CHAPTER 13 LINKING SPATIAL AND TEMPORAL ASPECTS OF CLIMATE THROUGH
QUANTITATIVE METHODS
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
o 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
o Like AGCMs, oceanic GCMs (OGCMs) simulate circulation, but in this case the
circulation remains in the hydrosphere
o “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
o 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
o 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
o Spectral models adopt the strategy of expressing atmospheric motion as
wavelike motion, using a series of waves
 Data for GCMs
o 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
o 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)
o East-to-west, north-to-south, and up-to-down velocities are simply represented as
the negative u, v, and w directions, respectively
o Thus, all motion (advection and convection) can be described by some
combination of the u, v, and w equations
o 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
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o 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
o Expresses the sum of the internal energy of the individual molecules comprising
the atmosphere and the kinetic energy that drives the synoptic- and planetaryscale motion of the atmosphere (i.e., the wind)
The Moisture Conservation Equation
o 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
o 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
o 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
o 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
o The most fundamental differences between GCMs and weather forecasting
models involve the difference in temporal scale
o The importance of accuracy in the initial conditions (initialization) is also
somewhat relaxed in GCMs
o 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
o 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
o 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
o 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
o Two main variants of eigenvector analysis have been used in climatological
studies: principal components analysis (PCA) and common factor analysis
(CFA)
o Eigenvector analysis, and particularly PCA, has been used in synoptic
climatology to delineate the major modes of variability in the atmospheric flow
Atmospheric Teleconnections
o Teleconnections describe correlations or “see-saws” in geopotential height or sea
level pressure patterns across a large area
o Can be a source of important regional- to planetary-scale climate impacts
 Extratropical Teleconnections in the Pacific: The Pacific Decadal Oscillation
o 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
o 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
o 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
o 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
o The North Atlantic Oscillation (NAO) is a see-saw in pressure patterns between
the Bermuda-Azores high and the Icelandic low
o 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
o 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
o 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