Example forward-difference

Consider the example of an ADCP with a beam angle of $20^{\circ }$, 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 $N=300$. The square of the velocity difference between bins separated by $\delta$ bins is then evaluated for each $t$. So for $t_1$, bin 1 and $\delta =1$, we get:

$D(1,1,1)={[v^{\prime }(1,1)-v^{\prime }(2,1)]}^2$

The forward-difference evaluatedfor bin 1 and is then can be evaluated for $1⩽\delta ⩽29$, whilst that for bin 2 is restricted