Spatial Field:
A spatial field is a function 
of spatial variables 
, or 
in 3D cases.
A spatial field is named a "scalar field" if the function takes on scalar values. For example, the concentration of a toxic substance in the soil at points with coordinates is a scalar field.
A spatial field is named a "vector field" if the function takes on vector values. For example, the vector of the velocity of wind 
at points with spatial 3D coordinates 
is a vector field.
Real measurements are normally made in a discrete set of points. Therefore, interpolation and approximation is often used to obtain a spatial field from a discrete set of measurements 
performed at a finite set of 
spatial points 
.