/**
\page IDW Inverse distance to a power (IDW) interpolation method
\section IDW Inverse distance to a power (IDW) interpolation method

Rainfall and other meterological data can be interpolated in space using the well known IDW interpolation technique.
Since many variations of this simple interpolation technique exist, the one used in cmf sis described.
Any spatial interpolation is a function of place and known data at places. The IDW function reads as:

\f{eqnarray*}
f(x,y,z,t) &=& \sum^N_{i=1}{f_i(t) w_i(x,y,z)} \\
w_i(x,y,z) &=& \frac{d_i(x,y,z)^{-p}}{\sum^N_{j=0}{d_j(x,y,z)^{-p}}}  \\
d_i(x,y,z) &=& w_z \left|z-z_i\right| + \sqrt{\left(x-x_i\right)^2 + \left(y-y_i\right)^2} 
\f}

where:

- \f$ x,y,z \f$ is the actual spatial position
- \f$ t \f$ is the actual time step
- \f$ N \f$ is the number of stations
- \f$ f_i(t) \f$ is a data value of station \f$i\f$ and time step \f$t\f$
- \f$ w_i(x,y,z) \f$ is a weight function of station \f$i\f$ for position \f$ x,y,z \f$
- \f$ d_i(x,y,z)\f$ is the distance / proximity function of station \f$i\f$ for position \f$x,y,z\f$
- \f$ p \f$ is the weighting power. A common value is \f$p=2\f$
- \f$ x_i, y_i, z_i \f$ is the spatial position of station \f$i\f$
- \f$ w_z \f$ is a weight parameter. This parameter can be used change the influence of height differences 
on the proximity of places. \f$w_z=0\f$ resolves in a pure horizontal distance calculation, while very heigh values (eg. 10 000)
resolve in an interpolation by height. Intermediate values (e.g. 10), depending on the height differences in the study area can 
lead to realistic distributions of spatiotemporal values in the landscape.
**/