## Testing an interpolation technique for building a continuous GOES-17 data series

In a previous post, we explored a data interpolation technique that involved running sections of missing GOES-17 Band 13 data through a shape-preserving piecewise cubic spline method in order to fill the data gaps for brightness temperature (BT). (That method was nicknamed ‘pchip’ interpolation.) In this post, we introduce a more advanced type of interpolation for data filling known as interpolation by Principal Component Analysis, or PCA interpolation. One benefit of PCA interpolation is that data does not need to be smoothed to create a believable interpolation. It is, however, more computationally intense and the interpolation requires more time.

To test PCA interpolation, artificial gaps are created in portions of the complete GOES-17 time series data and compared for accuracy. The longest real gap in the GOES-17 time series is approximately 31 hours. Twenty artificial gaps of 31 hours are created in the time series and run through PCA interpolation. Examples are shown below.

Clearly from the examples above, the PCA interpolation does not replicate the original data. Comparing the trends by eye, the PCA interpolation does not seem to mimic the original data well. However, the difference between the true BT and the interpolated BT is computed and has a mean of 1.2032 Kelvin, which is fairly low. 51.4% of all tested retrievals yielded a difference of less than 10 Kelvin. That is, for more than half of the tested retrievals, the filled interpolation is within 10 Kelvin of the original value.