Perspectives on Climate Modeling

Summer school-BNU-Beijing 5 Aug. 2006

Robert E. Dickinson Georgia Tech

Climate Model what does it do?Starts with known physical laws conservation of momentum, energy, & mass.Views atmosphere, oceans, land as a continuum (i.e. all spatial scales present satisfying same laws).Find and uses numerical approximations to the continuum physical laws.Integrate in time to develop climate statistics same as observed-evaluate success by extent of agreement.On global scale, this agenda very successful.

Climate ModelScaling/parameterizationNeed to describe details within the grid boxes

What limits success of climate models?Processes occur on smaller scales that are different than those resolved on the larger scales.These: a) affect the large scale rules b) change climate on scales that humans live on.Have to some extent been recognized for long time their inclusion has been called parameterization but better called scaling.

What is the problem?Many of the practical aspects of climate modeling are centered at the land surface Such modeling implicitly involves many spatial scaling issues, the more important ones may still be poorly represented; issue of land coupling to precipitation, limited by lacks in treatment of moist processes (convection, clouds, aerosol and cloud micro-physics, etc.).

Progression of Progress on this Topic.Assume state variables on resolved scale:Temperature, soil moisture, vegetation properties, Homogeneous turbulent fluxes, uniform precipitationLook for what not working because of excessive nonlinearity of processes.Find ways to efficiently include missing effects with adequate realism and generality

Examples of processes needed to be parameterized and how first done.Clouds and their effect on radiation and precipitation-put in as a fractional cover.Prescribed from observations; then correlated with relative humidity.Connections to precipitation neglected.Precipitation and its connection to humidity.All atmospheric water in excess of some critical relative humidty assumed converted to precipitation and moved to surface as rain or snow.

Other key examples of parameterization.Boundary layer turbulence-how it exchanges momentum, heat, and moisture between surface and boundary layer, and free atmosphere?How boundary layer processes connect to clouds and precipitation?Collective effect of leaves and roots extract water from soil & move to atmosphere?Moist convection how make clouds & P?

Collective impact of subgrid processesDynamical model viewpoint :Q, external parameters, X = state variable; changes according to:

d X/ dt = F(X,Q) (1)

X = [X] + X , the resolved and unresolved scales. Because of nonlinearities, to solve Eq.(1) for resolved scales, requires introducing some statistics of unresolved scales as additional degrees of freedom.

Climate is a Dynamic SystemForces on Climate systemClimate system responsesIMPACTSFeedbacksMany processes on many scales change and modify the changing state

What has been done & what needed?Have used simple conceptualizations of processes and with limited observations.Now with more advanced computational and observational tools, can look much more carefully at details of processes and establish more elaborate and realistic relationships.E.g. use cloud resolving and and large eddy resolving models.Advanced field programs and satellite data

Observations very importantLocal surfaceMeteorological systemField programsAircraftSatellite

Requires international cooperation and sharing.

ERBSSpaceborne Earth Observation SystemsToms-EPJasonACRIMSATEO-1SeaWiFSIceSat

Show Land is very complex Tibet Plateau from MODIS

Land Scaling from Modeling PerspectiveClimate model grid squares have sides of 100 km (within factor of 4 in either direction).Land-surface model describes processes on spatial scale of about 10 m (plot or point scale).If scaling assumptions are made part of this description, scale dependent -easily lost in model revision.e.g. Bonan (1996) LSM model p 91-canopy evaporation limited to 20% of precipitation, left out of newer CLM.

Rules for Scaling to a Climate ModelPlot scale Land-surface ModelGlobal Data SetsDescribing LandInterface to Atmospheric Model

Hydrological examples impacts of scaling Transpiration and soil evaporation depend nonlinearly on soil moisture. What if 50% W = 0, and 50% W =1.0,versus W=0.5?WET50%

Leaf evaporation of intercepted precipitation. What if P = 0.5 mm/h over all grid-square versus 5 mm/h over 10% of grid square?

How precipitation changed if Tibet Plateau e.g. all at 4.7 km versus a distribution of elevations from 3 km to 6 km?

Radiation Scaling

Current models

RealityThanks to B. Pinty for fig.

What changes if leaf area LAI = 3 of 100% versus 6 over 50% and 0 over 50%?How can we average the z0 roughness of forest and grasland?Such vegetation related averaging questions handled by the widely used Tiling approachBin by plant types (pfts)+ barren, glacier, lakeCan assume either:No competition for light, nutrients, waterCompetition for water (single soil column)

Issue of (Land) ComplexityHave a lot of little pieces (e.g. Ts or Ws)Want to make them add up to one (or a few) piecesView as a large number of dimensions want to project to one (or a few) dimensions.Commonly done by simple averaging of plots but for model may want more stringent physical requirements:

For reduction to low-dimensionality land modelProvide plausible two-way linkages to the large scale atmospheric variables.Provide connections between the low-dimensional variables.Maintain conservation of whatever is conserved energy, moisture,

Stochastic ViewpointAn available tool for climate modelingScience is what we see & efficient ways to summarize & use to infer what we have not seen.Various forms of mathematics provide such summarizing toolsClimate model formulation has traditionally been deterministic, but has always used statistics for summarizing and more sophisticated application are mostly recent, e.g. many papers using pdfs to help describe the formation of clouds.

Use of DistributionsIf we want to average a function of some variable, f(P), where P here is precipitation, cant simply put in an average P Need to average f(P) using all the values of P that occur.May be a lot of detail, but histogram summary statistic can provide all that is needed to do the average

%PExample of a distribution

Applied to land in climate modelSuppose N different values of P can occurCan compute a separate land model for each value we already do that for different points in space.Can simply use one of the Ps chosen randomly stochastic (Monte Carlo) sampling doing only one time probably worse than using the average P- but if done enough times, ends up sampling the distribution.b) is more economical, but it cannot give the land the P made by the atmosphere - fatal

A major old but new issueHow are land processes and P coupled?Depends on surface fluxes of heat and moisture (long-wave?) Connects to heterogeneities in these fluxes (elevation, variations in vegetation, soil wetness)Mediated through boundary layer Jarvis McNaughton suggested BL damps impacts of vegetation.

Top of Boundary LayerWeqa2qa1rc

What can be said?

AMIP II simulations AHS studyGLACE intercomparisons:Some of problem differences in land modelSome from differences in atmospheric model