# Validation of Sentinel-3 SLSTR Land Surface Temperature Retrieved by the Operational Product and Comparison with Explicitly Emissivity-Dependent Algorithms

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## Abstract

**:**

## 1. Introduction

## 2. Study Site and Ground Data

#### 2.1. Site

^{2}rice paddy area located near Valencia, Spain (39.274°N, −0.317°E; WGS-84). This extensive area is bordered by the city of Valencia in the north, the Mediterranean Sea in the east, and tree crops and small urban areas in the south and west. Due to rice phenology, over the year, three different homogeneous land covers alternate (Figure 1). Full vegetation covers July to mid-September; flooded surface (i.e., water) in December, January, and June; and bare soil from February to May, which is wet during February, and dry from March to May. These seasonal changes allow us to validate over three different homogeneous land covers at a single site (i.e., as if we were observing three different sites). The SLSTR L2 fraction of vegetation cover data in Figure 2 show the typical seasonal changes. The composition of the bare soil found at the rice paddy site is: 14% sand, 50% silt, and 37% clay, with 4.5 % of organic matter (further soil details are provided in [24]). Based on SLSTR Level 1 (L1) auxiliary data (See Section 2.3), over the year the atmospheric WVC at the study site varies between 0.5 and 4 cm.

^{2}) centered on the study area and for a Landsat TM5 scene (~16 km

^{2}). In [30], the authors analyzed the variability of 11 × 11 ASTER pixels (1 km

^{2}) centered on the study area, and obtained a SD < 0.3 K. In [27], the thermal variability of the area was studied for the three land covers present at the site with hand-held radiometer measurements along transects (~300 m long) through the station parcel on different dates: the SD values obtained were 0.5 K, 0.4 K, and 0.9 K for full vegetation, flooded soil, and bare soil, respectively.

#### 2.2. Ground Data

#### 2.2.1. SI-121 Radiometer

^{2}. A second SI-121 radiometer was set up at 53° from zenith to provide measurements representative of the downwelling hemispheric radiance [32]. Measurements were taken from both SI-121 radiometers every 4 s; the two radiometers were periodically cleaned and calibrated against a Landcal blackbody source P80P for temperatures ranging between 273 K and 313 K. The uncertainty obtained for both SI-121 radiometers was less than ±0.1 K. The manufacturer specification uncertainty (±0.2 K) was used instead the calibration uncertainty. During the Fiducial Reference Measurements for validation of surface temperature from satellites (FRM4STS) experiment in June 2016, the blackbody source was calibrated against the National Physics Laboratory (NPL) reference radiometer (AMBER), characterized with an uncertainty of 0.053 K [25]. The blackbody showed good agreement in the temperature range from 273 to 323 K with a root mean square difference (RMSD) of 0.05 K [33,34].

#### 2.2.2. CIMEL Electronique CE-312 Radiometers

#### 2.2.3. In-Situ Land Surface Emissivity

^{3}m

^{−3}, were used. For dry bare soil, emissivity values of the soil sample with soil moisture of 0.03 m

^{3}m

^{−3}were used.

#### 2.3. SLSTR Level 1 Data

## 3. LST Retrieval Algorithms

#### 3.1. Operational SLSTR LST Product

#### 3.2. Proposal of Two Algorithms Adapted to SLSTR

#### 3.2.1. CLAR Database and Simulation Dataset

_{0}− 6 K, T

_{0}− 2 K, T

_{0}+ 1 K, T

_{0}+ 3 K, T

_{0}+ 5 K, T

_{0}+ 8 K, and T

_{0}+ 12 K following the global analysis performed in [50]. The dataset contained a total of 16,044 different cases and was used to obtain the algorithm coefficients.

#### 3.2.2. Split-Window Algorithm

_{0}to a

_{10}are given in Table 2. Emissivities obtained for each land cover (Table 1) and WVC from SLSTR L1 auxiliary data were used for the application of the algorithm.

_{0}to a

_{5}) in Equation (3) were obtained from regression analyses between LST–T

_{11}and T

_{11}–T

_{12}in Figure 4, using the blackbody approach (ε = 1 and Δε = 0 [51]) and, therefore, the obtained coefficients are independent from emissivity. The emissivity correction term is controlled by α and β [52], which depend on atmospheric parameters (i.e., atmospheric transmissivity, at-surface brightness temperature, and effective atmospheric temperature).

_{AC}is the fitting error associated with the atmospheric coefficients (from a

_{0}to a

_{5}) and σ

_{α}and σ

_{β}are the fitting errors associated with α and β, respectively. The fitting error was defined as the standard error obtained from the regression analyses for each set of coefficients. The regression standard error was estimated by minimizing the sum of squared deviations from the predictions over the simulation dataset. The propagation uncertainty of the input parameters is expressed by Equation (6), where the partial derivative of $T$ with respect to each input parameter ${x}_{i}$ (i.e., emissivity, WVC, brightness temperatures) is estimated and multiplied by uncertainty $\delta {x}_{i}$. The experimental emissivity uncertainties in Table 1 were assigned and WVC uncertainty was assumed to be ±0.5 cm, which is considered to be a representative value [15,21]. Brightness temperature uncertainty is the noise equivalent error of the instrument, which is about ±0.05 K for the SLSTR thermal bands at 11 and 12 µm for a temperature of 270 K [53]. As the latter is a random uncertainty element, it must be divided by the square root of the number of pixels used to average the LST [54]. The mean and SD of the LST uncertainty contributions from each parameter are given in Table 3. Full vegetation and flooded soil were grouped together due to their similar emissivity values and were assigned the same emissivity uncertainties. For all cases, the main uncertainty sources were modeling and emissivity.

#### 3.2.3. Dual-Angle Algorithm

_{0}to c

_{2}are the atmospheric coefficients, ${T}_{n}$ and ${T}_{b}$ are the brightness temperatures corresponding to nadir view (n) and backward view (b). $\epsilon $ is the mean emissivity for SLSTR nadir and backward views ($\epsilon =0.5\left({\epsilon}_{n}+{\epsilon}_{b}\right))$ and ∆ε is the emissivity difference between nadir and backward views ($\Delta \epsilon ={\epsilon}_{n}-{\epsilon}_{b})$; $\alpha =\left({c}_{3}+{c}_{4}W+{c}_{5}{W}^{2}\right)$ ) and $\beta =\left({c}_{6}+{c}_{7}W\right)$ are functions modifying the impact of emissivity on LST retrieval, where W is the water vapor content. The coefficients determined for the two DAAs (one for each channel) are given in Table 2.

#### 3.3. Alternative Split-Window Algorithms

#### 3.3.1. Sobrino16 Split-Window Algorithm

_{0}− 5 K, T

_{0}, T

_{0}+ 5 K, T

_{0}+ 10 K, T

_{0}+ 20 K, where T

_{0}is the air temperature of the lowest level of the atmospheric profile. Additionally, five viewing angles (0°, 10°, 20°, 30°, and 40°) were simulated. Based on the uncertainties of the input parameters (emissivity, WVC and brightness temperatures) and model regression uncertainty, a final algorithm uncertainty of ±1.6 K was estimated [21].

#### 3.3.2. Zhang19 Split-Window Algorithm

_{0}as T

_{0}− 5 K, T

_{0}, T

_{0}+ 5 K, T

_{0}+ 10 K, T

_{0}+ 20 K when T

_{0}> 280 K, and T

_{0}− 5 K, T

_{0}, T

_{0}+ 5 K when T

_{0}≤ 280 K. Average emissivity (ε) was varied from 0.9 to 1.0 in steps of 0.02, and the difference in emissivity (∆ε) varied from 0.02 to −0.02 in steps of 0.005. Simulations were performed for two viewing angles and yielded a total dataset of 30,456 simulated cases. According to [22], the SWA uncertainty ranges between ±0.5 K and ±1 K, depending on WVC. These values represent the uncertainty of the algorithm and do not consider input parameters uncertainties.

#### 3.3.3. Zheng19 Split-Window Algorithm

_{0}, ranging from T

_{0}− 10 K to T

_{0}+ 30 K in steps of 5 K. Sixty emissivity spectra from the ASTER spectral library and the University of California–Santa Barbara Emissivity Library were used to simulate a dataset under five viewing angles (0°, 15°, 25°, 35°, and 45°), which resulted in a total of 2,550,200 different cases.

_{11}and five viewing angles. However, only the coefficients for nadir view and four brightness temperature and WVC subranges were published in [23]. For these subranges, an algorithm uncertainty ranging from ±0.6 K to ±2.1 K was estimated by propagating model regression uncertainty and emissivity uncertainty.

## 4. Validation of Satellite LST Products

#### 4.1. Analysis of In-Situ Measurements

#### 4.2. Operational SLSTR LST Product

_{SLSTR}−T

_{ground}), robust standard deviation (RSD, given by Equation (11)), and robust root mean squared difference (R-RMSD), which is obtained as the square root of the quadratic sum of the median and the RSD.

#### 4.3. LST Retrieved with Explicit Emissivity-Dependent Algorithms

#### 4.4. Proposed Dual-Angle Algorithms

## 5. Discussion

_{0}). These values were determined in [50] from statistical analysis of MODIS products MOD08 and MOD11 for air temperature and LST values, respectively. This statistical analysis showed that the range of temperatures used for the simulation dataset covers most of the cases found over natural surfaces [50]. A maximum increment of up to +20 K was used to produce Sobrino16 and Zhang19, although these increments were only for T

_{0}< 280 K on the latter. The Zheng19 SWA was produced with even larger increments of up to +30 K: this can be interesting for some applications (e.g., urban heat island, analyses of extreme temperatures), but can also cause an overfitting of retrieval coefficients, which in turn can increase retrieval uncertainty, particularly over the most common natural surfaces [64].

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**RGB true color compositions (R-G-B 4-3-2;

**top**) and false color compositions (R-G-B 8-4-3;

**bottom**) for three Sentinel-2 Multispectral Instrument (MSI) scenes. The three land covers at the site are: bare soil (April,

**left**), flooded soil, i.e., water (May,

**center**), full vegetation (August,

**right**). The location of the validation site is shown in the composition.

**Figure 2.**Fraction of vegetation cover given by the SLSTR L2 product as a function of day of year. A representative photo for each land cover is also shown.

**Figure 3.**Angular emissivity variation of the bare soil (

**left**) and flooded soil (

**right**) for the CE-312 channels centered on 11 and 12 µm.

**Figure 4.**LST–T

_{11}against T

_{11}–T

_{12}simulated from the CLAR database at the different view angles for the SLSTR SWA atmospheric coefficients retrieval. The regression functions corresponding to each angular dataset are plotted as lines in the same color as their corresponding data.

**Figure 5.**LST obtained with the fixed SI-121 radiometer compared to LST obtained along the transects with mobile CE-312 radiometers.

**Figure 6.**Operational Sentinel-3A SLSTR LST product against ground LST obtained from the SI-121 radiometer over the three seasonal land cover types at the Valencia rice paddy site. The dark grey and light grey shadows show 1-RSD and 3-RSD around the regression (dashed line).

**Figure 7.**LST retrieved from Sentinel-3A with emissivity-dependent algorithms against in-situ LST obtained from the SI-121 radiometer. Top left: Sobrino16. Top right: Zhang19. Bottom left: Zheng19. Bottom right: the proposed algorithm.

**Figure 8.**SLSTR LST retrieved with the dual-angle algorithms for the 11 µm channel (left; DAA11) and 12 µm channel (right; DAA12) against in-situ LST for the three seasonal land covers at the Valencia rice paddy site.

Land Cover | 8–13.3 µm | 10.9–11.7 µm | 10.2–11.0 µm |
---|---|---|---|

Flooded soil | 0.986 ± 0.005 | 0.991 ± 0.004 | 0.990 ± 0.004 |

Wet bare soil | 0.973 ± 0.012 | 0.977 ± 0.008 | 0.972 ± 0.011 |

Dry bare soil | 0.967 ± 0.016 | 0.972 ± 0.004 | 0.970 ± 0.005 |

Full vegetation soil | 0.983 ± 0.004 | 0.980 ± 0.005 | 0.985 ± 0.004 |

**Table 2.**Coefficients of the proposed split-window algorithm (Equation (3)) and the dual-angle algorithms (Equation (7)).

Coefficient | Split-Window | Coefficient | Dual-Angle 11 µm | Dual-Angle 12 µm |
---|---|---|---|---|

a_{0} (K) | 0.052 ± 0.013 | c_{0} (K) | −0.18 ± 0.02 | −0.27 ± 0.04 |

a_{1} (K) | 0.15 ± 0.02 | c_{1} | 2.03 ± 0.02 | 2.28 ± 0.04 |

a_{2} | 0.95 ± 0.02 | c_{2} (K^{−1}) | 0.114 ± 0.005 | 0.198 ± 0.007 |

a_{3} | −0.30 ± 0.03 | c_{3} (K) | 57.56 ± 0.15 | 66.02 ± 0.19 |

a_{4} (K^{−1}) | 0.305 ± 0.004 | c_{4} (K cm^{−1}) | 1.85 ± 0.11 | −4.35 ± 0.14 |

a_{5} (K^{−1}) | 0.202 ± 0.007 | c_{5} (K cm^{−2}) | −1.278 ± 0.018 | −0.81 ± 0.02 |

a_{6} (K) | 52.51 ± 0.18 | c_{6} (K) | 132.2 ± 0.3 | 139.4 ± 0.4 |

a_{7} (K cm^{−1}) | −0.11 ± 0.12 | c_{7} (K cm^{−1}) | −21.80 ± 0.07 | −26.05 ± 0.11 |

a_{8} (K cm^{−2}) | −1.004 ± 0.018 | − | − | − |

a_{9} (K) | 75.7 ± 0.2 | − | − | − |

a_{10} (K cm^{−1}) | −11.21 ± 0.06 | − | − | − |

**Table 3.**Mean and SD of the uncertainty contributions obtained for the simulation dataset. The different uncertainty sources (modeling uncertainty and input parameters: emissivity, δ(T)

_{ε}; WVC, δ(T)

_{W}; brightness temperature, δ(T)

_{BT}), and total SLSTR LST retrieval uncertainty are shown.

Surface | $\mathit{\delta}$ | Split-Window | Dual-Angle 11 µm | Dual-Angle 12 µm | |||
---|---|---|---|---|---|---|---|

Mean (K) | SD (K) | Mean (K) | SD (K) | Mean (K) | SD (K) | ||

Dry/Wet Bare Soil | $\delta {\left(T\right)}_{\epsilon}$ | 0.50 | 0.14 | 0.74 | 0.10 | 0.76 | 0.12 |

$\delta {\left(T\right)}_{W}$ | 0.09 | 0.04 | 0.03 | 0.02 | 0.04 | 0.02 | |

$\delta {\left(T\right)}_{BT}$ | 0.08 | 0.02 | 0.101 | 0.010 | 0.114 | 0.013 | |

$\delta {\left(T\right)}_{p}$ | 0.52 | 0.13 | 0.75 | 0.10 | 0.77 | 0.11 | |

$\delta {\left(T\right)}_{M}$ | 1.4441 | 0.0009 | 0.9203 | 0.0002 | 1.4996 | 0.0002 | |

$\mathit{\delta}\mathbf{\left(}\mathit{T}\mathbf{\right)}$ | 1.54 | 0.05 | 1.19 | 0.06 | 1.69 | 0.05 | |

Water / Full vegetation | $\delta {\left(T\right)}_{\epsilon}$ | 0.32 | 0.09 | 0.53 | 0.10 | 0.48 | 0.12 |

$\delta {\left(T\right)}_{W}$ | 0.04 | 0.03 | 0.05 | 0.02 | 0.10 | 0.02 | |

$\delta {\left(T\right)}_{BT}$ | 0.09 | 0.02 | 0.109 | 0.006 | 0.131 | 0.010 | |

$\delta {\left(T\right)}_{p}$ | 0.36 | 0.08 | 0.54 | 0.10 | 0.51 | 0.11 | |

$\delta {\left(T\right)}_{M}$ | 1.4362 | 0.0012 | 0.909 | 0.003 | 1.492 | 0.009 | |

$\mathit{\delta}\mathbf{\left(}\mathit{T}\mathbf{\right)}$ | 1.49 | 0.02 | 1.06 | 0.05 | 1.58 | 0.04 |

**Table 4.**Validation statistics for the operational Sentinel-3A SLSTR LST product against in-situ LST for the three land covers at the Valencia rice paddy site. All values are in Kelvin (K) and N is the number of data points.

All Data | Daytime | Nighttime | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MEDIAN | RSD | R-RMSD | N | MEDIAN | RSD | R-RMSD | N | MEDIAN | RSD | R-RMSD | N | |

All Surfaces | 1.3 | 1.3 | 1.8 | 194 | 1.8 | 1.2 | 2.2 | 98 | 1.0 | 1.0 | 1.4 | 96 |

Flooded soil | 1.8 | 1.1 | 2.2 | 44 | 2.2 | 0.7 | 2.3 | 19 | 1.8 | 1.3 | 2.2 | 25 |

Bare soil | 1.1 | 0.7 | 1.3 | 37 | 1.3 | 0.9 | 1.6 | 16 | 0.8 | 0.6 | 1.0 | 21 |

Vegetation | 1.3 | 1.4 | 1.9 | 113 | 1.7 | 1.5 | 2.2 | 63 | 1.0 | 0.9 | 1.3 | 50 |

**Table 5.**Validation statistics for the operational Sentinel-3B SLSTR LST product against in-situ LST for the three land covers at the Valencia rice paddy site. All the statistics are in Kelvin (K) and N is the number of data points.

All Data | Daytime | Nighttime | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MEDIAN | RSD | R-RMSD | N | MEDIAN | RSD | R-RMSD | N | MEDIAN | RSD | R-RMSD | N | |

All Surfaces | 1.5 | 1.2 | 1.9 | 107 | 1.6 | 1.3 | 2.0 | 41 | 1.3 | 1.0 | 1.7 | 66 |

Flooded soil | 2.1 | 0.6 | 2.2 | 48 | 2.5 | 1.1 | 2.7 | 15 | 1.9 | 0.7 | 2.0 | 33 |

Bare soil | 0.8 | 1.1 | 1.3 | 31 | 0.8 | 1.7 | 1.8 | 13 | 0.8 | 1.0 | 1.3 | 18 |

Vegetation | 1.0 | 1.3 | 1.6 | 28 | 1.4 | 0.9 | 1.7 | 13 | 0.5 | 1.2 | 1.3 | 15 |

**Table 6.**Validation statistics for the four emissivity-dependent split-window algorithms for the three land covers at the Valencia rice paddy site. All values are in Kelvin (K) and N is the number of data points.

MEDIAN | RSD | R−RMSD | N | ||
---|---|---|---|---|---|

All Surfaces | Sobrino16 | −0.8 | 0.9 | 1.2 | 198 |

Zhang19 | −0.7 | 1.1 | 1.3 | 198 | |

Zheng19 | 0.4 | 1.1 | 1.2 | 198 | |

Proposed SWA | −0.4 | 1.1 | 1.1 | 198 | |

Flooded Soil | Sobrino16 | −0.4 | 0.6 | 0.7 | 32 |

Zhang19 | −0.5 | 1.0 | 1.1 | 32 | |

Zheng19 | 1.0 | 0.7 | 1.2 | 32 | |

Proposed SWA | 0.0 | 0.6 | 0.6 | 32 | |

Bare Soil | Sobrino16 | −0.4 | 0.9 | 0.9 | 38 |

Zhang19 | −0.5 | 0.6 | 0.8 | 38 | |

Zheng19 | 0.9 | 0.7 | 1.2 | 38 | |

Proposed SWA | −0.2 | 0.9 | 0.9 | 38 | |

Full Vegetation | Sobrino16 | −1.0 | 1.0 | 1.4 | 128 |

Zhang19 | −0.9 | 1.2 | 1.5 | 128 | |

Zheng19 | −0.1 | 1.3 | 1.3 | 128 | |

Proposed SWA | −0.7 | 1.2 | 1.4 | 128 |

**Table 7.**Validation statistics for the different emissivity-dependent split-window algorithms. Results are shown for all data and separately for flooded soil, bare soil, and full vegetation cover. All values are in Kelvin (K).

Daytime | Nighttime | ||||||
---|---|---|---|---|---|---|---|

MEDIAN | RSD | R−RMSD | MEDIAN | RSD | R−RMSD | ||

All Surfaces | Sobrino16 | −0.8 | 1.2 | 1.5 | −0.9 | 0.8 | 1.2 |

Zhang19 | −0.5 | 1.3 | 1.4 | −0.9 | 0.8 | 1.2 | |

Zheng19 | 0.5 | 1.4 | 1.5 | 0.2 | 1.1 | 1.1 | |

Proposed SWA | −0.3 | 1.5 | 1.5 | −0.5 | 0.8 | 0.9 | |

Flooded Soil | Sobrino16 | −0.3 | 0.7 | 0.7 | −0.5 | 0.6 | 0.8 |

Zhang19 | −0.4 | 0.8 | 0.9 | −0.9 | 0.9 | 1.2 | |

Zheng19 | 1.1 | 0.6 | 1.3 | 0.9 | 0.9 | 1.3 | |

Proposed SWA | 0.2 | 0.7 | 0.8 | −0.1 | 0.7 | 0.7 | |

Bare Soil | Sobrino16 | −0.4 | 1.5 | 1.5 | −0.4 | 0.8 | 0.9 |

Zhang19 | 0.6 | 1.5 | 1.6 | −0.6 | 0.7 | 1.0 | |

Zheng19 | 0.8 | 1.4 | 1.6 | 1.0 | 0.5 | 1.1 | |

Proposed SWA | 0.2 | 1.5 | 1.5 | −0.2 | 0.6 | 0.6 | |

Full Vegetation | Sobrino16 | −1.3 | 1.5 | 1.9 | −1.0 | 0.7 | 1.2 |

Zhang19 | −0.7 | 1.5 | 1.7 | −0.9 | 0.8 | 1.2 | |

Zheng19 | 0.0 | 1.4 | 1.4 | −0.1 | 0.9 | 0.9 | |

Proposed SWA | −0.8 | 1.6 | 1.8 | −0.7 | 0.8 | 1.0 |

**Table 8.**Validation statistics of the dual-angle algorithms for SLSTR 11 and 12 µm channels at the Valencia rice paddy site. All statistics are in Kelvin (K) and N is the number of data points.

Dual-Angle 11 µm | Dual-Angle 12 µm | |||||||
---|---|---|---|---|---|---|---|---|

MEDIAN | RSD | R-RMSD | N | MEDIAN | RSD | R-RMSD | N | |

All Surfaces | 1.7 | 1.6 | 2.3 | 102 | 2.2 | 1.7 | 2.7 | 102 |

Flooded Soil | 0.6 | 1.0 | 1.1 | 15 | 1.0 | 2.3 | 2.5 | 15 |

Bare soil | 1.0 | 1.3 | 1.7 | 18 | 1.4 | 1.2 | 1.8 | 18 |

Vegetation | 2.1 | 1.2 | 2.5 | 69 | 2.6 | 1.5 | 3.0 | 69 |

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**MDPI and ACS Style**

Pérez-Planells, L.; Niclòs, R.; Puchades, J.; Coll, C.; Göttsche, F.-M.; Valiente, J.A.; Valor, E.; Galve, J.M.
Validation of Sentinel-3 SLSTR Land Surface Temperature Retrieved by the Operational Product and Comparison with Explicitly Emissivity-Dependent Algorithms. *Remote Sens.* **2021**, *13*, 2228.
https://doi.org/10.3390/rs13112228

**AMA Style**

Pérez-Planells L, Niclòs R, Puchades J, Coll C, Göttsche F-M, Valiente JA, Valor E, Galve JM.
Validation of Sentinel-3 SLSTR Land Surface Temperature Retrieved by the Operational Product and Comparison with Explicitly Emissivity-Dependent Algorithms. *Remote Sensing*. 2021; 13(11):2228.
https://doi.org/10.3390/rs13112228

**Chicago/Turabian Style**

Pérez-Planells, Lluís, Raquel Niclòs, Jesús Puchades, César Coll, Frank-M. Göttsche, José A. Valiente, Enric Valor, and Joan M. Galve.
2021. "Validation of Sentinel-3 SLSTR Land Surface Temperature Retrieved by the Operational Product and Comparison with Explicitly Emissivity-Dependent Algorithms" *Remote Sensing* 13, no. 11: 2228.
https://doi.org/10.3390/rs13112228