Page updated: October 23, 2020
Author: Curtis Mobley
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Historical Notation

As noted in Level 1, different fields of science have developed different terminology and notation for the same physical quantities. Tabel shows the ”historic” and ”modern” notations seen in oceanograpic literature. The recommended (modern) notation came into use the late 1970s and is employed, for example, in Jerlov (1976) and further refined in Morel and Smith (1982). The historic notation is generally found in works published before the late 1970’s, most notably in Preisendorfer’s 1977 opus magnum Hydrologic Optics.

Quantity SI Units Recommended

radiant energy J Q U
radiant power W Φ P
radiant intensity Wsr1 I J
radiance Wm2sr1 L N
plane irradiance Wm2 E H
downward plane irradiance Wm2 E d H()
upward plane irradiance Wm2 E u H(+)
scalar irradiance Wm2 E o h
downward scalar irradiance Wm2 E od h()
upward scalar irradiance Wm2 E ou h(+)
vector irradiance Wm2 E H
vertical net irradiance Wm2 E d Eu
emittance Wm2 M W
photosynthetically available
photonss1m2PAR or E PAR

Table 1: Terms, units, and symbols for radiometric quantities commonly used in hydrologic optics. The quantities as shown represent broadband measurements. For narrow band (monochromatic) measurements, add the adjective “spectral” to the term, add nm1 to the units, and add a wavelength index λ to the symbol, e.g., spectral radiance, Lλ or L(λ), with units of Wm2sr1nm1. PAR is inherently broadband.

It is occasionally convenient to distinguish conceptually between photons leaving a surface and photons arriving at a surface. In radiative transfer theory, field radiance L refers to the radiance of photons arriving at a surface; this is the quantity measured by a radiance meter. Surface radiance L+ is the radiance attributed to a real or imaginary surface emitting photons. Irradiance E refers to photons incident onto a surface; the corresponding measure of photons leaving a surface is denoted by radiant exitance or emittance M. Likewise, intensity can be subdivided into field intensity I and surface intensity I+. The figure summarizes this hierarchy of radiometric concepts.


Figure 1: The hierarchy of radiometric concepts.

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