Though this can perhaps be boring, familiarity with standard ways of describing the physical attributes of the atmosphere is necessary for accomplishing our goal.

This is the way we express concepts & quantities numerically. Because all commonly available data is described using decimal numbers, the rest of this discussion is.

602213670000000000000000

This can be expressed :

6.0221367 × 1023

Note that :

1023 = 100000000000000000000000 (23 0's)

  6.0221367
× 100000000000000000000000
  ------------------------
  602213670000000000000000

An interesting WWW page related with this.

Similarly for very small numbers. E.g., peak wavelength of solar energy emission :

.0000047 m = 4.7 × 10-6 m = 4.7 µm

Note again that :

10-6 = 1/1000000 = .000001

  4.7
× .000001
  ------------------------
  .0000047

Note that 10^-6 is easily determined (as is 4.7 × 10^-6) moving the decimal point 6 places left from 1.0 or 4.7, respectively; adding 0's where necessary, similarly as they were added for 10²³ above.

Introduced above (as most readers are aware) is notation for distance - meters (m) & micrometers (µm), mentioned below. Most common scientific notation prefixes are :

Prefix	Symbol	Magnitude
Giga	G	109
Mega	M	106
kilo	k	103
hecto	h	102
deka	da	101
deci	d	10-1
centi	c	10-2
milli	m	10-3
micro	u or µ	10-6
nano	n	10-9

Many others exist, but these should be memorized. Common terms evolve from such prefixes (or vice versa). E.g., a cent (¢), which is 10^-2 $. Note that capital letters are used for prefixes Mega & larger, small letters for others. Logically, capitals should be used for all multipliers (prefixes > 1) and small letters for all divisors (prefixes < 1). E.g., D could represent deka & d deci (and why use k for one and c for another ?). Several reasons exist for not doing so - especially conflicts with other symbols (e.g., K for carat). Because the English alphabet includes only 26 letters, some conflicts are inevitable. Else, you can eat sushi & watch sumo wrestling. Just kidding - a little humor can be entertaining The National Institute of Standards and Technology was designed partly for solving this problem, participating with international efforts for creating consistent standards.

Such are called MKS units (meter-kilogram-second), a subset of the Metric System. This concept is very useful because when doing complicated calculations, if you know your equations are correct and you express all quantities as MKS units, your answer must be MKS units. Such a calculation is efficient, and a final conversion to desired units is seldom more difficult than required conversions would otherwise be.

Square brackets are often used for dimensional analysis. I.e., Mass [M], Distance [L], Time [T], and Electric Current [E]. L is used for distance, standard term for which is "Length". I do not like that, because length is typically associated with width and height of specific objects. Distance is a more general term. I am not sure if [E] is the correct letter used for dimensional analysis - please correct me if you know this is wrong. Nobody is perfect - part of the process of becoming a good scientist is following a logical course of action until you discover a better one.

Example : Energy = Force × Distance = Mass × Acceleration × Distance = Mass × (Distance / Time²) × Distance = Mass × Distance² / Time². Thus, Energy's dimensions are expressed as [M][L²][T^-2].

3 other basis units for the International System of Units (SI) (1) (2) are :

Property	Standard measure	Symbol
Temperature	Degree Kelvin	°K
Luminous intensity	candela	cd
Substance Amount	mole	mol

I include these in a separate list because using all 7 is redundant. (Please be aware that some people who are funded to go to France and argue in English about these things think they have good reasons for including them together.) Temperature is related with internal energy of a substance, which can be expressed as a combination of M, L, and T, as illustrated. Heat capacity must be known though, which is determined from experimentation (i.e., temperature change), so if you say this should be included in the list above, I won't argue. If luminosity interests you, it is related with photon frequency and optics - expressible with very complicated combinations of M, L, T, and E. Substance amount is as simple as counting, previously discussed - though counting to Avagadro's number is impossible for a person & simple for a computer. A mole is a fundamental physical constant, as many others which are required for physical analysis; but not a fundamental property more so than mass, which mole's definition describes.

Units can be expressed many ways - distance can be expressed as feet, miles, furlongs, etc., each with their specific purposes. For our purpose, the following are most useful :

Mass This is seldom expressed other than as kg or g. Using table above, you should be able to see that 1 kg = 10^-3 g. This is often confused with weight.

Distance This is commonly expressed as m, cm, km, dam, µm, inch, foot, yard, and mile (statue & nautical). You should know conversion factors among these - which this page from Micro-Images provides. Exact values are perhaps not as important as being able to recognize (i.e., when viewing a weather map) things such as 50 miles being approximately 80 km, which is 80000 m, and a cloud with 5600 m altitude being about 18000 feet (high alto or low cirro type). A useful way for me of thinking of this when doing rough calculations is approximately 8 km for every 5 mi & a little more than 3 feet for every meter. I.e., I add a little to the 5600 to make it an even 6000, then multiply with 3. That's generally as accurate as changing cloud heights are estimated. Each person thinks differently, so make you own which serve you well.

Time Second, minute, hour, day, week, month, year, decade, century, and millennium are all commonly discussed. You should memorize that 3600 sec are in an hour, and 86400 sec in a day. Quite often hourly and/or daily meteorological observations must be converted to MKS units, which requires sec for time. Coordinated Universal Time is the standard time reference, which I obtain from the U.S. Naval Observatory. For common purposes is same as Greenwich Mean Time (GMT). Its relation with local standard time for all locations which interest you should be memorized. I suggest keeping standard time on your meteorological clock, because :

• UTC/GMT is printed on nearly all weather maps, for consistent reference from any Earth location - conversion to local standard time never changing.
• Such is the best representation of a consistent local time reference if time zones are well-chosen.

Adding 1 hour to standard time during daylight savings time is easy, for confirmation with commonly-used time.

Electric Current¹ Ampere (Amp) is the only common expression I am aware of. This is some ways rather important in our atmosphere - perhaps ways not realized as well as the obvious charge separation required for lightning. Little knowledge of electricity is required for effective weather forecasting though.

¹ Perhaps electric charge instead of current (which includes redundancy with time) should be a fundamental property. Such is expressed as Coulombs (C), fundamental charge quantity being that of an electron, 1.60217733 × 10^-19 C.

The purpose of this article is not teaching this material per se, but mentioning the notation and representations used most for our purpose.

Text is copyright of Joseph Bartlo, though may be used with proper crediting.