Weather &amp; Calamities

e_s = 0.6108\,\exp\!\left(\frac{17.27\,T}{T + 237.3}\right)

The maximum water-vapour pressure air can hold at a given temperature (Tetens formula).

Apparent Temperature (Heat Index)

AT = T_a + 0.33\,e - 0.70\,w_s - 4.00

How hot the air actually feels once humidity and wind are taken into account.

Beaufort Wind Scale

v = 0.836\,B^{3/2}

Converts a Beaufort force number into an approximate wind speed.

Wind Pressure (Dynamic)

P = \tfrac{1}{2}\rho v^2

The pressure a moving airmass exerts on a surface such as a wall or roof.

Radiative Forcing from CO₂

\Delta F = 5.35\,\ln\!\left(\frac{C}{C_0}\right)

Extra energy trapped by the atmosphere as carbon-dioxide concentration rises.

Planetary Equilibrium Temperature

T_e = \left[\frac{S(1-\alpha)}{4\sigma}\right]^{1/4}

The temperature a planet would settle at from sunlight alone, before greenhouse warming.

Global Warming Potential (GWP)

GWP = \frac{\int_0^{TH} a_x\, C_x(t)\, dt}{\int_0^{TH} a_r\, C_r(t)\, dt}

Warming caused by a gas over a time horizon, relative to the same mass of CO₂.

Sea-Level Rise (Thermal Expansion)

\Delta h = h\,\beta\,\Delta T

Rise in sea level as ocean water warms and expands.

Flood Return Period

T = \frac{n+1}{m}

The average interval between floods of a given size (Weibull plotting position).

Flood Encounter Probability

P = 1 - \left(1 - \frac{1}{T}\right)^{n}

Chance of experiencing at least one flood of return period T over n years.

Rational Method (Peak Runoff)

Q = C\,i\,A

Estimates peak stormwater discharge from a catchment.

Manning’s Equation (Channel Flow)

V = \frac{1}{n}\,R^{2/3}\,S^{1/2}

Average velocity of water flowing in an open channel or river.

Stream Discharge

NEWBasic

Q = A\,v

Volume of water flowing past a point per unit time.

Moment Magnitude (Mw)

M_w = \tfrac{2}{3}\log_{10}(M_0) - 10.7

The modern earthquake magnitude scale, based on the seismic moment released.

Tsunami Wave Speed

v = \sqrt{g\,d}

Speed of a tsunami in the open ocean (a shallow-water wave relative to its wavelength).