Chapter 5 Climate Models 5.1 Constructing a Climate Model 5.2* Numerical representation of atmospheric and oceanic equations atmospheric and oceanic equations 5.3 Parameterization of small scale processes 5.4 Climate simulations and climate drift 5.5** The hierarchy of climate models 5.6 Evaluation of climate model simulations for present day climate simulations for present day climate *Skip except mention of Fig. 5.9, **Skim Neelin, Climate Change and Climate Modeling, Cambridge UP

Typical atmospheric GCM grid 5.1 Constructing a Climate Model Figure 5.1 For each grid cell, single value of each variable (temp., vel.,…)  Finite number of equations Vertical coordinate follows topography, grid spacing varies Transports (fluxes) of mass, energy, moisture into grid cell  Budget involving immediate neighbors (in balance of forces, PGF involves neighbors) Effects passed from neighbor to neighbor until global Budget gives change of temperature, velocity, etc., one time step (e.g. 15 min) later 100yr=4million 15min steps Neelin, Climate Change and Climate Modeling, Cambridge UP

Vertical column showing parameterized physics so small scale processes within a single column in a GCM Figure b Treatment of sub-grid scale processes Neelin, Climate Change and Climate Modeling, Cambridge UP

Topography of western North America at 0.3  and 3.0  resolutions Figure c Resolution and computational cost Neelin, Climate Change and Climate Modeling, Cambridge UP

Supplemental: Topography of North America at 0.5  and 5.0  resolutions Neelin, Climate Change and Climate Modeling, Cambridge UP

Computational time = (computer time per operation)  (operations per equation)  (No. equations per grid-box)  (number of grid boxes)  (number of time steps per simulation) Increasing resolution: # grid boxes increases & time step decreases Half horizontal grid size  half time step (why? See below)  twice as many time steps to simulate same number of years Doubling resolution in x, y & z  (# grid cells)  (# of time steps)  cost increases by factor of 2 4 =16 In Fig. 5.3, 5 to 0.5 degrees  factor of 10 in each horizontal direction. So even if kept vertical grid same,  (# grid cells)  (# of t steps)= 10 3 Suppose also double vertical res.  2000 times the computational time i.e. costs same to run low-res. model for 40 years as high res. for 1 week To model clouds, say 50m res.  times res. in horizontal, if same in vertical and time  times the computational time … and will still have to parameterize raindrop, ice crystal coalescence etc. 5.1.c Resolution and computational cost Neelin, Climate Change and Climate Modeling, Cambridge UP

Computational costs cont’d Why time step must decrease when grid size decreases: Time step must be small enough to accurately capture time evolution and for smaller grid size, smaller time scales enter. A key time scale: time it takes wind or wave speed to cross a grid box. e.g., if fastest wind 50 m/s, crosses 200 km grid box in ~ 1 hour If time step longer, more than 1 grid box will be crossed: can yield amplifying small scale noise until model “blows up” (for accuracy, time step should be significantly shorter) [See Fig. 5.9 for an example of this] Examples of model resolutions in IPCC (2007) report: coarse 5  4°; typical ~2  2°; high 1° to 1.5° in lat. and longitude Neelin, Climate Change and Climate Modeling, Cambridge UP

Longitude-height cross-section through an ocean model grid Figure d An ocean model and ocean-atmosphere coupling Neelin, Climate Change and Climate Modeling, Cambridge UP

Atmosphere-ocean coupling in a GCM via energy fluxes and wind stress Figure 5.5 Neelin, Climate Change and Climate Modeling, Cambridge UP

Land surface types 5.1.d Land surface, snow, ice, and vegetation Figure 5.6 Neelin, Climate Change and Climate Modeling, Cambridge UP

Summary of equations for atmosphere and ocean models Equation NameModelCommentsCorresp.Eq. No. Horizontal velocity eqns.Atm/OceanPrognostic (u, v)Eq. 3.4, 3.5 Hydrostatic equationAtm/OceanEq. 3.8 Equation of stateAtmIdeal gas lawEq OceanEq Temperature equationAtmPrognostic (T)Eq OceanEq Continuity equationAtmEq OceanEq Moisture equationAtmPrognostic (q)Eq Salinity equationOceanPrognostic (S) Surface pressure eq.Atm1 levelEq Surface height eq.Ocean1 levelEq Surface temperature eq.Land1 or a few levels Soil moisture equationLanda few levels Snow cover equationsLand1 or a few levels Sea ice equations(Ocean)ice fraction, thickness Table 5.1 Neelin, Climate Change and Climate Modeling, Cambridge UP

5.2 Numerical representation of atmos. and oceanic eqns. Finite differencing of a pressure field [Skip] 5.2.a Finite difference versus spectral models Figure 5.7 Neelin, Climate Change and Climate Modeling, Cambridge UP

Spectral representation of a pressure field Figure 5.8 [Skip] Neelin, Climate Change and Climate Modeling, Cambridge UP

Simple time stepping scheme [Skim] 5.2.b Time-stepping and numerical stability  T ′/  t= −T ′/   (T′ n+1 -T′ n )/  t = −T′ n /  Time step  t must be small compared to physical time scales, here decay time , or extrapolating slope can give erroneous growth For advection,  t must be small rel. to timescale to cross grid box u/  x Figure 5.9 Neelin, Climate Change and Climate Modeling, Cambridge UP

"C" - Staggered grid [Skip] 5.2.c Staggered grids Figure 5.10 Neelin, Climate Change and Climate Modeling, Cambridge UP

Vertical mixing and fluxes of moisture 5.3a Mixing and surface fluxes 5.3 Parameterization of small scale processes Net flux across face of grid box due to mixing by smaller scale motions parameterized as proportional to difference in q at levels k, k-1 Evaporation flux of surface depends on difference between lowest level q and saturation value at surface Figure 5.11 Neelin, Climate Change and Climate Modeling, Cambridge UP

Change in environmental lapse rate Figure 5.12 [Skip] 5.3b Dry convection Neelin, Climate Change and Climate Modeling, Cambridge UP

Parcel stability Figure 5.13 [Skip] 5.3c Moist convection Neelin, Climate Change and Climate Modeling, Cambridge UP

Land surface model: soil moisture and evapotranspiration Figure 5.14 Runoff Soil capacity Precipitation Evapotranspiration Canopy (stomatal) resistance Aerodynamic resistance Soil moisture Leaf area index Canopy Interception 5.3d Land surface processes and soil moisture Neelin, Climate Change and Climate Modeling, Cambridge UP

Sea ice model processes 5.3e Sea ice and snow Figure 5.15 Neelin, Climate Change and Climate Modeling, Cambridge UP

Model typeComments Simple models(e.g., energy balance models) Intermediate complexity models (e.g., Cane-Zebiak model for ENSO, EMICs) Hybrid coupled models (ocean GCM with a simple atmosphere) Atmospheric GCM with a mixed- layer ocean Regional climate models (Boundary conditions from global climate models) Global atmospheric GCM with a regional ocean GCM (e.g., tropical Pacific) Global ocean-atmosphere GCM Earth system model with interactive vegetation and chemistry (includes interactive carbon cycle) Table The hierarchy of climate models [Skip] Neelin, Climate Change and Climate Modeling, Cambridge UP

Climate drift 5.5 Climate simulations and climate drift Examples of model integrations (or runs, simulations or experiments), starting from idealized or observed initial conditions. Spin-up to equilibrated model climatology is required (centuries for deep ocean). Model climate differs slightly from observed (model error aka climate drift); climate change experiments relative to model climatology. Figure 5.16 Neelin, Climate Change and Climate Modeling, Cambridge UP

Atm. component of NCAR_CCSM3 forced by observed SST (AMIP) Precipitation Climatology with observed (CMAP) 4mm/day contour June - August December-February Figure 5.17 AMIP=Atm. Model Intercomparison Project CMAP=CPC Merged Analysis of Precip. CPC=NOAA Climate Prediction Center CCSM=Community Climate System Model 5.6 Evaluation of climate model simulations for model simulations for present day climate present day climate 5.6a Atmos. model clim. from specified SST Neelin, Climate Change and Climate Modeling, Cambridge UP

Observed (CMAP) Precipitation Climatology June - August December-February Recall from Fig Neelin, Climate Change and Climate Modeling, Cambridge UP

4 mm/day Precipitation climatology contour Observed (CMAP) and coupled/uncoupled model Figure 5.18 NCAR_CCSM3 Coupled simulation climatology (20 th century run, ) & Atmospheric component forced by obs. SST (AMIP) 5.6b Climate model simulation of climatology June - August December-February Neelin, Climate Change and Climate Modeling, Cambridge UP

HadCM3 simulation precipitation climatology (20 th century run, ) Figure 5.19 July January Neelin, Climate Change and Climate Modeling, Cambridge UP

Observed (CMAP) Precipitation Climatology Recall Figure 2.13 Neelin, Climate Change and Climate Modeling, Cambridge UP July January

Observed (CMAP) and 5 coupled models 4 mm/day precip. contour Figure 5.20 Coupled simulation precipitation climatology (20 th century run, ) June - August December-February Neelin, Climate Change and Climate Modeling, Cambridge UP

Observed (CMAP) and 7 other coupled models 4 mm/day precip. contour Coupled simulation precipitation climatology (20 th century run, ) June - August December-February Supplemental Figure Neelin, Climate Change and Climate Modeling, Cambridge UP

NCAR_CCSM3 coupled simulation SST climatology (20 th century run, ) Figure 5.21 June - August December-February Neelin, Climate Change and Climate Modeling, Cambridge UP

Observed SST climatology Reynolds data set ( ) Recall Figure 2.16 July January Neelin, Climate Change and Climate Modeling, Cambridge UP

HadCM3 coupled simulation near surface air temperature (20 th century run, ) July January Figure 5.22 Neelin, Climate Change and Climate Modeling, Cambridge UP

Regions of sea ice concentrations > 15% for Mar. & Sept. Figure 5.23 March (light shading/blue contour) September (dark shading/pink contour) Contours repeat observed for comparison on 2 model simulations Neelin, Climate Change and Climate Modeling, Cambridge UP

Precipitation anomaly (mm/day) for Dec.-Feb. for the average of 5 El Nino events minus the average of 5 La Nina events Figure c Simulation of ENSO response CMAP Obs AMIP CCSM3 AMIP MRI Neelin, Climate Change and Climate Modeling, Cambridge UP

Shaded where statistically significant at 95% level. CMAP Obs AMIP CCSM3 AMIP MRI Precipitation anomaly (mm/day) for Dec.-Feb. for the average of 5 El Nino events minus the average of 5 La Nina events Figure 5.24 alternate Neelin, Climate Change and Climate Modeling, Cambridge UP

Upper tropospheric (200mb) geopotential height anomaly (mm/day) for Dec.-Feb. for the avg of 5 El Nino events minus the avg of 5 La Nina events Figure 5.25 NCEP reanalysis (observational product) AMIP CCSM3 AMIP MRI Neelin, Climate Change and Climate Modeling, Cambridge UP NCEP=National Centers for Environmental Prediction; Reanalysis has observations interpolated via a weather forecast model AMIP=Atm. Model Intercomparison Project CCSM=Community Climate System Model