Flow rate estimation in a lava tube based on surface temperature measurements. Issue 3 (22nd December 2016) - Melnik, Oleg
Summary: Formation of lava tubes is a common feature during effusive volcanic eruptions. Reduced heat losses of the flow inside the tube allow emplacement of long lava flows with surface exposure and cooling of the fresh lava only at the flow front. To judge potential hazard associated with lava flows, it is important to estimate the lava flow rate in a system of the tubes that develops inside the solidified flow. Thermal observations at the flow surface can provide potentially useful information on the location, size and flow rates of lava inside the tube. A simple model of a heat transfer from a lava tube to the atmosphere through solidified lava allows estimating the depth, the size of the lava tube and lava flow rate based on temperature measurements at the surface of the flow. Two cases are considered: cylindrical and elliptical cross-section of the tube. In the first case, simple analytical expressions are obtained, and in the second case, parameters are estimated by a fitting algorithm, which requires a solution of a non-linear heat conduction equation. Matlab scripts are provided for both cases.