# Climate Data Records of Vegetation Variables from Geostationary SEVIRI/MSG Data: Products, Algorithms and Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Algorithm Description

#### 2.1. SEVIRI/MSG

_{0}, k

_{1}, k

_{2}). The input of the FVC algorithm is atmospherically corrected BRDF k

_{0}parameters in the MSG channels 1, 2 and 3, while FAPAR uses all three BRDF parameters (k

_{0}, k

_{1}, k

_{2}) in order to correct surface’s reflectance anisotropy and minimize the effect of soil reflectance (see Figure 1). The algorithm to correct atmospheric effects and generate BRDF model parameters is fully described in [33], and in the ATBD of the Albedo MSG product [34].

#### 2.2. FVC Algorithm

**r**be the spectrum of each mixture pixel, i.e., a column vector (r

_{1},r

_{2},...,r

_{n}), where n is the total number of bands. When multiple scattering can be reasonably disregarded, the spectral reflectance of each pixel can be approximated by a linear mixture of pure spectra

**E**(the so-called endmembers) weighted by their corresponding fractional abundances:

**r =E f + ε,**

**E**[n × c] is the matrix of endmembers,

**f**is a vector with the c unknown proportions in the mixture, and

**ε**is the residual vector. The mixing equation is accompanied by two constraints: (1) the normalization constraint says proportions should sum up to one, and (2) the positivity constraint says that no endmember can make a negative contribution. The least-square principle establishes that the unknown parameters are those that minimize the Mahalanobis distance between the pixel

**r**and point

**E f**:

**χ2 =(r – E f)**

^{T}V(r)^{−1}(r – E f)**V**(

**r**) denotes the error matrix of the observations

**r**. The coarse spatial resolution of SEVIRI and the availability of only three spectral bands poses a significant challenge for endmember selection in traditional (deterministic) SMM. The FVC algorithm relies on a novel stochastic SMM which uses a statistical representation of the endmembers to accommodate their variability at a global scale. Each pixel is described by a multiple combination of two pure classes, the target (vegetation) and the background (soil). Both vegetation and soil classes are not treated as deterministic (i.e., using fixed endmembers) but they follow a statistical (multi-modal) distribution, which attempts to capture the variability of soils and vegetation components at a global scale. The main steps of the algorithm are now described (see Figure 2).

_{0}images were generated from all high quality observations (cloud- and snow-free) over a one-year period: a vegetated k

_{0}image corresponding to the peak of season and a devegetated k

_{0}image corresponding to the minimum canopy closure. The samples were chosen to be homogeneous over areas higher than SEVIRI spatial resolution, and the classification is based on the 1-km Global Land Cover 2000 (GLC2000) [35]. Training areas of non-vegetated class include desert areas, sparsely vegetated and shrublands. Vegetation areas were identified in crop and forest classes. Samples were further verified using purity methods to filter out possible outliers. In particular, pixels having less than 95% of soil/vegetation were excluded.

_{s}and G

_{v}are the number of Gaussian components for soil and vegetation, respectively. The algorithm uses the Expectation-Maximization (E-M) approach [37] to estimate the means ${\mathit{\mu}}_{k}$ and covariances ${\mathit{\Sigma}}_{k}$ of the individual Gaussian components. This simple iterative approach increases the log likelihood of the observed data and usually converges if the data conform reasonably well to the mixture model. The k-means algorithm is used to initialize the E-M parameters $\left({\mathit{\mu}}_{k},{\mathit{\Sigma}}_{k}\right)$

_{.}Multiple initializations are made to avoid numerical problems local maxima. We assume ellipsoidal unconstrained component covariance matrices and use the Bayesian Information Criterion (BIC) [38,39] to determine an appropriate number of Gaussian components. The value of BIC is the maximized log likelihood with a penalty for the number of parameters. The larger the BIC score, the stronger the evidence for the model. The determination of the number of Gaussian components takes into account not only the BIC score but also the requirement that the distributions must provide a faithful representation of the data. A typical number of 6-7 Gaussians for soil and 3-5 for vegetation has been used to represent the variability of the different SEVIRI geographical areas.

_{s}

**G**

^{.}_{v}. A model ${M}_{k}$ is defined a pair of class-conditional distributions for vegetation-soil ${M}_{k}\equiv ({f}_{soil\left(k\right)},{f}_{veg\left({k}^{\prime}\right)})$. At the SEVIRI resolution, different sets of soil and vegetation may yield to very similar mixtures. Let $p\left({M}_{k}|r\right)$ be the posterior probability or likelihood of model ${M}_{k}$ given pixel data

**r**, and $\pi \left({M}_{K}\right)$ the a priori probability of having the model ${M}_{k}$ at a particular pixel. Based on the Bayes theorem most often used in classification problems, the posterior probability assigned to a model ${M}_{K}$ is proportional to its likelihood times its prior probability:

**x**(vegetation) and

**x’**(soil) intercepts the region in the feature space centered at the mixture

**r**, and is zero otherwise. We considered around

**r**an envelope volume

**V**(

**r**) given by the radiometric uncertainties attached to the input, i.e., the covariance structure of the k

_{0}product.

**r**, as illustrated in Figure 3 considering a simplified bidimensional problem with 3 vegetation clusters (V

_{1}, V

_{2}, V

_{3}) and 3 soil clusters (S

_{1}, S

_{2}, S

_{3}). The size and orientation in the elliptical probability density contours are determined by the covariance of clusters ${\mathit{\Sigma}}_{k}$. It is obvious that (S

_{3}, V

_{1}) is the most likely model in the mixture. However, other different model combinations, such as (S

_{2}, V

_{1}) and (S

_{3}, V

_{2}), have non negligible probabilities and may yield to the same mixture spectrum.

_{1}, t

_{2}, … t

_{M}} over a seasonal period can be used to more reliably determine the likelihood of model ${M}_{K}$ in a mixture pixel

**r**, i.e.,:

_{0}images generated in step 1:

_{0}space of SEVIRI channels. Bare areas are predominantly found in sparsely vegetated and open shrublands (GLC2000 classes 19, 14 and 12) whereas purely vegetated areas are mostly found in close forest classes, herbaceous and croplands (GLC2000 classes 1, 2, 13 and 16). In this example, the best suited number of Gaussian components was 3 for vegetation and 6 for soil.

_{1}and V

_{2}with the darkest soil type S

_{1}.

**r**∈ °

^{3}[(k

_{0})

_{red}, (k

_{0})

_{NIR}, (k

_{0})

_{SWIR}] onto a feature space that makes the retrieval model more sensitive to changes in vegetation and minimize the sensitivity to soil background and noise in the inputs. Vegetation retrieval is specially hampered by the influence of undesired soil variability at SWIR wavelengths (1.6 µm), which is particularly large for the soils in Africa (see Figure 4b). This high variability has shown to be a cause for overestimation of FVC in semi-arid regions over dark soils (further insights will be given in Figure 5b). Latest version projects

**r**onto a new features space w ∈ °

^{5}, increasing the relative influence of channels 1 and 2 with respect to channel 3 ([(k

_{0})

_{red}, (k

_{0})

_{red}, (k

_{0})

_{NIR}, (k

_{0})

_{NIR}, (k

_{0})

_{SWIR}]). This strategy has served us to reduce possible biases due to SWIR background reflectance variability.

**r**, with mean and ${\mu}_{r}$ standard deviation ${\sigma}_{r}$. Using the standardised endmembers, $\hat{{E}_{i}}$ (i = 1,…,c), the unmixing is formulated as follows:

#### 2.3. LAI Algorithm

_{s}= cosθ

_{s}, being θ

_{s}the solar zenith angle, G(θ

_{s}) is the average extinction function [48], $T\left({\theta}_{\mathrm{s}}\right)$ and b is the backscattered parameter, which can be roughly assumed to be equal to 0.945 for all vegetation types [49]. The fraction of solar radiation intercepted by the vegetation (FIPAR), which coincides with FVC when the sun and the observer are both at zenith, i.e., $\mathrm{FVC}=\mathrm{FIPAR}\left({\theta}_{\mathrm{s}}=0\right)$ is expressed as:

_{s}) considering spherical orientation of the foliage. In order to avoid maximum LAI values in fully vegetated areas exceeding a value about 7, a coefficient a

_{0}in the range (1.04-1.07) is introduced in Equation (16):

#### 2.4. FAPAR Algorithm

_{s}=45°, θ

_{v}=60°, ϕ=0°). The soil contribution to the canopy reflectance was reduced at this oblique view using a vegetation index, called RDVI (Renormalized Difference Vegetation Index), defined as follows:

_{opt}refers to the RDVI computed in the optimal geometry. The reflectance in the optimal geometry for each spectral channel is estimated as follows [53]:

#### 2.5. Products Uncertainty Estimation

## 3. The SEVIRI/MSG Vegetation Products

_{0}, k

_{1}, k

_{2}), with k

_{2}presenting large uncertainties and noisy profiles on a short time scale, mainly in Western Africa.

#### Internal Consistency between the LSA SAF Products

## 4. Potential Applications of SEVIRI Vegetation Products

#### 4.1. Application 1: Monitoring of Seasonal Cycle and Phenology

#### 4.2. Application 2: Interrelation between Vegetation and Rainfall

#### 4.3. Application 3: The Detection of Inter-Annual Vegetation Trends over the Period 2004-2017

## 5. Summary and Conclusions

- NRT daily (MDFVC, MDLAI, MDFAPAR) and 10-days (MTFVC, MTLAI, MTFAPAR) products are generated and disseminated from LSA SAF since January 2004 over the geostationary Meteosat disk offering almost fifteen years of an alternative dataset to the user community.
- The 10-days (MTFVC-R, MTLAI-R and MTFAPAR-R) CDRs are provided as a suite of EUMETSAT climate products data records estimated consistently along the years using the latest versions of the whole processing chain algorithms. The 10-days products could be suitable for a community of users that requires observations representative of a 30-day period with at frequency of 10 days (e.g., numerical weather and climate models, and flood forecasting systems).
- The daily SEVIRI/MSG timeliness of the distribution of the observations and its smaller compositing period avoids possible shifts regarding the actual state of the vegetation (e.g., for an early estimate of key phenological parameters and seasonal production).
- The absence of gaps and the high temporal frequency and continuity of the products over Africa offer major potentials for NRT monitoring of land cover dynamics for applications that require frequent observations such as agriculture, and food management.
- The SEVIRI/MSG vegetation products have demonstrated its suitability to accurately resolving long term changes in large regions, allowing improving the understanding of interactions between land surface and climate.

## Supplementary Materials

_{0}and k

_{2}errors for a given k

_{1}error of 0.01. Two different cases have been considered: Low FAPAR values (a) and high FAPAR values (b)., Table S1: Cover-dependent clumping index values for LAI algorithm based on the GLC2000 land cover classification based on values obtained in [51], Table S2: VEGA products QF information. The default missing value for the product fields is −10. The associated error estimate fields for unprocessed pixels take different negative values, depending on the identified problem (default missing value = −10). Main identified problems in the VEGA products and empirical thresholds used to blind problematic areas. Note that although the missing value for the product fields is unique (−10), associated error estimate fields for unprocessed pixels take different negative values, depending on the identified problem (default missing value = −10).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Illustration of the model selection in a bidimensional feature space. Dashed lines join random spectra drawn from soil class S

_{3}and vegetation classes V

_{1}, V

_{2}and V

_{3}.

**Figure 4.**Illustration of the probabilistic mixing model concept over in the k

_{0}space of SEVIRI channels: (

**a**) channel 1 and 2; (

**b**) channel 2 and 3. Elliptical probability density contours associated with clusters (from V

_{1}to V

_{3}for vegetation and from S

_{1}to S

_{6}for soil). BDF and BEF correspond to broadleaved deciduous and broadleaved evergreen forest, respectively. BIC

_{s}and BIC

_{v}refer to the values of BIC for the soil and vegetation mixture models, respectively.

**Figure 5.**Projection of the SEVIRI/FVC product corresponding to the 15th of June 2015 onto the k

_{0}feature space of (

**a**) channels 1 and 2; (

**b**) channels 2 and 3. Red circles correspond to soil and vegetation pure pixels for the Southern Africa (SAfr) region.

**Figure 6.**MSG Daily LAI (top), FVC (middle) and FAPAR (bottom) LSA SAF product composition corresponding to the 17th of April 2014 products (left panels) and their respective error estimates (right panels). Location of the four LSA SAF geographical areas is also provided. Rectangles in the LAI field are associated to Euro, NAfr, SAfr and Same SEVIRI geographical regions for illustrating purposes.

**Figure 7.**Quality of the MSG daily FVC, LAI and FAPAR products based on the information provided by the mean values of its theoretical uncertainty along the year 2014. The levels of accuracy stand for: Optimal (Err(FVC/FAPAR)<0.05; Err(LAI)<0.5); Medium (0.05<Err(FVC/FAPAR)<0.10; 0.5<Err(LAI)<1.0); Low (0.10<Err(FVC/FAPAR)<0.12; 1.0<Err(LAI)<1.5); Poor (Err(FVC/FAPAR)>0.15; Err(LAI)>1.5).

**Figure 8.**Monthly fraction of valid pixels for daily MSG FVC product during the entire 2014 year over the four SEVIRI geographical areas.

**Figure 9.**Time series of LAI, FAPAR and FVC daily and 10-days products at a Deciduous Broadleaf Forest site.

**Figure 10.**Joint probability density plots between FGROUND and MSG daily LAI at several different periods of the year. Top Figures correspond to the Euro SEVIRI zone, whereas bottom Figures correspond to the SAfr SEVIRI region.

**Figure 11.**Comparison between LSA SAF products and equivalent MODIS and SPOT/VGT over a three-year period representative example at a site in Gabon.

**Figure 12.**Pearson correlation coefficient between time series of FVC and 3-month accumulated precipitation for the 2004-2017 period.

**Figure 13.**Time course of FVC and 3-month accumulated precipitation for an herbaceous region situated in Bostwana region (-23.1° N, 26.4° E).

**Figure 14.**Trend of inter-annual changes over Africa derived by applying the MRA-WT method to 10-days FVC time series (2004-2017).

Product | Identifier | Distribution | Temporal Resolution | Spatial Resolution | Target Accuracy |
---|---|---|---|---|---|

MDFVC | LSA-421 | NRT | 1-day | MSG pixel | Max [0.075,15%] |

MTFVC | LSA-422 | NRT | 10-days | MSG pixel | Max [0.075,15%] |

MTFVC-R | LSA-450 | CDR(^{1}) | 10-days | MSG pixel | Max [0.075,15%] |

MDLAI | LSA-423 | NRT | 1-day | MSG pixel | Max [0.5,20%] |

MTLAI | LSA-424 | NRT | 10-days | MSG pixel | Max [0.5,20%] |

MTLAI-R | LSA-451 | CDR(^{2}) | 10-days | MSG pixel | Max [0.5,20%] |

MDFAPAR | LSA-425 | NRT | 1-day | MSG pixel | Max [0.075,15%] |

MTFAPAR | LSA-426 | NRT | 10-days | MSG pixel | Max [0.075,15%] |

MTFAPAR-R | LSA-452 | CDR(^{3}) | 10-days | MSG pixel | Max [0.075,15%] |

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## Share and Cite

**MDPI and ACS Style**

García-Haro, F.J.; Camacho, F.; Martínez, B.; Campos-Taberner, M.; Fuster, B.; Sánchez-Zapero, J.; Gilabert, M.A. Climate Data Records of Vegetation Variables from Geostationary SEVIRI/MSG Data: Products, Algorithms and Applications. *Remote Sens.* **2019**, *11*, 2103.
https://doi.org/10.3390/rs11182103

**AMA Style**

García-Haro FJ, Camacho F, Martínez B, Campos-Taberner M, Fuster B, Sánchez-Zapero J, Gilabert MA. Climate Data Records of Vegetation Variables from Geostationary SEVIRI/MSG Data: Products, Algorithms and Applications. *Remote Sensing*. 2019; 11(18):2103.
https://doi.org/10.3390/rs11182103

**Chicago/Turabian Style**

García-Haro, Francisco Javier, Fernando Camacho, Beatriz Martínez, Manuel Campos-Taberner, Beatriz Fuster, Jorge Sánchez-Zapero, and María Amparo Gilabert. 2019. "Climate Data Records of Vegetation Variables from Geostationary SEVIRI/MSG Data: Products, Algorithms and Applications" *Remote Sensing* 11, no. 18: 2103.
https://doi.org/10.3390/rs11182103