# Evaluation of Coastal Sea Level Offshore Hong Kong from Jason-2 Altimetry
## 4 Methodology
### Altimetry Data Processing
#### 4.1.2 Choice of the Geophysical Corrections  
The geophysical corrections near the coast also need specific considerations. The first error source comes from the wet tropospheric correction because the onboard radiometer suffers from land contamination in the coastal area. A simple but effective approach is to extrapolate a model-based correction (using for example atmospheric reanalyses from the European Center for Medium-Range Weather Forecasts, ECMWF) but the corresponding spatial resolution is relatively low for coastal applications. Other approaches include an improved radiometer-based correction accounting for the land contamination effect [26], or the computation of GNSS-derived Path Delay (GPD, [27]). Since the GPD has not been included in the current versions of the three coastal products analyzed here, we used the decontaminated radiometer solution provided in PISTACH. Concerning the ionospheric correction, the imperfect coastal altimeter range measurements lead to significant errors, generating outliers in the correction values. We use the MAD (median absolute deviation) technique described in detail in Section 4.1.3 to detect and remove the outliers. The along-track profile of ionospheric corrections is further spatially low-pass filtered using a LOESS (LOcally Estimated Scatterplot Smoothing) method with a cutoff frequency at 100 km. The coastal ocean tide corrections, provided by global models, are also far from accurate. There are five different ocean tide solutions available in the products, computed by two scientific teams: (1) the Goddard Ocean Tide (GOT) models developed by [PERSON] et al. [28], and the Finite Element Solution (FES) models developed by [PERSON] et al. [29]. Two ocean tide solutions are provided in the official GDRs:GOT4.8 and FES2004. PISTACH contains two older versions of GOT: GOT00.2 and GOT4.7 as well as an upgraded version of FES: FES 2012. In Equation (1) we adopt the GOT4.8 ocean tide solution. [PERSON] [30] compared different tide solutions against 196 shelf-water tide gauges and 56 coastal tide gauges. Their accuracy was characterized by the RSS (root sum square) error of the eight main tidal components (Q1, O1, P1, K1, N2, M2, S2, K2). For the shelf-water gauges, the accuracy of GOT4.8 was 7.04 cm along European coasts and 6.11 cm elsewhere, while the accuracy of FES2012 was 4.82 cm and 4.96 cm respectively for the European coasts and elsewhere. For the coastal tide gauges, the accuracy of GOT4.8 and FES2012 were 8.45 cm and 7.50 cm respectively. In comparison, the accuracy of GOT4.7 and FES2004 in shelf-water were 7.77 cm and 10.15 cm respectively. These results illustrate the significant improvement in coastal ocean tide solution during the last 10 years. In Section 5.5, we also compare three tide solutions, GOT4.8, FES 2004, and FES 2012, to assess their relative performances. Another important altimetry correction is the sea state bias (SSB). The SSB depends on the retracking algorithm, because it contains the tracker bias. A careful analysis showed that for Jason-2 GDRs, the SLA obtained from MLE3 and MLE4 retrackers has large bias. From a statistical analysis based on cycles 1 to 238 for a couple of altimeter passes over the open ocean, we obtained: \(\mathit{SLA}_{\mathit{MLE3}}\)\(-\)\(\mathit{SLA}_{\mathit{MLE4}}\)\(+\)2.3 cm. Near the coast, this bias appeared to be even larger and even more critical as it was not constant. Figure 5 shows both MLE3 and MLE4 SSB corrections as a function of SWH for an arbitrary pass (cycle 16, pass #153). MLE3 SSB has a clear bias (\(\sim\)+3 cm) relative to MLE4 SSB. Moreover, MLE3 SSB seems to have many outliers, in particular near the coast. We concluded that the bias observed between MLE3 and MLE4 sea level estimates corresponds to a bias in the SSB corrections. Deeper investigation showed that the MLE3 SSB outliers are often related to large off-nadir angle values (not shown), probably erroneous given the good attitude control of Jason-2.