Retrievability

For the retrieval of surface properties from Earth observation data it is important to consider which factors determine the retrievability. Of course, only surface properties to which the observations are sensitive can in principle be retrieved, but it is equally important that a change in another surface property does not produce a similar response in the observations. This is the issue of linear dependence.

If two surface properties produce a proportionally equal response in all observables (i.e. spectral bands, moments of observation, viewing directions), then there is linear dependence, and one cannot determine which surface property was the cause of the observations. In Figure 1, three different situations are illustrated for the case of two surface properties and two observables.

In the left-hand diagram, property 1 only influences observable 1, and property 2 influences only observable 2. This case is very extreme and seldom occurs in practice, but the conclusion we can draw from the diagram is that in this case property 1 should be estimated from observable 1 and property 2 from observable 2. The middle diagram shows the more common situation that both surface properties influence both observables, albeit in different ways. In this case both properties can still be retrieved mathematically, since we can solve the associated system of two equations with two unknowns. The right-hand diagram illustrates the case of linear dependence. A change in both properties produces a similar change in the observables—perhaps of a different magnitude, but in the same direction. In this case one cannot retrieve both properties separately.

To summarize, the two main conditions for good retrievability are a high sensitivity and linear independence. The chance of encountering cases of linear dependence decreases with the number of independent observations, and since multiple observations are mostly independent, more surface properties can be retrieved and with a higher accuracy.