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

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.