A core concept behind the FIDUCEO FCDRs is the definition of error correlations between different observations so that this information can be used in the propagation of uncertainties to climate data records. In FIDUCEO we consider that errors may be correlated across a set of identified dimensions. On this page, we’ll briefly introduce two of three such dimensions: spatial and temporal. In the next lesson, we’ll move on to examine a third correlation dimension: spectral.
For the spatial and temporal dimensions, the appropriate error correlation dimensions depend on the imaging method of the instrument.
For low Earth orbit (LEO) platforms with across-track scanning, we have concluded that the most useful error correlation dimensions are:
- Element-to-element within a line (from one pixel to any other pixel in the line)
- Line-to-line within an orbit (from one line to other lines in the orbit for a particular element)
- Orbit-to-orbit within a few orbits (from one orbit to the (countable) orbits immediately before/after that orbit, for the same line within that orbit)
- Time-to-time over a longer duration (from one week, month or year (to be defined) to other weeks, months, years; for “slow” systematic effects )
For Geostationary Orbit Satellites (GEO) that take images in lines, the error correlation dimensions are slightly different:
- Element-to-element within a line (from one pixel to any other pixel in the line)
- Line-to-line within an image (from one line to other lines in the image for a particular pixel)
- Image-to-image within a few images (from one image to the (countable) images immediately before/after that image, for the same line within that image)
- Time-to-time over a longer duration (from one week, month or year (to be defined) to other weeks, months, years; for a ‘slow’ systematic effect)
- Time-to-time with a diurnal variation for effects that happen at certain solar angles
Effects can have different correlation structures for different dimensions. For example, a calibration performed once per line, with some rolling average between lines, would yield effects that would be fully correlated (systematic) for all elements within a line and would have a triangular-shaped correlation structure from line to line over an averaging window and would be uncorrelated (random) beyond those lines and from orbit to orbit. We’ll discuss correlation structures in more detail in a later recipe, but before we do, let’s briefly introduce the spectral correlation dimension, which we will do on the next page.