A history of mesoscale model development

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 expertise 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 development 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 regional NWP models as of around 2012. On the research side, it is even more true of universities and some government laboratories 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. E-mail: dudhia@ucar.edu

ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

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).

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 physical 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

Fig. 2. Schematic of physics and their interactions within a typical over the years, physical parameterizations undergo continuous

NWP model.

evolution and additions or replacements. This reflects where the uncertainties lie in atmospheric models. Unlike dynamics,

(1) Resolved cloud physics, also known as microphysics, no aspect of the physics has a set of equations as rigid as those

that handles cloud and precipitation processes including for the fluid dynamics. In every area of physics decisions have

moist phase changes and associated latent heating, water to be made regarding what is resolved or not by the dynamics,

and ice particles and their evolution an interactions, and what processes affect the atmospheric evolution most, and what

fall-out of precipitating particles. level of sophistication and computational expense is affordable

(2) Unresolved convective column physics, also known as for the application in mind. These types of decisions lead nat-

cumulus parameterization needed at coarser resolution urally to a wide range of parameterizations of different levels

to handle unresolved vertical latent-heat driven trans- of complexity and cost for each sub-category of the physics.

ports by updrafts and downdrafts within convection. Broadly, the categories of physics are as follows.

This may sometimes also include sub-grid shallow non-

31 January 2014

Jimy Dudhia

Table 1. List of Acronyms and Abbreviations. when developing, evaluating and improving weather prediction models.

ALADIN Aire Limitée Adaptation dynamique Développement InterNational (France)

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

Advanced Regional Prediction System (USA) arate component that only becomes important in specialized coupled applications such as long-term climate modeling, or

ARW Advanced Research WRF (USA) hurricane-surface interactions. In the model physics to be con- BATS

Biosphere-Atmosphere Transfer Scheme sidered here, the ocean and water surfaces will be taken as a COAMPS Coupled Ocean/Atmosphere Mesoscale Prediction

simple parameterization that provides the necessary fluxes to System (USA)

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

Consortium for Small-scale Modeling (Germany)

prognostic, way.

Eta Eta-coordinate model (USA) 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 th and 5 generation, GRAPES

GEM Global Environmental Multiscale Model (Canada)

Global/Regional Assimilation and PrEdiction System (MM4 and MM5) and Weather Research and Forecasting (China)

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

Global/Regional Integrated Model System (S. Korea) ameterizations and their development over time will also focus on these representative and widely used models that underwent

HARMONIE ALADIN-HIRLAM collaborative model (France/ Europe) their main development and growth of usage in the last 25

HIRLAM High Resolution Limited Area Model (Europe)

years.

HRM High Resolution Regional Model (Germany)

2. Dynamics and numerical methods LES

Large-Eddy Simulation LM

Lokalmodell (Germany) Some of the earliest mesoscale models were developed in MM5

Pennsylvania State University / NCAR Mesoscale the 1970’s in the United States Pennsylvania State University Model (5 th Generation)

(Anthes and Warner, 1978) and National Meteorological Center NCAR

National Center for Atmospheric Research (USA) (history documented by Shuman, 1989), United Kingdom

Meteorological Office (Tapp and White, 1976) and Australian NHM

Nonhydrostatic Model (Japan) Numerical Modeling Research Center (McGregor et al., 1978). NHMS

National Hydrometeorological Services The term “mesoscale models” here means atmospheric models NMM

Nonhydrostatic Mesoscale Model (USA) with sufficient physics for numerical weather prediction in NWP

Numerical Weather Prediction limited-area domains allowing for topography and map projec-

tion scale factors required for large areas. These are initialized PBL

Planetary Boundary Layer from, and take boundary conditions from, meteorological RAMS

Regional Atmospheric Modeling System (USA) gridded analyses, and have to least represent in some way all RSM

Regional Spectral Model (USA) of the physical processes listed as requirements in Section 1 to UM

Unified Model (United Kingdom) maintain credible analyses in their forecasts.

Another class of models being developed at the same time WRF

Weather Research and Forecasting Model (USA) were the more idealized cloud models (Miller and Pearce, 1974; Clark, 1977; Cotton and Tripoli, 1978; Klemp and Wilhelmson,

precipitating convection. 1978, for example) having limited physical processes that (3) Surface physics, including processes that lead to surface

would include microphysics, sub-grid turbulence and possibly heat and moisture fluxes that include those in the soil

surface effects like friction and topography, but rarely surface and related to vegetation and snow cover, and possibly

fluxes or radiative effects. Cloud models were designed to run urban areas.

in small areas covering maybe a single convective system (4) Vertical mixing and planetary boundary layer physics that

using uniform single-sounding initial conditions and grid sizes handle sub-grid vertical eddy transports especially of

of order one kilometer, and their dynamics was necessarily unresolved thermals near the ground, but also possibly

nonhydrostatic. Mesoscale model grid sizes were in the tens of elevated turbulence.

kilometers meaning that they could use the slightly simpler (5) Radiative physics, handling both longwave and short-

hydrostatic approximation to eliminate a vertical momentum wave components including the diurnal cycle, interaction

equation, and in contrast to cloud models that were often cast of radiation with clouds and aerosols, and fluxes of

in height-based coordinates, the earlier mesoscale models mostly radiation to and from the surface.

adopted pressure-based coordinates in which the hydrostatic Figure 2 illustrates that physics options should not be con-

approximation was much simpler. Later in the 1980’s nesting sidered as independent of each other, because there are direct

capabilities were developed for some of these models to allow and indirect interactions that are necessary to take into account

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

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 mesoscale 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 pioneered 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 potential energy is converted to updraft kinetic energy is a purely nonhydrostatic idea. For flow over topography the tilt associated with nonhydrostatic mountain waves occurs as the horizontal 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 precipitation 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 radiation 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 developed with simple microphysics, such as the classic warm-

31 January 2014

Jimy Dudhia

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 represent 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 important 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 saturation 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 microphysics schemes. Verifications of relative humidity in mesoscale 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 advected 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 precipitating 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 buoyancy-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 interactions (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 mesoscale models continues with the increasing use of double- moment schemes that predict number concentrations in addition 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 distributions 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 approaches (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 processes 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 transports. The scheme triggers only with convective instability in the column, allowing the condensation-driven updraft and subsidence fluxes that cause tropospheric warming and carry boundary-layer moisture to high levels. Some schemes also have evaporation-driven downdrafts, cooling the boundary

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), moisture 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 multiple updrafts, downdrafts if any, and convective mass flux magnitude 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 convective 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 enhanced 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 availability parameter, not keeping a time-dependent soil moisture variable. Later bucket models enabled a variable surface moisture 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

stability effects. The concept the concept of a separate smaller thermodynamic profiles near the ground. thermal roughness length or a viscous sub-layer, that resists

There are four primary approaches that are designed to work scalar fluxes more than for the momentum roughness length,

with vertical resolutions that have typically at least five levels has been found beneficial in many cases rather than the original

in the boundary layer, or lowest kilometre, and that can there- method of using the same roughness length for momentum and

fore resolve a PBL growth rate reasonably. One early widely scalars. Conversely in free convection an enhancement using,

used multi-layer approach with enhanced vertical diffusion for example, the convective velocity scale (Beljaars, 1995) in

based on stability was from Louis (1979). The second is an addition to the friction velocity in the thermal and scalar fluxes

extension of the bulk approach to also include a non-local flux (not momentum) is often used that represents the convective

term representing transport by thermals (Zhang and Anthes, boundary-layer eddies that are present even in weak mean

1982; Troen and Mahrt, 1986; Hong and Pan, 1996). These winds. Other non-stability dependent enhancements for coarse

schemes recognize that a well-mixed PBL is near-neutral but resolution have allowed for sub-grid variability (e.g., Mahrt and

still has vigorous heat transport through its depth despite the Sun, 1995), which alleviates biases seen in low-wind situations

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

independently of local downgradient fluxes and an added term Today’s mesoscale models have sophisticated land-surface

provides for this. It is activated by a positive surface heat flux, components that provide heat and moisture fluxes as lower

and in the Troen-Mahrt method also used by Hong and Pan boundary conditions for a separate boundary-layer model. For

(1996) and Hong et al. (2006) a column-constant (“gamma”) momentum, a stress that also depends on surface roughness

term adds to the local-gradient term in the sub-grid heat flux. and stability is defined as an input to the boundary-layer model.

Zhang and Anthes (1982) and Pleim (2007) represent thermals In mesoscale applications of up to a few days simulation, the

with a direct flux between the surface layer and other PBL water temperatures can be held constant and require no physics

layers (following ideas of Blackadar, 1979), a non-local mixing to predict them. The only physics associated with water sur-

approach known also as transilient mixing (Stull, 1984). Add- faces is in determining their drag effect that may depend on

itionally such approaches enhance the vertical diffusion co- waves. This is usually applied as a local windspeed-stress

efficient using a profile that maximizes within the PBL depth. relation such as that of Charnock (see Delsol et al., 1971). For

Entrainment may be handled by overshooting thermal depths, longer simulations, such as in regional climate applications,

or some schemes (YSU, Hong et al., 2006) may add an explicit the sea-surface temperature can be updated from data or

entrainment flux calculation. A third related approach uses a climatology. More sophisticated treatments involve coupling

mass-flux model, similar to cumulus schemes, to achieve the ocean and wave models to atmospheric models to predict the

non-local flux independent of the diffusion term (the eddy- entire system.

diffusivity mass-flux, EDMF, approach, e.g., Siebesma et al., 2007). These entrain mass in the lower PBL and detrain it in

d. Planetary boundary layer the upper part. The fourth approach is a turbulent-kinetic- energy (tke) approach pioneered by Mellor and Yamada (1974,

A complex sub-grid problem in mesoscale models is the re- 1982), and most modern tke schemes are variants on this presentation of the boundary layer, both in stable and unstable

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

Sukoriansky et al., 2005; Nakanishi and Niino, 2006). In Going beyond the bulk Deardorff approach described in the

mesoscale models, the tke has a prognostic equation and the previous section, has been deemed important to represent the

diffusion coefficient depends on its magnitude and a length correct growth and decay of the boundary layer, to improve the

scale. Turbulent kinetic energy responds to stability, shear and prediction of surface atmospheric properties, and to better

dissipation, and most models consider this part similarly, but develop diurnal convection. Even with improvements in the

they all differ primarily in methods of computing length scales. vertical resolution of the boundary layer, there are important

To date, these schemes have been applied as local schemes in sub-grid processes.

that the form of the vertical mixing remains as a diffusion For unstable boundary layers, there are a variety of methods

equation. Being local and downgradient, they have a tendency to handle sub-grid thermals that transport surface fluxes

towards leaving a slightly superadiabatic profile through the through the boundary layer. The primary role of the boundary-

PBL, and also a tendency to entrain less at the PBL top re- layer scheme in unstable conditions is to represent the process

sulting in cooler, moister and shallower PBLs than those that of mixing that takes place through thermals that have scales

have more vigorous entrainment. The tke approach has an near 100 meters, and are thus sub-grid scale in mesoscale, and

advantage in maintaining a memory of the turbulence, which even cloud-permitting-scale models. These thermals transport

may help with the evening transition, and, if the model add- heat, moisture and momentum quickly through the boundary

itionally advects this tke, there is also a downstream memory layer, and also entrain air from above as the boundary layer

as the air crosses different surface types. grows in the daytime. Without such a parameterization, re-

In models above the boundary layer there is also a vertical solved motion and/or local vertical mixing would be deficient

diffusion process that is typically parameterized in terms of the in representing the speed of this mixing giving unrealistic

local Richardson number to represent elevated turbulent layers.

ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES

As mentioned above, some PBL schemes also may include

be important in some situations (e.g., Dudhia, 1989). The shallow convection via carrying information about latent-heat-

introduction of more sophisticated atmospheric radiation produced buoyancy in cloud-topped boundary layers, but the

schemes that also handled water vapour, ozone and carbon majority of PBL schemes essentially just assume dry mixing

dioxide effects, advanced these schemes more to the present leaving resulting condensation to be handled by other physics.

state of the parameterization (Fu and Liou, 1992; Chou et al., For stable conditions a further challenge is that the model

1994; Mlawer et al., 1998). Radiation is still handled indepen- vertical resolution makes it difficult to represent the surface

dently in each model column using the plane parallel assump- behaviour just from the lowest model grid level that may be

tion in each model layer.

tens of meters above the ground because there is some Cloud fractions within a mesoscale model grid area can also decoupling in thin stable layers, and also some complex local

be considered by radiation schemes that then have to make an unrepresented behaviour such as drainage flows and inter-

overlap assumption for fractions at different model levels. mittent turbulence that impact the real surface fluxes.

Convective parameterized sub-grid clouds may contribute to For coarse-scale models with grid sizes larger than 10 km,

the cloud fraction, while microphysical schemes in mesoscale gravity wave drag may also be parameterized to represent the

models often consider their clouds to be uniform over the grid sometimes important momentum transport of unresolved oro-

area, so these may provide only zero and one as fractions, un- graphic gravity waves that break at high levels. This is like a

less the microphysics explicitly also includes a cloud fraction. non-local vertical momentum transport or stress.

At the surface, slope effects have been added in some Recently mesoscale models have been used increasingly for

models to account for resolved topographic gradients that wind-energy applications and some efforts have focused on

modify the surface solar flux. Three-dimensional effects bet- evaluating and improving surface winds in complex terrain

ween columns would strictly be needed as the grid aspect ratio with this consideration (Jimenez and Dudhia, 2012).

approaches one for small grid sizes, but adding these would be There are grey-zone issues for the PBL schemes too, but

complicated, and these effects are not considered necessary for these are likely not to occur in forecast applications until

most applications.

cloud-permitting model grid sizes become much less than Radiation interacts with the surface properties through its

1 km, which is computationally beyond present-day real-time albedo providing reflection, and emissivity with temperature mesoscale capabilities. Large-eddy simulation models (e.g.,

determining its radiated longwave flux. Clouds significantly Moeng et al., 2007) have already been designed to represent

impact the radiation, and ideally the microphysics schemes grid sizes one to two orders of magnitude below 1 km, and

would represent droplets and ice crystals in the same way as using their sub-grid methods will alleviate the need for PBL

radiation as done in recent work by (Liang et al., 2012; parameterizations by explicitly resolving the primary trans-

Thompson and Eidhammer, 2014), but often these are treated porting eddies in the boundary layer. At these scales, the

independently. Ozone and aerosols also have important im- formerly one-dimensional column-by-column boundary layer

pacts, especially on shortwave radiation and usually have been parameterization becomes a fully three-dimensional turbulence

represented with a climatology in mesoscale models, except problem with locally determined more isotropic sub-grid

for in specialized atmospheric chemistry models that can mixing processes. This amounts to a simplification of physics

predict their distributions.

at higher resolution that is somewhat similar to that in which As mesoscale models become used for solar energy appli- the cumulus scheme problem is alleviated by resolving the

cations there is an increased focus on aerosols that impact primary updrafts. In both cases, non-local sub-grid transports

direct radiation (Ruiz-Arias et al., 2013), with a challenge of are replaced by local and resolved transports.

providing near real-time information on them. Similarly the forecasting of clouds, including non-precipitating ones, be-

e. Radiation comes a more emphasized area of evaluation and improvement, given their radiative impact.

Early mesoscale models usually had very simple physics, with perhaps no cloud or precipitation explicitly predicted in

4. Conclusions

the atmosphere. However, representation of the diurnal cycle at the surface required at least a computation of surface

The last four decades have seen a rapid advancement of radiative fluxes, and this was first done with surface radiation

mesoscale numerical weather prediction models from the crude schemes that would take column-integrated precipitable water

100 km grids with few vertical levels and very simplified and use the relative humidity in atmospheric layers to estimate

physical processes to today’s models nearing 1 km grids with cloud fractions (e.g., Carlson and Boland, 1978). For the

sophisticated sub-grid representations of a variety of micro- atmosphere, some radiative cooling was also usually added to

physical processes, surface processes, turbulent mixing and at least get the mean diurnal clear-sky effect. Later as models

radiative transfer. The dynamics has evolved towards the less started to explicitly carry cloud and precipitation variables, it

approximated and more generally applicable nonhydrostatic made sense to have layer-by-layer radiation interact directly

equations, and numerical techniques have advanced to maintain with them giving cloud-radiative interaction profiles that may

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

31 January 2014

Jimy Dudhia

creasingly finer scales, the physics has had to evolve signifi- Beljaars, A. C. M., 1995: The parametrization of surface fluxes in large- cantly to handle the new separation of resolved and unresolved

scale models under free convection. Quart. J. Roy. Meteor. Soc., 121, processes, which is particularly noted as convective storms are

255-270.

becoming resolved turning the focus from cumulus param- Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. eterization development towards microphysical processes. This Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, 693-709.

will continue, as PBL schemes will face grey-zone issues as Blackadar, A. K., 1979: High resolution models of the planetary boundary the finer model grids start to partially resolve boundary-layer

layer. Advances in Science and Engineering. Vol. 1, No. 1, J. Pfafflin structures. In these cases physics from respectively older cloud-

and E. Ziegler, Eds., Gordon and Breach, 50-85. scale models and LES models have now fed into mesoscale

Bougeault, P., and P. Lacarrere, 1989: Parameterization of orography- models where they now interact with the full suite of NWP

induced turbulence in a mesobeta-scale model. Mon. Wea. Rev., 117, physics, complex terrain, and other aspects real-data meteor-

1872-1890.

ological situations. Hong and Dudhia (2012) discuss model Bubnova, R., G. Hello, P. Benard, and J.-F. Geleyn, 1995: Integration of the fully-elastic equations cast in the hydrostatic pressure terrain-following

grey-zone issues further. coordinate in the framework of the ARPEGE/ALADIN NWP system. Along with this development of model capabilities has been

Mon. Wea. Rev., 123, 515-535.

a rapidly growing usage across the world, both for research Carlson, T. N., and F. E. Boland, 1978: Analysis of urban-rural canopy and operational forecasts, spurred on by cheaper computing

using a surface heat flux/temperature model. J. Appl. Meteorol., 17, power and the availability of fully capable shared mesoscale

998-1013.

numerical weather prediction models. Chen, F., and J. Dudhia, 2001: Coupling an advanced land-surface/ hydrology model with the Penn State/NCAR MM5 modeling system.

High-resolution capabilities of computers and mesoscale Part I: Model description and implementation. Mon. Wea. Rev., 129, models have broadened their applications to short-term and

569-585.

local forecasting either for specific regions or nations, or for Clark, T. L., 1977: A small-scale dynamic model using a terrain-following specific applications such as wind and solar energy, air quality,

coordinate transformation. J. Comput. Phys., 24, 186-215. hydrology, road conditions, airport weather, and agriculture.

Chou, M.-D., and M. J. Suarez, 1994: An efficient thermal infrared Meanwhile at the coarser-scale end, mesoscale models are

radiation parameterization for use in general circulation models. NASA now also routinely applied to regional climate studies with ne- Tech. Memo, 84 pp. Cotton, W. R., and G. J. Tripoli, 1978: Cumulus convection in shear flow-

cessarily coarser grid sizes as they are run for years to decades three-dimensional numerical experiments. J. Atmos. Sci., 35, 1503-1521. to study climate effects, and coarser grids may also be used for

Cullen, M. J. P., 1993: The Unified Forecast Climate model. Meteorol. data assimilation over large areas, or ensemble forecasting, so

Mag., 122, 81-94.

it is necessary to maintain cumulus parameterizations and Deardorff, J. W., 1972: Parameterization of the planetary boundary layer simpler microphysics options for these types of applications.

for use in general circulation models. Mon. Wea. Rev., 100, 93-106. In summary, the term “mesoscale model” nowadays covers a

______, 1978: Efficient prediction of ground surface temperature and much broader range of scales and applications than when they moisture, with inclusion of a layer of vegetation, J. Geophys. Res.,

83(C4), 1889-1903.

first started being used. They are used for studies on con- Delsol, F., K. Miyakoda, and R. H. Clarke, 1971: Parameterized processes tinental scales to very local almost urban scales, and conse-

in the surface boundary layer of an atmospheric circulation model. quently the physics has to cover a range of scale-dependent

Quart. J. Roy. Meteor. Soc., 97, 181-208.

assumptions as outlined in this paper. Doms, G., and U. Schaettler, 1997: The nonhydrostatic limited-area model LM (Lokal-Modell) of DWD. Part I: Scientific Documentation.

Acknowledgments. The author would like to acknowledge the

Deutscher Wetterdienst, 155 pp.

A history of mesoscale model development