*Note: This page is highly mathematical.*

## Overview

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

### 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

### Constants

- ―
**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)

### Coordinates

- ―
**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/m^{2})

Normalized to Earth’s spherical surface area (as are heat and longwave fluxes):

- or ― [TOA] ―
**Mean Solar Irradiance**(units: W/m^{2}) - or ― [TOA] ―
**Incoming**(units: W/m**Solar Irradiance**/ Insolation^{2}) - ― [TOA] ―
**Net****solar irradiance absorbed**(units: W/m^{2}) - ― [atmosphere] ―
(units: W/m**Solar irradiance**absorbed by atmosphere^{2}) - ― [surface] ―
(units: W/m**Solar irradiance**absorbed by surface^{2})

### Heat Fluxes

- or ― [surface] ―
**Surface non-radiative heat loss**(latent and sensible heat flows from the surface to the atmosphere) (units: W/m^{2}) - or ) ― [surface] ―
**Surface****radiative heat loss**(units: W/m^{2}) - or ― [surface] ―
**Surface****excess heating**(units: W/m^{2}) - or ― [TOA] ―
**TOA****excess heating**(units: W/m^{2})

### Longwave Radiation Fluxes

- or ― [TOA] ―
**Outgoing longwave****radiation**(units: W/m^{2}) - or ― [surface] ―
at surface (units: W/m**Downwelling longwave****radiation**^{2}) - or ― [surface] ―
**Surface longwave****radiation****emissions**(upwelling from surface) (units: W/m^{2})

### Parameters

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/m^{2}) - ―
**Normalized greenhouse effect**(dimensionless, 0-1) - or ― Baseline
**longwave temperature boost**factor (units: dimensionless, ) - or ―
**Longwave effective transmittance**(units: dimensionless, 0-1) - or ―
**Longwave**(units: dimensionless, 0-1)**effective**absorptance - 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 variatio**n**temperature reduction**factor (units: dimensionless, ) - or ― Incremental
**temperature change anomaly**(units: K or ℃) - or ― Incremental
**temperature variation temperature shift**(units: K or ℃)

### Temperature

- or ―
**Surface temperature**

### Effective Emission Height Model Parameters

- or ―
**Upwelling/Outgoing effective emission temperature**(units: K) - or ―
**Downwelling effective emission temperature**(units: K)

### Forcing

- ― TOA ― Radiative
**forcing**(units: W/m^{2})

### Climate Response

- ―
**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})

## Averages

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)
- Temperature

### 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
- Forcing
- Climate response
- Longwave parameters
- Temperature distribution parameters
- Longwave baseline temperature boost factor
- Longwave transmission reduction
- Longwave recirculation fraction
- Radiant cooling reduction factor