On denoising satellite altimeter measurements for high-resolution geophysical signal analysis

Abstract

Satellite radar altimeter observations are key to advanced studies in ocean dynamics, particularly those focusing on mesoscale processes. To resolve scales below about 100 km, because altimeter measurements are often characterized by a low signal-to-noise ratio (SNR), low-pass filtering or leastsquares curve fitting is generally applied to smooth the data before analysis. Here, we present an alternative method. It is based on Empirical Mode Decomposition (EMD) developed to analyze nonstationary and non-linear processes, which adaptively projects a signal on a basis of empirical AM/FM functions called Intrinsic Modulation Functions (IMFs). Applied to a Gaussian noise signal, the EMD provides a set of IMFs with a predictable distribution of noise energy that can be exploited by waveletinspired threshold methods to provide an efficient approach to data denoising. The EMD method performs a local analysis of the SNR, does not require a priori assumptions about the underlying geophysical signal, e.g., its degree of smoothness or its compliance with a particular mathematical framework. The signal is simply assumed to be the sum of a piecewise-smooth deterministic part and a stochastic part. The proposed EMD-based denoising approach is therefore well suited for mapping non-linear features, such as strong gradients, and extreme values without significant smoothing. Using Jason-2, Cryosat-2, and Saral/AltiKa significant wave height measurements, the method provides an effective means of mapping overlooked geophysical variability of sea state at scales between about 100 km and 25 km, a range largely impacted by low SNR. Below 25 km, a spectral hump caused by inhomogeneities in the altimeter footprint essentially dominates the signal. In addition, the EMD method provides a consistent approach for longterm noise analysis and monitoring under global and local conditions. The proposed method is a step forward that will enable better exploitation of the unique set of altimeter observations that now covers more than 25 years.

Round Robin Assessment of Radar Altimeter Low Resolution Mode and Delay-Doppler Retracking Algorithms for Significant Wave Height

“…The preceding section described the intrinsic and short term variability affecting the precision of successive measurements. An extension of this analysis is to explore the variability as a function of length scale, i.e., an along-track spectral analysis, as in [35,57].…”

The Sea State CCI dataset v1: towards a Sea State Climate Data Record based on satellite observations

“…Recently, EMD analysis has been successfully applied to altimeter data to analyze wave-current interactions known to predominate at scales below 100 km (Quilfen et al, 2018;Quilfen and Chapron, 2019). For reference the method is fully described in (Quilfen and Chapron, 2020).…”

“…Each IMF is estimated using an iterative process called sifting that determines the AM/FM high-frequency part of any input signal. For a given data segment, the sifting operates in a few steps: 1) find the local maxima and minima; 2) interpolate along the maxima and minima to form an upper and a lower envelope; 3) calculate the average of the two envelopes and subtract it from the analyzed segment; 4) repeat the process from step 1 to 3 unless a stopping criterion has been met (see Huang et al, 1998;Quilfen and Chapron, 2020, for details). An example is shown in Figure 8 for a JASON-2 measurements record of about 1060-km length, for which the EMD method determined six IMFs to represent the full signal.…”

“…To address these limitations, new retracking techniques have been developed, which generally involve one or more of the following features: numerical solution of the radar equation (as opposed to using an analytical model), fitting of a selected portion of the waveform (Passaro et al, 2014;Thibaut et al, 2017;Peng and Deng, 2018), simultaneous multi-waveform processing (Roscher et al, 2017), and post-processing aimed at reducing correlated errors among consecutive estimations (Quilfen and Chapron, 2020;Quartly et al, 2019;Quartly, 2019). On top of this, several flavours exist of an analytical model to describe the viewing geometry of the DDA acquisitions (Moreau et al, 2018;Buchhaupt et al, 2018;Ray et al, 2015).…”

“…The PSD is the average of PSDs computed over all data segments covering the years 2014 to 2016 in the Agulhas region (10ºE -35ºE; 45ºS -33ºS). FromQuilfen and Chapron (2020).…”