Land surface models used in climate models neglect the roughness sublayer and parameterize within-canopy turbulence in an ad hoc manner. We implemented a roughness sublayer turbulence parameterization in a multilayer canopy model (CLM-ml v0) to test if this theory provides a tractable parameterization extending from the ground through the canopy and the roughness sublayer. We compared the canopy model with the Community Land Model (CLM4.5) at seven forest, two grassland, and three cropland AmeriFlux sites over a range of canopy heights, leaf area indexes, and climates. CLM4.5 has pronounced biases during summer months at forest sites in midday latent heat flux, sensible heat flux, gross primary production, nighttime friction velocity, and the radiative temperature diurnal range. The new canopy model reduces these biases by introducing new physics. Advances in modeling stomatal conductance and canopy physiology beyond what is in CLM4.5 substantially improve model performance at the forest sites. The signature of the roughness sublayer is most evident in nighttime friction velocity and the diurnal cycle of radiative temperature, but is also seen in sensible heat flux. Within-canopy temperature profiles are markedly different compared with profiles obtained using Monin–Obukhov similarity theory, and the roughness sublayer produces cooler daytime and warmer nighttime temperatures. The herbaceous sites also show model improvements, but the improvements are related less systematically to the roughness sublayer parameterization in these canopies. The multilayer canopy with the roughness sublayer turbulence improves simulations compared with CLM4.5 while also advancing the theoretical basis for surface flux parameterizations.
Numerical grid used to represent a multilayer canopy. The volume of
air from the reference height (
Distinct parameterizations of land surface processes, separate from the atmospheric physics, were coupled to global climate models in the mid-1980s with the Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al., 1986) and the Simple Biosphere Model (SiB; Sellers et al., 1986). While carbon cycle feedbacks have since gained prominence in terms of model development and study of biotic feedbacks with climate change (Friedlingstein et al., 2006, 2014), the fundamental coupling between plants and the atmosphere in climate models still occurs with the fluxes of momentum, energy, and mass over the diurnal cycle as mediated by plant physiology, the microclimate of plant canopies, and boundary layer processes. The central paradigm of land surface models, as originally devised by Deardorff (1978) and carried forth with BATS, SiB, and subsequent models, has been to represent plant canopies as a homogeneous “big leaf” without vertical structure, though with separate fluxes for vegetation and soil. A critical advancement was to analytically integrate leaf physiological processes over profiles of light and nitrogen in the canopy (Sellers et al., 1996) and to extend the canopy to two big leaves to represent sunlit and shaded portions of the canopy (Wang and Leuning, 1998; Dai et al., 2004).
In land surface models such as the Community Land Model (CLM4.5; Oleson et
al., 2013), for example, fluxes of heat and moisture occur from the leaves to
the canopy air, from the ground to the canopy air, and from the canopy air to
the atmosphere (Fig. 1a). The flux from the canopy to the atmosphere is
parameterized using Monin–Obukhov similarity theory (MOST). This theory
requires the displacement height (
Harman and Finnigan (2007, 2008) proposed a formulation by which traditional
MOST can be modified to account for the RSL. Their theoretical derivations
couple the above-canopy turbulent fluxes with equations for the mass and
momentum balances within the canopy. They tested the theory with observations
for eucalyptus and pine forests, and observations above a walnut orchard
further support the theory (Shapkalijevski et al., 2016). Harman (2012)
examined the consequences of the RSL in a bulk surface flux parameterization
coupled to an atmospheric boundary layer model. Here, we implement and test
the theory in a multilayer canopy model (Bonan et al., 2014). The
development of a multilayer canopy for the ORCHIDEE land surface model has
renewed interest in the practical use of multilayer models (Ryder et al.,
2016; Chen et al., 2016). The earlier multilayer model development of Bonan
et al. (2014) focused on linking stomatal conductance and plant hydraulics
and neglected turbulent processes in the canopy. The current work extends the
model to include canopy-induced turbulence. The RSL theory avoids a priori
specification of
This study is motivated by the premise that land surface models generally neglect canopy-induced turbulence, that inclusion of this is critical to model simulations, and that the Harman and Finnigan (2007, 2008) RSL theory provides a tractable parameterization extending from the ground through the canopy and the RSL. We show that the resulting within-canopy profiles of temperature, humidity, and wind speed are a crucial aspect of the leaf-to-canopy flux scaling. The previous model development of Bonan et al. (2014) included improvements to stomatal conductance and canopy physiology compared with CLM4.5. We contrast those developments with the RSL parameterization described herein and compare tall forest with short herbaceous vegetation to ascertain which aspects of the multilayer canopy most improve the model.
The canopy model has three main components: leaf gas exchange and plant hydraulics; a numerical solution for scalar profiles within and above the canopy; and inclusion of the RSL parameterization. It builds upon the work of Bonan et al. (2014), which describes leaf gas exchange and plant hydraulics for a multilayer canopy with sunlit and shaded leaves at each layer in the canopy. The calculation of leaf temperature and fluxes is solved simultaneously with stomatal conductance, photosynthesis, and leaf water potential in an iterative calculation. This method numerically optimizes water-use efficiency within the constraints imposed by plant water uptake to prevent leaf desiccation using the methodology of Williams et al. (1996). Radiative transfer of visible, near-infrared, and longwave radiation is calculated at each level and accounts for forward and backward scattering within the canopy. Bonan et al. (2014) used the radiative transfer model of Norman (1979). We retain that parameterization for longwave radiation, but radiative transfer in the visible and near-infrared wavebands is calculated from the two-stream approximation with the absorbed solar radiation partitioned into direct beam, scattered direct beam, and diffuse radiation for sunlit and shaded leaves in relation to cumulative plant area index as in Dai et al. (2004). This allows better comparison with CLM4.5, which uses the canopy-integrated two-stream solution for sunlit and shaded leaves. Soil fluxes are calculated using the layer of canopy air immediately above the ground. Temperature, humidity, and wind speed in the canopy are calculated using a bulk canopy airspace. Bonan et al. (2014) provide further details.
Here, we describe the formulation of the scalar profiles and the RSL, which
were not included in Bonan et al. (2014) and which replace the bulk canopy
airspace parameterization. Figure 1 shows the numerical grid. The
implementation is conceptually similar to the multilayer canopy in
ORCHIDEE-CAN and that model's implicit numerical coupling of leaf fluxes and
scalar profiles (Ryder et al., 2016; Chen et al., 2016). That numerical
scheme is modified here to include sunlit and shaded leaves at each layer in
the canopy and also the RSL (Harman and Finnigan, 2007, 2008). Whereas
ORCHIDEE-CAN uses an implicit calculation of longwave radiative transfer for
the leaf energy balance, we retain the Norman (1979) radiative transfer used
by Bonan et al. (2014). The grid spacing (
In the volume of air extending from the ground to some reference height above
the canopy, the scalar conservation equations for heat and water vapor, the
energy balances of the sunlit and shaded canopy, and the ground energy
balance provide a system of equations that can be solved for air temperature,
water vapor concentration, sunlit and shaded leaf temperatures, and ground
temperature. The scalar conservation equation for heat relates the change
over some time interval of air temperature (
The source–sink fluxes of sensible heat and water vapor are described by the
energy balance equation and are provided separately for sunlit and shaded
fractions of the canopy layer. The energy balance of sunlit leaves at height
These equations are discretized in space and time and are solved in an
implicit system of equations for time
The sunlit and shaded temperatures required for Eqs. (
At the lowest layer above the ground (
The numerical solution involves rewriting Eqs. (
The equation set has several dependencies that preclude a fully implicit
solution for
The solution to the scalar fluxes and profiles described in the preceding
section requires the aerodynamic conductance (
Neglecting the RSL, the wind speed profile is described by MOST as
With the assumption of a constant mixing length (
The aerodynamic conductance for scalars at level
Flow diagram for calculating the Obukhov length (
Harman and Finnigan (2007, 2008) provide a complete description of the RSL
equations and their derivation. Appendix A2 gives the necessary equations as
implemented herein. Use of the RSL parameterization requires specification of
the Monin–Obukhov functions
Profiles of leaf area density. Shown are three different canopy
profiles for: (i) grass and crop with
Land surface models commonly combine leaf and stem area into a single plant
area index to calculate radiative transfer, and CLM4.5 does the same. By
using plant area index, big-leaf canopy models assume that woody
phytoelements (branches, stems) are randomly interspersed among leaves. Some
studies of forest canopies suggest that branches and stems are shaded by
foliage and therefore contribute much less to obscuring the sky than if they
were randomly dispersed among foliage (Norman and Jarvis, 1974; Kucharik et
al., 1998). To allow for shading, we represent plant area density as
separate profiles of leaf and stem area. The beta distribution probability
density function provides a continuous profile of leaf area density for use
with multilayer canopy models, and we use a uniform profile for stem area,
whereby
CLM4.5 requires specific leaf area as an input parameter, and we use this
to calculate leaf heat capacity (per unit leaf area). Specific leaf area, as
used in CLM4.5, is the area of a leaf per unit mass of carbon
(m
Leaf heat capacity.
Site information for the four deciduous broadleaf forest (DBF),
three
evergreen needleleaf forest (ENF), two grassland (GRA), and three cropland (CRO)
flux towers, including mean temperature (
We evaluated the canopy model at 12 AmeriFlux sites comprising 81 site years
of data using the same protocol of the earlier model development (Bonan et
al., 2014). We used the six forests sites previously described in Bonan et
al. (2014) and included additional flux data for one forest (US-Dk2), two
grassland (US-Dk1, US-Var), and three cropland sites (US-ARM, US-Bo1, US-Ne3) to
test the canopy model over a range of tall and short canopies, dense and
sparse leaf area index, and different climates (Table 2). Tower forcing data
(downwelling solar and longwave radiation, air temperature, relative
humidity, wind speed, surface pressure, precipitation, and tower height) were
from the North American Carbon Program (NACP) site synthesis (Schaefer et
al., 2012) as described previously (Bonan et al., 2014), except as noted
below for the three Duke tower sites. The model was evaluated using tower
observations of net radiation, sensible heat flux, latent heat flux, and
friction velocity obtained from the AmeriFlux Level 2 dataset
(
Ryu et al. (2008) describe the US-Var grassland located in California.
CLM has been previously tested using flux data from the US-Ne3 and US-Bo1
cropland sites (Levis et al., 2012), and we used the same sites here. The
US-Ne3 tower site is a rainfed maize (
Major differences between CLM4.5 and ML
Summary of simulation changes to the turbulence parameterization and leaf biophysics.
Average Taylor skill score for the ML
Stoy et al. (2006) provide site information for the US-Dk2 deciduous broadleaf forest tower site located in the Duke Forest, North Carolina, which was included here to contrast the adjacent evergreen needleleaf forest and grassland sites. The US-Dk1 tower site in the Duke Forest provides an additional test for grassland (Novick et al., 2004; Stoy et al., 2006). Tower forcing and flux data for 2004–2008 were as in Burakowski et al. (2018).
We performed several model simulations to compare CLM4.5 with the RSL
enabled multilayer canopy. CLM4.5 and the multilayer canopy differ in
several ways (Table 3). To facilitate comparison and to isolate specific
model differences, we devised a series of simulations to incrementally test
parameterization changes (Table 4). The simulations discussed herein are as
follows.
CLM4.5 – Simulations with CLM4.5 using tower meteorology and site
data for leaf area index, stem area index, and canopy height. m0 – This uses the multilayer canopy, but configured to be similar to
CLM4.5 for leaf biophysics as described in Table 3. Stomatal conductance is
calculated as in CLM4.5. Leaf nitrogen declines exponentially with
greater cumulative plant area index from the canopy top with the decay
coefficient m1 – As in m0, but introducing a turbulence closure in the absence of the
RSL. Equations ( b1 – As in m1, but with stomatal conductance calculated using water-use
efficiency and plant hydraulics as in Bonan et al. (2014). b2 – As in b1, but with b3 – As in b2, but with plant area density calculated from Eq. ( b4 – As in b3, but with leaf heat capacity from Eq. ( r1 – As in b4, but with the RSL parameterization used to calculate r2 – As in r1, but
The multilayer canopy model has several changes to leaf biophysics compared
with CLM4.5. These differences are individually examined in the
simulations.
The final two simulations examine the RSL.
Simulations for US-UMB (July 2006). Shown are the average diurnal
cycle (GMT) of sensible heat flux, latent heat flux, friction velocity,
radiative temperature, and gross primary production (GPP) for the
observations (blue) and models (red). The shading denotes
Taylor diagram of net radiation, sensible heat flux, latent heat
flux, friction velocity, radiative temperature, and gross primary production
(GPP) for US-UMB. Data points are for the years 1999–2006 for CLM4.5 (blue)
and ML
Simulations were evaluated in terms of net radiation, sensible heat flux,
latent heat flux, gross primary production, friction velocity, and radiative
temperature. Radiative temperature for both the observations and simulations
was evaluated from the upward longwave flux using an emissivity of 1. The
simulations were assessed in terms of root mean square error (RMSE) for each
of the 81 site years. We additionally assessed model performance using
Taylor diagrams and the corresponding skill score (Taylor, 2001) as in Bonan
et al. (2014). Taylor diagrams quantify the degree of similarity between the
observed and simulated time series of a particular variable in terms of the
correlation coefficient (
Sensible heat flux in relation to the temperature difference
Root mean square error (RMSE) for latent heat flux for the eight simulations m0–r2. RMSE for each simulation is given as a percentage of the RMSE for CLM4.5 and averaged across all years at each of the seven forest sites. A negative value shows a reduction in RMSE relative to CLM4.5 and indicates model improvement. Changes in RMSE between simulations show the effect of sequentially including new model parameterizations as described in Table 4.
As in Fig. 7, but for sensible heat flux.
As in Fig. 7, but for friction velocity.
As in Fig. 7, but for radiative temperature.
Profiles of leaf temperature for US-UMB averaged for the month of
July 2006 at 14:00 local time
Profiles of wind
speed and air temperature for US-UMB (July 2006) at 14:00 local
time
The ML
Simulations for US-UMB illustrate these improvements for the forest sites,
where the influence of the RSL is greatest. For July 2006, CLM4.5
overestimates midday
Figure 6 shows the relationship between
Comparisons of ML-RSL and ML
Comparison of the suite of simulations (m0 to r2; Table 4) for forest sites
highlights the effect of specific parameterization changes on model
performance. The m0 simulation without a turbulence closure has a high RMSE
compared with CLM4.5 for
Leaf temperature profiles are consistent with the changes in
Wind speed and temperature profiles simulated with the RSL parameterization
are noticeably different compared with MOST profiles, as shown in Fig. 12 for
US-UMB. At midday, wind speed in the upper canopy is markedly lower than for
MOST, but whereas wind speed goes to zero with MOST, the RSL wind speed
remains finite. Midday MOST air temperature in the canopy increases
monotonically to a maximum of 28.5
The multilayer canopy with the RSL (ML
Additional improvement in
The influence of the RSL is evident in the improved relationship between
The influence of the RSL is also evident in nighttime
Another outcome of the RSL is seen in
The simulation of wind and temperature profiles is a key outcome of the
multilayer canopy and RSL. During the day, CLM4.5 simulates a warmer
canopy air space than those for ML
Various ad hoc changes have been introduced into the next version of the
Community Land Model (CLM5) to correct the deficiencies in
The canopy model encapsulates conservation equations for
The Harman and Finnigan (2007, 2008) RSL parameterization provides the necessary aerodynamic conductances and wind speed. It produces a comparable representation of surface–atmosphere exchange of heat, water, and carbon, including within-canopy exchange, to those based on Lagrangian dynamics (e.g., McNaughton and van den Hurk, 1995) and localized near-field theory (e.g., Raupach, 1989; Raupach et al., 1997; Siqueira et al., 2003; Ryder et al., 2016; Chen et al., 2016). Lagrangian representations have the advantage in that they retain closer fidelity to the underlying dynamics governing exchange. In contrast, however, the RSL formulation provides linked representations for both momentum and (passive) scalar exchange. This coupling, impossible with Lagrangian formulations as there is no locally conserved equivalent quantity to scalar concentration for momentum, reduces the degrees of freedom involved. The RSL's linked formulation also facilitates the propagation of knowledge about the transport of one quantity onto the transport of all other quantities considered. Unlike Lagrangian formulations, the RSL formulation also naturally asymptotes towards the standard surface layer representations as required, e.g., with increasing height above ground or for short canopies.
Furthermore, the components of the RSL formulation are far easier to observe
than those in the Lagrangian representations. In particular, the vertical
profile of the Lagrangian timescale (
The Harman and Finnigan (2007, 2008) RSL parameterization eliminates a priori
specification of roughness length and displacement height, but introduces
other parameters. Critical parameters are the drag coefficient of canopy
elements in each layer (
The plant canopies simulated in this study are dense canopies in the sense
that most of the momentum is absorbed by plant elements. Appendix A4 provides
a modification for sparse canopies (e.g., plant area index
The RSL parameterization has limits to its applicability;
For over 30 years, land surface models have parameterized surface fluxes
using a dual-source canopy in which vegetation is treated as a big leaf
without vertical structure and in which MOST is used to parameterize
turbulent fluxes above the canopy. The RSL parameterization of Harman and
Finnigan (2007, 2008) provides a means to represent turbulent processes in a
multilayer model extending from the ground through the canopy and the RSL
with sound theoretical underpinnings of canopy-induced turbulence and with
few additional parameters. The multilayer canopy improves model performance
compared to CLM4.5 in terms of latent and sensible heat fluxes, friction
velocity, and radiative temperature. Improvement in latent and sensible heat
fluxes comes primarily from advances in modeling stomatal conductance and
canopy physiology beyond what is in CLM4.5. These advances also improve
friction velocity and radiative temperature, with additional improvement from
the RSL parameterization. The multilayer model combines improvements in both
leaf biophysics and canopy-induced turbulence and both contribute to the
overall model improvement. Indeed, the modeling of canopy turbulence and
canopy physiology are inextricably linked (Finnigan and Raupach, 1987), and
the 30
Multilayer canopies are becoming practical for land surface models, seen in the ORCHIDEE-CAN model (Ryder et al., 2016; Chen et al., 2016) and in this study. A multilayer canopy facilitates the treatment of plant hydraulic control of stomatal conductance (Williams et al., 1996; Bonan et al., 2014), provides new ways to test models directly with leaf-level measurements in the canopy, and is similar to the canopy representations used in canopy-chemistry models (Stroud et al., 2005; Forkel et al., 2006; Wolfe and Thornton, 2011; Ashworth et al., 2015). Here, we provide a tractable means to simulate the necessary profiles of wind speed, temperature, and water vapor while also accounting for the RSL. While this is an advancement over CLM4.5, much work remains to fully develop this class of model and to implement the multilayer canopy parameterization in CLM. Significant questions remain about how well multilayer models capture the profiles of air temperature, water vapor, and leaf temperature in the canopy, how important these profiles are for vegetation source–sink fluxes, and how many canopy layers are needed to adequately represent gradients in the canopy. The testing of ORCHIDEE-CAN (Chen et al., 2016) has begun to address these questions, but high-quality measurements in canopies are required to better distinguish among turbulence parameterizations (e.g., Patton et al., 2011). The canopy model described here represents a necessary approach to rigorously and comprehensively evaluate process parameterizations for consistency with observations and theory prior to implementation in a full land surface model, where confounding errors are likely to affect the results. Moreover, multilayer canopies raise a fundamental question about the interface between the atmosphere and land surface. The coupling of the Community Land Model with the atmosphere depicts the land as a bulk source–sink for heat, moisture, and momentum, and these fluxes are boundary conditions to the atmosphere model. Multilayer canopy models simulate a volume of air extending from some level in the atmosphere to the ground. A critical question that remains unresolved is where does the parameterization of the atmospheric boundary layer stop and the land surface model begin.
The multilayer canopy runs independent of CLM4.5 but
utilizes common code (e.g., soil temperature). The canopy flux code is
available at
Equation (
The flux–gradient relationships used with Monin–Obukhov similarity theory
are
The RSL parameterization modifies Monin–Obukhov similarity theory by
introducing an additional dimensionless parameter
The functions
An expression for
The Schmidt number (
The Obukhov length is
The RSL theory of Harman and Finnigan (2007, 2008) was developed for dense
canopies. Sparse canopies can be represented by adjusting
EP, IH, and JF developed the RSL code. GB developed the numerical solution for scalar profiles in the canopy. GB and EP implemented the code in the multilayer canopy. GB and EP designed the model simulations. KO performed the CLM4.5 simulations. YL provided the US-ARM data, and EB processed the US-Dk1, US-Dk2, and US-Dk3 data. GB wrote the paper with contributions from all co-authors.
The authors declare that they have no conflict of interest.
The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work was supported by the National Science Foundation Science and Technology Center for Multi-Scale Modeling of Atmospheric Processes, managed by Colorado State University under cooperative agreement no. ATM-0425247. Edited by: Chiel van Heerwaarden Reviewed by: Metodija Shapkalijevski and one anonymous referee