Introduction to the effects table

Example effects table

In the second tutorial in this series, we examined an Uncertainty Tree Diagram for the Advanced Very High Resolution Radiometer (AVHRR). On this page will see how we might go about filling in an effects table for one of the error effects identified in this Uncertainty Tree Diagram. Specifically, we will look at the effect of detector noise on counts when measuring the calibration target, which contributes to uncertainty, C_\mathrm T.

In order to fill in an effects table for this effect, we need three pieces information:

• The uncertainty associated with the effect
• The sensitivity coefficient, which allows us to propagate uncertainties associated with that effect to uncertainties associated with the measurand
• The error correlation structure over spatial, temporal and spectral dimensions for this effect

We’ll look at each of these pieces of information in more detail in the sections below.

The associated uncertainty

The detector noise is variable and at different times can be much smaller or larger than the nominal figure that is widely assumed. Within the FIDUCEO project we use an approach based on the Allan Deviation to estimate the uncertainty due to evolving noise. More information on this technique can be found at this link.

The sensitivity coefficient

To determine the sensitivity coefficient for this effect, we can simply differentiate the measurement equation with respect to the calibration target counts. Note when the sensitivity coefficient is evaluated it will differ for each pixel since it is dependent upon the on the Earth count measured.

The error correlation structure

1. The fourth tutorial in this series, we saw that error correlation can be structured differently in different spatial and temporal dimensions. A summary of the error correlation structure for our chosen effect for different dimensions is given below.

• Within scanline – Since the calibration target is only measured once per scanline, the noise error is the same for all pixels across a given scanline. Therefore, we have an error correlation of 1 across the whole scanline for this effect. The correlation type is therefore ‘rectangular absolute’, extending over the full range of this dimension, so we record the correlation scale as in this as [- \infty,+ \infty].
• Between scanlines – The measurements of the calibration target counts are averaged in a rolling average as in the example in Tutorial 4. As we saw there this results in a ‘triangular relative’ correlation form, in this case with a base width of a defined number of scanlines, N
• Between orbits – Outside the averaging window there is no correlation
• Between channels – There is no correlation between channels

Bringing together

We now have all of the information required to fill in an effects table for our chosen effect. The completed effects table is shown below. 

Table descriptor		How this is codified
Name of effect		Calibration target counts radiometric noise
Affected term in measurement function		Calibration target counts ($C_\mathrm T$)
Channels / bands		Channel 3B, 4 and 5 (3.7µm, 11µm and 12µm)
Correlation type and form	within scanline [pixels]	Rectangular absolute
	from scanline to scanline [scanlines]	Triangular relative
	between images/orbits [orbits]	None
	between channels / bands	None
Correlation scale	within scanline [pixels]	$-\infty ,+\infty$
	from scanline to scanline [scanlines]	$\pm N$
	between images/orbits [orbits]	None
	between channels / bands	None
Uncertainty PDF shape		Digitised Gaussian
Uncertainty units		Counts
Uncertainty magnitude		Estimated from Allan deviation from calibration target views accumulated over a complete orbit.
Sensitivity coefficient