The MODIS EVI image collection is temporally smoothed using the median pixel value over consecutive time steps (represented by the j index in Eq. 1). We test here two time windows of 1 and 3 months using the eruption date as a reference point. This approach to temporal smoothing, used to reduce artefacts, was selected over filtering-based (e.g., Savitzky–Golay filters) or non-parametric statistical (e.g., double logistic function) methods for two main reasons. Firstly, these methods are sensitive to the density and the signal-to-noise ratio of the time series (Cai et al., 2017; Li et al., 2021). As volcanoes are vast topographic edifices, frequent clouds in their vicinity make the application of such algorithms unstable and unreliable. Secondly, we focus on the impacts occurring at a medium term rather than in the immediate aftermath of an eruption, where a vegetation index (VI) can capture signals that do not record impact (e.g., increase in soil brightness due to tephra deposit). As a result, the median value over a given time window presents the most stable and conservative smoothing method around volcanoes.

Multiple approaches have been developed to quantify VI anomalies for purposes ranging from early warning (e.g. Asoka and Mishra, 2015; Meroni et al., 2019; Rembold et al., 2019) to index-based parametric insurance (e.g. Martín-Sotoca et al., 2019). VI anomalies have also been used to monitor vegetation recovery after natural hazards (e.g. fires, Bright et al., 2019; volcanic ashfall, De Schutter et al., 2015), cropping intensities (e.g. Liu et al., 2020), long-term land degradation (Gonzalez-Roglich et al., 2019) or changes in vegetation dynamics (Kalisa et al., 2019). We adapt the approach of Poortinga et al. (2018) as a proxy for impact of volcanic ash on vegetation, hereafter named the cumulative difference index (CDI). The CDI is computed as 1CDIi,t=∑j,k∈NtVIi,j,k-VIi,j‾, where CDIi,t is the CDI value for pixel i for consecutive j values after the eruption up to time t, VIi,j,k is the median VI value for pixel i at a post-eruption period j in year k, Nt is a set of post-eruption periods that includes all j, k indices up to a time t, and VIij‾ is the long-term VI mean over the baseline (averaged over 5 years prior to eruption for pixel i and period j). VI is the vegetation index (here, EVI), and j is an arbitrary time window, referring to a subset of a year. Here, j considers a 1–3-month period, and the baseline considers 5 years of pre-eruption conditions. For the 2011 eruption of CC, the first CDI value (i.e., j=1, k=1, t=1) is simply the difference between the median VI value for April–June 2011 and the average of all April–June VI values in the period 2006–2010. The second CDI value would sum the differences over the set N2 (i.e., j=1,2, k=1, t=2).

Whilst most remote sensing indices rely on ratios of pre/post conditions to define a relative anomaly (e.g., Hope et al., 2012; see Sect. 3.2.2), the CDI relies on an absolute difference. It is important to note that therefore, by definition, pixels with high EVI values will result in larger CDI changes. However, the temporal evolution of the CDI offers a new approach to capture impact and recovery. Figure 3 illustrates idealized profiles that the CDI can adopt through time. Following Eq. (1), a scenario where the CDI gradient remains negative implies that post-eruption conditions are persistently lower than the baseline (i.e., P1 in Fig. 3). A CDI flattening and reaching a zero gradient indicates a return to pre-eruption conditions (P2 in Fig. 3). If the gradient of the CDI slope becomes positive after the inflection point, the post-eruption biomass production has exceeded pre-eruption conditions. If the CDI curve flattens at a negative CDI value, the total loss in biomass due to the eruption has been partly compensated for by a temporary increase (P3 in Fig. 3). Should the absolute CDI value become positive, the total biomass loss caused by the eruption has been either compensated for or exceeded by the gains (P4 in Fig. 3). The purpose of the model is to explore conditions explaining the magnitude of impact (i.e., minV in Fig. 3) and the duration to reach it (i.e., minT in Fig. 3). The shape of the CDI curve after reaching minV is not considered here, and minV for the case of P1 in Fig. 3 is the minimum value reached after 5 years post-eruption.

Deposit thickness and grain-size distribution are the two of the main physical aspects controlling the direct impact of ashfall on vegetation (Jenkins et al., 2015). Since available isopach maps represent only deposit thickness, we reconstructed the grain-size distribution of the deposit associated with the 4–30 June 2011 phase of the CC2011 eruption using Fall3D v8.0.1 (Folch et al., 2020). The model was initialized using hourly atmospheric conditions retrieved from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 dataset (Hersbach et al., 2020) and daily mean plume heights reported by Collini et al. (2013). We tested several modelling schemes (Table 3) and compared the outputs against the isopach in Fig. 1a. For this, isopachs were interpolated using a generalized additive model and converted to maps of tephra accumulation using a constant deposit density. We tested densities of 1000, 2000 and 2200 kg m-2 to provide a range of tephra thicknesses for each point. The Fall3D NetCDF output was converted to a multiband GeoTIFF with each band containing mass loads for different size fractions. Size fractions computed by Fall3D were grouped into lapilli (2–64 mm), coarse ash (1–0.25 mm) and fine ash (<0.25 mm). The GeoTIFF was uploaded as an asset to GEE.

Atmospheric data were obtained from GEE using the ERA5 Land monthly averaged climate dataset (Hersbach et al., 2020), which provides a global reanalysis of climate variables since 1981 at a spatial resolution of 0.1×0.1∘. As the nature of the adopted ML model does not allow for using time series as covariates (see Sect. 3.4), we instead retrieve the total precipitation and the surface air temperature and compute their mean over 1, 2, 3, 6 and 12 months before the eruption. Each variable is considered both as raw values and anomalies computed as the stand regeneration index (SRI; Hope et al., 2012). As for CDI, we used a 5 years pre-eruption baseline and normalized the closest pre-eruption value Vi,j,k by the mean value over the same period in the baseline Vi,j: 2SRIi,j,k=Vi,j,kV‾i,j.

For instance, a 3-month precipitation anomaly <1 suggests that the trimester before the eruption was characterized by relatively lower rainfall compared to the same period of the year in the 5-year baseline. By considering both raw values and anomalies, we explore the relevance of each variable and potential pre-existing climatic stresses whilst also investigating what time windows are relevant for vegetation impact. The model also includes the wind velocity at the time of the eruption from the ERA5 Land dataset.

In addition to atmospheric variables, the model includes the updated 1 km version of the Köppen–Geiger climate classification by Beck et al. (2018). The study area spans three of the five main categories (arid, warm temperate and polar), with two sub-types of arid (i.e. desert – hot arid and steppe – hot arid) and four sub-types of warm temperate (fully humid – warm summer, fully humid – cold summer, summer dry – warm summer, summer dry – cool summer).

Terrain data were obtained from the Shuttle Radar Topography Mission (SRTM; Farr et al., 2007) using the NASA's SRTM V3 product at a resolution of ∼30 m. Elevation, slope, aspect, eastness and northness (sine and cosine of aspect, respectively) were retrieved from GEE and used as features.

Land cover was obtained from Copernicus Global Land Service (CGLS) dynamic land cover map (CGLS-LC1000, Buchhorn et al., 2020), available on GEE at a spatial resolution of 100 m yearly from 2015–2019. The land cover type is retrieved from the discrete_classification band for the closest year to the eruption (here 2015, acknowledging that the 2015 dataset possibly includes a long-term change in land cover caused by the 2011 eruption). To test the impact of tephra on various types of vegetation, we extracted the cultivated and managed vegetation/agriculture class as a proxy for cropland and the shrubs, sparse and herbaceous vegetation classes (i.e., values 40, 20, 60 and 30, respectively). In addition, we extracted a composite forest class comprising all classes tagged with forest. In the study area, present forest classes include evergreen broad leaf, both closed (112) and open (122); deciduous broad leaf, both closed (114) and open (124); and closed forest, mixed (115) and forest, not matching any of the other definitions (116 and 126).

The main modelling challenge is to approximate complex functions mapping both minV and minT to the various investigated features. Decision trees and related methods form a general class of models suitable for such regression tasks. We opt for gradient-boosted trees, a category of decision trees that use an ensemble of so-called weak learners built sequentially to improve prediction accuracy (Müller and Guido, 2015) and capable of handling multicollinearity (Chen et al., 2022). Gradient-boosted trees have successfully been applied on EO problems (e.g., Hengl et al., 2017). Here, we used the XGBoost v.1.4.2 library, which provides an optimized and distributed implementation of gradient-boosted trees (Chen and Guestrin, 2016).

Gradient-boosted trees rely on a range of hyperparameters governing the model's bias-variance trade-off. Selected hyperparameters (Sect. 4.4.1) were tuned by minimizing the out-of-sample mean absolute error (MAE) computed through a 5-fold cross-validation scheme using scikit-learn's RepeatedKFold and 10 000 trees. We used the Optuna library (Akiba et al., 2019) optimized on a single GPU.

Gradient-boosted trees can accommodate non-linear effects and interactions but, as for many modern ML algorithms, come at the cost of limited interpretability. Model-agnostic interpretation methods shedding light on black-box models are actively being developed and, when applied on big EO data, provide a novel framework to identify and constrain the processes driving changes through time in Earth sciences (Batunacun et al., 2021; He et al., 2020; Sulova and Arsanjani, 2021). Amongst these, the Shapley additive explanations (SHAP) method of Lundberg et al., (2020), based on Shapley values (Shapley, 1956) and coalitional game theory, decomposes any prediction from a given model as a sum of the individual effects from each variable (Molnar, 2021). The method computes SHAP values, which quantify how a given feature act to change a model's mean prediction. We use here SHAP values to identify drivers of vegetation vulnerability in two ways. Firstly, the mean absolute SHAP value of a variable across all instances indicates a relative importance amongst all features. Secondly, individual SHAP values for a given feature and all instances provide insights into how a feature's value influences predictions. As this study does not attempt to perform out-of-sample predictions, SHAP values are computed on the full dataset. We use the TreeExplainer method of the SHAP library (Lundberg et al., 2020) to explain XGBoost's prediction.

Unlike SHAP values, permutation feature importance ranks features based on their direct impact on model performance (Breiman, 2001; Fisher et al., 2019). We use it as a complementary approach to SHAP values. Permutation importance is also computed on the full dataset using scikit-learn's permutation_importance function using 10 permutations of each variable and computing the change in the coefficient of determination R2.

A model is trained separately for each land cover class defined in Sect. 3.3, with one additional model trained on all land cover classes jointly and using the land cover class as a feature. Since XGBoost does not support multi-output regressions, each dataset is used as an input for two models trained using either minV or minT as a target variable (Fig. 3). To include some dependence between the two impact metrics, the model predicting minV is trained with minT removed from the features, whereas the model predicting minT is trained with minV in the list of features.

Table 4 presents the results of the optimization of hyperparameters on the dataset shown in Fig. 5d and the associated model metrics. The MAE and R2 were computed on both training and testing datasets using a cross-validation with five folds and three repeats. We compare training and testing prediction error as an indication of the degree of overfitting of the model. As expected, model metrics obtained on test datasets were lower than those using training data. Based on the R2 of the testing data and minV, models trained on all land cover classes and on herbaceous vegetation performed well (R2>0.9), followed by forests (R2>0.8) and crops (R2>0.7). The particularly low R2 value for sparse vegetation can be attributed to the presence of <10 % vegetated cover in this class, which is dominated by bare soil or rock. The R2 values of minT are consistently lower than those for minV and never exceed 0.6, which we partly attribute to its discrete nature.

Overall, the comparison of error metrics between testing and training sets reveals that models trained on the various datasets have various degrees of generalization ability, with the caveat that the validity of the insights provided by the different models should be considered in the perspective of their respective performances. The broadest dataset considering all land cover classes and minV results in high training (0.94) and testing (0.91) R2 values. We use this good performance and similarity between both values as an indication that the model is likely not overfitting and yields good generalization.

Tables 5 and 6 summarize feature importance for each land cover class using the mean absolute SHAP value and permutation importance. Although some differences exist, both methods yield similar results, thus implying that features that contribute the most to predictions (SHAP importance) also improve the model's generalization error (permutation importance). Unless specified, this section focuses on SHAP importance.

EVI and elevation are the two features that consistently rank in the top 10 of the most important variables across impact and land cover. For minT, minV is the most important variable, which suggests that both impact metrics are dependent. EVI ranks especially high, which indicates that the mean EVI value computed over the year before the eruption provides an important background level to the model. This result is a consequence of the cumulative sum of absolute differences behind the CDI, which implies that pixels with higher EVI values are prone to larger CDI impacts (Sect. 3.1.2). The variable lapilli is the most important for minV for all land cover classes but crops (SHAP value) and sparse (permutation importance) and ranks high when predicting minT for all and the forest land cover classes.

For forests, minV is best predicted, in decreasing order, by lapilli, EVI and elevation, which are respectively a deposit, a proxy for a biotic and an abiotic parameter. Note that using permutation importance instead of SHAP importance suggests that the third most important variable is surface temperature, which is correlated to elevation. In parallel, minT is driven by minV, lapilli, elevation and EVI, which indicates that the duration of impact is dominantly proportional to the magnitude of impact and the tephra load. In comparison, the minV of herbaceous vegetation is controlled by lapilli, EVI and the 6-month precipitation, which indicates the same hierarchy of importance of deposit, biotic and abiotic parameters as for forests, whereas minT is controlled by minV, EVI, the 3-month precipitation and fine ash. Interestingly, this suggests that impact duration does not primarily depend on any deposit variable, the most important of which (i.e., fine ash) is different to the parameter controlling the magnitude of impact (i.e., lapilli). As a final example, no deposit property ranks in the top three variables controlling the minV values of crops, which include climate, EVI and the 3-month precipitation anomaly. The first deposit parameter, fine ash, ranks fourth, which indicates that the vulnerability of crops to ash fallout is dominantly constrained by biotic and abiotic parameters. Fine ash ranks fifth for minT, which is mainly driven by minV, EVI and the slope, and illustrates how abiotic parameters can potentially dominantly control impact magnitude and duration.

SHAP dependence plots (Fig. 8) display, for each instance in the dataset (i.e., a point in Fig. 5d), the SHAP value of a given variable as a function of its actual value. For a given instance and a given variable, a negative SHAP value implies that the variable contributed to reducing the predicted value compared to the mean prediction of the model. Therefore, a negative SHAP value for minV implies a contribution to increase the magnitude of impact, whereas a negative SHAP value for minT implies a contribution to decrease the duration of impact.

Figure 8a is the dependence plots for lapilli. With loads ≤60 kg m-2 of lapilli, SHAP values are contained within 0±0.1 but drastically drop for larger loads. With lapilli dominantly impacting the vicinity of the volcanic source, <4 % of all instances are affected by accumulations >60 kg m-2, with those areas dominantly consisting of forests with additional vegetation classified as shrubs and herbaceous (Fig. 1c). Despite limited points, Fig. 8a suggests stepwise decreases in SHAP values for lapilli loads of ∼60, 230 and 550 kg m-2. Using a deposit density of 1000 kg m-3, thicknesses of 60, 230 and 550 mm span the D1–D4 damage states for forestry (Jenkins et al., 2014; Table 1). Using the pastoral class of Table 1 as an analogue for shrubs and herbaceous vegetation, these accumulations suggest that, for crops, substantial to major land rehabilitation is required before recovery. These observations confirm the relationships between minV, minT and the deposit load shown in Fig. 7: points affected by high lapilli loads result in minT values larger than ∼1300 d and an impact that persisted for years after the eruption. These high impact metrics explain why lapilli is the most important variable to predict minV. Lapilli is likely to cause a direct, physical impact from the high kinetic energies (e.g., Blake et al., 2015; Osman et al., 2019) and breakage from a static load and burial (Arnalds, 2013; Ayris and Delmelle, 2012), which is captured as a strong anomaly by our method and results as the most important variable. Plotting the dependence plot of lapilli for the model trained on the generic forest land cover class (Fig. 8b) indicates that the 2-month precipitation anomaly contributes to further explaining the influence on the SHAP value, with points with an anomaly <0.85 displaying lower SHAP values.

Dependence plots for coarse and fine ash (Fig. 8c, d) display similar – although less conspicuous – drops in SHAP values for accumulations of 12 and 1.7 kg m-2, respectively, with SHAP values on average 1 order of magnitude smaller than for lapilli. Considering that fine deposits are denser than coarser ones, a density range of 1000–2000 results in thicknesses of 6–12 and 0.9–1.7 mm for coarse and fine ash, respectively, which cover the D1–D3 damage classes for horticultural/arable and pastoral agriculture (Table 1). Note that these thicknesses should be regarded as minimum values as we convert here individual size fractions to total deposit thickness. Figure 8e–j also shows the effect of ash for models trained on specific land cover classes. For crops (Fig. 8e–f), coarse and fine ash are the 10th and the 4th most important variables, respectively. Coarse ash seems to induce drops in SHAP values for loads of 2, 4 and 10 kg m-2. There is clearly an effect of fine ash on SHAP values, but the oscillatory pattern is difficult to explain for loads ≤0.5 kg m-2, especially for the Csb climate class where most crops are found (i.e., warm temperate, summer dry, warm summer), and probably depends on additional variables not accounted for in the model (e.g., geographic distribution of plant-specific effects such as ash retention as a function of leaf morphology). Beyond 1 kg m-2, SHAP values are consistently negative. Coarse and fine ash are the 4th and the 14th most important variables for minV for herbaceous vegetation. The coarse ash shows more negative SHAP values when associated with fine ash. Fine ash is generally beneficial for herbaceous vegetation with low EVI values (Fig. 8h). For herbaceous vegetation, the most negative SHAP values are found for high-EVI with accumulations ≤1 kg m-2. Incidentally, such accumulations also correspond to the highest SHAP values. Since no covariate satisfactorily explains this contrasting behaviour, this is either due to a model artefact or to variables that are not accounted for in the model. For shrubs (Fig. 8i, j), coarse and fine ash are respectively the 7th and 12th most important variables. Coarse ash suggests a decrease in SHAP values for loads of ∼6 kg m-2, beyond which the magnitude of the negative effect increases with the lapilli load. Fine ash does not show any trend or sharp break.

Figure 9 shows SHAP dependence plots for variables other than the deposit. Figure 9a confirms the importance of EVI on minV, where all points with EVI <0.1 result in positive SHAP values and all points with EVI >0.3 result in negative SHAP values. This observation is partly a consequence of the use of Eq. (1), where the value of VIijk-VIij‾ is generally larger for higher EVI values. Figure 9a also suggest a dependence of this relationship on the load of coarse ash, which slightly increases SHAP values for low EVI but decreases them for higher values. Elevation is the third most important feature for predicting minV and shows a breakpoint at an altitude of ∼1000 m a.s.l. (Fig. 9b), below which SHAP values are dominantly negative. Above this elevation, SHAP values are generally positive, regardless of the intensity of ash accumulation. Land cover, the seventh most important feature, indicates that crops dominantly contribute to increasing impact in the model (Fig. 9c). Sparse vegetation also has a negative but less pronounced effect on SHAP values, whereas shrubs and herbaceous vegetations have a neutral effect. The SHAP values of forests tend to reduce the impact, which corroborates the higher resilience of trees to tephra fallout (Table 1).

Wind and precipitation partly control the residence time of ash on leaves and therefore the impact (Ayris and Delmelle, 2012). Although variables used here only consider pre-eruption atmospheric conditions, they are indirectly used as indicators for post-eruption patterns. The impact of wind speeds on SHAP values suggests breakpoints at 0.2 and 1.2 m s-1. SHAP values are strongly negative below 0.2 m s-1, generally positive up to 1.2 m s-1 and generally negative above (Fig. 9d). This supports the idea that wind contributes to reducing the residence time of ash on leaves, but the aeolian remobilization of ash at higher wind speeds can negatively impact vegetation (e.g., Arnalds, 2013; Craig et al., 2016b; Elissondo et al., 2016; Wilson et al., 2011a, b). Although depending on additional parameters (e.g., surface roughness, ash properties, soil humidity, rainfall intensity), an empirical value for onset of remobilization of 0.4 m s-1 has been used in the literature and agrees with our results (e.g., Folch et al., 2014; Liu et al., 2014). Leadbetter et al. (2012) observed that ash resuspension is suppressed if precipitation rates exceed 0.01 mm h-1, and our model indicates that most negative SHAP values occur for relatively dry climates. The most important precipitation variable for predicting minV with all land cover classes is the precipitation anomaly computed over 3 months before the eruption, which mostly shows a negative anomaly (i.e., anomaly <1; Table 6; Fig. 9e). This precipitation anomaly shows a clear break at a value of 0.87, for which SHAP values are dominantly negative below and positive above. Above a value of 1, SHAP values increase. Figure 9e shows a negative peak in SHAP values between an anomaly of 0.85–0.87 across all land cover classes but stronger for crops. Plotting SHAP values on a map (Fig. 9f), the spatial clustering of negative SHAP values corresponds to the location of crops between San Carlos de Bariloche and Comallo (Fig. 1). No variable unequivocally explains this spatial clustering.

With a mean absolute SHAP value >7 times larger than any other variable, minV is by far the most important for predicting minT (Fig. 10a), with a cut-off between positive (i.e., increasing the value of minT) and negative (i.e., decreasing minT) at a minV value of ∼0.15. The effect of EVI on minT is the opposite of minV (Fig. 9a): although high EVI values tend to increase the impact magnitude (lower minV), they generally contribute to reducing the impact duration (i.e., Fig. 10b). Interestingly, this trend disappears as minV increases. This can be explained by the fact that points affected by high minV values in Fig. 10b are associated with relatively high minT values (Figs. 7; 10a). These points are associated with damage classes suggesting land retirement, and their recovery is therefore independent of the pre-eruption EVI level. The 1-month precipitation anomaly is the fifth most important variable for minT (Fig. 10c), and SHAP values are mostly positive below an anomaly of 0.3 and mostly negative above 0.5. As for EVI, high minV values are less sensitive to the general trend. Finally, Fig. 10d shows the effect of the wind speed at the time of eruption on minT as a function of the climate. Wind speeds >4 m s-1 considerably increase minT, especially in an arid climate (i.e., BWk) where the vegetation is mostly shrubs, herbaceous and sparse. Points with positive SHAP values at wind speeds >4 m s-1 are characterized by accumulations of fine ash >0.5 kg m-2. In contrast, points with minimum SHAP values between wind speeds of 1.8–2.8 m s-1 correspond to crops close to Piedra del Aguila and show fine ash loads <0.5 kg m-2.