# Estimating Chlorophyll-a Concentration from Hyperspectral Data Using Various Machine Learning Techniques: A Case Study at Paldang Dam, South Korea

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## Abstract

**:**

^{2}of 0.99, a mean square error (MSE) of 1.299 μg/cm

^{3}, and showed a small discrepancy between observed and real values relative to other frameworks. These findings suggest that by combining hyperspectral data with dimension reduction and a machine learning algorithm, it is possible to provide an accurate estimation of chlorophyll-a. Using this, chlorophyll-a can be obtained in real time through hyperspectral sensor data input from drones or unmanned aerial vehicles using the learned machine learning algorithm.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hyperspectral Datasets

#### 2.2. Sampling Chlorophyll-a, Hyperspectral Sensor

#### 2.3. Data Preprocessing

#### 2.3.1. PCA

#### 2.3.2. PLS

#### 2.4. Machine Learning Algorithm

#### 2.4.1. SVR

#### 2.4.2. KNN

#### 2.4.3. Bagging

#### 2.4.4. Boosting

## 3. Results

#### 3.1. Perfromance Measures

- ${\mathrm{R}}^{2}$: This is an applied evaluation metric for fit regression models that is used mainly in hydrological studies [32]. However, there is a disadvantage that ${\mathrm{R}}^{2}$ increases unconditionally when the number of variables increases.
- Root mean square error (RMSE): This metric is obtained by applying the root to the mean of the total squared error (the sum of the individual squared errors). Therefore, it increases when the variance associated with the frequency distribution of error magnitudes increase [37].
- RSR (RMSE-observations standard deviation ratio): This metric standardizes RMSE using the standard deviation of the observations. Therefore, a lower RSR means better model performance and a lower RMSE [35].
- Percent bias (PBIAS): This measures the average tendency of the simulated data to be larger or smaller than their observed counterparts. That is, positive values indicate a model underestimation bias, and negative values indicate a model overestimation bias. It is useful for continuous long-term simulations and can help identify the average model simulation bias [36].

#### 3.2. Estimation

#### 3.3. Variable Importance

## 4. Discussion

^{2}values were obtained for seven machine learning methods, except for OLS, with the PLS preprocessing method. Using this method, chlorophyll-a can be estimated immediately without measuring water quality data using hyperspectral data acquired by drones and unmanned aerial vehicles.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Machine learning framework for chlorophyll-a estimation. Hyperspectral

_{i}denotes an $\mathrm{i}$ nm hyperspectral wavelength (i = 350 nm, …, 900 nm). The abbreviation in Figure 1 is described as follows. OLS (ordinary least squares), RF (random forest), ET (extra trees), GB (Gradient Boosting), AdaBoost (Adaptive Boosting), KNN (k-nearest neighbor), SVR (support vector regression), XGboost (Extreme Gradient Boosting).

**Figure 3.**Technological principle of hyperspectral sensor WISP station. Upper lens 2 point (①,②): Light must enter through the two lenses during measurement, not under overcast or rainy conditions. Side lens 1 point (③): The distance between the measurement point and the point to be measured is calculated; it is then installed such that the reflected light reaches the side lens point at a 48° angle, as illustrated on the left. This is the spectroscopic principle by which the reflected light is measured using a single wavelength band.

**Figure 4.**Chlorophyll-a and hyperspectral data observed through the sensor. The black dotted line is the chlorophyll-a observed at each time point, and the spectrum is the hyperspectral data for the bands, 350 nm to 900 nm, observed at each time point.

**Figure 5.**Chlorophyll-a distribution. Each dataset (gray bars) is divided into training (red) and testing (blue) subsets in chronological order.

**Figure 6.**An example diagram of a univariate time series k-neighbor with w = 3 and k = 3. The black dot is the observed value at each time.

**Figure 9.**Left-side figure shows the difference between the observed and fitted values using support vector regression for each preprocessing scheme, while the right-side figure shows the residual value.

Metric | Equation | Range (Optimal Value) |
---|---|---|

${\mathrm{R}}^{2}$ | ${\left\{\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{\overline{y}}^{obs}\right)\left({\mathrm{y}}_{i}^{\mathrm{pred}}-{\overline{y}}^{pred}\right)\text{}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{\overline{y}}^{obs}\right)}^{2}}\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{pred}-{\overline{y}}^{pred}\right)}^{2}}}\right\}}^{2}$ | 0.0~1.0 (1.0) |

NSE | $1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{y}_{i}^{pred}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{\overline{y}}^{obs}\right)}^{2}}$ | −∞~1.0 (1.0) |

d | $1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{y}_{i}^{pred}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left(\left|{\mathrm{y}}_{i}^{\mathrm{pred}}-{\overline{y}}^{obs}\right|+\left|{\mathrm{y}}_{i}^{\mathrm{obs}}-{\overline{y}}^{obs}\right|\right)}^{2}}$ | 0.0~1.0 (1.0) |

RMSE | $\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{y}_{i}^{pred}\right)}^{2}\text{}}$ | 0.0~∞ (0.0) |

RSR | $\frac{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{y}_{i}^{pred}\right)}^{2}}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mathrm{y}}_{i}^{\mathrm{obs}}-{\overline{y}}^{pred}\right)}^{2}}}$ | 0.0~∞ (0.0) |

PBIAS | $\frac{{{\displaystyle \sum}}_{i=1}^{n}{y}_{i}^{obs}-{y}_{i}^{pred}}{{{\displaystyle \sum}}_{i=1}^{n}{y}_{i}^{obs}}\times 100$ | −∞~∞ (0.0) |

Method | ${\mathbf{R}}^{2}$ | MSE | MAPE | NSE | d | PSR | |
---|---|---|---|---|---|---|---|

Baseline | OLS | 0.380 | 126.665 | 77.598 | −7.592 | 0.402 | 2.121 |

RF | 0.919 | 20.070 | 44.153 | −0.361 | 0.557 | 0.922 | |

ET | 0.986 | 18.878 | 42.474 | −0.281 | 0.569 | 0.912 | |

GB | 0.941 | 12.765 | 33.110 | 0.134 | 0.701 | 0.809 | |

AdaBoost | 0.908 | 22.93 | 47.754 | −0.555 | 0.502 | 0.963 | |

KNN | 0.925 | 17.284 | 39.489 | −0.172 | 0.617 | 0.898 | |

SVR | 0.991 | 1.299 | 8.365 | 0.912 | 0.977 | 0.297 | |

XGBoost | 0.948 | 10.908 | 30.194 | 0.26 | 0.742 | 0.765 | |

Standard Scaler | OLS | 0.122 | 337.646 | 178.614 | −21.904 | 0.305 | 1.04 |

RF | 0.919 | 19.967 | 43.996 | −0.354 | 0.558 | 0.921 | |

ET | 0.986 | 18.918 | 42.529 | −0.283 | 0.568 | 0.913 | |

GB | 0.947 | 11.282 | 31.21 | 0.235 | 0.732 | 0.772 | |

AdaBoost | 0.908 | 23.348 | 48.034 | −0.584 | 0.507 | 0.963 | |

KNN | 0.929 | 16.617 | 39.044 | −0.127 | 0.632 | 0.882 | |

SVR | 0.986 | 2.132 | 10.473 | 0.855 | 0.961 | 0.379 | |

XGBoost | 0.948 | 10.908 | 30.194 | 0.260 | 0.742 | 0.765 | |

Min-Max scaler | OLS | 0.737 | 45.016 | 48.533 | −2.054 | 0.685 | 1.604 |

RF | 0.919 | 19.967 | 43.996 | −0.354 | 0.558 | 0.921 | |

ET | 0.986 | 18.878 | 42.474 | −0.281 | 0.569 | 0.912 | |

GB | 0.947 | 11.282 | 31.21 | 0.235 | 0.732 | 0.772 | |

AdaBoost | 0.908 | 23.348 | 48.034 | −0.584 | 0.507 | 0.963 | |

KNN | 0.930 | 16.797 | 39.028 | −0.139 | 0.632 | 0.879 | |

SVR | 0.987 | 1.950 | 10.113 | 0.868 | 0.965 | 0.363 | |

XGBoost | 0.948 | 10.908 | 30.194 | 0.260 | 0.742 | 0.765 | |

PCA | OLS | 0.170 | 330.055 | 184.408 | −21.389 | 0.314 | 1.003 |

RF | 0.964 | 6.675 | 23.326 | 0.547 | 0.853 | 0.636 | |

ET | 0.986 | 5.820 | 22.345 | 0.605 | 0.861 | 0.589 | |

GB | 0.980 | 3.428 | 16.316 | 0.767 | 0.935 | 0.472 | |

AdaBoost | 0.962 | 8.479 | 27.148 | 0.425 | 0.82 | 0.68 | |

KNN | 0.928 | 16.752 | 39.179 | −0.136 | 0.63 | 0.884 | |

SVR | 0.982 | 2.602 | 11.776 | 0.824 | 0.953 | 0.419 | |

XGBoost | 0.981 | 3.229 | 15.499 | 0.781 | 0.935 | 0.459 | |

PLS | OLS | 0.171 | 330.243 | 184.598 | −21.402 | 0.314 | 1.002 |

RF | 0.983 | 4.291 | 17.468 | 0.709 | 0.928 | 0.51 | |

ET | 0.986 | 4.475 | 20.171 | 0.696 | 0.905 | 0.514 | |

GB | 0.988 | 1.875 | 10.351 | 0.873 | 0.969 | 0.356 | |

AdaBoost | 0.977 | 7.481 | 25.6 | 0.493 | 0.868 | 0.625 | |

KNN | 0.932 | 14.624 | 36.223 | 0.008 | 0.663 | 0.861 | |

SVR | 0.981 | 2.828 | 12.363 | 0.808 | 0.948 | 0.436 | |

XGBoost | 0.990 | 1.595 | 10.416 | 0.892 | 0.972 | 0.327 |

ML Model (with Preprocessing) | Hyperparameters | Type | Search Space | Optimal Parameters |
---|---|---|---|---|

OLS | - | - | - | - |

Random Forest (PLS) | min_samples_leaf | Discrete | 3, 5, 7, 10 | 3 |

max_depth | Discrete | 3, 4, 5, 6 | 6 | |

Extreme Tree (PLS) | min_samples_leaf | Discrete | 3, 5, 7, 10 | 5 |

max_depth | Discrete | 3, 4, 5, 6 | 6 | |

Gradient Boost (PLS) | min_samples_leaf | Discrete | 3, 5, 7, 10 | 10 |

n_estimators | Discrete | 100, 200, 300 | 300 | |

AdaBoost (PLS) | n_estimators | Discrete | 100, 200, 300 | 300 |

learning_rate | Discrete | 0.1, 0.05, 0.02, 0.01 | 0.1 | |

KNN (PLS) | n_neighbrs | Discrete | 3,5,7,9,11, | 5 |

weights | Categorical | “uniform”, “distance” | distance | |

algorithm | Categorical | “ball_tree”, “kd_tree”, “brute” | ball_tree | |

SVR (Baseline) | Kernel | Categorical | “rbf”, “sigmoid” | rbf |

C | Discrete | 10,30,100,300,1000 | 1000 | |

XGBoost (PLS) | max_depth | Discrete | 5, 6, 7 | 5 |

learning_rate | Discrete | 0.03, 0.05, 0.07 | 0.07 |

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**MDPI and ACS Style**

Im, G.; Lee, D.; Lee, S.; Lee, J.; Lee, S.; Park, J.; Heo, T.-Y.
Estimating Chlorophyll-*a* Concentration from Hyperspectral Data Using Various Machine Learning Techniques: A Case Study at Paldang Dam, South Korea. *Water* **2022**, *14*, 4080.
https://doi.org/10.3390/w14244080

**AMA Style**

Im G, Lee D, Lee S, Lee J, Lee S, Park J, Heo T-Y.
Estimating Chlorophyll-*a* Concentration from Hyperspectral Data Using Various Machine Learning Techniques: A Case Study at Paldang Dam, South Korea. *Water*. 2022; 14(24):4080.
https://doi.org/10.3390/w14244080

**Chicago/Turabian Style**

Im, GwangMuk, Dohyun Lee, Sanghun Lee, Jongsu Lee, Sungjong Lee, Jungsu Park, and Tae-Young Heo.
2022. "Estimating Chlorophyll-*a* Concentration from Hyperspectral Data Using Various Machine Learning Techniques: A Case Study at Paldang Dam, South Korea" *Water* 14, no. 24: 4080.
https://doi.org/10.3390/w14244080