*3.2. Ground-Based Measurements*

Ground positioning measurements were performed using RTK-differential GNSS, achieving centimetric accuracy after post-processing of the base station. The device used for this study was a Topcon® HiPer V GNSS receiver. The same base receiver was used both for ground measurements and for the navigation module of Hyper-DRELIO.

The in situ data for radiometric standardization and validation were measured with a GER 1500 field spectrometer (developed by Spectra Vista Corporation®), providing fast, at-target radiance measurements from 350 nm to 1050 nm. Each measurement was triplicated and averaged. A white SpectralonTM panel with a reflectivity of 99% allowed an indirect measurement of the irradiance. This Spectralon (Figure 2c) was a 40 × 40 cm white reference panel made of a fluoropolymer, which is highly reflective (the highest diffuse reflectance of any known material) and has Lambertian behavior [48]. This SpectralonTM panel is placed on flat ground near the take-off area. For the initial calibration, a grey SpectralonTM (Figure 2d), with a reflectivity of 20%, was also used. As 20% reflectivity is closed to the reflectance of bare mud, this grey SpectralonTM was also used to adjust the parametrization of the hyperspectral camera (aperture and sensor gain G) before the flight.

The spectrometer measurements were carried out in a flight-synchronous manner on different types of substrates. In order to limit the movements of the operators, which were very slow, difficult, and very destructive for the mudflat, these measurements were carried out around a fixed platform placed on the mud.

#### *3.3. Radiometric Correction Method*

Radiometric corrections aim to convert the raw digital numbers (DN) recorded by the sensor into remote sensing reflectance. Once the reflectance is computed, hyperspectral images can be exploited in different ways, such as computation of spectral indices for classification (e.g., [49,50]), study of the red edge position (e.g., [51]), or spectral unmixing [52].

For hyperspectral measurements acquired with drones, radiometric corrections were realized using complementary in situ data. Given the practical challenges in carrying out

surveys in mangrove or mudflat areas, the proposed method must be easy to implement, without adding embedded sensors and with as little equipment as possible. Computational routines to apply corrections were implemented in Matlab®, including several steps, which are summarized in Figure 3. During the acquisition, the signal was impacted by noise, called the dark current (DC) [53], which is partly function of sensor temperature and partly integration time. In our case, this DC is assumed steady. Furthermore, as the survey was focused on mudflats, the topographic effects could be neglected. Finally, as the flight altitude remained low (<150 m), we hypothesized that the at-target radiance was equal to the at-sensor radiance at 50 m height [54]. To validate this hypothesis, raw spectra (in DN) were measured by the hyperspectral camera above the white SpectralonTM panel, both from the ground and in flight. The mean difference between the "on ground" spectra and "on flight" spectra was about 7.5% with a standard deviation of 5.3% and a preserved shape of spectra.

**Figure 3.** Processing steps performed for radiometric corrections ("*i*" is the index of the pixel along the sensor array, in the across-track spatial dimension).

#### 3.3.1. Initial Calibration

Hyperspectral images suffer from variations or distortions of the spectrogram along the CCD array (possibly caused by the quality of the dispersive element or misalignments of the light from the slit). This results in vertical "stripes" in our push broom images. This spatial dependence of DN, and particularly its decrease towards the image edges, is called the "vignetting effect" for frame sensors [53] and corresponds rather to the "lining effect" for push broom sensors.

The calibration parameters aim to compensate for this effect and to convert DN to physical units of radiance. We chose an image-based calibration method, and we assumed a linear relationship between the DN and the at-sensor radiance [54,55], according to the following empirical transfer function (Equation (1)):

$$\text{Rad}\_{\mathbb{C}}(\lambda, \mathbf{i}) = \mathbf{a}(\lambda, \mathbf{i}) \times \text{DN}\_{\mathbb{C}}(\lambda, \mathbf{i}) / G\_{\mathbb{C}} + \mathbf{b}(\lambda, \mathbf{i}) \tag{1}$$

With the following:

λ: wavelength (nm);

i: index of the pixel in the sensor array;

RadC: at-sensor radiance (W·m−2·sr<sup>−</sup>1) during calibration step;

GC: sensor gain during calibration step;

DNC: digital number collected during calibration step;

a, b: calibration coefficients.

To calculate *a* and *b* coefficients, we considered the radiance measured by the field spectrometer above both white and grey Spectralon panels, and the DN measured simultaneously by the hyperspectral camera. Each Spectralon was thus targeted simultaneously by the GER1500 field spectrometer and by the hyperspectral camera, while the drone was on the ground, in such a way that the field spectrometer and the hyperspectral camera were at the same distance from the Spectralon panel and the measurements were synchronized. The *a* and *b* coefficients were calculated per pixel and per spectral band, according to the following equations (Equation (2)):

$$\begin{cases} \begin{array}{c} a(\lambda, \text{i}) = G\_{\mathbb{C}} \times \frac{Rad\_{Sp1}(\lambda, \text{i}) - Rad\_{Sp2}(\lambda, \text{i})}{\left[DN\_{Sp1}(\lambda, \text{i}) - DN\_{Sp2}(\lambda, \text{i})\right]}\\ b(\lambda, \text{i}) = Rad\_{Sp1}(\lambda, \text{i}) - \frac{a}{G\_{\mathbb{C}}} DN\_{Sp1}(\lambda, \text{i}) \end{array} \tag{2}$$

With the following:

*Sp*1, *Sp*2: ID of each Spectralon used for the calibration;

*RadSp*1, *Sp*2: radiance (W·m−2·sr−1) measured by the field spectrometer above the *Sp*<sup>1</sup> (respectively, *Sp*2) Spectralon;

*DNSp*1, *Sp*2: digital number collected by the hyperspectral camera above the *Sp*1 (respectively, *Sp*2) Spectralon.

To avoid local effects due to possible wear marks on the Spectralon surface, several hyperspectral lines were recorded by the hyperspectral camera (500 lines were selected and averaged) and 8 spectra were measured by the field spectrometer from various directions and averaged. To visually confirm the efficiency of this calibration, *a* and *b* coefficients were applied to *DNSp*<sup>1</sup> (respectively, *DNSp*2), measured above the white Spectralon (respectively, the grey Spectralon). The results above the white Spectralon, before and after calibration, are depicted in Figure 4, representing, in natural colors, the hyperspectral lines collected by the camera.

**Figure 4.** Hyperspectral lines collected above the white Spectralon by the hyperspectral camera before (**a**,**c**) and after (**b**,**d**) calibration. (**a**,**b**) represent, in natural colors, the hyperspectral lines collected by the camera; (**c**,**d**) represent the values of digital number (DN) (**c**) and radiance (**d**) along the sensor line for each spectral band (in colors).

This calibration step was carried out once (at least for the entire field campaign) and the coefficients were then applied to all the different following surveys. The *a* and *b* coefficients are exported to a "calibration file", which will be reused in the in situ standardization step.

## 3.3.2. In Situ Standardization

For each in situ survey, the collected data DNIS are calibrated using the *a* and *b* coefficients (Equation (1)). Applying Equation (1) enables compensation for the lining effects and provides a result with physical units of radiance; however, this is not the real in situ at-target radiance. Indeed, considering Equation (2), the *a* and *b* coefficients are related to the illumination conditions at the moment of the dual Spectralon measurements with both hyperspectral sensors during the calibration step. Therefore, Equation (1) needs to be standardized to the in situ atmospheric conditions at the time of the survey.

For each survey, before the flight, the irradiance was indirectly measured on the white 99% Spectralon panel, by the hyperspectral camera, held about 30 cm above the Spectralon. During this step, the operators had to be careful not to create shade on the Spectralon, which can be complicated when placing the drone-borne camera above it. As for the calibration step, to avoid local effects due to possible wear marks on the Spectralon surface, several hyperspectral lines recorded by the camera were selected and averaged. The irradiance before the flight was also measured with the field spectrometer, which was targeted to the white 99% Spectralon almost simultaneously with the hyperspectral camera, and from the same distance of about 30 cm, to serve as a reference for temporal variations of irradiance.

The sensor gain (*GIS*) at the time of the survey also needed to be taken into account. The in situ sensor gain (*GIS*) is adjusted before the flight, according to the illumination conditions, to avoid signal saturation. Therefore, it can be different from the gain GC used during the calibration step. Besides, if the flown-over area is expected to have a low reflectivity, the in situ gain in flight (*GIS\_Fl*) can also be parametrized differently from the in situ gain used, above the 99% Spectralon *GIS\_Sp*.

The in situ reflectance was calculated by forming the ratio of the upwelling radiation to the downwelling radiation. This is given by Equation (3):

$$R(\lambda, \mathbf{i}) = \frac{a(\lambda, \mathbf{i}) \times \frac{D N\_{IS\_{FI}}(\lambda, \mathbf{i}, \mathbf{i})}{G\_{IS\_{FI}}} + b(\lambda, \mathbf{i})}{a(\lambda, \mathbf{i}) \times \frac{D N\_{IS\_{Sp}}(\lambda, \mathbf{i})}{G\_{IS\_{Sp}}} + b(\lambda, \mathbf{i})} \tag{3}$$

With the following:

*GIS Sp*: sensor gain used during in situ measurements of the 99% Spectralon; *GIS Fl*: sensor gain used during the in situ flight;

*DNIS Sp*: digital number collected in situ by the hyperspectral camera of the 99% Spectralon; *DNIS Fl*: digital number collected in situ by the hyperspectral camera during the flight; *R*: resulting remote-sensing reflectance.

#### 3.3.3. Taking Temporal Variations of Irradiance into Account

The illumination changes during data acquisition are generally pointed as a source of difficulties in hyperspectral surveys [22,56]. Our approach to addressing this issue is almost comparable to the "dual-spectrometer" method, proposed for a ground-based system in Bachmann et al. [48], and consists of monitoring illumination change using a reference panel, simultaneously with data acquisition [22].

To mitigate the variations of ambient light, the field spectrometer regularly recorded the irradiance above the white Spectralon (with a time-step from 10 s to 20 s) (Figure 5a). The internal clock of the field spectrometer was synchronized with the GPS time (used in the header file of the hyperspectral camera). We hypothesized that the shape of the irradiance spectra would vary linearly over time, mainly according to a single, timedependent multiplying coefficient called τ (Figure 5b). The τ coefficients, calculated for

each field spectrometer record, were then interpolated over time to obtain a coefficient for irradiance evolution (τ(t)) throughout the survey (Figure 5c). This dimensionless coefficient represents the percentage of irradiance variation in comparison to the irradiance measured just when the in situ standardization was performed (t0). Therefore, τ is equal to 1 when the illumination does not change, greater than 1 if the illumination increases, and lower than 1 if it decreases. To take into account the variations of irradiance, Equation (3) is changed into Equation (4):

$$R(\lambda, \mathbf{i}) = \frac{a(\lambda, \mathbf{i}) \times \frac{DN\_{IS\_{Fl}}(\lambda, \mathbf{i}, \mathbf{t})}{G\_{IS\_{Fl}}} + b(\lambda, \mathbf{i})}{\pi(\mathbf{t}) \times a(\lambda, \mathbf{i}) \times \frac{DN\_{IS\_{Sp}}(\lambda, \mathbf{i})}{G\_{IS\_{Sp}}} + b(\lambda, \mathbf{i})} \tag{4}$$

where the τ coefficient represents the percentage of irradiance variation during the flight.

**Figure 5.** (**a**) Field spectrometer (GER 1500) measuring the irradiance variability above the white Spectralon. (**b**) Example of variability of the spectra measured by the field spectrometer during a flight. (**c**) Example of the τ coefficient interpolated (green line) from the percentage of irradiance variations measured (red dots) during the flight.

To complete this procedure of radiometric corrections, a signal enhancement was performed, using a minimum noise fraction (MNF) transform, as implemented in *ENVI*® software (modified from [57]). A forward transform is performed to manually identify the bands containing the coherent images and those containing noise-dominated images. Noise is removed from the data by performing an inverse transform using a spectral subset which only includes the bands with a high signal-to-noise ratio.
