Reading #1: Five Basic Laws Used by Meteorologists to Understand the Behavior of the Atmosphere

 

_____________________________________________________________

 

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). (Metr/Ocn 200).

 

 

 

_____________________________________________________________

 

 

2.    First Law of Thermodynamics -- 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 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        

Diabatic Change      

AdiabaticChange

                                           

 

 

_____________________________________________________________

3.    Hydrostatic Law (Obtained from the Equation of Vertical Motion) (Metr/Ocn 200) -- 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 (2)

 

Equatiion

 

where (PGA)v is the pressure gradient acceleration. av 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)v = g

 

The Hydrostatic Law is often written:

Equation

 

_____________________________________________________________

 

 

 

4.    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. The ONLY forces that affect air motion at the scales we are discussing in this class are PRESSURE GRADIENT FORCE, CORIOLIS FORCE and the FORCE of FRICTION. The right hand side of the equation below "says" that to understand exactly how an air parcel will be accelerated horizontally, you need to consider the SUM of the FORCES acting on each PARCEL.

 

 

_____________________________________________________________

 

 

 

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.

 

                                     

 

_____________________________________________________________

 

Relations useful for understanding weather maps and

resulting from combination of above equations

 

A. HYPSOMETRIC RELATION: Heating the atmosphere causes it to expand (special application of the gas law) obtained by substitution of (3) into (1).  This relation provides the basis of explaining many, many things that synoptic meteorologists see on weather maps and charts.

 

Thickness of layer between two pressure surfaces is directly related to the mean temperature of the layer.  Also, if we consider the thickness of a layer that is often of importance to synoptic meteorologists, the layer approximately between the ground (1000 mb) and about 6 km (500 mb), the Hypsometric Relation is

 

 

where k = R/g ln 2

 

 

.