4. Completing the effects table

Every “twig” on the measurement-function-centred uncertainty diagram represents an “effect” and each effect has an associated effects table. The effects table takes the form given in Table 2.

Note that the CDR effects table, unlike the FCDR effects table, includes a category of “maturity of analysis”. This is given a qualitative scale to describe the extent of the available information about this effect. It also provides an estimate of the importance of the effect for those effects that have low maturity.

Table descriptor
How this is codified

Name of effect   A unique name for each source of uncertainty in a term of the measurement function or processing chain as appropriate  
Affected term in measurement function   Name and standard symbol of affected term Usually an effect will only affect a single term, though there may be exceptions
Maturity of analysis Maturity of uncertainty estimate 4-point scale:
0 – Effect identified, no quantification performed (no further information in cells below)
1 – Rough estimates only
2 – Some analysis performed to estimate values
3 – Rigorous analysis performed
This allows for the fact in the CDR we haven’t thought everything through in detail and makes that very clear to users.   If the maturity is low, we may still be able to estimate if it is negligible or minor, or if it’s possibly significant (and therefore needs more work soon)
  Maturity of correlation scale estimate 0 – Not done
1 – Estimated
2 – Based on analysis, unsure about correlation shape
3 – Strong evidence
  If maturity of estimate is 0 or 1, how significant do you expect this effect to be? Negligible, Minor or Significant?  
Correlation type and form From level 1 One of the types defined in below, provided by name See below    
  Larger scale temporal [time]    
  Larger scale spatial [geospatial coordinates]    
Correlation scale From level 1 What is correlation scale See below
  Larger scale temporal [time]    
  Larger scale spatial [geospatial coordinates]    
Uncertainty PDF shape   Functional form of estimated error distribution for the term  
  units Units in which PDF shape is expressed (units of term, or can be as percentage etc) See comment below where uncertainty and sensitivity cannot be separated
  magnitude Value(s) or parameterisation estimating width of PDF  
Sensitivity coefficient   Value, equation or parameterisation of sensitivity of measurand to term.
Can also flag “included in uncertainty” (by making this equal 1)
Where the uncertainty and sensitivity coefficient cannot be separated the sensitivity coefficient should be one and the uncertainty is in units of the CDR measurand.

As with the FCDR effects tables, the CDR effects tables include information on the correlation scale.

For FCDR effects we may be propagating error spatial correlation information from either the full FCDR, or the Easy FCDR. If the full FCDR it will have the same properties as for the FCDR and those cells can be copied (or in practice, new tables are not needed).

If the Easy FCDR, then the correlation length scales are:

FCDR effect Shape Size
common effects rectangle absolute infinite for all dimensions
independent effects random none for all dimensions
structured effects Exponential_decay as propagated from the Easy FCDR
  Provided_by_pixel* vector propagated from Easy FCDR*

*(this depends on the decision we make at the Easy FCDR level). This would be true for the pixel-to-pixel and scanline-to-scanline boxes. At all other scales it’s random with no size.

For new effects at the CDR level, the correlation form must be provided. As well as all the correlation forms defined for the FCDR, two new correlation forms have been introduced: the exponential_decay and the provided_per_pixel forms. Thus the full set of available correlation forms are given in Table 3.

Correlation form Parameters Description
random none required For fully random effects there is no correlation with any other pixel
rectangle_absolute [-a,+b] (rectangle limits). Provide these per pixel/scanline/orbit as required. Allow for a way of representing [-∞,+∞]   [rmax] States correlation coefficient for all pixel / scanline / orbit pixels. Default is rmax = 1 (fully correlated) An effect is systematic within a range and different outside that range. For each pixel / scanline / orbit in range say number of pixels / etc either side that it shares a correlation with. For fully systematic effects notation to say “systematic with all”. If rmax is defined, then the correlation coefficient is one for the pixel with itself, and is rmax with all other pixels.
triangle_relative [n] – number of pixels/scanlines being averaged in simple rolling average (should be an odd number) Suitable for rolling averages over a window from (–n-1)/2 to (+n-1)/2 (i.e. for n pixels/scanlines being averaged) Assumes a simple mean, not a weighted mean. No rmax is needed, since it is always 1.
bell_shaped_relative [n] – number of pixels being averaged in a weighted rolling average, from which truncation range and standard deviation for Gaussian representation follow (truncation beyond ±n pixels, ) (n should be odd)   OR   [n,sigma] n: truncation from –n to +n, sigma: width of Gaussian representation (n should be odd)   Typically provided once per orbit file (some further consideration needed about first/last scanlines in an orbit)     Suitable for rolling averages over a window from (–n-1)/2 to (+n-1)/2 (i.e. for n pixels/scanlines being averaged). Assumes a weighted mean, for any weights (and thus also includes things like spline fitting). Also suitable for anything else where the assumption is that “closer pixels/scanlines are more correlated than further pixels”. This can use two terms – n gives the truncation range outside which the assumption is there is no (or negligible) correlation, and sigma gives how fast the correlation drops off. The derivation of the width sigma to use for a weighted rolling average is given in Appendix B.4.4.
repeating_rectangles [-a,+b,rmax,L,h,imax] per pixel/scanline/orbit etc (rmax,L,h will be same for different pixels)   Correlation coefficient assumed to be rmax for pixels/scanlines from –a to +b, and h for pixels/scanlines from L-a to L+b and from 2L-a to 2L+b and so on (iL-a to iL+b) for all integers i up to imax.
repeating_bell-shapes [n,sigma,L,h, imax] Correlation coefficient assumed to drop off as a truncated Gaussian for local pixels/scanlines etc in the range defined by n and a similar Gaussian with a peak of h and the same width for pixels/scanlines iL pixels apart on either side, for all integers I up to imax. 
Stepped_triangle_absolute [-a,+b,n] per pixel/scanline/orbit etc (n will be same for different pixels)   The step is a rectangular absolute from –a to +b with a correlation coefficient of one, after which the correlation coefficients drops for another a+b+1 lines, and then again. n is the number of calibration windows averaged. See Appendix B.4.5
xponential_decay [el,unit] el: Length scale of exponential decay. Unit: unit of that length scale (we need to think about how we make this machine-interpretable! – could be time or space depending on which row you’re considering]
Provided_by_pixel [vector of relative correlation] For the Easy FCDR propagation
Other A function describing the correlation Not yet implemented.