Example uncertainty analysis tree

Now that we’ve examined the general idea of an effect, and seen where effects might come from, let’s move on to look at some effects in relation to a real life example. The figure below shows a simplified uncertainty analysis tree centred on the measurement function for the Advanced Very High Resolution Radiometer (AVHRR). 

As we saw in the first recipe in this series, this diagram is designed to show the sources of uncertainty from their origin through to the uncertainty in the measurand. On the outside of the tree are the effects leading to uncertainty.

Looking at the diagram in more detail, moving clockwise from the top of the diagram:

The green branch details effects that lead to uncertainty in the calibration parameters a_0{}, a_1 and a_2 , which come from harmonisation (see later recipe in this series entitled ‘harmonisation’ for more details)

The blue branch details effects that lead to uncertainty in how well the measurement function describes the true physical state of the measurement process. These effects contribute to the uncertainty in the ‘plus zero’ term, u(0) ; the main assumption here is that the quadratic equation fully represents the instrument response and there is no higher order nonlinearity

The dark purple branch shows effects that contribute to the uncertainty in counts seen when looking at the Earth, u(C_E) ; these are sources of noise in the detector and amplified and in the digitisation of the signal for transmission purposes. These will create an independent (random) error from pixel to pixel

The light purple branch details the effects that lead to uncertainty, u(C_T) , in the counts seen when looking at the calibration target. Here again there is noise in the detector and amplifier, and in the digitisation of the signal. Each measurement of the internal calibration target (ICT) will have an independent noise error, but the ICT is only measured once per scan line, giving a structured random effect. We will discuss structured random effects in more detail in a later recipe.

The orange branch shows the effects that lead to uncertainty, u(L_T) in the calibration-target radiance. This comes predominantly from the measurement of the target temperature and thermal gradients across the target. Some aspects, e.g. thermometer calibration uncertainties create a systematic effect (a common error for the mission). Others vary around the orbit.

Notice here that very similar effects can influence different terms. For instance, the effect of ‘detector noise’ contributes to the uncertainty in Earth count and on-board calibration target counts. However, although these are similar, the do not have the same error.