Time-lapse camera observations of gas piston activity at Pu‘u ‘Ō‘ō, Kīlauea volcano, Hawai‘i

Abstract

Gas pistoning is a type of eruptive behavior described first at Kīlauea volcano and characterized by the (commonly) cyclic rise and fall of the lava surface within a volcanic vent or lava lake. Though recognized for decades, its cause continues to be debated, and determining why and when it occurs has important implications for understanding vesiculation and outgassing processes at basaltic volcanoes. Here, we describe gas piston activity that occurred at the Pu‘u ‘Ō‘ō cone, in Kīlauea’s east rift zone, during June 2006. Direct, detailed measurements of lava level, made from time-lapse camera images captured at close range, show that the gas pistons during the study period lasted from 2 to 60 min, had volumes ranging from 14 to 104 m³, displayed a slowing rise rate of the lava surface, and had an average gas release duration of 49 s. Our data are inconsistent with gas pistoning models that invoke gas slug rise or a dynamic pressure balance but are compatible with models which appeal to gas accumulation and loss near the top of the lava column, possibly through the generation and collapse of a foam layer.

Appendix

The position of the lava surface within the Drainhole vent is calculated by re-projecting the lava surface from the image plane to the vertical plain defined by the vent wall. To achieve this, we first calculate the time-lapse camera’s angular field of view, or angle of view (AOV), in the vertical direction using the equation:

$$ \alpha = 2 \cdot {\tan^{- 1 }}\left( {\frac{d}{2f }} \right) $$

(1)

where α represents the vertical AOV, d represents the size of the camera’s optical sensor in the vertical direction (5.32 mm for digital cameras with a 1/1.8″ optical sensor), and f represents the focal length (8.0 mm; obtained from image metadata). Solving for α, we find the camera’s vertical AOV to be 36.8°. The same value was achieved when calculating vertical AOV directly from photographs of a flat object (the side of a building) of known size and distance from the camera. We ignore the radial distortion of the camera lens because our object of interest—the rising and falling lava surface—is near the center of the image, where radial distortion is negligible.

The inclination of the camera and the horizontal distance from the camera to the targeted vent wall defines a right triangle (Fig. 6a; in gray). From this, we use the cosine function for a right triangle to calculate a length of 12 m for the FOV center line, or principal ray (Fig. 6a; dashed red line). We also know that the acute angle formed by the intersection of the projected image plane and the vertical plane is equivalent to the inclination of the camera (26°) because it is complementary to the angle between the camera’s principal ray and the vertical plane. To find the relative vertical position of the lava surface in any time-lapse image, we must imagine a line extending from the camera to the point of intersection between the lava surface and the vent wall. We refer to this line as the target ray (Fig. 6b; dashed blue line). When the slope of the target ray is steeper than that of the principal ray, the target ray passes through the projected image plane. We can then ratio the number of vertical pixels that comprise the segment of the projected image plane between the principal ray and the target ray (Fig. 6b; solid blue line) to the number of pixels that comprise half the vertical image frame (600 pixels). Cross-multiplying this with 18.5° (half of the AOV) gives us the angle between the principal ray and the target ray. The tangent function for a right triangle can then be used to calculate the length of the projected image plane between the principal ray and the target ray (Fig. 6b; solid blue line).

Fig. 6

Illustrations showing geometric details of time-lapse camera deployment at Drainhole vent. a Horizontal distance from camera to target (opposite wall of inner vent opening) is 11 m. Black dashed lines bound camera’s field of view; red dashed line represents camera’s principal ray, calculated length 12 m; red solid line, normal to principal ray, represents plane of projected image. b Black dashed lines bound camera’s field of view; red dashed line represents camera’s principal ray; blue dashed line represents target ray. Principal ray bisects projected image plane into upper and lower halves of 600 pixels each. Projected lava surface height represented by solid blue line; actual lava surface level represented by solid green line

We now define a new triangle bounded by the projected image plane, the vertical vent wall, and the target ray (Fig. 6b). For this triangle, the angle between the projected image plane and the vent wall is 26°, and the angle between the projected image plane and the target ray is a supplementary angle and can be readily calculated. Since we now know two angles and the length of the included side, we use the law of sines to find the length of the side that represents the level of the lava surface in the vertical plane (Fig. 6b; solid green line). Using a variation of this procedure, we calculate the vertical distance between the principal ray of the camera and the vent rim (because the principal ray was below the vent rim). We then add this value to our calculated measurement of the lava level below the principal ray to get the total distance from the vent rim to the lava surface.

This procedure is used to determine the position of the lava surface within the vent only when the surface is below the principal ray. A variation on this procedure is used when the lava surface rises above the camera’s principal ray. Inaccuracy in the inclination of the camera and the distance between the camera and the targeted vent or pit wall will lead to small errors in the calculated height of the lava surface, as will small errors in the value calculated for the camera’s angle of view. However, since the viewing geometry does not change from image to image, and because it is the relative change in the position of the lava surface that is important, we make no effort to quantify these errors and they are ignored.