Weather & Calamities

Meteorology, climate change and natural hazards — humidity, storms, global warming, floods, tsunamis and seismic activity.

Weather & Calamities brings together the key formulas used to describe the atmosphere, climate change, and natural hazards, from humidity and wind to floods, tsunamis, and seismic events. It’s a practical reference for students, exam prep, and professionals in engineering, environmental science, and emergency planning, because these equations help turn complex weather and disaster risks into measurable, usable values for prediction, design, and safety.

Saturation Vapour Pressure

NEWIntermediate

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)

NEWIntermediate

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

NEWIntermediate

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

Converts a Beaufort force number into an approximate wind speed.

Wind Pressure (Dynamic)

NEWIntermediate

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)

NEWIntermediate

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

Rise in sea level as ocean water warms and expands.

Flood Return Period

NEWIntermediate

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)

NEWIntermediate

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

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).