Natural disasters are topping the news lately. Northern California experienced devastating floods this January, followed by the severe Japanese earthquake near Kobe. Last year, Southern California experienced the Northridge earthquake, followed by severe wildfires in the summer. Man will never be able to live on Earth without risk from natural disasters. However, much of the loss of life and property can be directly attributed to a lack of planning and foresight. Some areas of the Earth's surface are more hazardous than others, and placing large populations in these areas is simply a disaster waiting to happen.
      It is impossible to build engineering structures that will be earthquake proof. There are too many unknowns related to the general severity, which is a function of duration, acceleration, and mix of frequencies of P, S, and surface waves. An unpredictable mix of amplitudes can result in constructive interference that peaks well beyond the average experienced in the general area. There even comes a point for most buildings when the law of diminishing returns makes it prohibitively expensive to design earthquake resistance above a certain threshold. Therefore, to reduce the risk of earthquake damage, one should site structures - when possible - in areas that have little or no risk of earthquakes.
      In 1969, Ian L. McHarg, noted landscape architect, wrote an influential book entitled Design With Nature. If you can find a copy somewhere, it is recommended reading. My personal copy is a discard from the Redwood City Public Library. In it, and through his previous work, he popularized the approach of transparent polygonal overlay analysis for evaluating optimal land use. His use of colored and variable density acetate overlays anticipated the development of raster geographic information system (GIS) overlay analysis. One might arguably call McHarg the spiritual father of GIS overlay analysis. In any event, he has been a seminal influence in the objective analysis of landscape for purposes of rational planning and development. Interestingly, his approach of simultaneously evaluating several layers of information has not been duplicated in commercial GIS.
      Most GISs require performing algebraic or Boolean manipulations on two layers (or three at most) and compounding pairwise the results for the final output. This is tedious if one has more than a half dozen data layers to simultaneously evaluate. Actually, when one converts a multispectral image into a thematic map of land use classes, the appropriate reclassifying of theme digital number (DN) values can shortcut the process of combining different data layers as derived from field mapping or extant maps, if the intent is to do a polygonal analysis of weighted classes.
      As an example of the computer application of polygonal overlay analysis, say the federal government wished to locate an environmentally dangerous facility - such as a nuclear fuel reprocessing plant or experimental nuclear reactor - with absolutely minimal chance of some natural disaster causing a release of radioactive nuclides into the atmosphere or groundwater. Some essential considerations would be:
     • Earthquake damage risk
     • Tornado frequency
     • Hurricane frequency
     • Flood and forest fire potential
     • Bedrock geology
      The first step would be to evaluate the earthquake, tornado, and hurricane risk. Then, when general regions were identified that minimized these risks, larger scale maps showing bedrock geology and topography could be analyzed further. One would want to site above the 1,000 year flood plain, on a relatively flat area, away from steep slopes that could provide a rock avalanche or channel waters from a cloud burst. One could use a digital elevation model (DEM) to both identify the benches of the flood plains and to derive a slope map. A proximity analysis could be used to identify flat to gentle slopes at a safe distance from steep slopes and mountain stream courses.
      The bedrock geology is necessary for several reasons. It is desirable to have a stable building-foundation since, all other things being equal, the stronger the foundation material the less structural damage that can be expected in the unlikely event of an earthquake. Should the unthinkable happen and the hazardous facility be damaged, one does not want anything percolating into the ground. Therefore, the site should be chosen for a shallow soil and impermeable bedrock. The judgement of an experienced engineering geologist might be necessary to properly code this data layer. However, as a first approximation, one could read the type of rocks from a geologic map and obtain what is called the seismic-wave propagation velocity from a reference book. High seismic velocities generally are desirable for foundations. Low seismic velocities, particularly those associated with sediments, are to be avoided. One cannot get the detail necessary on a national scale for foundation site-selection. The same thing is true for flooding potential. So, a facility siting analysis like this would have to be done in two steps.
      Let's do the first step. Examine the earthquake risk map (Figure 1). This is a shaded isoline map representing the subjective opinion of seismologists of the U.S. Geological Survey as to the damage-risk based on the location of known earthquake faults and the record of historical earthquakes. One can see that there are four arbitrary levels of risk. A simple Boolean AND/OR analysis approach (with only 0 and 1 values coded) may overstate or understate the risks.
      The first step in analysis would be to digitize the line map so that it can be input into a GIS. The highest risk area was coded with a value (50) equal to the number of tornadoes in the highest frequency tornado region. One might reasonable argue that any particular earthquake affects a much larger area than a single tornado and therefore earthquakes should be weighted more heavily. However, since this is primarily an exercise in illustrating overlay analysis principles, we will keep it simple.
      The converted digital map of tornado frequency (Figure 2) is a shaded isoline map showing the areal occurrences of tornadoes over a number of years. The values were recoded from brightness to a digital number that corresponds to the occurrence frequency interval. The values are: zero with unrecorded to less than 10 tornadoes; ten for 10 to less than 30; thirty for 30 to less than 50; and 50 for 50 or more tornadoes.
      Hurricanes would next be dealt with in a manner similar to what was done with tornadoes. Although hurricanes usually are accompanied by flooding that isn't a concern with tornadoes, the weighting could be the same since potential flooding could be dealt with explicitly in another data layer. We won't actually work with the hurricane data layer in this example, however.
      The earthquake and tornado data layers can be combined by arithmetic addition. The resulting map may possibly contain values from 0 to 100, although no values greater than 80 were actually produced. As coded, the values with the highest numbers should be avoided as potential location sites.
      Once general regions of low risk are identified, then these regions can be further analyzed by the use of additional overlays as explained above. Another analysis approach would have been to multiply the two data layers, pixel by pixel. That would give a much greater weight to co-occurrences of these two risks. However, that would require rescaling everything to prevent an overflow condition with digital number values greater than 255.
      It might be desirable to perform a low-pass filtration of the resulting image map to blur the boundaries. The original boundaries were arbitrary and the original maps were stylized to make them easier to interpret. However, for our application, it makes sense to explicitly deal with the reality that there is a transition from one probability zone to the next. A large convolution kernel for blurring would be appropriate.
      Figure 3 is the sum of the two data layers and has been pseudocolored with red hues of decreasing intensity. Speaking in general terms, the riskiest area in the country would be central Oklahoma and Kansas. (A Kansas salt mine was once seriously considered as an underground repository for nuclear waste, but that's another story.) The safest area would appear to be in southern Texas, around the Rio Grande. Of slightly greater risk (because of potential small earthquakes) would be the Rocky Mountains and the extreme northern Great Plains. Also, an elongate area northwest of the Appalachians, comprising eastern Kentucky, West Virginia, and western Pennsylvania has a combination of low earthquake damage risk and infrequent tornadoes.
      This example is a rather simplistic approach to overlay analysis that was chosen because it was thought that it would be easy to follow and understand. There are other more sophisticated things that could have been done. Boolean Algebra, using a sort of GO-NO GO test, is often used when a particular parameter is absolutely not allowed to be present or two or more things must be present simultaneously to require an acceptance or rejection decision. Complex mathematical formulas can be applied to each and every layer to recode data.
      Proximity analysis would be important both for cost and availability of construction materials and subsequent shipment of nuclear materials. In the real world, there are many other things that might well be considered in the analysis, not the least of which might be the environmental impact of construction on rare or endangered species.
      However, all of this goes beyond what space allows here. The intent was to demonstrate how a traditional, hand method of overlay analysis can be implemented with a modern raster GIS, with very little re-learning of principles necessary.

About the Author:
Clyde H. Spencer is a consultant specializing in technical and market aspects of remote sensing and GIS. In addition, he is currently teaching GIS courses part-time for the University of California, Berkeley. He can be reached at 408-263-6779.

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