Note: This page is highly mathematical.
This document offers a list of quantities I reference and symbols for these that I use on this site.
Some quantities are described by different people using different names and different symbols. Some quantities are likely unique to my own way of organizing concepts. I try to mostly use standard terms and symbols when these are well-established, but I’ve adjusted terms and symbols to try to achieve a measure of consistency.
Symbols come in two variants: long symbols and short symbols. Long symbols are often multi-letter, to support easier memory of what they are supposed to mean. Short symbols are a single letter (possibly with a subscript), to make it easier to work with them when doing serious mathematical analysis.
Some quantities are evaluated at the surface, while others are evaluated at “top of atmosphere” (TOA), at the interface between the atmosphere and space.
In what follows, I name the units in which quantities are most often presented. In most cases, SI units are specified, but there are exceptions. Any quantities in non-SI units should be converted to SI units when doing calculations.
Table of Contents
- List of quantities and symbols
Local and global quantities
For most quantities listed below, there is both a location-dependent version of the quantity that varies by location around the globe, and a global average version of the quantity. Sometimes the global average version is a straight average over the surface area of the planet, and sometimes it is a weighted average, weighted to make the averaging method appropriate to how that quantity is likely to be used.
In any text that uses quantities that have both location-dependent and global average versions, I will often explicitly say which version is being used. If not, this will often be clear from the context.
To indicate whether a quantity is global or location-dependent, I may use the notation or (where indicates latitude and longitude).
When I am using the convention the global version of is typically expressed as or where these notations represent unweighted and weighted global averages, respectively.
List of quantities and symbols
- ― Stefan-Boltzmann constant (units: W m-2 K-4)
- ― Speed of light in vacuum (units: m/s)
- ― Planck’s constant (J/Hz)
- ― Boltzmann constant (J/K)
- ― Latitude (units: radians formally, degrees informally)
- ― Longitude (units: radians formally, degrees informally)
- ― Location, an abbreviation for latitude and longitude
- ― Time (units: seconds formally)
- or ― Frequency of electromagnetic radiation (units: Hz)
- or ― Wavenumber of electromagnetic radiation (where is the speed of light) (units: cm-1)
- ― Wavelength of electromagnetic radiation (units: microns, 𝜇m)
Shortwave Radiation Fluxes
Not normalized to Earth’s spherical surface area:
- or ― [TOA] ― Total Solar Irradiance (units: W/m2)
Normalized to Earth’s spherical surface area (as are heat and longwave fluxes):
- or ― [TOA] ― Mean Solar Irradiance (units: W/m2)
- or ― [TOA] ― Incoming Solar Irradiance / Insolation (units: W/m2)
- ― [TOA] ― Net solar irradiance absorbed (units: W/m2)
- ― [atmosphere] ― Solar irradiance absorbed by atmosphere (units: W/m2)
- ― [surface] ― Solar irradiance absorbed by surface (units: W/m2)
- or ― [surface] ― Surface non-radiative heat loss (latent and sensible heat flows from the surface to the atmosphere) (units: W/m2)
- or ) ― [surface] ― Surface radiative heat loss (units: W/m2)
- or ― [surface] ― Surface excess heating (units: W/m2)
- or ― [TOA] ― TOA excess heating (units: W/m2)
Longwave Radiation Fluxes
- or ― [TOA] ― Outgoing longwave radiation (units: W/m2)
- or ― [surface] ― Downwelling longwave radiation at surface (units: W/m2)
- or ― [surface] ― Surface longwave radiation emissions (upwelling from surface) (units: W/m2)
Well-known environmental parameters:
- ― [surface] ― Emissivity (units: dimensionless, 0-1)
- ― [TOA] ― Albedo (units: dimensionless, 0-1)
- ― Lapse rate (environmental lapse rate in troposphere) (units: K/km)
Parameters characterizing the impacts of the atmosphere not being entirely transparent to longwave radiation (note: parameter values would be 1 or 0 for a LW-transparent atmosphere):
- or ― Greenhouse effect (units: W/m2)
- ― Normalized greenhouse effect (dimensionless, 0-1)
- or ― Baseline longwave temperature boost factor (units: dimensionless, )
- or ― Longwave effective transmittance (units: dimensionless, 0-1)
- or ― Longwave effective absorptance (units: dimensionless, 0-1)
- or ― Longwave cooling reduction factor (units: dimensionless, 0-1)
- or ― Longwave recirculation fraction (units: dimensionless, 0-1)
Parameters characterizing the impacts of temperature varying away from the average value (note: parameter values would be 1 or 0 for uniform temperatures):
- or ―Baseline temperature variation emissions boost factor (units: dimensionless, )
- or ―Baseline temperature variation temperature reduction factor (units: dimensionless, )
- or ― Incremental temperature change anomaly (units: K or ℃)
- or ― Incremental temperature variation temperature shift (units: K or ℃)
- or ― Surface temperature
Effective Emission Height Model Parameters
- or ― Upwelling/Outgoing effective emission temperature (units: K)
- or ― Downwelling effective emission temperature (units: K)
- ― TOA ― Radiative forcing (units: W/m2)
- ― Planck Response (units: W m-2 K-1)
- ― Environmental Climate Sensitivity (units: W m-2 K-1)
- ― Transient Climate Response (units: W m-2 K-1)
For some variables relevant to climate, it is most useful to consistently use a weighted average for that variable. How various quantities are averaged is indicated in the following sections.
Quantities Averaged in an Unweighted Manner
- All longwave, heat flow, and shortwave fluxes (aside from which is neither “local” nor an average)
Quantities Averaged in a Weighted Manner
- Emissivity ―
- Albedo ―
- Temperature Variation Change Anomaly ―
Quantities Averaged using Nonlinear Averaging
- Upwelling/Outgoing effective emission temperature ― Global average emission temperature is computed as .
- Downwelling effective emission temperature ― Global average emission temperature is computed as .
Averaging Not Classified
- Lapse rate
- Climate response
- Longwave parameters
- Temperature distribution parameters
- Longwave baseline temperature boost factor
- Longwave transmission reduction
- Longwave recirculation fraction
- Radiant cooling reduction factor