Dobsonian unit

Physical unit
Unit name	Dobsonian unit
Unit symbol	${\displaystyle \mathrm {DU} }$
Physical quantity (s)	Thickness of the ozone layer ( English total ozone )
dimension	${\displaystyle {\mathsf {N\;L^{-2}}}}$
In SI units	${\displaystyle \mathrm {1\,DU=0{,}446\,2\;{\frac {mmol}{m^{2}}}} }$
Named after	Gordon Dobson
Derived from	Mole , square meter

The Dobsonian unit (unit symbol: DU , from English Dobsonian unit ) is a measure of the concentration of trace gases such as ozone in the atmosphere. This concentration is given as the amount of substance within the complete air column over a unit area:

${\displaystyle \mathrm {DU} =\left[{\frac {n_{Ozon}}{A}}\right]}$

The unit is named after Gordon Dobson , who developed the first instrument to measure this quantity, the Dobsonian spectrophotometer .

Derivation and definition

To define the Dobsonian unit, the amount of ozone is first expressed as gas volume under standard conditions (STP) : ${\displaystyle n}$ ${\displaystyle V}$

${\displaystyle n_{Ozon}\cdot {\frac {V_{Ozon}}{n_{Ozon}}}=V_{Ozon},}$

namely with the help of the standard volume ${\displaystyle V_{m}={\frac {V}{n}}=22{,}414\,\mathrm {\frac {l}{mol}} .}$

This means that the thickness of the ozone layer is no longer given as the amount of substance per area, but as the volume per area. From the dimensional analysis, this corresponds to a length, namely the hypothetical thickness of the ozone layer, if it were to be concentrated on the ground as pure ozone:

${\displaystyle {\begin{alignedat}{2}&{\frac {n_{Ozon}}{A}}\cdot V_{m}={\frac {V_{Ozon}}{A}}&&=l_{Ozon}\\\Leftrightarrow &{\frac {n_{Ozon}}{A}}&&={\frac {l_{Ozon}}{V_{m}}}\end{alignedat}}}$

It is stipulated that a pure ozone layer with a thickness of 1 mm corresponds to exactly 100 DUs:

${\displaystyle {\frac {n_{Ozon}}{A}}=100\;\mathrm {DU} \Leftrightarrow l_{Ozon}=1\,\mathrm {mm} }$

or. ${\displaystyle {\frac {n_{Ozon}}{A}}=1\;\mathrm {DU} \Leftrightarrow l_{Ozon}=0{,}01\,\mathrm {mm} .}$

From the last two formulas it follows:

${\displaystyle \Rightarrow 1\,\mathrm {DU} ={\frac {0{,}01\,\mathrm {mm} }{V_{m}}}=\mathrm {\frac {0{,}01\cdot 10^{-3}\,m}{22{,}414\cdot 10^{-3}\,{\frac {m^{3}}{mol}}}} }$

and thus ${\displaystyle \mathrm {1\,DU=0{,}44615\,{\frac {mmol}{m^{2}}}} }$

with 1 mmol = 1 milli mol = 0.001 mol.

1 DU corresponds to each

• the mass per unit area (from the multiplication with the molar mass ) ${\displaystyle {\frac {m_{Ozon}}{A}}=21{,}41\,\mathrm {\frac {mg}{m^{2}}} }$ ${\displaystyle M_{Ozon}={\frac {m}{n}}=48\,\mathrm {\frac {mg}{mmol}} }$
• the area-related number (from the multiplication with the Avogadro constant ). ${\displaystyle {\frac {n_{Ozon}}{A}}=2{,}687\cdot 10^{20}\,\mathrm {\frac {Ozon-Molek{\mbox{ü}}le}{m^{2}}} }$ ${\displaystyle N_{\mathrm {A} }=6{,}022\cdot 10^{20}\mathrm {\frac {Molek{\mbox{ü}}le}{mmol}} }$

Typical orders of magnitude

The mean column height of the ozone layer is:

• at higher latitudes in summer sometimes over 500 DU
• in temperate latitudes between 300 and 400 DU
• less at the equator (because of the higher tropopause , the lower stratosphere , in which the ozone layer is mainly located, is restricted here )
• in the Antarctic spring, at the time of the ozone hole , far below 200 DU.

That would correspond to a thickness of the pure ozone of only a few mm, with an area-related mass of (In reality the ozone layer is several orders of magnitude thicker than just a few millimeters, since it is never available as pure ozone, but always finely distributed in the remaining components the air.) ${\displaystyle {\frac {m_{Ozon}}{A}}=(5..10)\,\mathrm {\frac {g}{m^{2}}} .}$

For comparison: in the case of smog , the limit value for ozone is around (different effects of ozone: desired UV filter at high altitude, irritation of the respiratory tract even in low concentrations near the ground). ${\displaystyle {\frac {m_{Ozon}}{V}}=0,18\,\mathrm {\frac {mg}{m^{3}}} }$

Web links

• Ozone bulletins of the German Weather Service , accessed on April 29, 2011.

Individual evidence

1. ^ Günter Warnecke: Meteorology and Environment: An Introduction . Springer Berlin Heidelberg, 1997, ISBN 978-3-540-61593-4 ( Dobsonian unit in the Google book search).
2. ^ Definition of the Dobsonian unit . In: The Ozone Hole Tour , Center for Atmospheric Science, University of Cambridge 1999, (German).
3. ↑ Antje Dethof: Assimilation of ozone data in the ECMWF model ( Memento from May 20, 2005 in the Internet Archive ) (PDF; 5.9 MB), ECMWF , 2005.