Removing Intra-1-Hz Covariant Error to Improve Altimetric Profiles of $\sigma^{0}$ and Sea Surface Height

Abstract

Waveform retracking is the process by which a simple mathematical model is fitted to altimeter returns. Over the ocean the waveform location, amplitude and shape can be fitted by models with 3-5 free parameters, which may in turn be linked to geophysical properties of the surface of interest principally sea surface height, wave height and normalized backscatter strength (0 , related to wind speed). However random multiplicative noise, which is due to the summation of power from multiple differently orientated surfaces, produces errors in the estimation of these model parameters. Examination of the correlations among parameters estimated for each waveform leads to simple empirical corrections that reduce the waveformto-waveform noise in geophysical estimates, resulting in smoother (and more realistic) along-track profiles of 0 and sea surface height. These adjustments are fundamentally dependent upon the waveform model and retracker implemented, but when applied show improved agreement between near-simultaneous measurements from different altimeter missions. The effectiveness of these empirical adjustments is documented fully for MLE-4 retracking of the Jason-3 altimeter, with reduction in the 1-second variance of 0 by 97%. However, the ideas are applicable and beneficial for data from other altimeters, with small improvements in 0 for MLE-3 and for AltiKa at Ka-band, whilst reductions in range variance of ⇠40% are noted for most retrackers evaluated.

Removal of Covariant Errors from Altimetric Wave Height Data

“…Similarly, for those algorithms that fit both amplitude (σ 0 ) and mispointing (ψ 2 ), which are both terms related to the power distribution in the trailing edge (see Figure 1b), there is a strong connection between their errors [7,8]. Quartly [7] showed how this property could be used to significantly improve the σ 0 estimates from the MLE-4 algorithm and, more recently, Zaron and deCarvalho [9] and then Quartly et al [10] have demonstrated how the Hs data can be utilised to provide smoother (more realistic) variations in range, and thus ultimately in sea level. Here, we take those ideas and explore the potential for the range information to be used instead to improve the quality of wave height estimates.…”

“…Since both estimates of range and wave height are derived from a few waveform bins on the leading edge of an LRM waveform, their estimates are sensitive to the existence of fading noise affecting the power levels within this section of the waveform (Figure 1b). Sandwell and Smith [11] showed that there was a correlation between the noise-induced anomalies in these two parameters, and Zaron and deCarvalho [9] and Quartly et al [10] have used this empirical connection to reduce the errors in range. The present paper demonstrates that the reverse procedure is equally applicable: using local anomalies in ζ (altitude minus range) to reduce the associated errors in SWH.…”

“…The coefficient, Γ, linking the anomalies in these two terms is found to vary slightly with Hs, with the nonuniformity being most marked for Hs < 1.5 m (Figure 3a)-recasting the empirical link so as to be between ζ and σ C (a term better describing the width of the waveform leading edge) did not improve this (Figure 3c). As noted for the analysis on improving σ 0 and ζ [10], the coefficient to improve Hs depends upon both the altimeter and the retracking algorithm used. The appropriate values of Γ for MLE-4 and MLE-3 are very similar, whereas a different value is needed for ALES applied to Jason data (not shown).…”

“…These correspond to overlapping circular footprints between 2 and 10 km in diameter depending upon wave height [14,15], but spaced at intervals of 330 m along track-thus, there should be minimal real physical change between neighbouring data points. Following Quartly et al [10], we detrend both the ζ and Hs measurements to emphasise the high-frequency variations which are due to the fading noise. In their work, they determined γ, the slope of the red line in Figure 2a governing the portion of ζ anomaly explained by SWH anomaly.…”

“…of the differences by ∼22%. Similar to the analysis for improving σ 0 and sea surface heights (ζ) data [10], the pertinent value of Γ will vary with both altimeter and retracker applied. Figure 8 provides a synopsis of similar analysis for MLE-4 processing of data from AltiKa, the Ka-band altimeter on the SARAL spacecraft.…”