MEDIAN BINNING

We usually add data into bins. When the data has erratic noise, we might prefer to take the median of the values in each bin. Subroutine medianbin2() (in the library, but not listed here) performs the chore. It is a little tricky because we first need to find out how many data values go into each bin, then we must allocate that space and copy each data value from its track location to its bin location. Finally we take the median in the bin. A small annoyance with medians is that when bins have an even number of points, like two, there no middle. To handle this problem, subroutine medianbin2() uses the average of the middle two points.

A useful byproduct of the calculation is the residual: For each data point its bin median is subtracted. The residual can be used to remove suspicious points before any traditional least-squares analysis is made. An overall strategy could be this: First a coarse binning with many points per bin, to identify suspicious data values, which are set aside. Then a sophisticated least squares analysis leading to a high-resolution depth model. If our search target is small, recalculate the residual with the high-resolution model and reexamine the suspicious data values.

 

medbin90
Figure 4 Galilee water depth binned and roughened. Left is binning with the mean, right with the median.

Figure compares the water depth in the Sea of Galilee with and without median binning. The difference does not seem great here but it is more significant than it looks. Later processing will distinguish between empty bins (containing an exact zero) and bins with small values in them. Because of the way the depth sounder works, it often records an erroneously near-zero depth. This will make a mess of our later processing (missing data fill) unless we cast out those data values. This was done by median binning in Figure but the change is disguised by the many empty bins.

Median binning is a useful tool, but where bins are so small that they hold only one or two points, there the median for the bin is the same as the usual arithmetic average.