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). The gas constant (R) can be viewed as a correction factor that is different for each gas (because of differences in molecular structure) and is usually given for so-called 'dry air'. 'Dry Air' means air without any water vapor. Since the molecular weight, size, and structure of diatomic nitrogen and diatomic oxygen are very similar, the gas constant for them is essentially identical. However, water vapor is a a large, bulky molecule for its molecular weight and the gas constant for it is much different. We deal with this by defining something called Virtual Temperature.

 

 

 

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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 ∆U is changes because of changes in sensible heat (∆q) and the work done due to expansion or contraction (∆W).

 

           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:  ithose 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 non-direct 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")

 

 

                                   

Total temp Change

Experienced by

Air Parcel  

Diabatic Change Experienced by Air Parcel  

Adiabatic Change Experienced by Air Parcel

                                           

 

 

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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 Navier-Stokes 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 az is very nearly zero…most 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 Dine’s 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, Dine’s Compensation states that upper tropospheric divergence is balanced by lower tropospheric convergence and vice versa.