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A Latin Hyper Cube is a way of determining risk factors and probability of each occurrence in Environmental Risk Assessment, but can be easily applied to anything. In the cube, each dimension is a variable in the system that is being assessed. A simple two dimensional cube follows:

              Concentration (mL/mm3)
              |      |       | 
       <10m/s | 15%  |  25%  |
              |      |       |
  Speed       ----------------
              |      |       |
       >10m/s | 10%  |  50%  |
              |      |       |

The X axis of the cube is the concentration of the chemical and the Y axis is the speed at which the chemical is traveling. This is a very simple cube. A complex cube can have several hundred variables (and therefore dimensions). The percentages inside the boxes of the cube represents the probability of each occurrence. i.e. There is a 15% chance that the chemical will have a concentration less than 10 mL/mm3 and will be traveling at a speed less than 10 m/s.

As I said a moment ago, a complex cube can have several hundred variables. For an environmental system including a farm, for example, a few variables can be soil moisture, chemical concentration in the soil, wind speed, chemical concentration in the air, irrigation water speed, chemical concentration in the water, breathing rate of the animals. chemical concentration in the plants, what type of plants, type of animals, weather, climate, geographic location, pesticides, what the bugs eat, the wild animals that eat the bugs, the people that eat food and milk products from the farm, ect. ect.

Each of these variables has its own dimension in the cube; thus it is called a hyper cube. Why it’s Latin? Your guess is as good as mine.