Climate Modeling Dr. Jehangir Ashraf Awan Pakistan Meteorological Department Source: Slides partially taken from A. Pier Siebesma, KNMI & TU Delft
Key Questions What is a climate model? What types of climate models are there?
What is a climate model? A mathematical representation of the many processes that make up our climate. Requires: Knowledge of the physical laws that govern climate Mathematical expressions for those laws Numerical methods to solve the mathematical expressions on a computer (if needed) A computer of adequate size to carry out the calculations
Important climate model components Radiation as it drives the system each climate model needs some radiation Dynamics description of the exchange of shortwave and longwave the movement of energy in the system both in the horizontal and vertical (winds, ocean currents, convection, bottom water formation) Surface processes the exchange of energy and water at the ocean, sea-ice and land surface, including albedo, emissivity, etc. Chemistry chemical composition of the atmosphere, land and oceans as well as exchanges between them (e.g., carbon exchanges)
Model resolution Depending on our question we need to decide how to divide the Earth in our model and how often we need to calculate the state of the system. Choices in space are 0-d (point) 1-d (e.g., 1 vertical column) 2-d (1 vertical layer, latitude and longitude), and 3-d (many layers, lat and lon) Examples: A global energy balance model treats the Earth as one point and has no time resolution Weather forecast models calculate the weather every few minutes every 10 km.
2. The Simplest Climate Model: 0-dimensional energy balance model
Energy Absorbed by the Atmosphere (1) 1) How much energy is reaching the top of the atmosphere from the sun? The solar flux received at the top of the atmosphere from the sun depends on the distance of the Earth from the sun. The average value of this flux is called the solar constant, S0, and has a value of 1367 Wm -2. Note that this value varies as the orbit of the Earth around the sun is not a perfect circle. 1367 Wm -2 S0
Energy Absorbed by the Atmosphere (2) 2) How much energy is directly reflected back to space? Some of the solar flux arriving on Earth is directly reflected back to outer space by clouds and the Earth surface. Clouds have a very high albedo * (up to 0.8). Taking all reflectors (clouds, ground, sea) together, the Earth has an albedo of approximately 0.3. Hence only 70 % of the solar flux arriving on earth is available to the system. AE*S0 S0 Albedo comes from a Latin word for whiteness
Energy Absorbed by the Atmosphere (3) 3) What is the total energy absorbed by the Earth? The flux we used so far describes the energy per unit area, hence we now know how much energy per square meter is available to the Earth from solar radiation. To calculate the total energy absorbed we need to multiply the flux with the area that intercepts that radiation. As we can see, that area (the shadow area) is a disk with the radius of the Earth: 2 R e
Energy Absorbed by the Atmosphere (4) E in 2 S 0 AS 0 R E Total energy absorbed Reflected flux Solar flux at TOA Area of a disk with radius of the earth or after some minor rearrangement: E in S 0 2 1 A R E
Energy Emitted by the Atmosphere (1) 1) How much energy is emitted per unit area from the Earth? For a good estimate of this number, we can assume that the Earth is a blackbody. By making that assumption we can now use the Stefan- Boltzmann law to calculate the flux of longwave (infrared) radiation as: F E T E 4 5.67 10 8 W m 2 K 4 where σ is the Stefan Boltzmann constant and T E the temperature at which the Earth emits radiation.
Energy Emitted by the Atmosphere (2) 2) How much energy is emitted in total from the Earth? Again, to find the total amount of energy emitted by the Earth we need to multiply the flux with the area over which energy is emitted. Longwave radiation is emitted from the entire Earth surface and hence: E out T E 4 A E T E 4 4 R E 2
Earth s Radiative Balance (1) On average the energy absorbed and emitted by Earth have to balance, as otherwise the system would heat or cool indefinitely. We can calculate the temperature the Earth emits at by assuming a balance of incoming and outgoing energy: E in E out
Earth s Radiative Balance (2) S 0 E in E out 1 A R 2 E T 4 2 E 4 R E S0 4 1 A) T 4 T 4 E S E 1 A 0 4 T E S 0 1 A 4 255K 18 C 4 The world s simplest climate model
Remarks We calculated that the temperature at which the Earth emits radiation is about -18 o C. If the Earth had no atmosphere, this would be the mean temperature at the surface. We know the observed mean surface temperature is about +15 o C. Hence the presence of the atmosphere increases the surface temperature by 33 o C. This is due to the Earth greenhouse effect, the magnitude of which can be calculated as: T g T S T E 15 C 18 C 33 C
The Greenhouse Effect How does it work? The atmosphere contains gases that absorb the infrared radiation emitted from the surface and then re-emit it from the atmosphere in all directions. Some of this radiation will therefore be emitted downwards and be an additional source of energy at the surface, which leads to a warming at the surface! Source: IPCC, 2007
General Circulation Models
Global climate models (GCMs) General Circulation Models (GCMs) are computer-driven models for weather forecasting, understanding climate and projecting climate change. There are both atmospheric GCMs (AGCMs) and ocean GCMs (OGCMs). An AGCM and an OGCM can be coupled together to form an atmosphere-ocean coupled general circulation model (AOGCM).
General circulation models Processes to include
Atmospheric model Component E-W wind N-S wind vertical balance mass Temperature Ideal Gas 6 equations for 6 unknowns (u,v,w,t,p,ρ) - Moisture often added as 7th equation
Atmospheric models - dicing up the world 2.5 deg x 2.5 deg grid
Atmospheric models - dicing up the world Vertical levels
Emission Scenarios In order to determine the impact of climate change in the future, we need to have an idea of the concentrations of greenhouse gases and other pollutants in the atmosphere to which climate is sensitive, in the years to come. These concentrations depend on their emissions from various sources, natural as well as man-made. Emissions scenarios describe future releases into the atmosphere of greenhouse gases, aerosols, and other pollutants and, along with information on land use and land cover, provide inputs to climate models.
Intergovernmental Panel on Climate Change (IPCC) Panel of scientists that synthesizes published research on climate including observations, modeling, and paleoclimate change 1990 1995 2001 2007 2013/14 First Assessment Report (FAR)Second Assessment Report (SAR) Third Assessment Report (TAR) CMIP1 & CMIP2 Fourth Assessment Report (AR4) CMIP3 Fifth Assessment Report (AR5) CMIP5 Coupled Model Intercomparison Project (CMIP) Defines the set of standard experiments (with IPCC guidance) Coordinates with modeling groups around the world who choose to participate Groups run the specified set of experiments with their model and contribute the output to the CMIP data base following protocols for uniform data conventions!
SRES Scenarios CMIP2(IPCC TAR), CMIP3 (IPCC AR4) SRES (Special Report on Emissions Scenarios, 2000) Projections of climate change in IPCC TAR (2001), AR4 (2007) Based on assumptions about driving forces such as patterns of economic and population growth, technology development, and other factors, major families of SRES emissions scenarios are: A1 (A1FI, A1T, A1B) A2 B1 B2 For details https://www.ipcc.ch/pdf/special-reports/spm/sres-en.pdf
Representative Concentration Pathways (RCP) CMIP5 (IPCC AR5) Consistent sets of projections of only the components of radiative forcing that are meant to serve as input for climate modelling. Conceptually, the process begins with pathways of radiative forcing, not detailed socioeconomic narratives or scenarios. Central to the process is the concept that any single radiative forcing pathway can result from a diverse range of socioeconomic and technological development scenarios.
RCP Four RCPs were selected, defined and named according to their total radiative forcing in 2100. RCP 8.5 Rising radiative forcing pathway leading to 8.5 W/m² in 2100. RCP 6 RCP 4.5 RCP 2.6/RCP 3-PD Stabilization without overshoot pathway to 6 W/m² at stabilization after 2100 Stabilization without overshoot pathway to 4.5 W/m² at stabilization after 2100 Peak in radiative forcing at ~ 3 W/m² by mid-century, returning to 2.6 W/m² by 2100
Climate Computing How many calculations does an atmospheric model alone have to perform: 2.5 x 2.5 degrees -> about 10,000 cells 30 layers in the vertical -> about 300,000 grid boxes At least 7 unknowns -> about 2.1 million variables Assume 20 calculations (low estimate) for each variable -> about 42 million calculations per timestep Time step of 30 minutes -> about 2 billion calculations per day 100 years of simulation -> 73 trillion calculations
Climate Computing Climate modelling requires the use of the most powerful supercomputers on Earth, and even with those we have to simplify the models. Climate modelling is therefore constrained by the computer capabilities and will be for the foreseeable future. McGuffie and Henderson-Sellers, 2005
Global Climate Models have their limitations GCMs have a coarse resolution (150~300 km) Land-sea mask Topography Convection, clouds, precipitation Land atmosphere interaction GCM RCM How can we increase the resolution?
Dynamical downscaling with regional climate models (RCMs) RCMs are GCMs, but: higher resolution (10km) limited domain Purpose: Better local representation RCM needs to be feeded at the boundaries with data from a GCM Acts like a looking glass. But.. which GCM should be used for downscaling????
Predictability Weather (atmospheric) prediction is essentially a initial value problem: timescale boundary conditions >> timescale prediction period (15 days) e.g. Continents, Glaciers, Atmospheric Composition, vegetation, solar constant, ocean temperatures can be kept constant! Atmosphere loses its memory after two weeks
Long lasting sea surface temperature (SST) anomalies: El Nino On timescales of seasons to years:
.. and is influencing the precipitation
El Niño Teleconnections But only at certain areas in the world..
Predictions at a seasonal scale Extension beyond the 15 days predictability horizon is possible through the thermal inertia of oceans, snow, soil Requires coupling of the atmosphere with the ocean (which is the most important source of inertia) So far only somewhat successful in the tropics. Outside the tropics the coupling between atmosphere and ocean is weak. In Europe there is little skill on the seasonal scale * Note that the problem is slowly shifting from a initial value problem (weather prediction) to a boundary condition (climate prediction) problem *therefore any seasonal numerical prediction of a horror winter in Europe does not have any skill.
Two types of predictions Edward N. Lorenz (1917 2008) Predictions of the 1 st kind Initial-value problem Weather forecasting Lorenz: Weather forecasting fundamentally limited to about 2 weeks Predictions of the 2 nd kind Boundary-value problem IPCC climate projections (century-timescale) No statements about individual weather events Initial values considered unimportant; not defined from observed climate state Climate modeling 38
Climate Predictions decadal (10yrs) to centennial is possible through changes of the boundary conditions of the atmosphere: through the ocean (1 to 10 year), through change in greenhouse gases (10+ years)