Stephen M. Baloga

Eruption rate, area, and length relationships for some Hawaiian lava flows

Abstract Volcanic geomorphologists have investigated various relationships between eruption rate and morphologic parameters of lava flows, particularly with regard to preferred statistical correlations and the conditions under which they are valid. Here we employ two simple models for lava flow heat loss by Stefan-Boltzmann radiation to derive eruption rate versus planimetric area relationships. Both of these models predict a linear relationship between eruption rate and planimetric area, modulated by distinct prefactors potentially sensitive to compositional and temperature differences among different flows. Regardless of any theoretical considerations, we show that eruption rate is highly correlated with planimetric area for the Hawaiian basaltic flows analyzed in this work. Moreover, this observed correlation is superior to those from other obvious combinations of eruption rate and flow dimensions. On the basis of the theoretical models for lava flow heat loss, the correlations obtained here suggest that the surfaces of Hawaiian flows radiate at an effective temperature much less than the inner parts of the flowing lava in agreement with numerous field observations. This work also indicates that eruption rate versus planimetric area correlations can be markedly degraded when data from different vents, volcanoes and epochs are combined. These previously unrecognized sensitivities identified by the thermal loss modeling may have contributed to past unresolved debates on relationships between eruption rates and morphologic dimensions.

Influence of crystallization and entrainment of cooler material on the emplacement of basaltic aa lava flows

A theoretical model is used to describe and investigate the effects of simultaneous crystallization, radiation loss, and entrainment of cooler material on the temperature of a well-mixed core of an active aa lava flow. Entrainment of crust, levee debris, and base material into the interior of active flows has been observed, but the degree of assimilation and the thermal consequences are difficult to quantify. The rate of entrainment can be constrained by supplementing the theoretical model with information on the crystallization along the path of the flow and estimation of the radiative loss from the flow interior. Application of the model is demonstrated with the 1984 Mauna Loa flow, which was erupted about 30°C undercooled. Without any entrainment of cooler material, the high crystallization rates would have driven temperatures in the core well above temperatures measured by thermocouple and estimated from glass geothermometry. One plausible scenario for this flow, which agrees with available temperature and crystallinity measurements, has a high initial rate of entrainment during the first 8 hours of travel (a mass ratio of entrained material to fluid core of about 15% if the average temperature of the entrained material was 600°C), which counterbalances the latent heat from approximately 40% crystallization. In this scenario, the model suggests an additional 5% crystallization and a 5% entrainment mass ratio over the subsequent 16-hour period. Measurements of crystallization, radiative losses, and entrainment factors are necessary for understanding the detailed thermal histories of active lava flows.

Transport of atmospheric water vapor by volcanic eruption columns

Contrary to assumptions often made in the literature, explosive volcanic eruptions are capable of transporting significant amounts of water into the stratosphere. In addition to the magmatic water component, atmospheric water vapor is entrained by the column at lower levels. A theoretical model for the conservation of mass, momentum, and thermal energy of four separate components (dry air, water vapor, liquid condensates, and solid particles) is used to determine the extent of atmospheric water redistribution. We examine the effects of water vapor condensation on dynamical characteristics and ambient water vapor transport. A simple technique is presented for deriving canonical forms for the complex system of ordinary differential equations governing the column components. Solutions of this model are presented that show the influence of different volcanic boundary conditions and a range of ambient water vapor distributions on transport of the buoyant column. We show that the water component (vapor + liquid) of small eruption columns rising through a wet atmosphere is dominated by entrained water, whereas larger columns are dominated by the magmatic water. This is due, in part, to the proportionately smaller entrainment surface area in relation to the control volume for the larger columns. We also show that a maintained column with an initial mass flux of 2.7 × 108 kg s−1 erupted into a wet atmosphere would inject 96 Mt of water vapor into the stratosphere over 24 hours, comparable to the annual input from methane oxidation or 100 midlatitude thunderstorms. This increase may accelerate the conversion of simultaneously erupted volcanic SO2 into sulfuric acid.

Sensitivity of buoyant plume heights to ambient atmospheric conditions: Implications for volcanic eruption columns

A theoretical model is developed to investigate the sensitivity of buoyant atmospheric plumes to a wide range of ambient atmospheric conditions, including the temperature gradient, the latitude of the source, and the season. The formulation highlights the compressibility of an ideal gas, internal consistency between the governing equations for the conservation of momentum and energy, and the explicit use of the equation of state. Specific results are presented for water vapor plumes and implications are developed for multicomponent (water vapor, silicate particles, and condensates) volcanic plumes. If plume cooling is due solely to adiabatic expansion and the entrainment and mixing of ambient air, then the atmospheric temperature gradient is shown to be a dominant influence on plume height. Changes in the atmospheric gradient of 10 K/km cause the height of a low-level plume to diifer by a factor of 2. We estimate the magnitude of this effect on volcanic plumes by considering water vapor erupted with equivalent heat fluxes. The sensitivity of plumes to ambient conditions is a result of the small density difference driving buoyancy. The plume density, in turn, is strongly controlled by the thermal energy of the system. Sensitivities associated with the thermal energy balance in the eruption column are also investigated. A modest thermal loss (1–2%/km) from the column by a process other than entrainment can result in a plume height significantly lower than one that cools by entrainment alone. Additional cooling of this magnitude could be caused by a variety of combinations of phenomena, including radiative heat loss and, possibly, the conversion of heat energy into turbulent rotational energy. For particle-laden plumes, there is the possibility of additional heat loss through the fallout of solids from the eruption column. To understand the details of the thermal energy balance in a plume, measurements must be made of the bulk plume temperature profile under known atmospheric conditions.

Eruption constraints on tube-fed planetary lava flows

We examine the role of pressure and gravity as driving forces in planetary lava tubes for Newtonian and power law rheologies. The tubes are assumed to have been filled with lava that was emplaced in constant diameter circular tubes in the laminar flow regime and had constant density, heat capacity, thermal conductivity, and viscosity. Our model provides relationships between tube dimensions, driving forces, and effusion rates and rheology parameters. In general, the pressure term in the driving force dominates for very small slopes, but the gravity term eclipses the pressure term as the slope increases. Applying the model to Alba Patera tube flows suggests effusion rates somewhere between 2 and 105 m3/s and viscosities between 102 and 106 Pa s, with tighter constraints (2 to 4 orders of magnitude) for specific tube sizes and travel times. These effusion rate results are lower and the viscosity ranges are higher than those found in previous studies. This allows eruptions that are closer in style to terrestrial basaltic eruptions, although the flows are still considerably larger in scale than the Hawaiian tube flows. We find that very low lava viscosities are not essential for Alba Patera lava tubes and that tube formation may be a better indicator of the steadiness of the eruption and the presence of low slopes than it is of low viscosities (e.g., 102 Pa s). In addition, this analysis suggests that the tube systems on the steep flanks of Olympus Mons are fundamentally different from those at Alba Patera. The Olympus Mons flows could not have roofed over, been continuously full, or maintained a continuous lava tube transport system in the assumed full, steady, and fully developed conditions.

Sulfur flows of Ra Patera, Io

Abstract Voyager 1 imaging data have been used to investigate the color and morphology of several radial flow-like features at Ra Patera, a broad volcanic structure at approximately 8° latitude and 325° longitude on the Galilean satellite Io (J1). It was found that downstream progressions of flow color and morphology are consistent with lava of a predominately sulfur composition cooling radiatively and erupting in the range of 470 to 520°K at effusion rates at 1010 to 1011 cm3/sec. This implies global resurfacing rates by volcanic flows on Io of the order of 1 cm/year. Calculated energy content and effusion rates for flows at Ra Patera, using the physical parameters of sulfur, are of the order of the largest known terrestial basaltic eruptions and are consistent with calculations of globally available energy.

Quantifying the effect of rheology on lava-flow margins using fractal geometry

This study aims at quantifying the effect of rheology on plan-view shapes of lava flows using fractal geometry. Plan-view shapes of lava flows are important because they reflect the processes governing flow emplacement and may provide insight into lava-flow rheology and dynamics. In our earlier investigation (Bruno et al. 1992), we reported that flow margins of basalts are fractal, having a characteristic shape regardless of scale. We also found we could use fractal dimension (D, a parameter which quantifies flow-margin convolution) to distinguish between the two endmember types of basalts: a′ a (D: 1.05–1.09) and pahoehoe (D: 1.13–1.23). In this work, we confirm those earlier results for basalts based on a larger database and over a wider range of scale (0.125 m–2.4 km). Additionally, we analyze ten silicic flows (SiO2: 52–74%) over a similar scale range (10 m–4.5 km). We note that silicic flows tend to exhibit scale-dependent, or non-fractal, behavior. We attribute this breakdown of fractal behavior at increased silica contents to the suppression of small-scale features in the flow margin, due to the higher viscosities and yield strengths of silicic flows. These results suggest we can use the fractal properties of flow margins as a remote-sensing tool to distinguish flow types. Our evaluation of the nonlinear aspects of flow dynamics indicates a tendency toward fractal behavior for basaltic lavas whose flow is controlled by internal fluid dynamic processes. For silicic flows, or basaltic flows whose flow is controlled by steep slopes, our evaluation indicates non-fractal behavior, consistent with our observations.

A method for estimating eruption rates of planetary lava flows

Abstract A model that accounts for radiative losses from a partially crusted hotter core can be used to constrain eruption rates of single-lobed planetary lava flows by assuming thermal characteristics are similar to terrestrial flows. Eruption rate can be expressed as a function of the area fraction of core exposed, initial core temperature, core temperature when the flow stops advancing, crust thickness, flow thickness, and the density and heat capacity of the lava.

A methodology for constraining lava flow rheologies with MOLA

Topography as measured by the Mars Orbiter Laser Altimeter (MOLA), when supplemented with imaging data, can be used to infer physical emplacement processes in lava flows on Mars with a level of detail analogous to what can be done with unobserved lava flow eruptions on Earth. MOLA, Viking Orbiter and Mars Orbiter Camera (MOC) data are used to develop new inferences regarding the rheology of a typical lava flow near Elysium Mons on Mars. We present a technique that uses MOLA Precision Experiment Data Records (PEDRs) to directly determine the longitudinal thickness profile of lava flows. This technique is preferable to using gridded topography derived from MOLA, particularly for features such as lava flows, with thickness variations at the same scale as their surroundings. Thickness profiles and underlying slope estimates can then be compared with results from rheologic models. The longitudinal thickness profile of the Elysium example discussed here exhibits a concave-up flow surface that is consistent with an exponential viscosity increase. The viscosity shows a relative increase of about 50 times over the length of flow examined when the density of the lava increases as a result of lava degassing.

New statistics for estimating the bulk rheology of active lava flows: Puu Oo examples

Downstream changes in lava rheology due to cooling, crystallization, and vesiculation have a strong influence on the final length and morphology of a lava flow. Three statistics are proposed to estimate the change in lava rheology with distance along the path of an active flow. These statistics correspond to three separate models of the volumetric flow rate dependence on the thickness of the flow. Each statistic is based on flow dimensions and topographic data that are often available from field measurements or remote sensing. One model assumes an elementary laminar Newtonian flow. A second empirical model often used to describe the flow of complex geologic materials, such as lahars, sediment-laden floods, and debris flows, is also investigated for comparison. A new volume-loss model is also proposed to account for stationary components such as levees and stagnant areas. The three statistics derived from these flow rate models are applied and interpreted for two well-defined lobes from episodes 2 and 18 of the 1983-1984 Puu Oo eruption. The power law dependence of the first two models results only in modest differences in the estimates of rheologic change along the flow path. However, the removal of lava from the active flow to construct stationary components produces significant differences in both the magnitude of computed rheologic changes and the ability to discern trends in rheologic changes along the path of the flow.