Satellite-derived oceanic observations are the primary source of data for analyzing large-scale, time-series oceanic features. However, due to the limited penetration of visible and infrared bands, these data are often affected by cloud cover, resulting in spatiotemporal gaps. This discontinuity limits their practical application. To mitigate the impact of missing values, long-term averaged data are widely used in many oceanic analyses (Sun et al., 2019a; Bonelli et al., 2022; Zemskova et al., 2022). However, these data often smooth out ocean characteristics and cannot detect short-term or sudden ocean phenomena. Therefore, reconstruction of missing satellite-derived data is receiving increasing attention.

Spatial interpolation methods have already been used to address the issue of missing data. Kriging interpolation, a geostatistical method, was employed to generate complete satellite-derived sea surface temperature (SST) and salinity data for Chesapeake Bay (Urquhart et al., 2013). Additionally, optimal interpolation (OI) is a common method for satellite-derived oceanic data reconstruction (Reynolds and Smith, 1994, 2007; Fieguth et al., 1998). Several OI-based SST datasets, such as NOAA OISST (https://www.ncei.noaa.gov/products/optimum-interpolation-sst, last access: 17 June 2026), and Extended Reconstructed SST (ERSST, https://www.ncei.noaa.gov/products/extended-reconstructed-sst, last access: 17 June 2026), have been used to understand and predict climate system variations (Pawar and San, 2022). The OI method assesses unknown values by combining multiple existing observations with a prior estimate, thereby minimizing the error variance of the predictive outputs. However, this method may artificially smooth the reconstructed fields, limiting the detection of mesoscale features (Martin et al., 2023).

Beckers and Rixen (2003) proposed the Data Interpolating Empirical Orthogonal Function (DINEOF) method, which can be considered a self-consistent data reconstruction method. In the DINEOF method, original time-series satellite-derived oceanic data are transformed into a spatiotemporal matrix. An iterative approach is then applied to this matrix to obtain the optimal EOF mode, and missing values are subsequently reconstructed based on this optimal EOF mode. Compared to the OI method, DINEOF achieves similar reconstruction accuracy with less computational cost and without requiring prior knowledge (Beckers et al., 2006). Therefore, this method has been widely applied to the reconstruction of satellite-derived oceanic variable fields (Alvera-Azcárate et al., 2016; Ji et al., 2018; Liu and Wang, 2018, 2023; Binh et al., 2022). In recent years, several improved DINEOF methods have also been proposed. To enhance the temporal continuity of time-series satellite-derived oceanic data, Alvera-Azcárate et al. (2009) applied a temporal filter technique before the EOF decomposition step in DINEOF. Moreover, because DINEOF aims to optimally reconstruct the overall spatiotemporal matrix while ignoring local optimal reconstruction, Ping et al. (2015) proposed the I-DINEOF method. This method divides the spatiotemporal data into multiple subregions and performs optimal reconstruction for each subregion, thereby improving reconstruction accuracy. Furthermore, the iterative procedure in DINEOF involves significant computational effort, and the optimal EOF mode may not be the best option for intermediate spatiotemporal matrices. Ping et al. (2016) proposed the VE-DINEOF method, which performs optimal reconstruction for each intermediate iterative matrix. In VE-DINEOF, the optimal EOF mode changes progressively with each iteration, thereby improving the reconstruction accuracy and speed of the DINEOF method.

In addition to reconstructing a single oceanic variable, Alvera-Azcárate et al. (2007) proposed a multivariate DINEOF method (Multi-DINEOF) for the reconstruction of multiple ocean variables. This method comprehensively considers the inherent spatiotemporal correlations between these variables, thereby improving reconstruction accuracy. Similarly, Wang et al. (2019) adopted the Multi-DINEOF approach to generate a complete long-term sea surface chlorophyll a (SCHL) dataset based on the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) and Moderate Resolution Imaging Spectroradiometer (MODIS) SCHL products. Wang et al. (2023) utilized wind field data, photosynthetically active radiation (PAR) data, SST data, sea surface salinity (SSS) data, sea surface density (SSD) data, mixed layer depth (MLD) data, sea surface height (SSH) data, and Hybrid Coordinate Ocean Model (HYCOM) reanalysis data as inputs for the Multi-DINEOF method to reconstruct a daily SCHL dataset in the Bay of Bengal. However, as shown in Fig. 1, the Multi-DINEOF method essentially remains a matrix-based DINEOF approach. It first transforms the input multivariate data into a matrix and then applies the original DINEOF approach to reconstruct the missing values. In Fig. 1, multivariate data are represented by different colors. M represents the spatial size of a specific input oceanic variable, K is the overall spatial size of multivariate data, and N represents the number of input oceanic variable images. The first matrix on the right-hand side represents the spatial modes obtained from the singular value decomposition (SVD), the second matrix is the singular value matrix, and the third matrix is the temporal modes. Therefore, the Multi-DINEOF method cannot fully exploit the intrinsic correlations among multiple variables, as different parameters (e.g., SST, SCHL, and SSW) are forced to be represented along the same dimension. Consequently, the extracted principal components may contain mixed and heterogeneous signals, hindering the identification of genuine inter-variable relationships and reducing the physical interpretability of the results. In addition, Multi-DINEOF is limited to characterizing pairwise (second-order) correlations and thus cannot effectively capture higher-order interactions across spatial, temporal, and variable dimensions. This limitation highlights the need to develop an advanced multivariate DINEOF framework that can comprehensively utilize these inter-variable dependencies.

Multivariate data essentially take the form of a third-order tensor. Therefore, compared with matrix-based reconstruction, applying a third-order tensor formulation can better preserve the intrinsic correlations among various variables and consequently improve reconstruction accuracy. Tensor decomposition represents data as a higher-order array (e.g., space × time × variable), thereby maintaining the native multi-dimensional structure of the dataset. This framework enables the simultaneous extraction of spatial, temporal, and inter-variable modes, preserving the inherent coupling among dimensions. Furthermore, each decomposed mode corresponds to a distinct physical meaning (e.g., spatial pattern, temporal variation, or variable contribution), which enhances both the interpretability and physical consistency of the analysis. Current research on the tensor decomposition has made significant progress, with several decompositions developed, such as higher order SVD (Kolda and Bader, 2009) and hierarchical SVD (Grasedyck, 2010). Kilmer et al. (2008) proposed the tensor SVD (T-SVD) decomposition technique, treating a third-order tensor as a matrix with each element being a tube. The tube-based strategy gives the T-SVD decomposition a form similar to the matrix SVD decomposition (Zeng and Ng, 2020). Therefore, the T-SVD decomposition can be easily integrated into the original DINEOF method. The T-SVD technique has been widely used in facial recognition (Hao et al., 2013), image denoising and reconstruction (Zhang et al., 2014; Zhang and Aeron, 2017; Hu et al., 2017a, b; Zhou et al., 2018; Sun et al., 2019b). Consequently, this study proposed a third-order tensor DINEOF model named T-DINEOF, based on the T-SVD decomposition. The effectiveness of the proposed T-DINEOF model for both overall and individual oceanic variables is demonstrated by comparing it with the Multi-DINEOF method and the original DINEOF method.

The structure of the remainder of this manuscript is as follows: materials will be introduced in the next section; the proposed T-DINEOF model will be presented in Sect. 3; comparisons of the reconstruction accuracies for both overall and individual oceanic variables will be demonstrated and analyzed in Sect. 4; the details of the proposed T-DINEOF model will be discussed in Sect. 5; and finally, conclusions will be given in Sect. 6.

This study used monthly L3 mapped 4 km MODIS Aqua satellite-derived SST and SCHL data from April 2015 to December 2022, which are available for download from Ocean Color (https://oceancolor.gsfc.nasa.gov/, last access: 17 June 2026) as well as monthly approximately 25 km L3 AMSR2 10 m above sea surface wind (SSW) version 8.2 data, which can be downloaded from Remote Sensing Systems (RSS, https://remss.com/missions/amsr/, last access: 17 June 2026), as experimental data. Due to the unavailability of SSW data for August and September 2022, the SST and SCHL data for the same period were also removed. Consequently, the number of input images for each oceanic variable is 91, indicating that the temporal dimension is 91. As shown in Eq. (1), long-wave infrared bands 11 and 12 µm aboard MODIS are employed to retrieve SST products based on a modified version of the nonlinear SST algorithm (Walton et al., 1998; Jia and Minnett, 2020). The combined OC3 / OC4 (OCx) band ratio algorithm (O'Reilly and Werdell, 2019, Eq. 2) and the color index (CI, Hu et al., 2019, Eq. 3), which establish the relationship between SCHL and spectral remote sensing reflectances (Rrs), are used to retrieve SCHL products. Channels that match the low frequency, specifically the 10.65 GHz footprint, are used to retrieve SSW products because they are less affected by the atmosphere and rain. Due to the similar ascending time (13:30 local time), oceanic variables derived from these two satellites are obtained under similar sea conditions. 1SST=aij0+aij1BT11µm+aij2(BT11µm-BT12µm)Tsfc+aij3(sec⁡(θ)-1)(BT11µm-BT12µm)+aij4(mirror)+aij5(θ*)+aij6(θ2) where BT_11 µm and BT_12 µm are the brightness temperatures at 11 and 12 µm, respectively; θ is the satellite zenith angle; Tsfc is the reference temperature; and aij0 to aij6 are regression coefficients determined regionally. The terms “mirror” and “θ*” represent correction factors associated with viewing geometry and instrument calibration. 2log⁡10(SCHL)=b0+∑i=14bilog⁡10Rrs(λblue)Rrs(λgreen)i3log⁡10(SCHL)=-0.4287+230.47×{Rrs(λgreen)-[Rrs(λblue)+(λgreen-λblue)/(λred-λblue)⋅(Rrs(λred)-Rrs(λblue))]} where Rrs represents the spectral reflectance, λ is the central wavelength of the target spectral band, and the coefficients b0-b4 are sensor-specific parameters.

Before constructing the third-order tensor, it is necessary to process the input data. Each MODIS SST pixel has a corresponding numeric quality level, with level 0 being the highest quality and level 4 being the lowest. In this study, only pixels with quality levels 0 (best) and 1 (good/acceptable) were flagged as existing pixels. During the reconstruction stage, due to the log-normal distribution of SCHL data (Campbell, 1995), the log-transformed SCHL data were used in the third-order tensor. Therefore, during the accuracy analysis stage, an inverse log-transformation was applied to the reconstructed SCHL data. According to the RSS website, SSW values greater than 50 or less than 0 were considered missing values in this study. To address the difference in spatial resolution between the MODIS SST and SCHL data and the AMSR2 SSW data, the SST and SCHL data were downscaled to the same resolution as the SSW data using the nearest-neighbor interpolation method. In addition, land areas in the spatially registered SST, SCHL, and SSW datasets were masked out using the land mask provided with the SSW data, which was generated by resampling the high-resolution MODIS land mask onto the target footprint. Due to the large uncertainties in satellite-derived oceanic parameters at high latitudes (Hoyer et al., 2012; Jia et al., 2024), and in order to reduce computational burden, this study focuses on mid-to-low latitude regions; therefore, the area between 60° N and 60° S was chosen as the experimental region. As shown in Fig. 2a, due to limitations in computational power, the experimental area was divided into three subregions, each spanning 40° of latitude from north to south (subregions 1–3). Furthermore, a 3×3 median filter was applied to each satellite-derived variable in each subregion to eliminate abnormal values. Since the ranges of SST, SCHL, and SSW are different, the max-min normalization method was used to scale each ocean variable in each subregion to the range [0–1]. The maximum and minimum values of each ocean variable in each subregion are shown in Table 1. In general, compared to SST and SSW data, log-transformed SCHL data are more concentrated, with smaller variations among different subregions. The highest SST in the mid-latitudes of the Northern Hemisphere is slightly higher than that in the equatorial region and the mid-latitudes of the Southern Hemisphere, while the lowest SST varies slightly among different subregions. The maximum SSW values in the mid-latitude regions are significantly higher than those in the equatorial regions.

Each type of processed data was stored in the corresponding m×n matrix, where m is the spatial dimension and n is the temporal dimension. The three matrices generated from the three satellite-derived variables were then combined to form the final third-order tensor. In this study, the dimensions of the final tensor for the three subregions are 119939×91×3, 174091×91×3, and 207779×91×3 after masking out land pixels.

In addition, the spatial and temporal proportions of missing data are shown in Fig. 2. In this study, the missing data ratio was calculated as the total number of missing values in the target variable, or across all three variables – after excluding land-masked areas in the target subregion – divided by the total number of data points in the corresponding tensor dimension or in the entire three-dimensional tensor. Additionally, by categorizing the time series data by date into their respective months, the missing data ratio for each month was obtained using the same method described above. Considering SST, SCHL and SSW data collectively (Fig. 2a), the global proportion of missing data is 17.02 %. The proportions of missing data in subregions 1, 2, and 3 are 19.37 %, 13.85 %, and 18.31 %, respectively, indicating that the equatorial region has a lower proportion of missing data compared to the mid-latitude regions. Typically, the proportions of missing data are higher from June to August than in other months, especially in subregion 3. The proportion of missing data in subregion 2 does not vary significantly across the months, while subregion 1 typically has a lower proportion of missing data from September to October.

The global proportion of missing SST data is 14.21 % (Fig. 2b). In subregions 1–3, the proportions are 17.26 %, 6.05 %, and 19.29 %, respectively, indicating that the proportion in the equatorial region is significantly lower than in the mid-latitude regions. Overall, the proportion of missing SST data is higher from June to August. Subregion 2 shows minimal temporal variation in SST missing data proportions. In contrast, subregions 1 and 3 exhibit opposite trends: from April to October, subregion 3 has higher proportions than subregion 1, peaking from June to August. However, in other months, subregion 1 has higher missing data proportions compared to subregion 3.

The global proportion of missing SCHL data is 30.38 % (Fig. 2c), which is the highest among the three oceanic variables. In subregions 1–3, the proportions are 29.24 %, 28.19 %, and 32.86 %, respectively, showing no significant differences. Overall, the proportions of missing data are typically higher from April to August and in December. In subregion 1, the proportions are lower from August to October but higher from December to January compared to other months. Subregion 2 shows higher missing proportions from August to October, while in the remaining months, the proportions in this subregion do not vary significantly. From April to September, the missing proportions in subregion 3 are obviously higher than in other months.

The global proportion of missing SSW data is 6.46 % (Fig. 2d), indicating that SSW has the most complete data among the three oceanic variables due to the penetration capability of microwave bands. In subregions 1–3, the proportions are 11.61 %, 7.32 %, and 2.77 %, respectively, indicating that the mid-latitudes of the Southern Hemisphere are least affected by missing data. Overall, the proportions of missing data remain relatively stable across months. In February and March, subregion 1 experiences a peak in missing values, while in subregion 3, the peak occurs from August to October. The proportions of missing values in other months for these two subregions do not vary significantly. In subregion 2, the proportion of missing values remains stable throughout the year.

Currently, several decomposition methods for third-order tensor, such as higher order SVD (Kolda and Bader, 2009) and hierarchical SVD (Grasedyck, 2010), have been proposed. The T-SVD decomposition has a form similar to that of the matrix SVD decomposition (Zeng and Ng, 2020). Therefore, this study incorporated the T-SVD decomposition method into the original DINEOF algorithm and proposed a T-DINEOF model. The algebraic framework of T-SVD is constructed by defining the tensor-tensor product, identity tensor, transpose, orthogonal tensor, and tubal rank (Braman, 2010; Kilmer and Martin, 2011; Kilmer et al., 2013; Kernfeld et al., 2015). Consequently, the decomposition and reconstruction of the third-order tensor based on the T-SVD method are introduced, followed by a detailed explanation of the T-DINEOF model.

The current multivariate DINEOF method essentially performs matrix-based reconstruction, which cannot fully utilize correlations between variables. With the development of third-order tensor research, there has been growing interest in the decomposition and reconstruction of third-order tensor. A T-DINEOF model based on the T-SVD technique was proposed in this study to better explore the relationships among multivariable data. Multiple accuracy metrics demonstrate that T-DINEOF outperforms the conventional Multi-DINEOF method both globally and across various subregions, indicating the superiority of third-order tensor reconstruction over matrix-based reconstruction. In addition, the proportion of missing data significantly impacts reconstruction accuracy. The experiments confirm that T-DINEOF shows a more substantial improvement in accuracy for regions with a high proportion of missing values. Furthermore, the correlations among different oceanic variables also affect reconstruction accuracy, with better performance observed when reconstructing multiple highly correlated variables together compared to reconstructing each variable individually. In addition, the statistical results demonstrate that even when data correlation is low, T-DINEOF still improves the reconstruction accuracy of the relevant oceanic variables. This improvement arises from performing tensor decomposition in a high-dimensional space (space × time × variable), which allows T-DINEOF to exploit cross-dimensional dependencies and capture coherent spatial–temporal patterns shared across variables. Consequently, the model can more effectively reconstruct low-correlation variables, as their spatial and temporal structures remain embedded within the overall tensor framework.

Although T-DINEOF outperforms the original DINEOF and Multi-DINEOF methods, it still relies on a single global optimal mode, which may not be ideal for capturing heterogeneous local dynamics within the study area or achieving the best reconstruction in specific regions and during intermediate iterations. Therefore, integrating improvements from original DINEOF methods and their variants into third-order tensor reconstruction is necessary. Furthermore, this study uses monthly oceanic variables, so temporal correlations are not considered. If daily or weekly data were used, incorporating temporal correlations among various oceanic variables would be essential for enhancing reconstruction accuracy. Additionally, compared to monthly data, daily or weekly datasets typically exhibit higher proportions of missing values. In this study, we demonstrated that T-DINEOF outperforms both Multi-DINEOF and Single-DINEOF in regions with high missing data proportions, suggesting that it may be more advantageous for reconstructing daily or weekly data (Fig. S2). However, due to the tensor operations involved, T-DINEOF requires longer computation times to reconstruct the same region. This may limit its application to larger-scale tensors, such as longer time-series images (91 scenes were used in this study) or tensors with more dimensions (three variables in this study). It is evident that, over the same time span, the volume of daily or weekly data is significantly greater than that of monthly data. Given the substantial data volume inherent in a third-order tensor, optimizing computational processes and accelerating processing speeds are crucial for the effective application of T-DINEOF to high-temporal-resolution datasets. Moreover, to unify MODIS SST and SCHL (high resolution) with AMSR2 SSW (low resolution), the nearest-neighbor method was used to downscale MODIS data to the AMSR2 resolution. Upscaling low-resolution data is an ill-posed nonlinear system problem that may introduce larger errors, whereas downscaling helps reduce error propagation. Therefore, MODIS SST and SCHL data were downscaled to the AMSR2 resolution rather than upscaling AMSR2 data to match the MODIS resolution. However, although the nearest-neighbor method is widely used for downscaling high-resolution imagery, it may still introduce artifacts that affect the reconstruction process. Consequently, adopting more advanced resampling techniques or using multi-source datasets with consistent spatial resolution could further improve reconstruction accuracy. Finally, it should be noted that if the source datasets contain systematic biases, such errors may be propagated through the reconstruction process, potentially affecting the accuracy of the final results. In particular, tensor-based methods may be more susceptible to such bias propagation, as errors in one variable can influence others through the coupled decomposition.

The optimal number of modes is an essential parameter for both T-DINEOF and Multi-DINEOF, typically determined by the smallest RMSE value at the cross-validation pixels during the iterative process. As shown in Fig. 17, during the iterative process, the RMSE distributions from the cross-validation pixels for T-DINEOF in the three subregions are lower than those for Multi-DINEOF, indicating superior reconstruction performance by T-DINEOF. In these three subregions, the optimal number of modes for T-DINEOF is 33, 37, and 34, respectively, compared to 31, 36, and 37 for Multi-DINEOF. The similarity in the optimal number of modes suggests that both methods converge after a similar number of iterations, but T-DINEOF consistently achieves lower RMSE values. In both the original DINEOF and Multi-DINEOF methods, 3 % of existing pixels are randomly selected as cross-validation pixels to determine the optimal number of modes. In this study, we individually selected 3 %, 10 % and 20 % of the existing pixels as the cross-validation pixels to analyze the impact of different proportions of cross-validation pixels on T-DINEOF. As shown in Fig. 18, the RMSE distributions for different proportions of cross-validation pixels are similar across the three subregions. The optimal numbers of modes and the corresponding RMSE values obtained from these varying proportions show only minor differences. This suggests that the proportion of cross-validation pixels has a negligible impact on determining the optimal number of modes for T-DINEOF. Since cross-validation pixels are considered as missing values in the process of determining the optimal number of modes, the fact that T-DINEOF yields similar optimal numbers of modes and corresponding RMSE values across different proportions of cross-validation pixels indicates its stability in handling varying amounts of missing data.

The global reconstruction accuracies of the T-DINEOF model under different proportions of cross-validation pixels are illustrated in Fig. 19. Overall, the accuracies obtained under the three proportions are quite similar, while the 3 % proportion yields relatively lower error values. This suggests that the proportion of cross-validation pixels has a minimal impact on the reconstruction accuracy of the T-DINEOF model. Therefore, consistent with the conventional DINEOF method, 3 % of the existing pixels were randomly selected as the cross-validation pixels in this study.

In this study, the order of the oceanic variables in the input third-order tensor, specifically, the third dimension, was SST–SCHL–SSW. To analyze the impact of variable ordering on T-DINEOF, two alternative input orders, SST–SSW–SCHL and SCHL–SSW–SST, were randomly selected for comparative analysis. As shown in Fig. 20, the reconstruction accuracies for SST, SCHL, and SSW, as well as for each individual oceanic variable, are similar across the different input orders, particularly for the SCHL and SSW data. For SST data, the order of input variables has a minor impact, with an average RMSE difference of 0.04 °C. Among the three selected input orders, the configuration that yields the best reconstruction performance is the SST–SCHL–SSW order. Since the T-DINEOF method is built on a tensor reconstruction framework, it simultaneously optimizes multiple variables during the reconstruction process, and the order of input variables has minimal effect on reconstruction accuracy, which is one of the method's key advantages.

Finally, the proposed T-DINEOF method, with its capability to reconstruct missing values in multi-dimensional spatiotemporal datasets, has broad applications beyond oceanography. In numerical weather prediction, it can fill gaps in key variables such as SST and SSW, improving data completeness and forecast accuracy by preserving inter-variable correlations. During natural disasters – such as hurricanes or harmful algal blooms – it helps restore data lost due to cloud cover or sensor failure, enabling more accurate real-time monitoring and timely emergency response. In marine biodiversity research, T-DINEOF ensures the continuity of datasets like SST and SCHL, which are critical for tracking ecological changes and assessing climate impacts. Additionally, in fisheries and aquaculture, reconstructed environmental baselines support stock assessments, site selection, and early detection of stressors such as hypoxia, thereby promoting sustainable resource management. Future research will focus on the following directions: achieving locally optimal reconstruction within the third-order tensor and refining the iterative process of the T-DINEOF model to further enhance its performance; integrating temporal autocorrelations among multiple oceanic variables into the tensor reconstruction framework to more comprehensively capture the dynamic coupling of oceanic parameters; and improving computational efficiency to enable large-scale, high spatiotemporal resolution reconstruction and applications of multiple oceanic variables.

This study proposed the T-DINEOF model, which leverages the T-SVD technique for multivariable data reconstruction, aiming to improve the accuracy of multiple oceanic variables reconstruction. In comparison to the Multi-DINEOF and original DINEOF methods, which rely on matrix-based reconstruction, T-DINEOF demonstrates superior accuracy for both overall and individual oceanic variables. This indicates that third-order tensor reconstruction more effectively utilizes the correlations among multiple oceanic variables, thus enhancing reconstruction performance. Additionally, T-DINEOF is particularly well-suited for regions with a high proportion of missing values, showing significant accuracy improvements. Even though the input SSW exhibits low correlation with SST and CHL, the T-DINEOF method is still able to achieve high-accuracy reconstruction of the SSW field.

Both T-DINEOF and Multi-DINEOF converge with a similar number of iterations; however, T-DINEOF achieves higher accuracy at convergence. Various proportions of cross-validation pixels yield similar optimal numbers of modes and corresponding RMSE values, suggesting that the proportion of cross-validation pixels does not significantly impact the T-DINEOF model. Additionally, the order of multiple oceanic variables in the third-order tensor has a minimal effect on the T-DINEOF model.

The T-DINEOF model represents a novel approach for reconstructing multiple oceanic variables. However, attaining local optimal reconstruction within the third-order tensor and optimizing the iterative process of the T-DINEOF model are crucial for further enhancing its performance. Additionally, integrating temporal correlations among multiple oceanic variables into the tensor reconstruction process requires further research. Furthermore, improving computational efficiency is essential for the large-scale reconstruction of multiple oceanic variables. One potential approach is to use machine learning methods (e.g., Random Forests, XGBoost, or neural networks) for the initial estimation of missing values, followed by the application of the T-DINEOF method for further refinement, thereby improving the algorithm's efficiency. Lastly, the effectiveness of the T-DINEOF method in reconstructing other types of datasets, such as sea surface salinity, and reanalysis products, will also be evaluated in future research.