# Retrieval of Seasonal Leaf Area Index from Simulated EnMAP Data through Optimized LUT-Based Inversion of the PROSAIL Model

^{*}

## Abstract

**:**

^{2}= 0.65, RMSE = 0.64) is adapted to simulated EnMAP data, generated from the airborne acquisitions. The comparison of the retrieval results to upscaled maps of LAI, previously validated on the 4 m scale, shows that the optimized retrieval method can successfully be transferred to spaceborne EnMAP data.

## 1. Introduction

## 2. Material & Methods

#### 2.1. Introduction to the Study Area

^{2}large test site in Southern Germany (Neusling, Lower Bavaria, central coordinates: 48.69°N, 12.87°E). The seasonal campaign was complemented by two additional acquisitions from the airborne sensor HySpex, which is operated by the German Aerospace Center (DLR) [20].

**Figure 1.**Locations of the elementary sampling units, presented as collected LAI values, for the six airborne acquisition dates (UL: 28 April 2012, UR: 8 May 2012, ML: 25 May 2012, MR: 16 June 2012, LL: 12 August 2012, LR: 8 September 2012). Fields that are cultivated with the crops investigated in this study (rapeseed, winter wheat, winter barley, sugar beet, maize) are highlighted in greenish colors. Field boundaries are displayed in yellow.

Acquisition Date | Sensor | Sun Zenith (°) | Sun Azimuth (°) |
---|---|---|---|

28 April | AVIS-3 | 42 | 132 |

8 May | HySpex | 45 | 115 |

25 May | AVIS-3 | 39 | 236 |

16 June | AVIS-3 | 28 | 146 |

12 August | HySpex | 42 | 133 |

8 September | AVIS-3 | 45 | 155 |

#### 2.1.1. Data Preprocessing

#### 2.1.2. Data Transfer to EnMAP Scale

#### 2.2. Parameter Retrieval through Look-Up Table Inversion

#### 2.2.1. Input Parameter Setting

Model | Parameter | Min | Max | Mean | Std. Dev. |
---|---|---|---|---|---|

PROSPECT-5b | Leaf chlorophyll content [µg/cm^{2}] | 0 | 90 | 50 | 40 |

Leaf carotenoid content [µg/cm^{2}] | 0 | 20 | 10 | 7 | |

Brown pigment content [-] | 0 | 1.5 | 0.2 | 0.8 | |

Equivalent water thickness [cm] | 0 | 0.05 | 0.02 | 0.025 | |

Leaf mass per unit leaf area [g/cm^{2}] | 0 | 0.02 | 0.01 | 0.01 | |

Structure coefficient [-] | 1 | 2.5 | 1.5 | 1 | |

4SAIL | Average leaf angle [°] | 30 | 80 | 60 | 20 |

Leaf area index [m^{2}/m^{2}] | 0 | 7 | 3.5 | 2.5 | |

Hot spot [-] | 0 | 1 | 0.45 | 0.6 | |

Soil coefficient [-] | 0 | 1 | 0.5 | 0.5 |

#### 2.2.2. Inversion Sequence

#### 2.3. Selection Criteria

#### 2.3.1. Band Selection

#### 2.3.2. Artificial Noise

^{2}) in the Gaussian distribution [36].

- ${R}_{ns}\left(\text{\lambda}\right)$ simulated reflectance value for band λ with noise
- ${R}_{sim}\left(\text{\lambda}\right)$ simulated reflectance value for band λ
- $\chi \left(0,\text{\sigma}\right)$ Gaussian distribution (mean value 0 and standard deviation σ)
- $\text{\sigma}\left(\text{\lambda}\right)$ uncertainties within the Gaussian distribution for band λ

#### 2.3.3. Cost Function

- ${R}_{msd}\left(\text{\lambda}\right)$ measured reflectance at band λ
- ${R}_{sim}\left(\text{\lambda}\right)$ simulated reflectance at band λ
- ${\overline{R}}_{msd}$ mean of measured reflectance among all bands

#### 2.3.4. Ill-Posed Problem & Averaging Method

#### 2.4. Design of Retrieval Procedure

## 3. Results

#### 3.1. Validation of the Estimation Quality

^{2}), slope (m) and intercept (b) of Theil-Sen regression and relative RMSE (RRMSE). Figure 2 presents the result of the inversion loop for the inverse-multiplicative noise type, which turned out to perform best among all five noise types. The figure contains eight accuracy (NSE) matrices, representing the combinations of the four cost functions and two averaging methods. Each matrix contains 441 squares, giving the accuracy for every possible combination of the 21 settings of corresponding noise (σ) and the number of considered fits, which also have been tested in 21 settings. This style of presentation was chosen, since it was expected that the two selection criteria having the greatest influence would be the amount of noise, i.e., the standard deviation (σ), which was added to the simulated data, and the number of multiple solutions, i.e., best fits (n), which were considered and averaged for the parameter retrieval.

**Figure 2.**Accuracy matrices for the inverse-multiplicative noise type. The matrices are sorted by cost function/averaging method and show the estimation accuracy (NSE) for each combination of noise variance and number of considered best fits. The blue-marked square at the Laplace/median matrix represents the combination (σ = 9%, n = 700) with the highest accuracy among all possible combinations of selection criteria, including noise type.

^{2}, slope (m) and normalized intercept (b) instead of NSE. Since the values of intercept strongly depend on the absolute values of the data in general, a normalized version was generated by dividing it by the standard deviation of the in-situ data. This ensures comparability and provides a more accurate assessment. Since the RMSE shows behavior almost identical to the RRMSE, it is not included.

**Figure 3.**Alternative accuracy matrices (RRMSE, R

^{2}, m, b) for the Laplace/median combination based on inverse-multiplicative noise, which has been identified as resulting in the highest accuracy based on the NSE. The marked square shows the position of the best solution selected by the NSE.

^{2}show a comparatively similar behavior to the NSE matrix of Figure 2, which almost confirms the position of the best fit. By contrast, slope and normalized intercept show a distinct deviation to the NSE pattern. Furthermore, the slope value of 0.68 lies far beyond the range of recommended values to indicate agreement [41]. As mentioned before, a divergent slope leads to an asymmetry between the observed and estimated data and therefore identifies the formerly determined best fit combination as inappropriate.

**Figure 4.**Accuracy matrix for the Laplace/median combination based on inverse-multiplicative noise after the rejection threshold for slope (0.8 ≤ m ≤ 1.2) and intercept (≤1.00) was applied. The red-marked square shows the combination with the highest accuracy (σ = 4%, n = 350), which resulted in a value for NSE of 0.62 after the exclusion of inappropriate combinations due to the thresholds. For comparison, the blue-marked square shows the position of the formerly identified ideal criteria combination, which had been derived without taking slope and intercept of the regression into account.

^{2}, RMSE and RRMSE provided higher accuracies in the original LUT setting, the scatter plot (Figure 5, left) shows an asymmetry which is distinctly reduced after the application of the rejection threshold (Figure 5, right). It is assumed that the asymmetry, which is visible through a high minimum and a low maximum value in the estimated data, originated from the input parameter setting of the LUT following a Gaussian distribution. Since most LAI values of the input data scatter around values >2.0 and <5.0, a consideration of a high number of solutions leads to strong generalization and consequently to a loss of information. This is due to the fact that, in addition to the LUT spectra that are based on matching LAI information, a high number of other spectra are considered, which are based on input parameters with the most common LAI values, i.e., >2.0 and <5.0. The amount of noise might have an influence as well, since all combinations based on values >5% were also rejected.

**Figure 5.**Correlation of observed and estimated LAI. (

**Left**) The scatter plot is based on the LUT criteria setting (Laplace/median, n = 700, σ = 9%, inverse-multiplicative noise), which resulted in the highest accuracy according to NSE; (

**Right**) The scatter plot is based on the highest accuracy after applying the slope/intercept rejection threshold (n = 350, σ = 4%).

**Figure 6.**Seasonal development of LAI for the five investigated crops throughout the growing period of 2012, derived from six data acquisitions.

#### 3.2. Transferability to the EnMAP Scale

**Figure 7.**Comparison of estimated LAI (8 May 2012), which was derived by the adapted LUT algorithm from simulated EnMAP data (

**Left**) and upscaled (from 4–30 m) LAI estimation based on the 4 m airborne data (

**Right**).

**Figure 8.**Standard deviation of all considered estimated LAI values (n = 350) before averaging, giving a spatial measure of model uncertainty for the retrieval of LAI from simulated EnMAP data (

**Left**) and from airborne data (

**Right**).

**Figure 9.**Difference map calculated from the LAI estimations based on simulated EnMAP and upscaled original airborne data (

**Left**) and density plot showing a pixel-wise comparison of both spatial data sets (

**Right**).

## 4. Discussion

## 5. Conclusions

^{2}= 0.65, RMSE = 0.64, RRMSE = 0.17, m = 0.80 and b = 0.77) applying the following strategy: (i) by using the Laplace Distribution as cost function; (ii) by adding an inverse-multiplicative noise type; (iii) by adjusting the noise level to σ = 4%; (iv) by averaging the best 350 out of 100,000 fits from the LUT and (v) by using the median as the averaging method. It was also found that the impact of noise level, averaging method and number of considered best fits on the retrieval quality was high, while the impact of noise type and cost function was low.

^{2}= 0.96, RMSE = 0.32, RRMSE = 0.18, m = 1.01 and b = 0.10), it was shown that the determined analysis method can successfully be applied to data constructed according to the radiometric, spectral and spatial characteristics of the upcoming EnMAP Hyperspectral Imager. Due to the lower radiometric and spectral quality of the satellite-based measurements compared to the airborne acquisitions, the model uncertainty was increased by 3% for the simulated satellite data. Taking this increased uncertainty into account, the proposed method will be applicable to real EnMAP data.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Locherer, M.; Hank, T.; Danner, M.; Mauser, W.
Retrieval of Seasonal Leaf Area Index from Simulated EnMAP Data through Optimized LUT-Based Inversion of the PROSAIL Model. *Remote Sens.* **2015**, *7*, 10321-10346.
https://doi.org/10.3390/rs70810321

**AMA Style**

Locherer M, Hank T, Danner M, Mauser W.
Retrieval of Seasonal Leaf Area Index from Simulated EnMAP Data through Optimized LUT-Based Inversion of the PROSAIL Model. *Remote Sensing*. 2015; 7(8):10321-10346.
https://doi.org/10.3390/rs70810321

**Chicago/Turabian Style**

Locherer, Matthias, Tobias Hank, Martin Danner, and Wolfram Mauser.
2015. "Retrieval of Seasonal Leaf Area Index from Simulated EnMAP Data through Optimized LUT-Based Inversion of the PROSAIL Model" *Remote Sensing* 7, no. 8: 10321-10346.
https://doi.org/10.3390/rs70810321