Two models combined can forecast lava flow accurately and promptly

Volcanoes claim lives in different ways, by spewing hot ash clouds and projectile tephra or by triggering tsunamis and mudflows. But flowing lava from a so-called effusive eruption does not often endanger life. Since lava rarely flows faster than people can walk, it’s usually easy to get out of the way. But a lava flow destroys all the roads, buildings, and agricultural land in its path, as shown in figure 1. It’s therefore important for scientists to be able to forecast the direction and distance that lava will flow, so that civil authorities can order evacuations or take other appropriate measures.

One precaution that’s sometimes employed is the building of earthen dams to divert lava away from developed or otherwise valuable land. Good forecasts can ensure that the dams, which take time and money to construct, are placed where they will be most effective. But modeling the flow of lava over uneven terrain is a complicated challenge in thermodynamics and rheology. As lava cools, it solidifies and eventually stops flowing. And uncertainty in measurements of the terrain complicates the prediction of what directions a flow will take.

In 1999–2000 Massimiliano Favalli, Maria Teresa Pareschi, and their colleagues from the National Institute of Geophysics and Volcanology in Pisa, Italy, developed DOWNFLOW, a stochastic model that forecasts the flow’s direction but not its distance. ¹ In 2001 Andrew Harris and Scott Rowland of the University of Hawaii in Honolulu presented FLOWGO, a model that forecasts how far lava will flow but not in what direction. ² Now, Robert Wright (also of Hawaii), Harris, and programmer Harold Garbeil have combined the two models to yield a computationally efficient tool for forecasting the direction and extent of a lava flow. ³

Go with the flow

In the late 1990s Wright and Harris were both interested in the possibility of using satellite data to produce more realistic lava-flow forecasts. A satellite measurement of the IR radiation from an active lava flow can be used to derive the effusion rate, the volume of lava emitted per unit time: The greater the heat flux, the greater the effusion rate. That rate, in turn, affects how far the lava can flow before it cools and solidifies. Over the course of an eruption, the effusion rate often changes substantially, but as Wright explains, “All the numerical models published at that time used a single, unchanging effusion rate to generate their predictions.” Satellites could provide updated effusion rate measurements as often as several times per day.

The FLOWGO model translates effusion rates into forecasts of lava flow lengths. It simulates lava flowing in a channel, meaning that the upper surface of the lava flows along with the bulk. As a parcel of lava moves through the channel, it loses heat to the ground below the channel, the levees to the sides, and the atmosphere above. The greater the effusion rate, the faster, wider, and deeper the lava is at its source, and the farther it can flow before solidifying.

With DOWNFLOW, Favalli and colleagues took a different approach. The model doesn’t explicitly simulate the lava flow to predict its direction but is instead a convenient means of getting the right answer. It’s based on the idea that given a terrain map of an area, calculating the path of steepest descent is easy. But that calculated path doesn’t fully represent the lava’s path. First, because terrain maps have finite resolution, the terrain is not exactly known. Second, a stream’s depth affects its flow: A deep enough stream can surmount obstacles to send branches flowing off in multiple directions.

The DOWNFLOW model accounts for both of those complications by randomly varying each point on the terrain within a range defined by the terrain’s uncertainty and the expected flow depth. The path of steepest descent is calculated for the modified terrain. That process is repeated many times—usually thousands or tens of thousands—and the flow area is taken to be the union of all the computed paths, as shown in figure 2(a). When the model is applied in practice, as it has been for recent eruptions of Mount Etna in Italy, flow lengths are estimated based on the statistics of past eruptions. Says Favalli, “I am still surprised that such a simple model is able to predict so well the areas invaded by gravity-driven fluids.”

To combine the models, Wright and colleagues used FLOWGO to compute the expected termination of each path computed by DOWNFLOW. Even with the extensive repetition, results can be generated more quickly than with other simulation techniques: Some 10 000 paths can be computed in just 20 minutes, whereas other methods take several hours. Furthermore, as Wright explains, “When we compared the DOWNFLOW/FLOWGO combination with other models, we found that it performed as well, and, in fact, better.”

The researchers are still working on implementing their model in real time. To test it, they instead used the early 1990s eruption of Mount Etna. Figure 2(b) shows the results for the effusion rate measured on 2 January 1992; the actual extent of the lava flow is shown by the largest outlined area in figure 2(a). For that date and several others during the same eruption, the model’s results agree well with observations. Says Wright, “The model doesn’t predict every twist and turn that a lava flow might take. Then again, no model can do that.”