This is *not* an exhaustive list of parameters, nor is it everything you need to know about thunderstorms... and it's definitely not a how-to for forecasting thunderstorms. (Maybe someday...)
Moisture is necessary in the middle or lower troposphere because without it, clouds and precipitation cannot be formed.
Instability is important, otherwise vertical development of storms is cut off.Lift is necessary because without it, storms cannot take advantage of their instability and moisture.
Moisture can be gauged from Skew-Ts, from looking at wet bulb and dew point temperatures. Lift can be surmised from synoptic-scale indicators of vertical motion (PVA, upper-level divergence, jet streak dynamics, lower-level WAA) or from model omega output. Shear is also easily read off of a skew-T or from raw radiosonde data.
To judge stability, a number of different indices are calculated. These can often give a good idea in advance if thunderstorms are possible on a given day.
The most important principle to keep in mind when dealing with instability is that warm air rises and cold air sinks. These indices tell to what degree that is occurring, and what that means to thunderstorm development. Some also account for moisture, which gives a somewhat more complete picture of the severe weather threat.
CAPE, or Convective Available Potential Energy, is the vertically integrated buoyancy of a parcel between the LFC (Level of Free Convection) and the EL (Equilibrium Level). It can be visualized on a Skew-T, and online Skew-Ts generally have a number for CAPE included.
CAPE is an amount of energy, and, like most parameters in the atmosphere, it is measured per unit mass so that it can be applied to any amount of air (or to a parcel). Thus, CAPE is measured in J/kg (Joules per kilogram).
The existence of CAPE indicates that upward motion will occur, as long as air is lifted to the LFC. Some sample values:
CAPE of 4000 J/kg is the strongest that any area generally sees in a season, and approximately 8000 J/kg is the strongest convection ever seen.
CIN, or Convective Inhibition, is the opposite of CAPE. It is the negative buoyancy which must be overcome by lift or thermodynamic processes in order to tap into the CAPE. It is also measured in J/kg.
LI, or Lifted Index, is a very popular and simple index for testing the instability of air. It is equal to T(env)-T(parcel) at 500 mb. The environmental temperature is read off of a skew-T or decoded from radiosonde data, and the parcel temperature is either the temperature a parcel of air from the surface would reach at 500 mb or the temperature that a mixed layer near the surface would reach at 500 mb (if there is mixing occuring).
A negative value of lifted index indicates that the parcel is warmer (positively buoyant; rising) than the environment at 500 mb. Some guideline values:/P>
SI, or Showalter Index, is similar to lifted index but lifts its parcel from 850 mb. It is a good indicator of elevated convection.
K-index accounts for lapse rate and moisture content. I have seen two different formulas for this:
K = (T(850 mb) - T(500 mb)) + Td(850 mb) - Tdd(850 mb)
K = (T(850 mb) - T(500 mb)) + Td(850 mb) - Tdd(700 mb)
where T is temperature, Td is dew point, and Tdd is dew point depression.
The Severe WEAther Threat index accounts for many different factors: moisture, instability, shear, and advection. It is, however, empirical and its numbers don't really have a physical meaning, unlike many of the other parameters listed here.
SWEAT = 12*(Td(850)) + 20*(TT-49) + 2*(V(850)) + V(500) + 125*(S + 0.2)
Vertical Totals, Cross Totals, and Total Totals are simple but effective indicators. Vertical Totals accounts for lapse rate, Cross Totals accounts for low-level moisture, and Total Totals does both.
VT = T(850)-T(500)
CT = Td(850)-T(500)
TT = VT+CT = T(850)-T(500)+Td(850)-T(500) = T(850)+Td(850)-2*T(500)
The Bulk Richardson number measures the amount of shear in a storm as compared to the amount of buoyancy. Too much buoyancy with too little shear means that storms will fire easily and over a large area without much organization. Too much shear means storms will be ripped apart.
BRN = (CAPE) / (0.5 * Δu2) where
Δu2 = [(u6-u500)2 + (v6-v500)2]
Many of these parameters are computed with data taken from skew-Ts, whose original source was a radiosonde. Most of the time, for severe weather, you will be using a 12 Z sounding, taken at 7:00 AM in the summer. Conditions at 500 mb may not have changed very much by the time storms are firing 9 hours later... but surface conditions certainly will have. (Think about it-- is it warmer at 4:00 PM than at sunrise?)
Stability can be altered by solar heating, warm/cold air advection, moisture advection, wind shifts, and more. Take these into account!
Around 700 mb or a little lower, there is often a pocket of warm air visible on a sounding. This warm air, known as a cap, prevents convection from occuring until it can be overcome. Warm air can rise until it reaches the cap, but then it is no longer positively buoyant, so it does not continue to rise. The cap is a good thing and a bad thing for convection.
Some cap is necessary for organized convection to occur. If there is no cap, storms will begin firing immediately and all over the place, and no storm out of the disorganized mess can really intensify. If some instability is allowed to build up under the cap, then when the cap is overcome, strong, organized convection is possible.
A cap can be broken when air at the surface warms sufficiely, air aloft cools and the cap is eroded away, or synoptic lift brings air into a region where it is buoyant again.
A cap which is too warm can be considered "unbreakable" if surface heating and lift cannot combine to move air past it. Air in the middle teens (degrees Celsius) at 700 mb usually is a sign of an unbreakable cap.
Gallus, Bill. "Mteor 417/517: Mesoscale Forecasting Laboratory". Courseworks, Iowa State University Bookstore, Spring 2001 edition.
Vasquez, Tim. "Weather Forecasting Handbook". Weather Graphics Technologies, 5th edition, 2002.
Vasquez, Tim. "Storm Chasing Handbook". Weather Graphics Technologies, 1st edition, 2002.
Jeff Haby's severe weather indices page
NWS Southern Region Weather School-- Thunderstorms
NWS St. Louis Convective Indices page
A bunch of Skew-T formulas
University of Oklahoma sounding info PDFs
The RAP Upper Air page