# Evaluating error correlation

## Examples of Type A methods

As we saw on the last page, in order to perform a Type A correlation evaluation we need to distinguish the error from the value, a feat that is only realistically possible if there is some way of independently estimating the error. On this page, we’ll look at two examples in which an independent estimate of the error can be obtained.

### Geolocation error in MVIRI

MVIRI is an instrument on a geostationary satellite. “Geostationary” means that the orbit of the satellite above the equator is synchronized with the rotation of the earth and that, in theory, the satellite has a fixed sub-satellite latitude and longitude. This way each image covers the same area of the globe. In practice, the orbit is slightly inclined leading to an apparent “wobbling” of the satellite around its theoretically fixed sub-satellite point. This leads to a deformation of the images. To mitigate this, the operational georectification procedure uses orbit information of the last 12 slots (= 6 hours) to compute deformation matrices that navigate each pixel to its true location in a reference grid. However a residual positioning error remains and it can be estimated at certain ‘ground control points’ where pronounced landmark features define accurate longitudes and latitudes of individual pixels.

In this analysis, the error at these ground control points can be directly evaluated. A study was performed to understand error correlation between neighbouring ground control points and between subsequent images. For example, this diagram shows the correlation in the longitude error between landmark pairs as a function of their separation distance in pixels (horizontal axis) and scanlines (vertical axis).

From this analysis, for multiple images, it was possible to calculate error correlation as a function of space and time (see graph below) using the correlation coefficient, which was calculated using statistical (Type A) methods.

### HIRS channel correlation for noise

The HIRS channel error correlation provides a second example of the application of a statistical (Type A) approach towards evaluating correlation.

The 19 thermal infrared channels on the HIRS instrument are measured using a filter wheel in front of two detectors. We were interested in determining whether there was any error correlation in the noise between the spectral channels. This could not be determined from the signal on the different channels; any correlation observed there would be from the physical processes and the fact the channels are observed near simultaneously. It was necessary to extract something related to “noise error”. To do this, we used the calibration of the HIRS instrument using an internal warm calibration target. This target is observed regularly in order to estimate the instantaneous gain. Multiple measurements of the internal warm calibration target are made to obtain an average observation for this calibration. In this example we considered the deviation of the individual raw measurements from that average observation over the calibration period, where the internal warm calibration target is considered stable. The error correlation of these deviations was obtained using the Pearson correlation coefficient and the results are shown in the figure below.

Here we see the error correlation between channel pairs as calculated statistically from the deviations of individual measurements of the internal warm calibration target from the average used in any calibration period. The diagonal represents the self-correlation, which is unity by definition, and the two detectors can be clearly seen.

Now that we’ve examined Type A methods of correlation evaluation, and looked at two examples of where they can be successfully applied, let’s move on to examine Type B methods in more detail, which we’ll do on the next page.