Reading #1: Five Basic Laws Used by Meteorologists to Understand the Evolution of Larger Scale Atmospheric Flow Patterns
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1. Ideal Gas Law (Equation of State) 
expresses the relationship of the pressure a gas exerts to the volume it
occupies and its temperature. (The product of the pressure a gas exerts and the
volume the gas occupies is directly proportional to the temperature of the gas).
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2. First
Law of Thermodynamics
The total energy of a system
includes internal, kinetic, potential and chemical energy. These are related,
respectively, to air parcel's temperature, characteristics of the three dimentional wind field, and
to the molecular properties of air. The "Conservation of Energy"
states that there is a balance between these, such that the total energy does
not change. The First Law of Thermodynamics is a conservation law that relates
to the internal energy only. It is a corollary of the more general "Conservation
of Energy". The Internal Energy ÆU is changes because of changes in
sensible heat (Æq) and the work done due to expansion or contraction (ÆW).
A manipulation of that
equation puts it into a form that makes it more conceptually accessible, as shown
below. The temperature changes experienced by an air parcel can be put into two
general categories: i. those
related to direct heating or chilling of the air parcel (termed sensible
or diabatic heating or cooling 
q divided by specific heat in equation below); and, ii. those related to nondirect heating or chilling associated
with expansion or contraction of the air parcel (termed adiabatic heating
or cooling).
The First Law of Thermodynamics
tells us how the air parcel"s temperature changes. It changes either by direct
addition of "heat" (such temperature changes are called "diabatic" or "sensible" and examples include
conductional warming or cooling, latent head addition etc.) and/or by contractional heating/expansional
cooling (such temperature changes are termed "adiabatic")



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3. Newton's Second Law of Motion  states that the acceleration experienced by an object is due to the sum of the forces acting on the object . (An object at rest will be accelerated in proportion to the forces that act on the object). (F = ma)
How Wind Develops ( Equation of Horizontal
Motion):  air motion can be understood on the
basis of the forces that cause air to move. In the absence of all other forces, at a
given elevation (say, sealevel or at 18000 feet), air tends to be accelerated
horizontally from regions of higher pressure to regions of lower pressure.
Note that in oceanography, the viscous forces /acclerations
between fluid parcels and the surrounding ocean must be added to the right hand
side of the equation. The resulting
equation of motion is known as the NavierStokes Equation.
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4. Hydrostatic Law (Obtained from the
Equation of Vertical Motion)  the upwards directed pressure gradient
acceleration acting on an air parcel (explained in class) is balanced by the
acceleration of gravity.
Can
also be derived as a special case special case of (3)
where (PGA)_{z} is the pressure gradient
acceleration. But at the synoptic scale a_{z} is very nearly zeroÉmost
often net vertical accelerations produce vertical velocities that are two or three orders of magnitude
smaller than horizontal velocities and often can be neglected on an order of
magnitude basis. Hence
(PGA)_{z} = g
or
The
Hydrostatic Law is often written:
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5. Conservation of Mass Applied to the
Atmosphere (Equation of Continuity ) – the fractional rate of
increase experienced by an air parcel (or air column, following its motion), is
equal to the convergence (negative divergence). For stationary air columns or parcels,
this simply means that net convegence of air into the column results in
increases in density and vice versa.
At the macroscale, synoptic scale, and mesoscale, in meteorology, the
density changes experienced by air parcels are one to two orders of magnitude
smaller than the three dimensional divergence term on the right. Thus, the equation can be rewritten
which is known as
DineÕs Compensation. When solved
for the change in vertical velocity, this equation, when applied to a layer,
says that divergence, say, at the top of the layer is balanced by upward motion
through the bottom of the layer.
For the whole troposphere, DineÕs Compensation states that upper
tropospheric divergence is balanced by lower tropospheric convergence and vice
versa.