# Emulation of Sun-Induced Fluorescence from Radiance Data Recorded by the HyPlant Airborne Imaging Spectrometer

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## Abstract

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## 1. Introduction

## 2. Methods and Materials

#### 2.1. Principles of Hyperspectral Data Emulation

#### 2.2. HyPlant Data and SIF Retrieval Using the Spectral Fitting Method

#### 2.3. Machine Learning Algorithms for Emulation

#### 2.4. Experimental Setup

- 1.
- The selected MLRAs have been evaluated using the training dataset. The default training settings were: 1000 random training samples, 20 PCs for the input, and 5 PCs for the output data.
- 2.
- PCAs were applied to the input and output data to reduce the feature space of both variables. To determine the optimal number of components, we varied the number of PCs in the input (from 1 to 50 PCs in steps of 5 while keeping the number of PCs in the output data constant at 5) and output data (from 1 to 10 PCs in steps of 1 while keeping the number of PCs in the input data constant at 20).
- 3.
- To investigate the effect of the number of samples on emulator performance we varied the number of samples from 200 to 7000 (200, 500, 700, 1000, 1500, 2000, 3000, 4000, 5000, 7000) while we fixed the number of PCs in the input and output data to 20 and 5, respectively.
- 4.
- The effect of the three different sampling strategies on emulator performance has been analyzed: (1) random sampling without classification, and segmented sampling according to (2) absolute number of pixels per class, and (3) relative number of pixels per class. Additionally, the impact of the number of classes used in unsupervised classification has also been tested by varying it from 1 to 50 classes (1, 2, 5, 10, 15, 20, 30, 40, 50).

#### 2.5. Emulation Validation

#### 2.6. Mapping Emulated SIF

#### 2.7. Developed Software for Emulation Applications

## 3. Results

#### 3.1. Analysis of SIF Emulation Strategies

#### 3.2. Application of the Emulator to a Subset of a Flight Line

#### 3.3. Application of the SIF Emulator to an Entire Flight Line and Adjacent Flight Lines

#### 3.4. Application of the SIF Emulator to All Flight Lines

## 4. Discussion

#### 4.1. Interpreting SIF Emulator Results

#### 4.2. Opportunities for Emulation of Spectral Products

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the dimensionality reduction and reconstruction processing steps of the emulator.

**Figure 2.**(

**a**) Location of the study area in the western part of Germany. (

**b**) RGB composite (700.1/754.4/674.4 nm) of the HyPlant FLUO mosaic consisting of seven flight lines (black framed areas) with the subset of flight line L2 used to build the emulator (red framed area). (

**c**) Enlarged view of the subset of flight line L2.

**Figure 3.**Flow chart showing the different parameters that were investigated to identify the optimal emulator. The grey boxes represent the analyzed parameters while the white ellipses indicate the different options tested for each parameter. The dark grey box represents the final emulator obtained with the optimal parameters of the analysis.

**Figure 4.**Spectral NRMSE (in %) results for the regression algorithms performance assessment as function of the five best regression algorithms, using (1000 samples, 20 PCA input, and 5 PCA output).

**Figure 5.**NRMSE (in %) (blue axis) and process time (orange axis) results for the KRR emulator performance assessment varying number of PCs in PCA input conversion (1000 samples, 5 PCA output) (

**b**), and PCA output conversion (1000 samples, 20 PCA input) (

**a**).

**Figure 6.**NRMSE (in %) (blue axis) and associated processing time (orange axis) of the KRR emulators (20 PCA input, 5 PCA output) built with a varying number of training samples.

**Figure 7.**Scatter plot of the SFM SIF map retrieved at 760 nm and the corresponding map emulated with the developed KRR model for the subset of flight line L2. The x-axis represents the SIF values retrieved with the SFM while the y-axis shows the SIF values estimated by the emulator. The dashed line represents the 1:1-line. Units are in (mW m${}^{-2}$ sr${}^{-1}$ nm${}^{-1}$).

**Figure 8.**L2 SFM (

**b**) and emulated SIF map at 760 nm (

**c**) as well as the absolute error map (

**a**) calculated as the difference of both maps.

**Figure 9.**Histogram and boxplot of the absolute error. Lower and upper box boundaries are the 25th and 75th percentiles, respectively; red line medians are the lower and upper whiskers 2th and 98th percentiles, respectively; red crosses are data falling outside the whiskers.

**Figure 10.**Scatter plot of the SFM SIF map retrieved at 760 nm and the corresponding map emulated with the developed KRR model for the entire flight line L2 (

**left**) and flight line L4 (

**right**). The x-axis represents the SIF values retrieved with the SFM while the y-axis shows the SIF values estimated by the emulator. The dashed line represents the 1:1-line. Units are in (mW m${}^{-2}$ sr${}^{-1}$ nm${}^{-1}$).

**Figure 11.**Subset of the emulated SIF mosaic at 760 nm using all investigated flight lines (

**left**). Absolute error map calculated for the emulated and the SFM SIF mosaic at 760 nm (

**right**).

Algorithm | Brief Description | References |
---|---|---|

Neural Networks (NN) | NN are an interconnected group of nodes. Each node represents an artificial neuron with a connection from the output of one neuron to the input of another. Using the training dataset, weights are established for each neuron and the model is able to capture the non-linear relationships of the model. NN is multi-output. | [31] |

Kernel ridge regression (KRR) | KRR minimizes the squared residuals in a higher dimensional feature space and can be considered as the kernel version of the regularized linear regression. KRR is multi-output. | [32,33] |

Multioutput Support Vector Regression (MOSVR) | MOSVR extends the single-output SVR by taking into account the nonlinear relations between features but also among the output variables, which are typically inter-dependent. MOSVR is multi-output. | [34] |

Gaussian process regression (GPR) | GPR is a nonparametric, Bayesian approach to regression. GPR has the ability to provide uncertainty measurements on the predictions. GPR is single-output. | [35,36] |

Matlab Gaussian process regression (GPRM) | GPRM is similar to GPR but with the option to change multiple kernels https://es.mathworks.com/help/stats/kernel-covariance-function-options.html?lang=en, accessed on 29 October 2021. These kernels were initially tested, and the evaluated best trade-off between accuracy and speed was for “Squared Exponential”. GPRM is single-output. | [35] |

Variational Heteroscedastic Gaussian Process Regression (VHGPR) | VHGPR is an anisotropic RBF kernel that has a scale, lengthscale per input feature, and a input-dependent noise power parameter as hyperparameters. VHGPR is single-output. | [37] |

**Table 2.**Statistics obtained from the performance of the models used. RMSE is in (mW m${}^{-2}$ sr${}^{-1}$ nm${}^{-1})$.

MLRA | RMSE | NRMSE (%) | Time Train (s) |
---|---|---|---|

Kernel ridge Regression | 0.30 | 6.09 | 0.57 |

Gaussian Processes Regression-Matlab | 0.30 | 6.71 | 10.55 |

Neural Network | 0.31 | 6.80 | 7.61 |

VH. Gaussian Processes Regression | 0.31 | 6.95 | 80.14 |

Gaussian Processes Regression | 0.31 | 6.96 | 23.80 |

Multioutput Support Vector Regression | 0.32 | 7.08 | 12.33 |

**Table 3.**Determined model performance for unknown flight lines based on different sampling strategies. RMSE is provided in the unit of SIF (mW m${}^{-2}$ sr${}^{-1}$nm${}^{-1})$.

Sampling | Flight Line | RMSE | NRMSE (%) | R^{2} |
---|---|---|---|---|

Random | L3 | 1.14 | 8.16 | 0.81 |

L6 | 0.98 | 5.72 | 0.87 | |

Relative | L3 | 1.22 | 8.76 | 0.78 |

L6 | 1.19 | 6.92 | 0.79 | |

Absolute | L3 | 1.09 | 7.83 | 0.80 |

L6 | 0.90 | 5.28 | 0.87 |

**Table 4.**Goodness-of-fit statistics obtained for the emulated SIF maps of all flight lines. The evaluation has been carried out by comparing the emulated SIF values with the corresponding values of SFM SIF maps on pixel basis.

Acquisition Time (LT) | Direction | Num Pixels (Milions) | Processing Time (s) | RMSE (mW m${}^{-2}$ sr${}^{-1}$ nm${}^{-1})$ | NRMSE (%) | R^{2} | |
---|---|---|---|---|---|---|---|

L1 | 13:54 | N | 2.3 | 185.50 | 0.62 | 5.19 | 0.85 |

L2 | 13:46 | S | 2.3 | 182.93 | 0.73 | 6.42 | 0.82 |

L3 | 13:38 | N | 2.3 | 187.17 | 0.69 | 5.13 | 0.81 |

L4 | 13:30 | S | 2.3 | 185.87 | 0.81 | 5.19 | 0.95 |

L5 | 13:22 | N | 2.3 | 188.52 | 0.80 | 5.06 | 0.91 |

L6 | 13:14 | S | 2.3 | 186.25 | 0.68 | 4.13 | 0.88 |

L7 | 13:06 | N | 1.3 | 68.00 | 0.58 | 5.57 | 0.68 |

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**MDPI and ACS Style**

Morata, M.; Siegmann, B.; Morcillo-Pallarés, P.; Rivera-Caicedo, J.P.; Verrelst, J. Emulation of Sun-Induced Fluorescence from Radiance Data Recorded by the HyPlant Airborne Imaging Spectrometer. *Remote Sens.* **2021**, *13*, 4368.
https://doi.org/10.3390/rs13214368

**AMA Style**

Morata M, Siegmann B, Morcillo-Pallarés P, Rivera-Caicedo JP, Verrelst J. Emulation of Sun-Induced Fluorescence from Radiance Data Recorded by the HyPlant Airborne Imaging Spectrometer. *Remote Sensing*. 2021; 13(21):4368.
https://doi.org/10.3390/rs13214368

**Chicago/Turabian Style**

Morata, Miguel, Bastian Siegmann, Pablo Morcillo-Pallarés, Juan Pablo Rivera-Caicedo, and Jochem Verrelst. 2021. "Emulation of Sun-Induced Fluorescence from Radiance Data Recorded by the HyPlant Airborne Imaging Spectrometer" *Remote Sensing* 13, no. 21: 4368.
https://doi.org/10.3390/rs13214368