Surface roughness parameters, namely the roughness length and displacement height, are an integral input used to model surface fluxes. However, most models assume these parameters to be a fixed property of plant functional type and disregard the governing structural heterogeneity and dynamics. In this study, we use large-eddy simulations to explore, in silico, the effects of canopy-structure characteristics on surface roughness parameters. We performed a virtual experiment to test the sensitivity of resolved surface roughness to four axes of canopy structure: (1) leaf area index, (2) the vertical profile of leaf density, (3) canopy height, and (4) canopy gap fraction. We found roughness parameters to be highly variable, but uncovered positive relationships between displacement height and maximum canopy height, aerodynamic canopy height and maximum canopy height and leaf area index, and eddy-penetration depth and gap fraction. We also found negative relationships between aerodynamic canopy height and gap fraction, as well as between eddy-penetration depth and maximum canopy height and leaf area index. We generalized our model results into a virtual “biometric” parameterization that relates roughness length and displacement height to canopy height, leaf area index, and gap fraction. Using a decade of wind and canopy-structure observations in a site in Michigan, we tested the effectiveness of our model-driven biometric parameterization approach in predicting the friction velocity over heterogeneous and disturbed canopies. We compared the accuracy of these predictions with the friction-velocity predictions obtained from the common simple approximation related to canopy height, the values calculated with large-eddy simulations of the explicit canopy structure as measured by airborne and ground-based lidar, two other parameterization approaches that utilize varying canopy-structure inputs, and the annual and decadal means of the surface roughness parameters at the site from meteorological observations. We found that the classical representation of constant roughness parameters (in space and time) as a fraction of canopy height performed relatively well. Nonetheless, of the approaches we tested, most of the empirical approaches that incorporate seasonal and interannual variation of roughness length and displacement height as a function of the dynamics of canopy structure produced more precise and less biased estimates for friction velocity than models with temporally invariable parameters.

Our ability to accurately predict mass and energy fluxes from the land
surface to the atmosphere at any timescale depends on the accuracy of the
surface drag parameterization (Finnigan, 2000; Mahrt, 2010). Over forested
environments, vertical mixing of canopy air with the free atmosphere above,
which is the process responsible for the exchange of energy, water vapor,
and CO

One common approach to incorporate canopy structure in the parameterization of roughness length into models in a more realistic way utilizes satellite imagery products to estimate vegetation structure and relate it to canopy–roughness relationships. For example, the SEBAL model (Moran, 1990) utilizes a function based on the normalized difference vegetation index (NDVI), while the METRIC model employs the Perrier function (Perrier, 1982). These canopy–roughness relationships have been shown to improve evapotranspiration estimates (Santos et al., 2012), but they are specific to sparse or short vegetative environments, such as agricultural systems, and are not typically recommended for forest environments (Bastiaanssen et al., 1998).

To incorporate the effects of canopy structure in denser and taller
vegetative environments such as forests, empirical functions have been
proposed using coarse canopy metrics such as canopy area index (the total,
single-sided area of all canopy elements within a 1 m

Roughness parameters have been shown to scale with structural
characteristics, such as the influence of area-index (vegetation area per
ground area) terms on

In this study, we use the Regional Atmospheric Modeling System (RAMS)-based Forest Large-Eddy Simulation (RAFLES; Bohrer et al., 2008, 2009) to conduct a virtual experiment to estimate the sensitivity of surface roughness parameters to specific characteristics of fine-scale canopy structure. RAFLES incorporates a prescribed 3-D domain that includes the vegetation leaf density and stem diameters and dynamically calculates the change to wind velocity as a function of leaf and stem surface drag in each voxel (Chatziefstratiou et al., 2014). The level of detail at which vegetation is represented in RAFLES makes it particularly suitable for conducting this series of virtual experiments that simulate the drag parameters over a simplistic set of virtual canopy structures that vary by structural component, including stand density and patch fraction, canopy height, leaf area index, and vertical profile of leaf density. The approach of prescribing drag in LESs to resolve site-level roughness was previously tested and shown to provide higher accuracy than the traditional roughness parameterization (Aumond et al., 2013). Finally, we use 10 years of direct observations of canopy-structure and roughness parameters (Maurer et al., 2013) to estimate the sensitivity of modeled friction velocity to temporal variation in canopy structure and its effects on roughness length. We compare these results with other approaches that may be used to represent canopy structure when modeling roughness parameters.

Monin–Obukhov similarity theory (MOST) describes the relationships between
the mean horizontal wind speed and the friction velocity in the inertial
sublayer (Monin and Obukhov, 1954). In brief, MOST describes this
relationship using a logarithmic function with parameters

Current understanding of aerodynamic properties near forest canopies within
the roughness sublayer (RSL) has led to empirical corrections to the MOST
model (Harman and Finnigan, 2007; De Ridder, 2010; Cellier and Brunet,
1992; Garratt, 1980; Mölder et al., 1999; Physick and Garratt,
1995; Raupach, 1992). These corrections allow us to utilize MOST with
meteorological observation within the RSL, which typically includes the
height range where eddy-covariance measurements of forest flux dynamics are
conducted across the globe. The RSL correction we used,

Contrary to the classic estimate of

We investigated the eddy-penetration depth (

The data used to test the effectivity of our LES-driven and other modeling
approaches originate from a mixed, deciduous forest site at the University
of Michigan Biological Station (UMBS) in northern, lower Michigan, USA
(45

We used wind fields and heat fluxes from RAFLES simulations results to calculate surface roughness parameters of simplified virtual forests. RAFLES (Bohrer et al., 2009) uses a 3-D heterogeneous canopy domain where leaf and stem areas are prescribed within each voxel. The leaf area density and the instantaneous wind speed within the voxel determine the drag force that is applied to wind flow through that grid cell within each time step. Common to the approach used in most LESs, it assumes the leaf area is composed of flat surfaces oriented downstream and neglects higher-order effects of leaf and stem shapes and sub-grid-scale wake generation (shown to be a small effect; Shaw and Patton, 2003). It is combined with radiation attenuation (given the leaf densities in the grid cells above) to determine the sensible and latent heat fluxes emitted from each grid cell. The model uses the finite volume approach for discretization of the simulation domain. It resolves the effects of volume restriction due to the volume of the vegetation (stems, branches) by reducing the aperture areas available for flux exchange between each pair of neighboring grid cells and by reducing the volume that is available for flow within each grid cell according to the volume of the vegetation present (Chatziefstratiou et al., 2014). It resolves sub-grid-scale turbulence using the Deardorff (1978) scheme, and includes a parameterization for sub-grid-scale turbulence dissipation due to leaf drag (Shaw and Patton, 2003).

Simulations consisted of 3 h of simulation time at a time step of 0.02 s. RAFLES uses a nested time-stepping scheme with higher frequency calculations for turbulence and even higher frequency calculations for pressure perturbations. Eight pressure and four turbulence time steps were nested in one model time step. Output data snapshots of all grid cells in the simulation domain were recorded every 2 s. The initial 2.5 h of simulation time were used as a “spin-up” period to ensure satisfactory turbulent mixing and semi-stability of the vertical profiles of turbulence and potential temperature. The latter half hour of simulation time was used for analysis, consisting of 300 2 s snapshots.

Synthetic virtual domains covered 1.25 km

Forest canopies are a complex array of 3-D structures. Many structural
characteristics, such as tree height, LAI, vertical leaf area density (LAD)
profile, and gap fraction, among others, affect the airflow inside and above
the canopy and, consequently, the resulting roughness parameters and
aerodynamic properties of the surface that describe such canopy structure.
Using synthetic cases representing different aspects of canopy structure, we
conducted a virtual experiment to test the sensitivity of roughness
parameters to four axes of canopy structure: (1) mean site-level LAI, ranging
from observed leaf-off conditions (LAI

Description of simulation cases used for sensitivity analysis of roughness parameters derived from an LES over variable canopy layouts, and the resulting roughness parameters for each simulation case. Canopy structure was varied along four axes – (a) LAI, (b) vertical LAD profile, (c) canopy height, and (d) gap fraction – and included an additional (e) realistic simulation case.

In the gap fraction cases, canopy gaps were randomly created across the
domain ranging from a single pixel (25 m

To calculate flux and wind statistics, we first calculated the mean value of
each model variable at each vertical model level over the entire horizontal
domain, and over all 300 time snapshots. We then rotated the horizontal wind
coordinates of each vertical level toward the downstream direction, such
that the resulting mean rotated downstream velocity is

We determined the effective aerodynamic canopy height,

We found that

Results of a three-way ANOVA to test any significance that maximum
canopy height (

We found positive

We found a negative

LES domain-averaged

LES domain-averaged aerodynamic canopy height (

Relationships were empirically determined using roughness parameters from each RAFLES simulation, except for those with “unnatural” vertical LAD profiles (i.e., the “upper”, “middle”, and “lower” LAD cases) as no patterns were observed between any roughness parameters and vertical LAD profile. Maximum canopy height was used instead of mean canopy height because maximum canopy height was more tightly correlated with each roughness parameter than mean canopy height. The resulting roughness parameters for each simulation are listed in Table 1.

We calculated a “biometric”

LES domain-averaged eddy-penetration depth (

The biometric approach, derived from our simulation results, provides
relationships between easily measurable characteristics of the canopy (i.e.,
LAI and maximum canopy height) and

“Classical” – fixed

“Explicit-LES” – fixed

“Yearly observed” – a purely empirical approach, using the values of

Numerous past studies have attempted to derive relationships between roughness parameters and other canopy-structure statistics. We chose two in this study:

Raupach (1994) calculated

and

where

Nakai et al. (2008a) calculated

and

where

The values of

Thirty-minute block-averaged friction velocity (

Modeled

The yearly observed method is dependent on long-term observations of wind,
temperature, heat flux, and friction velocity, which are rarely available in
forest sites. The other methods we tested do not require directly observed
roughness parameters. Of these methods, the “Raupach 94” approach had the
highest precision and lowest bias (slope

To date, despite a strong need by the modeling community, there is no single
consensus approach that relates roughness length and displacement height to
observable properties of canopy structure, such as LAI, height, leaf density,
and gap fraction. Furthermore, observations in our field site (Maurer et al.,
2013) and by others (Nakai et al., 2008a) have
shown that the roughness parameters in forests are not easily constrained by
leaf area or canopy height. Our underlying assumption in setting up this
model-based experiment was that the lack of a clear empirical relationship
between roughness parameters and canopy structure was due to the complexity
of canopy structure. We assumed that different characteristics of the canopy
drive different effects on roughness length and displacement height. In real
forests, many of the structural characteristics vary in time in different
ways, resulting in interacting and sometimes conflicting effects on
roughness length and displacement height. We set up a numerical experiment
that was designed to separate the effects of different observable
characteristics of canopy structure. We also hypothesized that, to some
degree, the difficulty in identifying a clear effect of canopy structure on
each of the roughness parameters is because roughness length and
displacement height values may trade off, such that similar solutions can be
fitted either with low

By testing the independent effects of different characteristics of canopy
structure through a set of controlled virtual experiments, we indeed found
that different roughness parameters where sensitive to different structural
characteristics. The aerodynamic canopy height (

We found positive

We found a linear relationship between

Vertical profiles of

We found no consistent correlations between roughness parameters and the mode of the vertical LAD profile, as the variability in roughness parameters over the range of LAD scenarios was extremely high (Table 1). Although the shape of the vertical profile of wind speed is apparently different between the “lower” and the “upper” LAD profiles (Fig. 7) there was no consistent canopy–wind or canopy–turbulence relationships that could be predicted by the bias of the vertical LAD curve (Fig. 7). LAD profiles may change in complex ways across the landscape and over many timescales (seasons, years, decades) due to disturbance or senescence. As our virtual experiment has shown, the effects of the vertical LAD profile are inconsistent with a simple representation of the vertical distribution of LAD using its vertical bias as a single descriptive characteristic. Our results indicate that site-level mean LAI and canopy height are easier to obtain and, in general, provide more reliable characteristics of canopy structure than the vertical profile of LAD.

Vertical profiles of

Our simulations did not detect a continuous increase to

The lack of canopy-structure effects on

Vertical cross section through the simulation results of

Vertical profiles of

Typically, surface roughness parameterization is used in models to directly
or indirectly predict the friction velocity, which is further used in the
surface flux calculations. To test the performance of different
parameterization approaches, we used data from 12 years of wind, friction
velocity, Obukhov length, and canopy-structure observations in a forest site
in Michigan. We compared six approaches that differ in whether (or not) they incorporate temporal variation into canopy structure, and in the
source of data they require to determine

The best performing approach for parameterization of roughness length and
displacement height was obtained using the annually observed values of
these parameters. The yearly observed model demonstrated

LESs with an explicit, prescribed canopy structure based on lidar observations of the canopy at a site can generate a surrogate virtual observations from which to evaluate the roughness parameters. However, these types of simulations are limited in their temporal domain (just a few hours as a representative of an entire decade). They are also dependent on high-resolution canopy lidar observations, which, to date, are not common. Parameterization approaches which rely on biometric observations, rather than on wind observations, may be the most reliable and broadly available method to estimate long-term roughness parameters. Our ability to estimate canopy-structure characteristics such as LAI, canopy height, and gap fraction over a broad range of spatial and temporal scales is continuously improving through the use of on-site biometric measurements as well as airborne and satellite remote sensing observations (Chen et al., 2002; Jonckheere et al., 2004; Zheng and Moskal, 2009).

As an indication for the potential of biometric approaches, the approach
suggested by Raupach (1994) performed even better than the combined yearly
observed approach (Table 3). However, this approach relies on stem census
observations. While such records are more common than flux sites, there is
still no broad global coverage for this type of observation. We tested two
biometric approaches that only required more commonly observable canopy
characteristics. LAI, canopy height, and gap fraction or stand density are
required by both the Nakai et al. (2008a) approach and the approach derived
by the virtual experiments in this study (the biometric approach) in order
to determine

The biometric method presented in this study is essentially a variant of the classical method, with the major difference being the use of a variable maximum canopy height as opposed to mean canopy height, and adding small perturbations to roughness length based on LAI and gap fraction (Eqs. 11–13). The limited success of this method can be attributed to some degree to the limited effect of interannual variability in canopy structure. However, a decade of observations in a site represents only a very narrow range of potential canopy structures. Our simulation results suggest that this method could potentially improve the prediction of friction velocity when applied to situations where canopy-structure variability is larger, such as after significant disturbance events.

In this study we used an LES, long-term meteorological observations, and
remote sensing of the canopy to explore the effects of canopy structure on
surface roughness parameters in a forest site. We performed a virtual
experiment to test the sensitivity of roughness parameters with respect to
four axes of variation in canopy structure: (1) leaf area index, (2) the
mode of the vertical profile of LAD, (3) canopy height, and (4) gap
fraction. We found consistent relationships between the aerodynamic canopy
height and LAI, maximum height, and gap fraction, as well as between

Nonetheless, most of the approaches we tested which used annually variable

We thank Peter Curtis and Christoph Vogel for running the AmeriFlux US-UMB and US-UMd sites, and for advice on conducting this study. We thank Ashley Matheny for editing the manuscript. We thank Brady Hardiman for the use of lidar data provided through an NSF-NCALM graduate seed award. This research was supported by the U.S. Department of Energy's Office of Science, Office of Biological and Environmental Research, Terrestrial Ecosystem Sciences program, under award nos. DE-SC0006708 and DE-SC0007041 and the AmeriFlux Management project under Flux Core Site agreement no. 7096915 through Lawrence Berkeley National Laboratory, with additional support from the National Science Foundation through grant DEB-0911461. K. D. Maurer was funded in part by an NSF IGERT fellowship (DGE-0504552) awarded through the UMBS Biosphere-Atmosphere Research Training (BART) program. W. T. Kenny was funded by the NASA Earth and Space Science Graduate Training Fellowship program (#NNX11AL45H). Simulations for this projects were run at the Ohio Supercomputer Center as part of resource allocation project PAS0409-4. Any opinions, findings, and conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Department of Energy. Edited by: P. Stoy