Boundary-Layer MeteorolDOI 10.1007/s10546-013-9823-0

ARTICLE

Large-Eddy Atmosphere–Land-Surface Modelling overHeterogeneous Surfaces: Model Development andComparison with Measurements

Yaping Shao · Shaofeng Liu · Jan H. Schween ·Susanne Crewell

Received: 10 May 2012 / Accepted: 26 March 2013© Springer Science+Business Media Dordrecht 2013

Abstract A model is developed for the large-eddy simulation (LES) of heterogeneousatmosphere and land-surface processes. This couples a LES model with a land-surfacescheme. New developments are made to the land-surface scheme to ensure the adequaterepresentation of atmosphere–land-surface transfers on the large-eddy scale. These include,(1) a multi-layer canopy scheme; (2) a method for flux estimates consistent with the large-eddysubgrid closure; and (3) an appropriate soil-layer configuration. The model is then appliedto a heterogeneous region with 60-m horizontal resolution and the results are compared withground-based and airborne measurements. The simulated sensible and latent heat fluxes arefound to agree well with the eddy-correlation measurements. Good agreement is also foundin the modelled and observed net radiation, ground heat flux, soil temperature and moisture.Based on the model results, we study the patterns of the sensible and latent heat fluxes, howsuch patterns come into existence, and how large eddies propagate and destroy land-surfacesignals in the atmosphere. Near the surface, the flux and land-use patterns are found to beclosely correlated. In the lower boundary layer, small eddies bearing land-surface signalsorganize and develop into larger eddies, which carry the signals to considerably higher lev-els. As a result, the instantaneous flux patterns appear to be unrelated to the land-use patterns,but on average, the correlation between them is significant and persistent up to about 650 m.For a given land-surface type, the scatter of the fluxes amounts to several hundred W m−2,due to (1) large-eddy randomness; (2) rapid large-eddy and surface feedback; and (3) localadvection related to surface heterogeneity.

Keywords Atmosphere–land interaction · Heterogeneous surfaces · Large-eddy simulation

Y. Shao (B) · S. Liu · J. H. Schween · S. CrewellInstitute for Geophysics and Meteorology, University of Cologne, Cologne, Germanye-mail: yshao@uni-koeln.de

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1 Introduction

In atmospheric numerical models, land-surface processes are commonly represented usingland-surface schemes. The first generation schemes were designed to estimate surface sensibleand latent heat fluxes in climate models (Manabe 1969). In the second generation schemes, thediurnal variations of the fluxes were considered by taking the force-restore approach to soil-temperature and moisture modelling (Bhumralker 1975; Deardorff 1978). More sophisticatedschemes (e.g. Dickinson et al. 1993) were developed in the 1980s and 1990s, with improvedtreatments for plant canopy and surface soil hydrology. The third generation schemes alsoinclude the components for plant physiology and photosynthesis, which enable the estimationof CO2 and other trace-gas fluxes (e.g. Oleson et al. 2007).

A basic assumption made in existing land-surface schemes is that land-surface processesare horizontally homogeneous and the transfers of the physical quantities are one-dimensional. Thus, the existing framework for land-surface parametrization appears to befundamentally inadequate for heterogeneous land surfaces. For example, the bulk transfermethod based on the Monin–Obukhov similarity theory (MOST) (Monin and Obukhov 1954)assumes that the atmospheric surface layer is in equilibrium with the surface and its evolutionis free from the effects of advection. Foken (2006) pointed out that the transfer mechanisms inthe heterogeneous atmospheric boundary layer can significantly deviate from MOST. Shaoet al. (2001) and Heinemann and Kerschgens (2005) have demonstrated that land-surfaceheterogeneity impacts strongly on the atmosphere and land-surface exchanges.

The parametrization of heterogeneous land-surface processes has been active since thelate 1990s (e.g. Giorgi and Avissar 1997). Progress has been made in dealing with spa-tially distributed land-surface properties, by using the techniques of mosaic (e.g. Ament andSimmer 2006) and parameter hierarchy (e.g. Oleson et al. 2007). It is now understood thatland-surface heterogeneity has two major effects on surface fluxes, known as the aggregationeffect and the dynamic effect. The aggregation effect occurs because the spatial variationsof the land-surface properties (albedo, hydraulic properties, etc.) result in spatial variationsof the land-surface state variables (soil moisture, soil temperature, etc.), and because thetransfer processes are non-linear, the aggregation of surface parameters does not necessarilyproduce the correct aggregation of fluxes. The techniques of mosaic and parameter hierarchyare commonly used to account for the aggregation effect. The dynamic effect occurs becausecontrasts in surface conditions generate turbulence and horizontal advection that leads tospatial variations in turbulent transfer. To date, no theoretical framework exists, equivalentto MOST, which effectively represents the dynamic effect.

Three-dimensional atmospheric and land-surface data are required to better understandand parametrize heterogeneous atmosphere–land-surface systems. Such data are difficult toobtain from field or laboratory measurements, but synthetic data can be generated using large-eddy simulation (LES) and land-surface coupled models. The emphasis on large eddies isimportant because they are the main contributors to the transfer processes in the atmosphericboundary layer, and their developments are closely related to the distribution of land-surfaceproperties. LES models have been under development since the 1960s (Smagorinsky 1963;Deardorff 1970; Moeng 1984), and are now widely used for atmospheric turbulent flowsimulations (Sullivan et al. 1998; Beare et al. 2004; Kleissl et al. 2006; Kumar et al. 2006).Earlier LES models were not coupled with land-surface schemes, and the simulations mostlyhad pre-specified land-surface forcing (e.g. Hechtel et al. 1990; Avissar and Schmidt 1998;Albertson et al. 2001; Raasch and Harbusch 2001; Letzel and Raasch 2003; Huang et al.2008; Maronga and Raasch 2013) with emphasis placed on the responses of the atmosphericboundary layer to the forcing. More recently, LES atmosphere–land-surface coupled models

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have been under development and have been applied to the simulation of boundary-layer flowsover synthetic (e.g. Patton et al. 2005; Huang and Margulis 2009) and natural heterogeneousland surfaces (e.g. Huang and Margulis 2010; Brunsell et al. 2011). However, the land-surfacemodels used are not adequately adapted to the large-eddy scale and the model results are notyet thoroughly validated against measurements.

In this study, a large-eddy simulation atmosphere–land-surface model, LES-ALM, isdeveloped, which couples a LES model with a new land-surface model adapted to the LESrequirements. In the new model, as detailed in Sect. 2, a multi-layer canopy scheme isemployed and the surface-flux computation is consistently formulated with the subgrid tur-bulence closure scheme and no longer requires MOST. The soil-layer configuration usedherein differs from that used in earlier studies because, as later shown, very thin soil lay-ers need to be used to capture the rapid exchanges between the land surface and the largeeddies. LES-ALM is then applied to a heterogeneous area and its performance tested againstobservations. The comparison confirms that LES-ALM is an adequate and powerful tool forstudying heterogeneous atmosphere–land-surface systems. Using the model simulations, weexamine the relation of large eddies to surface heterogeneity and the persistency of surfaceheterogeneity in the atmosphere. The emphasis is placed on the development and validationof the large-eddy model.

2 Large-Eddy Simulation Atmosphere–Land-Surface Model

2.1 Large-Eddy Simulation Model and Radiation Scheme

The LES-ALM model integrates a LES model with a radiation scheme and a land-surfacescheme. The LES model is the Weather Research and Forecast (WRF) model in its large-eddy mode, but improved by the inclusion of a vegetation canopy scheme. The flow isassumed to be compressible and non-hydrostatic. The model separates the turbulent flowinto a grid-resolved component and a subgrid component. Several subgrid closures can beselected (e.g. Smagorinsky 1963), but the k–l closure (Deardorff 1980) is used here. A subgridscaling velocity u∗s = Ck

√e/κ is defined, with e being the subgrid turbulent kinetic energy

(TKE) determined by solving the TKE equation (Skamarock et al. 2008), Ck is an empiricalparameter of about 0.15, and κ is the von Karman constant. The subgrid eddy viscosity canbe expressed as:

Km,sg = κu∗sl, (1a)

where l is a mixing length that differs for horizontal and vertical directions. Equation 1a isidentical to

Km,sg = Ckl√

e. (1b)

Suppose the horizontal and vertical grid resolutions are �x and �z, respectively. Then, weset lx = �x and lz = �z. The subgrid eddy diffusivity for a scalar (e.g. heat), Kh,sg, can beexpressed as

Kh,sg = Km,sg P−1r (2)

with Pr being the Prandtl number of about 0.3. For radiation estimates, the RRTMG schemeimplemented in the WRF model is adapted. This is a corrected k-distribution model for bothshortwave and longwave broadband radiation transfers (Mlawer et al. 1997). More detailscan be found in Clough et al. (2005) and Iacono et al. (2008).

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2.2 Large-Eddy Land-Surface Scheme

Numerous land-surface schemes have been proposed for numerical weather prediction andclimate models (e.g. Dickinson et al. 1993; Irannejad and Shao 1998; Ek et al. 2003; Olesonet al. 2007), but substantial modifications are necessary to suit the purpose of large-eddymodelling. In this study, a new land-surface scheme is proposed, which is based on the Noahcommunity land-surface model (Chen and Dudhia 2001), but with three new key featuresthat will be described below.

2.2.1 Explicit Multi-Layer Canopy Scheme

Due to the high resolution used for LES (�x ∼ 10 m, �z ∼ 1 m), a vertically resolvedcanopy layer is necessary (Fig. 1). The effects of vegetation on the flow are treated as sinks(sources) in the conservation equations for momentum, heat and moisture. The treatment ofvegetation as a momentum sink is not new (e.g. Shaw and Schumann 1992), but heat andmoisture sources in the context of land-surface modelling are critical for coupling a large-eddy flow model with a land-surface scheme. The drag induced by vegetation on the flow isexplicitly treated as a momentum sink in the equations of motion,

∂ ui

∂t+ ∂ ui u j

∂x j= −δi3g + εi j3 f u j − 1

ρ

∂ p

∂xi− ∂τi j

∂x j+ ν

∂2ui

∂x2j

+ SMi , (3)

where ui is the gird-resolved flow velocity, g is the acceleration due to gravity, f is theCoriolis parameter, ρ is the air density, p is pressure, τi j is the subgrid stress, ν is thekinematic viscosity, δi3 is the Kronecker operator and εi j3 is the alternating operator. SMi isthe canopy drag in the xi direction, given by

SMi = −αf CdV ui , (4)

where Cd is a dimensionless drag coefficient of 0.15 (Shaw et al. 1988), and depends oncanopy porosity and sheltering effects (Raupach 1992; Shao and Yang 2008; but not consid-ered in this study), V is the local wind speed, and αf is the vegetation frontal area density(frontal area per unit air volume, m2 m−3). For a given location (x, y), the vegetation frontalarea index (FAI, vegetation frontal area per unit land surface, m2m−2) can be estimated fromthe leaf area index (LAI) for given plant configuration (e.g. FAI = LAI for plants of sphericalshape). For a given vegetation type, a shape function (Fig. 1) for the vertical distribution ofthe frontal area, fv(z) (m−1) is specified, and αf can be estimated as

αf (x, y, z) = F AI (x, y) fv(z), (5)

with fv satisfying

∞∫

0

fv(z)dz = 1. (6)

Likewise, vegetation also acts as sources (sinks) for heat, moisture and carbon dioxide. Thesesources and sinks can be treated similarly as for momentum. The source term in the equationfor air temperature can be expressed as

ST = −αtCTV (T − Tc), (7)

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where αt is the leaf area density (total leaf area per unit volume, m2m−3), CT is a dimen-sionless exchange coefficient analogous to Cd, T is the air temperature in the canopy andTc is the canopy temperature. The source term in the equation for specific humidity can beexpressed as

Sq = −(1 − fwet)αqCq V [q − qs(Tc)] − fwetαqCdV [q − qs(Tc)] , (8)

where fwet is the fraction of wet vegetation, q is the specific humidity, αq = αt/2 and qs(Tc)

is the saturation specific humidity at canopy temperature, Tc. Taking the vegetation stomatalresistance into account, Cq can be expressed as

Cq = Cd

CdV rb + 1, (9)

where the bulk vegetation resistance is given by

rb = rst

αql, (10)

where l is a unit length. Many schemes for rst exist, and we follow the method describedin Noilhan and Planton (1989), which relates rst to several environmental control factors,including the root zone soil moisture.

As Eqs. 7 and 8 show, a scheme for canopy temperature, Tc, is necessary. Such a schemeinvolves the transfer of (shortwave and longwave) radiation, which in detail depends on theabsorbance, reflectance, distribution and orientation of the leaves, solar view angle, etc. Inthis study, a simple canopy temperature model is used, with which Tc can be estimated bysolving the following diagnostic equation,

αtεσT 4c = λs(Rs↓ + Rs↑)+ λl(Rl↓ + Rl↑)− ρcpST − ρL Sq , (11)

where ε is vegetation emissivity, σ is the Stefan–Boltzmann constant, λs and λl are theextinction coefficients for shortwave and longwave radiation, Rs↓ and Rs↑ are the downwardand upward shortwave fluxes, while Rl↓ and Rl↑ are the downward and upward longwavefluxes, respectively; ρ is air density, cp is the air specific heat capacity at constant pressureand L is the latent heat of vaporization. Details of the canopy temperature scheme, becauseof its complexity, will be fully described in a separate paper, but an outline is given in theAppendix.

2.2.2 Flux Formulation

The atmospheric surface layer is commonly divided into an inertial layer and a roughnesssublayer. In conventional land-surface models, fluxes are computed for the inertial layer usingthe bulk transfer method that can be formulated as follows.

Suppose the surface layer is homogeneous and stationary. Then, the profiles of meanwind, u, potential temperature, θ , and specific humidity, q, are almost logarithmic and themomentum flux, τ , sensible heat flux, H , and latent heat flux, LE, are constant in the vertical.The flux-gradient relationship for H (and similarly for L E) is expressed as

H = −ρcp Kh∂ T

∂z. (12)

The eddy diffusivity, Kh, is derived from MOST as

Kh = κu∗z

ϕh, (13)

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Fig. 1 LES model configuration. The vegetation canopy is vertically resolved in multiple layers, and thin soillayers are used to allow the land surface to respond on the large-eddy time scale

with ϕh being the MOST stability function and u∗ is the friction velocity. Using the bulkformulation, we have

H = −ρcp(Ta − T0)

rh, (14)

where rh is the aerodynamic resistance,

rh =z∫

z0

K −1h dz (15)

and Ta and T0 respectively are the reference-level air temperature and surface temperature.Using MOST, we find

rh = 1

κu∗

[ln

(z

z0h

)− ψh

(z

Lo

)], (16)

where Lo is the Obukhov length,ψh = ∫ zz0h(1 − ϕh)d ln z, and z0h is the roughness length for

heat. Although this type of flux formulation has been used in recent large-eddy atmosphereand land-surface coupled simulations, its applicability must be questioned for the followingreasons:

(1) The derivation of MOST assumes horizontal homogeneity with the effect of advectionbeing negligible. These assumptions do not hold on the scale of atmospheric large eddies.

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(2) The MOST similarity functions are empirically derived using averaged (e.g. over 15–30 min or over several km) boundary-layer measurements. We are not aware of MOSTsimilarity functions derived from large-eddy scale measurements.

(3) In the framework of a LES model, the MOST-based diffusivity and viscosity estimatesnear the surface are inconsistent with the model closure-based diffusivity and viscosityestimates, causing contradictions between model closure and boundary condition.

(4) Even if MOST were applicable, the similarity parameters could not be specified withconfidence (e.g. roughness length), especially in areas of land-surface heterogeneity,causing large uncertainties in flux estimates.

In contrast, in a LES model, the main fractions of the fluxes are computed by resolvingthe energy-containing eddies, and only the inertial sub-range parts of the fluxes need to beparametrized. We express a flux (e.g. H and L E) as the sum of a grid-resolved flux (Hg andL Eg) and a subgrid flux (Hsg and L Esg)

H = Hg + Hsg, (17a)

L E = L Eg + L Esg, (17b)

where Hg and L Eg are computed from the grid-resolved vertical velocity, w, air temperature,T , etc., namely,

Hg = ρcpwT , (17c)

L Eg = ρLwq. (17d)

H and L E calculated using Eqs. 17a, b are then included in the surface energy and waterbalance equations, i.e.

Rn − (Hg + Hsg)− (L Eg + L Esg)− G = 0, (17e)

P − (Eg + Esg)− I − Ro = 0, (17f)

where Rn is net radiation, G is ground heat flux, P is precipitation, I is infiltration andRo is surface runoff. Equation 17a–f represents an essential difference between large-eddyatmosphere–land-surface modelling and the conventional land-surface modelling. In the lattercase, Hg and Eg are zero.

Hsg and L Esg can be expressed as

Hsg = −ρcp(Ta − T0)

rh,sg, (18)

L Esg = −ρLβ(qa − qs(T0))

rq,sg, (19)

where Ta and qa are the air temperature and specific humidity at the lowest model level, T0

is the surface skin temperature and qs(T0) is the saturation specific humidity at T0. Variousformulations exist for the β parameter, which is usually assumed to be a linear function ofthe soil moisture in the top soil layer (Irannejad and Shao 1998).

For simplicity, we assume rh,sg = rq,sg, but these resistances can no longer be determinedfrom MOST. Instead,

rh,sg =z1∫

z0s

K −1h,sg(z)dz, (20)

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where z0s is a roughness length depending on local aerodynamic characteristics of the land-surface, and z1 is the lowest model level height. Suppose

Kh,sg(z) = Kh,sg(z1)

(z

z1

)n

(21)

with Kh,sg(z1) being estimated from the subgrid closure scheme (i.e. Eq. 2) for the first modellevel height, z1. For n = 1, Eqs. 20 and 21 give

rh,sg = z1

Kh,sg(z1)

[ln

(z1

z0s

)]. (22a)

For other n values, they give

rh,sg = z1

(1 − n)Kh,sg(z1)

[1 −

(z1

z0s

)n−1]. (22b)

It is sensible to use Eq. 22a for its simplicity, rather than Eq. 22b, which implies that theshape of Kh,sg(z) also affects rh,sg. In summary, the flux computation in a LES model differsfrom that of a conventional land-surface scheme in, (a) the main components of the fluxesare grid resolved; (b) the subgrid components are parametrized in consistency with the flowsubgrid closure; and (c) the flux computation does not rely on MOST, although the validityof Eq. 21 also requires further scrutiny.

2.2.3 Soil Temperature and Soil Moisture

Soil temperature obeys the heat diffusion equation

∂Ts

∂t= ∂

∂z

(νG∂Ts

∂z

)+ sT, (23)

where Ts is soil temperature, νG is the soil thermal diffusivity and sT is a temperature source.The soil moisture θ obeys the Richards equation

∂w

∂t= ∂

∂z

(KW

∂ (ψw + z)

∂z

)+ sw, (24)

where ψw is the hydraulic suction head, KW is the hydraulic conductivity and sw is a mois-ture source. The simplifications of the soil temperature and soil moisture equations to theone-dimensional Eqs. 23 and 24 are justifiable from scaling analysis even for large-eddysimulation.

In land-surface models used for weather prediction, it is appropriate to select the thick-nesses of the soil layers, for example, as 0.1, 0.3, 0.6, 1.0 m. However, for LES, much thinnerlayers must be selected to allow the land surface to respond to the effects of large eddies.Suppose the typical time scale of the atmospheric system is tA. Then, because the soil thermaldiffusivity, νG, is of the order of 10−6 to 10−7 m2 s−1, the corresponding thickness of the soillayer, �s, must satisfy

�s ∼ √νGtA. (25)

For tA= 1 day, �s is about 0.2 m; for tA = 10 min,�s is about 0.01 m. Thus, we set thethickness of the soil column as 0.2 m to allow for soil response to the diurnal variation of theatmosphere, and set the thickness of the first soil layer as 0.01 m to allow for soil responseto the large-eddy fluctuations. The soil-layer configuration used in LES-ALM is as shown inFig. 1.

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Fig. 2 Land-use map of the simulation area. For each of the nine land-use types, a set of vegetation parametersis assigned, i.e. leaf area index (LAI), vegetation height and vegetation cover fraction. The Selhausen andMerken measurement sites are marked by the black dots. A selected subset of the aircraft flight paths (whitelines) is projected onto the map. All flights were between 120 and 200 m above ground. The numbers standfor the start and end time of the selected flights. The black line represents the cross-section to be shown inFig. 10

3 Model Application Site and Simulation Set-up

3.1 Field Measurements

The model has been set-up to simulate a case from the FLUXPAT experiments con-ducted within the German research collaborative SFB/TR 32 “Patterns in Soil-Vegetation-Atmosphere-Systems: Monitoring, Modelling, and Data Assimilation” (Vereecken et al.2010). The FLUXPAT experiments include measurements of soil state parameters and efflux,plant structural parameters such as LAI, plant physiological status, micrometeorological quan-tities from surface (tower-based) to higher levels (by airplane). Measurements took place inthe Rur river catchment between Aachen and Cologne in western Germany, close to the JülichResearch Centre (50◦53′, 6◦27′, see Fig. 2). The area is arable land dominated by field cropsof sugar beet and two grain species (winter wheat and winter barley), which amount to about75 % of the cultivated plants in the area. Typical field sizes of the region are in the range ofone to a few hectares or a typical length scale of some 100 m. Measurements focused ona flat area of roughly 10 × 10 km2 about 100 m above mean sea level. Height differenceswithin the terrain are small with the wider bed of river Rur lying about 10 m lower than thesurrounding and a slight downhill slope of 20 m from south to north. Two main sites nearSelhausen and Merken were established.

In this study, we use micrometeorological measurements from two field plots with sugarbeet and harvested winter wheat, respectively. These measurements included standard airtemperature and humidity and turbulent fluxes using the eddy-covariance method. To char-acterize the development of the boundary layer, radiosondes were released every hour. Aresearch airplane flew at 120 m and 200 m above ground in a polygonal pattern and mea-sured meteorological parameters at 10 Hz to derive fluxes based on the eddy-covariancemethod (see Schmitgen et al. 2004). A part of the flight pattern can be seen in Fig. 2. Flights

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Table 1 Settings of model simulation

Characteristic Exp 1 Exp 2 Exp 3

Land-surface scheme New scheme withimprovementsbased on NoahLSM: an explicitmultilayercanopy scheme;much finersoil-layerconfiguration asshown in Fig. 1

Noah LSM: bulkcanopy; 4 soillayers: 0.1, 0.3,0.6, 1 m

As Exp 1, but withconventionalsoil-layerconfiguration

Surface layer scheme New scheme asdescribed byEqs. 20–22

MOST As Exp 1

Domain size 7.5 × 6.0 × 2.2 km3

Spatial resolution Horizontal: x =y = 60 m;Vertical:logarithmicallystretched withz varying from2 m near thesurface to 24 mfor z ≥ 80 m

Grid 125×100×100

Time step 0.2 s As Exp 1 As Exp 1

Simulation period 0800–2000 UTC, 5 Aug 2009

Lateral BCs Periodic

Upper BCs Constant pressurewith zerovertical velocity

were made under fair weather conditions, such that the influences of synoptic variations andclouds were minimized. The FLUXPAT campaigns covered different stages of plant growthand produced a comprehensive data set for model comparison. In this study, we use data fromAugust 5, 2009, a day with weak south-easterly winds of 3–4 m s−1 in the entire boundarylayer and no clouds except for some thin cirrus in the afternoon.

The land-use data used for the modelling are derived from the Advanced SpaceborneThermal Emission and Reflection Radiometer (Waldhoff 2010) data. The land-use map witha resolution of 15 m is shown in Fig. 2.

3.2 Model Initialization and Parameter Setting

The model domain covers a 7.5 ×6 km2 flat area with different land-use types. The upperboundary of the domain is 2.2 km above the ground. The model domain (7.5 ×6 × 2.2 km3)

is covered with 125 ×100 × 100 grid points, with �x = �y = 60 m and �z stretchedfrom 2 m near the surface to 24 m for z ≥ 80 m. Periodic boundary conditions are used forthe horizontal boundaries. The upper boundary is assumed to have a constant pressure andzero vertical wind. The layer between 1.8 and 2.2 km is assumed to be a damping layer.For comparison, three numerical experiments are carried out: one with the new land-surfacescheme (Exp 1), one with the original Noah land-surface scheme using MOST-based flux

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Fig. 3 Vertical profiles of potential temperature (a), humidity mixing ratio (b) and wind speed (c) obtainedthrough radiosounding (with minor smoothing) between 0758 and 0810 UTC, 5 August 2009. The data areused to initialize the model at 0800 UTC, 5 August 2009

Table 2 Soil temperature, soil moisture and surface albedo for different land types used to initialize theland-surface model

Land-use type Soil temperature (◦C) Soil moisture (m3 m−3) Surface albedo

Layer 1 Layers 2–4 Layers 1–4

Bare soil 20 18 0.20 0.33

Settlement 20 18 0.20 0.15

Bog – – – 0.08

Water – – – 0.08

Rapeseed 20 18 0.20 0.33

Beet 20 18 0.24 0.22

Grain 20 18 0.20 0.33

Pasture 20 18 0.24 0.19

Forest 20 18 0.24 0.14

formulations (Exp 2), and one with the new land-surface scheme but with the conventional(thick) soil-layer configuration (Exp 3). A summary of the simulation settings is given inTable 1. Exp 1 is used as the reference simulation for comparison.

The profiles of the atmospheric variables (wind speed, potential temperature, humidity,etc.) are idealized from the radiosonde for 0800 UTC, 5 August 2009 and used for initializingthe LES model (Fig. 3). As seen, an inversion existed at z = 1,500–1,700 m, with a lapserate of about 8 K km−1. A near surface inversion existed between 100 and 300 m and thebulk of the boundary layer was weakly stable. The humidity mixing ratio was between 5.5and 7 g kg−1, decreasing with height, and from 5.5 to 0.5 g kg−1 across the capping inversionlayer. The wind speed was about 3.6 m s−1 from the north-east.

There are nine land-use types in the simulation domain, each corresponding to a set ofvegetation parameters, including LAI, vegetation height and cover fraction. The soil type isassumed to be loam and uniform in space. The initial temperature of the top soil layer is set to20 ◦C based on observation, decreasing to 18 ◦C for the remaining layers. Soil moisture was

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Fig. 4 a Profiles of H , Hg and Hsg averaged over the model domain and the time period of 1300–1400UTC. The black full dots are the aircraft measurements of H along different flight paths and the red dot isthe corresponding average. Also shown is the profile of potential temperature, θ , and corresponding aircraftmeasurements (blue dots); b as (a), but for modelled L E , L Eg and L Esg, aircraft measured L E and specifichumidity, q; c Profiles of H , Hg and Hsg for the lower 200 m; d as (c), but for L E , L Eg and L Esg

measured for grain und sugar beet surfaces, but not for the other land-use types. The initialsoil moistures for the latter cases were set empirically with reference to the measurementsfor the grain and sugar beet surfaces, e.g. the forested area was assumed to be slightly wetterthan the sugar beet. The surface albedo varies between 0.08 and 0.33 according to fieldobservation. A summary of the initializations is given in Table 2.

4 Comparison of Model Results with Observations

4.1 Large-Eddy Simulated Flux Patterns

We first examine the general features of the model simulated fluxes. Figure 4a shows theprofiles of the time- and domain-averaged sensible heat fluxes, H, Hg and Hsg,and potentialtemperature, θ , and Fig. 4b shows those of latent heat fluxes, L E, L Eg and L Esg, and specific

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humidity, q . The time averages are for the 1-h period of 1300–1400 UTC (all time averagesrefer to this period, unless otherwise stated). For both Exp 1 and Exp 2, the profiles of Hare typical for a convective boundary layer, i.e., they linearly decrease with height until theinversion level (Fig. 4a). In the bulk of the boundary layer, H is mainly due to Hg, and Hsg

is negligible. Close to the surface, as the scale of turbulence is fine, Hsg dominates (Fig.4c). Below about the 40-m level, H increases slightly with height. This is probably due toan underestimate of Hg near the surface. The latent heat flux profiles (Fig. 4b, d) show thatL E increases with height to the inversion level. This result is consistent with the findingof Deardorff (1974) who conducted a large-eddy simulation of a convective boundary layerwithout a land-surface scheme. This profile of L E is caused by the entrainment of dry airfrom aloft, which contributes to a positive latent heat flux, but we do not have measurementsto verify the correctness of the simulated latent heat flux profile. With respect to Exp 1, Hfrom Exp 2 is generally lower due to its smaller value at the surface. As a consequence of theweaker thermal instability, L E from Exp 2 is also smaller in the upper part of the atmosphericboundary layer due to the weaker entrainment of dry air from aloft. Our comparison showsthat the formulation of the land-surface scheme can have a significant quantitative effect onthe flux profiles of the atmospheric boundary layer.

Also shown in Fig. 4a, b is the aircraft measurements of sensible heat flux, potentialtemperature, latent heat flux and specific humidity. These values are averaged along the flightpaths shown in Fig. 2. The simulated (Exp 1 and Exp 2 are almost the same) and observedpotential temperatures are in good agreement, while the simulated specific humidity (Exp1 and Exp 2 are almost the same) is slightly lower than the observed. This is similar tothe results of Zacharias et al. (2012) and probably due to advection of moist air that isnot included in the model. Since the model is run with no data assimilation, and given thestrong humidity decrease across the inversion layer and the mixing in the boundary layer, theslight decrease of specific humidity in time is expected. Therefore, the degree of discrepancybetween the modelled and aircraft-observed mixing ratio can be explained and is acceptable.The aircraft H and L E measurements show a large scatter between 50 and 400 W m−2. Thescatter is not surprising, as we shall also see from the model simulation (e.g. Fig. 8), theinstantaneous fluxes can vary greatly in space and time because large eddies move aroundwith considerable randomness. However, the averages of H and L E over all aircraft flightpaths are in reasonable agreement with the model estimates.

The time-averaged sensible and latent heat fluxes (Fig. 5) show that the near-surfacepatterns of H and L E are closely correlated with the land-surface properties. For example(Fig. 5a), the highest H values are found over the settlement areas, in excess of 400 W m−2,while the values of H over the forest, pasture and sugar beet surfaces are much smaller, ataround 120 W m−2. Over the lake surface, H is negative. The impacts of the land surface onthe patterns of LE are also visible (Fig. 5d): the largest L E values occur over the pasture andforest areas along the river, where the surface is moist and rough. Figure 5a, d also showsthat, while the features of land-surface properties are clearly reflected in the patterns of Hand L E , they quickly become fuzzy as a consequence of large-eddy mixing (Fig. 5b, e), andonly the larger land-surface features are identifiable.

At Merken, sensible and latent heat fluxes were measured using the eddy-correlation tech-nique over the (harvested) wheat and sugar beet surfaces. The fluxes of Exp 1 are calculatedusing Eq. 17a, b and then averaged over 30-min intervals for comparison with the measure-ments. Figure 6a shows that, for the wheat surface, H of Exp 2 is underestimated by as muchas 100 W m−2 from the late morning to the early afternoon. The agreement between thesimulated H of Exp 1 and the observation is much better. For the sugar beet surface (Fig. 6b),L E is overestimated in Exp 2, but the overestimate is reduced in Exp 1. In both Exp 1 and

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Fig. 5 a Patterns of sensible heat flux H (W m−2) at the 10-m level, averaged over the time period 1300–1400 UTC for Exp 1; b as (a), but for Hg; (c) as (a), but for Hsg; d–f as (a–c), but for L E , L Eg and L Esg,respectively

Fig. 6 a Comparison of the simulated and observed sensible heat fluxes (red) and latent heat fluxes (blue)for the harvested wheat surface. b As (a), but for the sugar beet surface

Exp 2, H is overestimated. The overestimation may be due to a variety of reasons, but themost likely is that the specified albedo for the sugar beet surface (0.22) is too low. Both thesimulation and the observations show a clear dependence of the partitioning of net radiationon the land-use type. Over the wheat surface, H dominates over L E , while over the sugarbeet surface, L E dominates over H . For both surfaces, Exp 1 correctly reproduced the diurnalcycles and the magnitudes of the dominating flux component. There are some discrepancies,but the improvements as a result of the new land-surface scheme are significant.

Figure 7 shows the comparison of the other quantities for the wheat surface, includingnet radiation, Rn, soil heat flux, G, soil temperature in the top 50-mm soil layer and airtemperature at 2 m, as well as soil moisture at 50-mm depth. The agreement of Rn betweenExp 1 and the observations is reasonable and is evidently better than that for Exp 2 (Fig. 7a).The simulated G at 100-mm depth and the observed G at 80 mm are in reasonable agreement,

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Fig. 7 a Comparisons of the simulated and observed net radiation, Rn; b simulated soil heat flux at 100 mm,and the measured soil heat flux at 80 mm below the surface; c simulated and observed soil temperature at 50mm below the surface (black) and air temperature at 2 m above the ground surface (blue); d Simulated andobserved soil moisture for the top soil layer; for the harvested wheat surface whose surface energy fluxes arecompared in Fig. 6a

but G of Exp 1 is up to 15 W m−2 lower than the observed values (at around 1400 UTC),while G of Exp 2 is more than 10 W m−2 higher than the observed values after 1400 UTC. Itis generally the case that G in deeper soil is smaller. This implies that the simulation of Exp 1using the new model is more consistent with the observation. Soil temperature and moistureare also better simulated in Exp 1 (Fig. 7c, d). The soil temperature of Exp 2 is very muchoverestimated, up to 5 ◦C higher than that observed for the time period after 1400 UTC. Thehigher soil temperature is a consequence of the low H , which is, in Exp 2, underestimated byabout 30 % for most of the daytime (Fig. 6a). This implies that the conductance used for theflux calculation in the old land-surface scheme is too small, and consequently, in comparisonto Exp 1, H is much lower even though the surface–air temperature difference is much larger.Both simulated air temperatures at the 2-m level are up to 2 ◦C higher than those observedfor the time period 1000–1700 UTC. The higher air temperature and lower soil heat flux areattributed to the use of the periodic boundary condition for the model run, while cool airadvection might have occurred in reality. At noon time, a higher air temperature implies alower ground heat flux and hence a lower soil heat flux. Based on the comparison with theairborne and ground-based observations, as well as the comparison between the experiments,we conclude that, despite some discrepancies, the model simulation of Exp 1 is successful.

Figure 8 shows the composite time-averaged profiles of H and LE, together with theirstandard deviations, for four different land-use types. The differences among the profiles

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Fig. 8 Time-averaged profiles of turbulent fluxes for different land-use types (solid) plus, minus their standarddeviation (dashed) for Exp 1. Top the whole BL, bottom the lower 200 m, left sensible heat flux, right latentheat flux

Fig. 9 a Simulated instantaneous surface L E versus H for all points in the simulation domain at 1300 UTCfor Exp 1. b As (a), but for Exp 3

above different land-use types are substantial, e.g. for forest and settlement areas. The differ-ences are largest close to the surface at about 20 m, but remain quite significant to fairly highlevels. The standard deviation shows that the scatter among the fluxes for a given surface typeis substantial. For H , the largest scatter occurs near the surface, while for L E , the largestscatter occurs at the inversion level.

Figure 9 is a scatter plot of the instantaneous L E and H for different land-surface types.Distinct Bowen ratios (H /L E) for different land surfaces are identifiable. For example, theBowen ratio is close to 0.4 for sugar beet, but considerably higher for bare soil and settlement(Fig. 9a). Figure 9a also shows that the scatter of H + L E for a given land-use type is large.This implies that the net radiation and ground heat flux also possess strong temporal andspatial variations as a consequence of the atmosphere–land-surface interactions. Because of

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Fig. 10 a Snap shot of a cross section of potential temperature and surface sensible heat fluxes at y = 2.5km (black straight line in Fig. 2) for Exp 1. b As (a), but for specific humidity and latent heat flux. A largeupdraft eddy at x = 2 km carries heat and moisture upwards, and a large downdraft eddy at x = 4 km carriesheat downwards and moisture upwards

the fine soil-layer configuration we used (Fig. 1), the temperature and moisture in the first soillayer vary rapidly with time as a consequence of the large-eddy fluxes and local advections,details of which will be discussed in a companion paper (Liu and Shao 2013, submitted).For comparison, the scatter of L E and H is plotted in Fig. 9b for a model run with theconventional soil layer configuration (Exp 3). In Exp 1 (Fig. 9a), the Bowen ratios are ingeneral larger, especially for the bare soil and settlement. This is due to the supply limitationof soil moisture in the thin top soil layer. In the thin soil layer configuration, the limiting effectof soil hydraulic conductivity to evaporation from bare soil surfaces is much more obvious.In Exp 3 (Fig. 9b), the scatter of H + L E for a given land-use type is much smaller, implyingthat this quantity has weaker temporal and spatial variations due to the weaker couplingbetween the land surface and the atmosphere and the weaker limiting effect of soil hydraulicconductivity on evaporation (as a consequence of the thicker soil-layer configuration).

4.2 Persistency of Land-Surface Heterogeneity

We now study how land-surface heterogeneity propagates and diminishes in the atmosphereand what role large eddies play in these processes. The model simulation allows a visualexamination of the large-eddy structures and the associated fluxes. As an example, Fig. 10shows snap shots of the x–z cross-sections of potential temperature and specific humidity,together with the surface sensible and latent heat fluxes. It is seen that the instantaneoussensible and latent heat fluxes vary over a wide range between zero and 1,000 W m−2. Con-vergence lines and divergence areas of horizontal flow often occur, accompanied by strongupdrafts and relatively weaker downdrafts as seen in Fig. 10a, b. The updrafts near the sur-face merge to build larger updrafts that carry heat and moisture to the upper boundary layer,as seen at x =2 km of Fig. 10a, b. At the same time, downdrafts from the inversion levelentrain warm (higher potential temperature) and dry air into the boundary layer and producenegative sensible heat fluxes and positive latent heat fluxes, as seen at x =4 km of Fig. 10a,b. These examples show that large eddies build efficient transport pathways from the surfaceto the upper atmospheric boundary layer. Thus, the mechanism of large-eddy transport in theatmospheric boundary layer differs profoundly from the mechanism of small-eddy diffusioncommonly described using K-theory (Holtslag and Moeng 1991). This difference is particu-larly evident in latent heat fluxes, which in the bulk of the boundary layer are not determined

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Fig. 11 Propagation of the effects of land-surface heterogeneity in the atmosphere for Exp 1. a Cross-sectionsof sensible heat fluxes at various times and levels. b H and LE averaged over 1300–1400 UTC

by the local vertical gradient of specific humidity, but the bottom-up transport of moist airand the top-down entrainment of dry air and the mixing of the convective thermals.

Figure 10 suggests that large-eddy transfer is determined both by the macroscopic structureof the boundary layer and the patterns of land-surface properties. As small eddies emergefrom the surface, they bear the signals of land-surface heterogeneity, but as the small eddiesorganize to build larger eddies, a process governed by the thermal-dynamic instability of theboundary layer, these land-surface signals weaken as a consequence of mixing. Then, if so,how persistent are the land-surface signals? In Fig. 11a, the cross-sections of instantaneousH are shown for z = 2, 10, 40, 160 and 640 m as a hierarchy. Near the surface (e.g. at z = 2 m),the patterns of the fluxes and the land types are closely correlated for every instant. However,the footprints of the land surface become more difficult to recognize at higher levels (e.g. at z= 40 m) for a given instant. At the same time, the low-level small eddies feed to the formationof larger eddies at higher levels. A hierarchic structure of turbulence is identifiable and, asa consequence, the patterns of the averaged fluxes do show a close link to the patterns ofland-use (Fig. 11b).

In Fig. 11b, hourly averages of H and L E for five different heights are shown. Thecorrelations between the patterns of the fluxes and the land-use are clearly identifiable forlevels below 160 m. Even at the 640-m level, the influence of land-surface heterogeneity isvisible. Thus, on average, the land-surface signals are surprisingly persistent. This impliesthat certain large-eddy types (e.g. warm updrafts) prevail over certain land-surface types (e.g.settlement), such that the land-surface heterogeneity persists on average in the atmosphericflow structure. For the simulation presented here this means that, if a blending height exists, itwould be well beyond the surface-layer depth. Figure 11b shows that, while the details of land-surface heterogeneity gradually diminish with height, the large features remain prominent.

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5 Summary

This paper is the first part of our study on atmospheric–land-surface interactions over het-erogeneous surfaces. We have presented a large-eddy simulation atmosphere–land-surfacemodel (LES-ALM) that is indispensable for the investigation of the specific scientific ques-tions related to land-surface heterogeneity, e.g., how do the effects of land-surface hetero-geneity propagate and persist in the atmospheric boundary layer. We have argued, based onnumerous numerical tests, that substantial improvements are necessary to the “conventional”land-surface schemes to ensure their adequacy for large-eddy simulation of atmosphere–land-surface processes. The improvements we have made in this study include, (1) an explicitmulti-layer treatment of the canopy layer; (2) a method for computing surface fluxes that isconsistent with the flow model subgrid closure; and (3) a thin soil-layer configuration. Themodel is then applied to the Selhausen–Merken experimental site in Germany, a heteroge-neous area with several land-use types (bare soil, forest, wheat, sugar beet, settlement etc.).A 12-h daytime simulation is made to evaluate the model performance, and the model resultsare compared with ground-based and airborne measurements. The model simulations of sen-sible and latent heat fluxes are found to be in good agreement with the observed fluxes. Goodagreement is also found between the modelled and observed net radiation, ground heat flux,soil temperature and soil moisture. The discrepancies that still exist between the modelledresults and the observations (e.g. 2-m air temperature) can be explained.

A number of sensitivity tests have been made and the results of representative ones (Table1) have been presented to assess the performance of the new land-surface scheme (Exp 1)with respect to the Noah land-surface scheme (Exp 2) and to assess the effect of soil-layerconfiguration (Exp 3). Exp 1 and 2 produced qualitatively similar H and L E profiles inthe atmospheric boundary layer, but significant quantitative differences between them arefound: Exp 2 produced smaller H , weaker thermal instability and smaller LE in the upperpart of the boundary layer due to the related weaker entrainment. The comparisons with thenear-surface measurements have shown that the overall performance of the new land-surfacescheme is more satisfactory in terms of sensible heat flux, H , and latent heat flux, L E , netradiation, Rn, soil heat flux, G, as well as top layer soil temperature and soil moisture. Whilethe improvements may be due to a combination of the modifications we have made to theland-surface scheme, the refinement of the soil-layer configuration appears to have had asignificant impact because the very thin top soil layer limits the availability of soil moisturefor evaporation and thereby profoundly affects the partitioning of net radiation into sensibleand latent heat fluxes (Exp 3).

An even more substantial difference between the present work and earlier studies is thatLES-ALM allows the atmosphere and the land surface to interact at the scale of large eddies,as seen from the fluctuations and the probabilistic distributions of the near-surface energyfluxes. A multi-layer canopy scheme has been proposed, but we have not thoroughly evaluatedits performance.

Using LES-ALM, we have made preliminary investigations on large-eddy scaleatmospheric land-surface exchanges. While many questions remain to be clarified, we havefocused on the patterns of sensible and latent heat fluxes, how such patterns come intoexistence, how large eddies are related to land-surface heterogeneity and how the effectsof land-surface heterogeneity persist in the atmosphere. The model simulation revealed acomplex image of flux patterns in the atmospheric boundary layer. Near the surface (e.g.below 10 m), the flux patterns are closely correlated with the land-use patterns, and whilethis correlation rapidly diminishes with height, it remains identifiable to a level of over60 m.

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It is shown that large-eddy transfer is determined both by the macroscopic structure of theboundary layer and patterns of land-surface properties. As small eddies emerge from near thesurface, they bear land-surface signals, but as they organize and develop into larger eddies, aprocess governed by the thermal-dynamic instability of the boundary layer, the land-surfacesignals weaken due to turbulent mixing. As a result, the instant flux patterns (unless very closeto the surface) appear to be unrelated to the land-use patterns, but on average, the correlationbetween the flux and land-use pattern is quite strong and persistent in at least the lower half ofthe atmospheric boundary layer. The relationship between the sensible and latent heat fluxesin the bulk of the boundary layer is rather interesting because the downward entrainment ofwarm and dry air from aloft results in a negative sensible heat flux but a positive latent heatflux in the upper part of the boundary layer. On occasions, the downward entrainment of thedry air can even make a significant difference to the latent heat fluxes near the surface.

Although the near-surface flux patterns and land-use patterns are closely correlated, thescatter of the fluxes for a given land-use type is substantial. Three sources for the scatter canbe identified: (1) large eddies generate randomness in the fluxes; (2) rapid feedback existsbetween the land-surface and large eddies; (3) surface heterogeneity causes local advectionbetween the grid cells. For example, warm and dry air from upstream dry areas can influencethe evaporation and heat exchange over the vegetated wet areas downstream. Owing to theadvection from the dry areas, evaporation in the wet areas is fostered, while heat exchangesuppressed.

Due to the very thin soil layers that must be used for the large-eddy simulation, therequirement for reliable land-surface input parameters and initial conditions is difficult tomeet. Thus, in general, the value of a large-eddy simulation atmospheric–land-surface modeldoes not lie in the quantitative accuracy of the model simulation for specific cases, but inits application to generate understanding of atmospheric–land-surface interactions that aredifficult to observe through experiments, and to support the interpretations of the observations.

Acknowledgments This work is supported by the DFG Transregional Cooperative Research Centre 32“Patterns in Soil-Vegetation-Atmosphere-Systems: Monitoring, Modelling and Data Assimilation”. We thankBruno Neininger (MetAir) for performing and processing of the aircraft measurements, Heiner Geiss (JuelichResearch Center), Martin Lennefer, Dirk Schüttemeyer, Stefan Kollet (University Bonn) who supported themicrometeorological measurements, Gerritt Maschwitz for launching the radiosondes.

6 Appendix: Canopy Temperature Scheme

The equation for canopy temperature, Tc, can be written as

cvg∂Tc

∂t= −�∇ · �R − αtεσT 4

c − ρcpST − ρL Sq (26)

where cvg is the volumetric vegetation heat capacity (J m−3 s−1), i.e., the energy required toincrease the temperature of vegetation per unit (air) volume, αt is the vegetation area density(total area per unit volume), ε is vegetation emissivity, ρ is air density, cp is air specific heatat constant pressure, L is the latent heat of vaporization of water, ST and Sq are as givenin Eqs. 7 and 8, �R is net radiation flux. Suppose net radiation is horizontally homogeneous,then, Eq. 26 becomes

cvg∂Tc

∂t= −∂Rn

∂z− αtεσT 4

c − ρcpST − ρL Sq , (27)

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Fig. 12 Schematic illustration of radiation transfer through vegetation canopy

where Rn is the vertical component of the net radiation. For simplicity, we divide the radiationspectrum into the shortwave (solar) and longwave (terrestrial) bands. Then, as illustrated inFig. 12, Rn for any given level can be expressed as

Rn = (Rs↑ − Rs↓)+ (Rl↑ − Rl↓). (28)

In general, radiation passing through a vegetation layer of thickness, ds, is scattered andabsorbed by leaves. The dependence of R on s can be expressed as

dR = −k Rds, (29)

where k is the canopy extinction coefficient. It therefore follows that

− ∂Rn

∂z= ks(Rs↑ + Rs↓)+ kl(Rl↑ + Rl↓), (30)

noting that dR↓ = −k R↓ds, ds = −dz, and therefore,

∂R↑∂z

= −k R↑, (31a)

∂R↓∂z

= k R↓. (31b)

In Eq. 30, ks and kl are respectively the extinction coefficients for shortwave and longwaveradiation. It follows that Eq. 27 becomes

cvg∂Tc

∂t= ks(Rs↑ + Rs↓)+ kl(Rl↑ + Rl↓)− αtεσT 4

c − ρcpST − ρL Sq . (32)

Suppose cvg is small, then the canopy temperature can be determined from the followingdiagnostic equation

αtεσT 4c = ks(Rs↑ + Rs↓)+ kl(Rl↑ + Rl↓)− ρcpST − ρL Sq . (33)

The treatment of the radiation fluxes is straightforward. Suppose the shortwave flux at thetop of the canopy, h, is Rsh. Then, the fraction of the shortwave radiation entering the canopy

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is (1 − avg)Rsh and the fraction reaching the surface is

Rs0 = (1 − avg)Rsh exp

⎛⎝−

h∫

0

ksdz

⎞⎠ . (34)

where avg is vegetation albedo. Thus, for a level z,

Rs↑ + Rs↓ = a0(1 − avg)Rsh exp

⎛⎝−

h∫

0

ksdz

⎞⎠ · exp

⎛⎝−

z∫

0

ksdz

⎞⎠

+ (1 − avg)Rsh exp

⎛⎝−

h∫

z

ksdz

⎞⎠ (35)

or

Rs↑ + Rs↓ = (1 − avg)Rsh

⎡⎣a0 exp

⎛⎝−

h∫

0

ksdz −z∫

0

ksdz

⎞⎠ + exp

⎛⎝−

h∫

z

ksdz

⎞⎠

⎤⎦ . (36)

where a0 is surface albedo. Suppose the atmospheric longwave radiation at the top of thecanopy is Rlh and the ground surface temperature is T0. Further, suppose the canopy layerbetween z and h is divided into Ia layers, and the vegetation layer between 0 and z is dividedinto Ib layers, each of δz thick (Fig. 12). Then

Rs↑ + Rs↓ = εσT 40 exp

⎛⎝−

z∫

0

kldz

⎞⎠ + Rlh exp

⎛⎝−

h∫

z

kldz

⎞⎠

+Ib∑

i=1

r(zi ) exp

⎛⎝−

z∫

zi

kldz

⎞⎠ +

Ia∑i=1

r(zi ) exp

⎛⎝−

zi∫

z

kldz

⎞⎠ (37)

with

r(zi ) = 1

2αt (zi )εσT 4

c (zi )δz (38)

where αt(zi )is the vegetation area density at level zi .

References

Albertson JD, Kustas WP, Scanlon TM (2001) Large-eddy simulation over heterogeneous terrain with remotelysensed land surface conditions. Water Resour Res 37(7):1939–1953

Ament F, Simmer C (2006) Improved representation of land-surface heterogeneity in a non-hydrostatic numer-ical weather prediction model. Boundary-Layer Meteorol 121:153–174

Avissar R, Schmidt T (1998) An evaluation of the scale at which ground-surface heat flux patchiness affectsthe convective boundary layer using large-eddy simulation model. J Atmos Sci 55:2666–2689

Beare RJ, Macvean MK, Holtslag AAM, Cuxart J, Esau I, Golaz J-C, Jimenez MA, Khairoutdinov M, KosovicB, Lewellen D, Lund TS, Lundquist JK, McCabe A, Moene AF, Noh Y, Raasch S, Sullivan PP (2004)An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol118:247–272

Bhumralker CM (1975) Numerical experiments on the computation of ground surface temperature in anatmospheric general circulation model. J Appl Meteorol 14:1246–1258

123

Large-Eddy Atmosphere–Land-Surface Modelling

Chen F, Dudhia J (2001) Coupling an advanced land surface-hydrology model with the Penn State-NCARMM5 modeling system. Part I: model implementation and sensitivity. Mon Weather Rev 129:569–585

Clough SA, Shephard MW, Mlawer EJ, Delamere JS, Iacono MJ, Cady-Pereira K, Boukabara S, Brown PD(2005) Atmospheric radiative transfer modeling: a summary of the AER codes. JQSRT 91:233–244

Deardorff JW (1970) A numerical study of three-dimensional turbulent channel flow at large Reynolds num-bers. J Fluid Mech 41:453–480

Deardorff JW (1974) On the entrainment rate of a stratocumulus-topped mixed layer. Q J R Meteorol Soc102:563–582

Deardorff JW (1978) Efficient prediction of ground surface temperature and moisture with inclusion of a layerof vegetation. J Geophys Res 83:1889–1903

Deardorff JW (1980) Stratocumulus-caped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18:495–527

Dickinson RE, Henderson-Sellers A, Kennedy P (1993) Biosphere-aAtmosphere Transfer Scheme (BATS)Version 1e as coupled to the NCAR Community Climate Model. TN387+STR, NCAR

Ek MB, Mitchell KE, Lin Y, Rogers E, Grummann P, Koren V, Gayno G, Tarpley JD (2003) Implementationof Noah land surface model advances in the National Centers for Environmental Prediction operationalMesoscale Eta Model. J Geophys Res 108:8851. doi:10.1029/2002JD003296

Foken T (2006) 50 Years of the Monin–Obukhov similarity theory. Boundary-Layer Meteorol 119:431–447.doi:10.1007/s10546-006-9048-6

Giorgi F, Avissar R (1997) Representation of heterogeneity effects in earth system modeling: experience fromland surface modeling. Rev Geophys 35:413–437

Hechtel LM, Moeng C-H, Stull RB (1990) The effects of nonhomogeneous surface fluxes on the convectiveboundary layer: a case study using large-eddy simulation. J Atmos Sci 47:1721–1741

Heinemann G, Kerschgens M (2005) Comparison of methods for area-averaging surface energy fluxes overheterogeneous land surfaces using high-resolution non-hydrostatic simulations. Int J Climatol 25:379–403.doi:10.1002/joc.1123

Holtslag AAM, Moeng C-H (1991) Eddy diffusivity and countergradient transport in the convectiveatmospheric boundary layer. J Atmos Sci 48:1690–1698

Huang HY, Margulis SA (2009) On the impact of surface heterogeneity on a realistic convective boundarylayer. Water Resour Res 45:W04425. doi:10.1029/2008WR007175

Huang HY, Margulis SA (2010) Evaluation of a fully coupled large-eddy simulation-land surface model andits diagnosis of land-atmosphere feedbacks. Water Resour Res 46:W06512. doi:10.1029/2009WR008232

Huang HY, Stevens B, Margulis SA (2008) Application of dynamic subgrid-scale models for large-eddy sim-ulation of the daytime convective boundary layer over heterogeneous surfaces. Boundary-Layer Meteorol126:327–348. doi:10.1007/s10546-007-9239-9

Iacono MJ, Delamere JS, Mlawer EJ, Shephard MW, Clough SA, Collins WD (2008) Radiative forcing by long-lived greenhourse gases: calculations with the AER radiative transfer models. J Geophys Res 113:D13103.doi:10.1029/2008JD009944

Irannejad P, Shao Y (1998) Description and validation of the atmosphere–land-surface interaction scheme(ALSIS) with HAPEX and Cabauw data. Glob Planet Change 19:87–114

Kleissl J, Kumar V, Menevea C, Parlange MB (2006) Numerical study of dynamic Smagorinsky models inlarge-eddy simulation of the atmospheric boundary layer: Validation in stable and unstable conditions.Water Resour Res 42: doi:10.1029/2005WR004685

Kumar V, Kleissl J, Meneveau C, Parlange MB (2006) Large-eddy simulation of a diurnal cycle of theatmospheric boundary layer: atmospheric stability and scaling issues. Water Resour Res 42: doi:10.1029/2005WR004651

Letzel MO, Raasch S (2003) Large eddy simulation of thermally induced oscillation in the convective boundarylayer. J Atmos Sci 60:2328–2341

Liu S, Shao Y (2013) Soil layer configuration requirement for large-eddy atmosphere and land surface coupledmodeling. Atmos Sci Lett. doi:10.1002/asl.426

Manabe S (1969) Climate and ocean circulation: 1. The atmospheric circulation and the hydrology of theearth’s surface. Mon Weather Rev 97:739–774

Maronga B, Raasch S (2013) Large-eddy simulation of surface heterogeneity effects on the convective bound-ary layer during the LITFASS-2003 experiment. Boundary-Layer Meteorol 146:17–44

Mlawer EJ, Taubman SJ, Brown PD, Iacono MJ, Clough SA (1997) Radiative transfer for inhomogeneousatmosphere: RRTM, a validated correlated-k model for the long-wave. J Geophys Res 102(D14):16663–16682

Moeng C-H (1984) A large-eddy simulation model for the study of planetary boundary-layer turbulence.J Atmos Sci 41:2052–2062

123

Y. Shao et al.

Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the ground layer of the atmosphere (inRussian). Tr Geofiz Inst Akad Nauk SSSR 151:163–187

Noilhan J, Planton S (1989) A simple parametrization of land surface processes for meteorological models.Mon Weather Rev 117:536–549

Oleson KW, Niu GY, Yang ZL, Lawrence DM, Thornton PE, Lawrence PJ, Stockli R, Dickinson RE, BonanGB, Levis S (2007) CLM3.5 Documentation. UCAR, http://cgd.ucar.edu/tss/clm/distribution/clm3.5

Patton EG, Sullivan PP, Moeng C-H (2005) The influence of idealized heterogeneity on wet and dry planetaryboundary layers coupled to the land surface. J Atmos Sci 62:2078–2097

Raasch S, Harbusch G (2001) An analysis of secondary circulations and their effects caused by small-scalesurface inhomogeneities using large-eddy simulation. Boundary-Layer Meteorol 101:31–59

Raupach MR (1992) Drag and drag partition on rough surfaces. Boundary-Layer Meteorol 60:374–396Schmitgen S, Gei H, Ciais P, Neininger B, Brunet Y, Reichstein M, Kley D, Volz-Thomas A (2004) Carbon

dioxide uptake of a forested region in southwest France derived from airborne CO2 and CO measurementsin a quasi-Lagrangian experiment. J Geophys Res 109(D14302). doi:10.1029/2003JD004335.

Shao Y, Yang Y (2008) A theory for drag partition over rough surfaces. J Geophys Res 113. doi:10.1029/2007JF000791

Shao Y, Sogalla M, Kerschgens M, Brücher W (2001) Effects of land-surface heterogeneity upon surfacefluxes and turbulent conditions. Meteorol Atmos Phys 78:157–181

Shaw R, Schumann U (1992) Large-eddy simulation of turbulent flow above and within a forest. Boundary-Layer Meteorol 61:47–64. doi:10.1007/BF02033994

Shaw RH, Hartog G, Neumann HH (1988) Influence of foliar density and thermal stability on profiles ofReynolds stress and turbulence intensity in a deciduous forest. Boundary-Layer Meterol 45:391–409

Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang X-Y, Wang W, Powers JG(2008) A description of the advanced research WRF Version 3. NCAR/TN-475+STR

Smagorinsky J (1963) General circulation experiments with the primitive equations, Part I: the basic experi-ment. Mon Weather Rev 91:99–164

Sullivan PP, Moeng C-H, Stevens B, Lenschow DH, Mayor SD (1998) Structure of the entrainment zonecapping the convective atmospheric boundary layer. J Atmos Sci 55:3042–3064

Vereecken H, Kollet S, Simmer C (2010) Patterns in soil–vegetation–atmosphere systems: monitoring, mod-eling, and data assimilation. Vadose Zone J 9:821–827. doi:10.2136/vzj2010.0122

Waldhoff G (2010) Land use classification of 2009 for the Rur catchment. doi:10.1594/GFZ.TR32.1Zacharias S, Reyers M, Pinto JG, Schween JH, Crewell S, Kerschgens M (2012) Heat and moisture budgets

from airborne measurements and high resolution model simulations. Meteorol Atmos Phys 117:47–61.doi:10.1007/s00703-012-0188-6

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