Climate Modelling

Climate Modeling

Numerical Modeling Basics If it is true, as every scientist believes, that subsequent atmospheric states develop from the preceding ones according to physical law, then it is apparent that the necessary and sufficient conditions for the rational solution of forecasting problems are the following: 3) A sufficiently accurate knowledge of the state of the atmosphere at the initial time 4) A sufficiently accurate knowledge of the laws according to which one state of the atmosphere develops from another - Vilhelm Bjerknes (1904)

Norwegian physicist and meteorologist “Father of modern meteorology”

http://www.uni-leipzig.de/~meteo/ORGA/BILDER/bjerkn.gif

History of Climate Modeling • Lewis Fry Richardson Attempted first numerical weather forecast while driving ambulances for the Red Cross in WWI Experiment was “A spectacular failure”

• Late 1940’s – Development of first electronic computers – Institute for Advanced Studies (IAS) in Princeton under Jule Charney produced first successsful NWP forecast

Jule Charney

John von Neumann

• Mid-late 1950s – First routine numerical weather forecasts by U.S. Joint Numerical Weather Prediction Unit – First efforts to regularly collect weather data at surface and upper atmosphere – Major general circulation modeling effort evolved into the Geophysical Fluid Dynamics Laboratory at Princeton University

Joseph Smagorinsky, Former GFDL Director

• Early to mid 1960s – Ocean models developed – Roles of sea ice, snow, land processes, and biosphere begin to be incorporated into general circulation models (GCMs)

Grid and Time Resolution • Computing power limits the amount of calculation that can occur • Thus, calculations are performed on a “grid” of points – Typically 5° x 5° horizontal grid (~ 555 x 555 km at the Equator) – Also divide the atmosphere into vertical layers

• Since we are stepping forward in time, climate models have 4 dimensions

Model Stability • As spatial resolution increases, the time resolution must also increase or climate models will not yield a stable solution (they will “blow up”) – This is called the CFL criterion, named after Courant, Friedrichs, and Lewy, and is represented mathematically as: Fastest signal propogating through the model domain (e.g. a gravity wave in the atmosphere with a speed of 300 m/s)

c∆t ≤1 ∆x

** Richardson used a 6 hour time step (∆x = 200 km) in his experiment. He would have had to used a time step of 8 minutes to find a stable solution

http://www.bom.gov.au/info/ftweather/images/modelling.gif

Vertical Layers • Climate models usually have less vertical slices than typical forecast models • Not equally spaced – More levels closer to ground and near the tropopause (things change quickly at those points

• Sigma Coordinate is typically used as the vertical coordinate

p σ= ps

Actual pressure

Surface pressure

Vertical Layers

Sigma Coordinate • Advantages – Conforms to natural terrain (mountains are represented in models) – Will never intersect the ground like a height coordinate – Simplifies mathematical equations in model

• Limitations – Complicates certain computations (pressure gradient force in sloped regions – Sometimes land points extend into oceans due to smoothing near mountainous terrain

Parameterization • Since by necessity our grid is large, many things occur at scales smaller than the grid size – Clouds

• Model cannot “see” these things • Parameterizations are employed to simulate the large-scale feedback that small scale features produce – Calculate an “average” cloudiness over a grid box

Typical Climate Model Parameterizations • Convection and Clouds – Mass, momentum, heat, moisture fluxes – Fluxes are usually much larger at scales smaller than a climate model grid size – Radiation interactions

• Turbulence • Radiation • Boundary Layer – Fluxes of heat, moisture, momentum

Gravity waves within a stratocumulus deck

Structure of a GCM

Fig. 10.1 page 256

Basic Meteorological Equations • Derived from basic laws of physics – Equation of state • Relates pressure, temperature, and density for dry air)

( P = ρRT

– Horizontal equations of motion • How the zonal and meridional wind change with time. Depends on latitude, pressure gradient force, and friction

– Hydrostatic Equation • Balance of vertical pressure gradient force with gravity

– Conservation of mass and energy • Continuity equation and First Law of Thermodynamics

Basic Meteorological Equations • These equations are called the primitive equations • The unknown values are zonal wind (u), meridional wind (v), vertical wind (w), density (ρ), pressure (p), and temperature (T)

Land Component of GCM • Must contain heat and moisture balance equations and a snow cover model • GCMs have been shown to be very sensitive to surface albedo and moisture characteristics

Ocean Component of GCM • Similar governing equations as atmosphere except: – Oceans are liquid – Ocean basin geometry is more complex

• Many important features in the ocean are too small to be realized in the model – Gulf Stream, Kuroshio currents less than 1° wide

Sea Ice Models • Sea ice: – Increases surface albedo – Inhibits exchanges of heat, moisture, and momentum – Alters local salinity

• Assume ice forms if sea surface temperature < -2°C • Also should predict movement of ice

Current Climate Models • Community Climate System Model (CCSM) – Supported by National Science Foundation (NSF) and Department of Energy, run by National Center for Atmospheric Reseach (NCAR) – 26 vertical levels, 2.8° x 2.8° horizontal resolution (atmosphere), 1° x 1° (ocean and ice) – 700 billion calculations to recreate one day

Supercomputer at NCAR

http://www.ucar.edu/communications/CCSM/overview.html

Can CCSM Model Earth’s Climate Accurately? • Reproduced Earth climate from 1870 – 2000, including El-Niños • Reproduced Earth climate in 1000 year simulation – Very close to proxy data – No “flux adjustment” (tweaking the numbers)

What Can’t CCSM Model? • • • • •

Ocean Eddies Impacts of rain and snowfall Carbon cycling Land surface changes with time More local / regional climate behavior

Much higher model resolution required to satisfy these desires!