# Rohn Emergency Scale

The Rohn Emergency Scale[1] is a scale on which the magnitude (intensity)[2] of an emergency is measured. It was first proposed in 2006, and explained in more detail in a peer-reviewed paper presented at a 2007 system sciences conference.[3] The idea was further refined later that year.[4] The need for such a scale was ratified in two later independent publications.[5][6] It is the first scale that quantifies any emergency based on a mathematical model. The scale can be tailored for use at any geographic level – city, county, state or continent. It can be used to monitor the development of an ongoing emergency event, as well as forecast the probability and nature of a potential developing emergency and in the planning and execution of a National Response Plan.

## Existing emergency-related scales

Scales relating to natural phenomena that may result in an emergency are numerous. This section provides a review of several notable emergency related scales. They concentrate mainly on weather and environmental scales that provide a common understanding and lexicon with which to understand the level of intensity and impact of a crisis. Some scales are used before and/or during a crisis to predict the potential intensity and impact of an event and provide an understanding that is useful for preventative and recovery measures. Other scales are used for post-event classification. Most of these scales are descriptive rather than quantitative, which makes them subjective and ambiguous.

1805 Beaufort scale[7]
1931 Modified Mercalli intensity scale[8]
1935 Richter magnitude scale[9] (superseded by the Moment magnitude scale)
1969 Saffir–Simpson scale[10]
1971 Fujita scale[11] (superseded by Enhanced Fujita scale in 2007[12])
1982 Volcanic explosivity index
1990 International Nuclear Event Scale[13]
1999 Air quality index[14]

## Variables common to all emergencies

According to the Rohn Emergency Scale, all emergencies can be described by three independent dimensions: (a) scope; (b) topographical change (or lack thereof); and (c) speed of change. The intersection of the three dimensions provides a detailed scale for defining any emergency,[1] as depicted on the Emergency Scale Website.[15]

### Scope

The scope of an emergency in the Rohn scale is represented as a continuous variable with a lower limit of zero and a theoretical calculable upper limit. The Rohn Emergency Scale use two parameters that form the scope: percent of affected humans out of the entire population, and damages, or loss, as a percentile of a given Gross National Product (GNP). Where applied to a specific locality, this parameter may be represented by a Gross State Product, Gross Regional Product, or any similar measure of economic activity appropriate to the entity under emergency.

### Topography

A topographical change means a measurable and noticeable change in land characteristics, in terms of elevation, slope, orientation, and land coverage. These could be either natural (e.g., trees) or artificial (e.g., houses). Non-topographical emergencies are situations where the emergency is non-physical in nature. The collapse of the New York stock market in 1929 is such an example, and the global liquidity crisis of August 2007[16] is another example. The model treats topographical change as a continuum ranging between 0 and 1 that gives the estimated visual fractional change in the environment.

### Speed of change

An emergency is typified by a departure from normal state of affairs. The scale uses the change of the number of victims over time and economical losses over time to calculate a rate of change that is of utmost importance to society (e.g., life and a proxy for quality of life).

## Emergency scale mathematical model

The scale is a normalized function whose variables are scope (S), topography (T), and rate of change (D), expressed as

${\displaystyle E=Emergency=f(S,T,D)}$.

These parameters are defined as follows:

### Scope

${\displaystyle {\hbox{Scope}}={\tfrac {\hbox{RawScope}}{\hbox{MaxScope}}}}$
where
${\displaystyle {\hbox{RawScope}}=\left({\tfrac {\hbox{Victims}}{\hbox{Population}}}+{\tfrac {\hbox{Monetary Losses}}{\hbox{GNP}}}\right)^{W}}$
where
${\displaystyle W=\left({\tfrac {\ln({\hbox{Victims}})}{\ln({\hbox{Monetary Losses}})}}\right)^{\beta }}$
β is a coefficient which the model creator calculated to be 1.26 ± 0.03,
and
${\displaystyle {\hbox{MaxScope}}=\left({\tfrac {0.7*{\hbox{Population}}}{\hbox{Population}}}+{\tfrac {0.5*{\hbox{GNP}}}{\hbox{GNP}}}\right)^{V}}$,
where
${\displaystyle V={\tfrac {\ln({\hbox{Victims}})}{\ln({\hbox{Monetary Losses}})}}}$

The model loosely assumes that a society whose majority of the population (70% in this model) is affected and half of its GNP is drained as a result of a calamity reaches a breaking point of disintegration. Sociologists and economists may come up with a better estimate.

### Topographical change

${\displaystyle {\tfrac {\hbox{Volume before the event}}{\hbox{Volume after the event}}}}$ or zero for non-topographical events.

### Rate of change

${\displaystyle {\tfrac {d({\hbox{Victims}})}{d({\hbox{Time}})}}}$ and ${\displaystyle {\tfrac {d({\hbox{Losses}})}{d({\hbox{Time}})}}}$

comprise the rate of change that is of utmost importance to society and therefore incorporated in the model.

## Simplified scale for public communications

In some instances, it may be preferable to have an integral scale to more simply and dramatically convey the extent of an emergency, with a range, say, from 1 to 10, and 10 representing the direst emergency. This can be obtained from the function above in any number of ways. One of them is the ceiling function[clarification needed]. Another one is a single number representing the volume under the 3D emergency scale.

## References

1. ^ a b Rohn, Eli and Blackmore, Denis (2009) A Unified Localizable Emergency Events Scale, International Journal of Information Systems for Crisis Response Management (IJISCRAM), Volume 1, Issue 4, October 2009
2. ^ "FEMA Intensity Scales". Archived from the original on 24 September 2010. Retrieved 13 September 2010.
3. ^ Gomez, Elizabeth, Plotnick, Linda , Rohn, Eli, Morgan, John, and Turoff, Murray (2007). Towards a Unified Public Safety Scale, Hawaii International Conference on System Sciences (HICSS), Waikoloa, Hawaii.
4. ^ Plotnick, Linda; Gomez, Elizabeth; White, Connie; Turoff, Murray (May 2007). "Furthering Development of a Unified Emergency Scale Using Thurstone’s Law of Comparative Judgment: A Progress Report". ISCRAM. CiteSeerX .
5. ^ Turoff Murray and Hiltz Roxanne (2008). Assessing the health information needs of the emergency preparedness and management community. Inf. Serv. Use 28, 3-4 (Aug. 2008), 269-280.
6. ^ Turoff, M., White, C., Plotnick, L., and Hiltz, S. R., Dynamic Emergency Response Management for Large Scale Decision Making in Extreme Events, Proceedings of ISCRAM 2008, Washington D.C. May.
7. ^ "The Beaufort Wind Scale". National Oceanic and Atmospheric Administration, Storm Prediction Center. Retrieved 13 September 2010.
8. ^ "Modified Mercalli Intensity Scale". U.S. Geological Survey, Earthquake Hazards Program. Retrieved 13 September 2010.
9. ^ "The Richter Magnitude Scale". U.S. Geological Survey, Earthquake Hazards Program. Archived from the original on 26 September 2010. Retrieved 13 September 2010.
10. ^ "The Saffir-Simpson Hurricane Wind Scale". National U.S. Oceanic and Atmospheric Administration - National Hurricane Center. Retrieved 13 September 2010.
11. ^ "Fujita Tornado Damage Scale". National Oceanic and Atmospheric Administration. Retrieved 13 September 2010.
12. ^ "The Enhanced Fujita Scale (EF Scale)". National Oceanic and Atmospheric Administration.
13. ^ IAEA fact sheet
14. ^ "Air-Quality Index". The U.S. EPA, NOAA and NPS AIRnow Project. Retrieved 13 September 2010.
15. ^ "The Emergency Scale Website". Archived from the original on 29 January 2011. Retrieved 8 March 2011.
16. ^ "CNN Money (2007)". Retrieved 13 September 2010.