The Sensor Footprint Function

How satellite observations are modeled as weighted averages of an underlying spatial field, and why the weighting function matters

## The problem

Satellite sensors don’t measure a single point — they measure a blurry weighted average over a region of the earth’s surface. The shape of that blur matters.

The idea

Each observation \(y_i\) is modeled as:

\[y_i = \frac{1}{|D_i|}\int_{D_i} g_i(s) v(s) \, ds + \varepsilon_i\]

where \(g_i(s)\) is the footprint response function — for OCO-2, approximately a super-Gaussian describing the sensor’s sensitivity across its footprint.

In SpatialBasis

[How the package handles footprint specification]

Example

[Code example]