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 Microscale
Meteorology Division, National Center for Atmospheric Research,
P. O. Box 3000, Boulder, CO 80307, U. S. A.
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).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, 4
thand 5
thgeneration,
(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.ALADIN Aire Limitée Adaptation dynamique Développement InterNational (France)
ARPS Advanced Regional Prediction System (USA)
ARW Advanced Research WRF (USA)
BATS Biosphere-Atmosphere Transfer Scheme
COAMPS Coupled Ocean/Atmosphere Mesoscale Prediction System (USA)
COSMO Consortium for Small-scale Modeling (Germany)
Eta Eta-coordinate model (USA)
GEM Global Environmental Multiscale Model (Canada)
GRAPES Global/Regional Assimilation and PrEdiction System (China)
GRIMs Global/Regional Integrated Model System (S. Korea)
HARMONIE ALADIN-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)
MM5 Pennsylvania State University / NCAR Mesoscale Model (5th
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)
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.
warm-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 mointerac-tions
of order 10 m s
−1or 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
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.
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.
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
in-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 mesocloud-scale
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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