Introduction

On January 17th, 2002 the Nyiragongo volcano, in the Democratic Republic of Congo, erupted along a huge system of fractures extending for more than 10 km, mostly along its southern flank down to the outskirts of the town of Goma (about 500,000 inhabitants), resulting in the most outstanding case ever of lava flow in a large town. This eruption, and the previous one at Nyiragongo in 1977, are also the only known cases in which people were directly killed by lava flows. About 100 persons, mostly children from the villages on the volcano flank, were killed by the very high velocity lava, which locally reached speeds of the order of 10 to 20 km/h (Tazieff 1977; Kilburn 2000; Komorowski et al. 2004). The arrival of two large lava flows in town caused a spontaneous exodus of about 300,000 people, who crossed the border with neighbouring Rwanda, fuelling concerns for the delicate relationships between the two countries. The eruption lasted only 1 day, after which about 15% of the town, including part of the international airport and the business centre, was destroyed and tens of thousands of people found themselves homeless (Baxter et al. 2004).

The 2002 fissure eruption occurred after a similar one in 1977 (Tazieff 1977), during which the fissure system and lava flows did not reach the town of Goma. The 1977 fissure system was reactivated and extended in 2002, with these two eruptions representing the only observed cases of activity outside the central crater of Nyiragongo since the volcano was first described in 1896 (Von Götzen 1896).

A first account of the eruption, its impact on the population, and the volcanic hazard a few days after the event is contained in a collection of reports by the groups of scientists involved in first-response operations (Allard et al. 2002; Halbwachs et al. 2002; Tedesco et al. 2002). A more comprehensive account of pre-eruptive observations, the eruption chronology and events, and post-eruptive phenomena is reported in Komorowski et al. (2004) and in a special volume dedicated to the 2002 Nyiragongo eruption (Capaccioni and Vaselli 2004). More recently, the reasons for the very high flow velocity of lava from the high altitude vents were investigated experimentally and theoretically (Giordano et al. 2007). Furthermore, a lava flow susceptibility map of the town of Goma was produced (Favalli et al. 2006), and isotopic disequilibria in the erupted lava were used to constrain the pre-eruptive history of the magma (Tedesco et al. 2007). All of the above papers provide evidence for the volcano-tectonic origin of the 2002 and 1977 eruptions, which are related to activity along the Albertine Rift, the western branch of the Great Rift Valley (Fig. 1).

Fig. 1
figure 1

The Virunga Volcanic Chain. Nyiragongo and Nyamulagira are located in the low portion of the Albertine Rift, between the Kamatembe Rift (KR) and Bufumbira Bay (BB). Other volcanoes of the Virunga chain are Karisimbi (K), Mikeno (M), Visoke (V), Sabinyo (S), Gahunga (G.) and Muhavura (Mh). The white dashed line represents state boundaries (DRC Democratic Republic of Congo, RW Rwanda, UG Uganda)

We here adopt the probabilistic lava flow path modelling approach used in Favalli et al. (2006) for a global investigation of lava flow hazard at Nyiragongo. Based on a definition of the probability of vent opening and of lava flow length, and on about 50,000 lava flow path simulations, we construct a hazard map for the entire cone of the volcano, including the towns of Goma (D.R.C.) and Gisenyi (Rwanda). The hazard map indicates that the probability that lava flows will reach the two neighbouring towns is high to very high, and the hazard is greatest in the areas of Goma largely devastated by the 2002 lava flow. The present map also highlights areas of low or relatively low hazard, which can be considered for future urban planning and for the relocation of villages on the volcano flanks. In a companion paper (Chirico et al. 2008) we use numerical simulations to investigate the possibility of protecting the urban areas through the construction of barriers, and make a proposal for the future development of Goma which minimizes the lava flow hazard in town.

DEM basis

The basis for the numerical simulation of lava flow paths and definition of lava flow hazard at Nyiragongo, the main objective of this work, is a Digital Elevation Model (DEM) of the volcano area. In a previous paper (Favalli et al. 2006) a 1:10,000 topographic map of Goma was digitized and used as the basis for the investigation of the susceptibility to lava flow invasion in town. The map covers only a small fraction of the volcanic area, although of primary importance, and cannot be used for the present purpose. The available maps with adequate coverage are a 1:50,000 geologic map made in the 1960s (Thonnard et al. 1965) and a 1:50,000 topographic map produced by the NIMA (National Imagery and Mapping Agency). However, as discussed in Favalli et al. (2006), none of these maps were useful in this study: the former because of its low accuracy and frequent line interruptions and crossovers, the latter because of its low resolution which hampered the reconstruction of historical lava flows. Fortunately, declassification in 2004 of the 90-m pixel DEM from the Shuttle Radar Topographic Mission (http://www2.jpl.nasa.gov/srtm) provided us with a sufficiently resolved digital basis for satisfactory model calibration and lava flow path reproduction, as shown below. Note that the SRTM DEM includes the 1977 lava flows, but not the 2002 flows. Favalli et al. (2006) have shown that the presence of the 1977 lava resulted in only minor modifications in the path of the 2002 lava flows, and that the presence of the 2002 lava is expected to have a comparably low effect. This is likely due to extremely low viscosity of the Nyiragongo lava (Giordano et al. 2007) and associated low thickness of lava flows.

Numerical model for the prediction of lava flow paths

In order to predict lava flow paths we employ the DOWNFLOW code, which has been previously used in lava flow hazard applications at the Mount Etna and Nyiragongo volcanoes (Favalli et al. 2005, 2006). The two-parameter code, extensively described in the above-referenced papers, is based on an evolution of the steepest descent path criterion. The first parameter (Δh) represents the maximum vertical perturbation (either positive or negative) applied randomly to the topography during each single steepest descent path calculation. The second parameter (N) represents the number of steepest descent path calculations performed from any single vent. While Δh defines the maximum basin which can be inundated by lava flows, N defines the fraction of that basin which is actually inundated.

The role of the two Δh and N model parameters in model calculations is shown in Favalli et al. (2006). The example in Fig. 2 helps better understand how the model works. We assume a topography and one lava flow-producing vent as in Fig. 2a. The vent is located on the margin of a topographic dip, with the dip rim having a complex shape. The model is conservative and assumes that the supply of lava from the vent is sufficient to fill the depression before overflowing the rim. The panels report the probability of lava flow invasion (increasing from red to yellow) over the considered topography, in terms of the number of times that each single pixel is reached by a lava path.

Fig. 2
figure 2

Example of the DOWNFLOW code applied to lava flow path estimation. a Assumed topography and vent location. b–d Distribution of the probability of lava flow invasion, increasing from red to yellow

Figure 2b reports the case of N = 1 (one single steepest descent path calculation). The computed lava flow path shows a thin stream which flows over the depression rim from its lowest altitude point. Figure 2c shows the calculation results for N = 1,000. In this case the lava stream is no longer thin, and there is incipient overflow of additional rim areas. Figure 2d adopts N = 3,000. In this case, the lava stream thickens, and additional but less probable lava streams from other low-altitude rim areas are produced and flow downhill.

The example above illustrates some of the most relevant behaviours of real lava flows, such as (1) filling of topographic depressions, (2) surmounting of topographic obstacles, and (3) lava flow spreading over the topography. In practice, with only two parameters the model is able to describe a variety and richness of lava flow behaviours, which in the real world depend in a complex way on the rheology and thermal properties of lava, as well as on other important parameters such as the mass flow-rate or local slope of the substratum and on processes such as crust formation and tunnelling and ephemeral vent opening, among others. The great advantage of the present model lies in its simplicity combined with its capability to effectively account for the basic characteristics of the propagation of lava flows. This approach, which is intrinsically probabilistic, guarantees a short computational time and allows a very large number of simulations for hazard purposes. The number of single descent path simulations done here and in Chirico et al. (2008) is of the order of 109, a number definitely hard to conceive for physically-based simulations. The present approach is therefore most useful when focusing on volcanic hazard, which requires a very large number of simulations to cover with sufficient accuracy a large portion of a volcanic area. Another situation in which the model can be used effectively is during real emergencies, since the short computational time (<1 s for a simulation from a single vent) and the simple information required (with a DEM and previous calibration, only the vent position is needed) allows real-time evaluation of probable lava flow paths.

In contrast, the lack of physical equations does not allow the definition of quantities which are essential for hazard purposes. The most important are the time of propagation of lava flows, with the model producing only a static picture of probable lava flow paths, and the maximum runout distance. Maximum runout distances must be introduced in model calculations to avoid poor estimates of lava flow hazard due to infinitely long predicted paths. In order to do so, an a-priori estimate of the runout distance of lava from each single considered vent is needed. Estimates from the present study are reported and discussed below.

Model calibration

Calibration of the two model parameters Δh and N for simulations over the SRTM DEM is done through comparison between model predictions and real lava flow paths observed at Nyiragongo. The only lava flows which can be readily reconstructed are those from the 1977 and 2002 eruptions. These are also those of greatest interest for the present purpose, since they are representative of the present state of the volcano and of the kind of lateral activity which is expected at Nyiragongo in the near future. As anticipated above, no eruptive activity other than the 1977 and 2002 eruptions has occurred outside the central crater of Nyiragongo in more than 100 years. Although no dating of previous volcanic activity is available, field inspections and popular recollection do not support the occurrence of lava flows on the volcano flanks in the last few hundred years. The present investigation therefore assumes that possible lateral eruptions in the next few decades will have similar characteristics to the 1977 and 2002 eruptions, which were very similar to each other.

Figure 3 shows the map of the 1977 and 2002 lava fields. The 2002 lava field previously mapped in Favalli et al. (2006) is now refined thanks to new satellite images. The complete set of satellite images used for mapping is reported in Table 1. These images were complemented with pictures and movies taken from helicopters in the days and months after the 2002 eruption (Favalli et al. 2006). As seen in Fig. 3, part of the eruptive fissures formed in 1977 were also reactivated in 2002. With respect to the 1977 system, the 2002 fissures appear to have mostly formed on the southern flank of the volcano and have propagated southward. The 2002 lava flows emerging from portions of the fissure system which were also active in 1977 inundated largely the same areas. As noted in Favalli et al. (2006), this suggests that the low thickness of lava flows (of the order of 1 m) and high fluidity of lavas were such that the presence of previous lava flows had a limited effect on the propagation of subsequent ones. Figure 4 reports an estimate of the volumes of single lava flows from the 1977 and 2002 eruptions based on field estimates of their average thickness; it emerges that the 2002 eruption discharged about twice the amount of lava discharged in 1977.

Fig. 3
figure 3

Mapping of the 1977 and 2002 lava flows and eruptive fissures. Background image Landsat 7 ETM+ (courtesy of Maryland University, Global Land Cover Facility: http://glcf.umiacs.umd.edu)

Fig. 4
figure 4

Estimated volumes of single lava flows from the 2002 (a) and 1977 (b) eruptions. Volume estimates have been refined with respect to those in Favalli et al. (2006) thanks to more accurate mapping and new estimates of the average lava thickness

Table 1 Satellite images used to map lava flows from the 1977 and 2002 eruptions at Nyiragongo

As already discussed (Favalli et al. 2005, 2006), the two model parameters Δh and N mostly depend on average lava flow thickness and DEM resolution. The principle for model calibration consists in finding a single pair of Δh and N values which best reproduces the entire lava field, irrespective of differences between lava flows originating from vents at different altitudes (Giordano et al. 2007). This corresponds to a “maximum simplicity” approach, which is maintained throughout the present investigation. When some assumptions must be made, as in the case of the definition of lava flow lengths or of the vent opening probability distribution discussed below, we stick to the data and observations as much as possible, translating them into a simplified, schematic picture. A-posteriori evaluation of the match between real and simulated flows, and between the final hazard map and the observed lava flow paths, is then used to assess the degree of oversimplification implied in the adopted approach.

The above “maximum simplicity” approach has some advantages when used within the present modelling framework. First of all, it tends to minimize the risk of conclusions too dependent on starting assumptions which may not accurately reflect data and observations. Secondly, it allows real-time application of the calibrated model during an emergency without requiring additional data on the specific characteristics of lava flows originating from different vents. The use of one single pair of model parameters for very fluid, thin lava flows originating from high altitude vents and for more viscous, thicker flows from low altitude vents (Giordano et al. 2007) obviously increases the approximation of the reproducibility and prediction of lava flow paths. Nonetheless, the method adopted in this work does not strictly require a very high accuracy to estimate the global hazard from lava flows on the flanks of the volcano.

Calibration of model parameters Δh and N is done by maximizing the ratio between the two areas corresponding to the intersection and the union of real and simulated flows, after having arbitrarily cut the simulated paths at the observed lava flow runout distance. The example in Fig. 5 illustrates this principle. The narrow area delimited by red lines in Fig. 5a corresponds to values of the above ratio exceeding 0.9 times the maximum value found in the investigated parameter space. The first panel in Fig. 5b shows a lava flow path simulation run with parameter values from inside this area (point 1 in Fig. 5a). Pairs of Δh and N corresponding to points below or above the red lines in Fig. 5a result in underestimation or overestimation, respectively, of the inundated areas (second and third panels in Fig. 5b).

Fig. 5
figure 5

Calibration of DOWNFLOW model parameters. a Calibrated pairs of Δh and N (area bounded by red lines). b Example applications: 1) model parameters corresponding to point 1 in a; 2) model parameters corresponding to point 2 in a, resulting in underestimation of inundated areas; 3) model parameters corresponding to point 3 in a, resulting in overestimation of inundated areas

As shown in Fig. 5, the best-fit value of Δh rapidly decreases with increasing N; above an N value of a few thousands, it then remains nearly constant. Such a trend helps illustrate the actual role of the two parameters. If the number of computed steepest descent paths for a vent is small, the simulated lava paths must be highly capable of surmounting obstacles in order to reproduce the actual spreading of the lava flow over the topography. When Δh is decreased sufficiently to define the maximum basin which can be inundated, a further increase in N above certain values does not substantially modify numerical results, since basin saturation is approached asymptotically.

The determined best-fit values are Δh = 0.4 m and N = 10,000. Figure 6 shows the comparison between real and simulated lava flow paths from the 2002 eruption, after having arbitrarily cut each simulated path at the observed maximum runout distance. About 80% of the real paths are well reproduced by the simulations. In most cases, the simulated paths accurately reproduce the shape and width of real lava flows and many of the non-inundated areas between different lava flow branches. Considering the relatively poor resolution of the initial 90-m pixel DEM, the match in Fig. 6 seems particularly good. The simulated paths tend to slightly overestimate lava flow widths and to produce additional small branches, especially in low altitude areas characterized by slight slopes.

Fig. 6
figure 6

Comparison between actual (white contours) and simulated (red) lava flows from the 2002 Nyiragongo eruption. Simulations employ the calibrated model parameters Δh = 0.4 m and N = 10,000. The dotted line is the state border

Lava flow lengths

As explained above, the adopted DOWNFLOW code does not allow the determination of lava flow lengths. This implies that such lengths must be estimated a-priori and assumed for the calculations. With this aim, we analysed the data from the 1977 and 2002 lava flows to check for the existence of a relationship between vent position and flow length. Figure 7 shows the length of single lava flows as a function of vent elevation (Fig. 7a) and distance from the central crater (Fig. 7b). Although there is some significant scatter, a tendency for lava flows to reach greater distances with decreasing vent altitude (or increasing vent distance from the central crater) emerges. The large deviation from this trend shown by the 2002 Goma lava flow (see Fig. 4) is at least partly due to the fact that the flow length is computed up to Lake Kivu, whereas the flow actually entered the lake, pouring about 1 Mm3 of lava into it (Halbwachs et al. 2002).

Fig. 7
figure 7

Length and volume of lava flows from the 1977 and 2002 Nyiragongo eruptions, plotted against: a, c vent elevation; b, d vent distance from the central crater. Squares in b show the length–distance relationship adopted in Fig. 8

The above trends are significantly improved by plotting the mean estimates of lava flow volumes shown in Fig. 4 (Fig. 7c,d). An increase in magma volumes discharged from vents at progressively lower altitudes (or progressively larger distances from the central crater) is well consistent with the geologic interpretation of both the 1977 and 2002 eruptions, according to which the central conduit system is drained as long as the fissure system propagates to greater distances and lower altitudes (Komorowski et al. 2004; Giordano et al. 2007; Tedesco et al. 2007).

The total number of data points (14) in Fig. 7 is too small for a reliable statistical analysis of length–altitude relationships. The inclusion of additional data, either from Nyiragongo eruptions or from other basaltic volcanoes, is hindered by the very poor knowledge of the previous history of the volcano, the intense weathering in the rainforest climate which prevents the acquisition of reliable data on ancient lava flows from remote sensing images, and the extremely peculiar rheology of Nyiragongo lava, which is responsible for the unusual behaviour of lava flows (Tazieff 1977; Giordano et al. 2007). For these reasons, we prefer to accept the uncertainty due to the relatively low number of data points on the investigated eruption dynamics (rifting on the volcano flanks) of the considered volcanic system rather than increase the uncertainty by adding information which may be largely misleading.

Following the above-stated principle of maximum simplicity, we subdivided the volcano area into three concentric sectors, and assigned a minimum and maximum possible length to lava flows originating from each of the sectors (Fig. 8). A lava flow originated from a given sector has a probability of 1 to reach the corresponding minimum distance and a probability of 0 to reach the corresponding maximum distance. A linearly decaying probability of 1 to 0 is assigned to intermediate distances. In order to evaluate the effects of the uncertainty on the adopted lava flow length–vent altitude relationships, we performed a sensitivity analysis by repeating the calculations with significantly different assumed flow lengths. The results of this sensitivity analysis are discussed below.

Fig. 8
figure 8

Assumed lava flow length distribution as a function of vent location. Numbers indicate minimum and maximum lengths (see text). The green area on the bottom right side represents the buttress of the rift rim

Probability of vent opening

As in the case of lava flow length, the vent opening probability was defined with reference to the 1977 and 2002 eruptions. These events suggest a tectonic tensional stress regime with an E–W oriented σ 3, which led to the opening, reactivation and extension of a system of dominant N–S fractures and minor SE–NW fractures (active in 1977 and re-activated in its upper portion in 2002) in the NW volcano sector (Fig. 3). We simplified this scenario by defining three areas with different vent opening probabilities, as in Fig. 9. Since the only eccentric eruptions in the last century occurred in 1977 and 2002, we assume that future eccentric eruptions in the next few decades will have similar characteristics and will possibly propagate the fissure system southward (Allard et al. 2002; Tedesco et al. 2002; Komorowski et al. 2004). We therefore arbitrarily assigned a vent opening probability corresponding to the red area in Fig. 9, i.e. 100 times larger than that in the external yellow area. The blue area represents a sort of “connection” between the highest and lowest probability areas, with a vent opening probability ten times lower and higher than, respectively, the fractured red and the external yellow areas. The gray area at the bottom-right corner of Fig. 9, corresponding to the buttress of the basement relief outside the Rift Valley, is assigned a zero vent opening probability.

Fig. 9
figure 9

Assumed distribution of the relative probability of vent opening. Eruptive fissures from 2002 (yellow) and 1977 (black) are also reported. The gray area on the bottom right side represents the buttress of the rift rim

In order to evaluate the relevance of the assumed vent opening probability distribution in the definition of lava flow hazard at Nyiragongo, we completed a sensitivity study by significantly modifying the distribution in Fig. 9. The results of this study are discussed below.

Note that the flanks of the volcano are studded with many monogenic and polygenic scoria cones (Capaccioni et al. 2004), some of which are visible in Fig. 3; they are distributed along many alignments not coinciding with the 1977 and 2002 fracture zones. There is unfortunately no dating available for any of these cones, and it cannot therefore be excluded that some of them are young. Field evaluation is complicated by intense weathering in the rainforest climate of the area; therefore, although no apparently young lava flows can be seen on the volcano flanks (apart from those produced in 1977 and 2002), the assumption that no other lava flows were produced in the last few hundred years is questionable. This is a limitation in the present hazard evaluation, which assumes that future venting will follow patterns observed in the 1977 and 2002 eruptions. As a consequence, the hazard evaluation in this paper should be taken as limited to the occurrence of future eruptions triggered by the same basic processes which led to the last two eccentric eruptions of the volcano.

Lava flow hazard map

In order to construct a lava flow hazard map for Nyiragongo, we resampled with a 30 m step by linearly integrating the original 90-m pixel DEM and performed one lava flow simulation (10,000 steepest descent path calculations with randomly perturbed topography and Δh = 0.4 m, as described above) every 90 m, in correspondence of each pixel constituting the original DEM. The probability P i that each pixel i is invaded by a lava flow in the case of a future eruption (a constrained probability, i.e., the absolute probability upon the occurrence of an eruption) is then given by

$$P_i = \sum\limits_j {P_{Vj} \times P_{ij} \times P_{Lij} } $$

where the subscript j refers to each vent from each single pixel, P Vj is the probability of vent opening at pixel j according to Fig. 9, P ij takes a value of 1 if pixel i is invaded by a lava flow originating from pixel j (irrespective of the distance between i and j) and of zero if it is not, and P Lij is the probability that a lava flow from pixel j reaches the distance along the flow to pixel i given in Fig. 8.

A total of about 54,000 simulation vents (and 5.4 × 108 steepest descent path calculations) spaced 90 m apart were considered. Figure 10 shows the resulting lava flow hazard map, where the different colours were chosen to illustrate areas with very low (<0.1%) to very high (8–20%) lava flow invasion probability. Figure 10 also shows the actual lava flow paths from the 1977 and 2002 eruptions. It is important to note that the data used to construct the hazard map derives only from the 90-m pixel SRTM DEM, the calibration of the two model parameters Δh and N, and the lava flow length and vent opening probability distributions in Figs. 8 and 9. On this basis, the fairly good match in Fig. 10 between areas of high to very high inundation probability and actual lava flow paths is quite satisfactory. This match is evident for lava flows at mid to low altitudes, but is lacking in the upper volcano areas. A closer match may have been obtained in these areas by increasing the probability of vent opening in regions approaching the central volcano crater.

Fig. 10
figure 10

Lava flow hazard map for Nyiragongo. Lava flows from the 1977 and 2002 eruptions are shown (white contours and dotted areas). The dashed lines are city boundaries (Goma in D.R.C., Gisenyi in Rwanda)

The hazard map in Fig. 10 suggests the following considerations. The two lava flows which entered Goma in 2002 correspond to the two most probable entry paths into town. The eastern lava flow, which produced the most devastation in town, also corresponds to the area of highest lava flow hazard on the flanks of Nyiragongo. This is due to the peculiarities of the hydrographic network on the southern flank of the volcano, particularly in the areas around the 1977 and 2002 system of fractures. The highest hazard area in Fig. 10 (in blue) corresponds to the natural basin of convergence for several valleys to the north (the red and orange high or intermediate-high hazard areas in Fig. 10), implying that lava flowing over a large portion of the southern volcano flank will necessarily tend to converge in the East Goma sector already devastated in 2002.

With respect to the map of susceptibility of invasion by lava flows in Goma reported in Favalli et al. (2006), the West Goma area now appears much safer. This is because the SRTM DEM used in this work allows the complete representation of the volcano topography, including the areas in relief north of the West Goma sector, which diverge lava flows towards either the eastern area of high hazard in town, or towards areas west of the town of Goma. Conversely, the low susceptibility area between the two 2002 lava flows in Goma, highlighted in Favalli et al. (2006), is confirmed here as a low to very low hazard area.

The town of Gisenyi in Rwanda is also subject to an intermediate to high lava flow hazard. This is not due to an unfavourable hydrography, which is instead an important factor in the definition of the two high hazard areas in Goma. On the contrary, most of the valleys north of Gisenyi trend towards the East Goma sector, thereby increasing the local hazard in the latter area. Intermediate-high hazard in Gisenyi instead derives from its proximity to the alignment of eruptive fractures, so that the probability of future vent opening in town or in its immediate proximity is high (see Fig. 9).

The map in Fig. 10 shows a high lava flow hazard for a vast area west of the central volcano crater, where two main valleys are located on the continuation of lava flows formed in 1977 and 2002. Should the corresponding eruptive fractures propagate towards lower altitudes, those areas, which are fortunately uninhabited, will likely be invaded by lava flows. Lastly, although we have conducted only a limited investigation of the deserted area north of the volcano, the simulated and observed lava flow paths suggest that the presence in the area of thick E–W trending lava flows from Nyamulagira volcano represent an efficient barrier to the northward propagation of lava flows from Nyiragongo.

Sensitivity analysis

In order to evaluate the robustness of the lava flow hazard map in Fig. 10, particularly in the urban areas close to Lake Kivu, we performed a sensitivity analysis by changing the adopted lava flow length and vent opening probability distributions in Figs. 8 and 9, and deriving corresponding lava flow hazard maps. In particular, we assumed that lava flows originating from each single vent can travel an infinite distance up to the domain boundaries (or to Lake Kivu), and considered two end-member conditions for vent probability distribution. The first end-member condition is represented by homogeneous probability over the entire domain. The second condition is represented by a highly specialized vent probability distribution reported in Fig. 11, whereby the relative probability increases towards both the fracture system of the 1977 and 2002 eruptions and the central Nyiragongo crater.

Fig. 11
figure 11

Vent opening probability distribution adopted in the sensitivity study

Figure 12 shows the results of the sensitivity analysis. Comparison between panels on the same line allows the effects of different vent opening probability distributions to be assessed for the lava flow length distribution in Fig. 8 (top) and for an infinite lava flow length (bottom). Comparison of panels in the same column allows instead the evaluation of the effects of different assumed lava flow length distributions for three different vent opening probability distributions corresponding to a homogeneous distribution (left), the one in Fig. 9 (central), and the highly specialized distribution in Fig. 11 (right). Figure 12b corresponds to the lava flow hazard map in Fig. 10.

Fig. 12
figure 12

Results of the analysis of the sensitivity of the hazard map to different assumed lava flow lengths (top vs. bottom panels) and different assumed vent opening probability distributions (from left to right: homogeneous vent opening probability; probability distribution from Fig. 9; probability distribution from Fig. 11)

Several considerations stem from the analysis of Fig. 12. As expected, largely different lava flow lengths and vent opening probability distributions significantly affect lava flow inundation probabilities. However, a dominant role is played by the morphology of the volcano flanks. The main conclusions derived above from the hazard map in Fig. 10 (or in Fig. 12b) do not change substantially when looking at the different panels in Fig. 12. In all cases, (1) the two areas of Goma destroyed by lava flows from the 2002 eruption represent the expected paths for the entry of lava into town; (2) the 2002 eastern lava flow in Goma corresponds to the area of highest hazard on the flanks of the volcano; (3) the town of Gisenyi in Rwanda is subject to significant lava flow hazard.

The most relevant differences concern absolute probabilities (as stated earlier, these are constrained probabilities, or probabilities constrained by the occurrence of an eruption) more than the distribution and extent of inundated areas. The assumption of infinite lava flow length (bottom panels) obviously results in a large increase in inundation probabilities at large distances from the central crater, where the lava flows coming from distant vents can concentrate. With respect to the hazard map in Fig. 10 (or in Fig. 12b), the homogeneous vent opening probability distribution (Fig. 12a) results, as expected, in a more distributed hazard over the volcano flanks. The very specialized vent opening probability distribution in Fig. 11 results in a hazard map (reported in Fig. 12c) substantially similar to that in Fig. 12b, with the exception that inundation probabilities in the farthest areas close to the lake decrease due to a relative decrease in vent opening probability in these areas.

Conclusions

This work presents a comprehensive map of lava flow hazard at Nyiragongo volcano, which in 2002 produced the most outstanding case of partial destruction of a big town due to the advance of lava. The adopted approach allows a probabilistic evaluation of future lava flow paths in the area, and coincides with the constrained hazard, i.e. the hazard assuming the occurrence of an eruption. The advantages and limitations of the employed model are clearly explained. One of the most significant advantages is the small computational time required by the code, which efficiently and effectively takes into account several aspects of the complex behaviour of lava flows and their interaction with a complex 3D topography. Such computational speed allows very detailed investigation, with about 54,000 vents and associated lava flows computed over an area of approximately 400 km2, and completion of an exhaustive sensitivity study on the assumed lava flow length and vent opening probability distributions. The latter study confirms the dominant role of volcano flank morphology in determining the areas of highest lava flow hazard. The major limitations of the adopted procedure are the uncertain definition of lava flow length and vent opening probability distributions. In order to limit conclusions not strictly rooted in the available data, we referred the future scenario to the 1977 and 2002 eruptions, which produced the only known cases of lava flows on the volcano flanks in more than 100 years. As a consequence, the hazard map from this work (reported in Fig. 10) must be referred to the occurrence of a future eruption caused by mechanisms similar to those which led to the 1977 and 2002 eruptions.

The hazard map in Fig. 10 shows that the eastern sector of Goma, which suffered the greatest devastation in 2002, corresponds to the area of highest hazard on the volcano. The two lava flows which entered Goma in 2002 followed the most probable entry paths into town. The two eastern and western areas devastated in 2002 are therefore expected to be invaded and destroyed again by lava flows in the future. The town of Gisenyi in Rwanda, which was not reached by lava flows in 2002, is characterized by intermediate to high hazard due to its proximity to the fracture alignment with highest probability of future venting.

In a companion paper (Chirico et al. 2008) we start from the hazard map in Fig. 10 and use numerical simulations and calibration from this work to investigate possible measures for the reduction of the local lava flow hazard through the construction of artificial barriers. The paper ends with a proposal for the future development of the town of Goma, which limits the possibility of future lava flows in the town to the sole case of venting directly within the town.