Metrology and Satellite Altimetry

Metrology and Earth Observation

In any area of science where measurements are involved, metrological methods support the provision of trustworthy data and robust uncertainties and to allow users to assess the fitness-for-purpose of a data set. The area of Earth observation (EO) is no different and the "QA4EO Five Steps" approach, originally developed in the FIDUCEO project provides guidance on how to apply metrological principles to Earth observation. Such a process provides a framework for thinking through an uncertainty budget, and recognises that it is not always possible to fulfil all criteria perfectly either because the information is not available (e.g. for historical sensors) or because of practical or scientific constraints. 

The Uncertainty budget for Sentinel-6 section of this website follows the QA4EO Five Steps applied to Sentinel 6. In particular, it reviews the first three steps: identifying the measurand at each stage of the traceability chain, identifying sources of uncertainty and how they feed into the uncertainty analysis process, and documenting what is known to help quantify those sources of uncertainty. Some initial work towards the fourth step (propagating uncertainties) is also considered for a key part of the traceability chain.

Application of Metrology to Satellite Altimetry

A metrological approach considers in detail each source of uncertainty from the origin as it propagates through to the application. Here we consider uncertainties associated with measured values (e.g., noise in the signal), and uncertainties associated with the models used in processing. Where theoretical models are used (e.g., models used in retracking), we consider the uncertainties associated with the assumptions that are built into the form of the model. Where empirical models are used (e.g., for sea state bias corrections), we consider the uncertainties associated with both the input data used to generate the lookup tables, and the uncertainties associated with the form of the empirical model.

The ASELSU project is concerned with understanding the impact these uncertainties have when generating the global mean sea level (GMSL) product and in its trend, as well as various other regional products. In the processing chain, the 1 Hz along-track product is first processed on a regional scale (1° latitude x 3° latitude grid over 10 days) before being processed globally.

To perform accurate uncertainty propagation, it is important to understand both temporal and spatial error correlation scales. Consider the following "dimensions of interest" (i.e., the dimensions over which we characterise the error correlation structure):

1. Fast time – time within a single measurement (within one pulse, freq. > 20 Hz)

2. Slow time – all other times, whether that be pulse to pulse (20 Hz), measurement to measurement (1 Hz), within a grid cell (10 days), or longer (seasons, years, decades).

3. Space – over space, whether that be within one regional box, within larger areas (multiple boxes), or globally.

Naturally, if a source of uncertainty is correlated only over the fast time, or some of the higher frequency slow times, and/or only affects local space (e.g., within one regional box), it will have low impact on GMSL due to averaging. In previous work, such effects have been considered together as "high frequency" terms. 

Another aspect of the metrological approach is to document and demonstrate traceability to SI. The SI unit that provides the traceability for altimetry is the second. Traceability comes from the onboard clock and the time signals from GNSS satellites. Mertikas et al. (2021) have documented the SI traceability of altimeter systems. 

Top-Down and Bottom-Up Approaches

A metrological uncertainty assessment is a 'bottom-up' approach. That is, the uncertainty assessment starts by considering the processing chain as a multi-stage measurement model and assesses sources of uncertainty introduced as input quantities at each stage of that chain. Uncertainties are propagated from earlier stages of processing to later stages. 

More traditionally in altimetry, uncertainty assessments have been made in a 'top-down' manner, where a power spectrum of the timeseries is calculated and information about sources of uncertainty and the error correlation spatial and temporal scales can be assessed from that. 

Both approaches are limited - the metrological approach is limited where information is not available to quantify uncertainties independently, the top-down approach cannot distinguish different sources of uncertainty with similar error correlation profiles, and can mix natural variability with instrument-related noise. The ASELSU project aims to combine the two approaches to provide the most information about uncertainty sources.