (2013a, b) to obtain fluxes of H₂O and CO₂ at these short timescales. This technique combines structure parameters of H₂O and CO₂ that are obtained from H₂O and CO₂ time series from an Infra-Red Gas Analyser (IRGASON system; see Sect. 2.3.7) with an exchange coefficient defined by the DBLS fluxes to finally calculate flux estimates of H₂O and CO₂. In other words, with u_* and L solved with the DBLS, Eq. (1) can be evaluated using structure parameters of trace gases x, where in this case x represents the specific density, q_x, of H₂O or CO₂.

2.3.7 Eddy covariance and ancillary micrometeorological measurements

A continuously running EC system was operated in the middle of the field (Fig. 1), comprising a three-dimensional sonic anemometer (Model CSAT-3, Campbell Scientific, Inc., Logan, Utah, USA) and an open-path infrared gas analyser (Model LI-7500, Li-Cor, Inc., Biosciences, Lincoln, Nebraska, USA). The sensors height was 2.34 m a.g.l. Raw data were sampled in 20 Hz mode and fluxes and averages were calculated as 30 min block averages using the TK3.11 software package developed at the University of Bayreuth, including corrections and quality control as given in Mauder and Foken (2011). Missing values in the calculated turbulent fluxes were filled with the marginal distribution sampling (MDS) method following Reichstein et al. (2005) which is implemented in the REddyProc software package (Wutzler et al., 2018). The station also included measurements of all components of the radiation budget (NR01, Hukseflux, Delft, the Netherlands), PAR (LI-190R, Li-Cor Inc. Biosciences, Lincoln, Nebraska, USA, and BF5, Delta-T Devices, Cambridge, UK), air temperature (T_air), and humidity (HMP45C, Vaisala Inc., Helsinki, Finland) at 2.4 m, and precipitation (Thies Clima type tipping bucket, distributed by Ecotech, Bonn, Germany) at 1.0 m a.g.l. Radiation measurements were taken at 2.5 m. Soil heat flux, temperature, and moisture were measured next to the station, more specifically, this was performed using the following parameters: 3 times HFP01SC at 3 and 8 cm, Hukseflux, the Netherlands; 3 times TCAV, Campbell Scientific, Logan, USA; and 1 cm, 5 cm, and 2 to 65 cm layer average, 2 times CS616, Campbell Scientific, Logan, USA, 2 to 6 cm layer average. In addition, we measured at five points distributed across the field using the wireless SoilNet sensor system (Bogena et al., 2010). One SoilNet point was placed next to the station, while the other four were placed next to the soil CO₂ efflux chambers described above. Each SoilNet point comprised a single soil heat flux measurement at 5 cm (HFP01SC, see above) and combined temperature and soil water content measurements in depths of 1, 5, 10, 20, 50, and 100 cm (SMT100, Truebner GmbH, Neustadt, Germany).

A second mobile EC station with instruments heights of 1.93 m a.g.l. was deployed in the immediate vicinity of the continuously monitoring station during the measurement campaign. The system comprised an IRGASON EC system (SN1185 Irgason EC150, Campbell Scientific, Inc., Logan, Utah, USA; PTB101B pressure sensor, Vaisala Inc., Helsinki, Finland) with an additional LI-7500 sensor (same manufacturer). Here, fluxes were processed with the LiCor EddyPro v6.2.2 software. Radiation (CM11 for global and CG2 for long-wave radiation, Kipp & Zonen B.V., Delft, Netherlands), ground heat flux (4× HFP01SC at 5 cm depth, Hukseflux, the Netherlands), and temperatures at depths of 2 cm (4×) and 8 cm (2×) were also measured at this station.

2.3.8 Canopy-level measurements of reflectance and sun-induced fluorescence (SIF): FloxBox

A field spectroscopy system was used (FLOX, JB Hyperspectral Devices UG, Düsseldorf, Germany) for canopy-level measurements of reflectance and SIF. FLOX is constructed for high temporal frequency acquisition of continuous top-of-canopy optical properties with a focus on sun-induced chlorophyll fluorescence. The system is equipped with two spectrometers: an Ocean Optics FLAME S, covering the full range of Visible and Near-Infrared (VIS-NIR) and an Ocean Optics QEPro, with a high spectral resolution (Full Width at Half Maximum, FWHM, of 0.3 nm) in the 650–800 nm range of the fluorescence emission. The optical input of each spectrometer is split between two fibre-optic cables that lead to a cosine receptor that measures solar irradiance and a bare fibre bundle that measures the target-reflected radiance. Spectrometers are housed in a Peltier thermally regulated box to keep the internal temperature lower than 25 ^∘C in order to reduce dark current drift. The signal is automatically optimized for each channel at the beginning of each measurement cycle, and two associated dark spectra are collected as well. Metadata such as spectrometer temperature, detector temperature and humidity, Global Positioning System (GPS) coordinates, and time are also simultaneously stored in the secure digital memory of the system. More detailed information about the system can be found in Wohlfahrt (2018) and in Campbell (2019).

2.3.9 Regional level measurements of reflectance and sun-induced fluorescence (SIF): HyPlant

An airborne high-performance imaging spectrometer (HyPlant) was used for regional-level measurements of the same quantities. Several flight lines over the 15 km × 15 km study site with 1–3 m pixel resolution were used. HyPlant is a hyperspectral imaging system for airborne and ground-based use, developed as a cooperative effort between Forschungszentrum Jülich GmbH (Germany) and the company SPECIM (Oulu, Finland). It consists of two sensor heads, named DUAL and FLUO. The DUAL module is a line-imaging push broom hyperspectral sensor, which provides contiguous spectral information from 370 to 2500 nm in a single device that utilizes a standard objective lens with 3 nm spectral resolution in the VIS-NIR spectral range and 10 nm spectral resolution in the SWIR spectral range. The FLUO module measures the vegetation fluorescence signal with a separate push broom sensor that produces data at high spectral resolution (0.25 nm) in the spectral window between 670 and 780 nm. The position and altitude sensor (GPS/INS sensor) provides, synchronously with the image data, aircraft position and altitude data for image rectification and geo-referencing. Both imagers are mounted in a single platform with the mechanical capability to align the field of view (FOV). A more detailed description of the sensor is given in Rascher et al. (2015).

Sun-induced fluorescence (F₆₈₇ and F₇₆₀) was retrieved in the two oxygen absorption bands according to the improved Fraunhofer Line Discrimination (iFLD) method. The iFLD method was initially proposed by Alonso et al. (2008) and was adapted to allow SIF retrievals from the FLUO module of the HyPlant sensor (Rascher et al., 2015). Surface reflectance and vegetation indices were calculated after an atmospheric correction using the MODTRAN software package was applied. The atmospheric correction was performed using the MODTRAN software package (for an overview of the data processing of HyPlant, see Siegmann et al., 2019). For the reason of easier comparison of SIF values with other methods of this paper, the commonly used SIF units (mW m⁻² sr⁻¹ nm⁻¹) were replaced by a substitute (nmol m⁻² sr⁻¹ s⁻¹) using conversion factors of 6.35 for and 5.74 for F₆₈₇ and F₇₆₀, respectively.

2.3.10 Boundary layer and cloud remote sensing measurements

The JOYCE remote sensing facility (Löhnert et al., 2015) (located at a distance of 5 km from the test site) provided continuous information about boundary layer and cloud characteristics. Specifically, microwave and lidar measurements were used to compare the CLASS model results (see Sect. 2.4) with the inferred boundary layer depth. This comparison was completed by vertical profiles measured by the routine radio soundings at Essen (station ID EDZE/10410 at a distance of 75 km).

2.4.1 Modelling leaf-level photosynthesis

Leaf-level photosynthesis was modelled using the representation of photosynthetic biochemistry, as included in CLASS (Vilà-Guerau de Arellano et al., 2015), which was originally developed by Goudriaan (1986) and further adapted to meteorological applications by Jacobs and de Bruin (1997). As this model describes the relationship between stomatal conductance (g_s) and photosynthesis (A), it is usually referred to as the A-g_s sub-model. In short, plant transpiration and CO₂ assimilation as part of the surface energy balance model are represented by a two-big-leaves model, one for sunlit leaves and one for shaded leaves (Jacobs and de Bruin, 1997; Pedruzo-Bagazgoitia et al., 2017). The exchange at the leaf surface depends on the gradient of atmospheric CO₂ and an internal leaf CO₂ concentration, which depends on the water vapour deficit and leaf conductance. The CO₂ exchange is upscaled to the canopy level by integrating over the leaf area index (LAI).

Available field measurements were used for improving the model settings at the leaf level. The parameters representing the initial value of the light use efficiency (α₀) and the temperature-normalized maximum leaf-level photosynthesis rate (A_m,max298) were fitted using light-response curves (Fig. 5) and CO₂-response curves (Fig. 3b) collected on 8 May 2018 (1 d after IOP 1). Table 3 summarizes the optimized values used in the A-g_s (sub)model to simulate the leaf-level photosynthesis. The A–PAR curves contain only the lower light intensity values (0–200 µmol m⁻² s⁻¹) for which the light response is near linear and not limited by CO₂ diffusion into the leaf. As leaf-level measurements of A_max indicated a decline in photosynthetic capacity in the course of the growing season (Fig. 5c), we performed additional measurements of A_m,max298 to represent the observed seasonal decline for IOP 2 and IOP 3. The impacts on these optimized values are shown and discussed in the Supplement.

2.4.2 Modelling the diurnal variability of landscape surface fluxes and boundary layer dynamics

The fundamental assumption of the mixed-layer model is that under convective conditions the atmospheric boundary layer (ABL) dynamics lead to profiles of the meteorological state variables that are uniform (well-mixed) with height. As a result, these state variables are governed by horizontally averaged 0-dimensional slab equations: one equation for the evolution through time of the slab variable and another for the difference between the residual layer (in the morning transition) and the free tropospheric values and the slab value, i.e. the jump at the interface between residual layer and ABL. The ABL dynamics are governed by the mixed-layer equations of potential temperature (heat), specific humidity (moisture), CO₂, and two horizontal wind momentum components. In addition, there is an equation that governs the boundary layer growth, which depends on the buoyancy flux at the surface and the jump in the virtual potential temperature at the interface between the atmospheric boundary layer and the free troposphere.

A key feature of the model is its representation of the sub-daily variability of the land–atmosphere interactions (van Heerwaarden et al., 2010; Vilà-Guerau de Arellano et al., 2015). The net ecosystem exchange is calculated as a result of the assimilation of CO₂ by plants and the CO₂ soil efflux. We calculate the assimilation rate from photosynthesis and the stomatal aperture measurements at leaf level (see Sect. 2.4.1), upscaled to canopy level (Ronda et al., 2001). This model depends on the diurnal variability of PAR, temperature (T_air and T_air,p), and the water vapour deficit (VPD). The two-big-leaves approach is used (sunlit and shaded) to take the different contributions of direct and diffuse radiation into account (Pedruzo-Bagazgoitia et al., 2017). The soil efflux is calculated as a function of the soil temperature and moisture. Other relevant physical processes include a radiation transfer model, the Penman–Monteith equation included in the surface energy balance, and the possibility of adding large-scale forcings such as vertical subsidence motions and large-scale advection of momentum, heat, moisture, and CO₂. Within the context of CloudRoots, it is important to mention that the model assumes a horizontal homogeneous surface. While the experimental field itself is quite homogeneous, it is surrounded by other land use types at a spatial scale that will affect the boundary layer. In that respect, and in setting the initial and boundary conditions for the numerical case, we assume that the boundary layer dynamic is governed by a sensible heat flux that is an aggregate of all the fields shown in Fig. 1b.

3.1.1 Stomatal conductance and sap flow

Our leaf-level measurements revealed clear diurnal patterns in g_sw during all the IOPs (Fig. 3). The observed daily maximum g_sw decreased over the growing season. This daily maximum g_sw occurred at an earlier time during each IOP. Specifically, the 30 min average daily maximum g_sw declined from 0.84 mol m⁻² s⁻¹ (around 10:00 UTC, 12:00 LT) during IOP 1 and 0.83 mol m⁻² s⁻¹ (around 10:00 UTC) during IOP 2 to 0.30 mol m⁻² s⁻¹ (between 05:30 and 06:30 UTC) during IOP 3. The weather during IOP 2 was characterized by large cumulus clouds passing over the field site, which were made visible in the large fluctuations in PAR (Figs. 3b, 11 and 12). The cloud-related changes in light intensity induced consistent stomatal opening–closing responses during IOP 2. The relatively low g_sw observed during IOP 3 probably reflects the continuing drought that characterized the 2018 growing season in combination with the relatively high VPD and high temperatures. Sap flow measurements were performed during IOP 2 and IOP 3 (Fig. 3b and c) and one earlier non-IOP day (7 June) (Fig. 4). Measurements of sap flow revealed clear diurnal patterns for all measurement days and consistent responses to cloud-induced changes in light intensity during IOP 2 (Fig. 3b). These responses were comparable to the observed responses in g_sw during IOP 2. Interestingly, the notable decline in leaf-level g_sw between IOP 2 and IOP 3 was neither reflected in the measurements of sap flow nor in the ET measurements with the eddy covariance. For IOP 3, the ET measured by the eddy covariance had still maximum values of 300 W m⁻². Thereafter, the decrease in ET started 1 week afterwards (5 July) with values lower than 100 W m⁻². This discrepancy could partly be explained by increases in VPD and wind speed between IOP 2 and IOP 3. The more probable causes are senescence effects on physiological control of transpiration and the physical reactions to heat of the wheat tillers, which were noticeably wilting between IOP 2 and IOP 3. This observation has so far not been reported in the literature. Further studies of the relationships between senescence and simultaneously occurring changes in the heat and physical properties of wheat tillers are needed to explain this phenomenon.

Figure 3Diurnal changes in photosynthetically active radiation (PAR) and vapour pressure deficit (VPD) measured for (a) IOP 1, (b) IOP 2, and (c) IOP 3. Leaf-level measurements of stomatal conductance of water vapour (g_sw) in (b) and (c) compared to tiller-level measurements of sap flow (E_sap). Leaf-level measurements of g_sw (blue markers) were averaged over 30 min intervals (blue line). Sap flow measurements represent the 1 SD confidence interval (shaded region) of measurements on 24 tillers averaged over 30 min timescales.

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3.1.2 Observed versus modelled leaf-level photosynthesis

One of the main aims in CloudRoots is to improve the mechanistic modelling of photosynthesis and stomatal aperture. To this end, we calibrate the constants of the A-g_s model using systematic in situ field observations. Figure 5 shows the dependencies of leaf-level photosynthesis of A_leaf on PAR (Fig. 5a) and the leaf-internal CO₂ concentration (Fig. 5b) and the long-term decline in maximum light-saturated photosynthesis (Fig. 5c). Our observations indicate the need to calibrate the model depending on the functional type of the plant, in particular the dependence of A_leaf on PAR, during the field campaign. Table 2 summarizes the new constant values used in the A-g_s model adjusted to the winter wheat crop conditions.

Figure 6 shows a comparison of the model results of A_leaf using the new constants and the measurements of A_leaf and NPP together with the diurnal variation in PAR and VPD during the three IOPs. Our measurements and model results of A_leaf showed clear diurnal patterns during each IOP, and a consistent decline over the three IOPs. The decline in A_leaf was comparable to the decline in A_max (Fig. 5c) and probably reflects a combination of seasonal decay in photosynthetic capacity and increasing stomatal limitations owing to persistent drought, especially during IOP 3. The magnitude of the seasonal decline in A_leaf was comparable to the seasonal decline in NPP derived from EC data. Cloud-induced changes in PAR during IOP 2 also induced changes in A_leaf. The A-g_s model reproduced the diurnal patterns in A_leaf during each IOP, as well as the cloud-induced changes in A_leaf during IOP 2. The agreement is very satisfactory during IOP 1, which was characterized by cloudless conditions and the maturity of winter wheat. The model underestimated A_leaf during IOP 3, which was a result of the strong stomatal limitations that influenced the measurement of A_max on which the model parameterization from IOP 3 was based. The model furthermore overestimates the decline in A_leaf between 14:00 and 19:00 UTC, which probably reflects a misrepresentation of the temperature and VPD sensitivity of Triticum aestivum.

Figure 4Sap flow measured using the heat balance method for 7 June 2018 (non-IOP day).

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3.2.1 Concentration profiles of H₂O and CO₂, temperature and wind speed

Figure 7 shows selected 30 min mean profiles of χH₂O and χCO₂, temperature, and wind speed versus height (z) above ground level during IOP 1 and IOP 2. Over the diurnal cycle, χCO₂ concentrations fell between 08:00 and 13:00 UTC from 370 to 360  µmol mol⁻¹ in the mid-canopy during IOP 1 but stagnated slightly below 370 µmol mol⁻¹ during IOP 2. This seasonal reduction in CO₂ uptake was also observed in measured A_leaf, i.e. see the decrease of the maximum values in Fig. 6. The lowest values were observed during local noon, simultaneous with the highest PAR values (Fig. 5b). χCO₂ minima were located in the upper third of the canopy during IOP 1 and during the middle third during IOP 2. The highest χCO₂ values were found near the soil surface due to soil respiration, lower light intensity caused by shadowing, and a low amount of photosynthetic organs in the stems. Maximum χCO₂ concentrations were measured in the morning and evening hours and peaked at about 475 and 420 µmol mol⁻¹ during IOP 1 and IOP 2, respectively. The photosynthetic CO₂ uptake by plants is highly related to plant transpiration. Consequently, χH₂O in the canopy space was higher than in the air above the canopy. The highest values were found directly above the soil surface and were caused by evaporation and due to plant transpiration within the canopy.

Figure 7Selected (08:00, 13:00 and 18:30 UTC) 30 min mean profiles of the H₂O and CO₂ mole fractions (χH₂O, χCO₂), wind speed (u_p), and temperature (T_air,p) measured at high vertical resolution during IOP 1 (upper row) and IOP 2 (lower row). Shaded areas indicate the 95 % confidence interval resulting from the standard deviation between individual profiles sampled within a 30 min average interval. The dashed lines indicate the canopy heights.

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The highest temperatures appeared near the canopy top (Fig. 7d, e, j and l). In the late morning of IOP 2, the temperature reached a distinct maximum just below the canopy top (Fig. 7j). This phenomenon has been reported in previous studies (Ney and Graf, 2018) and is caused by the changing solar incidence angle. A low angle of incidence in the morning and afternoon limited the heating to an area just below the canopy surface. Previous studies have shown that the presence of such a pronounced temperature maximum has the potential to increase thermal stability within the canopy and thus inhibit the vertical turbulent exchange of sensible heat (Gryning et al., 2001; Ney and Graf, 2018; Sikma et al., 2020). It can be assumed that the sensible heat flux within the dense plant stand was largely determined by the entire canopy. In other words, during the day, mixing near the soil surface was impeded by stable temperature stratification, while in the evening cooling expanded upwards from the soil surface (Fig. 7f). In general, the processes described above were more pronounced during IOP 2 with its greater canopy height than with the lower canopy during IOP 1. The vertical wind profile showed consistently low wind speeds within the dense canopy (<0.5 m s⁻¹). Above the canopy layer, the wind speed increased in a log-like profile up to a maximum of 2 m s⁻¹.

3.2.2 Profiles of gross primary production

The detailed profile observations presented in the previous section enable us to calculate height-resolved estimates of gross primary production A. Using the 30 min averages of the vertical profiles for temperature, moisture, and CO₂ in the canopy, A is determined using the A-g_s model (Jacobs et al., 1997; Ronda et al., 2001). A (mg m⁻² s⁻¹) is calculated as follows:

where LAD (m${}_{\mathrm{leaf}}^{\mathrm{2}}$ m⁻³) is the leaf area density, A_m(h) is the CO₂ primary productivity (mg m${}_{\mathrm{leaf}}^{\mathrm{2}}$ s⁻¹) as a function of height h, R_d(h) (mg m${}_{\mathrm{leaf}}^{\mathrm{2}}$ s⁻¹) is the CO₂ dark respiration as a function of h, α (mg J⁻¹) is the light use efficiency, and PAR(h) (W m${}_{\mathrm{leaf}}^{-\mathrm{2}}$) is the amount of available photosynthetically active radiation within the canopy. Solar-zenith-angle-related variation in PAR intrusion and differences between atmospheric and skin values for temperature, moisture, and CO₂ are neglected. Figure 8a shows the winter wheat LAD applied in the calculation.

Figure 8(a) Leaf area density (m${}_{\mathrm{leaf}}^{\mathrm{2}}$ m⁻³) on 7 May 2018 as a function of height (h) normalized to the maximum canopy h (h_c). The profile is typical for winter wheat, as defined by Olesen et al. (2004). (b) Time evolution of CO₂ gross primary production A (mg m⁻³ s⁻¹) on 7 May 2018 as function of h normalized to h_c. The profile is obtained using the profile measurements and using Eq. (2).

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Figure 8b shows that the entire canopy contributes to the photosynthetic activity but with maximum A at $h/h_{\mathrm{c}}=\mathrm{0.7}$ (h_c: canopy height). This is primarily caused by the extinction of PAR within the canopy and reduced leaf density distribution close to the ground (Fig. 8a). Maximum diurnal productivity is found at around $h/h_{\mathrm{c}}=\mathrm{0.7}$, with the diurnal maximum at 12:00 UTC. Integration over the canopy shows minor discrepancies with respect to the bulk A-g_s model calculation, as the profile data allows for a more precise evaluation of photosynthetic activity. The profile measurements combined with Eq. (2) therefore allows for an improved modelling of the photosynthetic CO₂ uptake of vegetation depending on height and the understanding of mechanisms. More accurate estimates of CO₂ gross primary production still require improved knowledge of plant canopy micrometeorology (Drewry et al., 2014).

Figure 9Source partitioning results for (a) H₂O and (b) CO₂ fluxes for IOP 1. Dashed grey lines show the measured latent heat flux (ET_ec) and net ecosystem exchange (NEE_ec) in half-hourly time steps. Values with subscript index p indicate estimates based on inversed profile concentration measurements (Sect. 3.4). Error bars for evaporation calculated from microlysimeters (E_lysi) and soil respiration measurements (R_s,ch) indicated to 1 SD. (ET_ec: evapotranspiration measured as latent heat flux L_vE by the eddy covariance system; E: evaporation; Tr_p: transpiration; NPP: above-ground net primary production; R_s: soil respiration).

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3.2.3 Profile-based partitioning of H₂O and CO₂

Figure 9 shows the measured fluxes of latent heat, NEE, and soil respiration, as well as their partitioning based on the inversion of vertical high-resolution concentration profiles into the soil evaporation and plant transpiration and the R_s and NPP components. In this section, positive values indicate a flux from the surface and plants into the atmosphere and vice versa. During IOP 1, measured latent heat flux (L_vE, hereafter referred to as ET_ec) showed a typical daily pattern under clear sky conditions (Fig. 9a) with maximum ET_ec at noon (345 W m⁻²). Evaporation E of both methods displayed comparable values in the morning and evening but differed at midday. In the morning, the evaporation estimated using the profile measurements and method (E_p) and the lysimeter observations (E_lysi) both consistently suggested low E∕ ET fractions with E below 10 W m⁻². Towards noon, E_p increased to 25 and E_lysi to 60 W m⁻², and in the afternoon E_lysi reached a maximum of 101±41 W m⁻² (no E_p available). Estimated Tr_p increased to about 290 Wm⁻² at 11:00 UTC, this being the highest diurnal proportion of ET. Lower Tr_p levels around 12:00 UTC are probably due to a sub-optimal performance of the profile-based partitioning at this particular time. For example, none of the available inversion methods, including the algorithm by Santos et al. (2011) used here, include the effect of local thermal stability varying with height. Figure 7 demonstrates that thermal stability increased from the canopy top towards the ground around noon of IOP 1 (Fig. 7e), which may have contributed to the large increase of humidity towards the surface (Fig. 7b) due to the lack of mixing.

Figure 10(a) Net primary production (NPP) versus photosynthetic active radiation (PAR). (b) Latent heat (L_vE) versus net radiation (Q^*). In both figures, the observation period encompasses clear and cloudy skies during a 2-week period starting on 7 May 2018 at 03:30 UTC (sunrise) and ending on the 20 May 2018 at 19:40 UTC (sunset). The solid line represents the median of the data. The lower and upper boundaries of the shaded area are the 25th and 75th percentiles of the data, respectively.

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Variations in CO₂ fluxes NEE, NPP, and R_s during IOP 1 are shown in Fig. 9b. NEE_ec followed a typical diurnal cycle, with strong negative fluxes during the day and slightly positive values (carbon source) during transition times. The highest NEE was observed before noon (−25 µmol m⁻² s⁻¹). NPP_p followed the graph of NEE_ec, with higher values (−26 µmol m⁻² s⁻¹) in the morning hours than during the afternoon under comparable PAR values. This behaviour coincides with the photosynthesis rate observed at leaf level in Fig. 6a and provides further evidence that carbon uptake by plants was limited due to stomatal occlusion caused by the increase in VPD (Fig. 6a) and/or T_air in the afternoon. Profile-based R_s,p ranged between 0.5 and 6 µmol m⁻² s⁻¹ with higher values around noon. Compared to measured R_s,ch, R_s,p lay within the standard deviations of R_s,ch, though R_s,p was significantly lower during the morning and evening hours.

3.3.1 Cloud-induced diffuse fertilization effect on evapotranspiration

One of the main aims of CloudRoots was to obtain observational evidence of the effects of clouds on the CO₂ assimilation and ET. Figure 10 shows the net primary production (NPP) (Fig. 10a) and L_vE (Fig. 10b), both measured using the eddy covariance, observed under a wide range of clear and cloudy skies as a function of PAR and compared to Q^* at the top of the canopy (van Diepen and Moene, 2019). We analyse a 2-week period of observations, between 7 and 20 May 2018. The effect of the different direct and diffuse radiation due to cloud perturbations is distinguishable with an enhancement of NPP under clear conditions whereas L_vE is reduced. Clouds affect plant photosynthesis by increasing the fraction of diffuse solar radiation that arrives at the top of the canopy (Kanniah et al., 2012). With a larger contribution of diffuse solar radiation and within the canopy, the radiation spreads more equally over all leaves and thereby increases the light-use efficiency of a canopy (Farquhar and Roderick, 2003). At a constant level of radiation at the top of the canopy, the increased light-use efficiency results in enhanced canopy photosynthesis, which is known as the diffuse fertilization effect (Roderick et al., 2001). This phenomenon is especially noticeable for canopies with a high LAI (Knohl and Baldocchi, 2008; Dengel and Grace, 2010). In CloudRoots and due to the high values of LAI (values between 4.5 and 5.5 m⁻²), we expect situations in which diffuse fertilization occurs, but here the question is how it influences L_vE. Previous large-eddy simulation modelling studies by Pedruzo-Bagazgoitia et al. (2017) have shown that under conditions dominated by clouds with a small optical depth, i.e. thin clouds, L_vE is enhanced with respect to its clear-sky values at the same radiation level.

Figure 11IOP 2 (15 June 2018) time series of (a) sensible heat flux (H) at 1 min intervals with a displaced-beam laser scintillometer (DBLS) and at 10 min intervals with an eddy covariance system (EC), combined with scaled time series of photosynthetically active radiation (PAR, scaled by 1500 µmol m⁻² s⁻¹) and wind speed (U, scaled by 6 ms⁻¹); (b) turbulent exchange coefficient K_T; and (c) structure parameter of temperature, $C_T^{\mathrm{2}}$, that together make up H in the DBLS method following Eq. (1).

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We find that the observed L_vE is higher rather than lower during clear conditions (less diffuse light) than under more diffused cloudy conditions. At constant Q^*, the median of L_vE is always higher under clear skies than for cloudy skies. The diffuse fraction plays a minor role and the decrease on L_vE under cloudy conditions is mainly due to the reduction in the incoming shortwave radiation. Our observations indicate that L_vE is driven by the partitioning of direct and diffuse radiation but also other effects such as diurnal variations of temperature, and the link to VPD may partially compensate for the different distribution of direct and diffuse radiation caused by clouds. The higher VPD values during the day partly offset the more optimal PAR conditions and therefore cause a closing of the stomatal that leads to decreases in L_vE. For both clear and cloudy skies, the shaded area below the median represents conditions before 11:30 UTC and the shaded area above the median represents conditions after 11:30 UTC, i.e. implying a hysteresis loop (Zhang et al., 2014). This spread in L_vE at a constant level of Q^* is caused by a difference in VPD between morning (before 11:30 UTC) and afternoon (after 11:30 UTC). This is because on a clear day the VPD raised rapidly due to its non-linear dependence on temperature relative to a cloudy day. In a typical clear day at CloudRoots, the value of 200 W m⁻² for Q^* is crossed twice: once in the morning and once in the afternoon. When 200 W m⁻² is crossed in the morning, the VPD is around 1000 Pa and reaches a value of 2000 Pa in the afternoon. On the other hand, on a cloudy day with similar values of around 200 W m⁻² the VPD remains almost constant through the entire day and with a value of 1000 Pa at 11:30 UTC.

The influence of VPD on L_vE also has the effect that the diurnal cycles of Q^* and L_vE are out of phase due to its dependence on leaf temperature. Q^* is primarily a function of incoming shortwave radiation and VPD of air temperature at the leaf surface. As a result, Q^* and VPD peak at different times of the day. Q^* peaks at maximum incoming shortwave radiation (local noon is at 11:30 UTC), and near-surface VPD times when air temperature peaks, which is around the time at which $Q^{*}=\mathrm{0}$ (17:00 UTC). The diurnal cycle of the sun implies there is a short period around 11:30 UTC when Q^* does not change. On the contrary, air temperature increases almost linearly around 11:30 UTC due to the approximately constant Q^*, as does VPD. Therefore, peak values for L_vE are found between the moments of maximum Q^* and of maximum VPD. For this dataset, the peak of L_vE is around 12:00 UTC for both clear and cloudy skies, although the peak for cloudy skies is less distinct due to the more fluctuating daily cycle of Q^*. Because Q^* and L_vE are out of phase, the highest values for L_vE do not occur in the bin with the highest net radiation, but rather in the bin of 400–500 W m⁻² (which roughly contains data from 11:00 UTC and after 12:00 UTC).

3.3.2 Cloud-induced radiation perturbations and response by turbulent fluxes

The short interval fluxes (1 min) of the double-beam laser scintillometer (DBLS) technique enable us to study the vegetation response to rapid radiation perturbations due to changes in cloud cover. The goal here is to illustrate this potential by discussing selected time series under changing cloud conditions during IOP 2. The morning of IOP 2 was characterized by rapidly changing cloud conditions due to the overpass of a shallow cumulus cloud deck. A breakdown of the 1 min DBLS sensible heat flux in terms of contributions from turbulent exchange (K_T) and the measure for temperature fluctuations ($C_T^{\mathrm{2}}$) is given in Fig. 11. This figure also depicts, on the same axes, scaled time series of wind speed and PAR that can be regarded as proxies that fuel mechanically induced turbulence (wind speed) and buoyancy turbulence (radiation in general) as well as photosynthesis (PAR).

Figure 12IOP 2 (15 June 2018) time-series of (a) latent heat fluxes (LvE) at 1 min intervals with a displaced-beam laser scintillometer (DBLS) and at 10 min intervals with an eddy covariance system (EC) combined with scaled time series of photosynthetically active radiation (PAR, scaled by 1500 µmol m⁻² s⁻¹) and wind speed (U, scaled by 6 ms⁻¹). Panel (b) is the same as (a) but for the CO₂ flux ($F_{{\mathrm{CO}}_{\mathrm{2}}}$).

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First of all, the 1 min DBLS fluxes of H closely follow the cloud cover induced radiation changes, but with a time-lag of 45–120 s (Fig. 11a). This is similar to those reported by van Kesteren et al. (2013b). H fluxes measured with EC techniques even when estimated over the relatively short interval of 10 min, which is not a standard output, are not capable of capturing such rapid dynamic behaviour of the flux regime (Fig. 11a). The dynamic behaviour in the DBLS H is mainly governed by fluctuations in T expressed by $C_T^{\mathrm{2}}$ (Fig. 11c) and to a lesser extent by changes in the exchange coefficient K_T (Fig. 11b). Note that is impossible to fully distinguish the three variables H, K_T, and $C_T^{\mathrm{2}}$ from each other as they are all interconnected, e.g. K_T is defined in terms of the Obukhov length L, which in turn depends on H and u_*. Nevertheless, our high-time-resolution observations demonstrate that changes in PAR induce very fast responses of the transported quantity T (Fig. 11c). Even in the absence of strong wind-induced variations in K_T, these T variations lead to approximately similar dynamic behaviour of H. On top of this, the additional but smaller wind-induced fluctuations in K_T are also reflected in H and lead to “noise” in the variability of H compared to the cloud-induced on–off behaviour of PAR.

Figure 13(a) Aerial map of F₇₆₀ on 26 June 2018 with measurement locations used to combine with mobile (circles) and stationary (triangles) measurements. (b) Diurnal changes in F₇₆₀ on different days of the campaign as 5 min measurement averages depicted in the same colours as observation locations in (a).

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Next we examine how soon the fluxes of H₂O and CO₂ respond to the cloud induced radiation changes. Figure 12 demonstrates that there is indeed a fast response, and the 1 min resolution fluxes of H₂O and CO₂ allow us to precisely determine a delay time of approximately 2 min for the increases in CO₂ uptake and transpiration of H₂O relative to the changes in PAR. The delay is once again undetectable with the standard 30 min eddy covariance results (Fig. 12). This behaviour is in line with what was concluded about the state of the vegetation observed at leaf level (Sect. 3.1). As the vegetation is not water-stressed and is at a stage of development at which it is still actively growing, it will react rapidly to changes in radiation, i.e. it is in a radiation-limited regime. Under the conditions of our study, stomata appear to have reacted only slowly or remained constantly open because leaves were unstressed or reacting only slowly to cloud-induced changes. Moreover, the timescale of a light-induced stomatal response (maximum values of 20 min; Van Kesteren, 2013b) is normally larger than the timescale of most fluctuations in radiation. Our suggested explanation is that the 1 to 2 min delay time observed between radiation and turbulent fluxes is due to processes associated with the inertia of the leaf in addition to turbulent transport between the leaf and laser path due to, e.g. the small but not negligible storage of heat, H₂O and CO₂ in the canopy layer. However, we need further evidence to disentangle the separation in delays between H₂O and CO₂ fluxes.