## How do I generate my FCDRs?

The FCDR is determined by applying the measurement function to the input data to generate the Earth radiance in each pixel. The FIDUCEO FCDRs are also cleaned up so there are no duplicate pixels and orbit files go from equator to equator.

## Easy or Full FCDR

Uncertainty information is typically complex, particularly for the multi-variate radiance data comprising level 1 satellite imagery. Simplification and summary of uncertainty information increases its conceptual accessibility and ease of application, at the cost of reducing the scientific benefits of the uncertainty information to derived geophysical products at level 2+. In CDRs and similar geophysical products, it is recommended:

- To include rigorous uncertainty information to support the application of the data in contexts such as policy, climate modelling, and numerical weather prediction reanalysis
- To quantify uncertainty consistently with international metrological norms
- To provide uncertainty information per datum if necessary to discriminate observations with lesser and greater uncertainty
- To quantify uncertainty across spatial scales of averaging/aggregation of data

Part of level 2+ uncertainty arises from the propagation of level 1 uncertainty through the processes of image classification, retrieval and aggregation that are typically involved in transformations to higher processing levels.

The purpose of the “easy-FCDR” products from FIDUCEO is to provide level 1 data users with sufficient radiance uncertainty information to propagate uncertainty to higher-order geophysical products with adequate rigour (or to use the radiance in data assimilation with knowledge of the radiance observation error covariances). The aim is to be “as simple as possible, but not simpler”.

## Easy FCDR

Easy-FCDR products will provide users with (re)calibrated satellite radiances, viewing geometry and geolocation data in a net-CDF format as conveniently as possible (e.g., duplicates suppressed, orbits consolidated).

Additionally, there will be uncertainty data in each product. These will consist of:

- Per-pixel, per-channel magnitude of radiance uncertainty
- Per-product, per-channel length-scales of cross-element and cross-line radiance error correlation
- Per-product cross-channel radiance error correlation

## Full FCDR

The full FCDR contains a record for each source of uncertainty with the full effects table. The uncertainty associated with the measurand in a single pixel due to this effect is given by multiplying the sensitivity coefficient by the uncertainty.

The uncertainty associated with the measurand due to multiple effects is obtained by adding the uncertainties associated with the measurand due to individual effects in quadrature (that is taking the square root of the sum of the squares). This assumes that individual effects have no error correlations. This will not be the case for multiple harmonisation parameters determined simultaneously. Therefore a more general form of the equation is:

u^{2}(L_{E,t}) = \underbrace{\sum_{i=1}^n \Bigg(\cfrac{\delta L_{E,t}}{\delta x_{i}}\Bigg)^{2} u^{2} (x_{i})}_{\text{effects table effects}} + \underbrace{\sum_{j=1}^m \Bigg(\cfrac{\delta L_{E,t}}{\delta a_{j}}\Bigg)^{2} u^{2} (a_{j})}_{\text{harmonisation coefficients variance}} + \underbrace{2\sum_{j=1}^{m-1} \sum_{k=j}^m \Bigg(\cfrac{\delta L_{E,t}}{\delta a_{j}}\Bigg)\Bigg(\cfrac{\delta L_{E,t}}{\delta a_{k}}\Bigg) u(a_{j}, a_{k})}_{\text{harmonisation coefficients covariance}}

Here the first summation is over the effects with an effects table, each treated as metrologically independent of each other, with uncertainty and sensitivity coefficient obtained from the effects tables. The harmonisation coefficients are treated by the other two terms. However, this simple analysis does not take into account the error correlation between spectral channels or the error correlation between different image pixels.

**Useful Documents**

Block, T. & Embacher, S., 2017, CDR/FCDR file format specification

Merchant, C.J.; Holl, G.; Mittaz, J.P.D.; Woolliams, E.R. *Radiance Uncertainty Characterisation to Facilitate Climate Data Record Creation*, Remote Sens, 2019, 11, 474.

Merchant C. & Woolliams, E., 2017, Mathematical notation for FIDUCEO publications

Taylor, M., 2018, How to CURUC

Block, T. & Embacher, S., 2017, CDR/FCDR file format specification

Block, T. & Embacher, S., 2018, D3_4 CDR/FCDR Writer/Reader Usage