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9 Meso-scale, Regional and Global Atmospheric Models

9 Meso-scale, Regional and Global Atmospheric Models

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3 Atmospheric Boundary Layer and Atmospheric Modelling










y (m)










































y (m)




x (m)


Fig. 3.15. An example for DNS application to wind erosion modelling. Five roughness elements (cylinders with a diameter of 5 mm and height of 10 mm) are mounted

on the surface and DNS is applied to determine (a) the momentum fluxes (in N m−2 )

and (b) flow speed (in m s−1 ) in the vicinity of the roughness elements (An Li, with


Regional-climate models have similar spatial resolutions as regional-weather

models, but focus on atmospheric changes on a time-scale much longer than

the synoptic time scale, e.g. seasonal, annual or even decadal. However, the

traditional boundaries between the models are rapidly diminishing with the

ever increasing computing power. For instance, a meso-scale model can be

used for large-eddy simulation as well as numerical weather predictions.

Most atmospheric models consist of a dynamic framework, a number of

modules for physical processes and techniques for data assimilation. The equation system commonly used for numerical weather prediction consists of seven

basic equations: three equations for velocity components, the continuity equation, the thermodynamic equation, the moisture equation and the equation

of state. If dust transport is also of concern, the dust concentration equation can be added to the equation system. To account for the effect of surface

topography, the σ coordinate system (x, y, σ) is often used. The vertical coordinate σ is defined to be p/ps , with p being the atmospheric pressure at a point

and ps that at the surface direct beneath it (Simmons and Bengtsson, 1984).

In the σ coordinate system, the equations for numerical weather prediction


3.9 Meso-scale, Regional and Global Atmospheric Models

∂(ps uu) ∂(ps uv) ∂(ps uσ)


(ps u) = −







− RT

+ Fu + Du

+f ps v − ps




∂(ps vu) ∂(ps vv) ∂(ps v σ)


(ps v) = −







− RT

+ Fv + Dv

−f ps u − ps










∂(ups ) ∂(vps ) ∂(σp

˙ s)











= −cp u





+QT + FT + DT




=− u






− cp σ˙

− σ˙


+ RT




d ln ps






+ Qq + Fq + Dq



In the above equations, σ˙ is the vertical ‘velocity’ in the σ coordinate system

and φ = gz is the geopotential. Fu and Fv are the horizontal frictional forces,

and FT and Fq are the heating and moisture changes arising from subgrid scale

vertical turbulent exchange. QT and Qq are the heat and moisture source/sink

terms, and Du , Dv , DT and Dq are the lateral diffusions of momentum, heat

and moisture, respectively. The hydrostatic assumption is embedded in the

equations of motion and in the continuity equation. This assumption is valid

for modelling large-scale atmospheric systems and the spatial resolution needs

to be larger than 5 km. For higher resolution, the effects of surface topography

and convection may generate strong vertical accelerations which violate the

hydrostatic assumption. For modelling sub-synoptic atmospheric systems and

intense weather events, such as squall lines, non-hydrostatic models are necessary. Therefore, meso-scale models are mostly non-hydrostatic while regional

and global models are mostly hydrostatic. The equation system can be solved

numerically using various numerical schemes and computational grids (e.g.

Lin et al. 1997). The horizontal resolution of numerical weather-prediction

models ranges from several kilometres to several tens of kilometres and in the

vertical, about 30 layers are employed with smaller increments in the lower

part of the atmosphere.

The operation of regional models requires initial and boundary conditions.

The preparation of the initial input data is normally based upon objective

analysis, which combines observed data from meteorological networks with a

model forecast from a previous time step. Objective analyses are produced routinely by meteorological services. Interpolation of the data from the pressure


3 Atmospheric Boundary Layer and Atmospheric Modelling

surfaces to the σ levels is then carried out using methods such as cubic-spline

interpolation. Sometimes, extrapolation is also required using assumed lapse

rates for temperature and thermal-wind relationships for the wind components. Dynamical consistency of the initial fields also needs to be preserved.

The requirement for boundary conditions is normally fulfilled through

nesting the regional model in a global model. Most regional models can also

be self-nested, which allows the model to be run over selected areas with increased resolution. Model simulations at higher resolutions are carried out by

first running the model with the coarse-resolution data. During these runs,

the model outputs atmospheric variables to data files for every nesting time

step (e.g. 6 hr). These data files are then processed, i.e. data from the coarse

mesh are interpolated to the fine mesh and adjusted to the heights of the

new topography, horizontal wind components, temperature and mixing ratio are interpolated to the new model levels using spline functions. Finally,

the model is run on the chosen higher-resolution sub-domain. Regional models also require other data sets for modelling the physical processes. These

data sets are commonly those for ocean-surface temperature and land-surface

properties, including topography, surface roughness lengths, vegetation characteristics and soil properties. It is important that these data sets are also

adequately involved in the preparation of model input data and in the nesting


Figure 3.16a shows an example of running a regional model for the Australian region with self-nesting. In this case, the model is run with a hori-

Fig. 3.16. Simulated near-surface wind (arrows, ms−1 ) and temperature (contours,

C) for the 9 February 1996 dust-storm event in central Australia, (a) with a horizontal resolution of 50 km over the Australian region and (b) with a horizontal

resolution of 10 km over the framed area in (a) using self-nesting. A cold front can

be identified as the region of large temperature gradient

3.9 Meso-scale, Regional and Global Atmospheric Models


zontal resolution of 50 km, with the boundary conditions derived from the

Limited Area Prediction System of the Australian Bureau of Meteorology,

which provides the input data at a horizontal resolution of 75 km. This particular weather event generated intense dust storms in the Simpson Desert of

Australia. In order to examine the details of the frontal system, the regional

model is run in the self-nested mode for a selected area with the spatial resolution increased from 50 km to 10 km. Figure 3.16b shows the simulated results

near the cold front. While the simulation with a coarse grid reveals the general features of the frontal system, the higher resolution model gives a more

detailed structure of the frontal system. As wind erosion is strongly variable

in space, it is very useful to obtain atmospheric data at high resolution. Since

the late 1980s, dust models have been constructed based on regional weather

models. These dust models now have considerable skill for the simulation and

prediction of dust storms (Uno et al. 2006).

Climate models can take many forms ranging from simple one-dimensional

energy balance models to complex three-dimensional time-dependent general

circulation models (GCMS) of the atmosphere and ocean. From the perspective of wind erosion, climate models are mainly used to study the global dust

cycle and the effect of dust on climate change (Zender et al. 2003; Ginoux et al.

2004; Tanaka and Chiba, 2006). For these types of studies, three-dimensional

time-dependent GCMS are more applicable, as detailed simulations of atmospheric parameters, such as wind and precipitation, can be obtained.

Climate is generally considered to represent the average behaviour of

the climate system (including the atmosphere, hydrosphere, lithosphere,

cryosphere and biosphere) over some long period of time. It is not associated

with the exact sequence of daily weather fluctuations. Because of the inherent

unpredictability of atmospheric and ocean flows, climate models are unable

to predict the day-to-day sequence of weather events beyond a very few

weeks. The true utility of climate models lies in their ability to predict the

statistical properties of some future climate state. This statement applies also

to long-term wind-erosion modelling.

Global climate models use a similar set of governing equations to regional

models, formulated mostly also in the σ coordinate system. With the rapid

increase of computing power, climate models are being run with increased horizontal and vertical resolution and increased sophistication in the treatment of

the complex physical, geo-chemical and bio-ecological processes. As a result,

the distinction between climate models and weather models has become less

obvious, apart from detailed numerical procedures. However, we note that, as

climate models attempt to model climate changes over long-time periods, the

fundamental interactions between the atmosphere, the ocean and other components of the climate system become more and more important. Despite this,

improvements in climate modelling in recent years have certainly provided the

necessary prerequisite for the assessment and prediction of wind-erosion climatology and led to new opportunities in wind-erosion studies.


Land-Surface Modelling

Wind erosion, a land-surface process itself, is closely related to other landsurface processes, in particular to soil hydrological and surface bio-ecological

processes which determine the status of soil moisture and vegetation cover.

Wind erosion occurs only if the soil is depleted of moisture and the lack of

vegetation cover is serious, as the capacity of the surface to resist wind erosion

depends critically on these factors. Hence, land-surface modelling is of critical

importance to wind-erosion studies.

Land-surface modelling is in itself an important research topic, as vegetation and soil play a major role in the climate system through their exchange

of mass, energy and momentum with the atmosphere. On the other hand,

atmospheric conditions (wind, temperature and precipitation) also strongly

affect the processes of the biosphere and the continental hydrosphere. The interactions between the land surface and the atmosphere constitute an active

research area. Sophisticated land-surface models for the simulation of these

interactions have been developed in recent years. For atmospheric, hydrological and bio-ecological modelling, a land-surface scheme produces a range of

useful outputs, such as (1) soil and vegetation temperatures; (2) surface net

radiation, sensible-heat flux, latent-heat flux, ground-heat flux and soil-heat

fluxes; (3) soil moisture and (4) flux components related to soil-water balance,

including infiltration, soil water fluxes, runoff and drainage. As far as winderosion modelling is concerned, we are most interested in soil moisture in the

very top soil layer. In this chapter, we shall concentrate on the simulation of

soil moisture using land-surface models.

Integrated wind-erosion modelling, as will be described in Chapter 9, and

land-surface modelling have much in common. Apart from soil moisture, the

parameterisations used in land-surface models for estimating friction velocity

and the methodology used for the treatment of heterogeneous surfaces are

directly transferable to wind-erosion modelling. Furthermore, wind-erosion

and land-surface models share a considerable proportion of input data for

soil, vegetation and surface aerodynamic properties.

Y. Shao, Physics and Modelling of Wind Erosion,

c Springer Science+Business Media B.V. 2008



4 Land-Surface Modelling

4.1 General Aspects

The land surface mainly consists of soil (down to the water table) and vegetation. The interest in land-surface modelling originates from the need to

provide atmospheric models with better lower-boundary conditions through

the specification of the exchanges of momentum, energy and mass between the

atmosphere and the land surface. The central task of a land-surface model is to

quantify these exchanges which, as shown later, are closely related to surface

soil hydrological processes, and hence the modelling of soil moisture becomes

one of the critical issues for climate and weather models.

The processes which influence these exchanges are very complex, as they

depend both on atmospheric conditions and the physical and bio-ecological

properties of the land surface. The representation of these processes in a landsurface scheme is much simplified. Figure 4.1 shows the concept for such a

land-surface scheme. We are mainly concerned with the energy and water balance of the land surface, including the unsaturated soil layer and plants. The

starting point is the soil-temperature equation and the soil-moisture equation

of an unsaturated soil layer

1 ∂Gt



+ sh


Cs ∂z




+ sw





where T is soil temperature, Cs is volumetric soil heat capacity (Cs = ρs cs ,

ρs is soil density and cs is specific heat capacity of the soil), θ is volumetric

soil water content, Gt and Gw are the heat flux and the volumetric water flux

through the soil, respectively, sh is a source/sink term for soil heat related to

the possible phase change of soil water, and sw is a source/sink term for soil

moisture related to processes such as transpiration.

Pores of various sizes occur in soil and a proportion of these pores is filled

with liquid water. The relative volume of this water in a unit volume of soil is

defined as volumetric soil water content, θ, often simply called soil moisture.

If all soil pores are filled with water, the soil is saturated and the value of

soil moisture is the saturation soil moisture, θs . Under natural conditions,

soil cannot be dried completely and a small proportion of water is always

trapped in the smallest pores. The minimum value of soil moisture under

natural conditions is the air-dry soil moisture, θr . Both θs and θr depend on

soil type (see Section 4.6).

In Equations (4.1) and (4.2), land-surface properties are assumed to be

horizontally homogeneous. The solution of these two equations involves the

energy and water fluxes at the interface between the atmosphere and land, as

shown in Fig. 4.1. At the interface, Gt is affected by solar, atmospheric and

land-surface radiations, turbulent heat transfer, evaporation and heat transfer in the soil, while Gw is affected by precipitation, evapotranspiration and

runoff. A land-surface scheme is, in principle, the algorithm required to solve

4.1 General Aspects








& Evaporation



Leaf drip




Flood Flow

Sensible Heat



Soil water flux

Ground heat flux


Fig. 4.1. An illustration of energy and water balance of the land surface. The energy balance is affected by solar, atmospheric and land-surface radiations, turbulent

heat transfer, evaporation and ground heat flux. Rs and Rl denote shortwave and

long wave radiations, respectively. The water balance is affected by precipitation,

evapotranspiration, runoff and drainage

this equation system for a given land-surface configuration. The processes represented in a land-surface scheme can be broadly divided into three categories:

sub-surface thermal and hydraulic processes, bare soil transfer processes and

vegetation processes.

Let us now consider a unit area of land surface. In the vertical direction,

the soil column is represented by a number of soil layers as shown in Fig. 4.1.

Simplification of the land-surface configuration in the horizontal direction is

also required. Figure 4.2 shows examples for how the complex land surface is

represented. The unit area of land surface is further divided into n sub-units,

each of which has a different soil and vegetation type (Fig. 4.2a). The energy

and soil-water conservation can be considered separately for each sub-unit and


4 Land-Surface Modelling




σf1= 0








σf1= 0






Fig. 4.2. An illustration showing how complex land surfaces are simplified in a

land-surface scheme. A unit area of the land surface is further divided into n subunits, each of which has a different soil and vegetation type. The fraction of ith soil

type is si and the fraction of jth vegetation type is σf j . Figures (a), (b) and (c)

represent a successive simplification of the land surface (From Irannejad, 1998)

¯ can be estimated through

the (energy or any other) flux for the unit area, X,

a weighted average of the Xi for each individual sub-unit, i.e.,




Xi si


with si being the fraction of land surface for the ith sub-unit. This strategy

can be simplified to two soil types and two land types for each unit area

(Fig. 4.2b). A further simplification occurs if each unit area contains only

one soil type and one land-use type (Fig. 4.2c). Most land-surface schemes

use simplest configuration and treat the vegetation as a big leaf covering

the fraction σf of the land surface. Of course, the land surface in reality is

highly heterogeneous, due to natural and anthropogenically-induced ecosystem diversity, complex morphology, soil variability and atmospheric forcing.

Because most of the land-surface processes are highly nonlinear, heterogeneity

can profoundly affect the exchanges of momentum, water and energy between

the surface and the atmosphere. In more recent land-surface schemes which

account for the subgrid-scale variations of surface characteristics and/or atmospheric variables, configurations (a) and (b) are increasingly used.

4.2 Surface Energy Balance

At the top of the atmosphere, the solar radiation is 1367 ± 3% Wm−2 .

Figure 4.3 shows the averaged energy balance of the Earth’s system in relative

terms. About 30% of the incoming solar radiation is reflected by the surface

and the atmosphere or scattered by the atmosphere back to space. Of the

4.2 Surface Energy Balance

Shortwave Radiation


Ref. from



Longwave Radiation

Emitted from

Scattered from


atmosphere Ref. from





Convective Fluxes

Emitted from



Emitted from




Abs. by clouds




Abs. by Atmos



Abs. from









Emitted from



Abs. from




Latent heat Sensible Heat

from surface from surface

Fig. 4.3. Energy balance of the Earth system in percentage (After Bryant, 1997)

effective energy remaining in the system about 70% is transmitted through

the atmosphere and absorbed by the Earth’s surface. To balance the absorbed

energy, the surface releases energy to the atmosphere through long wave radiation and turbulent transfers of sensible and latent heat. The Earth’s surface

provides about 2/3 of the energy input for the atmosphere and is hence the

major immediate energy source for atmospheric processes. The surface is the

only source of moisture. Evapotranspiration of water from the surface and

its condensation in the atmosphere is the link between the energy and water

cycles in the Earth’s system.

The evolution of soil moisture is closely related to that of soil temperature.

This is because surface latent-heat fluxes due to evaporation and transpiration

are coupled with the surface sensible-heat flux through the surface energybalance equation

Rn (T0 ) − λl Ev (T0 ) − H(T0 ) − Gt0 (T0 ) = 0


where Rn is surface net radiation, λl Ev , is latent-heat flux with Ev being

evaporation, H is sensible-heat flux, and Gt0 is ground heat flux. All energy

fluxes are functions of the surface (skin) temperature T0 . The net radiation,

Rn , is a result of three radiation fluxes

Rn = (1 − α)Rs + εRl − εσT04


where σ is the Stefan–Boltzmann constant, Rs is downward shortwave radiation, Rl is downward long wave radiation, α is the surface albedo and ε is the

surface emissivity. The emissivity of a substance according to Kirchhoff’s law

is equal to its absorptivity for the same wavelength range. Emissivity of the

natural substances on the Earth’s surface ranges from 0.90 to 0.99. However,

in land-surface schemes a universal emissivity is usually assumed for all surface types. A value of 0.98 can be taken as the representative for both soil and


4 Land-Surface Modelling

vegetation. Since | Rl − σT04 | is usually small, this assumption does not lead

to a large error in calculating the surface energy balance. The soil surface temperature, T0 , is commonly calculated by iterative solution of Equation (4.3)

until the energy balance is achieved to within a specified accuracy. All terms

in Equation (4.3) are either directly or indirectly dependent on soil moisture.

Albedo depends on surface characteristics, solar geometry, and spectral

distribution of incident solar radiation. Albedo needs to be parameterised and

its parameterisation varies in different land-surface schemes. Splitting the solar

spectrum into visible and near-infrared regions for calculating surface albedo

has been used, for instance, by Dickinson et al. (1986, 1993). Sellers et al.

(1986) and Xue et al. (1991) not only account for the radiation wavelength,

but also differentiate between the direct and diffused radiation in calculating

surface albedo. However, most land-surface schemes (e.g. Wetzel and Chang,

1988; Noilhan and Planton, 1989) use a single all-spectrum albedo for each soil

type, each vegetation type or each surface type (soil and vegetation). Different

albedo values are assigned to different vegetation types. For instance, albedo

varies between 0.19 (summer) and 0.23 (winter) for range-grassland, between

0.16 (summer) and 0.17 (winter) for deciduous forest and 0.12 for coniferous

forest and tropical forest. Almost all land-surface schemes modify the soil

surface albedo according to soil moisture. This is done for instance by using

the empirical relationship

αs = αr +

θ − θr

(αs − αr )

θs − θr


where αs and αr are prescribed albedos at saturation soil moisture, θs , and

air-dry soil moisture θr , respectively, θ is the soil moisture in the top soil layer.

Depending on soil colours, αs varies approximately between 0.13 to 0.26, while

the corresponding values of αr are about twice as large.

4.3 Soil Moisture

The simplest scheme for modelling the evolution of soil moisture is the singlelayer bucket scheme. The soil layer is considered to be a bucket with no

drainage at its lower boundary and to act as a reservoir for precipitation

until it is full. The excess water is treated as surface runoff and is not available for evapotranspiration (Fig. 4.4). The depth of the soil layer is commonly

chosen as 1 m, based on the fact that soil moisture within this layer shows

clear annual variations. Central to the bucket scheme are the concepts of field

capacity, θf c , and wilting point, θwp , which reflect the hydraulic properties

of different soils. Observations show that the rate of water flow in an unsaturated soil decreases once θ reaches a value close to θs . The soil moisture at

which internal flow almost ceases is considered to be a physical property of

the soil and is known as field capacity. The wilting point is defined as the soil

4.3 Soil Moisture









Soil water flux



(a) Bucket

(b) Force−Restore

Fig. 4.4. (a) A representation of the bucket scheme for soil-moisture simulation.

(b) as for (a), but of the force-restore scheme. Pr , Ev and Ro are precipitation,

evapotranspiration and runoff, respectively

moisture below which water extraction by plant roots presumably ceases and

plants wilt. The available soil moisture, θa , is defined as

θa = θ − θwp


The temporal variation of θa is determined by the soil water budget equation:

P r − R o − Ev






where hB is bucket depth, Pr is precipitation and Ro is runoff. Runoff is

calculated as

θwp ≤ θ < θf c



Ro =

P r − Ev

θf c < θ ≤ θ s

Evaporation occurs at its potential rate, Ep , when soil moisture is higher than

a critical level of 0.75θf c . Otherwise, a moisture availability factor, β, is used

to adjust the potential rate of evaporation, according to

Ev = βEp


with β = min(1, θa /0.75θf c ).

The bucket scheme is simple. In most circumstances, it produces reasonable estimates for soil moisture over a depth of hB (about 1 m). However, as

far as wind erosion is concerned, we are mostly interested in the soil moisture

of the very top layer, which is probably less than 10 mm deep. For this reason, a direct application of the bucket scheme is inadequate for wind-erosion

modelling. One possibility is to divide the soil profile into different zones,

each of which behaves as a single layer bucket. In this case, precipitation cascades from the upper to the lower zones, when the upper zones reach the

field capacity. The zoned-bucket scheme is a considerable improvement over

the single-layer bucket scheme. One other shortcoming of the bucket scheme

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