Vector Fields

So far in this course, we have only considered attribute data types that are single-valued, whether that value is categorical or numerical. In spatial analysis, we frequently encounter attributes that are not conveniently represented in this way. In particular, we may need to use vectors to represent some types of data.

A vector is a quantity that has both value (or magnitude) and direction. The most obvious vector in real-life applications is wind, which has a speed (its magnitude or strength) and direction. Without wind direction information, wind speed information is not very useful in many applications. For example, an aircraft navigator needs to know both wind speed and direction to accurately plot a course and to estimate arrival times or fuel requirements.

The most fundamental vector field is the gradient field associated with any scalar (i.e., simple numerical) field. This often has practical applications. For example, the gradient field of atmospheric pressure is important in meteorology in determining the path of storm systems and wind directions.