Past and Future Climate Simulation Lecture 3 – GCMs: parameterisations (1) From last time – discretising the advection equation (2) Parameterisations:

Past and Future Climate Simulation

Lecture 3 – GCMs: parameterisations

(1) From last time – discretising the advection equation

(2) Parameterisations: clouds/precip, land surface, dust, the oceans.

(3) Implementation: boundary conditions, initial conditions.

(4) Model output and model-data comparison

(5) Experimental Design

(6) Model tuning

2 main parts to atmospheric GCM:

1) Adiabatic (no heat exchanged) – e.g. advection, surface friction.

2) Diabatic (heat exchanged) – e.g. radiation, boundary layer, clouds

Adiabatic advection of a tracer. E.g. a volcanic ash cloud moving around the equator, in a wind of constant speed, u:

180E 180E 180E180W 180W 180W

u

Example of numerics – atmospheric tracer

name A B C D E F G H I J

longitude 0 36E 72E 108E 144E 180E 216E 252E 288E 324E

Initial Concentration

0 1 0 0 0 0 0 0 0 0

U=0.1A0=0, B0=1, C0=0,……

A1=0, B1=B0-0.1, C1=C0+0.1,D1=0,……name A B C D E F G H I J

longitude 0 36E 72E 108E

144E 180E 216E 252E 288E 324E

Initial Concentration 0 1 0 0 0 0 0 0 0 0

Concentration after 1 timestep

0 0.9 0.1 0 0 0 0 0 0 0

Concentration after 2 timesteps

0 0.81 0.18 0.01 0 0 0 0 0 0

Excel demonstration

2 main parts to atmospheric GCM:

1) Adiabatic (momentum equation, last lecture)

2) Diabatic (heat exchanged) – e.g. convection, radiation (including clouds, greenhouse gases, aerosols), precipitation, surface energy balance. All parameterisations.

e.g. precipitation:

If (relative humidity > 85%) then

precipitation = (relative humidity - 85%)*constant

relative humidity = 85%

e.g. convection:

If (temperature gradient > 10oC/km) then

clouds = 1

temperature gradient = 10oC/km

precipitation

(2) Parameterisations

e.g. land surface and turbulence:

(1) Potential dust source regions

e.g. aerosols (here, dust):

(2) Wind speed….

~ u3 with a threshold….

(3) Gusts….

convection

(4) Soil moisture….

(5) Wet deposition…

(6) Dry deposition…(7) Evaluation

Simulate just the uppermost approx 50m of the ocean (homogeneous slab of water).

Typically, atmosphere calculates the surface energy fluxes for each gridbox (net-solar, net-infrared, sensible, latent heats). The sum will not be zero; this is the net energy flux at the surface. If it is positive, the ocean absorbs this and warms up appropriately. If it is negative the ocean will cool down.

Need to parameterise ocean heat transport! Therefore no good for time periods/climates very different from modern.

1) 2)

e.g. oceans:

(3) Configuring Models – boundary conditions/initial conditions

Boundary Conditions: Prescribed (by the user) fields. e.g. land- sea mask.

The model can not change these.

May be time-varying (e.g.SST).

Initial Conditions: Fields used for initialising the model.

After first timestep, model calculates. e.g. surface temperature

Land-sea mask

Boundary conditions

Orography

Sub-gridscale orography

Bathymetry

Surface albedo (for models not predicting vegetation)

Sea surface temperatures (for models without an ocean)

Incoming solar radiation

Greenhouse gases, aerosols

Initial conditions

Surface Temperature Pressure in mid-atmosphere

Cloud cover Soil moisture

+ for ocean: temp,salinity,u,v,seaice

(4) Model output and model-data comparison

Produce a ‘climatology’

Model-data comparison…

Surface Temperature: observations

Surface Temperature: HadCM3

How good are GCMs?(1) temperature

Precipitation: observations

Precipitation: HadCM3

Seaice: observations vs models

How good are GCMs?(2) Precip and seaice

How good are GCMs?(3) El Nino

(5) Experimental Design

Key concept: Testing hypotheses.

Typically, a ‘control’ + a number of ‘sensitivity studies’

• Modify a boundary condition…

“If everyone painted their roofs white, could this mitigate against global warming?”

• Modify an internal parameter…

“Can the fact that all models predict too-cold poles in deep-time palaeoclimates be due to the lack of anthropogenic aerosols?”

• Modify an initial condition…

“Was the Sahara bistable in the mid-Holcoene, 6,000 years ago?”

• Change a parameterisation…

“Does poor representation of clouds in models result in poor ENSO simulation?”

• Change the whole model…

“Which is the best model to use for future climate prediction?”

(6) Model Tuning

We know that internal model parameters affect the control climate produced by a model…often these are not well constrained by data.

Therefore we can legitimately ‘tune’ the model towards observations of modern climate by ‘tweaking’ these parameters…

For a small number of parameters, we can cover ‘parameter space’ well…but….N=Ax , where N is number of simulations, A is how well we sample the parameter space, and x is the number of parameters….soon become unmanageable.

So, various approaches, including random sampling…..

And ‘latin hypercube’ sampling…..

Skill score generated, and then experiments ranked...

Tuned model outperforms original model…..

observations tuned model original model