Sea State Bias Research Articles

Trace-Norm Regularized Multi-Task Learning for Sea State Bias Estimation

Sea state bias (SSB) is an important component of errors for the radar altimeter measurements of sea surface height (SSH). However, existing SSB estimation methods are almost all based on single-task learning (STL), where one model is built on the data from only one radar altimeter. In this paper, taking account of the data from multiple radar altimeters available, we introduced a multi-task learning method, called trace-norm regularized multi-task learning (TNR-MTL), for SSB estimation. Corresponding to each individual task, TNR-MLT involves only three parameters. Hence, it is easy to implement. More importantly, the convergence of TNR-MLT is theoretically guaranteed. Compared with the commonly used STL models, TNR-MTL can effectively utilize the shared information between data from multiple altimeters. During the training of TNR-MTL, we used the JASON-2 and JASON-3 cycle data to solve two correlated SSB estimation tasks. Then the optimal model was selected to estimate SSB on the JASON-2 and the HY-2 70–71 cycle intersection data. For the JSAON-2 cycle intersection data, the corrected variance (M) has been reduced by 0.60 cm2 compared to the geophysical data records (GDR); while for the HY-2 cycle intersection data, M has been reduced by 1.30 cm2 compared to GDR. Therefore, TNR-MTL is proved to be effective for the SSB estimation tasks.

Improving precision of high-rate altimeter sea level anomalies by removing the sea state bias and intra-1-Hz covariant error

This paper assessed the precision of 20-Hz sea level anomaly (SLA) estimates with different sea state bias (SSB) corrections from reprocessed Jason-1/2/3 and Sentinel-3A data over the period of 2002–2019 within 100 km from the entire Australian coast. The altimeter waveforms were retracked by the modified Brown-peaky (MBP) retracker for Jason missions and by the SAMOSA+ retracker for Sentinel-3A. We recalculated the 20-Hz and composite SSB corrections using a regional parametric model from 20-Hz retracked estimates of the SLA, significant wave height (SWH) and wind speed. The composite SSB correction, which was recomputed after removing the retracker-dependant correlated error in 20-Hz SLA, is found to achieve better performance than other SSB corrections in the study area. Applying the 20-Hz and composite SSB corrections has reduced ~10% and ~13% of noise, respectively, in the MBP-retracked 20-Hz Jason SLA estimates, while only ~2% of noise reduction is shown by applying the 1-Hz standard SSB correction. It is also found that the improvement of retracked Sentinel-3A SLA estimates by SSB corrections is very low (~3%), indicating a dedicated SSB correction model should be developed for the SAR mode altimeter.As a result, the precision of composite SSB-corrected SLA estimates for all Jason missions can be retained at the level of 5.1 ± 1.1 cm until 3 km from the Australian coast, which is slightly lower than that of Sentinel-3A (4.2 ± 0.9 cm). The degradation within 3 km from the coast mainly corresponds to the along-track direction for MBP-retracked Jason SLA estimates, and the across-track direction for SAMOSA+ retracked Sentinel-3A SLA estimates, respectively.

Preliminary Evaluation and Correction of Sea Surface Height from Chinese Tiangong-2 Interferometric Imaging Radar Altimeter

In this study, we performed preliminary comparative evaluation and correction of two-dimensional sea surface height (SSH) data from the Chinese Tiangong-2 Interferometric Imaging Radar Altimeter (InIRA) with the goal of advancing its retrieval. Data from the InIRA were compared with one-dimensional SSH data from the traditional altimeters Jason-2, Saral/AltiKa, and Jason-3. Because the sea state bias (SSB) of distributed InIRA data has not yet been considered, consistency was maintained by neglecting the SSB for the traditional altimeters. The results of the comparisons show that the InIRA captures the same SSH trends as those obtained by traditional altimeters. However, there is a significant deviation between InIRA and traditional altimeter SSHs; consequently, systematic and parametric biases were analyzed. The parametric bias was found to be related to the incidence angles and a significant wave height. Upon correcting the two biases, the standard deviation significantly reduced to 8.1 cm. This value is slightly higher than those of traditional altimeters, which typically have a bias of ~7.0 cm. The results indicate that the InIRA is promising in providing a wide swath of SSH measurements. Moreover, we recommend that the InIRA retrieval algorithm should consider the two biases to improve SSH accuracy.

Validation of Sentinel-3A SRAL Coastal Sea Level Data at High Posting Rate: 80 Hz

Altimetry data of two and a half years (June 2016–November 2018) of Sentinel-3A SRAL (S3A-SRAL) were validated at the sampling frequency of 80 Hz. The data were obtained from the European Space Agency (ESA) Grid Processing On Demand (GPOD) service over three coastal sites in Spain: Huelva (HU) (Gulf of Cadiz), Barcelona (BA) (Western Mediterranean Sea), and Bilbao (BI) (Bay of Biscay). Two tracks were selected in each site: one ascending and one descending. Data were validated using in situ tide gauge (TG) data provided by the Spanish Puertos del Estado. The altimetry sea level anomaly time series were obtained using the corrections available in GPOD with the exception of the sea state bias (SSB) correction, not available at 80 Hz. Hence, the SSB was approximated to 5% of the significant wave height (SWH). The validation was performed using two statistical parameters, the Pearson correlation coefficient (r) and the root mean square error (rmse). In the 5–20-km segment with respect to the coastline, the results were 6–8 cm (rmse) and 0.7–0.8 (r) for all the tracks. The 0–5-km segment was also analyzed in detail to study the land effect on the altimetry data quality. The results showed that the track orientation, the angle of intersection with the coast, and the land topography concur to determine the nearest distance to the coast at which the data retain a similar level of accuracy than in the 5–20-km segment. This “distance of good quality” to shore reaches a minimum of 3 km for the tracks at HU and the descending track at BA.

Improving Sea Level Anomaly Precision from Satellite Altimetry Using Parameter Correction in the Red Sea

An improved Fourier series model (FSM01) method is used in geophysical and environmental corrections to enhance the final product of the along-track Jason-2 sea level anomaly (SLA) data and extend it near the Red Sea borders. In this study, the ionospheric correction range, wet tropospheric correction range, sea state bias correction range, and dry tropospheric correction range are enhanced and improved using FSM01, which helped to retrieve three more tracks (106, 170, and 234) earlier neglected by the distribution centers and extend the tracks toward the coast. The FSM01 SLA is compared with Jason-2 SLA and Archiving Validation and Interpretation of Satellite Oceanographic (AVISO) SLA for the available five tracks, in which the FSM01 SLA shows a good agreement and higher correlation with the Jason-2 SLA compared with that of AVISO, in addition to filling the gaps in the times series of all tracks. The newly retrieved tracks are also compared with those retrieved by AVISO, and both data points show similar variability, with FSM01 SLA showing no gaps in the time series. The FSM01 SLA was also extended toward the coast and showed high correlation with the coastal tide measurements.

Sea state bias in altimetry measurements within the theory of similarity for wind-driven seas

The theory of similarity for wind-driven seas is applied to the physical analysis of the problem of sea state bias (SSB) in altimetry measurements. Dimensionless wave steepness and pseudo-age derived from altimetry measurements are expected to provide {physically relevant and accurate enough} SSB estimates. Analysis of Jason-1,2,3 and SARAL/AltiKa data within the approach shows the similarity and robustness of SSB distributions re-casted onto space of wave pseudo-age and steepness. This result is considered as a ground for developing a new parametric model of SSB and for analysis of underlying physical effects.

Assessing the effects of sea-state related errors on the precision of high-rate Jason-3 altimeter sea level data

Abstract The investigation of ocean surface topography variation by low-resolution mode (LRM) altimeters at length scales shorter than 100 km is limited by cm-scale measurement noise. Spectral analysis of along-track altimeter data has been used to highlight the issue and to illustrate that one significant noise source stems from correlation between significant wave height (SWH) and range errors that is inherent to any waveform retracking algorithm. This paper focuses on improved characterization and reduction of these high-rate correlated errors that arise from this altimeter measurement process. Specifically, it addresses the effects of sea-state related errors in high rate (20-Hz) Jason-3 satellite sea level data that may possibly impact both short-scale and longer-scale data via interplay with the sea state bias (SSB) correction. Among the suite of standard corrections used to extract sea surface height (SSH) from the raw altimeter range, the empirical SSB term is designed to remove correlation between range and SWH measurements, but not explicitly short-scale error between the two. In this paper, we report that the efficacy of the SSB correction varies with wavelength and it does not remove all correlated signal at high wavenumbers. Following several recent studies, an independent high-frequency adjustment (HFA) is developed to remove these residual correlated errors. Both SSB and HFA are applied on SSH estimations at the 20-Hz rate, improving both 20-Hz and 1-Hz data. Jason-3 data are used as a test bed. Both corrections and net results are specific to MLE4 Jason-3 waveform retracking. Because the reported updated SSB models provide nearly unbiased continuity from Jason-1 to Jason-3 SSB time-series and the MLE4 retracking algorithm is the standard for these missions, the Jason-3 HFA solution can be applied to earlier Jason data with implications for improving the combined 16-year Jason record. By design, the HFA does not impact wavelengths greater than 200 km which is the acting domain of the SSB correction. Applying both the SSB and HFA corrections leads to a global SSH variance reduction nearing 35% in average. The SSH denoising approach through the computation of an additional HFA term is applicable for any LRM ocean altimeter.

Sea level anomalies using altimetry, model and tide gauges along the African coasts in the Eastern Tropical Atlantic Ocean: Inter-comparison and temporal variability

Abstract Because of sparse in situ measurements, the use of altimeter and ocean models are currently the only options to understand the coastal variability of sea level anomalies (SLA) near the African coasts of the Eastern Tropical Atlantic Ocean (ETAO: 35°S–25°N; 25°W–African coasts). In this study, three SLA products derived from altimetry (X-TRACK and CMEMS) and from a regional ocean model (NEMO) are validated near the coast using the 14 tide gauges (TGs) available in the region. Statistical analysis (correlation, standard deviation and root mean square) are performed to compare our three products with the TG. We then analyze the sub-seasonal to inter-annual variability of SLAs (i.e. from 20 days up to 2 years) over the period January 2008–December 2014. We found a very good agreement between altimetry, model and TGs near the coasts of Senegal (10°N–25°N) and Gulf of Guinea (10°S–10°N). This is not the case near the coast of Benguela (south of 10°S) and is mainly explained by the combined effects of the position of TGs (located in semi-enclosed bays), the geophysical corrections used in the computations of the SLA derived from altimetry (i.e. tide, dynamical atmospheric correction -DAC- and sea state bias -SSB-). In addition, the low spatial resolution of the CMEMS and model data do not allow a good description of the small scale oceanic and atmospheric variability, which dominates in the Benguela upwelling system. We then show, with all products, that the temporal variability of SLA is mainly seasonal (annual and semi-annual) throughout the ETAO region. The altimetry data also show some inter-annual (15–24 months) variability in the equatorial band, which can be related to equatorial Kelvin waves. This is less pronounced with the NEMO model and does not appear over the whole equatorial band. We show that high spatial resolution and improved altimetric geophysical corrections near the coast can each reduce near-shore data errors by up to 10%. However, despite these improvements, agreements between SLA products are still unsatisfactory in the Benguela region, suggesting that efforts need to be intensified on geophysical corrections and in increasing the temporal and spatial resolution of data near the coast. Moreover, there exist gaps in TG measurements, along the West African coast, especially in the Benguela region. The TG network should thus be completed.

Sea State Bias Variability in Satellite Altimetry Data

Sea State Bias (SSB) contributes to global mean sea level variability and it needs cm-level range adjustment due to the instrumental drift over time. To investigate its variations and correct the global and regional sea level trend precisely, we calculate the temporal and spatial variability of the SSB correction in TOPEX, Jason-1, Jason-2 and Jason-3 missions, separately, as well as in the combined missions over the period 1993–2017. The long-term trend in global mean operational 2D non-parametric SSB correction is about −0.03 ± 0.03 mm/yr, which accounts for 1% of current global mean sea level change rate during 1993–2016. This correction contributes to sea level change rates of −1.27 ± 0.21 mm/yr and −0.26 ± 0.13 mm/yr in TOPEX-A and Jason-2 missions, respectively. The global mean SSB varies up to 7–10 mm during the very strong ENSO events in 1997–1998 and 2015–2016. Furthermore, the TOPEX SSB trend, which is consistent with recently reported sea level trend drift during 1993–1998, may leak into the determined global sea level trend in the period. Moreover, the Jason-1/2 zonal SSB variability is highly correlated with the significant wave height (SWH). On zonal average, SSB correction causes about 1% uncertainty in mean sea level trend. At high SWH regions, the uncertainties grow to 2–4% near the 50°N and 60°S bands. This should be considered in the study of regional sea level variability.

Improved Sea State Bias Estimation for Altimeter Reference Missions With Altimeter-Only Three-Parameter Models

This paper presents an in-depth study concerning the development of a sea state bias (SSB) model designed with three parameters exclusively derived from altimeter data and globally applied to all reference altimeter missions. The proposed technique, first tested for the Jason-1 mission, proves to have a good performance for a wide range of ocean conditions when compared with the state-of-the-art SSB corrections currently in use. In addition to the significant wave height ( $H_{s}$ ) and wind speed ( $U~_{{10}}$ ), a third predictor acting as a mediator parameter gathered by the mean wave period ( $T_{z}$ ) has been used. Two different empirical algorithms for altimeter ocean wave period have been tested and implemented, improving the SSB model performance in some ocean regions. The methodology relies on nonparametric modulation and statistical techniques based on smoothing splines embedded in a generalized additive model. This SSB modeling approach shows good performance when applied to all reference missions, in particular to TOPEX and Jason-2 missions, slightly reducing the explained variance of sea-level anomaly (SLA) when compared with the established SSB models. The approach is computationally efficient, capable of generating a stable SSB model using a small training data set when little information is available, as is the case with the recent Jason-3 mission. Model performance is assessed by comparison with existing SSB corrections for each reference mission, intercomparisons during the period of the tandem phases, and by SLA variance analysis, providing a consistent set of SSB corrections for the four reference missions.

Using a stacked-autoencoder neural network model to estimate sea state bias for a radar altimeter.

This paper constructed a stacked-autoencoder neural network model (SAE model) to estimate sea state bias (SSB) based on radar altimeter data. Six cycles of the geophysical data record (GDR) from Jason-1/2 radar altimeters were used as a training dataset, and the other 2 cycles of the GDR from Jason-1/2 were used for testing. The inputs to this SAE model include the significant wave height (SWH), wind speed (U), sea surface height (SSH), backscatter coefficient (σ0) and automatic gain control (AGC), and the model outputs the SSB. The model includes one input layer, three hidden layers and one output layer. The SSBs in the GDR of Jason-1/2 were obtained from a nonparametric model based on the SWH and U as input variables; thus, the model has high accuracy but low efficiency. The SSBs in the GDR of HY-2A were computed using a four-parameter parametric model that uses the SWH and U as input variables; therefore, this model’s computational speed is high but its accuracy is low. Thus, we used the HY-2A radar altimeter as an unseen validation dataset to evaluate the performance of the SAE model. Then, we analyzed the contrasting results of these methods, including the differences in the SSB, explained variance, residual error and operational efficiency. The results demonstrate not only that the accuracy of the SAE model is superior to that of the conventional parametric model but also that its operational efficiency is better than that of the nonparametric model.

Sea Surface Wind Speed Retrieval and Validation of the Interferometric Imaging Radar Altimeter Aboard the Chinese Tiangong-2 Space Laboratory

This study focuses on the retrieval and validation of sea-surface wind speeds using data from the interferometric imaging radar altimeter (InIRA) aboard the Chinese Tiangong-2 space laboratory. First, an empirical model, KuLMOD2, is proposed, which is a revised version of the former Ku-band low incidence model (KuLMOD) that directly relates the normalized radar cross section σ 0 to both the wind speed and incidence angle. The revised model extends the ranges of the incidence angle and wind speed and is thus applicable to the new InIRA data. The model coefficients are estimated by fitting precipitation radar data from the Tropical Rainfall Measuring Mission and collocated wind data from the European Centre for Medium-Range Weather Forecasts. The wind speeds are then retrieved from the InIRA data using KuLMOD2. For more efficient retrieval, a lookup table method is used to find the wind speed solution. Finally, the InIRA wind speeds are validated using collocated Advanced Scatterometer (ASCAT) wind speeds. The validation of the InIRA wind speed data shows that InIRA can capture regional changes and that the data have a bias of 0.02 m/s and a root-mean-square error of 1.58 m/s. This suggests that the InIRA data alone can provide valid wind speeds for future sea state bias correction of InIRA-derived sea-surface heights and that the InIRA data can act as a complement to data from other spaceborne wind sensors.

Improving the precision of sea level data from satellite altimetry with high-frequency and regional sea state bias corrections

The sea state bias (SSB) is a large source of uncertainty in the estimation of sea level from satellite altimetry. It is still unclear to what extent it depends on errors in parameter estimations (numerical source) or to the wave physics (physical source).By improving the application of this correction we compute 20-Hz sea level anomalies that are about 30% more precise (i.e. less noisy) than the current standards. The improvement is two-fold: first we prove that the SSB correction should be applied directly to the 20-Hz data (12 to 19% noise decrease); secondly, we show that by recomputing a regional SSB model (based on the 20-Hz estimations) even a simple parametric relation is sufficient to further improve the correction (further 15 to 19% noise decrease).We test our methodology using range, wave height and wind speed estimated with two retrackers applied to Jason-1 waveform data: the MLE4 retracked-data available in the Sensor Geophysical Data Records of the mission and the ALES retracked-data available in the OpenADB repository (https://openadb.dgfi.tum.de/). The regional SSB models are computed parametrically by means of a crossover analysis in the Mediterranean Sea and North Sea.Correcting the high-rate data for the SSB reduces the correlation between retracked parameters. Regional variations in the proposed models might be due to differences in wave climate and remaining sea-state dependent residual errors. The variations in the empirical model with respect to the retracker used recall the need for a specific SSB correction for any retracker.This study, while providing a significantly more precise solution to exploit high-rate sea level data, calls for a re-thinking of the SSB correction in both its physical and numerical component, gives robustness to previous theories and provides an immediate improvement for the application of satellite altimetry in the regions of study.

Sea State Bias Estimation with Least Absolute Shrinkage and Selection Operator (LASSO)

With the sea-level rising, the measurement of sea surface height (SSH) is attracting more and more attention in the area of oceanography. Satellite radar altimeter is usually used to measure the SSH. However, deviation between the measured value and the actual one always exists. Among others, the sea state bias (SSB) is a main reason to cause the deviation. In general, one needs to estimate SSB first to correct the measured SSH. Currently, existing SSB estimation methods more or less have shortcomings, such as with many parameters, high prediction error and long training time. In this paper, we introduce an effective and efficient linear model called LASSO to the SSB estimation. The LASSO algorithm minimizes the residual sum of squares under the condition that the sum of the absolute values of each coefficient is less than a certain constant. In the implementation of LASSO, we use the significant wave height and wind speed to fit the LASSO model. Hence, the applied model has only 3 parameters, corresponding to the two inputs and a bias. Experimental results on the data of JASON-2, JASON-3, T/P and HY-2 radar altimetry show that LASSO performs better than geophysical data records (GDR) and ordinary least squares (OLS) estimator. Moreover, from the running time, we can see that LASSO is very efficient.

Sea State Bias of ICESat in the Subarctic Seas

The fine spatial resolution of laser altimeters makes them potentially valuable to oceanography studying features at mesoscale, close to land, and in the marginal ice zone. To fulfill this promise, we must understand laser sea state bias (SSB). SSB occurs in the measurement of sea surface height in the presence of waves when the altimeter observations are preferentially influenced by particular parts (e.g., wave troughs) of the wave-covered surface. Radar altimeters have received considerable attention relating radar SSB to wave properties and wind speed. Comparatively, little attention has been devoted to the SSB of laser altimeters, and the studies of laser SSB which have been done have led to indeterminate or ambiguous results even as to sign. Here, we find that to make changes in satellite dynamic ocean topography (DOT) from the Ice, Clouds, and Land Elevation Satellite (ICESat) period, 2004–2009, to the CryoSat-2 period, 2011–2015, consistent with hydrography plus ocean bottom pressure in the subarctic Greenland and Norwegian seas, we need to correct the ICESat DOT for SSB. On average, ICESat SSB is −18% of significant wave height in excess of 1.7 m.

Validation of Sea Surface Wind Speeds from Satellite Altimeters and Relation to Sea State Bias

Validation of Sea Surface Wind Speeds from Satellite Altimeters and Relation to Sea State Bias

Plasmaspheric Electron Content Inferred from Residuals between GNSS-Derived and TOPEX/JASON Vertical TEC Data

The plasmasphere, which is located above the ionosphere, is a significant component of Earth’s atmosphere, and the plasmasphere electron content (PEC) distribution is determined by different physical mechanisms to those of the ionosphere electron content (IEC). However, the observation for the PEC is very limited. In this study, we introduced a methodology (called zero assumption method, which is based on the assumption that PEC can reach zero) to extract the PEC over TOPEX/JASON (T/J) and global navigation satellite system (GNSS) overlapping areas. Results show that the daily systematic bias (T/J vertical TEC > GNSS-derived vertical TEC) for both low (2009) and high (2011) solar activity condition is consistent, and the systematic bias for JASON2 and JASON1 is different. We suggest that systematic biases predominantly arise from the sea state bias (SSB), especially the tracker bias. After removing the systematic bias, we extracted reliable PEC inferred from differences between GNSS-derived vertical TEC and T/J vertical TEC data. Finally, the characteristics of the plasmaspheric component distribution for different local times, latitudes, and seasons were investigated.

Assessment of radar altimetry correction slopes for marine gravity recovery: A case study of Jason-1 GM data

Marine gravity anomaly derived from satellite altimetry can be computed using either sea surface height or sea surface slope measurements. Here we consider the slope method and evaluate the errors in the slope of the corrections supplied with the Jason-1 geodetic mission data. The slope corrections are divided into three groups based on whether they are small, comparable, or large with respect to the 1 microradian error in the current sea surface slope models. (1) The small and thus negligible corrections include dry tropospheric correction, inverted barometer correction, solid earth tide and geocentric pole tide. (2) The moderately important corrections include wet tropospheric correction, dual-frequency ionospheric correction and sea state bias. The radiometer measurements are more preferred than model values in the geophysical data records for constraining wet tropospheric effect owing to the highly variable water-vapor structure in atmosphere. The items of dual-frequency ionospheric correction and sea state bias should better not be directly added to range observations for obtaining sea surface slopes since their inherent errors may cause abnormal sea surface slopes and along-track smoothing with uniform distribution weight in certain width is an effective strategy for avoiding introducing extra noises. The slopes calculated from radiometer wet tropospheric corrections, and along-track smoothed dual-frequency ionospheric corrections, sea state bias are generally within ±0.5 microradians and no larger than 1 microradians. (3) Ocean tide has the largest influence on obtaining sea surface slopes while most of ocean tide slopes distribute within ±3 microradians. Larger ocean tide slopes mostly occur over marginal and island-surrounding seas, and extra tidal models with better precision or with extending process (e.g. Got-e) are strongly recommended for updating corrections in geophysical data records.

A novel model of estimating sea state bias based on multi-layer neural network and multi-source altimeter data

ABSTRACTIn this article, we propose a novel model for estimating sea state bias (SSB) based on multi-layer neural network and multi-source altimeter data from the Topex/Poseidon (T/P), Jason-2, and Jason-3 altimeters. Significant wave height (SWH), wind speed (U) and backscatter coefficient (σ0) are considered as the inputs of the multi-layer neural network, while the corresponding SSB as outputs. The neural network has four layers, with structure 3-3-6-1. Data from three seasons are employed for the neural network training, and the trained model is applied for the SSB estimation on the HY-2 altimeter data. To show the effectiveness of the adopted model, the correlations between SSB and SWH, U and σ0 are analyzed. Moreover, the explained variance and residual error are compared with a conventional parametric model for SSB estimation. The results demonstrate that multi-layer neural network trained on multi-source altimeter data performs superior to the conventional SSB estimation model.

Nonparametric estimations of the sea state bias for a radar altimeter

To estimate the sea state bias (SSB) for radar altimeter, two nonparametric models, including a Nadaraya-Watson (NW) kernel estimator and a local linear regression (LLR) estimator, are studied based on the Jason-2 altimeter data. Selecting from different combinations of the Gaussian kernel function, spherical Epanechnikov kernel function, a fixed bandwidth and a local adjustable bandwidth, it is observed that the LLR method with the spherical Epanechnikov kernel function and the local adjustable bandwidth is the optimal nonparametric model for the SSB estimation. The comparisons between the nonparametric and parametric models are conducted and the results show that the nonparametric model performs relatively better at high-latitudes of the Northern Hemisphere. This method has been applied to the HY-2A altimeter as well and the same conclusion can be obtained.