# Spatial Downscaling of MODIS Chlorophyll-a with Genetic Programming in South Korea

^{*}

## Abstract

**:**

^{nd}-, 3

^{rd}-, and 4

^{th}-degree) to illustrate their performances for downscaling MODIS Chl-a. The obtained results indicate that GP with R

^{2}= 0.927 and RMSE = 0.1642 on the winter day and R

^{2}= 0.763 and RMSE = 0.5274 on the summer day provides higher accuracy on both winter and summer days than all the applied MPR models because the GP model can automatically produce appropriate mathematical equations without any restrictions. In addition, the GP model is the least sensitive model to the changes in the input parameters. The improved downscaling data provide better information to monitor the status of oceanic and coastal marine ecosystems that are also critical for fisheries and fishing farming.

## 1. Introduction

^{nd}), third-order (3

^{rd}), and fourth-order (4

^{th}) polynomials. The developed models were utilized for Chl-a downscaling over the western coast of South Korea.

## 2. Study Area

^{2}) (Figure 1). The Yellow Sea is a shallow marine ecosystem with the average and maximum water depths of 44 m and 103 m, respectively [38]. There is clear seasonality in sea surface temperature (SST) over the Yellow Sea, where January is the coldest month with an average SST of 4–7 °C and July is the warmest, with an average SST of 26–27 °C [39]. There are a total of 339 fish species in the Korean West Sea [40]. Over the past few years, some fish species, such as small yellow croaker, hairtail, large yellow croaker, and flatfish have exhibited continuous declines due to overharvesting, degraded marine ecosystem quality, and several unknown factors [41].

## 3. Materials and Methods

_{4k}) and S-2A at 10 m (defined as X

_{10}), were acquired, and S-2A data were resampled to 4 km MODIS resolution (denoted as X

_{4k}); (2) the most important S-2A band combinations (X

_{4k}) were chosen by utilizing the support vector machine recursive feature elimination (SVM-RFE) method; (3) MODIS Chl-a downscaling from 4 km to 10 m was performed by regressing X

_{4k}to Y

_{4k}, calculating the residual at 4 km (${\mathsf{\epsilon}}_{4\mathrm{k}}$), and adding the interpolated residual (${\mathsf{\epsilon}}_{10}$) to the estimated fine-resolution Chl-a (${\widehat{\mathrm{Y}}}_{10}$); (4) the obtained downscaled maps were compared with visual comparison, validated with in situ data, and all the applied methods were assessed using sensitivity analysis. A complete explanation of the aforementioned steps is described in Section 3.1, Section 3.2, Section 3.3, Section 3.4.

#### 3.1. Data Description

#### 3.2. Preprocessing

_{10}). Since the study region had a remarkable number of islands (Figure 1), the reflectance caused by islands could decrease the accuracy of the applied models. Therefore, the third step of preprocessing aimed to separate water from land pixels to improve the downscaling results. The most commonly used indices, namely, the normalized difference vegetation index (NDVI) and normalized difference water index (NDWI), have already been employed for land-water separation purposes [54,55,56,57,58]. In the current study, land-water separation was performed by utilizing the NDWI index. The formula of this index is as follows:

_{10}) to 4 km resolution of MODIS Chl-a (X

_{4k}) using the nearest neighbor method [59]. Then, MODIS Chl-a and S-2A images at 4 km (Y

_{4k}and X

_{4k}) were used as dependent and independent variables, respectively, to develop GP and MPR models. Additionally, the developed models were applied to S-2A images at 10 m (X

_{10}) to estimate downscaled Chl-a at 10 m spatial resolution.

_{4k}). This method is a widely used technique for feature selection that has been utilized in a wide variety of remote sensing research studies [60,61,62]. To perform feature selection, multiple mathematical operations, including multiplication, addition, subtraction, rationing, averaging, and square transformation, were used to calculate 597 various combinations of the resampled S-2A bands at 4 km, and the computed combinations served as the input for the feature selection method. Then, SVM-RFE was trained on the calculated dataset using the MODIS Chl-a concentration (Y

_{4k}) and S-2A band combinations (X

_{4k}) as the predictand and predictor variables, respectively. As a result, relevant combinations for the downscaling procedure were chosen.

#### 3.3. Downscaling

_{4k}) and 10 m (X

_{10}), $\widehat{\mathrm{Y}}$ is the estimated MODIS Chl-a at 4 km (${\widehat{\mathrm{Y}}}_{4\mathrm{k}}$) and 10 m (${\widehat{\mathrm{Y}}}_{10}$), and f represents a nonlinear regression function developed by GP and MPR techniques.

_{4k}and X

_{4k}was established using all the applied methods as 2

^{nd}-degree MPR, 3

^{rd}-degree MPR, 4

^{th}-degree MPR, and GP. From the 636 pixels of the independent (X

_{4k}) and dependent (Y

_{4k}) variables, 445 pixels were used for training, and the remaining 191 pixels were reserved for the validation of the models. Standardization was a prerequisite step before training all the applied methods to ensure that all variables remained on the same scale. Therefore, the standardization of all independent variables (X

_{4k}) in the training and validation set was performed by subtracting the mean and dividing by the standard deviation of the training set. This preprocessing sped up the convergence and allowed efficient training of the network. Then, the estimated Chl-a at 4 km (${\widehat{\mathrm{Y}}}_{4\mathrm{k}}$) was subtracted from the original MODIS Chl-a at 4 km (Y

_{4k}) as follows:

#### 3.4. Sensitivity Analysis

_{i,n}is the elementary effects (EEs) assessed for the i-th input variable using the n-th sample point. EEs are employed to specify noninfluential inputs for a computationally costly mathematical model or for a model with a great number of input parameters, where the costs of evaluating other SA methods such as variance-based methods are not reasonably priced.

#### 3.5. Mathematical Background

#### 3.5.1. Multiple Polynomial Regression

^{th}order polynomial model with one variable Equation (6) is the general form of the polynomial model that indicates the nonlinear relationship between one predictand and one predictor variable.

^{nd}), third-order (3

^{rd}), and fourth-order (4

^{th}), were trained and compared.

#### 3.5.2. Genetic Programming

## 4. Results

#### 4.1. Preprocessing

^{2}= 0.996 for winter (panel (a)) and R

^{2}= 0.939 for summer (panel (b)). Therefore, it can be concluded that the grid-fill method exhibits good performance for the reconstruction of MODIS Chl-a values. Note that the reason for the better performance of the method on the winter day than on the summer day might be related to the presence of more missing values in the selected scene of the summer day that occurs due to high cloudiness on the summer day.

#### 4.2. Downscaling Results

^{nd}, 3

^{rd}, and 4

^{th}) and GP were trained with the four determined band combinations as predictors and MODIS Chl-a as a predictand at low-resolution (4 km). Then, a residual correction was performed utilizing the described methodology in the downscaling section (Section 3.3), and Equations (3)–(4) to produce high-resolution Chl-a maps (Y

_{10}). To assess the accuracy of the downscaling technique, the final downscaled maps (i.e., Y

_{10}) were validated with the original MODIS Chl-a maps at a pixel size of 4 km. For this purpose, sample values were extracted from the downscaled maps (Y

_{10}) within a 3 × 3 window around the center of each MODIS Chl-a pixel, and the mean of each sample was calculated and compared with the original MODIS Chl-a (Figure 5 and Table 3).

^{nd}-degree MPR. According to the performance indices, the accuracy of the models was ranked as GP > 2

^{nd}-degree MPR > 3

^{rd}-degree MPR > 4

^{th}-degree MPR for the winter day. For the summer day, the rank was GP > 3

^{rd}-degree MPR > 2

^{nd}-degree MPR > 4

^{th}-degree MPR. Overall, the GP exhibited the best performance for the winter and summer days.

^{2}= 0.927 and RMSE = 0.1642 on the winter day, compared to the MPR models (2

^{nd}-, 3

^{rd}-, and 4

^{th}-degree). The same result can be seen on the summer day (the best performance in the GP model), as shown in the bottom panels of Figure 5. Furthermore, it can be seen that all the applied models estimate Chl-a better at lower concentrations than at higher concentrations, particularly in the range of 1.5–3.5 mg m

^{−3}, as presented in Figure 5.

#### 4.3. Model Evaluation

#### 4.3.1. Visual Comparison

^{nd}-degree MPR. From Figure 6, the major trend of Chl-a is fairly modeled with GP and 2

^{nd}-degree MPR but specific and substantially high values are not captured in both models such as the values in the near coastal area. However, the residual model can additionally capture this high variability and produce a reliable estimate in the final stage, as seen in the last column of Figure 6. According to the results illustrated in Table 3, and the panels in the last column of Figure 6, 4

^{th}-degree MPR cannot estimate the Chl-a values at 10 m resolution as accurately as the other models, especially in coastal areas. This phenomenon indicates that the GP and 2

^{nd}-degree MPR can capture the most variation in high Chl-a concentrations at 4 km resolution.

#### 4.3.2. In Situ Validation

^{2}and RMSE are presented in Figure 9 for the winter day (left panel) and the summer day (right panel). The computed p-values (Figure 9) shows that R

^{2}of all models is statistically significant (p-values lower than 0.05). In general, the R

^{2}of the GP model was higher than that of the other models for the winter and summer days, which were 0.59 and 0.47, respectively, as shown in Figure 9. Additionally, the RMSE of the GP model was smaller than that of the other models for the winter and summer days, at 0.766 and 0.483, respectively.

#### 4.3.3. Sensitivity Analysis

^{nd}-degree MPR model is the most sensitive model (${\mu}_{}^{*}$ values ranged from 0.09 to 1.24 for the winter and 0.94 to 2.42 for the summer day), while the GP model is the least sensitive model (${\mu}_{}^{*}$ = 1.45 and 1.4 for B2/B3 band combination in winter and summer days, respectively) to the changes in the predictor variables. In addition, the sensitivity of the MPR models increases on the summer day compared to that of the winter day, while the GP model shows a slight decrease to the changes of the B2/B3 band combination on the summer day compared to that of the winter day.

^{nd}-degree MPR show comparable accuracy (Figure 5 and Table 3) on both winter and summer days, the GP model with the least sensitivity to the changes in the input parameters is more effective than the 2

^{nd}-degree MPR for downscaling Chl-a. Additionally, SA results show that the accuracy of all models is strongly related to the accuracy of the remote sensing data; this further confirms the need for atmospheric correction as an essential task in the downscaling procedure [71].

## 5. Discussion and Conclusions

^{nd}, 3

^{rd}, and 4

^{th}) and GP model to downscale MODIS Chl-a; (iv) assessment of the results with original MODIS Chl-a maps at a pixel size of 4 km and in situ measurements.

^{nd}-degree MPR, but specific and substantially high values are not captured with both models such as the values in near coastal areas. This drawback of the models can be solved with the residual correction that makes it an essential procedure to improve the accuracy of the spatial downscaling model.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Downscaling workflow. Note that the goal of the present research is to downscale Moderate Resolution Imaging Spectroradiometer (MODIS) Chl-a from coarse resolution (4 km) to high resolution (10 m).

**Figure 4.**1:1 scatter plots of the original MODIS Chl-a vs. reconstructed Chl-a by the grid-fill method on (

**a**) the winter day (2016.2.2) and (

**b**) the summer day (2016.8.4).

**Figure 5.**1:1 scatter plots of the original MODIS Chl-a at 4 km pixel size vs. downscaled MODIS Chl-a at 10 m pixel size; (

**a**) the winter day (2016.2.2): (

**a-1**) 2

^{nd}-degree MPR, (

**a-2**) 3

^{rd}-degree MPR, (

**a-3**) 4

^{th}-degree MPR, (

**a-4**) GP, and (

**b**) the summer day (2016.8.4): (

**b-1**) 2

^{nd}-degree MPR, (

**b-2**) 3

^{rd}-degree MPR, (

**b-3**) 4

^{th}-degree MPR, and (

**b-4**) GP.

**Figure 6.**Detailed maps showing the downscaling steps for all models on the winter day (2016.2.2); (

**a**) 2

^{nd}-degree MPR, (

**b**) 3

^{rd}-degree MPR, (

**c**) 4

^{th}-degree MPR, and (

**d**) GP.

**Figure 7.**Detailed maps showing the downscaling steps for all models on the summer day (2016.8.4); (

**a**) 2

^{nd}-degree MPR, (

**b**) 3

^{rd}-degree MPR, (

**c**) 4

^{th}-degree MPR, and (

**d**) GP.

**Figure 8.**Histogram and fitted normal distribution of MODIS Chl-a for (

**a**) the winter day (2016.2.2) and (

**b**) the summer day (2016.8.4). $\mathsf{\delta}$ and $\mathsf{\theta}$ are the coefficient of variation (COV) and skewness coefficient, respectively. Note that the COV and skewness coefficient values for a normal distribution are zero. The skewness coefficient indicates that the distribution of the summer day data presents more non-normality than that of the winter day.

**Figure 9.**1:1 scatter plots of downscaled MODIS Chl-a and in situ data for all methods using two measured data at 0–15 cm depth; (

**a**) the winter day (2016.2.2) and (

**b**) the summer day (2016.8.4).

**Figure 10.**Sensitivity measure index (${\mu}_{}^{*}$) for the winter day (2016.2.2); (

**a**) 2

^{nd}-degree MPR, (

**b**) 3

^{rd}-degree MPR, (

**c**) 4

^{th}-degree MPR, and (

**d**) GP. Note that the higher values of ${\mu}_{}^{*}$ for a given parameter indicate higher sensitivity of the model to the changes of the parameter.

**Figure 11.**Sensitivity measure index (${\mu}_{}^{*}$) for the summer day (2016.8.4); (

**a**) 2

^{nd}-degree MPR, (

**b**) 3

^{rd}-degree MPR, (

**c**) 4

^{th}-degree MPR, and (

**d**) GP. Note that the higher values of ${\mu}_{}^{*}$ for a given parameter indicate higher sensitivity of the model to the changes of the parameter.

Band Name | Central Wavelength (µm) | Spatial Resolution (m) |
---|---|---|

B1-Coastal aerosol | 0.443 | 60 |

B2-Blue | 0.490 | 10 |

B3-Green | 0.560 | 10 |

B4-Red | 0.665 | 10 |

B5-Vegetation red edge | 0.705 | 20 |

B6-Vegetation red edge | 0.740 | 20 |

B7-Vegetation red edge | 0.783 | 20 |

B8-NIR | 0.842 | 10 |

B8A-Narrow NIR | 0.865 | 20 |

B9-Water vapor | 0.940 | 60 |

B10-SWIR-Cirrus | 1.375 | 60 |

B11-SWIR | 1.610 | 20 |

B12-SWIR | 2.190 | 20 |

MODIS | Sentinel-2A MSI | Chl-a Measurements |
---|---|---|

2016.2.2 | 2016.2.2 | 2016.2.1 |

2016.8.4 | 2016.8.4 | 2016.8.1 |

Date | Performance Statistics | Model | |||
---|---|---|---|---|---|

2^{nd} Degree MPR | 3^{rd} Degree MPR | 4^{th} Degree MPR | GP | ||

2016.2.2 | MAE | 0.108 | 0.144 | 0.150 | 0.108 |

(Winter) | MBE | −0.014 | −0.012 | −0.020 | 0.011 |

RMSE | 0.168 | 0.207 | 0.219 | 0.164 | |

R^{2} | 0.922 | 0.886 | 0.872 | 0.927 | |

2016.8.4 | MAE | 0.360 | 0.383 | 0.409 | 0.341 |

(Summer) | MBE | −0.056 | −0.044 | −0.068 | −0.030 |

RMSE | 0.562 | 0.542 | 0.595 | 0.527 | |

R^{2} | 0.732 | 0.753 | 0.704 | 0.763 |

^{2}is the coefficient of determination.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mohebzadeh, H.; Yeom, J.; Lee, T. Spatial Downscaling of MODIS Chlorophyll-a with Genetic Programming in South Korea. *Remote Sens.* **2020**, *12*, 1412.
https://doi.org/10.3390/rs12091412

**AMA Style**

Mohebzadeh H, Yeom J, Lee T. Spatial Downscaling of MODIS Chlorophyll-a with Genetic Programming in South Korea. *Remote Sensing*. 2020; 12(9):1412.
https://doi.org/10.3390/rs12091412

**Chicago/Turabian Style**

Mohebzadeh, Hamid, Junho Yeom, and Taesam Lee. 2020. "Spatial Downscaling of MODIS Chlorophyll-a with Genetic Programming in South Korea" *Remote Sensing* 12, no. 9: 1412.
https://doi.org/10.3390/rs12091412