Effusion rate controls on lava flow length and the role of heat loss: a review

Walker (1973;  107) argued that, for a limited set of compositions and flow types, effusion rate (E) was the principal influence on flow length, sparking a series of studies into the volume and cooling limits on flow extension. We here review these works, as well as the role of heat loss in controlling flow length. We also explore the applicability of Walker's idea to a larger compositional and morphological range. Heat loss plays a fundamental role in determining flow core cooling rates, thereby influencing cooling-limited flow length. Field measurements allow classification of four flow types with respect to heat loss. In this classification as we move from poorly insulated to well insulated regimes, decreased heat losses increase the length that a flow can extend for a given E, composition, morphology, or amount of cooling: (1) immature tube-contained, basalt - thin tube roofs provide minimal insulation, allowing cooling rates of c .1 0 22 8 Cs 21 so that at low E, these flows extend only a few hundred metres; (2) poorly crusted, basalt - open channels with hot surface crusts also exhibit cooling rates of c .1 0 22 8 Cs 21 so such flows extend a few kilometres at E , 1m 3 s 21 ; (3) heavily crusted, dacite - heat losses are reduced when thick crusts form, reducing core cooling rates to c .1 0 24 8 Cs 21 so these flows can potentially extend several kilometres even at low E and despite very high viscosities (10 9 -10 10 Pa s); (4) master tube-contained, basalt - thick tube roofs insulate flow, reducing heat losses and cooling rates to c .1 0 23 8 Cs 21 . These cooling rates mean that at low E, tube-contained flows can extend tens to hundreds of kilometres. Basically, if composition, insulation, and morphology are held constant flow length will increase with effusion rate. Our aim is to review G. P. L. Walker's pioneering work into the emplacement of lava flows, focusing on his studies of the relationship between effusion rate and eventual flow length, and the subsequent work that this inspired. Walker's ideas on this topic followed observations of active lava flow emplacement during a terminal (summit) effusive eruption at Mt Etna (Italy) during 1966, and the work was completed during 1967-1973. The work comprised a series of three papers. The first, 'Thick- ness and viscosity of etnean lavas' (Walker 1967), was published in Nature and examined the influence of viscosity and slope on flow emplacement, dimen- sions and morphology. The second, 'Compound and simple lava flows and flood basalts' (Walker 1972), published in Bulletin of Volcanology, set up stan- dard definitions and nomenclature for lava flow units and compound lava flows, and examined the conditions under which different flow architectures are built. Finally, 'Lengths of lava flows' (Walker 1973; in the Philosophical Transactions of the Royal Society of London) rounded the series off by demonstrating that effusion rate is the principal factor that influences not only flow length, but also flow field type, with viscosity being a secondary factor. With higher effusion rates, long simple flows tend to be emplaced, whereas at lower effu- sion rates, multiple short flows pile up around a vent to build compound flow fields. We focus on the main theme of this third paper and the influence that this has had on subsequent study and debate, before examining the role of thermal insulation and heat loss on determining and modifying effusion rate-flow length relation- ships. A relationship that governs the interplay between flow length, heat loss and effusion rate was recognized by Walker (1973). In the conclusion of the 'Lengths of lava flows' paper he stated:

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title: Flow-Units in Basalt
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title: The variation of magma discharge during basaltic eruptions
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title: Pahoehoe and aa in Hawaii: volumetric flow rate controls the lava structure
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title: Mapping lava flow hazards using computer simulation
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title: A preliminary thermal budget for lava tubes on the Earth and planets
abstract: Lava tubes are a very common and important feature in mafic lava flows. The insulation provided by lava tubes allows molten lava to travel large distances from the vent with little cooling. This paper presents the first attempt to quantify the processes that control this cooling. The resulting thermal budget balances heat loss by (1) conduction, (2) convection of air in the wall rocks, (3) vaporization of rainwater, and (4) radiation out of skylights against (1) viscous dissipation, (2) latent heat released during crystallization, and (3) the cooling of the lava. When applied to the Waha'ula tube on Kilauea Volcano, Hawaii, this thermal budget reproduces the observed ∼1°C/km cooling of the lava inside the active tube. The thermal budget is also used to compare the insulating ability of hypothetical lava tubes in a continental flood basalt setting, on the ocean floor, Venus, the Moon, and Mars. This analysis demonstrates the large effect of rainfall and atmospheric convection, the importance of the volumetric flux of lava through the tube, and the overwhelming importance of compositional (i.e., rheological) differences. This work suggests that basaltic tube-fed flows several hundred kilometers long can be produced by eruptions with effusion rates of only a few tens of cubic meters per second. Thus even the longest lava flows observed in our solar system could have been produced by low to moderate effusion rate eruptions, if they were tube-fed.

title: Kīlauea summit overflows: their ages and distribution in the Puna District, Hawai'i
abstract: The tube-fed pāhoehoe lava flows covering much of the northeast flank of Kīlauea Volcano are named the 'Ailā'au flows. Their eruption age, based on published and six new radiocarbon dates, is approximately AD 1445. The flows have distinctive paleomagnetic directions with steep inclinations (40°–50°) and easterly declinations (0°–10°E). The lava was transported ∼40 km from the vent to the coast in long, large-diameter lava tubes; the longest tube (Kazumura Cave) reaches from near the summit to within several kilometers of the coast near Kaloli Point. The estimated volume of the 'Ailā'au flow field is 5.2±0.8 km3, and the eruption that formed it probably lasted for approximately 50 years. Summit overflows from Kīlauea may have been nearly continuous between approximately AD 1290 and 1470, during which time a series of shields formed at and around the summit. The 'Ailā'au shield was either the youngest or the next to youngest in this series of shields. Site-mean paleomagnetic directions for lava flows underlying the 'Ailā'au flows form only six groups. These older pāhoehoe flows range in age from 2750 to <18,000 BP, and the region was inundated by lava flows only three times in the past 5000 years. The known intervals between eruptive events average ∼1600 years and range from ∼1250 years to >2200 years. Lava flows from most of these summit eruptions also reached the coast, but none appears as extensive as the 'Ailā'au flow field. The chemistry of the melts erupted during each of these summit overflow events is remarkably similar, averaging approximately 6.3 wt.% MgO near the coast and 6.8 wt.% MgO near the summit. The present-day caldera probably formed more recently than the eruption that formed the 'Ailā'au flows (estimated termination ca. AD 1470). The earliest explosive eruptions that formed the Keanakāko'i Ash, which is stratigraphically above the 'Ailā'au flows, cannot be older than this age.

title: Lengths of Hawaiian lava flows
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title: Effusion rate and the shape of aa lava flow-fields on Mount Etna
abstract: The maximum distance attained by lava flows on Mount Etna increases linearly with an increasing effusion rate for flows greater than 1 km long. By considering lava as a Bingham fluid, a simple model of the shape of a lava flow-field in terms of flows and conduits can be constructed. Calibration of this model using the flow distance-effusion rate relationship enables the variation of effusion rate during the eruption that produced the flow-field to be calculated. Analysis of the historical flank eruptions of Etna indicates a favored range of effusion rate from 15 to 45 m3/s.

title: The 1983 Etna eruption: Event chronology and morphological evolution of the lava flow
abstract: The event chronology of the 1983 Etna eruption is summarized, and the development of a compound lava field at different time intervals during the eruption is described as observed from aerial photographs.The morphological evolution of the lava fronts has been compared with effusion rate and principal modifications occurring in the main channel, and it has been inferred that the development of the lava flow units is related to the formation of lava tunnels and particularly of lava channels. The total volume of lava emitted has been estimated to be 100±20×106 m3 according to two different methods. Finally, the comparison with previous historical eruptive activity shows a good correlation to other quiet eruptions.

title: Formation of lava tubes and extensive flow field during the 1991–1993 eruption of Mount Etna
abstract: Detailed mapping during the 1991–1993 eruption of Mount Etna has shown that there is a relationship between tumuli, ephemeral vents, lava tubes, and their parent lava flows. During this eruption, many tubes formed in stationary, inflated ‘a’a lava flows. Ephemeral vents at the fronts of these stationary flows and above lava tubes fed secondary lava flows, many of which subsequently developed new tubes. The resulting complex network of tubes, ephemeral vents, and secondary flows was responsible for most of the widening, thickening, and lengthening of the 1991–1993 Etna lava flow field. The supply of relatively uncooled lava via tubes to distal parts of this flow field allowed lava to flow 3 km farther from the vent than the longest channel-fed lava flow. Our observations suggest that lava tubes play a more important role in the formation of extensive ‘a’a flow fields on Etna than has previously been recognized.

title: Lava flow cooling estimated from Landsat Thematic Mapper infrared data: The Lonquimay Eruption (Chile, 1989)
abstract: Surface temperatures of a 1989 andesite lava flow at Volcan Lonquimay, Chile, derived from an analysis of Landsat Thematic Mapper (TM) infrared data, show a progressive cooling of crusted lava from 250°C to 170°C down a 1.5 km segment of the flow. These results are obtained by solving “dual-band” equations for the two short-wavelength infrared TM bands, assuming that the lava surface can be represented by two thermal components, exposed core and chilled crust, and unlike previous investigations, by predetermining the temperature of the hot component rather than the cool component. This approach is consistent with both observational data and theoretical models, and shows that any exposed core of the flow occupies tiny fractions, possibly less than 0.03%, of the surface area. As a result, the crust made by far the greatest contribution to radiative heat losses, estimated at between 1 and 3 MW per 30×30 m pixel, along most of the flow's length. Convective heat transfer into the air above the flow is about two thirds the corresponding radiative flux. These estimated surface heat losses suggest thicknesses of less than 1 m for a conductive thermal boundary layer component of the crust. Radiance values in the thermal infrared band 6 of the TM image are consistent with temperatures derived from the short-wavelength infrared data and reveal the thermal manifestation of a topographic step beneath the flow.

title: Modeling of the steady-state temperature field in lava flow levées
abstract: The rationale of lava flow deviation is to prevent major damage, and, among the possible techniques, the opening of the flow levees has often been demonstrated to be suitable and reliable. The best way to open the levees in the right point, in order to obtain the required effect, is to produce an explosion in situ, and it is then necessary to map with the highest precision the temperature field inside the levees, in order to design a safe and successful intervention. The levees are formed by lava flows due to their non-Newtonian rheology, where the shear stress is lower than the yield stress. The levees then cool and solidify due to heat loss into the atmosphere. In this work we present analytical solutions of the steady-state heat conduction problem in a levee using the method of conformal mapping for simple geometrical shapes of the levee cross-section (triangular or square). Numerical solutions are obtained with a finite-element code for more complex, realistic geometries.

title: 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.

title: Cooling and crystallization of lava in open channels, and the transition of Pāhoehoe Lava to 'A'ā
abstract: Samples collected from a lava channel active at Kīlauea Volcano during May 1997 are used to constrain rates of lava cooling and crystallization during early stages of flow. Lava erupted at near-liquidus temperatures (∼1150  °C) cooled and crystallized rapidly in upper parts of the channel. Glass geothermometry indicates cooling by 12–14  °C over the first 2 km of transport. At flow velocities of 1–2 m/s, this translates to cooling rates of 22–50  °C/h. Cooling rates this high can be explained by radiative cooling of a well-stirred flow, consistent with observations of non-steady flow in proximal regions of the channel. Crystallization of plagioclase and pyroxene microlites occurred in response to cooling, with crystallization rates of 20–50% per hour. Crystallization proceeded primarily by nucleation of new crystals, and nucleation rates of ∼104/cm3s are similar to those measured in the 1984 open channel flow from Mauna Loa Volcano. There is no evidence for the large nucleation delays commonly assumed for plagioclase crystallization in basaltic melts, possibly a reflection of enhanced nucleation due to stirring of the flow. The transition of the flow surface morphology from pāhoehoe to 'a'ā occurred at a distance of 1.9 km from the vent. At this point, the flow was thermally stratified, with an interior temperature of ∼1137  °C and crystallinity of ∼15%, and a flow surface temperature of ∼1100  °C and crystallinity of ∼45%. 'A'ā formation initiated along channel margins, where crust was continuously disrupted, and involved tearing and clotting of the flow surface. Both observations suggest that the transition involved crossing of a rheological threshold. We suggest this threshold to be the development of a lava yield strength sufficient to prevent viscous flow of lava at the channel margin. We use this concept to propose that 'a'ā formation in open channels requires both sufficiently high strain rates for continued disruption of surface crusts and sufficient groundmass crystallinity to generate a yield strength equivalent to the imposed stress. In Hawai'i, where lava is typically microlite poor on eruption, these combined requirements help to explain two common observations on 'a'ā formation: (a) 'a'ā flow fields are generated when effusion rates are high (thus promoting crustal disruption); and (b) under most eruption conditions, lava issues from the vent as pāhoehoe and changes to 'a'ā only after flowing some distance, thus permitting sufficient crystallization.

title: Viscosity of hydrous rhyolitic melts inferred from kinetic experiments, and a new viscosity model
abstract: Viscosity of hydrous silicate melts is a critical property for understanding magma transport, bubble growth, volcanic eruption, and magma fragmentation. We report new inferred viscosity for hydrous rhyolitic melt in the viscosity range of 109 to 1015 Pa·s based on the kinetics of hydrous species reactions in the melt upon cooling (i.e., based on the equivalence between the glass-transition temperature and the apparent equilibrium temperature), as well as data from bubble-growth experiments. By combining viscosity data of rhyolitic melts containing from 6 ppm to about 8.0 wt% total H2O (both our own data and literature data), we propose the following relation for the dependence of viscosity on total H2O content at a given temperature and pressure: where η is viscosity and 1/η is fluidity, η1 is the viscosity of the dry melt, x is the mole fraction of total dissolved H2O, n and η2 are two fitting parameters, and η2 can be interpreted to be the viscosity of the hypothetical melt consisting of pure H2O. The above simple equation appears to work well in modeling viscosity of hydrous rhyolitic melts. Using the above functional form and a weighted nonlinear regression, experimental data covering 570 to 1920 K and 0.0006 to 8.2 wt% total H2O are used to obtain the following non-Arrhenian model for the viscosity of Mono Crater rhyolitic melts: logη = -log{exp(18.5611 - 49584/T) + exp[1.47517 - (1795.5/T)1.9448]x1+ (1812.2/T)2} where T is in K, and x is the mole fraction of total dissolved H2O on a single oxygen basis. The 2σ uncertainty in the above 6-parameter formula is 0.36 in terms of logη (for experimental data with errors smaller than 1 log unit), much less than uncertainties in all previous models for hydrous rhyolitic melt. We hence recommend its use for predicting the viscosity of high-SiO2 and calc-alkaline rhyolitic melts. Our model shows that a minute H2O content can still affect the melt viscosity significantly, especially at low temperatures (i.e., high viscosity). For example, at 973 K, the viscosity of rhyolitic melt increases by 1.2 orders of magnitude from a melt with 0.1 wt% total H2O to a melt with less than 100 ppm total H2O. Because a nominally “dry” melt may still contain some H2O, such as several hundred ppm, it is critical for experimentalists to report its total H2O content for viscosity measurements. Some inconsistency in literature viscosity data might be attributable to small variations in H2O content in the samples.

title: Dynamics of lava flows
abstract: Extensive lava flows, like those of the Columbia plateau of Washington state, require thicknesses only of the order of meters and temperatures only slightly above the melting point to spread over distances of the order of hundreds of kilometers. Other things being equal, the spreading distance is proportional to the cube of the thickness of the flow.

title: Simulating lava flows by an improved cellular automata method
abstract: Lava-flow morphology is determined by cooling rate, viscosity, yield strength, eruption rate, topography, total mass, and other various factors. We have made a numerical flow model, assuming nonisothermal laminar Bingham flow, in which we take the self-gravity and cooling mechanisms into account. Because the calculation method is a type of cellular automata on square meshes, we can apply our numerical model on any actual topography based on a dense-grid digital elevation model. A method of eliminating the mesh shape dependence, which is a well-known problem of cellular automata, is also presented. This reduced random space method enables us to calculate large-scale lava flows in a short time without numerical instability, and obtain mesh-free reliable results. This method is applicable to any other cellular automata type algorithm with ease. We validate our simulation code using data from a real lava flow.

title: FLOWGO: a kinematic thermo-rheological model for lava flowing in a channel
abstract: We present a kinematic, self-adaptive, numerical model to describe the down-flow thermal and rheological evolution of channel-contained lava. As our control volume of lava advances down a channel it cools and crystallizes, an increasingly thick and extensive surface crust grows, and its heat budget and rheology evolve. By estimating down-flow heat and velocity loss, our model calculates the point at which the control volume becomes stationary, giving the maximum distance lava flowing in the channel can extend. Modeled effusion rates, velocities, widths, surface crust parameters, heat budget, cooling, temperature, crystallinity, viscosity, and yield strength all compare well with field data collected during eruptions at Mauna Loa, Kĩlauea, and Etna. Modeled lengths of 25–27, 2.5–5.7, and 0.59–0.83 km compare with measured lengths of 25–27, 4, and 0.75 km for the three flows, respectively. Over proximal flow portions we calculate cooling, crystallization, viscosity, and yield strength of 1–10°C km–1, 0.001–0.01 volume fraction km–1, 103–104 Pa s, and 10–3–102 Pa, respectively. At the flow front, cooling, crystallization, viscosity, and yield strength increase to >100°C km–1, 0.1 volume fraction km–1, 106–107 Pa s, and 103–104 Pa, respectively, all of which combine to cause the lava to stop flowing. Our model presents a means of (a) analyzing lava flow thermo-rheological relationships; (b) identifying important factors in determining how far a channel-fed flow can extend; (c) assessing lava flow hazard; and (d) reconstructing flow regimes at prehistoric, unobserved, or remote flows.

title: The simulation model SCIARA: the 1991 and 2001 lava flows at Mount Etna
abstract: Cellular Automata (CA), a paradigm of parallel computing, represent an alternative to differential equations for modelling and simulating very complex phenomena, whose evolution is based on local interactions of their constituent parts. A CA model for lava flow simulations, SCIARA (‘Simulation by Cellular Interactive Automata of the Rheology of Aetnean lava flows’) was developed and improved according to an empirical CA method for simulating macroscopic phenomena. Its last version, SCIARA-hex1, was applied to the 1991 lava flow of the 1991–1993 eruption of Etna. The simulation results are satisfying within limits to forecast the lava flow path. It was also applied during the eruption of Etna in the summer of 2001, when a new eruption threatened the town of Nicolosi. This ‘real time’ application proved that SCIARA is a reliable and flexible tool for forecasting lava flow paths and for assessing hazard in the Etnean area.

title: The 1975 sub-terminal lavas, mount etna: a case history of the formation of a compound lava field
abstract: The 1975 sub-terminal activity was characterised by low effusion rates (0.3–0.5 m3 s−1) and the formation of a compound lava field composed of many thousands of flow units. Several boccas were active simultaneously and effusion rates from individual boccas varied from about 10−4 to 0.25 m3s−1. The morphology of lava flows was determined by effusion rate (E): aa flows with well-developed channels and levees formed when E > 2 × 10−3 m3 s−1, small pahoehoe flows formed when 2 × 10−3 m3 s−1 >E > 5 > 10−4 m3 s−1 and pahoehoe toes formed when E < 5 × 10−4 m3 s−1. There was very little variation with time in the effusion temperature, composition or phenocryst content of the lava. 
 
New boccas were commonly formed at the fronts of mature lava flows which had either ceased to flow or were moving slowly. These secondary boccas developed when fluid lava in the interior of mature aa flows either found a weakness in the flow front or was exposed by avalanching of the moving flow front. The resulting release of fluid lava was accompanied by either partial drainage of the mature flow or by the formation of a lava tube in the parent flow. The temperature of the lava forming the new bocca decreased with increasing distance from the source bocca (0.035°C m−1). It is demonstrated from the rate of temperature decrease and from theoretical considerations that many of the Etna lavas still contained a substantial proportion of uncooled material in their interior as they came to rest. The formation of secondary boccas is postulated to be one reason why direct measurements of effusion rates tend, in general, to overestimate the total effusion rates of sub-terminal Etna lava fields.

title: Some physical requirements for the emplacement of long basaltic lava flows
abstract: Long basaltic lava flows (over 100 km in length) require specific emplacement conditions to prevent the lava from freezing as it is transported to the flow front. The minimum dimensions of the lava transport systems (tubes, channels, or sheets) require that the flow have a volume greater than several cubic kilometers. Long lava flows are emplaced on slopes less than 10% (∼5°) and the lava being transported must cool at a rate less than 0.5°C/km. We show that there are two modes by which thermally efficient, long distance lava transport can be achieved: (1) “rapid” emplacement in which the lava flows so quickly that it does not cool excessively despite large heat losses and (2) “insulated” emplacement in which heat loss is minimized. We here estimate cooling in the rapid mode using a modified version of a previously published thermal model for aa flows and find that, for a range of inputs appropriate for subaerial terrestrial condition, effusion rates of at least 3100 to 11000 m3/s, channel flow velocities in excess of 4–12 m/s, and minimum channel depths of 3–17 m are required for basaltic flows >100 km in length. For emplacement in the insulated mode, we construct a very simple heat balance model for roofed sheet flows which shows that extremely long sheet-fed flows are possible with velocities as low as 0.2–1.4 m/s, flow thickness of 6–23 m, and minimum effusion rates of the order of 50–7100 m3/s. Also, earlier work has suggested that tube-fed flows more than 100 km long can be produced at effusion rates as low as several tens of m3/s and with tube diameters of a few tens of meters. We argue that flows emplaced in the rapid mode should be morphologically similar to channel-fed aa flows while those emplaced in the insulated mode should be similar to tube-fed or sheet-like inflated pahoehoe flows. This leads to several field criteria for distinguishing these two modes of emplacement in ancient lava sequences. Additional constraints on the emplacement of long lava flows are expected from the continued study of the formation and evolution of lava channels, tubes, and sheets.

title: Terrestrial analogs and thermal models for Martian flood lavas
abstract: The recent flood lavas on Mars appear to have a characteristic “platy-ridged” surface morphology different from that inferred for most terrestrial continental flood basalt flows. The closest analog we have found is a portion of the 1783–1784 Laki lava flow in Iceland that has a surface that was broken up and transported on top of moving lava during major surges in the eruption rate. We suggest that a similar process formed the Martian flood lava surfaces and attempt to place constraints on the eruption parameters using thermal modeling. Our conclusions from this modeling are (1) in order to produce flows >1000 km long with flow thicknesses of a few tens of meters, the thermophysical properties of the lava should be similar to fluid basalt, and (2) the average eruption rates were probably of the order of 104 m3/s, with the flood-like surges having flow rates of the order of 105–106 m3/s. We also suggest that these high eruption rates should have formed huge volumes of pyroclastic deposits which may be preserved in the Medusae Fossae Formation, the radar “stealth” region, or even the polar layered terrains.

title: Effects of Martian conditions on numerically modeled, cooling‐limited, channelized lava flows
abstract: We used the FLOWGO thermorheological model to examine the effects of Martian gravitational and environmental conditions on the cooling-limited behavior of lava flowing in a channel. The largest effect is due to the lower gravity on Mars as compared to Earth, which causes lava to flow more slowly. The lower velocity means that heat loss per distance down a Mars channel is greater even though the lower velocity also produces a higher percentage cover of insulating crust. Gravity alone causes the Mars flow to be >65 km shorter than an Earth flow with an equivalent volumetric flow rate. The cooler ambient Mars atmosphere causes a slight increase in heat loss by forced convection. This slows the flow a bit more, resulting in a very slight increase in heat loss per distance by all mechanisms, and decreases the modeled flow length by ∼1 km, a difference well below our model uncertainty. Replacing terrestrial values of atmospheric density, viscosity, thermal conductivity, heat capacity, and cubic expansivity makes convection less efficient and increases flow length by ∼15 km. Nevertheless, at the same volumetric flow rate, lava flows ∼50 km less far under Martian conditions than under terrestrial conditions. Our specific model flow has a volumetric flow rate of ∼5000 m3 s−1 and traveled ∼190 km down a channel on a constant 7° slope. This volumetric flow rate is slightly less than the maximum rates during the 1783–1785 Laki eruption and is 5–10 times greater than those of typical Mauna Loa eruptions.

title: The effect of crystallization on the rheology and dynamics of lava flows
abstract: The dynamics of a lava flow is studied by a two-dimensional model describing a viscous fluid with Bingham rheology, flowing down a slope. The temperature in the flow is calculated assuming that heat is transferred through the plug by conduction and is lost by radiation to the atmosphere at the top of the flow. Taken into account is that the increasing crystallization takes place in the flow as a consequence of cooling. The lava viscosity and yield stress are expressed as a function of crystallization degree as well as of temperature: in particular it is assumed that yield stress reaches a maximum value above the solidus temperature, according to experimental data. Dynamical variables, such as velocity and thickness of the flow, are calculated for different values of the maximum crystallization degree and the flow rate. The model shows how the lava flow dynamics is affected by cooling and crystallization. The cooling of the flow is controlled by the increase of yield stress, which produces a thicker plug and makes the heat loss slower. The increasing crystallization has two opposing effects on viscosity: it produces an increase of viscosity, but at the same time produces an increase of yield stress and hence reduces the heat loss and keeps the internal temperature high. As a consequence, lava flows are significantly affected by the dependence of yield stress on temperature and scarcely by the maximum crystallization degree.

title: Influence of crystallization and entrainment of cooler material on the emplacement of basaltic aa lava flows
abstract: 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.

title: Heat loss measured at a lava channel and its implications for down-channel cooling and rheology
abstract: During May 2001 we acquired 2016 thermal images over an ~8-h-long period for a section of active lava channel on Mount Etna (Italy). We used these to extract surface temperature and heat-loss profi les and thereby calculate core cooling rates. Flow surface temperatures declined from ~1070 K at the vent to ~930 K at 70 m. Heat losses were dominated by radiation (5 × 10 W m) and convection (~10 W/m). These compare with a heat gain from crystallization of 6 × 10 W/m. The imbalance between sinks and sources gives core cooling (δT/δx) of ~110 K/km. However, cooling rate per unit distance also depends on fl ow conditions, where we distinguished: (1) unimpeded, high-velocity (~0.2 m/s) fl ow with low δT/δx (0.3 K/m); (2) unimpeded, low-velocity (~0.1 m/s) fl ow with higher δT/δx (0.5 K/m); (3) waning, insulated fl ow at low velocity (~0.1 m/s) with low δT/δx (0.3 K/m); and (4) impeded fl ow at low velocity (<0.1 m/s) with higher δT/δx (0.4 K/m). Our data allow us to defi ne three thermal states of fl ow emplacement: insulated, rapid, and protected. Insulated is promoted by the formation of hanging blockages and coherent roofs. During rapid emplacement, higher velocities suppress cooling rates, and δT/δx can be tied to mean velocity (V mean ) by δT/δx = aV mean . In the protected case, deeper, narrow channels present a thermally effi cient channel, where δT/δx can be assessed using the ratio of channel width (w) to depth (d) in w/d = aδT/δx.

title: Flow and convective cooling in lava tubes
abstract: Tube-fed basaltic lava flows with lengths ranging from 10 to 200 km are inferred to exhibit similar amounts of cooling. To explain the wide range of implied cooling rates, we consider forced convection as a dominant cooling process in lava tubes and present solutions that express mean temperature versus distance down the tube as a function of flow rate and flow cross section. Our models treat forced convective thermal losses in steady laminar flow through a lava tube with constant temperature walls and constant material properties. We explore the effects of different wall temperature and heat flux rate boundary conditions for circular tube and parallel plate flows over a range of tube sizes, plate spacings, eruption temperatures, and volume flow rates. Results show that nonlinear cooling rates over distance are characteristic of constant wall temperature for a piecewise parallel plate/circular tube model. This provides the best fit to temperature observations for Hawaiian tubes. Such a model may also provide an explanation for the very low (∼10°C) cooling observed in ∼10 km long Hawaii tube flows and inferred in longer ∼50 to 150 km tube-fed flows in Queensland. The forced convective cooling model may also explain similar flow morphologies for long tube-fed basaltic lava flows in a wide variety of locations, since small variations in eruption temperature or flow rate can accommodate the entire range of flow lengths and cooling rates considered. Our results are consistent with previous suggestions that long basaltic flows may be a reflection of low slopes, a particularly steady moderate eruption rate, and well-insulated flow, rather than of high discharge rates.

title: Thermal efficiency of lava tubes in the Pu'u 'ō'Ō-Kupaianaha eruption
abstract: We have applied glass geothermometry to a suite of 37 pairs of glassy lava samples collected on Kilauea's east - rift zone, from the upper and lower ends of the episode 48 lava-tube system, when the Kupaianaha pond was active (1986-90). We also present data on a small suite of skylight samples collected from 1986 through the end of episode 48 (in 1991), plus some data on skylight-coast sample pairs from episodes 51 and 53. The results for the pond-coast pairs are as follows: (1) From November 1986 through January 1988 (15 months), the average change in inferred quenching temperature from pond to coast (for 12 sample pairs) is 12.4°C, and the average increase in crystal content (inferred from the observed enrichment of TiO 2 and K 2 O in glasses in coastal samples) is 11 to 12 weight percent. (2) From February 1988 through November 1989 (23 months), the average change in inferred quenching temperature from pond to coast (for 25 sample pairs) is 8.4°C, and the average increase in crystal content is 4 to 5 weight percent. Within this part of the data set, pond and coastal temperatures rise and fall together much of the time, even though these temporal fluctuations are at or below the limit of resolution of glass geothermometry ΔT≤3°C). (3) The minimum temperature difference for any pond-coast pair is 7°C. Of 37 sample pairs, 24 have ΔT=7-9°C, over the entire 3-year period. In about half of the skylight samples, the enclosed glasses have MgO contents consistent with the location at which the samples were collected along the lava-tube system. Glasses in the rest of the skylight samples are displaced to lower MgO contents; such samples may not be consistently as well quenched as the pond and littoral spatter samples. The data from episodes 51 and 53 are from a new tube system that was somewhat shorter than the episode 48 (Kupaianaha) lava tubes. The best-documented temperature difference observed for this 10-km long lava tube (6°C) gives exactly the same rate of temperature decrease with distance (0.6°/km) as the limiting ΔT value of 7°C observed for the 12-km-long Kupaianaha lava-tube systems. This cooling rate may represent the limiting thermal efficiency of tubes of the current eruption.

title: Field measurements of heat loss from skylights and lava tube systems
abstract: We present temperature measurements made at skylights in the active flow field of Kilauea Volcano between 1995 and 2000. Spot temperature measurements of the lava stream within the lava tube revealed surface temperatures of 1017–1132°C. This compared with lava core temperatures of 1161 ± 3°C. The difference is the result of surface cooling due to radiation at the skylights. A FLIR thermal imager recorded a down-tube lava surface temperature decrease followed by a surface temperature recovery due to entrainment of the crust down flow of the skylight. The temperature of hot air expelled from skylights reached a maximum of 600°C. From these field data, we place constraints on heat loss from the skylight and lava tube. Heat losses due to conduction and circulation of air in wall rocks around the tube are 103–104 and 104–106 W m−1 down tube, respectively. At skylights, heat losses due to radiation and forced convection are 1.5 × 105 W m−1 over the skylight length and 5 × 105 W per skylight, respectively. For a 10-km-long tube, the total heat loss is between 5 × 108 and 1 × 1010 W for a fully roofed tube with an additional 1.1 × 106 W lost per 4 m × 1 m skylight. In terms of cooling rates, 1.2°C km−1 is a minimum resulting from heat losses at fully roofed tubes with no skylights. Heat loss and cooling rate will, however, increase with skylight area.

title: The changing morphology of an open lava channel on Mt. Etna
abstract: An open channel lava flow on Mt. Etna (Sicily) was observed during May 30–31, 2001. Data collected using a forward looking infrared (FLIR) thermal camera and a Minolta-Land Cyclops 300 thermal infrared thermometer showed that the bulk volume flux of lava flowing in the channel varied greatly over time. Cyclic changes in the channel's volumetric flow rate occurred over several hours, with cycle durations of 113–190 min, and discharges peaking at 0.7 m3 s−1 and waning to 0.1 m3 s−1. Each cycle was characterized by a relatively short, high-volume flux phase during which a pulse of lava, with a well-defined flow front, would propagate down-channel, followed by a period of waning flow during which volume flux lowered. Pulses involved lava moving at relatively high velocities (up to 0.29 m s−1) and were related to some change in the flow conditions occurring up-channel, possibly at the vent. They implied either a change in the dense rock effusion rate at the source vent and/or cyclic-variation in the vesicle content of the lava changing its bulk volume flux. Pulses would generally overspill the channel to emplace pāhoehoe overflows. During periods of waning flow, velocities fell to 0.05 m s–1. Blockages forming during such phases caused lava to back up. Occasionally backup resulted in overflows of slow moving ‘a‘ā that would advance a few tens of meters down the levee flank. Compound levees were thus a symptom of unsteady flow, where overflow levees were emplaced as relatively fast moving pāhoehoe sheets during pulses, and as slow-moving ‘a‘ā units during backup. Small, localized fluctuations in channel volume flux also occurred on timescales of minutes. Volumes of lava backed up behind blockages that formed at constrictions in the channel. Blockage collapse and/or enhanced flow under/around the blockage would then feed short-lived, wave-like, down-channel surges. Real fluctuations in channel volume flux, due to pulses and surges, can lead to significant errors in effusion rate calculations.

title: Lava tube morphology on Etna and evidence for lava flow emplacement mechanisms
abstract: Lava tubes play a pivotal role in the formation of many lava flow fields. A detailed examination of several compound ‘a‘a lava flow fields on Etna confirmed that a complex network of tubes forms at successively higher levels within the flow field, and that tubes generally advance by processes that include flow inflation and tube coalescence. Flow inflation is commonly followed by the formation of major, first-order ephemeral vents which, in turn, form an arterial tube network. Tube coalescence occurs when lava breaks through the roof or wall of an older lava tube; this can result in the unexpected appearance of vents several kilometers downstream. A close examination of underground features allowed us to distinguish between ephemeral vent formation and tube coalescence, both of which are responsible for abrupt changes in level or flow direction of lava within tubes on Etna. Ephemeral vent formation on the surface is frequently recorded underground by a marked increase in size of the tube immediately upstream of these vents. When the lining of an inflated tube has collapsed, ‘a‘a clinker is commonly seen in the roof and walls of the tube, and this is used to infer that inflation has taken place in the distal part of an ‘a‘a lava flow. Tube coalescence is recognised either from the compound shape of tube sections, or from breached levees, lava falls, inclined grooves or other structures on the walls and roof. Our observations confirm the importance of lava tubes in the evolution of extensive pahoehoe and ‘a‘a flow fields on Etna.

title: Extended cooling and viscous flow of large, hot rhyolite lavas: implications of numerical modeling results
abstract: A common misconception about rhyolite lava flows is that they cannot advance far from their vents and are constrained to be small due to their high viscosities. Although a high-viscosity lava will indeed flow quite slowly, it may advance a great distance if the lava efficiently retains heat and thus mobility, and if the available magma supply is large. To evaluate this possibility, a finite-difference numerical model was used to determine the rate of heat loss from units interpreted to be large rhyolite lavas. Cooling of such 100–300 m-thick units is very slow and is further retarded by a vesicular carapace and by evolution of latent heat. Thermal history alone suggests that large, thick lava flows could remain active for several decades. To constrain the duration of flow advance of these units, their inferred apparent viscosities are compared with those of active lava flows. Mean flow velocity of some large rhyolites in southwestern Idaho, USA, was estimated based on the observation that the units must still have been advancing by viscous flow at the start of spherulite crystallization, indicating perhaps a 10- to 18-year flow duration, based on studies of Obsidian Dome, California. Mean flow velocities would have been roughly 0.59 to 2.5 km/yr, and calculated average apparent viscosities of the flows ranged from 1.8 to 3.6 orders of magnitude greater than the viscosity of the lava itself. This relationship also holds for active andesite and basaltic andesite block lava flows, which have apparent viscosities 2.7 to 4 orders of magnitude greater than lava viscosities. This implies that large rhyolites may indeed have been emplaced in the same manner as less-silicic block lavas, and that long distance viscous flow is not unrealistic for rhyolite lavas. A good example of a large-volume lava is the 15-km 3 Rhyolite of the Badlands (SW Idaho), where vent relations show that lava effused from a fissure and advanced up to 9 km. More extensive rhyolites could also be emplaced solely by effusion. Extended flow of these lavas may lead to the remelting and removal of basal crumble breccias, and to the formation of welded shard textures in their margins, both processes tending to obscure the lava flow origin of the units. The great dimensions of lava-like rhyolitic units with volumes of 10 to at least 200 km 3 are not a sufficient reason to assume they erupted as ignimbrites.