Dynamical Models

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Dynamical Models
Training Course on Climate Information,
Approaches and Tools for Assessing and Managing
Climate Risks
Christopher Cunningham
Centro de Previsão de Tempo e Estudos Climáticos
Instituto Nacional de Pesquisas Espaciais
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Outline

• The Climate System
• Atmospheric General Circulation Models
• Coupled Ocean Models
• Dynamical Downscaling

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The climate system is a highly non-linear coupled
system
The components of the climate system are open,
nonisolated subsystems
They interact on a wide range of spatial and
temporal scales
They are strongly coupled and are characterized
by intense interactions at various time and space
scales ranging from micro trough meso to
planetary scales
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Daily, Intraseasonal, Seasonal, Interannual, and
Decadal Variations
Short range weather variation Hours thunderstorms, tornadoes, squall lines, fronts, . Diurnal cycle Organized convection Cyclones, Eeasterly waves, Depressions, .
Medium range weather variations Blocking Growth, decay of tropical, tropospherical disturbances
Intraseaonal variations Madden Julian Oscillation (MJO), Monsoon Intraseasonal variations, Pacific North American (PNA) variations, Annular modes
Seasonal mean variations Persistent droughts Floods Persistent hot and cold days Anomalous number and tracks of cyclones
Interannual variations ENSO, QBO, TBO, NAO, NAM, SAM
Decadal variations PDO, Thermohaline circulation, Sahel drought, Decadal ENSO
Climate change Solar, Volcanoes, Greenhouse gases, Land use change
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CLIMATE MODELS arenumerical representations of
the fundamental equations that describe the
behavior of the climate system and the
interactions across its components atmosphere,
ocean, cryosphere, biosphere, chemosphere
Climate models a scientific definiton
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Brief history of climate modelling (I)

• 1922 Lewis Fry Richardson
• basic equations and methodology of numerical
  weather prediction
• 1950 Charney, Fjørtoft and von Neumann (1950)
• first numerical weather forecast (barotropic
  vorticity equation model)
• 1956 Norman Phillips
• first general circulation experiment (two-layer,
  quasi-geostrophic hemispheric model)
• 1963 Smagorinsky, Manabe and collaborators at
  GFDL, USA
• 9 level primitive equation model
• 1960s and 1970s Other groups and their offshoots
  began work
• University of California Los Angeles (UCLA),
  National Center for Atmospheric Research (NCAR,
  Boulder, Colorado) and UK Meteorological Office

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Brief history of climate modelling (II)

• 1980s First coupled model simulations
• 1990s onwards Era of model intercomparisons
• AMIP, CMIP, SMIP, ENSIP, PMIP
• 2000 onwards Multi-model ensemble seasonal
  forecasting systems
• DEMETER
• 2004 EU ENSEMBLES Project combined
  seasonal-to-decadal and climate change
  multi-model ensembles
• 2007 IPCC Fourth Assessment Report
• climate projections to 2100 from 18 coupled
  ocean-atmosphere-cryosphere models.

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Incremental development of climate/earth system
models
These models are, in effect, a synthesis as well
as a measure of our current understanding of the
coupled system
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Climate modeling what for?
The problem is not wether our climate will change
but rather in what direction and from what causes
it will be changed
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What are Climate Models?

• Climate Models are huge computer codes based on
  fundamental mathematical equations of motion,
  thermodynamics and radiative transfer
• Climate models are extensions of weather forecast
  models
• These equations govern
• Flow of air and water - winds in the atmosphere,
  currents in the ocean.
• Exchange of heat, water and momentum between the
  atmosphere and the earths surface
• Release of latent heat by condensation during the
  formation of clouds and raindrops
• Absorption of sunshine and emission of thermal
  (infra-red) radiation

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The equations of a climate model(atmosphere)
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A taste of numeric techniques
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Horizontal discretization

• Grids
• regular grids
• stretched grids
• rotated grids
• reduced grids
• Numerical formulation
• Finite difference
• spectral methods
• finite elements

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Horizontal discretization
The spectral method involves representing the
spatial variations in terms of finite series of
orthogonal functions called basis functions
For the Cartesian geometry the appropriate set of
basis functions is a double Fourier series in x
and y.
For the spherical Earth the appropriate basis
functions are the spherical harmonics
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Vertical discretisation
Sigma Coordinate

• Sigma coordinates are terrain following.
• They do not intersect the surface as do other
  coordinate types.

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Vertical discretisation
At sfc ? coordinates (A0)
TOA p coordinates (B0)
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HadCM3
19 Atmospheric Levels
Atmospheric resolution 3.75 by 2.5 degrees
Ocean resolution 1.25 by 1.25
20 Ocean Levels
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Physical parametrizations in atmospheric models

• There are three types of parametrization
• Processes taking place on scales smaller than the
  grid-scale, which are therefore not explicitly
  represented by the resolved motion
• Convection, boundary layer friction and
  turbulence, gravity wave drag
• All involve the vertical transport of momentum
  and most also involve the transport of heat,
  water substance and tracers (e.g. chemicals,
  aerosols)
• Processes that contribute to internal heating
  (non-adiabatic)
• Radiative transfer and precipitation
• Both require the prediction of cloud cover
• Processes that involve variables additional to
  the basic model variables
• e.g. land surface processes, carbon cycle,
  chemistry, aerosols, etc)

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Physical parametrizations in atmospheric models
Processes that are not explicitly represented by
the basic dynamical and thermodynamic variables
in the basic equations (dynamics, continuity,
thermodynamic, equation of state) on the grid of
the model need to be included by parametrizations.
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O3, H20, CO2, CH4, N2O
Radiation is the driving force of the atmospheric
motions
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Radiation
AGCMs require net (upward, downward) radiative
fluxes at

1. the TOA in order to determine the overall energy
   budget of the surface-atmosphere system
2. The surface for the determination of the surface
   temperature
3. The net radiative heating profile is needed for
   the thermodynamic tendency calculations

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Radiation
K.s-1
The object of a radiative transfer
parametrization is to calculate terms I and II
for clear and/or cloudy conditions
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Radiation Schemes
The processes that need to be parameterized are
essentially of molecular scale for gaseous
absorption and micron scale for particulate
scattering
Deal separately with the solar region and the
thermal region
In each region the spectrum is split up into
several spectral bands (typically 5-10)
The effects of Rayleigh scattering, absorbing
gases, clouds and aerosols are parametrized in
each band
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Cloud particles interact strongly with SW and LW
radiation
Scatter the visible and absorb the IR
GCMs cannot resolve clouds, but knowledge of
their amount and properties is essential for the
calculation of radiation fields and precipitation
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The cloud amount for a grid region must be
related to the other predicted climate variables
Many schemes, from the 1970s onwards, based cloud
cover on the relative humidity (RH)
RHcrit critical relative humidity at which
cloud assumed to form (function of height,
typical value is 60-80)
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Unified Model cloud microphysics scheme
All of these parameterizations must be viewed as
extremely simplistic compared with the real
atmospheric processes that lead to cloud cover
It is here that some of the major uncertainties
in climate sensitivity arise
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Radiation Schemes clouds
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Convection
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Convection
Considering pure radiative equilibrium, the
thermal structure is buoyantly unstable to small
vertical displacements of air.
The absorption of SW radiation at the Earths
surface and emission of LW radiation in the
middle troposphere continuously destabilize the
troposphere
Under these circumstances small displacements are
reinforced by buoyancy until finite amplitude
develops
Adjacent to a reservoir of moisture, convective
overturning maintains the global mean troposphere
near neutral moist stability
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Why is Convection(parameterization) Important?

• Convective storms can significantly influence
  vertical stability and large-scale flow patterns
  by
• Redistributing heat, moisture, and momentum
• Producing cloud cover that affects surface
  temperatures

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What is Convective Parameterization?

• Cumulus or convective parameterization schemes
  are procedures that attempt to account for the
  collective influence of small-scale convective
  processes on large-scale model variables
• Climate models with grid spacing larger than that
  of individual thunderstorms or storm clusters
  need to parameterize the effect that convection
  has on larger-scale model variables in each grid
  box

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Formulation of Convective Parameterizations
Determine occurrence/localisation of convection

• How does the large-scale weather pattern control
  the initiation, location, and intensity of
  convection

Determine vertical distribution of heating,
moistening and momentum changes

• What are the properties of parameterized clouds

Determine the overall amount of the energy
conversion, convective precipitationheat release

• How does convection modify the environment

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Convection Schemes
The first convection schemes simply adjusted the
temperature profile the moist adiabatic
adjustment scheme (Manabe 1965)
When ? of the model exceeds ?crit the model ? is
adjusted back to ?crit
The adjustment procedure acts to cool the sfc and
warm the upper troposphere
Thus the adjustment can be viewed as a process
that mixes warmer air near the surface up through
the atmosphere
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Convection Schemes
Subsequently schemes based on moisture budgets
which attempted to represent forcing by the large
scale were introduced (e.g. Kuo 1974)
The moisture convergence into a model column
In Kuo schemes convective precipitation is
assumed to occur following model-scale
convergence of moisture
A fraction b of Mq is available to moisten the
atmosphere, while the remaining fraction, (1- b)
condenses and rains out.
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Convection Schemes

• Most contemporary convection schemes use a
  mass-flux approach, with buoyant plumes
  entraining and detraining to reach different
  levels. For example
• Arakawa and Schubert (1974)
• Gregory and Rowntree (1990)
• Tiedtke (1989)
• Kain and Fritsch (1990)

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Boundary layer processes
The PBL is the layer close to the surface within
which vertical transports by turbulence play
dominant roles in the momentum, heat and moisture
budgets.
There are a myriad of different types of boundary
layers in different environments. The PBL is
strongly driven by the underlying surface.
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The evolution of the PBL and its interaction with
the free atmosphere is enormously complex.
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Boundary layer transports
The simplest way to calculate turbulent
transports in the boundary layer is to use
K-theory, by analogy with molecular diffusion.
The diffusion coefficients are functions of
stability, etc based on Monin-Obukhov Similarity
Theory
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Land surface processes

• Why the land surface processes are important to
  the atmosphere?

The surface of the planet is a lower boundary
condition to the atmospheric circulation (1/3)
The sensible and latent heat fluxes at the
surface are the lower boundary conditions for the
enthalpy (internal energy energy due to
expansion) and moisture equations in the atmophere
The sharpest vertical gradients happen to be near
the surface
We live on it!
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Surface processes

• Surface schemes are needed to
• 1. Calculate the fluxes of heat, moisture and
  momentum between the surface and atmosphere
• 2. Calculate surface temperature and other
  variables

The key issues in land surface parameterization
are i) the role of vegetation in controlling
evapotranspiration and rainfall interception ii)
an adequate description of heat and water
transfer in the soil and iii) for high latitudes
and over mountains a correct description of
energy/water exchanges for the cryosphere.
Models now contain quite detailed representations
of evaporation, interception and vertical
transfers of heat and moisture in the soil
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Atmospheric GCMs require time series of the
fluxes of radiation, sensible and latent heat,
and momentum across the air-land interface to
serve as lower boundary conditions
These can be specified by calculations which
involve the surface parameters of albedo (?),
roughness lenght, and (soil) moisture
availability.
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Surface Radiation Balance
LWu
LWd
SWu
SWd
In most GCMs, the land albedo fields are simply
prescribed as fixed fields
1
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Land surface processes
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Land surface processes
Sensible heat flux (conduction to the air)
W.m-2
Latent heat flux (energy released to the air by
evaporation) W.m-2
Heat flux into the ground W.m-2
Energy used for photosynthesis W.m-2
H and LE normally make up the bulk of Rn and the
magnitude of the ratio of sensible to latent heat
release into the atmosphere can be an important
determinant of the local and regional climate
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Surface Energy Balance Storage in the ground
( Given by the AGCM )
SWd
LWd
LWu
SWu
Dry soil, isothermal and homogeneous
D
TT(t)
G
Td
W.m-2

• ? albedo
• emissivity
• Cs heat capacity (J.K-1.m-3)
• Td temperatura do solo profundo (K)

Depends on the volume fractions of soil, organic
matter, water and air.
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Turbulent Fluxes
Rn
t
LE
H
f2
fórmula geral
r12
F1?2
D
T
f1
G
F1?2 fluxo turbulento de 1 a 2 f1 e f2
concentração em 1 e 2 r12 resistência entre 1 e
2
E evaporação (kg m-2 s-1) LE fluxo de calor
latente (W m-2) H fluxo de calor sensível (W
m-2) fluxo de momentum (kg m-1 s-2)
t
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Momentum Flux ?
no slip
(dado)
ur (ur, vr)
zr
Rn
t (tx, ty)
ra
ur 0
z0
D
T
G
zr nível de referência (m) z0 comprimento de
rugosidade (m) ra resistência aerodinâmica (s
m-1)
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Sensible Heat Flux H
( Given by the AGCM )
Tr
zr
Rn
t
ra
H
T
D
T
W m-2
G
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Latent Heat Flux H
(dado)
er
zr
Rn
t
ra
LEw
H
es(T)
D
T
G
W m-2
p pressão (hPa) L 2,5 x 106 J kg-1 e 0,622
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Modelling the land surface and its heterogeneity
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Modelling the land surface and its heterogeneity
er
er
Tr
ur
zr
LEs LEc
SWd
LWd
ra
LEi
ra
H
ra
t
ra
es(T)
z0 d
es(T)
T
rc
u 0
LWu
SWu
rsoil
qs(T)
T
D
T
G
Td
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Predicted u, T, q
PBL and Surface
No Condensation
Stable Condensation
Convective Condensation
Zero Cloud Fraction
Cloud Fraction Stable
Cloud Fraction Conv
Radiation
Spectral Blocking
Dissipation Terms
Gravity Wave Drag
Solution of the PEs
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The Ocean

• The ocean is an incompressible fluid forced
  thermally and mechanically, primarily at its
  surface
• It is heated by solar radiation and cooled by
  evaporation and thermal emission from the
  surface
• No internal heating, but salinity strongly
  affects the density and hence the circulation

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Basic properties of the Ocean

• Density
• At SLP ocean is 1000x more dense than the
  atmosphere
• Heat capacity
• Specific heat capacity is 1200x atmosphere
• 2.5m of ocean has same heat capacity as whole
  atmosphere
• Turbulent conductivity (compared to diffusion in
  the land)
• Velocities
• Ocean moves and adjusts 1000x more slowly than
  the atmosphere a source of memory in the
  climate system

Advective mid-latitude internal Rossby waves
Atmos. 10 m/s 10 m/s
Ocean 1-10 cm/s 1cm/s
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Global Annual Mean Hydrological Cycle
107-7136
More prp than evap
More evap than prp
The great reservoir of moisture !
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Ocean-Atmosphere Interaction

• The ocean and atmosphere interact continuously
• Fluxes of heat, fresh water and momentum (
  numerous chemical species)

Precipitation
Evaporation
Surface boundary layer
Qnet heat
windstress
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Coupled Ocean-Atmosphere Modelling

• Dynamical coupling with atmosphere, seaice, and
  land runoff

• Ocean surface temperature can change in response
  to atmospheric forcing, and the atmosphere, in
  turn, is affected by the new ocean surface
  temperature

• OGCMS necessarily have wind, heat and water
  forcing, geographically correct domain geometry,
  and the equation of state for seawater...all with
  their inescapable approximations

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Swamp Model
S F? - F? - H LE 0

• SST calculated from a surface energy balance only
  (no heat storage

• No heat storage, no ocean currents

• Sensitivity experiments (variations in the solar
  constant or in the atmospheric CO2 )

• Only annual mean forcing from the sun !

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Mixed-Layer Ocean Model
S F? - F? - H LE ?cph?tT
50 to 100m of water

• Allows seasonal cycle

• Surface energy balance plus heat storage

• No ocean currents, no upwelling

• Sensitivity experiments (variations in the solar
  constant or in the atmospheric CO2 )

• Flux correction (a source of heat) to compensate
  the lack of currents and upwelling

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Flux Adjustment (Q-flux)
Difference between annual-mean SST from year 10
of the coupled-model integration with no flux
adjustment and the smoothed initial state,
showing systematic SST errors in the coupled
model 10-yr average.(Murphy, 1995). Source
adapted from Hartmann, 1994
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Ocean-Atmosphere Coupling
The most complicated step in the global model
hierarchy
Surface energy balance heat storage ocean
currents upwelling subgrid-scale mixing
processes
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OGCM CGCM initialization/forecast runs
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CPTECs Coupled GCM V.1.0
Coupled Forecast
Initialization
AGCM
Atmos FCSTs
Tau Heat
OGCM
SFC Fluxes
OGCM
IC
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What is downscaling (or Regional Climate
Modelling)?

• Downscaling is a method for obtaining
  high-resolution climate or climate change
  information from relatively coarse-resolution
  global climate models (GCMs).
• Downscaling techniques enhance or add value to
  the regional information provided by GCMs.

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Types of Downscaling

• Dynamical
• Nested regional (or limited area) climate models
  (RCMs)
• High and variable resolution GCM experiments
• Statistical methods use empirical relationships
  between GCM outputs and local climate statistics
• Principal Component Analysis
• Regression analysis
• Neural network methods

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Dynamic Downscaling Regional (or Limited Area)
Climate Models

• Objective To provide added value to regional
  information provided by global reanalyses or
  GCMs
• Dynamical models based on primitive equations
  with both hydrostatic (e.g., RegCM3) and
  non-hydrostatic formulations (e.g., MM5, RAMS)

http//www.meted.ucar.edu/mesoprim/models/print.ht
m
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We live on a high resolution world

• Due to their relatively coarse resolution, GCMs
  are unable to include the effects of regional
  features.

land-ocean contrasts
inland bodies of water
complex topography
complex land use
also air pollution, urban heat island effects
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Why to downscale?
Typically, GCMs have a resolution coarser than 2
latitude-longitude
GCMs provide the response of the general
circulation to large scale forcings
Regional Models give the response to local
forcings, normally sub-grid processes in the GCMs
The direct result of the poor spatial resolution
of GCMs is a serious mismatch of spatial scale
between the available climate forecasts and the
scale of interest to most climate forecast users
Some applications also require climate forecasts
with higher temporal resolution. Most crop
models, for example, require daily weather input.
GCM daily precipitation shows very low daily
variability and many high errors compared to
observations (Mearns et al. 1990).
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Added Value
300 km

• Regions of complex topography and/or land use
• Regional and local atmospheric circulations(e.g.,
  narrow jet cores, mesoscale convective systems,
  sea-breeze type circulations, tropical storms)
• Processes at high frequency temporal
  scales(e.g., precipitation frequency and
  intensity distributions, monsoon onset and
  transition times)

60 km
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Two types of boundary conditionsInitial and
Lateral

• Initial terrain, land cover types, SSTs, soil
  moisture
• Lateral
• Sources Reanalysis (e.g., NCEP-NCAR Reanalysis
  or ERA-40) or GCM
• Required fields surface pressure, temperature,
  humidity, horizontal winds (usually 6 hourly
  data)

Image source http//www.cics.uvic.ca/scenarios/pd
f/workshop/rcms.pdf
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Lateral Boundary Conditions
Horizontal view
Marbaix et al. (2003)
model top
Greater nudging
Vertical view
Forcing from large scale at the interior of the
domain
s level
surface
Less nudging
Nudging term
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Seasonal Rainfall Comparision Wet Year 1974
Station Area Averaged Value 781.7 mm
Hulme 0.5 deg Area Averaged Value 781.6 mm

• ECHM overload the rainfall amounts
• RSM general pattern is provided by global model
• ITCZ further south
• ITCZ with strong convective activity
• RSM captured the gradient
• RSM dry too much

RSM Area Averaged Value 467.4 mm
ECHAM Area Averaged Value 1229.2 mm
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RCMs Issues to Consider

• Lateral boundary conditions
• Fixed - no two-way interactions (analogous to
  two-tier vs. one-tier prediction system)
• Presence of systematic errors
• Domain choice
• RCM
• Spin-up
• Model physics

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ATMOSPHERE
Mesoscale Dynamics
Aerosols Chemistry
Clouds Precipitation
Radiation
Boundary Layer
Precipitation
Radiation
Surface Fluxes
Albedo
LAND/OCEAN SURFACE
Snow Sea Ice
Biosphere Soils
Hydrology Lake
Ocean Fluxes
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Summary

• The atmosphere is a fluid on a rotating planet
• Drag at the surface and within the atmosphere
  affects the momentum budget
• Water vapour evaporates from the surface,
  condenses to form clouds and heats the atmosphere
  when it is lost through precipitation
• Heating from solar radiation and cooling from
  thermal radiation
• Models therefore need to include equations for
• 3 components of wind (or vorticity divergence),
  including Coriolis and drag
• equation of state and conservation of water
• thermodynamics, including heating by condensation
  and radiation
• The ocean is also a fluid, but incompressible. It
  is heated by solar radiation and cooled by
  evaporation and thermal emission from the
  surface. No internal heating, but salinity
  strongly affects the density and hence the
  circulation
• Additional models have been developed to include
  the land surface, cryosphere, atmospheric
  chemistry and aerosols, carbon cycle etc
• Processes that are sub-grid in scale are modelled
  by parametrizations