The study area encompasses the Bay of Bengal ( Figure 1 ), situated between 5°–24°N and 79°–123°E. The climate in this region predominantly constitutes tropical oceanic monsoon type, featuring minor variations in daily and annual temperatures. Observed SST averages fall within the range of 25–29°C, with an estimated annual temperature range of about 6°C (Roxy et al., 2014; Thompson et al., 2017). Notably, the average humidity exceeds 80%, and annual precipitation ranges from 1500–2000 mm. This climate pattern results in frequent cloud cover, particularly during the rainy season, posing challenges for optical remote sensing. The study area stands out for its sparse chlorophyll-a concentration data records. Moreover, the Bay of Bengal is among the world’s most active tropical cyclone regions. Consequently, investigating missing data reconstruction in this tropical region holds both practical significance and theoretical value.

On October 7, 2014, the severe tropical cyclone Hudhud developed in the Andaman Sea, subsequently traversing the Andaman Islands toward the Bay of Bengal ( Figure 1 ) (Chacko, 2017). Hudhud brought substantial cloud cover, leading to widespread missing data in daily chlorophyll-a concentration records. Given the brief duration of tropical cyclones, daily data reconstruction proves invaluable in illustrating spatial and temporal chlorophyll-a concentration patterns during short-term cyclones or typhoons. Notably, the reconstruction of daily chlorophyll-a concentration data in the tropical study area around the time of severe tropical cyclone Hudhud encountered formidable challenges.

Level-3 integrated daily chlorophyll-a concentration data, generated using the OC5 algorithm (ChlOC5) (Gohin et al., 2010), were combined with Level 2 ChlOC5 data from various sensors: the Medium Resolution Imaging Spectrometer, the MODerate Resolution Imaging Spectroradiometer, the Sea-Viewing Wide Field Sensor, the Visible and Infrared Imaging Radiometer Suite, and the Ocean and Land Color Instrument. The spatial resolution of Level-3 integrated data was 4 km ( Table 1 ). As depicted in Figure 2A , multi-year average data coverage in the study area exhibits significant variability. Most areas in the region of interest feature data coverage of around 25-35%, with notably low coverage of approximately 10-15% in the estuarine coastal zone ( Figure 2A ). Data coverage in October 2014 varies widely, ranging from 3.92% to 82.88%, with a 31-day average coverage of 39.13% ( Figure 2B ). The presence of only a limited 31-day dataset in a tropical sea area with persistent data scarcity throughout the year presents considerable challenges for data reconstruction studies.

Besides, the wind field data of the advanced scatterometer, the photosynthetically available radiation (PAR) data, and the thermal infrared and microwave remote-sensing data from satellite observations of the SST, the SSS, the sea surface density (SSD), the mixed layer depth (MLD), and the SSH were analyzed in this study ( Table 1 ). Moreover, the Hybrid Coordinate Ocean Model (HYCOM) reanalysis data, combining remote-sensing, in-situ measured, and model-simulated datasets, were utilized, encompassing SST, SSS, SSH, Eastward Sea Water Velocity (U-velocity), and Northward Sea Water Velocity (V-velocity) parameters ( Table 1 ). Table 1 details the spatial resolutions of the datasets, ranging from 4 km to 25 km for ChlOC5 and PAR data, and 0.25° for SST, SSH, SLA, Wind Speed, and Wind Stress. The resolution for MLD, SSS, and SSD data is 25 km, while HYCOM reanalysis data has a resolution of 1/12°. All datasets, as shown in Table 1 , are formatted in Network Common Data Form (NetCDF) format. For easier processing, ChlOC5 and PAR data were resampled to 9 km in MATLAB 2018. Subsequently, all data were integrated into a 3D dataset in MATLAB 2018 for subsequent reconstruction steps, marking the completion of data preprocessing.

Marine physical environmental factors, such as SST, wind, sea surface flow field, SSH, and sea-surface chlorophyll-a concentration data, are all impacted by atmospheric and marine dynamics ( Figure 3 ). These factors are inherently interconnected, enabling the utilization of these connections to reconstruct missing data. However, disparities exist between the reconstructed chlorophyll-a concentration data and data reconstructed from other environmental parameters.

Figure 4 illustrates the spatial distribution of daily chlorophyll-a concentration data (ChlOC5) prior to, during, and subsequent to the occurrence of cyclone Hudhud spanning from October 1 to October 30, 2014. In the period preceding the cyclone’s occurrence (October 1–5, 2014, depicted in Figures 4A–C ), a substantial expanse was occupied by daily data points that were missing. During the passage of cyclone Hudhud (October 7–13, shown in Figures 4D–G ), the deficiency in data coverage became more severe, with a considerable area devoid of any data. As the cyclone traversed the region (as evidenced in Figures 4H–O ), a substantial portion of data was still found to be absent, except for the case depicted in Figure 4M , where the data coverage was extensive. This absence of data coverage hindered the subsequent analysis of variations in chlorophyll-a concentration post the cyclone’s passage.

Figure 5 displays the daily reconstructed chlorophyll-a concentration data achieved through the implementation of the ExDINEOF technique. Upon scrutinizing the spatial arrangement, it can be observed that the reconstructed data effectively reinstated the situation of missing data across a substantial area. The outcomes of the reconstruction were determined to be comprehensive, devoid of any missing data points. Across the overall reconstruction, the values exceeded 1 mg/m³ within the northern coastal region of the Bay of Bengal, particularly at the Ganges River estuary. In certain extreme instances, the values even reached 3 mg/m³. In contrast, for vast offshore regions, the reconstructed values predominantly ranged from 0.1 to 0.3 mg/m³. Moreover, in the middle region of the Bay of Bengal, northwest of the Andaman Islands (as depicted in Figure 1 ), a significant striped area characterized by maximal chlorophyll-a concentrations was observable. On October 1, 2014, prior to the arrival of cyclone Hudhud, the chlorophyll-a concentration within the striped region was approximately 0.25 mg/m³ ( Figure 5A ), only slightly higher than that of neighboring areas. Additionally, the striped pattern with respect to chlorophyll-a concentration was not distinctly discernible. However, between October 3 and 7, an augmentation in chlorophyll-a concentration was evident in that region ( Figures 5B–D ). By October 13, when cyclone Hudhud made landfall ( Figure 5G ), the chlorophyll-a concentration had risen to approximately 2 mg/m³. Subsequently, the concentration continued to increase, reaching its pinnacle of around 3 mg/m³ ( Figure 5I ), after which it began to recede, stabilizing around 0.3 mg/m³. Ultimately, by October 29, the chlorophyll-a concentration further diminished to roughly 0.2 mg/m³.

Upon analyzing the reconstructed data graph ( Figure 5 ), it becomes apparent that near 90°E and 18°N, situated in the northern sector of the Bay of Bengal, a circular region characterized by low chlorophyll-a concentration began to take shape gradually from October 1 ( Figures 5A–F ). Between October 15 and 19, this circular pattern became distinctly evident, exhibiting a peripheral chlorophyll-a concentration of approximately 0.1 mg/m³. The central portion of the circle manifested a slightly elevated chlorophyll-a concentration ranging from 0.2 to 0.3 mg/m³ ( Figures 5H–J ). This circular pattern persisted until October 29 ( Figure 5O ).

By comparing Figures 4 and 5 , it can be inferred that the ExDINEOF methodology exhibited commendable efficacy in reconstructing the daily missing data within confined regions both before and after the occurrence of tropical cyclone Hudhud. The deficient chlorophyll-a concentration data within the time series were adequately reconstructed within local contexts, whether preceding, during, or succeeding the cyclone’s passage. Furthermore, the formation and dissipation of the circular region characterized by lower chlorophyll-a concentration, which would have remained obscured due to data gaps in the initial dataset, were clearly elucidated. This successful demonstration further attests to the practicality of the ExDINEOF reconstruction approach.

To further evaluate the method’s efficacy, namely the ExDINEOF method, alongside DINEOF and the bidirectional autoregressive model (BAR) approaches, were utilized to reconstruct variations in chlorophyll-a concentrations within the study region during and subsequent to the passage of the rapidly changing typhoon. A comparison of the methods was performed based on the spatial distribution of the reconstructed outcomes.

The bidirectional autoregressive model (BAR) employed in this research entails the repetition of forward and backward time-series vectors within MATLAB. The values of the reconstructed missing-like metadata are determined via calculating the mean values of both the forward and backward autoregressive models (Zhang et al., 2009). It can be discerned from Figure 6 that the correlation coefficient between times T and T+1 for chlorophyll-a concentration stands at 0.72, surpassing the requisite threshold of 0.5. As such, the essential prerequisites for BAR data reconstruction are fulfilled.

Through the application of the EOF approach, the reconstructed chlorophyll-a values within the region of missing data undergo iterative decomposition and synthesis until the cross-validated error attains its minimum. The optimal eigenmode retention is then ascertained, aligning with the most effective reconstruction of data. The time series of daily chlorophyll-a concentrations data for the study area was preprocessed using MATLAB and organized into a three-dimensional m×n matrix, where m signifies the daily ChlOC5 data within the study region (spatial, two-dimensional), and n denotes the count of time series ChlOC5 data points (temporal, one-dimensional). For the purpose of extracting oceanic pixels, a land mask was applied to the m×n matrix. Subsequently, the DINEOF package was employed on this matrix to complete the missing daily chlorophyll-a ChlOC5 data.

Figure 7 illustrates the original ( Figures 7A, E, I, M, Q ) and reconstructed daily ChlOC5 data during the occurrence of severe tropical cyclone Hudhud, derived through traditional univariate DINEOF, BAR, and ExDINEOF data reconstruction methods. Figures 7B, F, J, N, R presents the reconstructed data using the BAR method, focusing on both temporal and spatial dimensions of pixel reconstruction. Consequently, when substantial areas exhibited missing daily data for extended durations, the BAR method encountered challenges in obtaining sufficient samples for autoregressive modeling. In such scenarios, reconstruction would falter due to the absence of valid data, giving rise to noise points due to unnatural pixel transitions (depicted by red circles in Figures 7B, F, G, N, R ), consequently failing to capture the surge in bloom and the attenuation of chlorophyll-a concentration information. Clearly, the DINEOF method experienced failure in reconstruction due to the significant lack of original sample data (depicted by red oval boxes in Figures 7C, G, K, O, S ).

By contrasting the reconstruction outcomes attained via various methods, as exhibited in Figure 7 , it becomes evident that the ExDINEOF approach yielded the most comprehensive spatial distribution of reconstructed results, encompassing the most intricate temporal variations, and offering the most exhaustive local details. In summary, when compared with the commonly adopted univariate DINEOF and BAR methods, the ExDINEOF approach showed superior performance in terms of daily reconstruction for small-scale regions in relation to spatial distribution.

Overall, in Region B (depicted in Figure 1 ), traversed by cyclone Hudhud within the central-western expanse of the Bay of Bengal, the flow field’s velocity exhibited continuous augmentation, reaching its zenith during October 9–13 ( Figures 11E–G ). Notably, during intense winds, the sea surface height (SSH) in the region diminished to its nadir during October 9–13, subsequently showing a gradual ascent. The reconstructed chlorophyll-a concentration achieved its zenith during October 15–19 ( Figures 5H–J ), subsequently experiencing a decline. Moreover, a circular striped area with low SST was discernible in the region during October 9–15 ( Figures 12E–I ). The SSH and SST values exhibited an inverse relationship with the chlorophyll-a concentration. Specifically, lower SSH and SST values corresponded to higher chlorophyll-a concentration. However, a discernible time lag existed between SSH, SST, and chlorophyll-a concentration, with the maximal chlorophyll-a concentration occurring approximately 4–5 days subsequent to the nadir in SSH and SST values ( Figure 13F ).

It should be noted that both Region B and Region A (corresponding to the regions of Figure 1 ) displayed areas characterized by low SSH but high flow rates. However, Region A exhibited low chlorophyll-a concentration. As depicted in Figure 12 , an anomalous region with considerably lower SST (approximately 3°C below surrounding areas) was evident in Region B, contrasting with Region A’s elevated SST values ( Figure 13D ).

In conclusion, a discernible correlation emerged between chlorophyll-a concentration and the variation of environmental factors. Specifically, anti-clockwise cyclonic winds ( Figure 13A ) induced anti-clockwise sea surface current rotation, culminating in an anti-clockwise vortex ( Figure 13B ). These forces dispersed surface waters into adjacent regions, consequently lowering sea surface height within the eddy zone compared to its surroundings ( Figure 13C ). This, in turn, triggered the upwelling of cooler nutrient-rich waters from the depths to the surface through Ekman Pumping, leading to lower sea surface temperatures than neighboring regions ( Figure 13D ).

Phytoplankton underwent distinct movements based on the sea layers. On the one hand, Ekman pumping led to the upwelling of subsurface phytoplankton into the sea surface layer. On the other hand, phytoplankton blossomed in the mixed layer post-upwelling of cold water. Adequate temperature, ample light, and nutrients from cold water beneath facilitated phytoplankton bloom, peaking 4-5 days after the severe tropical cyclone passage ( Figures 13F , 5I, J ). Subsequently, nutrient depletion reduced phytoplankton amounts ( Figures 5M–O ). Reflecting upon this and taking environmental elements into account, the ExDINEOF-based reconstructed chlorophyll-a concentrations excellently documented phytoplankton development pre, during, and post the severe tropical cyclone passage. These findings underscore the efficacy of employing the ExDINEOF technique for reconstructing daily-scale chlorophyll-a concentrations.

Figure 14 shows the spatial distribution of points (red data points within the red oval box) displaying correlation coefficients exceeding 0.8 ( Figures 14A–L ) and hovering around 0.6 ( Figures 14M–R ) between reconstructed and original data. As highlighted by Figure 14 , the distribution of points with correlation coefficients exceeding 0.8 and around 0.6 lacks a discernible pattern. To probe into the reasons behind discrepancies between original satellite and ExDINEOF-reconstructed data, the relative error encompassing the entire Bay of Bengal was calculated.

To scrutinize the technical proficiency of ExDINEOF, an evaluation of the spatial distribution of relative errors was executed on several days following the severe tropical cyclone Hudhud’s transit. Data for October 16 and 18 pertained to phytoplankton blooms, while data for October 24 and 25 related to phytoplankton extinction.

Figure 15 displays the original satellite data in the left column (a, d, g, j), outcomes of ExDINEOF reconstruction in the middle column (b, e, h, k), and relative errors between the two in the right column (c, f, i, l). The spatial distribution of relative errors generally fell below 0.3 across most areas. Especially on October 25, when phytoplankton were diminishing, relative errors were mostly below 0.1. Notably, ExDINEOF didn’t manifest significantly higher relative errors in the nearshore area—typically marked by substantial errors and complex influencing factors. This highlights ExDINEOF’s applicability in nearshore regions characterized by high turbidity, dynamics, and complexity. Regions featuring substantial relative errors were predominantly situated near the phytoplankton blooms zone within the central Bay of Bengal.

Instances of rapid phytoplankton blooms and extinctions are marked by their high-frequency characteristics in remote sensing data. The spatial distribution of the relative errors provides insight. Notably, ExDINEOF successfully reconstructs a significant portion of the high-frequency information, displaying reasonable spatial distribution and discernible texture features. However, certain aspects of high-frequency information remain filtered out due to the inherent low-pass filtering nature of DINEOF. Consequently, the relative errors exhibit greater magnitudes in areas where phytoplankton blooms and extinctions manifest prominently.

ExDINEOF and DINEOF methods distinctly diverge in outcomes, suggesting distinct intrinsic mechanisms at play. The conventional DINEOF method hinges on an extensive time series of sample datasets to identify trends within data. This method then extracts key modes of these trends to define the overall spatio-temporal characteristics of the original dataset, thus excelling at recuperating trends within long-term data. However, DINEOF tends to filter out spatial information at small and medium scales, as well as high-frequency information, over short timespans, treating them as noise.

In contrast, ExDINEOF eschews dependence on extended sample information, reconstructing missing data based on inherent nonlinear correlations between various environmental factors and simultaneous chlorophyll-a concentrations. These correlations arise as both factors are simultaneously influenced by atmospheric and oceanic dynamical processes. ExDINEOF captures high- and low-frequency information adeptly, demonstrating heightened sensitivity to high-frequency information (i.e., day-scale, rapid non-long-term shifts). This renders ExDINEOF effective in reconstructing missing chlorophyll-a concentrations within dynamic, nearshore water bodies. This distinction likely underpins differences in time series accuracy.

Conventional DINEOF has some drawbacks: (1) It inherently performs low-pass filtering and smoothing within three-dimensional spatio-temporal data across time and space dimensions. A limited set of key modes characterizes the overall spatio-temporal traits, favoring long-term trend analysis. However, this method erases small-to-medium-scale spatial and temporal information as noise. (2) Randomly selected cross-validation data for DINEOF reconstruction can incorporate anomalous values, propagating errors if these data points are flawed. The selection of such data significantly influences subsequent error determination, optimal reconstruction mode, and the number of reconstructions. (3) To ensure reconstruction precision, pixels within time series covering less than a certain ratio (2%) must be preemptively removed, marking them as land areas. Failing to do so results in the reconstructed image becoming an average of the original, potentially leading to reconstruction failure. This issue historically prompted reconstructions on a monthly scale to ensure adequate data samples (Wang and Liu, 2014; Wang et al., 2019).

ExDINEOF supersedes original DINEOF due to: (1) Embracing the self-adaptive nature of original mono-variate DINEOF, negating the need for prior variable correlation values. (2) Recovery of the same variable’s correlations at different moments and of different variables at the same moment. (3) Utilization of spatial and temporal proximity to reconstruct missing data based on closely correlated factors’ signals. (4) Incorporating multiple data sources like thermal infrared remote sensing, optical remote sensing, microwave remote sensing, numerical modeling, and observations, all influenced differently by clouds and thus complementary ( Figure 3 ).