Chapter 13 linking spatial and temporal aspects of climate through quantitative methods computerized Climate Models

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Computerized Climate Models

  • General circulation models (GCMs) generally involve the prediction of the global atmospheric circulation based on dynamical conditions rather than by analog comparisons, and are characterized by their spatial resolution, temporal resolution, and time step

  • Types of General Circulation Models

  • Atmospheric GCMs (AGCMs) may provide adequate simulation of atmospheric motion at short time scales but may not be applicable at climatological time scales because they only consider processes occurring in the atmosphere rather than in exchanges between the atmosphere and the lithosphere, hydrosphere, cryosphere, and biosphere

  • Like AGCMs, oceanic GCMs (OGCMs) simulate circulation, but in this case the circulation remains in the hydrosphere

  • Coupled” atmosphere-ocean GCMs (AOGCMs) include an ability to simulate not only the circulations of both the atmosphere and ocean, but also the feedbacks and energy transfer between those two fluids

  • In some cases, output from a global-scale GCM may be used as input to a regional climate model (RCM), which zoom in on the particular region of interest and contain much greater spatial resolution

  • Representing the Earth-Ocean-Atmosphere System in GCMs

  • Grid point models represent atmospheric phenomena by dividing the earth into equidistant points with imaginary three-dimensional “boxes” centered on those points representing the smallest area in the atmosphere for which motion can be calculated by the model

  • Spectral models adopt the strategy of expressing atmospheric motion as wavelike motion, using a series of waves

  • Data for GCMs

    • Because meteorological data are not collected at equally-spaced locations around the earth (except in the case of satellite data), the data at the network of grid points are most likely to be interpolated computationally using spatial interpolation methods from the available, collected data

The Seven Basic Equations

  • All GCMs and all weather forecasting models use the seven basic equations (in some form) to analyze and forecast atmospheric flow and behavior

  • Navier-Stokes Equations of Motion

    • Three equations – one governs velocity in the west-to-east direction (the positive “u” direction), another is for south-to-north velocity (positive v), and the third is for down-to-up velocity (positive w)

    • East-to-west, north-to-south, and up-to-down velocities are simply represented as the negative u, v, and w directions, respectively

    • Thus, all motion (advection and convection) can be described by some combination of the u, v, and w equations

    • The equations themselves describe the rate of change of u, v, and w over time at each grid point, and the rate of change of a velocity over time is actually acceleration

    • The Primitive Equations of Motion are simplified forms of the first two equations, which along with the hydrostatic equation, can be used to model atmospheric motion simplistically

  • The Thermodynamic Energy Equation

  • Expresses the sum of the internal energy of the individual molecules comprising the atmosphere and the kinetic energy that drives the synoptic- and planetary-scale motion of the atmosphere (i.e., the wind)

  • States that the change in moisture content at a grid point is equal to the sum of the contribution of moisture via advection and the contribution via phase changes

  • The Continuity Equation

  • Total mass must be conserved (i.e., constant) in any model, so the amount of mass entering any imaginary three-dimensional “box” centered on a grid point must be balanced by the amount of mass leaving another adjacent “box”, and the amount of mass leaving the imaginary “box” of interest must be balanced by mass entering an adjacent “box”

  • The Equation of State

  • Expresses the relationship between pressure, density, and temperature so that they can be used in the other equations

  • Similarities and Differences Between GCMs and Weather Forecasting Models

    • Both types of models use the same general equations to simulate atmospheric motion and energy, moisture, and momentum exchanges, as the same physical processes affect the circulation of the atmosphere whether it is at “weather” or “climate” time scales

    • The most fundamental differences between GCMs and weather forecasting models involve the difference in temporal scale

    • The importance of accuracy in the initial conditions (initialization) is also somewhat relaxed in GCMs

    • GCMs place greater importance on representing interactions and feedbacks between the atmosphere and the lithosphere, hydrosphere, and biosphere

Statistical Techniques

  • Several statistical techniques of importance in climatology are simple methods that are used across the spectrum of natural and social sciences

  • Eigenvector analysis provides a useful suite of information because these techniques are the only ones that allow for simultaneous examination of variability and changes in climate across space and time

  • Uses matrix algebraic procedures to transform that matrix of data (where, for example, the weather stations constitute the spatial variable and months in the time series are a temporal variable) into two other matrices, the first of which has the first entity’s variables (in this example, the set of all of the weather stations in the study area) along the rows and the loading for each eigenvector along the columns, and the second of which contains the second entity’s variables (in this example, all of the monthly weather observations) along the rows and the score for each eigenvector along the columns

  • If the variable in the loadings matrix is a spatial variable (as in this example), then the loadings for each component can be mapped using isoline maps

  • The score for a given eigenvalue tells the magnitude of the influence on the explained variability on that eigenvector (mapped by the loadings matrix) during each time unit of the time series

  • Two main variants of eigenvector analysis have been used in climatological studies: principal components analysis (PCA) and common factor analysis (CFA)

  • Eigenvector analysis, and particularly PCA, has been used in synoptic climatology to delineate the major modes of variability in the atmospheric flow

Atmospheric Teleconnections

  • Teleconnections describe correlations or “see-saws” in geopotential height or sea level pressure patterns across a large area

  • Can be a source of important regional- to planetary-scale climate impacts

  • Extratropical Teleconnections in the Pacific: The Pacific Decadal Oscillation

  • Like the El Niño phase of the Southern Oscillation (SO), the “warm phase” of the PDO is characterized by a periodic warming of the tropical central and eastern Pacific Ocean

  • Unlike the SO, the primary “signature” of the PDO is apparent not only in the tropical Pacific, but also in the extratropical north Pacific Ocean

  • The PDO fluctuates much more slowly than the SO – a PDO regime may last 20 – 30 years, during which one phase of the oscillation tends to dominate, while the SO fluctuates back and forth over periods of 2 – 7 years

  • Extratropical Teleconnections in the Atlantic Ocean

  • The Atlantic Multidecadal Oscillation (AMO) refers to a cycling of warm and cold surface waters over time scales ranging from about 15 to 30 years

  • The North Atlantic Oscillation (NAO) is a see-saw in pressure patterns between the Bermuda-Azores high and the Icelandic low

  • The Arctic Oscillation is a NAO-like oscillation in which the “see-saw” in pressure exists throughout most of the troposphere between the north polar region and the mid-latitudes

  • Teleconnections over North America

  • The Pacific-North America (PNA) pattern represents the oscillation between geopotential height in the mid-troposphere of northwestern North America, with opposing heights upwind in the northern Pacific and downwind in the southeastern United States

  • Tropical-Northern Hemisphere (TNH) teleconnection has nodes in the Aleutian low area and the subtropical Mexico/southeastern U.S. region, with a center of opposite sign over northeastern Canada

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