Geography Reference
In-Depth Information
The general set of partial differential equations governing the motions of the
atmosphere is extremely complex; no general solutions are known to exist. To
acquire an understanding of the physical role of atmospheric motions in determin-
ing the observed weather and climate, it is necessary to develop models based on
systematic simplification of the fundamental governing equations. As shown in
later chapters, the development of models appropriate to particular atmospheric
motion systems requires careful consideration of the scales of motion involved.
1.2
PHYSICAL DIMENSIONS AND UNITS
The fundamental laws that govern the motions of the atmosphere satisfy the princi-
ple of dimensional homogeneity . That is, all terms in the equations expressing these
laws must have the same physical dimensions. These dimensions can be expressed
in terms of multiples and ratios of four dimensionally independent properties:
length, time, mass, and thermodynamic temperature. To measure and compare the
scales of terms in the laws of motion, a set of units of measure must be defined for
these four fundamental properties.
In this text the international system of units (SI) will be used almost exclusively.
The four fundamental properties are measured in terms of the SI base units shown
in Table 1.1. All other properties are measured in terms of SI derived units , which
are units formed from products or ratios of the base units. For example, velocity
has the derived units of meter per second (m s 1 ). A number of important derived
units have special names and symbols. Those that are commonly used in dynamic
meteorology are indicated in Table 1.2. In addition, the supplementary unit desig-
nating a plane angle, the radian (rad), is required for expressing angular velocity
(rad s 1 ) in the SI system. 1
In order to keep numerical values within convenient limits, it is conventional to
use decimal multiples and submultiples of SI units. Prefixes used to indicate such
multiples and submultiples are given in Table 1.3. The prefixes of Table 1.3 may
be affixed to any of the basic or derived SI units except the kilogram. Because the
Table 1.1
SI Base Units
Property
Name
Symbol
Length
Meter (meter)
m
Mass
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
1
Note that Hertz measures frequency in cycles per second, not in radians per second.
 
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