Physical Climate Models

1
Physical Climate Models

• Simulate behavior of climate system
• Ultimate objective
• Understand the key physical, chemical and
  biological processes that govern climate
• Obtain a clearer picture of past climates by
  comparison with empirical observation
• Predict future climate change
• Models simulate climate on a variety of spatial
  and temporal scales
• Regional climates
• Global-scale climate models simulate the
  climate of the entire planet

2
Climate Processes

• Three processes that must be considered when
  constructing a climate model
• 1) radiative - the transfer of radiation through
  the climate system (e.g. absorption, reflection)
• 2) dynamic - the horizontal and vertical transfer
  of energy (e.g. advection, convection,
  diffusion)
• 3) surface process - inclusion of processes
  involving land/ocean/ice, and the effects of
  albedo, emissivity and surface-atmosphere energy
  exchanges

3
Constructing Climate Models

• Basic laws and relationships necessary to model
  the climate system are expressed as a series of
  equations
• Equations may be
• Empirical derivations based on relationships
  observed in the real world
• Primitive equations that represent theoretical
  relationships between variables
• Combination of the two
• Equations solved by finite difference methods
• Must consider the model resolution in time and
  space i.e. the time step of the model and the
  horizontal/vertical scales

4
Simplifying the Climate System

• All models must simplify complex climate system
• Limited understanding of the climate system
• Computational restraints
• Simplification may be achieved by limiting
• Space and time resolution
• Parameterization of the processes that are
  simulated

5
Model Simplification

• Simplest models are zero order in spatial
  dimension
• The state of the climate system is defined by a
  single global average
• Other models include an ever-increasing
  dimensional complexity
• 1-D, 2-D and finally to 3-D models
• Whatever the spatial dimension, further
  simplification requires limiting spatial
  resolution
• Limited number of latitude bands in a 1-D model
• Limited number of grid points in a 2-D model
• Time resolution of climate models varies
  substantially, from minutes to years depending on
  the models and the problem under investigation
• To preserve computational stability, spatial and
  temporal resolution must be linked
• Can pose problems when systems with different
  equilibrium time scales have to interact as a
  very different resolution in space and time may
  be needed

6
Parameterization

• Involves inclusion of a process as a simplified
  function rather than an explicit calculation from
  first principles
• Sub-grid scale phenomena, like thunderstorms,
  must be parameterized
• Not possible to deal with these explicitly
• Other processes are parameterized to reduce
  computation required
• Certain processes omitted from model if their
  contribution negligible on time scale of interest
• Role of deep ocean circulation while modeling
  changes over time scales of years to decades
• Models may handle radiative transfers in detail
  but neglect or parameterize horizontal energy
  transport
• Models may provide 3-D representation but contain
  much less detailed radiative transfer information

7
Modeling Climate Response

• Ultimate purpose of a model
• Identify response of the climate system
• Change in the parameters and processes that
  control the state of the system
• Climate response occurs to restore equilibrium
  within the climate system
• If radiative forcing associated with an increase
  in atmospheric CO2 perturbs the climate system
• Model will assess how the climate system responds
  to this perturbation to restore equilibrium

8
Model Equilibrium

• Model may require many years of simulated change
  to reach equilibrium
• Final years of simulation averaged

9
Nature of the Model

• One of two modes
• Equilibrium mode
• No account taken of energy storage processes that
  control evolution of climate response with time
• Assume climate responds instantaneously following
  system perturbation
• Transient mode
• Inclusion of energy storage processes
• Simulate development of a climate response with
  time
• Models typically run twice
• In a control run with no forcing
• In a test run including forcing and perturbation
  of the climate system

10
Climate Sensitivity

• Critical parameters
• In the most complex models
• Climate sensitivity calculated explicitly through
  simulations of processes involved
• In simpler models
• Climate sensitivity is parameterized by reference
  to the range of values suggested by the more
  complex models
• This approach, where more sophisticated models
  are nested in less complex models, is common in
  the field of climate modeling

11
Data-Model Comparisons

• Models constructed to simulate Modern circulation
• Changes based on Earth History inserted in model
• Climate output compared with observations

12
One-Dimensional Models

• Simplified representation of of entire planet
• Model driven by global mean incoming solar
  radiation and albedo
• Single vertical column of air divided into layers
• Each layer contains important constituents (dust,
  greenhouse gases, etc)
• Layers exchange only vertically

13
Types of Models

• Energy balance models (EBMs)
• Simulate two fundamental climate processes
• Global radiation balance
• Latitudinal (equator-to-pole) energy transfer
• Radiative-convective models (RCMs)
• Simulate detailed energy transfer through the
  depth of the atmosphere
• Radiative transformations that occur as energy is
  absorbed, emitted and scattered
• Role of convection

14
EBMs

• 0-D EBMs
• Earth is a single point in space
• Global radiation balance modeled
• In 1-D models latitude is included
• Temperature for each latitude band is calculated
• Using latitudinal value for albedo, energy flux,
  etc.
• Latitudinal energy transfer estimated from linear
  empirical relationships
• Difference between latitudinal temperature and
  global average temperature

15
RBMs

• Surface albedo, cloud amount and atmospheric
  turbidity
• Used to determine heating rates atmospheric
  layers
• Imbalance between net radiation at top and bottom
  of each layer determined
• If calculated vertical temperature profile (lapse
  rate) exceeds some stability criterion (critical
  lapse rate)
• Convection is assumed to take place (i.e. the
  vertical mixing of air) until the stability
  criterion is no longer breached

16
Two-Dimensional Models

• Multi-layered atmosphere coupled with Earths
  physical properties averaged by latitude
• Allows simulations of climatic processes that
  vary with latitude
• Angle of incoming solar radiation
• Albedo of Earths surface
• Heat capacity changes

17
Statistical-Dynamical Models

• Combine horizontal energy transfer modeled by
  EBMs with the radiative-convective approach of
  RCMs
• Equator-to-pole energy transfer is more
  sophisticated
• Parameters like wind speed and wind direction
  modeled by statistical relations
• Laws of motion are used to obtain a measure of
  energy diffusion
• Particular useful to investigate role of
  horizontal energy transfer and processes that
  directly disturb that transfer

18
2-D Models

• Advantage
• Simulate long intervals of time quickly and
  inexpensively
• Disadvantage
• Not sensitive to climate processes that depend on
  geographic position of continents and oceans

19
Three-Dimensional Models - GCM

• 3-D representation of Earths surface and
  atmosphere
• Most sophisticated attempt to simulate the
  climate system
• 3-D model based on fundamental laws of physics
• Conservation of energy
• Conservation of momentum
• Conservation of mass
• Ideal Gas Law

20
GCMs

• Represent key features affecting climate
• Spatial distribution of land, water, ice
• Regional variation in heat capacity and albedo of
  surface
• Elevation of mountains and glaciers
• Concentrations of greenhouse gases
• Seasonal variations in solar radiation
• Calculations at interactions of grid boxes

21
GCMs

• Atmospheric variables at each grid point requires
  the storage, retrieval, recalculation and
  re-storage of 105 figures at every time-step
• Models contain thousands of grid points
• GCMs are computationally expensive
• Can provide accurate representations of planetary
  climate
• Simulate global and continental scale processes
  in detail
• GCMs cannot simulate synoptic regional
  meteorological phenomena (e.g.,tropical storms)
• Play an important part in the latitudinal
  transfer of energy and momentum
• Spatial resolution of GCMs limited in vertical
  dimension
• Many boundary layer processes must be
  parameterized

22
Sensitivity Test

• Control case established
• Modern climate simulated
• One boundary condition altered at a time
• Model output compared with present day climate
  simulation
• Information reveals impact of that boundary
  condition
• Boundary condition examples
• Continental configuration
• Ice sheet expansion
• Solar radiation influx
• Greenhouse gas concentrations

23
Model Resolution

• Can it image New Zealand? this is probably now
  out of date! (2 lat x 3 long)

24
Atmospheric and Ocean GCMs

• Atmospheric GCM more sophisticated
• Much detail known about atmospheric circulation,
  elevations, landmasses, etc.
• Ocean GCM primitive
• Rudimentary knowledge of oceanic circulation
• Deep water formation
• Difficult to model important small features
• Fast-moving narrow currents

25
Oceanic GCMs

• Similar in construction to atmospheric GCM
• Lower boundary seafloor
• Water column divided grid boxes
• Low resolution, fewer layers/boxes, biology
• Output temperature, salinity, sea ice, gases

26
Atmospheric and Ocean GCMs

• Oceanic GCMs simulates circulation over several
  years to decades
• Atmospheric GCMs simulates circulation over
  several hours to weeks
• Basic incompatibility between models
• A-GCMs may be used to drive O-GCMs
• Asynchronous coupling
• Atmospheric conditions drive ocean
• Oceanic conditions drive atmosphere
• Alternation keeps systems from getting wacky

27
Geochemical Models

• Mass balance models
• Follow movement of Earth materials from one
  reservoir to another
• Physical or chemical form
• Models focus on sources, rates of transfer and
  depositional fate of materials
• Commonly trace fate of materials using a
  geochemical tracer
• Example 18O content of seawater

28
One-way Mass Transfer Models

• Movement from source to sink
• Movement from one reservoir to another
• If materials transferred has unique chemical or
  physical signature
• Flux rate (mass transfer time-1) can be
  determined
• Example calving of icebergs
• Influx of ice-rafted debris
• Determined by physical sedimentology
• Quantified by point-counts

29
Mass Balance Equations

• Simple mass balance
• Ftotal F1 F2 F3
• Tracer mass balance
• TR (F1T1 F2T2 F3T3)/(F1 F2 F3)
• TR is the mean value of tagged inputs
• Mass balance of two components in system
• Tracer entering tracer leaving
• TR ƒinTin (1 ƒout)Tout

30
Tracer Mass Balance Example

• Global carbon redox balance
• Average d13C of carbon on Earth -4.6
• CO2 in hydrothermal vents
• Average d13C of carbonates 0.6
• Average d13C of organic carbon -25.4
• Know
• 13C entering 13C leaving
• dR ƒodo (1 ƒo)dcarb
• 4.6 ƒo(-25.4) (1 ƒo)0.6
• 20 of carbon buried in marine sediments is
  organic carbon

31
Chemical Reservoirs

• Earth reservoirs
• Atmosphere, ocean, ice, vegetation and sediments
• Ocean most important reservoir
• Interacts with other reservoirs
• Receives weathering products
• New minerals deposited in sediments
• Tracer is carried to ocean, mixed and trapped in
  sedimentary mineral archive

32
Steady State Tub

• If flux of tracer into and out of reservoir are
  equal, the system is at steady state

33
Residence Time

• Time it takes for tracer to pass through tub
• Residence time reservoir size/flux
• Residence time of tracer typically gt mixing time
  of the ocean (1500 y)
• Tracer distribution homogenous
• Tracer concentration or isotopic composition is
  everywhere equal
• Records whole-ocean chemistry during deposition

34
Reservoir Exchange Models

• Models can be designed to track reversible
  exchange between different sized reservoirs

35
Reservoir Exchange

• Monitor cycling of tracers between reservoirs
  through time
• Tracer with distinctive value moves freely
  between reservoirs
• Typically between small and large reservoirs
• Ocean and atmosphere, vegetation, land
• Monitors change in size of smaller reservoir
• Tracer exchange detected in sedimentary minerals
• Exchange produces change in volume and tracer
  value in ocean

36
Reservoir Exchange Example

• Change in the d18O of seawater
• d18O of glacial ice and seawater different
• Change in glacial ice volume
• Produces small changes in the oxygen isotopic
  composition of seawater
• Change in seawater d18O recorded
• Calcareous shells or sediment porewater
• Glacial ice small reservoir and ocean large
  reservoir

37
Time-Dependent Models

• Most geochemical models assume steady-state
  conditions
• Time-dependent models assume steady-state only
  during equilibrium conditions
• Steady-state conditions imply no change in
  reservoir size
• Time-dependent models allow changes in reservoir
  size
• From one equilibrium state to another
• Under equilibrium
• Steady-state conditions prevail

38
CO2 and Long-Term Climate

• What has moderated Earth surface temperature over
  the last 4.55 by so that
• All surface vegetation did not spontaneously
  catch on fire and all lakes and oceans vaporize?
• All lakes and ocean did not freeze solid?

39
Greenhouse Worlds

• Why is Venus so much hotter than Earth?
• Although solar radiation 2x Earth, most is
  reflected but 96 of back radiation absorbed

40
What originally controlled C?

• In solar nebula most carbon was CH4
• Lost from Earth and Venus
• Earth captured 1 in 3000 carbon atoms
• Tiny carbon fraction in the atmosphere as CO2
• 60 out of every million C atoms
• Bulk of carbon in sediments on Earth
• CaCO3 (limestone and dolostone) and organic
  residues (kerogen)
• Venus probably had similar early planetary
  history
• Most carbon is in atmosphere as CO2
• Venus has conditions that would prevail on Earth
• All CO2 locked up in sediments were released to
  the atmosphere

41
Earth and Venus

• Water balance different on Earth and Venus
• If Venus and Earth started with same components
• Venus should have either
• Sizable oceans
• Atmosphere dominated by steam
• H present initially as H2O escaped to space
• H2O transported "top" of the Venusian atmosphere
• Disassociated forming H and O atoms
• H escaped the atmosphere
• Oxygen stirred back to surface
• Reacted with iron forming iron oxide

42
Planetary Evolution Similar

• Although Earth and Venus started with same
  components
• Earth evolved such that carbon safely buried in
  early sediments
• Avoiding runaway greenhouse effect
• Venus built up CO2 in the atmosphere
• Build-up led to high temperature
• High enough to kill all life
• If life ever did get a foothold
• Once hot, could not cool

43
Why Runaway Greenhouse?

• Don't know why Venus climate went haywire
• Extra sunlight Venus receives?
• Life perhaps never got started?
• No sink for carbon in organic matter
• Was the initial component of water smaller than
  that on Earth?
• Did God make Venus as a warning sign?

44
Early Earth Faint Young Sun

• Solar Luminosity 4.55 bya 25 lower than today
• Faint young Sun paradox
• If early Earth had no atmosphere or todays
  atmosphere
• Radiant energy at surface well below 0C for
  first 3 billion years of Earth history
• No evidence in scant Archean rock record that
  planet was frozen

45
Early Earth A Greenhouse World

• Earth was more Venus-like during Archean
• Models indicate that greenhouse required
• Several greenhouse gases
• H2O, CO2, CH4, NH3, N2O
• H2O and CO2 most likely
• 102-103 x PAL CO2

46
Archean Atmosphere

• Faint young Sun paradox presents dilemma
• 1) What is the source for high levels of
  greenhouse gases in Earths earliest atmosphere?
• 2) How were those gases removed with time?
• Models indicate Suns strength increased slowly
  with time
• Geologic record strongly suggests Earth
  maintained a moderate climate throughout Earth
  history (i.e., no runaway greenhouse like on
  Venus)

47
Source of Greenhouse Gases

• Input of CO2 and other greenhouse gases from
  volcanic emissions
• Most likely cause of high levels in Archean