# Application of Synthetic DINCAE–BME Spatiotemporal Interpolation Framework to Reconstruct Chlorophyll–a from Satellite Observations in the Arabian Sea

^{1}

^{2}

^{3}

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## Abstract

**:**

^{−3}and 0.4682 mg m

^{−3}, respectively; compared with in situ Chl–a data, the RMSE and MAE values for the DINCAE–BME–generated Chl–a product were 0.6196 mg m

^{−3}and 0.3461 mg m

^{−3}, respectively. Moreover, DINCAE–BME exhibited better performance than the DINEOF and DINCAE methods. The spatial distribution of the Chl–a product showed that Chl–a values in the coastal region were the highest and the Chl–a values in the deep–sea regions were stable, while the Chl–a values in February and March were higher than in other months. Lastly, this study demonstrated the feasibility of combining the BME method and DINCAE.

## 1. Introduction

_{2}data. In SST interpolation, Gao et al. [24] demonstrated that the BME method outperformed the optimum interpolation method and the OK method. He et al. [25] improved the accuracy of the BME method by utilizing a novel covariance method (i.e., the contigogram) in BME prediction. Lang et al. [26] combined the BME method with the physical oceanography formula to improve ocean pollution predictions.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Satellite Data

#### 2.3. In Situ Data

^{−3}. The in situ data were used to validate the performance of the DINEOF, DINCAE and DINCAE–BME methods. The in situ data were matched with the nearest remote sensing data, including Aqua, Terra and S–NPP. The root–mean–square error (RMSE), the mean absolute error (MAE) and R

^{2}were calculated for each matched group of data. The results are shown in Table 1.

#### 2.4. Cross–Validation

#### 2.5. Methods

#### 2.5.1. DINEOF

**X**with S × N dimensions, where the spatial dimension of

**X**is S and the temporal dimension of

**X**is N. The process of singular value decomposition (SVD) can be described with the following equation:

**U**denotes the spatial decomposition vector, which has S × R dimensions, and

**V**denotes the temporal decomposition vector, which has N × R dimensions.

**D**is a diagonal matrix consisting of eigenvalues of dimensions R × R. $\rho $ is the singular value and K is the number of singular values. Hence, when giving the specific

**U**and

**V**matrix,

**X**can be reconstructed using Equation (1). However, the process of reconstruction with the given

**U**and

**V**matrix only works when the observation data are complete. In reality, observation data have large amounts of missing data that must be pre–processed before construction.

**X**

_{0}. Then, the

**U**,

**V**and

**D**matrix is obtained through SVD with

**X**

_{0}. The missing data for point (i, j) ∈ I can be obtained by truncated EOF reconstruction according to the following equation:

#### 2.5.2. DINCAE

_{ij}and the corresponding error variance ${\widehat{\mathit{\sigma}}}_{ij}$ were defined as:

^{−3}(mg ∙ L

^{−1})

^{−2}, and ${T}_{ij1}$ and ${T}_{ij2}$ are the estimated value and error variance for the DINCAE output layer, respectively. When a neural network is trained by iteration, it is common to observe overfitting problems, which means that the model can fit the trained dataset well but works poorly with the test dataset. Some strategies can be adopted to avoid the overfitting phenomenon effectively:

- During the training phase, Gaussian–distributed noise can be added to the input data. With the random noise, the model can address the overfitting problem and its robustness can be boosted;
- Dropout [31], which makes the neural units randomly inactive in a fully connected layer, has proven its effectiveness in solving the overfitting issue in many studies [32]. Similar to the Gaussian–distributed noise, the above method was only implemented in the training phase and disabled during the reconstruction phase;
- The activation function, which is used to enhance the nonlinear fitting capacity of a model, is widely applied after the fully connection layer and convolution layer. The formula for the rectified linear unit (Relu) is as follows:

#### 2.5.3. BME

- (a)
- Prior stage. The purpose of the prior stage was to obtain the prior probability density function by using various types of knowledge, such as physical laws, scientific theory, spatiotemporal covariance models, etc. Based on the general knowledge, the constraint equation can be described as the following:

- (b)
- Meta prior stage. The work in this stage comprised data processing, including hard and soft data preparation. The soft data had inherent uncertainty, such as that in low–precision remote sensing data, and they used three kinds of data formats: the interval format, probability format and function format. In this study, Chl–a data from the Aqua satellite were considered as hard data and used for DINEOF and DINCAE modeling, while the soft data were generated from the DINCAE output data, the original Terra data and the original S–NPP data, as shown in Figure 6.The detailed process was as follows: the matched–up and paired data from the Aqua test dataset and the DINCAE output data/Terra data/S–NPP data were respectively used to build a linear model for calibration; then, all the DINCAE output data/Terra data/S–NPP data were introduced into the corresponding linear model to generate soft Chl–a data with a uniform–distribution probability density function by setting the upper and lower limits of the 95% confidence intervals of the linear models’ outputs as the upper and lower limits of the uniform distribution. The linear regression results are shown in Table 2. Further, the in situ Chl–a data were matched and compared with the linear model output (or estimation) to determine the priority of the soft data strategy chosen from among DINCAE–generated soft data, TERRA–generated soft data and S–NPP–generated soft data. Given that the R
^{2}values of the linear regression models for the in situ data and three kinds of estimations were 0.4661, 0.7246 and 0.6239, the priority for the choice of strategies for the soft data was set as Terra > S–NPP > output of DINCAE. Thus, the hard and soft data were prepared. In this study, the hard and soft data were both used for BME modeling.

- (c)
- Posterior stage. The main purpose of the posterior stage was to obtain the posterior probability distribution by making use of general knowledge, hard data and soft data. The process of determining the posterior probability distribution essentially involved solving the condition probability formula shown in the following equation:

#### 2.5.4. DINCAE–BME Framework

## 3. Results

#### 3.1. Hyperparameter Experiment

^{−3}when the EOF mode was 3. The results with different EOF modes for the DINEOF reconstruction process are shown in Table 3. Convergence was achieved for EOF–1, EOF–2, EOF–3, EOF–4, EOF–5 and EOF–6 after 66, 83, 78, 75, 99 and 300 iterations, respectively. In addition, the total variance in the reconstructed matrix was 7.4069 mg m

^{−3}, while the total variance in the initial matrix was 17.6303 mg m

^{−3}.

#### 3.2. Cross–Validation Result

^{−3}and 1.8824 mg m

^{−3}, respectively. For the pure DINCAE, the MAE and RMSE were 0.7147 mg m

^{−3}and 2.9860 mg m

^{−3}. It was obvious that the hold–out cross–validation result for DINCAE–BME was better than that for the other methods. Furthermore, it was evident that the performance of DINCAE was better than that of DINEOF, which proved that DINCAE is more suitable for reconstructing Chl–a data.

#### 3.3. Validation with the In Situ Data

^{2}, slope and intercept values of 0.6225, 1.1667 and −0.0276 mg m

^{−3}, respectively. Compared to the other methods, DINCAE–BME also had lower RMSE and MAE values of 0.6196 mg m

^{−3}and 0.3461 mg m

^{−3}, as shown in Table 5, indicating that the reconstructed data from DINCAE–BME were closer to the in situ Chl–a measurements.

#### 3.4. Reconstruction Statistics

^{−3}. The situation in the (a) region has also been observed in other studies [7,35]. Secondly, the (b) region showed higher activity than the (a) region; in contrast, Chl–a values in the (c) region were relatively low, with the values of most of the points remaining below 1.0 mg m

^{−3}. Finally, it was observed that the (d) region was the region of high productivity; the Chl–a values of some of the points were kept above 4.0 mg m

^{−3}and the overall trend was that the values gradually decreased from near the shore to the sea. This was mainly attributed to terrigenous input. Frequent human activities and the continuous discharge of sewage into the ocean due to the needs of industrial development have led to the eutrophication of water bodies, resulting in the proliferation of algae and the phenomenon of high Chl–a values [36].

^{−3}for the rest of time. The Chl–a values in the (b) and (c) regions were consistent with the previous time trends. It was found that the Chl–a values in the (d) regions remained in a relatively stable temporal distribution with high values.

## 4. Discussion

#### 4.1. Methodology

#### 4.2. Product Analysis

^{−3}and the overall trend was a gradual decrease from near the shore to the sea, which may have been caused by terrigenous input. Due to frequent human activities and the emission and diffusion of pollutants, the eutrophication of coastal seawater is leading to large outbreaks of phytoplankton, resulting in high Chl–a values. The (a) and (b) regions also remain active situations, with Chl–a values at most points above 2.0 mg m

^{−3}, while the Chl–a values in the (c) region were relatively low. The high concentration of nutrients in the (c) region combined with the influence of various factors resulted in the explosive increase in Chl–a values in the (a) region from February to March [40]. Chl–a values in the (b) region were similar to those in the (a) region in terms of temporal distribution. The difference was that Chl–a values were higher in the (b) region than in the (a) region most of the time. This was mainly because the (b) region was located near Mumbai, and human activities are more frequent than in the (a) region. More importantly, the (a) region was situated with the Arabian Sea to the east and the Persian Gulf to the west, which is a relatively connected gulf. The (b) region was more closed than the (a) region, and there was relatively less material exchange with the deep–sea area, which may have had an influence on Chl–a.

## 5. Conclusions

^{2}values for the interpolated products were 0.3461 mg m

^{−3}, 0.6196 mg m

^{−3}and 0.6225 mg m

^{−3}, respectively. The results showed that DINCAE–BME had smaller errors compared to pure DINCAE, which supported the utility of combining the DINCAE and BME procedures. Furthermore, the DINCAE method and the DINEOF method were evaluated using validation data and in situ data. The MAE and RMSE computed using in situ data and the reconstruction results from DINCAE were 0.3797 mg m

^{−3}and 0.8117 mg m

^{−3}, while the two indicator values for DINEOF were 1.2645 mg m

^{−3}and 1.9580 mg m

^{−3}. It was found that DINCAE performed better than DINEOF in the task of Chl–a interpolation in the NAS because of its capacity to capture nonlinear and mutated relationships. In addition, the results showed that the DINCAE–BME framework increased the coverage of Chl–a data from 17% to 100% with a high–accuracy interpolation value. The spatial distribution of the reconstruction results showed that the Chl–a values in the coastal region were high because of human activity, and those in the gulf region were higher than those in the deep–sea region. The temporal distribution of the results showed that values for Chl–a in winter were higher than in summer, and the values in autumn were higher than in spring. The difference between the results for 2020 and 2021 verified the conclusion that COVID–19 had an impact on the marine environment by limiting human activity. Furthermore, the inclusiveness of BME was further demonstrated by its capacity to absorb the multi–source information.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The red square represents the location of the NAS in the map of Asia. Yellow dots represent the locations of the in situ Chl–a measurements from the Argo data.

**Figure 2.**Percentages of Chl–a data coverage for the NAS from 2020 to 2021. The gray area represents the land.

**Figure 3.**Aqua, Terra, S–NPP and the three satellites’ combined monthly percentages of coverage from 2020 to 2021.

**Figure 7.**Hyperparameter–finding experiments for DINCAE. The optimal dropout rate was chosen from (0.7, 0.8, 0.9) and the optimal jitter std was chosen from (0.05, 0.10, 0.15).

**Figure 9.**Comparison of the reconstructed data from different methods and in situ data. The match counts for DINEOF, DINCAE and DINCAE–BME were 74, 152 and 156.

**Figure 10.**Mean values for the DINCAE–BME reconstruction results in a time series. (a) Region representing the Gulf of Oman; (b) region representing the Gulf of Khambhat, which is near India; (c) region representing the deep–sea region of the NAS; (d) region representing the coastal region.

**Figure 11.**Monthly interpolation results for Chl–a with the DINCAE–BME from January to December 2020.

**Figure 12.**Monthly interpolation results for Chl–a with the DINCAE–BME from January to December 2021.

**Figure 13.**Difference in monthly interpolation results for Chl–a obtained with DINCAE–BME from January to December, generated by subtracting 2020 results from 2021 results in months.

Satellite | Count | RMSE (mg m^{−3}) | MAE (mg m^{−3}) | R^{2} |
---|---|---|---|---|

Aqua | 59 | 0.3855 | 0.1255 | 0.7432 |

Terra | 73 | 0.4237 | 0.1556 | 0.7246 |

S–NPP | 67 | 0.4637 | 0.2368 | 0.6240 |

N | Slope | Intercept (mg m^{−3}) | R^{2} | |
---|---|---|---|---|

DINCAE | 1,304,562 | 0.8139 | 0.1227 | 0.6910 |

Terra | 702,350 | 0.9290 | 0.2827 | 0.5500 |

S–NPP | 817,499 | 1.4663 | 0.1227 | 0.6552 |

EOF Mode | Expected Error (mg m^{−3}) | Iterations | $\mathbf{Convergence}\mathbf{Achieved}\left({10}^{-3}\right)$ |
---|---|---|---|

1 | 3.7971 | 66 | 0.9864 |

2 | 3.6473 | 83 | 0.9815 |

3 | 3.6089 | 78 | 0.9867 |

4 | 3.6710 | 75 | 0.9983 |

5 | 3.7443 | 99 | 0.9959 |

6 | 3.8118 | 300 | 1.0510 |

Method | MAE (mg m^{−3}) | RMSE (mg m^{−3}) |
---|---|---|

DINEOF | 2.9710 | 4.9573 |

DINCAE | 0.7147 | 2.9860 |

DINCAE−BME | 0.4682 | 1.8824 |

Number of Matched In Situ Data Samples | Method | RMSE (mg m ^{−3}) | MAE (mg m ^{−3}) | R^{2} | Slope | Intercept (mg m ^{−3}) |
---|---|---|---|---|---|---|

74 152 156 | DINEOF | 1.9580 | 1.2645 | 0.2871 | 0.1655 | 0.8682 |

DINCAE | 0.8117 | 0.3797 | 0.4661 | 0.3900 | 0.1448 | |

DINCAE–BME | 0.6196 | 0.3461 | 0.6225 | 1.1667 | −0.0276 |

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## Share and Cite

**MDPI and ACS Style**

Yan, X.; Gao, Z.; Jiang, Y.; He, J.; Yin, J.; Wu, J. Application of Synthetic DINCAE–BME Spatiotemporal Interpolation Framework to Reconstruct Chlorophyll–a from Satellite Observations in the Arabian Sea. *J. Mar. Sci. Eng.* **2023**, *11*, 743.
https://doi.org/10.3390/jmse11040743

**AMA Style**

Yan X, Gao Z, Jiang Y, He J, Yin J, Wu J. Application of Synthetic DINCAE–BME Spatiotemporal Interpolation Framework to Reconstruct Chlorophyll–a from Satellite Observations in the Arabian Sea. *Journal of Marine Science and Engineering*. 2023; 11(4):743.
https://doi.org/10.3390/jmse11040743

**Chicago/Turabian Style**

Yan, Xiting, Zekun Gao, Yutong Jiang, Junyu He, Junjie Yin, and Jiaping Wu. 2023. "Application of Synthetic DINCAE–BME Spatiotemporal Interpolation Framework to Reconstruct Chlorophyll–a from Satellite Observations in the Arabian Sea" *Journal of Marine Science and Engineering* 11, no. 4: 743.
https://doi.org/10.3390/jmse11040743