# Harmonisation

## What is Harmonisation?

Harmonisation is the process of recalibrating a satellite sensor based on match-up information with another sensor, or series of sensors. It takes in “match-ups” – moments where two instruments saw (almost) the same location at (almost) the same time and uses these to determine new harmonisation coefficients for the sensor. These harmonisation coefficients generally refer to physical attributes of an instrument that can be better estimated from the harmonisation process than from available pre-flight or on-board calibration information and harmonisation can be considered a recalibration of the sensor.

Harmonisation removes biases between sensors in a series. It is, however, important to distinguish harmonisation from simple bias correction and from homogenisation.

## How can FIDUCEO help?

In FIDUCEO we developed methods for the simultaneous harmonisation of a whole sensor series – using all the match ups between pairs of sensors and between some of those sensors and a reference as a large set of simultaneous equations from which we determine the set of harmonisation coefficients for the entire series in one go.

Obtaining information about long-term environmental and climate trends requires the analysis of decadal-scale time series of observations made by different sensors. To ensure that such comparisons are meaningful, it is essential to determine the radiometric differences between sensors and the uncertainties associated with those differences.

Most sensors are calibrated prelaunch, where calibration means establishing the basic model (measurement equation) for translating a measured signal (e.g. in counts) into the required measurand (e.g. radiance). However, this model may also make allowance for in-orbit factors; for example, it may account for gain changes of the instrument throughout the orbit due to variations in self emission by using parameters that estimate the gain from an in-orbit calibration process (e.g. measuring an internal calibration target). The calibration model therefore typically contains several parameters or corrections (calibration coefficients), some of which are determined pre-launch, others determined in-orbit.

For most of the satellite instruments that were considered in FIDUCEO there were potential problems with using pre-launch coefficients when analysing in-orbit measurements.  The pre-launch testing generally had the aim of confirming that the instrument met its design specifications rather than that of determining the optimum set of calibration parameters. The FIDUCEO targets were long-standing historic sensor series. For such sensors, the sensor behaviour in-orbit can be very different from its behaviour during pre-launch testing and more scientific value can be derived from considering the series as a whole, for both the FCDR and the derived CDRs.

Therefore, some level of adjustment to the initial calibration parameters is required to allow for in-orbit behaviour. Within FIDUCEO we defined recalibration as obtaining new calibration coefficients and/or a new calibration model for the sensor from some external information. This may be done by comparing the output of one satellite to a more radiometrically accurate sensor using appropriate match-ups, such as simultaneous nadir overpasses (SNOs).

Recalibration goes beyond the common approach of bias correction, which has the same aim but performs the correction differently. Recalibration adjusts the calibration coefficients, leading to new measured values, whereas, in bias correction, an offset or factor is applied to the existing measured values. Bias correction is more common for an operational update of a sensor providing near real-time data, and is the approach adopted for the current GSICS Corrections. In FIDUCEO, we considered that recalibration is more appropriate and effective for reprocessing historical satellite missions to create improved FCDRs.

When we perform a comparison of two sensors using match-ups we must take into account the fact that those two sensors are not observing exactly the same thing. This is in part due to uncertainties in the collocation process itself, which must be allowed for as part of any sensor-to-sensor comparison. However, a more significant difference is due to differences in the spectral response functions (SRFs) of the two instruments, even when nominally observing the same ‘band’.  In FIDUCEO, we did not aim to ‘correct for’ SRF differences by translating the measured values of the test sensor as though they were taken by the reference sensor (‘homogenisation’). Instead, we aimed to reconcile the calibration of different sensors given their estimated SRF differences. After recalibration, the sensor series is then ‘harmonised’. We therefore have four different concepts, as summarised in Table 1.

 Aim Method Bias correction Recalibration Respecting satellite SRF differences while reconciling calibration GSICS definition for ‘Sensor equivalent calibration’ FIDUCEO definition for ‘harmonisation’ Adjusting for SRF differences and calibration differences GSICS definition for ‘Reference sensor normalised calibration’ FIDUCEO definition for ‘homogenisation’

Within the FIDUCEO project our aim was to perform harmonisation. We obtained new recalibrated L1 products from raw counts, such that the spectral characteristics of each instrument were preserved. The harmonisation process itself involved refitting the calibration parameters (recalibration) using match-ups, taking into account all error covariances in both the instrument and the match-up process.

## The FIDUCEO approach to harmonisation

Our approach to harmonisation uses the well-established approach of inter-calibrating satellite sensors based on simultaneous nadir overpasses (SNOs), or match-ups, where two sensors observe the same Earth scene at the same time with similar viewing geometry (within a given tolerance).

For a given match-up between sensor i and sensor j the expected difference, K, between sensors due to, for example, spectral response, should equal the measured difference between the sensors, as,

K=L_{i} – L_{j}

or in the case of match-up between a sensor j and a reference sensor,

K = L_{ref} – L_{j}

where L_{ref} is the match-up observation as measured by the reference sensor.

For a set of ill-chosen calibration parameters for sensor i and sensor j the above equations would not be well satisfied. It is the role of the harmonisation processing is to reconcile these expected and measured match-up sensor differences for the full set of match-up observations available for all sensors and the reference sensor(s). The problem then becomes a large non-linear regression problem, solving together for new calibration parameters.