Now that fundamental quantities are discussed, I mention specifics and ways combinations of such are used for describing physical phenomena.

Temperature is a fundamental weather-related quantity, likely most important. It is proportional with energy (please see below) of molecules in a substance, rotational/vibrational energy of solid and liquid molecules, and translational energy of gas molecules. When a substance acquires heat, such typically (i.e., for almost all substances) causes expansion because increased motion separates molecules, though

water is a common exception. This principle makes thermometers effective for temperature measurement, heating causing experimentally-determined expansion rates. Thus, temperature is 0 if all molecular motion ceases. Such is called absolute 0, and is represented as 0 °K. °K refers to Kelvin temperature scale (° symbol is not standard for this) which absolute 0 and the freezing and boiling temperatures of water with standard atmospheric pressure define. Kelvin scale is a centigrade scale - cent meaning hundredths. 100 centigrade ° are included between freezing and boiling temperatures. Thus, "the Centigrade scale" is very similar with the Kelvin scale, except using 0 °C & 100 °C for freezing and boiling temperatures, respectively. °C actually more commonly refers to the Celsius scale, which differs very slightly from Centigrade. The Fahrenheit scale is commonly used, 32 °F and 212 °F chosen for freezing and boiling temperatures. Thus, a ° K & C represent the same temperature difference, which equals 1.8 °F. Mentioning these seemingly obvious things is parctically useful - e.g., for surface maps with °F and upper air charts with °C, being able to quickly judge how much warmer 25 °C is than 46 °F and realizing that 80 °F is not twice as warm as 40 °F, nor 30 °C 3 × as warm as 10 °C, but 300 °K is 20 % warmer than 250 °K, etc. Some temperatures should be memorized for reference :

• Freezing and boiling water temperatures with standard atmospheric pressure.
• Triple point of water is .01 °C = 273.16 °K = 32.02 °F, temperature at which gas, liquid, and solid phases exist in equilibrium (with pressure of 6.11 mb - 166 × less than standard)

• All equivalent °F temperatures for each 5 °C for [-40 °C, 50 °C], especially middle values
• Average Earth surface temperature is about 15 °C = 288.15 °K = 59 °F
• Maximum recorded Earth surface shelter temperature was 70 °C = 158 °F (for 2 minutes) in Portugal, or 58.0 °C = 136.4 °F at Azizia, Lybia (sustained)
• Minimum recorded Earth surface shelter temperature is approximately -88 °C = -127 °F at Vostok, Antarctica
• Diurnal temperature range of about 11 °C or 20 °F is common at midlatitudes, record temperatures often being about that same amount greater/less than normal temperatures

Fundamental kinematic and dynamic quantities and their units are now presented, for reference regarding topics discussed below :

Quantity	Units
Area	m2
Volume	m3
Density	kg/m3
Speed	m/sec
Acceleration	m/sec2
Force	kg m/sec2 = N
Pressure	kg/(m sec2) = N/m2 = Pa
Energy	kg m2/sec2 = J
Power	kg m2/sec3 = J/sec = W

Note that all are combinations of [M], [L], and [T], fundamental quantities previously discussed, and units measured for a phenomenon determine its characteristics (i.e., whether it is a speed, a power, an energy, etc.). Names for new units shown are : N : Newton, Pa : Pascal, J : Joule, W : Watt.

Below some concepts regarding motion and statics are mentioned. These are obviously not intended as comprehensive, but are a good introduction, meant for illustrating most relevant concepts. I cannot emphasize too much how useful study of basic (physics) mechanics is regarding weather study. Being thoroughly aware of physics involved with atmospheric motion, you'll understand why you observe what you do and develop a 'feel' for it, which is helpful for deciding how fast a storm may develop, how much snow may occur, etc.

Area = Distance². This involves 2 dimensions, length and width :

Volume = Distance³. This involves 3 dimensions, length, width and height.

Density = Mass ÷ Volume. This describes how much matter is contained in a volume, which is very relevant regarding atmospheric thermodynamics, for which air densities are of great consequence. A dense object feels 'heavy', while one not dense 'feels light'.

Speed = Distance ÷ Time. E.g., if air travels 20 miles during 2 hours, its average speed is 10 miles/hour. This differs from velocity, which is a vector quantity - speed and direction.

Acceleration = Speed change ÷ Time. Thus, it specifies speed rate of change to a specific direction. E.g., if a rising thermal with speed 2 m/sec accelerates, speed a minute later becoming 5 m/sec, its acceleration is 3 m/sec ÷ 60 sec = 1/20 m/sec² = .05 m/sec² :

Note that an accelration can occur with constant speed - if curving as in the example below.

Description of motion as above is called kinematics. "Air" and "thermal" above are treated as objects (technically, particles), though they consist of many objects (molecules). Such a treatment is often sufficient for analysis though, especially regarding solid objects.

The above describe linear motion. Because we live on a rotating planet, and because rotating weather systems are so common, rotational kinematics should be studied also, which include the concepts of angular speed and centripetal acceleration :

Now Newton's 3 Laws of Motion should be mentioned :

• Every body persists in its state of rest or uniform motion in a (straight) line unless it is compelled to change that state by forces impressed on it.
• Acceleration of an object is a consequence of the sum of all forces acting on it, related as : F = m a ; F = Total force acting on mass m, a = acceleration.
• To every action there is an opposed and equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

The 1^st and 3^rd Laws are basically the original descriptions (interpreted & simplified), the 2^nd later interpretation of the general idea. These are very important regarding atmospheric phenomena (perhaps the foundation of such), and should not only be memorized, but become part of the way you view events if not already so - especially the 1^st & 2^nd Laws. I am not so sure regarding the 3rd Law - I suppose it depends how you interpret it; though if nothing else, it can help analysis.

If you study Physics very much, you will/did discover that such laws are not perfect, but are such a good description that they are sufficient for predicting planetary motions (e.g., eclipses, transits, etc.) using the Universal Law of Gravitation. Now dynamics, which involves description of forces responsible for observed motions, can be discussed :

Force = Mass × Acceleration. Acceleration of an object (i.e., a mass, because all objects have mass) is a consequence of all forces acting on it. This is the 2^nd Law, used as a foundation for atmospheric theory and modeling. Note how the 1^st and 2^nd Laws compliment each other. Any object with uniform motion (i.e., constant velocity) is considered being at rest (resting). This is so because all motion is relative, so a reference frame can be defined which coincides with any object. For planetary studies, our sun is a natural reference, and for atmospheric studies, earth's rotational axis, which are resting with velocity 0 when used as references. If a force acts on any such resting object, an acceleration occurs, inversely proportional with mass of the object. I.e., great force is needed for moving a very massive object, which experience indicates.

Gravity is a force inherent with any object, proportional with its mass, which the Universal Law of Gravitation describes :

F = G m₁ m₂ / r²

G : Universal gravitation constant = 6.6720 × 10^-11 m³ kg^-1 sec^-2
m₁ : mass of object 1
m₂ : mass of object 2
r : radial distance between 1 & 2

It acts in a direction between centers of mass of the objects.

Gravitation is thus a quite weak force (considering how little you feel the force keeping you on the huge earth). Note that though seemingly implied, it is not necessarily an attraction - abscence of a repelling force from all directions because one object blocks it from another can produce the same effect. Considering mass and radius of Earth (original determination of which was difficult !), a gravity force (F_g) at Earth's surface can be considered :

F_g = G m_e m / r_e²

m_e : Earth mass = 5.98 × 10²⁴ kg
r_e : Earth radius = 6367000 m

Thus,

F_g / m = (6.67 × 10^-11)(5.98 × 10²⁴) / 6367000² = 9.84 m/s² = g

g : gravitational acceleration on Earth

g is the symbol customarily used for representing Earth gravity. This situation is more complicated because we live on a rotating, nonuniform planet. Thus, what we consider "gravity" is a sum of contributions of all masses which Earth consists of (rock, iron ore, nickel, oil, etc.) and a centrifugal force - an imaginary force because of our natural reference as Earth's rotational axis chosen :

The consequence of all of such considerations is the geoid. Because a fluid such as water achieves equilibrium with gravity, the geoid defines sea level, which is not any perfect shape because of mass inconsistencies below. Each time people or other creatures drill, tunnel or redistibute earth mass, they alter gravity and thus the geoid slightly (even rain showers redistributing water among lakes). Gravity is constantly measured, changes or discrepancies noted. This is relevant because concepts such as geopotential height use gravity as a basis. A first order approximation for gravitational acceleration around Earth is :

g = (9.80616)(1 - 2.59 × 10^-3 cos{2(Lat)})(1 - 3.14 × 10^-7 Z) m/s²

Lat : latitude
Z : altitude above sea level

9.80616 m/s² being the standard value for gravitational acceleration at Lat = 45° and sea level.

Pressure = Force / Area. Because weight is a force, a fine description for atmospheric pressure is "weight of air above a location". On Earth,

W = m g

W : weight

is an expression of weight - product of mass and gravity. Because of such, it decreases as altitude in our atmosphere increases (unless vertical air accelerations are very large). It is often measured using depth of a column of mercury which it can support. Because average atmospheric pressure at Earth's surface is very nearly 100000 = 10⁵ Pa, this value was called a bar (b) (perhaps referring the column of mercury supported). Meteorologists most often use millibars for atmospheric pressure, 1002 mb being easier for dealing with than 1.002 b. You may notice that a millibar is also a hectopascal, another term commonly-used. Standard atmospheric pressure (1 (standard) atmosphere) at sea level is 1013.25 mb, though I believe the global average is more like 1011 mb. Inches of mercury (column supported) is another commonly-used measure, standard value being 29.92 inches. Thus, the weight mentioned above is equivalent with about that of a 30 inch mercury column, which is same weight as about 31.6 feet of water (mercury is a dense substance !). Among common pressure conversions are :

1 atmosphere = 1013.25 mb = 29.92 inches mercury
1 mb = 1 hPa = 2.95 hundredths of an inch of mercury
1 inch of mercury = 33.865 mb

Energy = Force × Distance. This acquires many forms, translational energy, heat energy, electromagnetic energy, etc., and includes anything which can be described using units of energy. 2 common descriptions for mechanics are kinetic energy (KE) and potential energy (PE). Kinetic energy describes energy associated with translational motion :

KE = 1/2 m s²

m : mass
s : speed

Thus, a force applied along a distance equivalent with kinetic energy can be responsible for causing such motion. Notice that if an object is resting (i.e., moving with constant velocity), its kinetic energy does not change, specification of which depends with reference frame; and any further force applied changes kinetic energy, which can be an opposing force decreasing it or an additional force increasing it. According to kinetic theory, temperature of a gas (e.g., air) is proportional with root-mean-square speed of its molecules :

1/2 m s_rms² = 3/2 k T

m : mass of gas molecule
s_rms² : root-mean-square speed of gas molecules
k : Boltzmann constant
T : absolute temperature

I plan discussion of this later regarding thermodynamics, root-mean square speed (sort of average speed of molecules), etc..

Potential energy describes distribution of masses wrt (with respect to) a reference datum :

PE = m g d

d : distance above datum

Total mechanical energy (ME) can be described as a sum of kinetic energy & potential energy :

ME = KE + PE

Note that the reference frame and datum determine such specification, natural ones for Earth atmospheric studies being Earth's rotational axis and mean sea level, though the ground is often used as reference as in this diagram.

Power = Energy change ÷ Time, or Energy change = Power × Time. E.g., suppose 10 100 Watt (power) light bulbs shine for an hour :

(10)(100 W) × (1 hour) = 1 kW-hour

or

(10)(100 W) × (3600 sec) = (1000 J/sec)(3600 sec) = 3600000 J = 3.6 MJ.

The conversion :

1 kW-hour = 3.6 MJ

is very useful, because energy is often expressed using W-hour or KW-hour, not only regarding electrical power, but also solar power. J is preferable, which should only be used regarding solar energy (i.e., earth heating). Because global solar energy at Earth's surface during a clear summer day near noon at midlatitudes is about 1000 W/m², a square meter (horizontal) surface on ground receives about 3.6 MJ energy during an hour of those conditions (but does not absorb all of it). The solar constant is 1370 W/m², such that average solar energy reaching earth is about 342 W/m². This is the fundamental source of energy for earth, driving weather.

Text and images are copyright of Joseph Bartlo, though may be used with proper crediting.