# Investigating the Impact of Wildfires on Lake Water Quality Using Earth Observation Satellites
## 2 Materials and Methods
### Data and Statistical Analysis  
According to the SPR approach adopted in this study [9; 10], which describes the transport of burned materials to lakes through terrestrial pathways, from the initial 2024 lakes of the Lakes_cci dataset, an initial selection of lakes to be considered in our data analysis was performed. To achieve this, similar types of wildfires were identified and grouped together based on the type of land cover type burned and on the frequency of fires. Hierarchical cluster analysis was performed using Sorensen distance with flexible beta linkage. The resulting dendrograms were grouped according to the minimization of the indicator (\(p\)-value = 0.010) [39]. Our data analysis focused on the period 2017-2020 since during the last decade wildfire occurrence has escalated, and also for data consistency as satellite-derived Chl-a and turbidity products of the selected timeframe derive from the same optical sensor (OLCI onboard Sentinel-3 A/B). A classification of lake trophic status was carried out on the basis of mean Chl-a concentration, calculated for the period 2017-2020, according to OECD (1982): oligotrophic < 2.5 mg m\({}^{-3}\); mesotrophic from 2.5 to 8 mg m\({}^{-3}\); eutrophic from 8 to 25 mg m\({}^{-3}\); hypertrophic > 25 mg m\({}^{-3}\). Satellite-derived BA data were used to calculate the ratio of burned area/burnable area (sum of burned area and unburned area) (BA/A) for each lake investigated; in particular, in our investigation we considered the ratio for the maximum area burned in the whole lake catchment (0-50 levels identified with the HydroBASINS dataset) and the ratio for the closest catchment area burned around a lake, identified in the first four steps (level 0-4) calculated for each lake for each year. An Analysis of Variance (ANOVA or Kruskal-Wallis) test and box plots were used to investigate Chl-a and turbidity concentration differences between depth groups (shallow (<7 m), medium (7-15 m), and deep (>15 m) lakes, according to [40]), as well as trophic status (oligotrophic, mesotrophic, eutrophic, hypertrophic) and burned land cover vegetation. A Stepwise Multiple Linear Regression (SMLR; [41]) was performed to investigate the most likely factors that explain maximum annual Chl-a and turbidity peaks among the variables: lake surface area, length of shoreline, shoreline development, lake volume, mean water depth, mean long-term discharge, mean water residence time, elevation, latitude and longitude, catchment area, ratio catchment area/lake area, mean SPI for the period (2017-2020), SPI mean per year, mean BA/A ratio (2017-2020), maximum BA/A ratio per year, BA/A level 0-4 per year, total precipitation, normalized difference between max Chl-a peak and mean Chl-a per year, and normalized difference between max turbidity peak and mean turbidity per year. The concentration of Chl-a and turbidity peaks following a fire event was calculated using the \"zoo\" R package [42]. A lowess line (a locally weighted non-parametric smoothing method) was fitted to the dataset with a data span of 10% and a window half-width of 5 days, allowing for the identification of local maxima; missing daily values were linearly interpolated, which should not change the maximum value recorded, but may reduce the accuracy of the result. The average satellite observation frequency for the dataset over the study period was 1.7 days, which is close to the recommended sampling frequency of once every two days required to detect short-term perturbations in phytoplankton dynamics [43] and compares favorably with large-scale in situ synoptic sampling efforts. It is also well above the frequencies recommended by EU policy [44; 45; 46]. The timing of Chl-a and turbidity peaks after a fire occurrence were also identified by this analysis.