A history of mesoscale model development

Asia-Pac. J. Atmos. Sci., 50(1), 121-131, 2014

DOI:10.1007/s13143-014-0031-8

REVIEW

A History of Mesoscale Model Development

Jimy Dudhia

National Center for Atmospheric Research, Boulder, Colorado, U. S. A.

(Manuscript received 23 October 2013; accepted 17 January 2014)© The Korean Meteorological Society and Springer 2014

Abstract: The development of atmospheric mesoscale models from

their early origins in the 1970’s until the present day is described.

Evolution has occurred in dynamical and physics representations in

these models. The dynamics has had to change from hydrostatic to

fully nonhydrostatic equations to handle the finer scales that have

become possible in the last few decades with advancing computer

power, which has enabled real-time forecasting to go to finer grid

sizes. Meanwhile the physics has also become more sophisticated

than the initial representations of the major processes associated with

the surface, boundary layer, radiation, clouds and convection. As

resolutions have become finer, mesoscale models have had to change

paradigms associated with assumptions related to what is considered

sub-grid scale needing parameterization, and what is resolved well

enough to be explicitly handled by the dynamics. This first occurred

with cumulus parameterization as real-time forecast models became

able to represent individual updrafts, and is now starting to occur in

the boundary layer as future forecast models may be able resolve

individual thermals. Beyond that, scientific research has provided a

greater understanding of detailed microphysical and land-surface

processes that are important to aspects of weather prediction, and

these parameterizations have been developing complexity at a steady

rate. This paper can just give a perspective of these developments in

the broad field of research associated with mesoscale atmospheric

model development.

Key words: Mesoscale modeling, numerical weather prediction,

physics parameterization

1. Introduction

Today, regional mesoscale atmospheric models are essential

tools in a variety of meteorological applications. Here we will

outline a history of their development from the 1970’s when

they were used with grid sizes of tens of kilometers to simulate

mesoscale weather systems over several days until now when

their use has extended to cloud-resolving kilometer and sub-

kilometer scales or their timeframes have extended to months

or years for regional climate applications. Similarly their usage

has expanded from the few expert groups developing these

models at universities and government laboratories to broader

categories of users sharing community models, such as MM5

and WRF. In fact, the advent of community models has led to a

rapid and continuing increase in the number of groups running

atmospheric models by providing fully developed and tested

models that are made easy to port, configure and initialize,

accelerating research and applications. This has also been fa-

cilitated by the considerable increase in computer power for a

given cost and the capability for each user group to have their

own computer rather than having to share a supercomputer as

was the case in the earlier years.

The challenge of simulating the atmosphere with fidelity to

reality has been met with a great deal of success, but there are

many technical areas within the model that have been advanced

to make this possible. It is precisely because modelling the

atmosphere requires a range of disciplines and expertise that

the concept of a community or shared model has been suc-

cessful. Very few individual centers would have all the expert-

ise required for developing a full atmospheric model in-house

and from scratch, so by bringing together experts from a range

of research disciplines, it is made almost necessary that de-

velopment is a shared effort leading therefore to shared usage.

This has happened both in operational and research model

development. On the operational side, over the last few decades

several consortia of national hydrometeorological services

(NHMSs) have developed and/or shared models (Europe’s

HIRLAM, France’s ALADIN, Germany’s COSMO and HRM,

United Kingdom’s UM) while some nations have used freely

available research-community models developed in the US

(WRF, MM5, Eta, RAMS). Today over eighty nations run

their own regional forecast model(s), many of these shared as

listed above, and this number is growing according to World

Meteorological Organization statistics (Technical Progress Re-

port at http://www.wmo.int/pages/prog/www/DPFS/Progress-

Reports/2011/2010_GDPFS-NWP.html) as more nations gain

their own computing resources and expertise with model usage.

Figure 1 summarizes the global status of NHMSs using re-

gional NWP models as of around 2012. On the research side, it

is even more true of universities and some government labora-

tories that they don’t have all the expertise required to develop

in-house models, and they rely on community models as a

basic tool for their research. A necessary ingredient required is

a central institution that takes it as their duty to maintain the

community code, including supporting its usage, providing tu-

torials for new users and documentation, and acting as a center

for new developments from the community to become part of

the shared model.

Corresponding Author: JimyDudhia, Mesoscale and MicroscaleMeteorology Division, National Center for Atmospheric Research,P. O. Box 3000, Boulder, CO 80307, U. S. A.E-mail: [email protected]

122 ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

Atmospheric models suitable for weather prediction consist

of several distinct components each with their own scientific

considerations, while the model as a whole is the sum of these

parts and their interactions. For the purposes of this article we

will separate the dynamical and numerical aspects of the

model from the physical parameterizations that are themselves

subdivided into categories.

The dynamical and numerical parts of the model, while

contributing importantly to efficiency, effective resolution and

its capabilities, whether high-resolution or global, are also less

variable in their effect on model results than changes in phy-

sical parameterizations would be. Obviously the dry dynamical

equations of the atmosphere are well known, and methods of

solution have evolved that can numerically represent these

equations efficiently in models. In regional models, the main

evolution has been from hydrostatic to nonhydrostatic models

and this will be discussed in the next section. Models are built

around a dynamical core, and while this stays relatively fixed

over the years, physical parameterizations undergo continuous

evolution and additions or replacements. This reflects where

the uncertainties lie in atmospheric models. Unlike dynamics,

no aspect of the physics has a set of equations as rigid as those

for the fluid dynamics. In every area of physics decisions have

to be made regarding what is resolved or not by the dynamics,

what processes affect the atmospheric evolution most, and what

level of sophistication and computational expense is affordable

for the application in mind. These types of decisions lead nat-

urally to a wide range of parameterizations of different levels

of complexity and cost for each sub-category of the physics.

Broadly, the categories of physics are as follows.

(1) Resolved cloud physics, also known as microphysics,

that handles cloud and precipitation processes including

moist phase changes and associated latent heating, water

and ice particles and their evolution an interactions, and

fall-out of precipitating particles.

(2) Unresolved convective column physics, also known as

cumulus parameterization needed at coarser resolution

to handle unresolved vertical latent-heat driven trans-

ports by updrafts and downdrafts within convection.

This may sometimes also include sub-grid shallow non-

Fig. 1. Map showing distribution of NHMSs using regional numerical weather prediction models. Colors show related models(some countries use multiple models, so only one example is shown for illustrative purposes). The main colors show WRF-ARW(tan), WRF-NMM (red), ALADIN (dark blue), COSMO (light blue), HIRLAM (green), UM (pink), HRM (purple), MM5 (orange),no model (white).

Fig. 2. Schematic of physics and their interactions within a typicalNWP model.

31 January 2014 Jimy Dudhia 123

precipitating convection.

(3) Surface physics, including processes that lead to surface

heat and moisture fluxes that include those in the soil

and related to vegetation and snow cover, and possibly

urban areas.

(4) Vertical mixing and planetary boundary layer physics that

handle sub-grid vertical eddy transports especially of

unresolved thermals near the ground, but also possibly

elevated turbulence.

(5) Radiative physics, handling both longwave and short-

wave components including the diurnal cycle, interaction

of radiation with clouds and aerosols, and fluxes of

radiation to and from the surface.

Figure 2 illustrates that physics options should not be con-

sidered as independent of each other, because there are direct

and indirect interactions that are necessary to take into account

when developing, evaluating and improving weather prediction

models.

We will not consider ocean modeling here as that is a sep-

arate component that only becomes important in specialized

coupled applications such as long-term climate modeling, or

hurricane-surface interactions. In the model physics to be con-

sidered here, the ocean and water surfaces will be taken as a

simple parameterization that provides the necessary fluxes to

the atmosphere and that can evolve only in a specified, not

prognostic, way.

In Section 2, we will describe the evolution of model

dynamics and numerical methods, with particular attention to

the Penn State/NCAR Mesoscale models, 4th and 5th generation,

(MM4 and MM5) and Weather Research and Forecasting

model (WRF). Similarly in Section 3, the various physical par-

ameterizations and their development over time will also focus

on these representative and widely used models that underwent

their main development and growth of usage in the last 25

years.

2. Dynamics and numerical methods

Some of the earliest mesoscale models were developed in

the 1970’s in the United States Pennsylvania State University

(Anthes and Warner, 1978) and National Meteorological Center

(history documented by Shuman, 1989), United Kingdom

Meteorological Office (Tapp and White, 1976) and Australian

Numerical Modeling Research Center (McGregor et al., 1978).

The term “mesoscale models” here means atmospheric models

with sufficient physics for numerical weather prediction in

limited-area domains allowing for topography and map projec-

tion scale factors required for large areas. These are initialized

from, and take boundary conditions from, meteorological

gridded analyses, and have to least represent in some way all

of the physical processes listed as requirements in Section 1 to

maintain credible analyses in their forecasts.

Another class of models being developed at the same time

were the more idealized cloud models (Miller and Pearce, 1974;

Clark, 1977; Cotton and Tripoli, 1978; Klemp and Wilhelmson,

1978, for example) having limited physical processes that

would include microphysics, sub-grid turbulence and possibly

surface effects like friction and topography, but rarely surface

fluxes or radiative effects. Cloud models were designed to run

in small areas covering maybe a single convective system

using uniform single-sounding initial conditions and grid sizes

of order one kilometer, and their dynamics was necessarily

nonhydrostatic. Mesoscale model grid sizes were in the tens of

kilometers meaning that they could use the slightly simpler

hydrostatic approximation to eliminate a vertical momentum

equation, and in contrast to cloud models that were often cast

in height-based coordinates, the earlier mesoscale models mostly

adopted pressure-based coordinates in which the hydrostatic

approximation was much simpler. Later in the 1980’s nesting

capabilities were developed for some of these models to allow

regional refinement (e.g., Zhang et al., 1986), and with the

Table 1. List of Acronyms and Abbreviations.

ALADINAire Limitée Adaptation dynamique Développement InterNational (France)

ARPS Advanced Regional Prediction System (USA)

ARW Advanced Research WRF (USA)

BATS Biosphere-Atmosphere Transfer Scheme

COAMPSCoupled Ocean/Atmosphere Mesoscale Prediction System (USA)

COSMO Consortium for Small-scale Modeling (Germany)

Eta Eta-coordinate model (USA)

GEM Global Environmental Multiscale Model (Canada)

GRAPESGlobal/Regional Assimilation and PrEdiction System (China)

GRIMs Global/Regional Integrated Model System (S. Korea)

HARMONIEALADIN-HIRLAM collaborative model (France/Europe)

HIRLAM High Resolution Limited Area Model (Europe)

HRM High Resolution Regional Model (Germany)

LES Large-Eddy Simulation

LM Lokalmodell (Germany)

MM5Pennsylvania State University / NCAR Mesoscale Model (5

th Generation)

NCAR National Center for Atmospheric Research (USA)

NHM Nonhydrostatic Model (Japan)

NHMS National Hydrometeorological Services

NMM Nonhydrostatic Mesoscale Model (USA)

NWP Numerical Weather Prediction

PBL Planetary Boundary Layer

RAMS Regional Atmospheric Modeling System (USA)

RSM Regional Spectral Model (USA)

UM Unified Model (United Kingdom)

WRF Weather Research and Forecasting Model (USA)

124 ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

steadily increasing computer power it was becoming clear that

nonhydrostatic mesoscale models would be needed. The Tapp

and White (1976) UK Met Office model had been an early

nonhydrostatic model used for mesoscale applications, later

updated by Cullen (1993), and others followed. Dudhia (1993)

developed a nonhydrostatic dynamical core for MM5 adapting

the coordinate from sigma-pressure of the hydrostatic meso-

scale model, MM4, to sigma-reference-pressure, which was

more height-like. The nonhydrostatic equations permitted sound

waves and used the time-splitting techniques of Klemp and

Wilhelmson (1978) to handle them, but incorporated the MM4

physics with temperature and pressure as variables in place of

potential temperature and Exner function used by Klemp and

Wilhelmson as is typical of cloud-scale models. A similar

technique to MM5 was adopted by Germany (LM, Doms and

Schaettler, 1997). At about this time the Tripoli and Cotton

(1982) cloud-scale nonhydrostatic model was being converted

to a mesoscale model (RAMS) by adding the necessary physics

components, real terrain and mapping capabilities, and cloud

to mesoscale model development also took place for ARPS

(Xue et al., 1995).

The above models are grid-point or Eulerian models, but

nonhydrostatic models using semi-Lagrangian techniques had

also by 2000 been developed in Canada (GEM, Tanguay et al.,

1990) while regional spectral models were developed with

nonhydrostatic capabilities in France (ALADIN-NH, Bubnova

et al., 1995) and the US (RSM, Juang et al., 1997).

Today many of the world’s NWP centers run nonhydrostatic

models: WRF (ARW−Klemp et al., 2007 and NMM−Janjic,

2003), MM5, COAMPS and RSM in the US and various

countries, ALADIN/ HIRLAM/ HARMONIE (France and

European consortium), COSMO (Germany and consortium),

UM (UK and partners), GEM (Canada), NHM (Japan),

GRAPES (China), etc. However, it is only in the last decade

that national NWP operational grid-sizes have been in the 4

km or less range that can fully test nonhydrostatic dynamics in

convective situations (reviewed by Saito et al., 2007).

Lateral boundary conditions for regional forecast models

most often come from global models that are run first (not

needing boundary conditions). A limited number of centers

(~15) run global models and this number has not been growing

over the last decade. The NHMSs often obtain global model

boundary conditions via data made available by the global

modelling NHMSs either within their consortium or made

freely available in near real-time on the Web by some centers

(e.g., NCEP). The most common method of driving regional

models is via a Davies relaxation zone occupying the points

nearer the boundaries, where a time- and space-interpolated

external analysis is used for nudging the primary atmospheric

variables. However, there are methods such as spectral coupling

(e.g., NCEP’s RSM) where longer waves are also provided to

the regional model interior. Methods of seamlessly unifying

global and regional models using a local refinement were pion-

eered within Canada’s GEM model, and for research purposes

for MM5 by Dudhia and Bresch (2002), and are ongoing with

NCAR’s new variable-grid MPAS model (Skamarock et al.,

2012) and in other current global model development efforts.

Advection techniques have also been divided among the

semi-implicit semi-Lagrangian approach (e.g., UM, GEM,

GRAPES, HIRLAM(option)) and explicit Eulerian approaches

used by the others listed above. Another separation is whether

to consider sound waves with split steps following the Klemp

and Wilhelmson approach (MM5, WRF, NHM) or implicitly

(Tapp and White, 1976; GEM, RSM, ALADIN, NHM(option))

with the latter approach requiring a global Helmholtz solver

for the pressure. The time-split approach has the benefit of all

the computations being local which allows for easier paral-

lelization on large computers by reducing the inter-processor

communication stencil to just nearby neighboring points, which

reduces the volume of data that needs to be passed and this

leads to more efficiency.

The dynamics also has a “grey zone” where it has to be

decided whether nonhydrostatic dynamics is necessary. The

general rule is that if horizontal scales become short enough to

be comparable with vertical scales of features, nonhydrostatic

dynamics is needed. Thunderstorms have aspect ratios near

one and therefore fundamentally require the correct dynamics,

noting that parcel theory whereby convective available poten-

tial energy is converted to updraft kinetic energy is a purely

nonhydrostatic idea. For flow over topography the tilt associ-

ated with nonhydrostatic mountain waves occurs as the hori-

zontal scale of the topography reduces towards 1 km but is not

seen at more than 10 km mountain widths (e.g., see Dudhia,

1993). It is very clear that convection-permitting models have

to be nonhydrostatic, and these would be in the range of grid

size less than 5 km, while at 10 km, the dynamics is well

approximated as hydrostatic. The grey-zone scale, defined here

by dynamical aspect ratio, of 5-10 km is similar to what we

will see later for convective parameterization.

3. Physics parameterizations

a. Resolved moist processes.

Grid-scale saturation was initially, in low-resolution meso-

scale models, often handled without explicit cloud or precipi-

tation variables, just having the function of releasing latent

heat and providing precipitation immediately at the surface

below. For large-scale mesoscale weather models, this approach

was adequate as a first-order representation, while surface radi-

ation would approximate cloud fractions with empirical func-

tions of humidity in the column above to obtain the primary

cloudiness effect. Such models only need to add water vapour

as an advected variable in addition to the dynamical variables

of the model. Grid-scale condensation is typically achieved by

large-scale vertical motion associated with synoptic conditions

or orography or other diabatic cooling that may occur from

simple radiative schemes or advective processes over colder

surfaces. Meanwhile the early cloud-scale models were de-

veloped with simple microphysics, such as the classic warm-

31 January 2014 Jimy Dudhia 125

rain Kessler (1969) scheme that represents not only cloud

condensation and evaporation according to saturation level, but

also the production of rain by droplet growth (autoconversion)

and accumulation of cloud by falling rain (accretion) and its

evaporation and fall speed. These required additional advected

variables for cloud and rain, and such schemes were adequate

for the idealized thunderstorm dynamics or squall line studies

of those models, representing the major latent heating effects

of the updrafts and downdraft formation that help the

organization. By the mid 1980’s these simpler microphysics

schemes were also being added to mesoscale models (e.g.,

Hsie et al., 1984).

In mesoscale models, grid homogeneity has been commonly

assumed when dealing with microphysical quantities (e.g.,

WRF), but some models have also considered that there may

be cloudy and clear fractions (e.g., GRIMs), or even variability

within a cloud (e.g., subcolumn methods, Pincus et al., 2006).

The lack of cloud fractions becomes less of an approximation

as the grid size reduces, but there are some instances such as

unresolved cumulus fields where this would be beneficial.

Later a layer of complexity was added with ice processes,

following ideas such as Rutledge and Hobbs (1983) to repre-

sent the initiation and growth of ice crystals, aggregation into

snow particles, and their fall and melting terms. Dudhia (1989)

adapted these for a mesoscale model (MM4) to obtain impor-

tant tropical stratiform processes, and later recognized the im-

portance of ice-crystal fall-speed for multi-day simulations to

not overestimate ice cloud coverage. This need becomes even

more clear in regional climate applications when verified

against outgoing longwave radiation (OLR) that is dominated

by the cirrus extent. With ice saturation being lower than water

saturation, various methodologies were adopted to handle sat-

uration processes below freezing, sometimes with a weighted

saturation level between that of water and ice based on either

temperature or species present. Dudhia (1989) preferred the ice

particles to respond only to ice saturation levels, however, and

this approach has been carried through to many current micro-

physics schemes. Verifications of relative humidity in meso-

scale models indicated the necessity of ice-phase processes in

preventing high biases in the upper troposphere. Another aspect

of this mesoscale ice approach was to carry only three

variables, vapour, ice/cloud, and snow/rain, to reduce advection

cost. Below the freezing level, only water processes were

handled, while above was ice, enforcing freezing/melting for

transport or fall at the freezing level. While efficient, this 3-

class approach cannot be used at higher resolution because

supercooled water and gradual melting were precluded. Later

so-called mixed-phase 5-class schemes added the extra ad-

vected variables (Hong et al., 1998; Reisner et al., 1998; Hong

et al., 2004). Mesoscale models typically have long time steps

for 10 km grids and fine vertical resolutions, perhaps 100 m,

for the surface and boundary-layer processes. When precipi-

tating species such as rain are explicitly carried, their fall terms

may have to be treated on split sub-steps, or use Lagrangian

methods (e.g., Juang and Hong, 2010), for numerical stability

if their fall speed can move them more than one vertical level

in a model time-step as occurs at these mesoscale resolutions.

Cloud-resolving models typically have time steps and grid

sizes that do not run into these limits.

As mesoscale model grid sizes refine to much less than 5

km, an important dynamical transition takes place as individual

updrafts may be represented explicitly with their large buoy-

ancy-driven vertical motions, which is a nonhydrostatic effect.

Reaching these “convection-permitting” scales, as they are

called, it is recognized that the microphysics needs at least a 6-

class approach (e.g., Lin et al., 1983; Tao et al., 1989; Hong

and Lim, 2006), to distinguish the snow from denser ice

particles (graupel/hail) formed through mixed-phase interac-

tions (riming) that are associated with resolved vertical motions

of order 10 m s−1 or more. This is important because schemes

with snow and ice alone would underestimate the fall speeds

and rain intensity close to the convective cores, and typically

the rainfall is formed by mixed-phase growth through the ice

phase and melting.

Development of microphysics schemes for cloud and meso-

scale models continues with the increasing use of double-

moment schemes that predict number concentrations in add-

ition to mass mixing ratios (e.g., Thompson et al., 2008;

Morrison et al., 2009; Lim and Hong 2010). The removal of

internal assumptions regarding number concentrations increases

the flexibility of these schemes to adapt to the availability of

cloud condensation or ice nuclei and to better represent fallout

processes such as size-sorting. The categorization into ice,

snow and graupel is fairly standard, but somewhat arbitrary, as

it is recognized that real particles do not so sharply divide

along these lines, and recent work (e.g., Dudhia et al., 2008) is

aimed at a better gradation of particle densities and size distri-

butions at least for fall-speed calculations. Bin microphysics

models that represent each size bin separately and carry a

hundred or more arrays have been developed for research

purposes, but are many years away from being usable in

mesoscale models on a regular basis. These are, however,

increasingly being used in helping to develop the bulk ap-

proaches (e.g., Lebo and Morrison, 2013).

b. Unresolved convective processes

Mesoscale models with grid sizes more than 10 km add-

itionally have to represent sub-grid convective column pro-

cesses associated with updrafts and downdrafts that correspond

to unresolved mass transports. This is known as the cumulus

parameterization problem. In a hydrostatic framework, these

schemes are not allowed to produce a net mass flux, and

therefore all updraft sub-grid transports are balanced by a

combination of environmental subsidence and downdraft trans-

ports. The scheme triggers only with convective instability in

the column, allowing the condensation-driven updraft and sub-

sidence fluxes that cause tropospheric warming and carry

boundary-layer moisture to high levels. Some schemes also

have evaporation-driven downdrafts, cooling the boundary

126 ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

layer. The complexity of the convective sub-grid processes has

led to a wide variety of cumulus parameterizations. The main

classes are the adjustment type (Betts and Miller, 1986), mois-

ture convergence type (Kuo, 1974; Kuo and Anthes, 1984) and

mass-flux type (e.g., Arakawa and Schubert, 1974;Tiedtke,

1989; Kain and Fritsch, 1990; Grell, 1993).

Adjustment schemes use a post-convective mixed profile as

a target for relaxation, while the more common mass flux

schemes explicitly handle the transport processes and updraft

properties. The schemes vary according to how they trigger,

how they handle entrainment and detrainment, single or multi-

ple updrafts, downdrafts if any, and convective mass flux mag-

nitude among other things. The convective mass flux deter-

mines the heating and precipitation rate and how quickly the

instability is removed, and is a key parameter that governs how

active a scheme is. The mass-flux profile also has a major in-

fluence on the resolved-scale response and differs markedly

among schemes according to their internal assumptions. The

earlier Kuo-type approach used moisture convergence in a

column to determine convective rainfall, while Arakawa-

Schubert, designed for larger grid sizes, used a quasi-equilibrium

approach whereby convection balances the large-scale desta-

bilization rate. Other approaches empirically define a time

scale over which the instability is removed to determine the

mass flux required (Betts-Miller, Kain-Fritsch, Tiedtke).

Some convective schemes now also transport momentum

either as a passive scalar or accounting for in-cloud pressure

gradients (e.g., Han and Pan, 2011). There are indications that

momentum transport can be important in organized convective

systems in a sheared environment, and that in some situations

this transport can be countergradient, not just a downgradient

mixing effect.

As grid sizes have evolved below 10 km, there are so-called

“grey-zone” issues where the assumptions of the convective

scheme become invalid, but also the grid size is too coarse to

permit resolved updrafts. The main problem with mass flux

schemes in particular is their assumption that the grid column

contains the updraft and all its associated subsidence, but in

reality subsidence may be broader than the column size. Note

that these schemes still work because their heating drives a

resolved vertical motion and subsidence, but it is not clear

whether the net effect of this will be realistic. There is also a

balance between resolved clouds and convective ones that lead

to a wide variety of convective rainfall ratios between schemes,

some providing the majority, some leaving most to resolved

scales. Convective schemes tend to release instability quickly,

possibly too quickly in many cases as evidenced by an early

bias in the diurnal precipitation maximum over land areas,

which is commonly seen. On the other hand, if left to resolved

scales, there is often a delay followed by large convection

when the grid size is too coarse to properly represent the con-

vective development from shallow to deep clouds.

Some recent efforts (e.g., Grell and Freitas, 2013) have been

made to design grey-zone parameterizations that can auto-

matically transition from fully parameterized to resolved con-

vection based on measures that depend on the grid size or that

can spread the subsidence effect beyond the convective grid

column.

Even at cloud-permitting scales, shallow convection may still

need to be parameterized to represent non-precipitating vertical

mixing driven by shallow instability. Some models consider

this as a part of the deep convection scheme; others may

consider it part of the planetary-boundary layer scheme, or as a

standalone scheme. There are two basic classes of shallow

scheme: the mass-flux type (Han and Pan, 2011) and the en-

hanced vertical mixing type (Tiedtke et al., 1988). Such schemes

are typically active over large areas, and especially over oceans

have a significant impact on mean thermodynamic profiles in

the lower troposphere.

c. Surface processes

Early schemes were designed with low vertical resolution in

mind and perhaps only one model level in the lowest kilometre

representing the boundary layer (Deardorff, 1972). These used

bulk aerodynamic formulas to relate the lowest level values to

surface fluxes that depend on a given surface temperature. A

surface temperature is specified, such as commonly is done for

water points, or a prediction is made by a land-surface model

or simple energy budget. Originally the land may have been

represented by a single-layer slab using a so-called force-

restore method that predicted its temperature based on an

energy budget with a deeper layer providing a restoring force

to a longer-term fixed temperature (e.g., see Deardorff, 1978).

These models had the basics to capture the diurnal cycle and

variable thermal inertia, but were limited in response time and

often treated moisture simply through a climatological avail-

ability parameter, not keeping a time-dependent soil moisture

variable. Later bucket models enabled a variable surface mois-

ture that responded to rainfall and evaporation, and possibly

snow cover changes, but it was only the advent of multi-layer

land-surface models (BATS−Wilson et al., 1984; SiB−Sellers

et al., 1986; Noah−Chen and Dudhia, 2001) that finally allowed

the more complex moisture flux associated with vegetation

and the root zone so that evapotranspiration process could be

handled more properly. The land models may contain multiple

(e.g., two to six) layers of soil temperature and moisture and

possibly canopy and snow-cover fields too as prognostic

variables with diffusion and water drainage in the soil.

As inputs from the atmosphere, land models require “ex-

change coefficients” that provide information on the stability

and wind. These coefficients are the proportionality factor

between, for example, ground to lowest-layer temperature

difference and heat flux. With this information the land model

can provide consistently updated surface temperatures and heat

fluxes, similarly for moisture flux. The method of computing

these coefficients uses similarity theory that takes advantage of

empirical profiles that have been found to be universal in the

surface layer. These profiles can relate the lowest model level

values with fluxes or stresses at the surface taking into account

31 January 2014 Jimy Dudhia 127

stability effects. The concept the concept of a separate smaller

thermal roughness length or a viscous sub-layer, that resists

scalar fluxes more than for the momentum roughness length,

has been found beneficial in many cases rather than the original

method of using the same roughness length for momentum and

scalars. Conversely in free convection an enhancement using,

for example, the convective velocity scale (Beljaars, 1995) in

addition to the friction velocity in the thermal and scalar fluxes

(not momentum) is often used that represents the convective

boundary-layer eddies that are present even in weak mean

winds. Other non-stability dependent enhancements for coarse

resolution have allowed for sub-grid variability (e.g., Mahrt and

Sun, 1995), which alleviates biases seen in low-wind situations

on coarse grids.

Today’s mesoscale models have sophisticated land-surface

components that provide heat and moisture fluxes as lower

boundary conditions for a separate boundary-layer model. For

momentum, a stress that also depends on surface roughness

and stability is defined as an input to the boundary-layer model.

In mesoscale applications of up to a few days simulation, the

water temperatures can be held constant and require no physics

to predict them. The only physics associated with water sur-

faces is in determining their drag effect that may depend on

waves. This is usually applied as a local windspeed-stress

relation such as that of Charnock (see Delsol et al., 1971). For

longer simulations, such as in regional climate applications,

the sea-surface temperature can be updated from data or

climatology. More sophisticated treatments involve coupling

ocean and wave models to atmospheric models to predict the

entire system.

d. Planetary boundary layer

A complex sub-grid problem in mesoscale models is the re-

presentation of the boundary layer, both in stable and unstable

conditions.

Going beyond the bulk Deardorff approach described in the

previous section, has been deemed important to represent the

correct growth and decay of the boundary layer, to improve the

prediction of surface atmospheric properties, and to better

develop diurnal convection. Even with improvements in the

vertical resolution of the boundary layer, there are important

sub-grid processes.

For unstable boundary layers, there are a variety of methods

to handle sub-grid thermals that transport surface fluxes

through the boundary layer. The primary role of the boundary-

layer scheme in unstable conditions is to represent the process

of mixing that takes place through thermals that have scales

near 100 meters, and are thus sub-grid scale in mesoscale, and

even cloud-permitting-scale models. These thermals transport

heat, moisture and momentum quickly through the boundary

layer, and also entrain air from above as the boundary layer

grows in the daytime. Without such a parameterization, re-

solved motion and/or local vertical mixing would be deficient

in representing the speed of this mixing giving unrealistic

thermodynamic profiles near the ground.

There are four primary approaches that are designed to work

with vertical resolutions that have typically at least five levels

in the boundary layer, or lowest kilometre, and that can there-

fore resolve a PBL growth rate reasonably. One early widely

used multi-layer approach with enhanced vertical diffusion

based on stability was from Louis (1979). The second is an

extension of the bulk approach to also include a non-local flux

term representing transport by thermals (Zhang and Anthes,

1982; Troen and Mahrt, 1986; Hong and Pan, 1996). These

schemes recognize that a well-mixed PBL is near-neutral but

still has vigorous heat transport through its depth despite the

lack of a local gradient. It is clear that thermals transport heat

independently of local downgradient fluxes and an added term

provides for this. It is activated by a positive surface heat flux,

and in the Troen-Mahrt method also used by Hong and Pan

(1996) and Hong et al. (2006) a column-constant (“gamma”)

term adds to the local-gradient term in the sub-grid heat flux.

Zhang and Anthes (1982) and Pleim (2007) represent thermals

with a direct flux between the surface layer and other PBL

layers (following ideas of Blackadar, 1979), a non-local mixing

approach known also as transilient mixing (Stull, 1984). Add-

itionally such approaches enhance the vertical diffusion co-

efficient using a profile that maximizes within the PBL depth.

Entrainment may be handled by overshooting thermal depths,

or some schemes (YSU, Hong et al., 2006) may add an explicit

entrainment flux calculation. A third related approach uses a

mass-flux model, similar to cumulus schemes, to achieve the

non-local flux independent of the diffusion term (the eddy-

diffusivity mass-flux, EDMF, approach, e.g., Siebesma et al.,

2007). These entrain mass in the lower PBL and detrain it in

the upper part. The fourth approach is a turbulent-kinetic-

energy (tke) approach pioneered by Mellor and Yamada (1974,

1982), and most modern tke schemes are variants on this

original method (Bougeault and Lacarrere, 1989; Janjic, 1994;

Sukoriansky et al., 2005; Nakanishi and Niino, 2006). In

mesoscale models, the tke has a prognostic equation and the

diffusion coefficient depends on its magnitude and a length

scale. Turbulent kinetic energy responds to stability, shear and

dissipation, and most models consider this part similarly, but

they all differ primarily in methods of computing length scales.

To date, these schemes have been applied as local schemes in

that the form of the vertical mixing remains as a diffusion

equation. Being local and downgradient, they have a tendency

towards leaving a slightly superadiabatic profile through the

PBL, and also a tendency to entrain less at the PBL top re-

sulting in cooler, moister and shallower PBLs than those that

have more vigorous entrainment. The tke approach has an

advantage in maintaining a memory of the turbulence, which

may help with the evening transition, and, if the model add-

itionally advects this tke, there is also a downstream memory

as the air crosses different surface types.

In models above the boundary layer there is also a vertical

diffusion process that is typically parameterized in terms of the

local Richardson number to represent elevated turbulent layers.

128 ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

As mentioned above, some PBL schemes also may include

shallow convection via carrying information about latent-heat-

produced buoyancy in cloud-topped boundary layers, but the

majority of PBL schemes essentially just assume dry mixing

leaving resulting condensation to be handled by other physics.

For stable conditions a further challenge is that the model

vertical resolution makes it difficult to represent the surface

behaviour just from the lowest model grid level that may be

tens of meters above the ground because there is some

decoupling in thin stable layers, and also some complex local

unrepresented behaviour such as drainage flows and inter-

mittent turbulence that impact the real surface fluxes.

For coarse-scale models with grid sizes larger than 10 km,

gravity wave drag may also be parameterized to represent the

sometimes important momentum transport of unresolved oro-

graphic gravity waves that break at high levels. This is like a

non-local vertical momentum transport or stress.

Recently mesoscale models have been used increasingly for

wind-energy applications and some efforts have focused on

evaluating and improving surface winds in complex terrain

with this consideration (Jimenez and Dudhia, 2012).

There are grey-zone issues for the PBL schemes too, but

these are likely not to occur in forecast applications until

cloud-permitting model grid sizes become much less than

1 km, which is computationally beyond present-day real-time

mesoscale capabilities. Large-eddy simulation models (e.g.,

Moeng et al., 2007) have already been designed to represent

grid sizes one to two orders of magnitude below 1 km, and

using their sub-grid methods will alleviate the need for PBL

parameterizations by explicitly resolving the primary trans-

porting eddies in the boundary layer. At these scales, the

formerly one-dimensional column-by-column boundary layer

parameterization becomes a fully three-dimensional turbulence

problem with locally determined more isotropic sub-grid

mixing processes. This amounts to a simplification of physics

at higher resolution that is somewhat similar to that in which

the cumulus scheme problem is alleviated by resolving the

primary updrafts. In both cases, non-local sub-grid transports

are replaced by local and resolved transports.

e. Radiation

Early mesoscale models usually had very simple physics,

with perhaps no cloud or precipitation explicitly predicted in

the atmosphere. However, representation of the diurnal cycle

at the surface required at least a computation of surface

radiative fluxes, and this was first done with surface radiation

schemes that would take column-integrated precipitable water

and use the relative humidity in atmospheric layers to estimate

cloud fractions (e.g., Carlson and Boland, 1978). For the

atmosphere, some radiative cooling was also usually added to

at least get the mean diurnal clear-sky effect. Later as models

started to explicitly carry cloud and precipitation variables, it

made sense to have layer-by-layer radiation interact directly

with them giving cloud-radiative interaction profiles that may

be important in some situations (e.g., Dudhia, 1989). The

introduction of more sophisticated atmospheric radiation

schemes that also handled water vapour, ozone and carbon

dioxide effects, advanced these schemes more to the present

state of the parameterization (Fu and Liou, 1992; Chou et al.,

1994; Mlawer et al., 1998). Radiation is still handled indepen-

dently in each model column using the plane parallel assump-

tion in each model layer.

Cloud fractions within a mesoscale model grid area can also

be considered by radiation schemes that then have to make an

overlap assumption for fractions at different model levels.

Convective parameterized sub-grid clouds may contribute to

the cloud fraction, while microphysical schemes in mesoscale

models often consider their clouds to be uniform over the grid

area, so these may provide only zero and one as fractions, un-

less the microphysics explicitly also includes a cloud fraction.

At the surface, slope effects have been added in some

models to account for resolved topographic gradients that

modify the surface solar flux. Three-dimensional effects bet-

ween columns would strictly be needed as the grid aspect ratio

approaches one for small grid sizes, but adding these would be

complicated, and these effects are not considered necessary for

most applications.

Radiation interacts with the surface properties through its

albedo providing reflection, and emissivity with temperature

determining its radiated longwave flux. Clouds significantly

impact the radiation, and ideally the microphysics schemes

would represent droplets and ice crystals in the same way as

radiation as done in recent work by (Liang et al., 2012;

Thompson and Eidhammer, 2014), but often these are treated

independently. Ozone and aerosols also have important im-

pacts, especially on shortwave radiation and usually have been

represented with a climatology in mesoscale models, except

for in specialized atmospheric chemistry models that can

predict their distributions.

As mesoscale models become used for solar energy appli-

cations there is an increased focus on aerosols that impact

direct radiation (Ruiz-Arias et al., 2013), with a challenge of

providing near real-time information on them. Similarly the

forecasting of clouds, including non-precipitating ones, be-

comes a more emphasized area of evaluation and improvement,

given their radiative impact.

4. Conclusions

The last four decades have seen a rapid advancement of

mesoscale numerical weather prediction models from the crude

100 km grids with few vertical levels and very simplified

physical processes to today’s models nearing 1 km grids with

sophisticated sub-grid representations of a variety of micro-

physical processes, surface processes, turbulent mixing and

radiative transfer. The dynamics has evolved towards the less

approximated and more generally applicable nonhydrostatic

equations, and numerical techniques have advanced to maintain

stability, efficiency and accuracy. With this application to in-

31 January 2014 Jimy Dudhia 129

creasingly finer scales, the physics has had to evolve signifi-

cantly to handle the new separation of resolved and unresolved

processes, which is particularly noted as convective storms are

becoming resolved turning the focus from cumulus param-

eterization development towards microphysical processes. This

will continue, as PBL schemes will face grey-zone issues as

the finer model grids start to partially resolve boundary-layer

structures. In these cases physics from respectively older cloud-

scale models and LES models have now fed into mesoscale

models where they now interact with the full suite of NWP

physics, complex terrain, and other aspects real-data meteor-

ological situations. Hong and Dudhia (2012) discuss model

grey-zone issues further.

Along with this development of model capabilities has been

a rapidly growing usage across the world, both for research

and operational forecasts, spurred on by cheaper computing

power and the availability of fully capable shared mesoscale

numerical weather prediction models.

High-resolution capabilities of computers and mesoscale

models have broadened their applications to short-term and

local forecasting either for specific regions or nations, or for

specific applications such as wind and solar energy, air quality,

hydrology, road conditions, airport weather, and agriculture.

Meanwhile at the coarser-scale end, mesoscale models are

now also routinely applied to regional climate studies with ne-

cessarily coarser grid sizes as they are run for years to decades

to study climate effects, and coarser grids may also be used for

data assimilation over large areas, or ensemble forecasting, so

it is necessary to maintain cumulus parameterizations and

simpler microphysics options for these types of applications.

In summary, the term “mesoscale model” nowadays covers a

much broader range of scales and applications than when they

first started being used. They are used for studies on con-

tinental scales to very local almost urban scales, and conse-

quently the physics has to cover a range of scale-dependent

assumptions as outlined in this paper.

Acknowledgments. The author would like to acknowledge the

US National Science Foundation for its support of the National

Center of Atmospheric Research, and in particular its funding

of the Weather Research and Forecasting model’s development

and user services. Significant support for the author’s work has

also been received through the years from the US Air Force

Weather Agency, Federal Aviation Administration, and De-

partment of Energy.

Edited by: Song-You Hong, Kim and Yeh

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