The CHATS experiment took place in the spring of 2007 in one of Cilker Orchard's walnut blocks in Dixon, California, USA. A detailed description of the site, instrumentation and data treatment has been provided by Patton et al. () and Dupont and Patton (). Here we focus on the specific observations used in this study and on the criteria used to select the representative cases.

The observations analysed in this study were made on a 30 m mast located near the northernmost border of the orchard site in order to ensure a fetch of about 1.5 km for the predominantly southerly winds see Figs. 1a and 3 in . The average height of the trees (hc) was estimated to be 10 m. Wind, temperature and specific humidity were measured at 13 levels on the mast see . The shortwave and longwave radiation above the canopy were measured at 6 m above the canopy top. The soil properties were measured at a depth of 0.05 m. The National Center for Atmospheric Research (NCAR) Raman-shifted eye-safe aerosol lidar (REAL) monitored reflectivity in order to evaluate the evolution of the boundary-layer height, h . The lidar measurements enabled us to retrieve the evolution of h from the aerosol backscatter signal (see Supplement for the method and the data treatment procedures). The leaf area index (LAI) was also measured before and after the growing (leaf out) season . Although the LAI varied from 0.7 to 2.5 m2 (leaf area) m-2 (surface area) depending on the seasonality (before and after leaf out), we took the value of 2.5 for the LAI to represent a fully vegetated canopy. It is important to note that due to the sparseness of the orchard canopy the insolation at the ground was relatively high, leading to a high amount of available energy at the soil. As a consequence, the soil-related fluxes of sensible and latent heat were relatively important for the turbulent exchange processes within and above the canopy .

The CHATS data set is used in our study to initialize and constrain our soil–vegetation–atmosphere modelling system. The model evaluation of the diurnal variability of the state variables in and above the roughness sublayer makes use of diurnal observations of the mean and turbulent variables at the same heights (at the canopy top (10 m) and at 19 m above the canopy) as for the selected study cases (Sect. ).

An atmospheric boundary-layer model with a zero-order jump approach, based on mixed-layer theory , was used to calculate the evolution of the well-mixed (slab) state variables and the evolution of boundary-layer height. It is based on the vertical integration of the slab-averaged governing equations of thermodynamic variables and atmospheric constituents well above the canopy. At the upper boundary of the atmospheric model, the thermal inversion layer sepa rates the well-mixed layer (MXL) from the free troposphere (FT). This separation is represented by a finite jump in the constituent under consideration (FT values minus MXL value) over an infinitesimal depth. At the bottom, we included a representation of the surface roughness-sublayer (RSL), which is characterized by steep mean gradients, connecting the surface to the lower part of the atmospheric surface layer (ASL). The ASL then connects the RSL to the MXL (Fig. ). The predicted boundary-layer state variables (wind speed, potential temperature and specific humidity) and the boundary-layer height (h) by the model are presented later in this section.

Based on the mixed-layer model, the diurnal variability of the mean thermodynamic variables and atmospheric constituents reads as follows: d〈φ〉dt=(w′φ′‾)s-(w′φ′‾)eh+Advφ, where (w′φ′‾)s and (w′φ′‾)e are the vertical turbulent kinematic fluxes of a certain variable φ (φ≡u,v,θ,q) at the lower (surface) and upper (entrainment) boundaries respectively; h is the boundary-layer height, while Advφ is the advection of the corresponding quantity of interest. The chevrons “〈φ〉” represent the variables within the mixed layer. For a more complete description of the mixed-layer governing equations, see van Heerwaarden et al. () and Ouwersloot et al. (). In what follows, we incorporate the most physically sound roughness-sublayer model in the surface scheme of our modelling system (following the concept of Harman ). We calculated the surface fluxes in Eq. () as follows: (w′φ′‾)s=(φs-φ(zr))raφ+rsφ, where φs and φ(zr) are the mean vector (wind velocity) and scalar (potential temperature, specific humidity) quantities at roughness length (z0φ) and at a given reference height within the RSL (zr). For momentum z0φ≡z0M, while for scalars z0φ≡z0H. The aerodynamic resistance in Eq. () is calculated at zr and is related to the drag coefficient (Cφ) and the mean wind speed (|U|) at the same height: raφ=(Cφ(zr)|U(zr)|)-1. The stomatal resistance, rsφ, in Eq. () is equal to zero for momentum and heat. Its definition and computation for moisture is presented and explained in van Heerwaarden et al. ().

The influenced Cφ(zr) and φ(zr) due to the canopy presence are calculated using the following expressions: Cφ(zr)=κ21[ln⁡zrz0M-ΨMzrL+ΨMz0ML+Ψ^Mz,dt,L]1[ln⁡zrz0φ-ΨφzrL+Ψφz0φL+Ψ^φz,dt,L], and φ(zr)=φs-(w′φ′‾)sκu*[ln⁡zrz0φ-ΨφzrL+Ψφz0φL+Ψ^φ(z,dt,L)], where κ is the von-Kármán constant of 0.41 . The friction velocity is computed as u*=CM(zr)|U(zr)|.

The functions ΨMzrL, ΨMz0ML, ΨφzrL, Ψφz0φL are the integrated diabatic stability functions for momentum and scalars, while Ψ^M(zr,dt,L) and Ψ^φ(zr,dt,L) represent the roughness-sublayer functions for momentum and scalars . Stability-dependent roughness lengths for momentum and other scalars (z0M and z0φ respectively) included in Eqs. () and () are described in detail in Harman ().

The displacement height, dt, in Eqs. () and () is defined as the distance from the conventional displacement plane, at actual height, d, to the canopy top, at actual height hc: dt=hc-d (see Fig. ). Based on Harman and Finnigan (), dt is calculated as follows: dt=β2Lc, where, Lc, is canopy adjustment length scale, defined as Lc=(cda)-1, where a is the canopy's leaf area density which is assumed to be constant with height , while cd is the leaf drag coefficient, calculated from the observations at the canopy top (cd=u*2/(|U|)2). The canopy adjustment length scale (Eq. ) is defined as a measure of the distance over which an internal boundary layer with no prior knowledge of a tall canopy would need to equilibrate (adjust) to the presence of a canopy . For the given CHATS experiment, Shapkalijevski et al. () have shown that Lc= 16 m under near-neutral and weakly unstable conditions. Under strongly unstable conditions Lc≈ 10 m, while under strongly stable conditions Lc> 20 m. Another critical stability-dependent variable in Eq. () is β, which indicates the ratio between the friction velocity and the mean wind speed at canopy top β=u*|U|. Based on our CHATS analysis , we find that under weakly unstable, near-neutral and weakly stable atmospheric conditions β has constant value of 0.3, consistent with . Under strongly unstable conditions, this variable increases up to 0.4, while under strongly stable conditions it decreases to nearly 0.25. Based on estimates at the CHATS site, we assume values of 0.3 and 16 m for β and Lc. The sensitivity of the calculated surface fluxes and boundary state variables to the values of β and Lc is presented and discussed in Sects.  and .

Finally, the RSL functions Ψ^M(zr,dt,L) and Ψ^φ(zr,dt,L), are non-linear integrals, which are solved numerically. For a detailed theoretical description and derivation of these RSL functions, see .

To initialize and validate our modelling system, we selected observations from a representative day from the second phase of the CHATS campaign (from 13 May to 12 June) focusing on the walnut trees after leaf out (fully vegetated canopy). The representative case is based on two requirements that the data satisfied: (i) well-mixed conditions and (ii) well-developed RSL. Our assumption of a well-mixed boundary layer is justified for sunny (cloudless) days characterized by convective conditions. Moreover, the lidar data (see figures in the Supplement) showed quite a homogeneous signal, which in the absence of radiosoundings implies well-mixed conditions of up to 500 m height at noon (12:00 LT, local time). In order to ensure the maximum influence (fetch) of the canopy on the atmospheric flow, leading to a potentially well-developed RSL, we selected data with predominantly southerly winds, since the measurement tower was placed at the northernmost part of the orchard field Fig.1. Based on these requirements, we selected observations from 27 May 2007 at CHATS. To test the robustness of the model results, we also analysed an additional day (31 May 2007) with different wind forcings (northerly varying to southerly winds over the course of the day).

Several systematic experiments were performed, in which the representation of the drag coefficient and the impact of the RSL on mean gradients (Eqs. –), as well as the inclusion of various large-scale forcing were varied. The standard MOST runs (abbreviated to M) were performed by omitting the roughness-sublayer functions in Eqs. ()–(). The large-scale forcing consists of mean vertical velocity subsidence, advection of cold and moist air and increased boundary layer drying due to a drier free troposphere (see next paragraph). Table  summarizes the processes included in the numerical experiments.

The numerical experiment which does not take subsidence into account has prescribed zero subsidence (no divergence of the mean horizontal wind), while the numerical experiments with subsidence have imposed constant divergence of the mean horizontal wind (Appendix ). Moreover, and based on the observed temporal evolution of the potential temperature and specific humidity at 29 m, we set constant advective cooling and moistening to specific moment in time in our numerical experiments (Appendix ). No advection of momentum has been imposed in the momentum budget. Furthermore, to represent the increased BL drying from the free troposphere, we modified the specific humidity lapse rate in the free troposphere (γq) depending on the BL height (Appendix ). For instance, to represent the observed temporal evolution of the specific humidity at 29 m during the day on 27 May 2007, we prescribed a modification of the γq=10-4 kg kg-1 m-1 when the BL height reaches 450 m (based on observations), while the initial γq was set equal to 0 units (see Table ).

The numerical experiments started at 08:00 LT, which is equivalent to 15:00 coordinated universal time (UTC), and lasted for 9 h. In the absence of initial measurements at the residual layer (roughly 350 m), we imposed the upper boundary conditions of the model to optimize the representation of the temporal evolution of the potential temperature, specific humidity, wind direction and boundary-layer height (Tables  and in Appendix ). We used the observations at the highest measurement level at the tower (29 m above ground surface) to evaluate the model results away from the canopy, where the RSL effects are minimal.

Furthermore, we put special emphasis on validating the modelled quantities at the canopy top (z=zr=dt) and compared them with the corresponding observations at the same height. We selected the canopy top (10 m above the ground surface) as a reference level due to the largest expected RSL effects on the flow . We note that the area of the orchard is rather small (∼ 1 km2) to be capable of influencing the development of the boundary-layer dynamics . However, in the model, we extrapolated the characteristic surface fluxes and mean gradients, assuming that the area of this orchard is sufficient to drive the main processes at the CBL dynamics.

Finally, the initial value of z0M= 0.7 m used in all the numerical runs (Appendix ) was estimated based on the approach developed by Raupach () for a LAI of 2.5 and β= 0.3. Thus, the initial value of the roughness length for scalars, z0M= 0.095 m (see Table ), is calculated as ln⁡z0Mz0H=2 see . For the standard MOST runs (MXL+MSAD), we used invariant (fixed) z0M and z0φ with values equal to their corresponding initial values, while, when including the RSL, we used stability-dependent formulation for z0M and z0φ .

We start our analysis by evaluating the modelling system to represent the observations of the selected study cases. Figure a, b shows the observed and modelled components of the net radiation: downwelling (↓) and upwelling (↑) shortwave (SW) and longwave (LW) radiation fluxes above the canopy (measured at 6 m above the canopy top). The various radiation components are well reproduced by the model.

Figure c, d shows the four terms of the surface-energy balance (Rn = SH + LE + G) for both cases. The surface fluxes in the model are calculated from the differences between the surface and the roughness sublayer (reference height) values of the mean quantities and the transfer coefficients for momentum and scalars (see Sect. , Eq. ). While the net radiation fluxes compare satisfactorily with the observations, the modelled daily averaged values of SH and LE are overestimated at around 60 and 20 % larger than the observed SH and LE respectively for both case studies (27 and 31 May 2007). The average daily difference in the modelled and observed ground flux is up to 5 W m-2. The diurnal variations in the observed LE and SH are well captured by the model, for instance the rapid decay of SH towards the end of the day relative to LE.

Our explanation of this overestimation is the frequently observed imbalance of the observed surface-energy system . This hypothesis is corroborated by an observed daily average difference of up to -30 % of SH + LE + ΔQs compared to Rn-G for the case of 27 May and -20 % on 31 May (Fig. ), even when the heat storage contribution (ΔQs) is included in the observed SEB (up to 5 % energy input in the total balance). The ΔQs is the sum of the sensible (ΔQa) and latent (ΔQw) heat storage in the air column (including the canopy space) below the flux measurements by eddy covariance (EC). The method used to calculate ΔQs from the observed potential temperature and specific humidity at the levels within and above the canopy, but below the height of EC observations, is based on that described by McCaughey and Saxton () and later used in Oliphant et al. (). Note that presented G accounts for the heat storage in the soil are calculated following Oliphant et al. (). The heat stored in the biomass and the energy used in the photosynthesis are neglected in our case, since according to Thom et al. (), Ohta et al. () and Jacobs et al. () these two terms are negligibly small (less than 2 % of total Rn). The values of the surface-energy imbalance at CHATS are similar to those found by a number of other observational studies, showing an average of up to 20 % surface-energy imbalance, as listed in Sect. 3.7 of Foken (). With regard to our own research, it is important to note that, related to this non-closure of the observed SEB, the observed SH and LE are too low, so the modelled SH and LE are more likely to be the correct values.

The comparison presented here confirms that our modelling system is capable of reproducing the diurnal variations in radiation with sufficient accuracy. As in many other studies see, the observed surface-energy balance does not remain closed, but has deviations of similar magnitude as observed in other studies of layers above high canopy.

Figure  shows the observed and modelled diurnal evolution of the boundary-layer height, mixed-layer potential temperature and specific humidity for the case of 27 May 2007. The boundary-layer height (Fig. a), h, increases during the morning hours from 350 m to up to 500 m at around 11:00 LT, after which h remains almost constant before it starts to decay at around 14:00 LT. In the absence of data on the vertical profiles of potential temperature and specific humidity in the mixed layer and the entrainment zone, we are unable to judge whether this more rapid growth until 11:00 LT is due to a progressive growth of the CBL into a residual layer above the canopy . Since our aim is to study the RSL effects on CBL dynamics, here we focus our analysis on the numerical experiments described above.

It is important to mention that h, as observed by the lidar backscatter data, is very sensitive to the morning–noon transition (08:00–10:00 LT) and late afternoon–evening (after 16:00 LT) transition conditions. This is due to possible non-uniform backscatter profiles, which can contain multiple maximum gradients, impairing the ability of the automated method to retrieve h (see Supplement). Therefore, the accuracy of the observations of h is better under well-mixed conditions (from 10:00 to 16:00 LT in our case). During this period, only the model runs that take into account the subsidence and advective cooling (MXL+RSAD and MXL+RSA) capture the evolution (relatively steady) of the h sufficiently well after the morning transition (Fig. a, in connection with Table 1). This result implies a significant influence of the subsidence and, to a lesser extent, the effects of advective cooling on boundary-layer growth for the given case. Figure a also shows that the effect of the RSL on the evolution of h is insignificant (MXL+RSAD vs. MXL+MSAD).

The role of the large-scale advective cooling on the CBL dynamics was also recorded through the diurnal evolution of the potential temperature (Fig. b) at 29 m above the ground. The level of 29 m is considered to be representative of the mixed-layer values, since it is either located within the mixed layer or in the upper part of the surface layer, where deviations compared to mixed-layer values are small. Therefore, we employ it as the most representative of the mixed-layer characteristics. Between 10:00 and 12:00 LT, a non-local advective cooling process resulted in a slow-down in the increase of the potential temperature. We hypothesize that the rapid temperature drop before noon is related to the advection of cold air due to a sea-breeze front, which is frequently observed around noon at the CHATS site . We took this process into account in our numerical experiment (MXL+RSA) by imposing a constant advection of cold air between 10:00 and 17:00 LT (Table ). The strength of the advective cooling in the model was arbitrarily chosen to provide the best representation of the observed mixed-layer quantities (Table , Appendix ). As Fig. b shows, while taking only surface forcings, entrainment processes and subsidence into account does not suffice to represent this case (experiment MXL+RS), the potential temperature evolution is captured well if the advection is taken into account (experiment MXL+RSA) as well.

Similar behaviour of the diurnal evolution of the specific humidity at 29 m above the ground surface was observed (Fig. c). Here, the large-scale advective process is displayed by a significant jump in the magnitude of the specific humidity (from 7.9 g kg-1 to as much as 8.5 g kg-1) immediately after 10:00 LT. In the absence of observed specific-humidity profiles, we hypothesize that this increase in moisture content is due to an air mass transported by the sea-breeze front coming from the bay area (east and south-east). It is also possible that during the morning transition this sudden change is caused by the existence of a residual layer, which connects to a growing shallow layer . However, as mentioned before, since there are no data to explain the latter, but also because the main focus of this study is the effects of the RSL on the CBL dynamics, we limited our analysis to the numerical experiments described above. After this increase, q remains steady until the end of the day (17:00 LT). We related this behaviour of q after noon to the drying associated with the entrainment of free tropospheric (drier) air into the boundary layer, which can be driven by returned flow over the complex topography . Based on the observed q in the hours after 11:00 LT, the transport of dry air from the free troposphere is dominant, preventing a rise in the specific humidity, which results in a relatively constant value. The diurnal evolution of the specific humidity is well represented by the model run, which takes the subsidence, advection and drying from the free troposphere into account (MXL+RSAD). On the other hand, the model runs which do not take the drying (MXL+RSA) and the advection and drying (MXL+RS) into account overestimate the specific humidity after 11:00 LT.

The analysis presented in Fig.  shows that the complex boundary-layer structure at the CHATS site is highly dependent on the large-scale effects, including subsidence, advective cooling and moistening, as well as entrainment of dry air from the free troposphere.

The observed diurnal variability of the wind enables us to further verify the role of the large-scale forcing and the local canopy. Here, we compare the observed and modelled temporal evolution of the wind direction, individual wind speed components and absolute wind velocity (Fig. ). The model is well able to represent the observed temporal evolution of wind, except for the period between 10:00 and 11:00 PLT, when outliers are present in the observed wind components (Fig. c) and, consequently, the wind direction (Fig. a). These outliers are associated with sharp changes in the wind forcing (northerly winds present between 10:00 and 11:00 LT), a phenomenon observed daily before noon throughout the whole campaign (based on the observed time series) see also . Combining the individual wind components closely approximates the wind speed, which displays an almost constant acceleration during the day (Fig. b) and (after 11:00 LT) an almost constant friction velocity (see Fig. c).

The results of the case study of 27 May 2007 are corroborated by those of the case study of 31 May 2007 (not shown), showing similar patterns and structure of the CBL dynamics in both cases.

In summary, our modelling system is capable of reproducing the land–canopy–atmosphere characteristics of the case studies with satisfactory accuracy at a height well above the canopy. In the following section, we study the impact of the canopy on the boundary-layer state variables within the roughness sublayer near the canopy top.