3.2.1 Jason-2 altimetry products

The time span in this study covers 6.5 years: from July 2008 to December 2014. The coastal Jason-2 products analyzed in this study are X-TRACK, ALES, and PISTACH.

The retrackers available in the different L2 products are summarized in Table 2. The standard GDRs include two solutions: MLE3 and MLE4. The mechanisms of these two retrackers are similar: fitting the waveform to a Brown model [18] based on the MLE (essentially, nonlinear least squares) techniques. MLE3 estimates three parameters: epoch (i.e., altimetric range), significant wave height (SWH), and amplitude (i.e., backscatter coefficient), while MLE4 also retrieves the square of off-nadir angle. The PISTACH products provide four retrackers: OCE3, RED3, ICE1, and ICE3 [15]. OCE3 is essentially the same as the MLE3. ICE1 is a modified threshold retracker. RED3 and ICE3 are the sub-waveform counterparts of OCE3 and ICE1, respectively. ALES is an improved version of RED3, in which the subwaveform length can vary from 39 bins (for SWH = 1 m) to 104 bins (i.e., the entire waveform, for SWH ≥17 m).

In PISTACH and X-TRACK, state-of-the-art geophysical corrections other than those of the official GDR are provided. For X-TRACK, the ocean tide solution and the DAC are provided individually, while in PISTACH, two to three values are given for each correction. Different sets of correction terms obviously lead to different coastal sea level estimates.

Coastal Altimetry: A Promising Technology for the Coastal Oceanography Community DOI: http://dx.doi.org/10.5772/intechopen.89373

#### Figure 5.

Map showing the study area, the selected Jason-2 pass 153 (black and colored line) and the Quarry Bay tide gauge (red circle) located 10 km away from the Jason-2 pass.


#### Table 2.

Overview of different retrackers applied in different altimetry products.

#### 3.2.2 Tide gauge data

The Quarry Bay tide gauge (located at 114.22°E, 22.28°N) regularly measures sea level with an accuracy of ≤1 cm and is well calibrated every other year [36]. The

tide gauge lies near the northern coast of the HK Island, separated from the Kowloon Peninsula by the Victoria Harbor (see Figure 5), where 95% of the shoreline is shaped by human activity [37]. Thus, sea level on this area is expected to be intensively influenced by anthropogenic activities. Hourly tide gauge data are archived and distributed by the Sea Level Center of the University of Hawaii (https://uhslc.soest.hawaii.edu).

A harmonic analysis was first applied to the tide gauge data in order to remove the tidal signals from the sea level time series. A bias (defined as the time-averaged sea level value) was also removed to make the sea level anomaly (SLA) consistent with the altimetry data. Finally, the hourly tide gauge data were interpolated to the Jason-2 satellite overhead time. The tide gauge-based sea level time series interpolated to the closest Jason-2 observations is shown in Figure 6. A large seasonal cycle due to the monsoon can be observed, modulated by high-frequency variations up to several tens of cm. A peak in the tide gauge sea level time series can be noticed at cycle 228. It is caused by a storm surge associate d with the Typhoon Kalmaegi that angrily attacked on the HK coast before sunrise on 16 September 2014. The Jason-2 altimeter flew over the HK area at 3:45 am (local time) on that day, and the peak captured the typhoon event. Although it would be quite valuable for the storm surge investigation, in our analysis this peak was eliminated as an outlier.

#### 3.3 Methodology

#### 3.3.1 Altimetry data processing

As indicated above, current coastal altimetry products differ in terms of content. Therefore, in the beginning of the processing the different data sets were merged to obtain homogeneous variables for further comparison. Because there is no waveform data in PISTACH, we used the waveforms provided in ALES and merged PISTACH and ALES using the measurement time common to all products. We also projected all the along-track, cycle-by-cycle L2 data onto the X-TRACK 1-Hz reference grids to benefit from the X-TRACK improved corrections.

Once all the propagation and geophysical corrections are removed, the sea surface height (SSH, i.e., the sea level referred to a reference ellipsoid) can be deduced from the altimeter range. If we further remove a mean sea surface in order to

Figure 6. HK tide gauge sea level time series (in meters) interpolated to Jason-2 observations.

eliminate the influence of the geoid undulation, the sea level anomaly (SLA) can be obtained. In this study, we use SLA data, computed as follows:

$$\text{SLA} = H - R - \Delta R\_{imo} - \Delta R\_{dry} - \Delta R\_{wet} - \Delta R\_{sib} - \Delta R\_{tide} - \Delta R\_{DAC} - \text{MSS} \tag{6}$$

In Eq. (6), H is the satellite height, R is the altimeter range, ΔRiono, ΔRdry, and ΔRwet are the ionospheric, dry, and wet tropospheric corrections, respectively, ΔRssb is the sea state bias, ΔRtide is the tide correction (sum of the ocean tide, pole tide, and solid Earth tide), ΔRDAC is the dynamic atmospheric correction, and MSS is mean sea surface.

At the coast, R is often not directly available, so it can be derived as follows:

$$R = T + E \times (\mathfrak{c}/2) + D + \mathfrak{M} + \mathfrak{O}.\mathfrak{I80} \tag{7}$$

where T is the onboard tracking range, E is the retracked offset (with time dimension), "c/2 (c being the light velocity)" is the scaling factor from time to range, D is the Doppler correction, M is the instrument imperfection bias [38, 39], and 0.180 is a bias (in meters) due to wrong altimeter antenna reference point [40].

In this study, SLA time series are computed using the altimeter ranges by six retrackers: ALES, MLE3, MLE4, RED3, ICE1, and ICE3. Eq. (7) was used to compute R in the first step, and then Eq. (6) was applied to derive the SLA. To validate our calculation method, we compared our MLE4 SLA with the equivalent official "ssha" parameter in the GDRs and found a very good consistency.

#### 3.3.2 Sea level data analysis

After generating the SLA time series, useful oceanography information can be retrieved. Because of the presence of monsoon, the annual and semi-annual signals are both significant near the HK coast. Therefore, to the first order, SLA variations can be modeled as follows:

$$\begin{split} \text{SLA}(t) &= a\_1 \cos \left(2\pi t / T\_{year}\right) + a\_2 \sin \left(2\pi t / T\_{year}\right) \\ &+ a\_3 \cos \left(4\pi t / T\_{year}\right) + a\_4 \sin \left(4\pi t / T\_{year}\right) + a\_5 t + a\_6 + \varepsilon(t) \end{split} \tag{8}$$

where Tyear = 365.2425 days, ε(t) is the residual SLA, and a1 to a6 are the regression coefficients to be estimated. The estimation uncertainty of the coefficients can be determined from the square root of the diagonal elements in the covariance matrix of the coefficient vector. The linear trend can be inferred from a5 annual/semi-annual amplitude, and phase can be deduced from a1 to a4:

$$A\_{annual} = \sqrt{a\_1^2 + a\_2^2};\ A\_{semi-annual} = \sqrt{a\_3^2 + a\_4^2} \tag{9}$$

$$\Phi\_{annual} = \arctan(a\_2/a\_1); \ \Phi\_{semi-annual} = \arctan(a\_4/a\_3) \tag{10}$$

#### 3.4 Results

Some results are reported here, in which the sea level for a certain cycle is the average of all the valid measurements within ≤10 distance from the coast. Interested readers can refer to [41] for more details.

#### 3.4.1 Solutions derived from the different Retrackers

For each retracker, we computed a spatially averaged 20-Hz SLA time series as well as the associated 20-Hz noise level (defined as the standard deviation of

the 20-Hz SLA series). ALES solution provides the lowest noise level after editing, and MLE4 is slightly less noisy than MLE3. Concerning the three experimental retrackers used in PISTACH, ICE3 has the lowest noise level, and RED3 is slightly less noisy than ICE1.

Sea level trends of are summarized in Table 3 (except for OCE3 in PISTACH, which is the same as MLE3). As a reference, after correcting for VLM, we find a trend of +5.5 2.0 mm/yr. at the tide gauge site.

MLE3 and ALES trends are both close to the tide gauge trend (within 0.5 mm/ yr). The trends estimated from MLE4 are slightly lower than for ALES and MLE3 but the difference is within the error bar. The trends deduced from the PISTACH retrackers disagree significantly with the tide gauge trend: both ICE3 and RED3 show unrealistic large values (>+5 cm/yr), while ICE1 shows a negative trend of 2 cm/yr. The ICE1 retracker may be inherently not accurate enough to derive trends, but ICE3 and RED3 data surprisingly display large jumps of about +20 cm. This would severely influence the corresponding sea level trend estimates. In the remaining part of the study, we concentrate on MLE3, MLE4, and ALES which, in the context of our study, appear to be the best available retrackers for Jason altimetry.

#### 3.4.2 Coastal seasonal signal along the Jason-2 pass

The amplitude and phase of the seasonal signal are also computed for all sea level time series. The results are shown in Table 4. The altimetry annual phases lie around 340° and are significantly larger than the tide gauge-based phase. Amplitudes are also slightly larger. The semiannual phases lie around 240° and are very close to the tide gauge-based phase. Amplitudes are slightly smaller. We cannot exclude the possibility that there is some local seasonal signal at the tide gauge site.

### 3.4.3 Relative performances of MLE4, MLE3, and ALES near Hong Kong

The sea level residuals obtained after removing the trend and seasonal signal are shown in Figure 7 for MLE3, MLE4, ALES, and the tide gauge data. A 3-month low pass filter was applied to the different SLA time series to reduce the intrinsic 59-day erroneous signal discovered in Jason altimetry missions [42, 43]. The standard deviations of the altimetry SLA residuals with respect to the tide gauge residuals,


Table 3.

Estimated linear trend and associated uncertainty (mm/yr) as a function of sea level data source and case.


#### Table 4.

Estimated annual/semiannual amplitude (cm) and phase (degree) as a function of sea level data source and case.

Coastal Altimetry: A Promising Technology for the Coastal Oceanography Community DOI: http://dx.doi.org/10.5772/intechopen.89373

#### Figure 7.

Detrended and deseasoned SLA time series based on ALES, MLE3, and MLE4, with 3-month smoothing (tide gauge SLA—Noted TG—Is shown as reference).


#### Table 5.

Deseasoned and detrended SLA standard deviation w.r.t. tide gauge sea level (cm).

before and after the 3-month smoothing, are given in Table 5. The improvement due to the smoothing is significant, the standard deviations decreasing by more than 50%. The consistency between the altimetry and tide gauge residuals is about 5 cm, which is encouraging given that the study area is quite complex. ALES SLA has a slightly larger standard deviation with respect to tide gauge sea level.
