the precis climate model formulation (hadrm3p) tanzania meteorological agency, 29 th june – 3 rd...

The PRECIS Climate Model Formulation (HadRM3P)

Tanzania Meteorological Agency, 29th June – 3rd July 2015

PRECIS Workshop

© Crown copyright Met Office

Goal of session

• To provide an overview of the scientific formulation of PRECIS


• The PRECIS RCM formulation comes from a GCM

• Designed to simulate the climatology of all regions reasonably well

One model formulation

© Crown copyright Met Office© Crown copyright Met Office

General Description

• Global/Regional climate models are models of the climate system, including the atmosphere, oceans, land-surface and more.

• The advective (relating to motion) and thermodynamical (relating to heat) evolution of atmospheric pressure, winds, temperature and moisture (prognostic variables) are simulated, while including the effects of many other processes.physical processes.

• Other useful meteorological quantities (diagnostic variables) are derived consistently within the model from the prognostic variables, such as precipitation, evaporation, soil moisture, cloud cover and many more.


Main components of climate models

• Atmospheric dynamics

• Model grid

• Physical parameterizations

• Initial and boundary conditions of the model


Atmospheric dynamics

• The evolution of pressure, winds, temperature and moisture are governed by the laws of energy and conservation.

• Conservation of momentum

• Conservation of mass

• Conservation of energy


Horizontal equation of motion(the conservation of momentum)

• Newton’s 2nd law: Force = Mass Acceleration

• The change in velocity of an air parcel is dependent on • the Coriolis force

• the pressure gradient force

• gravity

• friction

12 r

Dp

Dt

UU g F


The hydrostatic assumption(taking vertical motions out of the model)

• At synoptic scales, vertical accelerations due to the conservation of momentum are small and may be ignored.

• Newton’s equation in the vertical then simplifies to

• Relates vertical pressure variations with gravity and atmospheric density

• I.e. there are only two explicit forces acting in the vertical (pressure gradient force and gravity) and these act to cancel each other out

p

z

dg

d


Hydrostatic equilibrium

Pressure decreases withheight:

upwards ‘pressuregradient force’

acting through the parcel

Mass of air parcel:

downwards force due togravity

Earth

TOA


Vertical equation of motion(the conservation of mass)

• The continuity equation:

• Relates changes in density with divergence in the wind velocity field.

• Vertical motions are inferred from areas of convergence and divergence in the horizontal wind field (and assuming incompressibility of the atmosphere).

• Areas of convergence and divergence in the horizontal diagnose a vertical transfer of mass between vertical layers.

1 DU 0

Dt


Atmospheric heat and moisture(the conservation of energy)

• First law of thermodynamics:

• heat added = change in internal energy + work done

• Equation of state for a gas :

• Temperature and water vapour are also advected

• Temperature/moisture at a point in the atmosphere can change either due to cooler or warmer/drier or moister air being blown to that point (advection), or from local effects such as evaporation or condensation arising from the equation of state and the first law of thermodynamics

pv RT


Discretizing the model equations

• All model equations are solved numerically on a discrete 3-dimensional grid spanning the area of the model domain and the depth of the atmosphere and ocean

• The model simulates values at discrete, evenly spaced points in time

• The period between each point in time is called the model’s timestep

• Spatially, data are average over a grid box

• Temporally, data can be assumed to be instantaneous

time

o


Vertical exchange between layersof momentum, heat and moisture

Horizontal exchangebetween columnsof momentum, heat and moisture

Vertical exchangebetween layersof momentum, heat and saltsby diffusion, convectionand upwelling

Orography, vegetation and surface characteristics included at each grid box surface

Vertical exchange between layersby diffusion and advection

The three dimensional model grid

15° W60° N 3.75°

2.5°

11.25° E47.5° N


Length of timestep

• The numerical stability criterion for this model insists that we can not allow a parcel of air to travel more than one grid length in distance in one timestep

• Knowledge of the grid length and maximum wind speeds will give the maximum possible timestep

• time = distance/speed

• Assuming maximum wind speed, u = 166 ms-1

• ~150km resolution 15 minute timestep

• ~50km resolution 5 minute timestep

• ~25km resolution 2.5 minute timestep



• Atmosphere and ocean dynamics

• Model grid




The model grid

• Hybrid vertical coordinate

• Combination of terrain following and atmospherics pressure

• 19 vertical levels (lowest at ~50m, highest at 5Pa)

• Regular lat-lon grid in the horizontal

• ‘Arakawa B’ grid layout

• P = pressure, temperature and moisture related variables

• W = wind related variables

W

P

PP

P

W


The rotated pole

• The coordinate pole of the RCM grid is usually rotated

• The RCM’s north pole is not in the usual position

• This ensures numerical stability without the need for non-physical filtering

• Avoids high latitudes where filtering is necessary

• RCM grid boxes are quasi-regular in area• All grid boxes are near the equator


Rotated pole example

Full RCM domain on its own rotated lat-lon grid

Full RCM domain projected onto the regular lat-lon grid




• Model grid




Physical processes


Parameterization of physical processes

• Important processes occur in the atmosphere on scales smaller than those which are resolved by the grid of the dynamical part of the model.

• The effects of these unresolved (sub-grid scale) processes are deduced from the large scale state variables predicted by the model (wind, pressure, temperature, moisture).

• This procedure is called parameterization.


Physical parameterizations• Some examples:

• Clouds and precipitation

• Radiation

• Atmospheric aerosols

• Boundary layer

• Land surface

• Gravity wave drag

The strategy or method in which a sub-grid scale process is parameterized by the model is referred to as a scheme. Many different schemes for dealing with various physical processes have been developed by climate scientists. Each climate model (including PRECIS) will use a different set of schemes as part of its unique formulation.


Clouds and precipitation

• ‘Large scale’ and convective processes are treated separately

• In general:• Cloud droplets may be liquid or frozen

• Precipitation is partitioned into snow (solid) and rain

• Solid/liquid/large scale/convective/total precipitation data are output by the model as separate diagnostics

• See STASH codes 4203, 4204, 5205, 5206, 5216 in Appendix C


Large scale clouds and precipitation

• Results from the large scale movement of air masses affecting grid box mean moisture levels

• Due to dynamical ascent (and radiative cooling and turbulent mixing)

• Cloud water and cloud ice are simulated

• Conversion of cloud water to precipitation depends on

• the amount of cloud water present

• precipitation falling into the grid box from above (seeder-feeder enhancement)

• Precipitation can evaporate and melt


Convection and convective precipitation

• Cloud formation is calculated from the simulated profiles of

• temperature

• pressure

• humidity

• aerosol particle concentration

• Entrainment and detrainment

• Anvils of convective plumes are represented


Radiation

• The uneven distribution of solar heating is the ultimate driving force of the general circulation and the original source of all the atmosphere’s available energy


Radiation

• The daily, seasonal and annual cycles of incoming heat from the sun (shortwave insolation) are simulated

• Short-wave and long-wave energy fluxes modelled separately

• SW fluxes depend on

• the solar zenith angle, absorptivity (the fraction of the incident radiation absorbed or absorbable), albedo (reflected radiation/incident radiation) and scattering (deflection) ability

• LW fluxes depend on

• the amount an emitting medium that is present, temperature and emissivity (radiation emitted/radiation emitted by a black body of the same temperature)

• Radiative fluxes are modelled in 14 discrete wave bands spanning the SW and LW spectra


Atmospheric aerosols

• The spatial distribution and life cycle of atmospheric sulphate aerosol particles are simulated

• Other aerosols (e.g. soot, mineral dust) are not included

• Sulphate aerosol particles (SO4) tend to give a surface cooling:

• The direct effect (scattering of incoming solar radiation more solar radiation reflected back to space)

• The first indirect effect (increased cloud albedo due to smaller cloud droplets more solar radiation reflected back to space)

• Natural and anthropogenic emissions are prescribed source terms (scenario specific)


Anthropogenic surface and near-surface SO2 emissions


Boundary layer processes

• The atmospheric or planetary boundary layer is the part of the atmosphere which is directly influenced by the surface.

• A few tens of metres to 1-2 km deep depending on the stability


Boundary layer processes

• Turbulent mixing in the lower atmosphere• Sub-gridscale turbulence mixes heat, moisture and momentum through

the boundary layer

• The extent of this mixing depends on the large scale stability and nature of the surface

• Vertical fluxes of momentum • ground atmosphere

• Fluxes depend on atmospheric stability and roughness length


Surface processes: MOSES

• Exchange of heat and moisture between the earth’s surface, vegetation and atmosphere

• Surface fluxes of heat and moisture• Precipitation stored in the vegetation canopy• Released to soil or atmosphere• Depends on vegetation type

• Heat and moisture exchanges between the (soil) surface and the atmosphere pass through the canopy

• Sub-surface fluxes of heat and moisture in the soil• 4 layer soil model• Root action (evapotranspiration)• Water phase changes • Permeability depending on soil type • Run-off of surface and sub-surface water to the oceans

• Moses II: tiled representation of sub-grid heterogeneity• Changed vegetation types with respect to Moses I

q, T

q, T

q, T

q, T

q, T

q, T


Gravity wave drag

• Flow over mountains can generate waves in the atmosphere

• Waves can propagate vertically, reducing stability

• These waves exert a drag on the flow

• Orientation of orography is taken into account

Wind direction




• Model grid




Initial conditions

• All climate models require information about the initial state of the atmosphere at the beginning of the climate model experiment. These are the initial conditions of the model experiment.

• At the beginning of an experiment, the RCM needs values for all of the prognostic variables throughout the atmosphere and deep soil.

• Derived as much as possible from the same source as the driving GCM or reanalysis experiment


Boundary conditions

• The three dimensional grid of a GCM has no lateral (North-South, East-West) boundaries. The upper boundary is the end of the atmosphere where it contacts outer space. The lower boundary is either the surface of the land or the bottom of the ocean.

• As such the GCM (and RCM) require information about the topography of the Earth’s surface, called surface boundary conditions.

• As RCMs model a limited area, they have an additional requirement of having “input” data provided for them at their outside edges, i.e. their lateral boundaries.


Lateral boundary bonditions

• LBCs = Meteorological boundary conditions at the lateral (side) boundaries of the RCM domain

• They constrain the prognostic variables of the RCM throughout the simulation

• ‘Driving data’ comes from a GCM or analyses

• Lateral Boundary condition variables:

• Wind

• Temperature

• Water vapour

• Surface pressure

• Sulphur variables (for Hadley Centre GCMs)

S tat e va ria b les

State variables

State variables

Stat

e va

riab

les


Other boundary conditions and model inputs• I• Constant data applied at the surface

• Land-sea mask

• Orographic fields (e.g. surface heights above sea level, StDev of altitude)

• Vegetation and soil characteristics (e.g. surface albedo, height of canopy)

• Time varying data applied at the surface• Sea Surface Temperatures and Sea Ice fractions

• Anthropogenic SO2 emissions

• Dimethyl sulphide (DMS) emissions (annual cycle data applied)

• Time varying data applied throughout the atmosphere

• Atmospheric ozone (O3)

• Greenhouse gases (CO2, CH4, N2O, CFCs) concentrations from the same emission scenario used by driving GCM or historical if reanalyses are used

• Constant data applied throughout the atmosphere

• Natural SO2 emissions volcanos

• Annual cycle data applied throughout the atmosphere

• Chemical oxidants (OH, HO2, H2O2 )


Summary

• Models utilise a finite three-dimensional resolution and timestep

• Models solve (integrate) the governing differential equations of mass, momentum and energy

• Sub-grid scale processes are parameterized• Prognostic variables take information from timestep

to timestep• Other quantities diagnosed – diagnostic variables• Initial conditions and boundary conditions are

necessary components of the model.

Further reading

• Annex 1 of the PRECIS handbook:• Jones, R.G., Noguer, M., Hassell, D.C., Hudson,D., Wilson,S.S,

Jenkins,G.J.. and Mitchell, J.F.B. (2004) Generating high resolution climate change scenarios using PRECIS, Met Office Hadley Centre, Exeter, UK 40pp April 2004.

• Weather@home paper: • Massey, N., R. G. Jones, F. E. L. Otto, T. Aina, J.M. Murphy, S. S.

Wilson, D. C. Hassell and M. R. Allen, (2014) Weather@home – development and validation of a very large ensemble modelling system for probabilistic event attribution. Q.J.R.Meteorol.Soc.

• Both the handbook and paper are included in the PRECIS installation:

• $UMDIR/docs/PRECIS_Handbook.pdf

• $UMDIR/docs/RCM_Papers/HadAM3P_formulation.pdf


the precis climate model formulation (hadrm3p) tanzania meteorological agency, 29 th june – 3 rd...

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