A model for lava flows with two thermal components

Abstract

A mathematical model is presented for the cooling of an active flow with two separate thermal components. One component is a crust that cools by radiation and generally thickens with time. The other component is an inner core that is vertically isothermal and partially exposed at the top surface, where heat is lost by radiation. This model provides a more realistic description of active lava flows than the existing models that assume thermal homogeneity in each vertical cross section perpendicular to the direction of flow advance. Characteristic time scales for heat loss from the core are comparable to typical durations for the emplacement of single‐lobed basaltic flows. The two‐component model predicts fractional areas of exposed core between 0.001 and 0.1, consistent with several types of observations of lava flows. Predicted temperature changes for the crust and core, as a function of distance from the vent, also comparable favorably to the limited observations available for active flows. Depending on eruption duration, fraction of exposed core, flow thickness, and initial eruption temperature, the thermal interaction between the crust and the core can have a significant effect on the core temperature, the growth of the crust, and various averages of thermal losses by radiation. This analysis suggests that flow dimensions may be strongly influenced by thermal dynamics in the core if emplacement duration is long, the fraction of exposed core is maintained at a high level, or the initial eruption temperature is low.

Field measurements of heat loss from skylights and lava tube systems

“…Surface temperature measurements of lava streams made with thermal infrared thermometers typically record an integrated surface temperature that represents the average temperature captured within the instrument's FOV. The effective radiation of the flow surface (T surf , in kelvin) can thus be described using two thermal components [Crisp and Baloga, 1990]:…”

“…where T hot is the temperature of the hotter portion of the lava surface, T crust is the temperature of the cool crust, and f c is the surface area fraction occupied by cooled crust [Crisp and Baloga, 1990;Oppenheimer, 1991]. If we take T hot as 1130°C (based on our highest TIRT measurements using the Land/Minolta 152) and T surf of 1100°C (TIRT measurements with the Raytek) and assume T crust is at a temperature $50 -100°C less than T hot , then we can place loose constraints on f c , i.e., the surface fraction covered by cooled crust.…”

The 1997 eruption of Okmok Volcano, Alaska: a synthesis of remotely sensed imagery

“…5) and lava radiance. Three values are shown for lava surface temperature, which span the range of possible values for average lava surface temperature (which itself is an area-weighted composite of the radiance of incandescent cracks and cooling crust ; Crisp and Baloga, 1990). A temperature of 1000 ‡C would approximate a fully incandescent surface, while a value of 250 ‡C would represent an aPa lava surface with a well-developed crust (Crisp and Baloga, 1990).…”

“…Three values are shown for lava surface temperature, which span the range of possible values for average lava surface temperature (which itself is an area-weighted composite of the radiance of incandescent cracks and cooling crust ; Crisp and Baloga, 1990). A temperature of 1000 ‡C would approximate a fully incandescent surface, while a value of 250 ‡C would represent an aPa lava surface with a well-developed crust (Crisp and Baloga, 1990). Since Band 3 is highly sensitive to radiance from hot surfaces (hundreds of degrees Celsius), very little of the hot surface is required to produce a pixel-inte- For an assumed background temperature of 0 ‡C, the pixel-integrated temperature is shown here for three high-temperature surfaces (1000, 500, 250 ‡C), for both Bands 3 and 4.…”

A new simplified approach for simultaneous retrieval of SO<sub>2</sub> and ash content of tropospheric volcanic clouds: an application to the Mt Etna volcano

“…Clearly, these advantages are partially offset by the limited precision of the result due to the approximations introduced to simplify the procedure and reduce the computation time. Nevertheless, all the algorithms of this kind, like Split Window (Prabhakara et al, 1974;McMillin, 1975;Price, 1984), Dual Band (Crisp and Baloga, 1990;Dozier, 1981), and NDVI (Rouse et al, 1973;Roderick et al, 1996), were founded on this differential basis, and their widespread use is due to their simplicity, user friendliness, and speed. The novel VPR procedure presented here was designed with the aim of providing an easier, faster, but nevertheless reliable simultaneous assessment of volcanic ash and SO 2 columnar quantities.…”