Dating Lava Flows of Tropical Volcanoes by Means of Spatial

Dating Lava Flows of Tropical Volcanoes by Means of

Spatial Modeling of Vegetation Recovery

Long LI 1,2 *, Lien Bakelants 3, Carmen Solana 4, Frank CANTERS 5, Matthieu

KERVYN 2

1. School of Environmental Science and Spatial Informatics, China University of

Mining and Technology, Daxue Road 1, Xuzhou 221116, P.R. China

2. Department of Geography & Earth System Science, Vrije Universiteit Brussel,

Pleinlaan 2, Brussels 1050, Belgium

3. Department of Transport and Regional Economics, University of Antwerp,

Prinsstraat 13, Antwerp 2000, Belgium

4. School of Earth and Environmental Sciences, University of Portsmouth,

Burnaby Building, Burnaby Road, Portsmouth PO1 3QL, UK

5. Cartography and GIS Research Group, Department of Geography, Vrije

Universiteit Brussel, Pleinlaan 2, Brussels 1050, Belgium

* Corresponding author: [email protected]; [email protected]

This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/esp.4284

Abstract

The age of past lava flows is crucial information for evaluating the hazards and risks posed by effusive volcanoes, but traditional dating methods are expensive and time- consuming. This study proposes an alternative statistical dating method based on remote sensing observations of tropical volcanoes by exploiting the relationship between lava flow age and vegetation cover. First, the factors controlling vegetation density on lava flows, as represented by the normalized difference vegetation index

(NDVI), were investigated. These factors were then integrated in pixel-based multi- variable regression models of lava flow age to derive lava flow age maps. The method was tested at a pixel scale on three tropical African volcanoes with considerable recent effusive activity: Nyamuragira (Democratic Republic of Congo),

Mt Cameroon (Cameroon) and Karthala (the Comoros). Due to different climatic and topographic conditions, the parameters of the spatial modeling are volcano-specific.

Validation suggests that the obtained statistical models are robust and can thus be applied for estimating the age of unmodified undated lava flow surfaces for these volcanoes. When the models are applied to fully vegetated lava flows, the results should be interpreted with caution due to the saturation of NDVI. In order to improve the accuracy of the models, when available, spatial data on temperature and precipitation should be included to directly represent climatic variation.

Keywords: Dating lava flows; NDVI; remote sensing; Nyamuragira; Mt Cameroon;

Karthala

1 Introduction

Lava flow age is important data for an improved understanding of the eruptive behavior and temporal pattern of activity of the source volcanoes. Dating eruptions to estimate return periods is therefore critical for hazard and risk assessment (e.g. creation of volcanic hazard maps).

From a geological point of view, rocks can be dated by relative or absolute approaches: relative dating (e.g. using stratigraphic relationships) is difficult in application while absolute dating (e.g. cosmogenic, radiocarbon and paleomagnetic dating techniques) is expensive and time-consuming, and requires materials which are several hundreds of years old, thus less applicable to recent lavas (Watchman and Twidale, 2002). Lichenometry (McCarthy, 2007) and obsidian hydrations

(Higgins et al., 1972) require presence of lichen on lava surfaces or volcanic glass in lavas, respectively. In addition, their accuracy relies greatly on the appropriate calibration for the specific environmental context (Naveau et al., 2007; Rogers, 2008).

Another obvious source for dating lava flows is historical written or oral records (e.g.

Solana, 2012). However, the historical records are scarce and fragmented for most volcanoes and their reliability is not guaranteed, as they can be inaccurate and ambiguous, particularly in developing regions like Africa (Brown et al., 2014; Ernst et al., 2008). Moreover, most of the above-mentioned methods are not usable for volcanoes with restricted or no field accessibility as lava samples are needed for analysis.

Remote sensing techniques offer unparalleled opportunities to study volcanoes, their processes and products (Hooper et al., 2012; Pyle et al., 2013; Rowland et al., 1994,

2003). It has been demonstrated that remote sensing is valuable in mapping,

monitoring and even dating lava (Blackett, 2014; Cashman and Sparks, 2013;

Dietterich et al., 2012; Eskandari et al., 2015; Li et al., 2017). Early studies have confirmed the usefulness of Landsat data for relative dating of lava flows: Landsat 1 data was firstly used for relative dating of the Craters of the Moon volcanic field, USA

(Lefebvre and Abrams, 1976) and Landsat MSS (Multi-Spectral Scanner) and TM

(Thematic Mapper) imagery were later reported to allow age discrimination of five groups of basaltic lava flows of historical to Tertiary age in a Saudi Arabian site

(Blodget and Brown, 1984) and of vegetated lava flows in the Menengai Caldera,

Kenya, based on vegetation parameters (Blodget and Heirtzler, 1993). Thermal infrared emissivity has also been correlated to the age of Hawaiian lava flows

(Abrams et al., 1991; Kahle et al., 1988). Normalized LiDAR intensity was shown to be useful to determine a relative chronology of lava flows on Mt Etna, Italy: it decreases for those erupted between 1865 to 1999 but increases with lava flow age for those erupted in the last 6 years preceding the data analysis (Mazzarini et al.,

2007). Spectral unmixing of lava flows from Nyamuragira (Democratic Republic of

Congo) enabled the identification of three lava endmembers, representing young-, intermediate- and old-aged lava flow groups (Li et al., 2015a). These studies highlight the possibility of dating lava flows by mean of remote sensing of lava surfaces.

Spectral signals of lava surfaces, which indicates the change in reflectance of lava surfaces at different wavelengths, are complex and dependent on several factors and processes (e.g. Rothery and Lefebvre, 1985; Li et al., 2015b), some of which change over time and can provide estimation of lava surface age. In (semi-)arid environments, chemical weathering affects the reflectance of lava with increasing impact over time (Abrams et al., 1991; Kahle et al., 1988; Li et al., 2015a; Rothery

and Lefebvre, 1985). In more humid climates, the growth of lichens first alters the shapes of lava spectra (Li et al., 2015b; Stretch and Viles, 2002). Here, following the pioneer species, vegetation also emerges on lava surfaces, increasing the reflectance of the surfaces in the near infrared band (Head et al., 2013; Li et al.,

2015a).

The rate of vegetation recovery is controlled by multiple factors. For example,

Nyamuragira’s lava flows require ∼15 years for vegetation to be prominent and ∼40 years for it to cover over half of the lava surfaces (Li et al., 2015a)—indicating that time is playing a critical role in the process of vegetation recovery on lava surfaces.

In addition to time, climate also contributes considerably to vegetation growth.

Tropical climates are characterized by high temperatures, insolation and precipitation, which favor the fast growth of plants in the absence of a shadow effect.

In mountainous terrains, elevation is closely correlated with temperature and rainfall

(Aplet et al., 1998; Aplet and Vitousek, 1994; Daly et al., 1994; Li et al., 2015b;

Pórtoles et al., 2011). Examples include Mauna Loa volcano, Hawai’i (USA), where more rapid vegetation succession is observed at lower elevations (Aplet and

Vitousek, 1994), and Mt Cameroon (Cameroon), where a negative correlation between NDVI (Normalized Difference Vegetation Index; see definition in Section 3.1) and elevation range was identified (Bonne, 2006). As such, in mountainous terrains, elevation can be used as a proxy for climate.

Other topographic factors, such as slope angle and slope orientation, may also impact vegetation establishment (Auslander et al., 2003; Nadal-Romero et al., 2014).

Slope steepness can affect vegetation growth by creating variation in solar radiation incidence, wind velocity and soil type, and by accelerating surface runoff and soil erosion. The effect of slope orientation is often linked to water availability in local

climatic variation and creates contrasted vegetation cover in different slope orientations (Albaba, 2014; Bochet et al., 2009; Nadal-Romero et al., 2014).

The pattern of vegetation colonization is also an important factor that controls the rate of vegetation colonization on lava flows. Vegetation colonization on lava surface often starts from the edge of the lava flow, where it is in direct contact with preserved vegetation (Kepfer-Rojas et al., 2014; Li et al., 2015a; Del Moral and Grishin, 1999).

This is consistent with the observation that distances to remnant plants is one of factors influencing the rate and trajectory of ecological succession in other settings

(Poulsen et al., 2007; Wang et al., 2013).

Modeling the relations between these factors offers the potential for dating lava flows but so far no studies have integrated them to model the age of lava flows. Therefore, in this study, vegetation recovery on lava flows of contrasted age is investigated through examining the influence of time, elevation, slope angle, slope orientation and distance to lava flow edge on vegetation characteristics. Using a statistical approach and NDVI of lava flows, this study aims to construct models for dating lava flows for three tropical African volcanoes, Nyamuragira (DRC), Mt Cameroon (Cameroon) and

Karthala (the Comoros).

2 Study areas

2.1 Nyamuragira

Nyamuragira (aka Nyamulagira) is a basaltic shield volcano situated in the Virunga

Volcanic Province, DRC (Figure 1). It has a tropical climate, with more rainfall in the wet season—ranging from October to May—than in the dry season—between June and September. No climate data is available for Nyamuragira but observations from the nearby city of Goma (1531 m above sea level, 28 km southeast of the summit)

show that average annual temperature and precipitation are 19.8°C and 1192 mm respectively (Climate-data.org, n.d.). The presence of Lake Kivu SW of the volcano increases the precipitation on the southern flank of the volcano (Thiery et al., 2015).

The volcano is 3058-m-high, with a 2×2.3 km2 summit caldera and an extensive >1100 km2 lava flow field. Over 40 eruptions have been recorded at

Nyamuragira since the 17th century, making it the most active African volcano

(Smets et al., 2015). Some of the eruptions originate from the caldera but most occur from the numerous cones and fissures on the flanks (Colclough, 2006; Smets et al.,

2015). So far, 27 lava flows erupted between 1938 and 2012 have been dated and mapped (Head et al., 2013; Smets et al., 2010). This eruption frequency poses a major threat to the villages around Goma.

2.2 Mt Cameroon

Mt Cameroon is a stratovolcano located on the west coast of Cameroon (Figure 2).

In general Mt Cameroon has a tropical seasonal climate with a wet season starting in

April/May and a dry season starting in October/November. The southwestern flank of

Mt Cameroon, however, is influenced by the Atlantic ocean and experiences rainfall throughout the year with a yearly rainfall locally reaching 10000 mm (World Wildlife

Fund, 2014). The northern and eastern flanks receive less rain.

With a height of 4095 m a.s.l. (above sea level) and a volume estimated at 1200-

1300 km3, the massive steep-sided volcano is one of the largest on the African continent (Kervyn et al., 2014; Suh et al., 2003). The volcano is elongated in a NE-

SW direction parallel to the 1600 km long Cameroon Volcanic Line and has no central crater. Its surface is covered by a large number of cones, spread parallel to the 1600-km-long Cameroon Volcanic Line (Bonne et al., 2008; Kervyn et al., 2014).

Seven eruptions were recorded since the start of the 20th century, the most recent ones in 1999 and 2000 (Suh et al., 2003). Historical lava flows reached agricultural and residential land and endangered nearby residents (Bonne et al., 2008).

2.3 Karthala

Karthala is an active shield volcano situated on Grande Comore Island off Eastern

Africa (Figure 3). Its tropical climate is under oceanic influence with a hot and rainy season from November to April and a cool and dry season from May to October

(Battistini and Vérin, 1984; Monticelli, 2012). An annual rainfall of >4000 mm is observed on the southwestern flank with only 2000 mm on the northeastern flank.

The elevation gradient is large but poorly constrained (Louette et al., 2008).

Karthala is 2361 m high and has a 3 × 4 km2 summit caldera. This volcano has erupted over 30 times since the 19th century with the most recent eruption recorded in January 2007 (Smithsonian Institution, 2013). Eruptive activity of this volcano threatens the surrounding population and environment (Morin and Gaillard, 2012).

3 Modeling lava flow age using linear regression

3.1 Data acquisition and preparation

Image data used in the study includes multispectral imagery acquired by the ETM+

(Enhanced Thematic Mapper Plus) sensor onboard Landsat 7, and the ALI

(Advanced Land Imager) sensor onboard the Earth Observing-1 Mission satellite.

Topography was obtained from the DEM (Digital Elevation Model) acquired by

SRTM (Shuttle Radar Topography Mission) collecting topographic data over nearly

80% of Earth’s land surfaces. They were selected for each of the volcanoes to obtain

NDVI and topographic parameters, respectively (Table 1). All the spatial data were

geometrically rectified and georeferenced in the same projected coordinate system for each volcano.

The NDVI, which is the ratio of the difference between spectral reflectances in near infrared and red regions to their sum—(NIR-RED)/(NIR+RED), was adopted in this study to quantify vegetation on lava flows, as NDVI can effectively provide vegetation biomass information (Rouse et al., 1974) and is widely used and easy to obtain

(Hatfield and Moran, 2014). It was calculated from at-sensor reflectance data derived from the multispectral satellite imagery.

Elevation, slope angle and slope orientation are here considered as proxies for spatial climatic variations which, as discussed in the introduction, control vegetation colonization on lava surfaces. The values of these parameters were extracted at pixel scale from the corresponding DEMs for each volcano. Slope orientation was also calculated at a lower resolution. The 30 m DEM datasets were first downsampled to obtain 1 km resolution slope orientation maps, which were then upsampled to 30 m. This decreases the spatial heterogeneity of the slope orientation parameter and, more importantly, provides contextual information for each pixel which might be more relevant if slope orientation is assumed to reflect flank-specific climatic conditions. Orientation is considered a categorical variable—it was divided into eight direction categories, each of them having a range of 45°. With north

(337.5°-22.5°) serving as the reference, the remaining seven orientation categories were integrated as dummy variables in the modeling procedure.

Vegetation recovery requires formation of a soil substrate and colonization of plant species. The colonization often occurs as a front propagation from the nearest source of seeds (Del Moral and Grishin, 1999). The distance to seed source is therefore relevant to model vegetation recovery (Kepfer-Rojas et al., 2014). In

tropical volcanic regions, lava flows usually border forests and the distance to seed source is equivalent to the distance to lava flow edge. On satellite imagery, defining the distance is easy for Mt Cameroon and Karthala where different lava flows show limited overlap and are separated by several decades. The issue is more complex for Nyamuragira due to spatial overlap of lava flows which were emplaced within a short period. For the ease of processing and modeling, a simple computation of the distance to lava flow edge was also used for Nyamuragira. This parameter was defined as the shortest distance between any lava flow pixel and the border of the lava flow, also considering kīpukas (i.e. patches of surviving vegetation after emplacement of lava flows) fully surrounded by the lava flow. It is noted that distance to lava flow edge evolves as lava flows age but the interaction between the two variables are however not included for the simplicity of modeling.

Accurate mapping of lava flows and eruption dates are also important for both modeling and validation. Lava flow age information and outlines (except for the undated lava flows of Mt Cameroon) were obtained from existing maps (Bachèlery and Coudray, 1993; Bonne et al., 2008; Smets et al., 2010). The outlines of the undated flows of Mt Cameroon were digitalized from 30 m resolution satellite imagery based on visual interpretation of spectral contrast with surrounding vegetation. All the outlines were shrunk by one image pixel (30 m) to exclude mixed pixels from the analysis. Lava flows within calderas (e.g. the 1956 lava flow of

Nyamuragira, the lava flows of Karthala erupted between 1991 and 2007) or covered by later lava flows (e.g. the 1957 lava flow of Nyamuragira) were excluded in the modeling as they are continuously affected by volcanic activity and thus not suitable for the vegetation recovery aspects of the study.

3.2 Model concept

Based on the assumption that vegetation recovery on lava flow is controlled by soil development over time, rainfall, temperature, and distance to diaspore sources, we assume that NDVI can be modeled using proxies of these physical parameters, i.e.

NDVI = f(Age, Elevation, Slope, Aspect, Distance to edge). Assuming that NDVI is mainly controlled by lava flow age and not strongly correlated with other geographic factors, it is possible to inversely to construct an age estimation model, where Age = f(NDVI, Elevation, Slope, Aspect, Distance to edge). In order to build this model for age estimation, a multiple linear regression approach was applied, which models the relationship between two or more independent variables and a dependent variable by fitting a linear equation to the observed data (Rao et al., 2008). Given 푁 independent variables, the model can be expressed as follows (Rao et al., 2008):

푁 Y = 훽0 + 𝑖=1 훽𝑖푋𝑖 + 휀 (1) where 푌 is the dependent variable (lava age), 푋𝑖 the independent variables (the spatial variables in Table 1 and their transformed forms), 훽0 the intercept, 훽𝑖 the regression coefficient of the 𝑖푡ℎ independent variable, and 휀 a random error term representing unexplained variation in the dependent variable. The coefficients are obtained using the least squares technique where the error term 휀 is minimized. The transformed forms include quadratic terms of the variables (e.g. elevation2) and interaction terms (e.g. elevation*slope).

The model was build based on stepwise linear regression. In this approach the most significant or least significant variable is iteratively added to or removed from the multi-variable linear model based on its statistical significance (Draper and Smith,

1998). At each step of addition or removal of a potential independent variable,

resultant models are assessed by means of the p value of an F-statistic (p-value

<0.05 for statistical significance) (Draper and Smith, 1998). In spite of some recognized limitations, stepwise regression remains prevalent in research studies

(Whittingham et al., 2006)—simply because it is effective in identifying optimal variables among many, correlated or not, for constructing a good predictive model.

As such, it helped to determine what the most significant factors are controlling vegetation recovery on lava surfaces.

3.3 Binary correlation

As an initial analysis, we wish to understand how the observed vegetation on lava surfaces, quantified by NDVI, is correlated with lava surface age and other potential controlling factors. This would provide a basis for the modeling of lava flow age. Both simple and partial correlation analyses were conducted using the Spearman rank correlation coefficient, which assumes no specific distribution of the variables.

Spearman rank correlation coefficient measures the strength of a monotonic relationship between two variables, and ranges between -1 and 1: a higher/weaker absolute value indicates a stronger/weaker monotonic relationship and a positive/negative value means a positive/negative monotonic correlation (Mukaka,

2012). Partial correlation measures the degree of association between two variables, by holding other controlling variables constant or by removing the effects of them

(Finn, 1974). Correlation analysis was conducted for all the variables and the correlation between NDVI and other variables would provide a basis for the modeling of lava flow age. In addition, in order to characterize multicollinearity, an independent variable’s variance inflation factor (VIF) was calculated, which is a means to detect multicollinearities between the independent variables of a model (see details and

equation in Kennedy (2008)). A rule of thumb is that if the VIF>10, the multicollinearity is high and the variable should be excluded (Hair et al., 2009).

3.4 Sampling strategy

Satellite data at 30 m resolution enables lava flows to be represented by a large number of pixels. Considering all the pixels in the modeling process is however not only computationally expensive but also leads to potential overfitting. Hence the models were constructed with a selection of pixels. As such, a stratified sampling procedure was performed: 20% of pixels were randomly selected from each lava flow and then constituted the entire modeling sample. Random sub-parts of this sample were used for model calibration (see Section 4.4.1).

3.5 Model calibration

Model fit can be measured by the residuals-based adjusted coefficient of determination (adjusted R2) and the root mean square error (RMSE) (Rao et al.,

2008). The robustness of the models was tested using the following procedure proposed by Vanmaercke et al. (2014). First, a random number of pixels were randomly selected from the modeling pixels (i.e. the 20% of all the pixels for each volcano, see Section 3.4) and used for calibration. Then the resultant model was applied to predict the age of the remaining pixels of the sample. The procedure was repeated 1000 times. For each iteration, the Nash-Sutcliffe efficiency (NSE) was calculated to determine the relative magnitude of the residual variance (noise) compared to the measured data variance (information) using the following equation for the test data:

푛_푡 2 𝑖=1(푦푡_𝑖−푦 푡_𝑖) 푁푆퐸 = 1 − 푛 _푡 2 (2) 𝑖=1(푦푡_𝑖−푦푡_푚푒푎푛 )

푡ℎ where 푛_푡 is the number of observations, 푦푡_𝑖 the 𝑖 observed value of the dependent variable, 푦 푡_𝑖 the corresponding predicted value of the dependent variable, given by the calibrated model, and 푦푡_푚푒푎푛 the mean observed value of the dependent variable. The model efficiency indicates how well the observed data fits the simulated data (Nash and Sutcliffe, 1970). It ranges between –∞ and 1: (1)

NSE=1 corresponds to a perfect model; (2) 0

3.6 Model validation

In addition, the models were validated by applying the models to the entire lava field, as only 20% of the pixels from the lava flows were used for modeling. Comparison between predicted lava age and recorded lava age for historical lava flows can reveal how reliable the models are to predict undated lava surfaces. Tentative prediction of the age of undated lava flows was also performed to examine if the models return realistic estimates and to evidence any model bias when modeling age beyond the range of observed values.

4 Results

4.1 Relationship between NDVI and other variables

Spearman rank correlation analysis was performed between the NDVI and potential controlling variables on a pixel scale and the corresponding coefficients were calculated (Table 2). The results are shown as graphs of mean NDVI against the classes of elevation, slope and distance to the edge (each class is independent), and

also of mean NDVI against lava flow age on a lava flow scale, because scatter plots are not effective in illustrating the trends for such a large amount of observations

(Figures 4-7). The effect of orientation on NDVI cannot be visually represented in a comparative way as each lava flow is characterized by only one or two flank orientations, but the variable is included in the modeling. In general, for the three volcanoes, variance in NDVI is mostly explained by lava age while the influence of other variables, such as elevation, slope and distance, is site-specific. Partial correlation analysis shows that each of the variables (elevation, slope, distance) remains correlated, though weakly, with NDVI after controlling for the other three variables (Table 2), suggesting that the significant effects of the spatial variables on

NDVI are not because of confounding (see the definition of confounding in

Pourhoseingholi et al. (2012)).

For all three volcanoes, lava flow age shows a clear and positive correlation with

NDVI (Table 2 and Figure 4), which can be modeled through linear regression. Data of Nyamuragira and Mt Cameroon show a better fit than those for Karthala: age explains over 85% of the variance in NDVI for Nyamuragira and for Mt Cameroon but less than 60% for Karthala.

Elevation has a weak correlation with NDVI, particularly for Nyamuragira and

Karthala (Table 2 and Figure 5). Trends of NDVI with elevation vary for different lava flows but on the whole, NDVI tends to be non-linearly correlated with elevation: for most lava flows NDVI values increase with elevation at low altitude until a certain elevation threshold is reached (∼2000 m at Nyamulagira, ∼1500 m at Mt Cameroon and ∼1400m at Karthala) above which NDVI values decrease. This non-linear relationship is most evident for Karthala. For Nyamuragira and Karthala, the trend of

NDVI increasing with elevation dominates the overall relationship between elevation and NDVI.

Correlation between NDVI and slope angle is very weak for all volcanoes (Table 2 and Figure 6). A weak trend of NDVI increasing and then decreasing with slope is observed for Nyamuragira. At Cameroon, NDVI of lava flows increases as slope increases, except for the 1909 flow. It seems more complicated for the lava flows of

Karthala but in general a slight increase and then decrease in NDVI is observed for many lava flows as they become steeper. Slope angle is positively correlated with elevation at all three volcanoes and the impact of slope gradient on NDVI remains after controlling for the effect of elevation (Table 2).

NDVI and distance to lava flow edge are poorly correlated as well (Table 2 and

Figure 7). The graphs of Figure 7 however highlight some systematic effect of the distance to lava flow edge on average NDVI value. At Nyamuragira, NDVI of most of the lava flows decreases with distance. A decrease in NDVI is also noticed at least in the first 200 m from the flow edge at Mt Cameroon except for the 1922 flow.

Regarding Karthala, NDVI decreases with distance when distances are shorter than

200 m. For larger distances, the variation of NDVI is more variable and sometimes shows an increasing trend, especially for older flows. When elevation, slope and age are also considered, the relationship between NDVI and distance becomes clearer.

Figure 8 shows how NDVI values vary over distance to lava flow edge when NDVI is corrected for the effect of age, elevation and slope. The residuals of NDVI decrease as distance to lava flow edge increases in the case of Nyamuragira. This relationship could be fitted by quadratic regression (Figure 8b). Although this analysis highlighted an influence of elevation and distance to edge on NDVI, the correlation was not strong when considering all lava pixels. This suggests that it is reasonable to

use NDVI and the other geographic factors as independent explanatory factors for constraining a linear regression model of lava flow age.

When lava flow age was the dependent variable, the VIF values of the independent variables used in our study were calculated and were all less than 2 for the three volcanoes (Table S1). Thus, the multicollinearity was low and these variables were kept for constructing multi-variable regression models of lava flow age.

4.2 Simple regression models of lava flow age

In order to test the prominence of NDVI as sole age predictor, based on the correlation between NDVI and lava flow age (Table 2 and Figure 4), simple regression models with NDVI as the only independent variable were built using the randomly selected pixels (

Table 3). These linear regression models are volcano-specific. Nyamuragira’s model obtains the best model fit (lowest RMSE and highest adjusted R-squared) (Table 4).

For Mt Cameroon’s model, the high coefficient for the NDVI variable is weakened by its negative intercept. The large intercept of Karthala’s model is due to the relatively older ages of the volcano’s lava flows, compared to those of the other two volcanoes.

Note that these simple linear models are not valid for all ages. The model of Karthala, for example, is unsuitable for very fresh lava flows whose NDVI values might be very small, as their predicted age will be around 100 years.

4.3 Multi-variable regression models of lava flow age

In light of the correlation analysis, a number of variables and transformed variables were regarded as candidate terms for a linear multi-variable model of lava flow age (

Table 3): linear terms of the variables (e.g. NDVI, which has a linear relationship with lava flow age); quadratic terms of the variables (e.g. elevation2); interaction terms

(e.g. elevation*slope); and a constant term. Orientation was also included in the form of linear terms represented by seven dummy variables. The multi-variable models for the three volcanoes are given in

Table 3.

As expected, addition of more variables and terms leads to a decrease in RMSE and an increase in adjusted R-squared of the models, which is more noticeable for

Nyamuragira and Mt Cameroon (Table 4). In the stepwise regression, addition of orientation changed the model fit significantly for Mt Cameroon’s model, suggesting a strong influence of orientation on the model fit and a need to compare with a model not including orientation (

Table 3).

Both the models with context-based orientation and with pixel-based orientation show a better model fit than those without orientation (Table 4). The models with context-based orientation also outperform the models with pixel-based orientation.

The improved model fit, particularly for Mt Cameroon, highlight the added value of using context-based orientation. As a result, the multi-variable models with pixel- based orientation were not be further considered in this study. Differences in model fit between the multi-variable regression models with and without context-based orientation are small for both Nyamuragira and Karthala but remarkable for Mt

Cameroon. When orientation is removed from the multi-variable model of Mt

Cameroon, the RMSE increases from <10 to >20 and adjusted R-squared decreases from 0.92 to 0.63. Inclusion of the context-based orientation in the multi-variable models of Nyamuragira and Karthala does not seem to affect the model fit substantially.

4.4 Model calibration and validation

4.4.1 Model calibration

Robustness tests were performed on the multi-variable regression models with and without context-based orientation. The NSE values are generally stable for the three volcanoes (Error! Reference source not found.). Whether or not orientation is included in the models does not seem to have a strong impact on the NSE values for the models of Nyamuragira and Karthala. Yet this is not the case for Mt Cameroon’s models: the model efficiency values are around 0.9 for the model with orientation and just over 0.6 for the model without orientation.

All the models are robust: as long as ≥10% of the sampled pixels are used for calibration, the NSE values remain systematically similar. The variables and terms added in the models remain significant and do not depend on a particular selection of pixels for model calibration. On the other hand, the prediction quality is slightly decreased when too many pixels are used for the calibration, e.g. >90% for Mt

Cameroon and Karthala.

4.4.2 Model validation

The multi-variable models based on the randomly selected 20% of pixels were also used for age estimation on the three volcanoes’ entire historical lava flow fields

(Error! Reference source not found.-Error! Reference source not found.). The histograms of prediction errors (i.e. predicted age minus real age) show that the age of lava surfaces is slightly overestimated for Nyamuragira and Mt Cameroon, and slightly underestimated for Karthala (Error! Reference source not found.).

Karthala’s model has the largest variance, followed by the two models of Mt

Cameroon, with lowest variance being obtained by the model of Nyamuragira. The predicted age was compared with real age for individual lava flows (Error!

Reference source not found.).

The multi-variable regression model with orientation of Nyamuragira resulted in homogeneous colors for individual lava flows in the predicted lava flow age and the prediction error maps (Error! Reference source not found.) and predicted values concentrating around the 1:1 line (Error! Reference source not found.a). The ages of very young and very old lava flows were shown to be slightly underestimated. The

1938-40 and 1951-52 lava flows have large internal standard deviations and are more underestimated than the youngest lava flows, i.e. the 2002, 2001 and 2000 flows. The age of most of the intermediate-aged lava flows is slightly overestimated

except for the 1976-77 and 1986 flows which show a larger overestimation.

Vegetation on the two lava flows located in the southwestern part of the volcano might benefit from the proximity to Lake Kivu and thin tephra from nearby eruptions.

The standard deviation (<5 years) for most lava flows are generally small, meaning that for all pixels within the same flow estimated age is similar. Larger underestimation errors are noticed especially on the distal lobes and lateral edges of the lava flows on the south flank, located close to inhabited areas. Pattern of error within individual flow lobes suggest that the effect of the distance to the lava flow edge is not properly modeled for specific flows (e.g. 1958 flow north of the flow field).

Both the multi-variable regression models with and without context-based orientation were applied for Mt Cameroon. For both models, results are characterized by low within-flow age variation (Error! Reference source not found., Error! Reference source not found., Error! Reference source not found.b and Error! Reference source not found.c). The only exception is the 1909 flow whose age is more overestimated at higher altitudes, especially for the model without orientation. Larger within-flow errors are observed for the model without orientation. The model with context-based orientation shows a pattern of error depending on elevation for several flows, but with opposite trends on the different flanks, suggesting an important impact of the context-based orientation parameter on the model results. In general, predicted age and real age agree well, implying a good prediction performance of Mt Cameroon’s multi-variable regression models.

Regarding Karthala, high within-flow age variation is obtained especially for flows erupted in the 1900s (Error! Reference source not found. and Error! Reference source not found.c). Spatial patterns in age estimation are noticed within single flows, suggesting an incorrect modeling of the effect of elevation and/or distance to

the edge for certain flows. The predicted age and real age match well for lava flows older than 80 years, with errors in mean lava flow age <20 years. For the young lava flows of Karthala, i.e. the 1977 and 1972 flows, the ages are seriously overestimated with very large mean errors of ∼50 and ∼100 years respectively. The multi-variable regression models of Karthala fail to reliably estimate ages for young lava flows.

5 Discussion

5.1 Understanding factors controlling lava flow age

Investigating the relevant spatial/environmental factors is vital to gain an insight into how, with time, vegetation recovers on lava flows. The correlations among these variables were generally (very) weak, except for that between NDVI and lava flow age. A principal component analysis was not applied here as the number of variables used in the study was small and it is often difficult to interpret artificial components resulting from such a decorrelation analysis. In addition, the use of stepwise regression approach can also penalize the inclusion of the correlated variables. The low VIF values also suggests low multicollinearity among these variables for modeling of lava flow age.

The relationship between NDVI and age can be characterized by linear regression, with high correlations for Nyamuragira and Mt Cameroon (Figure 4). Despite of a likely better model fit, quadratic regression between age and NDVI is ruled out because quadratic curves opening downward will induce lower age estimates to be obtained when NDVI continues to rise. This is against the logic of the natural process of vegetation colonization. A logarithmic regression model was also tested but it returned a lower model fit than the linear regression model. Still, linear regression has its drawback: the linear correlation is restricted to lava flows younger than a

certain age, as NDVI will never go beyond the maximum NDVI value of the climax vegetation in a specific environment, even if lava flows are very old. Assuming a

NDVI of 1 and using the linear relationships between NDVI and lava flow age in

Figure 4, the age threshold is ~93, ~388 and ~333 years for Nyamuragira, Mt

Cameroon and Karthala respectively. The relationship between NDVI and age is therefore not valid beyond the period of full recovery of the vegetation to its climatic state. Age prediction of lava flows should therefore be interpreted with care and applied only to flows with a NDVI value clearly lower than the surrounding vegetation.

One factor that should be considered when investigating the relationship between

NDVI and age is the age distribution of dated lava flows. An even age distribution can guarantee that all age is included and the age models would not be biased by the age used for calibration. If a volcano would have only lava flow of the last 10 years, or only dated flows on its lower flank, it would be more difficult to constrain evolution of vegetation for a longer time or at higher elevations respectively.

In contrast, the relationship between vegetation fraction of lava flow extracted from the same satellite image of Nyamuragira through spectral unmixing, and lava flow age was modeled as a quadratic function (Li et al., 2015a). One could argue that vegetation fraction has the same limitation as NDVI being bounded by a maximum value of 1. It should be noticed though that NDVI and vegetation fraction do not have a linear relationship (Jiang et al., 2006) and that deriving reliable vegetation fraction estimates from spectral data depends greatly on endmember selection (Heinz and

Chein-I-Chang, 2001; Tompkins, 1997).

As a proxy for climate, elevation is shown to have an important impact on vegetation growth, which can be characterized by a quadratic relationship: NDVI increases at lower elevations and decreases at higher elevations (Figure 5). This can be

explained by precipitation and temperature change with elevation. At Mt Cameroon, annual rainfall gradually declines at higher elevations and is less than 2000 mm at the summit (Battistini and Vérin, 1984; Louette et al., 2008), and average temperature decreases at a rate of approximately 1°C per 150 m of elevation (World

Wildlife Fund, 2014). In the case of Karthala, an annual precipitation of ∼2700 mm was registered in the federal capital city of Moroni on the western coast at ∼29 m a.s.l (Figure 3b) and over 4000 mm at Mvuni at ∼370 m a.s.l, just ∼6.9 km east of

Moroni (World Meteorological Organization, 2016).

Vegetation does not seem to be affected by increasing slope in low slope ranges but is generally constrained at high slopes (Figure 6). This agrees with the finding of previous studies (Bochet et al., 2009; Nadal-Romero et al., 2014) and can be explained by the fact that high slopes require plants to establish quickly and to be tolerant of fluctuating soil moisture and potentially poor nutrient availability.

Distance to lava flow edge is considered as a proxy parameter for the proximity to seed sources, which is important for the start of vegetation recovery (Kepfer-Rojas et al., 2014). In general, NDVI is lower at longer distances from the lava flow edge

(Figure 7-Figure 8); this could be explained by the fact that it is more difficult for seeds to reach bare lava surfaces—the number of seeds in a location decreases with the distance from the source (Howe and Smallwood, 1982; McClanahan, 1986;

Nathan and Muller-Landau, 2000). On the other hand, revegetation is easier in proximity to remnant vegetation (Beach and Halpern, 2001). These findings suggest that lava flows with smaller widths and more kīpukas are more likely to have easy and fast vegetation recovery and, vice versa. A good example is Nyamuragira’s

1991-93 flow, which is the widest lava flow but has a lower NDVI than younger lava flows due to its larger thickness and width and the absence of kīpuka. Results shown

in Figure 7-Figure 8 however highlight that the relationship of NDVI with distance to the lava flow edge is not linear and might take a different form in function of flow age or local context. It should be noted that it is difficult to define the distance to seeds in the context of a very active volcanic area with overlapping lava flows of contrasted age, such as Nyamuragira—the flow edge might not always correspond to presence of seed sources and the distance to the flow edge might vary during vegetation recovery due to emplacement of new flow lobes.

In addition to the factors examined in the study, other factors might also influence vegetation recovery, such as deposition of wind-blown sediment (e.g. tephra)

(Deligne et al., 2013), lava composition, surface roughness (Smathers and Dieter,

1972), and destruction by fire or by humans (which will be discussed in the following section). Examining all factors influencing vegetation recovery on lava flows is difficult because it will complicate the modeling. Impacts can also be site-specific.

5.2 Modeling

The results of model development show a good model fit between mean NDVI and lava flow age, which allows to construct flow-scale regression models for dating lava flows. However, the aim of this research was to check whether a good age estimate can be obtained by building a model taking into account the characteristics of individual pixels. Therefore, two types of regression models based on pixel observations were constructed: simple models with NDVI only, and multi-variable models using both pixel- and context-based orientation. It is no surprise that model fit for simple regression models is low, because noise induced by the spatial variation in vegetation recovery within a single lava flow is inevitably included when the modeling is done at pixel scale. On the other hand, the simple regression models

suggest that age can only explain part of the variance in NDVI, from 75% for

Nyamuragira to <20% for Karthala. This highlights the need to include more vegetation-controlling factors in the models. The improved model fit of the multi- regression models shows the contribution of the added variables and terms (

Table 3-Table 4).

The models developed in this study differ in the form and also in the number of terms included, depending on the specific impact of the various controlling factors on vegetation growth on lava flows, which have been already discussed in this paper.

Interaction terms exist because one of the spatial variables may have a different effect on the NDVI depending on the value of another spatial variable, e.g. distance and elevation. It may occur that due to the effect of elevation low distances correspond to low NDVI but long distances correspond to high NDVI (Figure 8). This agrees with our observations that vegetation propagates inward on a lava flow more rapidly at lower elevations than at higher elevations. Interpretation of interaction terms in the models is however complex. The interaction term of Elevation*Distance in the model of Nyamuragira implies that the effect of distance to edge on estimating lava age varies for different values of elevation. It is likely to be related to variation in lava flow geometry with elevation (lava flows become narrower at steeper slope angles commonly found close to the vents), but more work is required to confirm this hypothesis. Specific interactions between lava age and some of the spatial- environmental variables were not examined in this study but its influence could be investigated in future work.

Slope orientation is included in the multi-variable modeling for the three volcanoes because of its strong effect on NDVI. This can be accounted for by the impact of the volcano topography on local climatic conditions, and therefore the contrasted insolation and precipitation received on different volcano flanks. Context-based orientation proves better than pixel-based orientation as an explanatory variable in the modeling because it better represents the orientation of a volcano’s flank rather than local slope orientation. The coefficient of the orientation dummy variable

indicates that other variables being kept equal, lava flows in the specific orientation are a number of years older (positive coefficients of orientation dummy variables) or younger (negative) than lava flows in the north orientation.

An issue with the inclusion of the slope orientation variables is that model calibration might be strongly influenced by a large flow in a given orientation. The model of

Nyamuragira includes all the seven dummy variables except for O8 (northwest) (

Table 3). The large coefficients for O5 (south) and O6 (southwest) might result partially from less favorable conditions for vegetation regrowth, but it is also influenced by the presence of old and large lava flows (the 1938-40 and 1948 flows).

These tend to artificially increase the modeled age of other lava flows on the south- and southwest-facing flanks (e.g. the 1976 and 1986 flows). Model results suggest that for lava flows of similar age, lower NDVI values are found on these flank orientations. This is in opposition with the finding that the presence of Lake Kivu induces higher precipitation on the southern flank (Thiery et al., 2015). This effect is most probably overshadowed by human activity on lava flows, especially on the

1938-40 flow whose distant part has been deforested or converted to local settlements.

For Mt Cameroon, the high negative coefficients of the orientation dummy variables included in the model suggest that these orientations tend to decrease the lava flow age estimate for a given NDVI value. The issue here is that each of the six dated lava flows are located on contrasted flanks, which results in a bias, with specific flank orientation being associated with specific flow age due to insufficient age variation for each flank orientation. As for Karthala, flank orientations are also significant model parameters as they are associated with the uneven distribution of rainfall on the volcanic island: the southwestern flank gets more rainfall than the other flanks and the north receives less (Louette et al., 2008). In conclusion, flank orientation is an important environmental factor controlling vegetation recovery of lava flows, but its actual impact can only be correctly calibrated in the model if sufficient flows of different ages are found on each flank orientation.

A certain amount of variance cannot be accounted for by the models, notably for

Karthala. This unexplained variance, responsible for low adjusted R-squared, can be

attributed to two main reasons. First, data quality varies. Outlines of lava flows were digitalized from satellite imagery or aerial photos, so the result relies on the image analyst and the imaging techniques used—errors could not be fully compensated by simply shrinking lava surfaces by one pixel. Data for Nyamuragira’s lava flows are known to be reliable as they are based on recent volcanic products and have been well mapped with errors reportedly controlled within one pixel (Smets et al., 2010).

Borders of Karthala’s lava flows were based on a geological map produced in 1993

(Bachèlery and Coudray, 1993) and errors were probably increased by map digitalization. Cloud coverage on parts of the satellite imagery used, which is common for tropical volcanoes, has caused part of the lava flows, in particular of Mt

Cameroon and Karthala, to be unusable for modeling, which makes the models less representative for the affected lava flows.

Second, human activity affects the spectra of lava flows. As a result of protection of a natural reserve (Virunga National Park), residents have limited disturbing impact on

Nyamuragira’s lava flows except for some parts on which towns and villages are located, e.g. the 1938-40 flow, or in the proximity of settlements where illegal wood collection and charcoal production are common practices, reducing the effective vegetation coverage. At Mt Cameroon, high elevations limit mass access to the steep volcano slopes which remain less affected by human activities above 800 m a.s.l. However, at Karthala, impact of human activity on lava flows is significant across the island of Grande Comore. At low elevations, particularly in coastal areas, many buildings and roads have been constructed on lava flows. For example, a runway to the island’s airport (Prince Said Ibrahim International Airport) was built on the western branch of the 1859 flow at an elevation of ∼20 m. At elevations <140 m on the same lava flow, mining activities and possibly sea salt spray also affect the

spectra of the lava surface. At higher elevations, burning of recovering vegetation might also affect the age and vegetation density relationship. In brief, to improve model performance, improving the data quality of lava flows and focusing on areas unaffected by humans seems be to a practicable approach.

An alternative modeling approach to tackle the question of vegetation colonization on lava flows would be to characterize and model the change in NDVI values for a recent lava surface relative to a climax vegetation representative for the environment and climate in which the lava flow was emplaced, as is often done for studies assessing vegetation recovery after forest fires (Gouveia et al., 2010; Hope et al.,

2012). The reference point can be the NDVI value of the area before the lava was emplaced, for flows of the last decades (see De Schutter et al., 2015), or existing pristine vegetation—area not impacted by lava emplacement in the last century—in similar environmental conditions to the lava flow surface. Although this would deserve further study, we expect that such an approach might be challenging for volcanoes with high density and frequency of lava flows and large gradients of vegetation with elevation and slope orientation.

5.3 Application of models

The dating approach presented in this study can estimate absolute lava flow age. It is also useful for relative age dating by producing a sequence of relative dates of lava flows (Error! Reference source not found.). Products of the approach can support hazard and risk assessment of effusive volcanoes through further understanding the behavior of specific volcanic systems and the return period of eruptions.

Both Mt Cameroon and Karthala have multiple lava flows of unknown age (Figure 2-

Figure 3). The next step forward was to test if the statistical models built in this study could be applied to estimate the age of these undated flows. Hence the multi- variable regression models of Mt Cameroon (with and without context-based orientation) and Karthala (with context-based orientation) were used for estimating the age of these undated flows.

The two models of Mt Cameroon produce different results: the orientation model returns ages ranging from ∼70 to ∼163 years while the model without orientation estimates all the lava flows to be younger than 90 years (Error! Reference source not found. and Table 5). Based on the results of the orientation model, four lava flows (U1 to U3 and U8) are suggested to have erupted before 1900 and four (U4 to

U7) after 1900, with two (U1 and U2) likely resulting from the same eruption (in

1866). According to the model without orientation, however, all the lava flows are shown to have erupted between 1930-1950 with two (U1 and U5) dated in 1933.

Further observation of the result of the orientation model reveals that the predicted age of the eight lava flows of Mt Cameroon (Error! Reference source not found.) decreases in clockwise direction starting from U8—a clear trend which is very similar to the historical lava flows of Mt Cameroon (Figure 3). These findings seem to confirm that the orientation variable introduces a bias in the modeling and that the results produced by the model without orientation are more plausible. It is noted that both results claim that the U7 eruption occurred in 1930 and the prediction for this lava flow seems to have a higher degree of reliability than for other flows. These results however should be considered with caution, as no reports or historical references to these relatively recent flows have been found.

The orientation model of Karthala indicates that the four undated lava flows are older than 100 years, with most produced in the 1850s (Error! Reference source not found. and Table 5). Karthala’s model was shown to have a low model fit (Table 4) and to overestimate the age of young lava flows (Error! Reference source not found. and Error! Reference source not found.). Unfortunately, it is impossible to validate the accuracy of the predictions since not all lava flows have been recorded/mapped in detail (Smets et al., 2015; Smithsonian Institution, 2013).

Predicted age shown here could though serve as a reference for other studies.

6 Conclusions

This study demonstrates the potential for dating lava flows by spatial modeling of the ecological process of vegetation recovery using spatial variables derived from remote sensing image data and provides an insight into the spatial pattern of vegetation colonization on lava flows.

Customized lava flow dating models were constructed using a remote sensing and statistical approach for Nyamuragira, Mt Cameroon and Karthala. All three African volcanoes are characterized by tropical climates facilitating rapid vegetation regrowth on new lava flow surfaces. Spatial variables, i.e. elevation, slope, orientation and distance to lava flow edge, were investigated for their relationship with the normalized difference vegetation index (NDVI), and then incorporated in regression models in order to date lava flows.

The results confirmed that lava flow age (i.e. elapsed time since emplacement) is the most significant determinant of vegetation colonization on lava surfaces. As expected, with time more vegetation colonizes lava flows. Hence, the correlation

between age and NDVI ultimately determines the performance of the regression models.

Robust tests show that the multi-variable regression models obtained for different volcanoes have different explanatory power, with Nyamuragira’s and Mt Cameroon’s models being far more robust than Karthala’s model. When applied to entire lava fields, models for Nyamuragira and Mt Cameroon produce good age estimates with low errors for lava flows, as opposed to Karthala where lava surfaces are less pristine due to disturbance from human activity.

The multi-variable models have been applied to estimate the age of undated lava flows at Mt Cameroon and Karthala. Due to the possibility of saturation of NDVI, prediction using the models is more suitable for lava flows whose ages are covered by the calibration datasets. For Nyamuragira and Karthala model performance is increased by orientation, for Mt Cameroon though the model including orientation seems biased.

Spatial variables affecting vegetation colonization on lava flows were also evaluated in this study. Elevation as a proxy for temperature and precipitation has an impact on vegetation recovery: vegetation recovery is faster at low elevations but more difficult at high altitudes due to climatic constraints. The effects of slope and orientation are volcano-specific. It is found that orientation obtained at a low spatial resolution can represent flank-specific climatic conditions and contributes to explaining variation in vegetation recovery on different flanks. Vegetation density decreases overall as distance to lava flow edge increases, especially for recent lava flow surfaces, highlighting the significant importance of surviving vegetation in the primary succession after eruptions. Addition of these spatial variables substantially increases

the model fit of simple regression models with NDVI only. Model form and fit however vary with volcanoes.

Deriving lava flow age extends the usefulness of estimating vegetation coverage and recovery rate on recently emplaced lava flows, both of which are already important information required for post-eruption environmental impact assessment, land planning and population settlement of populations. The dating approach presented in this study can acquire absolute lava flow age and it is also useful for relative age dating by producing a sequence of relative dates of lava flows, supporting hazard and risk assessment of effusive volcanoes through further understanding the behavior of specific volcanic systems and the return period of eruptions. Increasing human activity on volcanic regions and particularly on volcanic islands is an important factor modifying the accuracy of the models. Lava flows cannot remain untouched, so and it is therefore recommended to mask out affected areas. Other possible measures to improve the accuracy of the models would be considering interaction terms between lava flow age and distance to lava flow edge, as the effect of lava flow edge is expected to be most important in the first phase of vegetation recovery. Using land surface temperature and precipitation data instead of elevation as a proxy for climate-related conditions would also help to constrain and interpret the model, although climatic data are often unavailable at a local scale for tropical volcanoes.

Acknowledgements

Long Li wishes to thank the China Scholarship Council (CSC) for funding his research work at VUB. This study contributes to a project funded by the Priority

Academic Program Development of Jiangsu Higher Education Institutions (Surveying

and Mapping Science and Technology discipline). We are grateful to Prof. Dr.

Longqian Chen, Dr. Jianlin Zhao, and Dr. Matthias Vanmaercke for sharing their expertise in statistics and modeling, and to an anonymous associate editor and two anonymous reviewers for their constructive comments and suggestions.

Conflicts of Interest

The authors declare no conflict of interest.

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Tables

Table 1 Datasets used for each volcano in this study and variables that were extracted from these data sources.

Volcano Image data Vector data for lava flows Nyamuragira Landsat ETM+ (acquisition 23 lava flows erupted from 1938 to date : 31-Jan-2003) ; 2002 were obtained from (Smets et SRTM DEM (30 m) al., 2010); the 1956 and 1957 flows were excluded from the modeling. Mt Landsat OLI (10-Jan-2015); Six lava flows erupted in 1909, Cameroon SRTM DEM (30 m) 1922, 1959, 1982, 1999 and 2000 were obtained from (Bonne et al., 2008) and eight undated lava flows were digitalized by the author. Karthala EO-1 ALI (27-Aug-2008); 12 lava flows erupted from 1848 to SRTM DEM (30 m) 1977 and four undated lava flows were digitalized based on (Bachèlery and Coudray, 1993). Lava flows erupted in the 1990s and 2000s were excluded from the modeling. Variables Remote sensing imagery was - Age (i.e. the interval, in decimal used used for deriving NDVI; year, between the ending date of SRTM DEM for lava emplacement and the - Elevation (in meter) acquisition date of satellite image) - Slope (0°- 90°) (Li et al., 2015a) - Orientation (pixel- and context- - Extent of lava flows (vector data in based, 0°- 360°, 8 categories) ArcGIS shapefile format) - Distance to flow edge (in meter)

Table 2 Spearman rank correlation coefficients between NDVI and potential controlling variables on a pixel scale: elevation, slope, distance and age. The associated p-values with the correlation coefficients are <0.001. As orientation is a categorical variable, its association with NDVI is not described by correlation coefficients here. Correlations between age and spatial variables were not considered in order not to complicate the modeling. There is a rule of thumb to describe the strength of the correlation using the absolute value of the correlation coefficient: 0∼0.30, very weak (shaded in lawn green); 0.30∼0.50, weak (pale green); 0.50∼0.70, moderate (yellow green); 0.70∼0.90, strong (dark sea green); and 0.90∼1.0, very strong (dark green) (Mukaka, 2012).

Nyamuragira Simple Spearman rank correlation Partial Spearman rank correlation NDVI Elevation Slope Distance Age NDVI Controlling variables NDVI 1 -0.076 -0.111 -0.134 0.893 Elevation 0.378 Slope, Distance, Age Elevation 1 0.266 -0.208 Slope 0.001 Elevation, Distance, Age Slope 1 -0.170 Distance -0.357 Elevation, Slope, Age Distance 1 Age 1 Mt Cameroon Simple Spearman rank correlation Partial Spearman rank correlation NDVI Elevation Slope Distance Age NDVI Controlling variables NDVI 1 -0.339 0.038 0.149 0.667 Elevation -0.255 Slope, Distance, Age Elevation 1 0.576 -0.133 Slope 0.284 Elevation, Distance, Age Slope 1 0.124 Distance -0.048 Elevation, Slope, Age Distance 1 Age 1 Karthala Simple Spearman rank correlation Partial Spearman rank correlation NDVI Elevation Slope Distance Age NDVI Controlling variables NDVI 1 0.157 0.255 -0.055 0.348 Elevation 0.259 Slope, Distance, Age

Elevation 1 0.171 -0.017 Slope 0.173 Elevation, Distance, Age

Slope 1 -0.120 Distance -0.080 Elevation, Slope, Age Distance 1 Age 1

Table 3 Different types of models of lava flow age constructed for Nyamuragira (NY), Mt Cameroon (MC) and Karthala (KA). The regression coefficients are significant based on their t-statistics with associated p-values. Multi-variable regression models built with pixel-based orientation have poorer model fits and are not shown here.

Simple models with NDVI Multi-variable models with context- Multi-variable models without orientation only based orientation NY MC KA NY MC KA NY MC KA NDVI 84.671 230.534 59.859 76.606 14.641 44.378 87.397 211.618 45.156 Elevation -0.066 0.028 -8.499E-03 -0.059 -9.915E-03 Elevation^2 1.501E-05 -1.046E-05 -1.175E-05 -1.339E-05 -1.195E-05 Slope -0.937 -0.927 -1.626 -3.485 -0.672 Slope^2 -0.011 -0.014 -0.013 0.048 0.014 Distance 0.012 6.754E-03 0.087 5.481E-03 0.079 0.068 Distance^2 -9.232E-06 -2.225E-05 -8.942E-06 1.447E-04 O2 0.156 -10.569 O3 2.331 -48.424 O4 5.282 -57.698 -2.455 O5 13.83 -54.693 -8.042 O6 9.96 -79.244 -8.844 O7 -1.624 -8.768 O8 -6.955 -5.259 Elevation*Slope 4.763E-04 3.376E-04 9.912E-04 7.686E-04 3.104E-04 1.155E-03

Elevation*Distance 4.216E-06 -1.326E-05 2.752E-05 8.809E-06 -3.016E-05 3.083E-05 Slope*Distance 1.053E-03 -5.887E-03 5.050E-04 5.871E-03 -3.210E-03 Constant -3.717 -18.722 102.733 60.683 93.826 120.896 52.605 1.061 119.468

Table 4 Model fit of the models constructed for Nyamuragira, Mt Cameroon and Karthala (

Table 3). In the simple models, Nyamuragira’s model obtains the best model fit. The multivariable models with context-based orientation tend to perform better than those with pixel-based orientation. Inclusion of orientation parameter makes a difference in improving the model fit, notable for Mt Cameroon.

Model Volcano RMSE Adj. R2 Simple models with NDVI only Nyamuragira 10.036 0.762 Mt Cameroon 22.878 0.551 Karthala 27.703 0.143 Multi-variable models with pixel- Nyamuragira 7.993 0.849 based orientation Mt Cameroon 15.061 0.805 Karthala 24.378 0.384 Multi-variable models with context- Nyamuragira 7.924 0.852 based orientation Mt Cameroon 9.628 0.920 Karthala 23.294 0.394 Multi-variable models without Nyamuragira 8.847 0.815 orientation Mt Cameroon 20.829 0.627 Karthala 23.641 0.376

Table 5 Age prediction of undated lava flows of Mt Cameroon and Karthala. Lava flow age (± standard deviation) was calculated by averaging the age of all pixels on the same lava flow. The eruptions of Mt Cameroon and Karthala were estimated in relation to the acquisition dates of the Landsat 8 image (10-Jan-2015) and ALI image

(27-Aug-2008), respectively (see Table 1).

Undated lava Model with context- Estimated Model without Estimated flows based orientation eruption context-based eruption orientation Mt U1 149 ± 7 1866 82 ± 12 1933 Cameroon U2 149 ± 7 1866 73 ± 15 1942 U3 127 ± 7 1887 84 ± 16 1931 U4 71 ± 6 1944 65 ± 20 1949 U5 106 ± 10 1909 81 ± 13 1933 U6 99 ± 11 1915 80 ± 11 1934 U7 84 ± 5 1930 85 ± 14 1930 U8 163 ± 6 1852 67 ± 15 1948 Karthala U1 133 ± 9 1876 — — U2 152 ± 14 1856 — — U3 149 ± 16 1859 — — U4 155 ± 13 1853 — —

Figures

Figure 1 Location map of Nyamuragira volcano showing lava flows erupted between

1938 and 2002 (Smets et al., 2010) displayed in different colors with blue being the oldest and red being the youngest lava flows. The hillshade image and the contour lines at 200m interval are derived from the 30m resolution SRTM DEM. The yellow solid line is the border between the Democratic Republic of Congo and Rwanda.

Figure 2 Location map of Mt Cameroon with lava flows erupted between 1909 and

2000 (Bonne et al., 2008) displayed in different colors with blue being the oldest and red being the youngest lava flows. Undated lava flows (U1-U8) were manually digitalized from satellite imagery and highlighted in pink color. The hillshade image and the contour lines at 500m interval are derived from the 30m resolution SRTM

DEM.

Figure 3 Location map of Karthala volcano with lava flows erupted between 1857 and 1977 (Bachèlery and Coudray, 1993) displayed in different colors with blue being the oldest and red being the oldest lava flows. Undated lava flows (U1–U4) are highlighted in pink color. The hillshade image and the contour lines at 200m interval are derived from the 30m resolution SRTM DEM.

Figure 4 Relationship between mean NDVI and lava flow age (linear fitting shown by red lines with the 95% confidence interval shaded in pink) on a lava flow scale: (a)

Nyamuragira; (b) Mt Cameroon; and (c) Karthala. Standard deviation of NDVI of all pixels for each age class is displayed as error bars (one standard deviation). The slope and intercept errors of the linear relationship are (0.0009, 0.026) for

Nyamuragira, (0.0005,0.03) for Mt Cameron and (0.0007, 0.084) for Karthala respectively.

Figure 5 Relationship between mean NDVI and elevation ranges on a lava flow scale: (a) Nyamuragira; (b) Mt Cameroon; and (c) Karthala. The x labels represent independent elevations classes, e.g. <1250m and <1500m labels standing for elevations ranging from 0 to 1250 m and from 1250 to 1500m, respectively.

Figure 6 Relationship between mean NDVI and slope ranges on a lava flow scale: (a)

Nyamuragira; (b) Mt Cameroon; and (c) Karthala. The x labels represent independent slope classes, e.g. <5° and <10° labels standing for elevations ranging from 0 to 5° and from 5 to 10°, respectively.

Figure 7 Relationship between mean NDVI and distance ranges on a lava flow scale:

(a) Nyamuragira; (b) Mt Cameroon; and (c) Karthala. The x labels represent independent distance classes, e.g. <100 and <200m labels standing for elevations ranging from 0 to 100 and from 100 to 200m, respectively.

Figure 8 Scatterplots of NDVI against distance to lava flow edge for all lava flows of

Nyamulagira, with the colorbar showing elevation; (b) Scatterplots of corrected NDVI against distance to lava flow edge, which are fitted by a quadratic curve with an adjusted R2 of 0.84.

Dating Lava Flows of Tropical Volcanoes by Means of

Spatial Modeling of Vegetation Recovery

Long LI 1,2 *, Lien Bakelants 3, Carmen Solana 4, Frank CANTERS 5, Matthieu

KERVYN 2