Example forward-difference

Consider the example of an ADCP with a beam angle of <math>20^{\circ}</math>, configured with a vertical bin size of 10 cm, recording profiles at 1 second intervals with a data segment length of 300 seconds. The Level 1 QC of the data identified that good data was typically returned from bins 1 to 30.

The velocity data from a single beam for a single data segment can therefore be visualised as:

with <math>N=300</math>. The square of the velocity difference between bins separated by <math>\delta</math> bins is then evaluated for each <math>t</math>. So for <math>t_1</math>, bin 1 and <math>\delta=1</math>, we get:

<math>D(1,1,1) = \left[v^\prime(1,1) - v^\prime(2,1)\right]^2</math>

The forward-difference evaluatedfor bin 1 and is then can be evaluated for <math>1\leqslant\delta\leqslant29</math>, whilst that for bin 2 is restricted