# Assessing Landsat Images Availability and Its Effects on Phenological Metrics
## 2 Materials and Methods  
A survey of available Landsat 7 and 8 surface reflectance data for Brazil was carried out using the cloud computing platform Google Earth Engine (GEE) because it possesses a public data archive including all available Landsat and Sentinel imagery and allows parallel processing [23; 24; 25; 26]. GEE has been used successfully used to carry out remote sensing-based studies over huge areas at the global level [19; 27] and national level [28; 29; 30]. Landsat Collection Level 1 data are organized into three tier categories (Real-Time, Tier 1, and Tier 2) based on data quality and processing level. This assessment was limited to the Tier 1 collection, which contains the highest radiometric and geometric quality images. These data are intercalibrated between Landsat sensors and recommended by the United States Geological Survey (USGS) for time series analysis. The number of valid observations, at pixel level, was computed using the cloud mask information. The availability of valid observations (without clouds) by biome and the spatial and temporal distribution of valid observations were evaluated. Heat maps were elaborated to show the distribution of valid observations throughout the year in the different biomes. The heat maps were combined with a hierarchical cluster to show the similarity of temporal distribution pattern between biomes (see upper part of Figure 1). In the next step, the study focused on an area encompassing a large portion of the State of Ceara (Red rectangle in Figure 2) that belongs to the Brazilian Northeast semi-arid, known as the Caatingas Dominium [31]. This ecoregion of deserts and xeric shrulands [32], belongs to the Koppen-Geiger Bsh climate dominium semi-arid with summer and autumn rainfalls and dry winter [33]. A stack of twelve maps representing the number of valid monthly observations was classified using the K-means algorithm. K-means is one of the most common clustering algorithms, is simple to implement, guarantees convergence and scales to large data sets. It carries out clustering, making the intra-cluster observations similar while keeping the clusters as different as possible. In this study, each resulting cluster represents a different temporal pattern of data availability. The average and the variance of the number of monthly available valid observations were computed for each cluster. As the following step, we modelled the effect of the lack of valid observations on phenological metrics estimation. For that, a curve fitting method proposed by [PERSON] et al. [34] was applied to a high temporal resolution Sentinel Normalized Difference Vegetation Index (NDVI) dataset obtained from an overlapping area between two paths of the Sentinel satellites. We chose the [PERSON] method because [PERSON] [35] identified it as the most robust among four models to determine the phenological metrics for vegetation,  
Figure 1: Flowchart showing Landsat imagery processing in GEE for entire Brazil (**upper part**) and availability patterns and phenological metrics assessment for the Northeast area in R (**lower part**). presenting a single growth season. This enables us to obtain NDVI curves for dry tropical forest plots that we used as references. Incomplete data were generated from the reference curves following the different availability patterns observed in the Northeast semi-arid area. For this, likely acquisition dates were modelled for each pattern of image availability (cluster) by computing the expected number of valid monthly observations in a given availability pattern generating random numbers from a Gaussian distribution based on the average and standard deviation previously calculated. Then, time series of NDVI values were generated using the reference curve equation and adding random noise to consider the degradation of received radiance at the sensor due to atmospheric effects and instrumental (sensor) noises. A curve was fitted to these incomplete NDVI data, and phenological metrics were extracted according to [PERSON] et al. [34].