An investigation of the on-board microwave radiometer of satellite Altimetry for studying the atmosphere variability

Since its first launching, the ability of satellite Altimetry in providing reliable and accurate ocean geophysical information of the sea surface height (SSH), significant wave height (SWH), and wind speed has been proven by numerous researchers, as it was designed for observing the ocean dynamics through nadir range measurement between satellite and the sea surface. However, to achieve high level accuracy, environmental and geophysical effects on the range measurement must be accurately determined and corrected, particularly the effects from the atmospheric water vapor which can divert altimeter range up to 3–45 cm. Thus, satellite Altimetry is originally equipped with the on-board microwave radiometer to measure the water vapour content for correcting the range measurement. To our knowledge, no one has attempted to apply the on-board radiometer for atmospheric studies. In this present work, we attempt to optimize the on-board radiometer data for studying the atmosphere variability due to the El Niño– Southern Oscillation (ENSO) phenomena. We convert the on-board water vapor data into the precipitable water vapour (PWV), and we then investigate whether the derived PWV can capture the variability of ocean–atmosphere phenomena due to ENSO as accurate as the conventional Altimetry-derived sea level anomaly (SLA). Based on our analysis using the empirical orthogonal function (EOF), the results show convincing argument that Altimetry-derived PWV are reliable in examining the atmospheric fluctuation as the correlation of its primary principal component time series (PC1) with Oceanic Nino Index (ONI) is higher (0.87) than SLA (0.80). These results may reinforce the confidence in the ability of satellite Altimetry for ocean–atmospheric studies.


Introduction
During the last three decades of radar Altimetry development, the milestones marked not only in monitoring and understanding ocean dynamics at mesoscales level and greater, but also in the study of coastal oceanography, inland water hydrology, and climate have surpassed expectations (Abdalla et al. 2021).It has been ascertained to be a valuable tool in providing ocean geophysical information of sea surface heights (SSHs), significant wave heights (SWHs), wind speed, etc.As reported in numerous researches, the accuracy of Altimetry satellite in measuring sea level variation is up to 2-3 cm in the open ocean and up to 4 cm in the coastal region with the latest missions and retracking algorithms (Shum et al. 1995;Gómez-Enri et al. 2008a, 2008b;Valladeau et al. 2012;Abdullah et al. 2016;Cipollini et al. 2016;Abdullah 2018).
The primary trigger for these hydro-meteorological events is the complex interaction (coupling) between the atmosphere and ocean variabilities (Gupta et al. 2009;Jayawardena 2015;Debele et al. 2019), that is generally due to the interchange energy of solar radiation at the overlapping boundary of the atmosphere and the ocean (Fedorov 2008;Xie 2009;Misra 2014).While the influence of ocean-atmospheric coupling to the ocean part has been proven to be well perceived through satellite altimeter-derived sea level, the atmospheric part is yet to be elaborated.According to the latest technology of satellite Altimetry, we believe that the satellite is capable to provide reliable data not only for the ocean dynamics, but also for the atmosphere.This is because satellite Altimetry is not only equipped with the radar system to measure the sea surface, but also it is equipped with the microwave radiometer to measure atmospheric water vapour.The radiometer measurement initially provides the wet path delay correction for the main altimeter range measurement (Eymard et al. 1994;Blanc et al. 1996;Fernandes et al. 2015Fernandes et al. , 2021)).This perspective develops a new potential for satellite Altimetry to also be exploited to observe the atmosphere.However, study regarding the employment of altimeter microwave radiometer for atmosphere observation is still limited, albeit the effort to improve the accuracy of the satellite Altimetry microwave radiometer has been a focus on several research since the wet path delay (path delay caused by tropospheric water vapour) has a significant effect on Altimetry range measurement.The uncertainty of wet path delay or wet tropospheric correction (WTC) from Jason-1 radiometer measurement is approximately 0.74 ± 0.15 cm (Brown et al. 2004).Apart from that, the accuracy of microwave radiometer measurement has been enhanced on each follow-on satellite mission (Brown 2010;Maiwald et al. 2016;Fernandes and Lázaro 2018).With this accuracy, the benefit of radiometer measurement should be acknowledged, not only to provide correction for the altimeter range, but also for the purpose of the atmosphere observation.Thus, the aim of this present study is to investigate the applicability of the on-board radiometer in studying the interannual ocean-atmospheric phenomena caused by ENSO and to compare the results against those derived from the sea surface measurements in the form of sea level anomaly (SLA).
The research area selected for this study is the Pacific Ocean as it has significant influence on climate variability, particularly over equatorial zone.In the interannual timescale, the ocean and atmosphere variability in the Pacific Ocean are predominantly influenced by anomalous climate mode of ENSO, which involves non-periodic fluctuation in winds, sea surface temperatures (SST), and air pressure of the underlying atmosphere (Southern Oscillation) across the equator over the tropical eastern Pacific Ocean (Philander 1985;Holton and Dmowska 1989;Timmermann et al. 2018).In addition, this area is selected because there are numerous previous studies on that area which can thoroughly validate our results, as the primary aim of this study is merely to investigate the applicability of the on-board microwave radiometer to capture the atmospheric variability during ocean-atmosphere phenomena (in this case ENSO).It is not intended to elaborate a new physical signature of the event.
ENSO phenomenon relates to walker circulation due to the forces of pressure gradient caused by high-pressure area over the eastern Pacific and low-pressure system over Maritime Continent (Wang et al. 2000;Chang et al. 2004;Zhang et al. 2016).La Niña is caused by an extremely strong walker circulation, which results in colder ocean temperatures in the central and eastern tropical Pacific Ocean, owning to enhanced upwelling.During this phase, the trade winds are stronger, resulting warmer ocean temperature over western Pacific Ocean.Deep convection is more concentrated in Indonesia, thus resulting heavy rainfall over the region.At a certain point, the walker circulation experience weakening or reversal (which comprises trade winds), causing the upwelling of cool deep-sea water to dwindle or vanish.This situation causing the sea surface to reach temperatures above average, thus creating El Niño.During this phase, when the trade wind anomalously is weak, the sea temperature over the eastern part become warm.Thus, the deep convection of walker circulation moves to the east, resulting lower precipitation in Indonesia.
This phenomenon has major influence over the tropics and subtropics climates, particularly when this oscillations pattern become extreme (Wang et al. 2000;Chang et al. 2004;Han and Huang 2009;Zhang et al. 2016).It causes intense weather, such as floods and droughts in several regions in the world.Regions bordering the Pacific Ocean are the most affected, causing major problems particularly to the developing countries that depend on agricultures (e.g., Garden 2014; Chang-Yang et al. 2016;Luo and Lau 2020;Qian et al. 2020) and fisheries (e.g., Salinger 2013;Kumar et al. 2014;Lehodey et al. 2020) as part of their economic resources.
This paper is divided into four Sections.Sect."Introduction": Introduction is an introductory section which discusses the primary premise of the research, including the aim and expected outcomes of this study.Sect."Data and Methodology": Data and Methodology explains the attributes of Altimetry data used, including the observation period and missions involved.This section also includes the procedure used in deriving Altimetryderived SLA and PWV anomalies.Sect."Results and discussions": Results and discussion provides deliberate analysis and discussion regarding the variability of SLA and PWV during ENSO and the interrelation between those variables in the Pacific Ocean.Sect."Conclusions and remarks": Conclusion and Remarks summarises the findings of the research.The expected progress in the future study using Altimetry data for ocean-atmosphere interrelation are also discussed.

Altimetry data base
The data of 30 years from January 1993 to December 2022 from five (5) satellite missions: TOPEX, Jason-1, Jason-2, Jason-3, and Sentinel-6a are utilised to derive SLA and PWV.The timeline of all missions is shown in Fig. 1.The data are retrieved from Radar Altimeter Database System (RADS) and Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO).The temporal resolution of the data is 9.9 days and the sampling interval along track is ~ 6 km.The details description of the satellite's tracks geometry is provided in Table 1.The spatial map of the study area including satellite passes used in the study and highlighted passes and points used in across equator and along equator analysis, respectively, are indicated in Fig. 2. The derivations of SLA and PWV are provided in Sect."Altimetry-derived SLA" and Sect."Altimetry-derived PWV", respectively.

Altimetry-derived SLA
The basic concept of satellite altimeter operation is to measure height or distance between the satellite and the sea surface using a nadir pointing microwave instrument called Radar Altimeter (Gommenginger et al. 2011).The measured distance (called "the range") is then used to determine the value of sea surface height (SSH), which is the height between the instantaneous sea surface and reference ellipsoid, by computing the different value between the satellite position and the measured distance.Meanwhile, SLA is defined as the height between the instantaneous sea surface and mean sea surface height (MSS).The distinction between SSH and SLA is described in Fig. 3. SLA from satellite Altimetry range measurement can be extracted as in the following equation (Andersen and Scharroo 2011): where H is the satellite altitude above reference ellipsoid.R retracked = c t 2 is the computed range from travel time, t , observed by altimeter radar, and c is the speed of light.R retracked is corrected observed range using waveform retracking algorithm, MLE-3 (Thibaut et al. 2010).h dry is dry tropospheric correction, h wet is wet tropospheric correction, h iono is ionospheric correction, h ssb is seas state bias correction, h MSS is mean sea surface height, h tides is tide corrections (including ocean tide, solid earth tide, pole tide, and tide loading) and h atm is dynamic atmospheric corrections (including high frequency fluctuation and inverse barometer correction).Details about (1) the corrections and models used to derive SLA are tabulated in Table 1.

Altimetry-derived PWV
The on-board microwave radiometer is used to derive three main elements in the atmosphere: water vapour, cloud liquid water, and wind driven variations on sea surface by collecting the radiations that are reflected by the ocean.These elements are utilised to derive wet tropospheric delay for range measured by altimeter radar.
The retrieval of wet tropospheric delay or correction, R wet , involves two processing stages.The first stage is to calibrate the output of brightness temperatures and to remove any correlation between the hardware physical temperature and the brightness temperatures, which includes: (i) the correction of hardware losses from the system component to attain the antenna temperature and (ii) the elimination of on-earth and off-earth side lobe contamination from the antenna temperature to get the brightness temperatures (Brown et al. 2004).The second stage is to retrieve the wet tropospheric correction from brightness temperatures.It begins with the following equation for estimating cloud liquid, L z , and wind speed, W , from brightness temperatures (Keihm et al. 1995): (2) where T b f is the measured brightness temperature cor- responding to the frequency, f , and l 0 , l f , w 0 , and w f are predetermined coefficients.Subsequently, the path delay induced by water vapour is retrieved through two-step statistical inversion.The first step is computation of the initial estimate of the path delay value, PD (1) , using coefficients associated with wind speed, which can be expressed as where B (1) are coefficients for the initial value associated with wind speed.The second step is computation of the final path delay value, PD (2) , using coefficient associated with wind speed and the initial path delay value, and can be expressed as where B as coefficient of final value associated with wind speed and the initial path delay value.Thus, the total wet path delay, WPD , can be obtained by adding the cloud liq- uid component to the final path delay value, as shown in Eq. ( 6).The wet tropospheric correction, R wet , which is a negative value of WPD is estimated in Eq. ( 7): The acquired R wet value can then be used to compute the total water vapour concentration in a specific atmospheric column, referred to as PWV , as expressed in the following equation (Fernandes et al. 2021): where R v = 4.61527m 3 /kg.K is the specific gas con- stant for the water vapour, ρ = 997kg/m 3 is the density of water, k 3 = 3.7765 * 10 −5 K 2 /mbar , k 2 ′ = 17K /mbar , and T m is the mean temperature of atmosphere.Since T m is not recorded by the altimeter satellite, its value is acquired using existing Global Pressure Temperature (GPT) model.This model is retrieved from European Centre of Medium Range Weather Forecast reanalysis v5 (ECMWF ERA5), which is able to provide yearly data variation from earth pressure and temperature (Böhm et al. 2007).As the T m data are provided in a grid format with 1° resolution, meanwhile, the altimetry data used are (3) = B (1) (5) along track data, T m values are interpolated using linear interpolation to the altimetry observation points.The period of T m is also similar to the altimetry observation period.
Please note that, for Jason-1, Jason-2, and Jason-3 satellite missions, atmosphere water vapour content data are provided in the raw satellite data file in unit kg/m 2 and final PWV can be simply calculated by multiplying the data with water density value.However, for TOPEX and Sentinel-6a satellite missions, the data are not included in satellite data file, instead it is provided as wet tropospheric correction, R wet .Therefore, to standardise the data, R wet is used to derive PWV for all missions.
R wet has been through thorough validation using multiple independent data sets, including GNSS-derived path delay (Fernandes et al. 2010), European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Model, Global Precipitation Measurement (GPM), etc. (Fernandes et al. 2015;Fernandes and Lázaro 2018).With the significant works the accuracy of wet tropospheric correction nowadays is up to 1-3 cm (Fernandes et al. 2021).

Extraction of inter-annual signal
To effectively analyse the Walker Circulation that associates with interannual phenomena (in this case, ENSO), annual harmonics and dominant climatology component for inter-seasonal phenomena must be eliminated from SLA and PWV time series, to retrieve the variables' anomaly.
As these inter-seasonal components depict the homogenous state without anomalous variation, they can be modelled by averaging long period data.The modelled components are the long-term mean and trends, and frequent seasonal oscillation for each variable, using the following equations: where ∇M is the variable anomaly, t is time, M is the vari- able observed values, M is the variable long term mean, T and S are the trend and seasonal components of the vari- able time series, respectively.The elements for the trend and seasonal components are estimated using simple least square adjustment.The trend component is determined using the simple linear model and the seasonal component is determined by the first three harmonics of the annual cycle.T and S can be defined as follows: (9) where a tr and b tr are the constant and the gradient term of the linear trend component, respectively.ω is the fre- quency of 1 year, which can be defined as 2π 365.25day −1 ; thus, a k and b k for k = 1, 2, &3 are sine and cosine terms for the first three harmonics of the annual cycle.The period of data to resolve these components using least square adjustment is 30 years (January 193 to December 2022).The exact round number of years for the base period is necessary to minimise bias from non-complete annual harmonics cycle.However, decadal signals are neglected in the modelling and remain in the time series, as their oscillations are insignificant and has not influence the pattern of interannual variability.
To analyse the influence of interannual phenomena to the SLA and PWV variabilities, for instance, ENSO, annual harmonics and dominant climatology component are eliminated from SLA and PWV time series.Subsequently, simple average is performed to extract monthly data from all the available data observed in the respective month.The seasonal signal modelling and elimination are applied to all observed data in all 1 Hz altimeter observations used in the study.Figure 4 shows the derived SLA and PWV time series overlaid with the modelled climatological components, and SLA and PWV anomaly after climatological components have been eliminated from the time series, respectively.

Validation of altimetry-derived PWV
To determine the capability of Altimetry-derived PWV in capturing the state of water content in the atmosphere, PWV derived from ECMWF ERA5 WTC model is used to validate the Altimeter-derived PWV.This ECMWF ERA5 WTC model is retrieved from AVISO database.T m used in ECMWF-derived PWV are similar to the values used in Altimeter-derived PWV.The comparison is conducted on every 1 Hz measurements over the study region.Temporal resolution of both data is 9.9 days, corresponding to the Altimeter's temporal resolution.For validation purposes, correlation coefficient between both data sets is computed and histogram of deviation of difference is plotted.The statistical results are indicated in Table 2 and Fig. 5.There is a high positive correlation between the two data sets which yields correlation coefficient value of 0.976, showing that Altimetry-derived PWV is in a good agreement with ECMWF-derived PWV.The Root Mean Square Difference (RMSD) is 2.545 mm and the normalised (NRMSD) or the ratio of the RMSD to the standard deviation of difference (STDD) is 1.011 mm.The RMSD values indicate that the discrepancy between both data sets is insignificant.From the histogram of the difference (Fig. 5b), the difference appears to be normally distributed with the symmetrical bell shape.The peak value is close to zero, signifies that the mean differences are extremely small.The discrepancies are probably caused by random error (e.g., sensor noise, electromagnetic interference, etc.) rather than error in derivations or caused by inaccurate data.

Variability of SLA and PWV during El Niño and La Niña
The intensity of ENSO is defined by the Oceanic Nino Index (ONI), which the average of 3 months of ocean SST anomaly in the central tropical Pacific (5°N-5°S, 120°-170°W).El Niño and La Niña conditions are considered to be present when the ONI is higher than 0.5 and lower than −0.5, respectively, which is warmer and cooler than average.Figure 6    Theoretically, a walker circulation during ENSO season upholds an equilibrium state in the tropical ocean and atmosphere, in which during El Niño the eastern Pacific Ocean is characterised by higher sea level and deeper thermocline as the atmospheric pressure is low.Low atmospheric pressure is driven by relatively increasing precipitation (Ji et al. 2000;Lau and Yang 2003;Tsonis et al. 2003;Gastineau et 2009;Stuecker et al. 2017).Whereas, in the Maritime Continent (western Pacific Ocean), the sea level is lower as the atmospheric pressure is higher resulted from decreasing precipitation.The opposite situation occurs during the La Niña season (Chang et al. 2004;Jia et al. 2016;Zhang et al. 2016).These patterns are apparent in the spatial plot of Pacific Ocean in Figs.7 and 8, which depict the variation of PWV and SLA during the highest, neutral,  Similar patter also shown during La Niña with the contradict increasing (up to 9 mm) and decreasing (down to −14 mm) anomalies regions.
Noted that the number of parameters that influence SLA variability are significantly higher than parameters that affect PWV, yielding the different in general pattern throughout the entire study region.However, the main concern is the changes in the convection and subsidence areas of walker circulation during ENSO event, which are in the central Pacific and Maritime Continent.As apparent in the figures, the fluctuation of SLA and PWV anomaly during El Niño and La Niña are similar and highly correlated with ONI (Fig. 9), which is higher than 0.8 and lower than −0.8.As expected, since ONI is determined based on the SST observed in the highlighted region (black box in the figures) over the central Pacific, its correlation with SLA and PWV over this area is positive.As aforementioned, the nature of these variables over the Maritime Continent are contrast with that of in the central Pacific, particularly during extreme events (high and low ONI), resulting in negative correlations with ONI.

Principal component analysis
A standard Empirical Orthogonal Function (EOF) analysis has been performed on the Altimetry-derived SLA and PWV to identify and discrete the underlying dominant variations from timeseries of both SLA and PWV variables.The primary leading principal component (PC1) for PWV and SLA, which, respectively, explain 35% and 42% of the total variance, have generated significant contrast spatial pattern over central Pacific and Maritime Continent.However, SLA forms a pole like pattern; meanwhile, for PWV, the mode is centred in the central Pacific.According to the spatial patterns, prompt analysis can consider that EOF PC1 of both SLA and PWV are associated with ENSO variability (Fig. 10).The argument is further supported by the high correlation coefficient of both PWV and SLA correspondent time series PC1 with ONI, which are 0.87 and 0.80, respectively (Fig. 11).The spatial plot of secondary principal component (PC2), which explains 13% and 10% of the total variance for PWV and SLA, respectively, show similar pattern to EOF PC1 with the low coefficients shifted slightly eastward and westward, respectively (see Fig. 12).However, the correspondent time series have almost zero  (Figs. 13 and 14).This is because there are apparent temporal disparities between PC2 oscillation and ONI.This indicates that there is likely to be ENSO propagation features in PC2 of PWV and SLA signals.
Standard EOF is incapable in encapsulating propagating signal as a single mode, instead it captures the signals from several independent modes, resulting in low correlation of two similar variations of different phases.
However, the discrepancies are varied through the entire time series for both PWV and SLA.Thus, the time series is divided into several shorter periods and only three (labelled as a, b, and c in Figs. 13 and 14) significant oscillations during extreme ENSO are selected for cross correlations analysis.The selected period of short time series is 1.5 years before and after (3 years in total) the maximum ONI of the ENSO cycle.This range is selected as the minimum period of ENSO cycle is 2.5-3 years (Tudhope et al. 2001;McPhaden et al. 2006).The cross correlations are computed to determine the temporal discrepancies that contribute to maximum correlations between the variables and ONI.The results in Figs. 13 and 14 show the temporal lags for maximum correlation.
The highest correlation for PWV and SLA are during ENSO cycle c, from May 2014 to April 2017, with maximum correlation −0.95 by 2 month lag and 0.87 by 8 month lag, respectively.Meanwhile, the lowest correlation for PWV is during ENSO cycle A, from May 1996 to April 1999, with maximum correlation −0.63 by 5 month lag and for SLA is during ENSO cycle B, from June 2008 to May 2011, with maximum correlation −0.58 by -5 month lag.According to these results, when compared to ONI, temporal lags for PWV and SLA are not similar and inconsistence for every cycle.Thus, it is unreliable to draw a conclusive decision whether there are ENSO propagation features in PC2 of PWV and SLA signal.There is high probability that the signal is from local variation or other phenomena, which is not significantly related to ENSO.Although ITCZ varies seasonally, and the seasonal oscillation have been removed from the data set, however, the seasonal variations remain.
The ITCZ is defined as a cloud belt created by a high concentration of uprising air driven by the convergence of north-easterly and south-easterly trade winds (Smith 2003).The ITCZ position changes seasonally in response to the warmest area, theoretically it will travel to north during boreal summer and south during boreal winter.However, ITCZ in the eastern Pacific remains in the northern hemisphere during both seasons.This is driven by the equatorial asymmetry in SST and formation of stratus cloud in the southern Pacific, which probably prompted by the land-sea distribution (Xie and Philander 1994;Xie 1996).
However, it is too early to draw a solid conclusion that the PC2 is associated with ITCZ propagation as the assumption is only based on spatial patterns of the PWV and SLA.Further validation using other independent data (e.g., satellite imagery, precipitation, wind, etc.) with temporal propagations and more insightful analyses are required to substantiate the assumption.Nevertheless, phenomena that associate with PC2 is worth to be investigated as the percentage of total variance, particularly for PWV is rather significant (13%).

Conclusions and remarks
Comprehensive analyses have been conducted to identify and compare the interannual oscillation signature related to ENSO in altimeter-derived SLA and PWV time series.
According to variability analysis across equator, the fluctuation of SLA and PWV associated well with ENSO oscillation as the increasing and decreasing anomalies spatially and temporally similar to ONI.Spatial plots also indicate that the variation of SLA and PWV during La Niña and El Niño are parallel to the equilibrium theory of walker circulation, which is SLA and PWV anomalies are higher in the central Pacific and lower in the Maritime Continent during El Niño and conversely during La Niña.The signature of ENSO in Altimetry-derived SLA and PWV variability for 30 years is undeniably substantial as the correlations between both variables with ONI at ENSO region are acceptably high (> 0.8).
A standard EOF analysis is performed to identify the variability modes of SLA and PWV that occur in the Pacific Ocean.Two dominant modes are identified with pole-like spatial characteristics.The primary component, PC1 for both variables fully explain the ENSO variations as they have high correlation with ONI, particularly for PWV with correlation coefficient of 0.87, and SLA with correlation coefficient of 0.80.However, for secondary component, PC2, there is no conclusive evidence that associate its oscillation with ENSO as almost zero correlations are found for both SLA and PWV.Based on the EOF pattern for PC2, the signal most probably associated with another dominant event in the Pacific Ocean, which is ITCZ.
As per these results, the capability of satellite Altimetry in observing the atmosphere through PWV derived from on-board microwave radiometer data is comparable, and even better in some cases with the altimeter-derived SLA.The variability of PWV is consistent with the ENSO interannual transition, temporally and spatially, showing that the ability of satellite Altimetry in observing atmosphere variability is as reliable and accurate as perceiving ocean geophysical oscillation.These results reinforce the confidence in the ability of satellite Altimetry for oceanatmospheric studies.
As the satellite Altimetry capability in providing accurate sea level measurement has been recognised many years ago, and the new potential of observing atmospheric water vapour has so far shows substantially satisfactory results, the aim to optimise the satellite by utilising synchronous altimeter-radiometer measurement to observe ocean-atmosphere coupling in support of hydro-meteorological hazard mitigation is highly feasible.Altimetry satellite might not be able to measure daily weather, particularly rainfall, which highly variable through time and space, as its highest temporal resolution is approximately 9-10 days and longer data post processing.However, it is reliable enough to monitor longer periodic phenomena, such as ENSO, Indian Ocean Dipole (IOD), Madden-Julian Oscillation (MJO), and the oscillation of Inter-Tropical Convergence Zone (ITCZ), which associate with monsoon.
Using both ocean and atmosphere measurement from satellite Altimetry not only present a new potential of the satellite itself, but also a way to overcome the drawback of previous ocean-atmosphere studies, which has temporal and spatial disparities as each variable were observed using different platforms at different time and locations.

Fig. 1 Fig. 2
Fig. 1 Timeline of satellite Altimetry missions used in the study

Fig. 3
Fig. 3 Principal of satellite Altimetry observation.Note that the altitudes are not to the scale

Fig. 4
Fig. 4 Example of the time series of raw data overlapped with the estimated climatology components and anomaly (raw data minus climatology) for SLA (a) and PWV (b) at a point located at ENSO 3.4 region depicts the variation of PWV and SLA from lower to upper latitude for ascending (Pass 82) and descending (Pass 247) passes derived at ENSO region.The PWV and SLA are plotted during different phases of ENSO (El Niño, neutral, and La Niña).The fluctuations of both variables are associated with ONI as it increases (decreases) during high ONI (low ONI) approaching the ENSO region.During the extreme El Nino with ONI value up to 2.71, the anomalies of PWV and SLA in the central Pacific increase up to 15 mm and 17 cm, respectively.Conversely, during La Nina event with negative ONI value −1.77, PWV and SLA anomalies in the central Pacific decrease down to approximately -8 mm and -9 cm, respectively.Compared to the natural condition when ONI value −0.01,

Fig. 5 a
Fig. 5 a Scatter plot of monthly average Altimetry-derived PWV and ECMWF PWV over study area.b Histogram of PWV difference between Altimetry-derived PWV and ECMF-derived PWV in the validation area

Fig. 6
Fig. 6 PWV and SLA across ENSO 3.4 region for pass 82 (ascending) and pass 247 (descending) during three different phases of ENSO determined by ONI

Fig. 7
Fig. 7 Spatial map of anomaly PWV during three different phases of ENSO determined by ONI.The rectangular block shows the ENSO 3.4 region

Fig. 8
Fig. 8 Spatial map of anomaly SLA during three different phases of ENSO determined by ONI.The rectangular block shows the ENSO 3.4 region

Fig. 9
Fig. 9 Spatial map of correlation coefficients between PWV (top) and SLA (bottom) with ONI for 30 years along track data over Pacific Ocean

Fig. 10
Fig. 10 Principal loading map of primary principal component from EOF analysis on the Altimetry-derived PWV (top) and SLA (bottom) for along track data over Pacific Ocean

Fig. 12
Fig. 12 Principal loading map of secondary principal component from EOF analysis on the Altimetry-derived PWV (top) and SLA (bottom) for along track data over Pacific Ocean

Fig. 13
Fig. 13 Time series of secondary principal component for Altimetry-derived along track PWV overlapped with ONI and the cross correlation for selected period

Fig. 14
Fig. 14 Time series of secondary principal component for Altimetry-derived along track SLA overlapped with ONI and the cross correlation for selected period

Table 2
Statistical results of comparison between Altimetryderived PWV and ECMWF-derived PWV