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Visibility: How Applicable is the Century-Old Koschmieder Model?

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  • 1 School for the Environment, University of Massachusetts Boston, Boston, Massachusetts
  • | 2 State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, China
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Abstract

Koschmieder proposed that visibility is inversely proportional to the extinction coefficient of air, and this model has been widely adopted during the past century. Using radiative transfer theory, the authors present a general relationship for the law of contrast reduction and point out that the Koschmieder model is workable only to situations when a common-size object can be viewed tens of kilometers away. However, the Koschmieder model is not applicable for viewable distances of hundreds of meters when the angular dimension of an object is significantly greater than the eye resolution of the human being. The authors further separate the term “visible” into “simple detection” or “detectability” and “clear identification” or “identifiability” and point out that the Koschmieder model is applicable to identifiability, but not necessarily for detectability. In addition, the way of calculating contrast is revised to follow the concept of brightness constancy. The results of this effort advocate the measurement and distribution of detectability in harsh weather conditions, as such data offer more useful and important information for daily life.

Corresponding author address: Zhongping Lee, School for the Environment, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, MA 02125.E-mail: zhongping.lee@umb.edu

Abstract

Koschmieder proposed that visibility is inversely proportional to the extinction coefficient of air, and this model has been widely adopted during the past century. Using radiative transfer theory, the authors present a general relationship for the law of contrast reduction and point out that the Koschmieder model is workable only to situations when a common-size object can be viewed tens of kilometers away. However, the Koschmieder model is not applicable for viewable distances of hundreds of meters when the angular dimension of an object is significantly greater than the eye resolution of the human being. The authors further separate the term “visible” into “simple detection” or “detectability” and “clear identification” or “identifiability” and point out that the Koschmieder model is applicable to identifiability, but not necessarily for detectability. In addition, the way of calculating contrast is revised to follow the concept of brightness constancy. The results of this effort advocate the measurement and distribution of detectability in harsh weather conditions, as such data offer more useful and important information for daily life.

Corresponding author address: Zhongping Lee, School for the Environment, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, MA 02125.E-mail: zhongping.lee@umb.edu
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