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 Symbol	Historic Symbol

radiant energy	$J$	$Q$	$U$
radiant power	$W$	$Φ$	$P$
radiant intensity	$W s r^{- 1}$	$I$	$J$
radiance	$W m^{- 2} s r^{- 1}$	$L$	$N$
plane irradiance	$W m^{- 2}$	$E$	$H$
downward plane irradiance	$W m^{- 2}$	$E_{d}$	$H (-)$
upward plane irradiance	$W m^{- 2}$	$E_{u}$	$H (+)$
scalar irradiance	$W m^{- 2}$	$E_{o}$	$h$
downward scalar irradiance	$W m^{- 2}$	$E_{o d}$	$h (-)$
upward scalar irradiance	$W m^{- 2}$	$E_{o u}$	$h (+)$
vector irradiance	$W m^{- 2}$	$\vec{E}$	$\vec{H}$
vertical net irradiance	$W m^{- 2}$	$E_{d} - E_{u}$	—
emittance	$W m^{- 2}$	$M$	$W$
photosynthetically available radiation	$p h o t o n s s^{- 1} m^{- 2}$	$P A R$ or $E_{P A R}$	—

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

n m^{- 1}

to the units, and add a wavelength index

λ

to the symbol, e.g., spectral radiance,

L_{λ}

L (λ)

, with units of

W m^{- 2} s r^{- 1} n m^{- 1}

. 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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