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Scientists measure two different things: fountain height, a length, and eruption or effusion rate, a volume per unit time. Height comes from field angles, distances, or calibrated images. A rate requires an estimate of how much lava was produced and the time and area over which that production occurred. A tall fountain does not, by itself, provide a discharge rate.
What is being measured?
A lava fountain is a jet or curtain of incandescent magma fragments and gas above a vent or fissure. Its height describes the vertical extent of the visible fountain. Eruption rate describes lava output, usually in cubic metres per second (m³/s), cubic metres per day, or another volume-per-time unit. The two quantities can change independently: a gas-rich eruption may throw fragments high without producing a proportionally large lava flow, while a low fountain can feed a substantial lava channel.
Scientists therefore report the measurement boundary and the averaging interval. A statement such as “the fountain was 40 metres high” is not interchangeable with “the eruption discharged 40 m³/s.” To estimate the latter, researchers need volume, time and a clearly defined spatial area.
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Two sight angles and a measured distance
The U.S. Geological Survey’s Hawaiian Volcano Observatory method uses basic surveying geometry. An observer measures the angle from eye level to the top of the fountain and a second angle from the same eye level to its base. The horizontal distance from the observer to the fountain is measured separately. A laser rangefinder can measure distance and angle and calculate a height; an inclinometer and compass are alternatives listed by USGS. The method is described in USGS Hawaiian Volcano Observatory guidance.
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- Choose a viewing position with a reasonably unobstructed line of sight and measure the distance to the vent or visible fountain base.
- Hold the instrument at a known, consistent eye height. Measure the upward angle to the top boundary.
- From the same eye height, measure the downward angle to the base boundary.
- Use trigonometry to calculate the vertical segment above eye level and the segment below it, then add them.
If the distance is d, the top angle is θtop and the base angle is θbase below horizontal, the idealized height is d × tan(θtop) + d × tan(θbase). The calculation assumes the distance is measured to the relevant vertical plane and that both angles refer to the same observation point. Sloping ground, an uncertain vent position or a large horizontal offset can add error.
Defining the top and base
USGS defines the top as the upper boundary of the optically dense fountain column: the region in which most lava rises and falls back. It is not the highest isolated glowing particle. Gas can loft sparse fragments tens or hundreds of metres above the dense body, and including those outliers would make measurements inconsistent from one observation to the next.
The base can be harder to see because lava, spatter and cinder accumulate around the vent. Observers may use a visible glowing crack or another unobscured fissure exposure rather than the top of a pile that has built up during the eruption. Reporting the boundary rule is essential when comparing heights from different observers or dates.
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How cameras turn a fountain into a time series
Fixed cameras and repeatable boundaries
When access is unsafe or the fountain changes rapidly, scientists use fixed webcams or timelapse cameras. A camera is calibrated against known distances or topographic features so that image pixels can be converted to height. Analysts then apply the same dense-column boundary rule to every frame. The result is a height-versus-time series rather than a single field reading.
A USGS data release dated September 22, 2026, for the continuing 2024–2026 Kīlauea summit eruption shows the time resolution possible with this approach: cameras recorded images at 0.5–1.0-minute intervals, and staff generally measured the main fountain body once per minute. Sparse particles above the continuous body were excluded. The release supplies both measurements and source images. Its August 2026 version covered episodes 1–50; USGS reported that 54 episodes had occurred by then, with later episodes to be added in a future version. Because the eruption and data coverage evolve, those episode counts apply to that dated release, available at the USGS data page.
Automated analysis of video
Long videos can be processed frame by frame to reduce the burden of manual measurements. In the study of the 2022 Mauna Loa summit eruption, researchers analyzed roughly seven hours of webcam footage—more than 87,000 frames. An automated method measured fountain heights, fissure lengths and the volume of ejecta in flight, demonstrating how ordinary monitoring video can provide quantitative early-eruption parameters when the viewing geometry is suitable. The study is published by USGS at “Onset and evolution of summit lava fountaining during the Mauna Loa 2022 eruption.”
Image methods still require quality checks. Steam, darkness, a changing camera position, lens deposits, overlapping fountains or a blocked base can make the apparent edge ambiguous. Analysts record those limitations rather than treating every frame as equally precise.
How scientists estimate lava output from mapped flows
The basic volume-over-time calculation
For a mapped lava flow, the simplest estimate is:
Volume ≈ flow area × average thickness
and
Average rate = estimated volume ÷ the selected elapsed time.
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The selected period and area determine what the number means. A rate for one channel over ten minutes is not the same quantity as a whole-eruption average for an entire flow field. Researchers therefore state whether they are measuring a short-term interval, one flow unit, one vent, or the complete eruption.
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The review by Sonia Calvari, Jonathan Dehn and A. Harris distinguishes several commonly confused terms. An instantaneous effusion rate describes output at a particular moment. A time-averaged discharge rate averages output over a specified interval. An eruption rate can mean cumulative volume divided by the time since the eruption began, while a mean output rate uses final volume divided by the total eruption duration. These definitions and their measurement problems are discussed in the 2007 Bulletin of Volcanology review.
Measuring thickness and volume
Field crews can measure thickness at many points along flow margins, but edge measurements may not represent the interior. Channels may be hollow or partly drained, so assuming that the full height of a channel rim is filled with lava can overestimate volume.
For broader coverage, scientists use airborne radar, lidar or overlapping aerial photographs processed with structure-from-motion (SfM). They create a pre-eruption elevation model and a post-eruption model, align them with ground control, and subtract one from the other. The resulting thickness map can be integrated across the flow area to estimate volume.
USGS described a preliminary map of the 2018 Kīlauea lower East Rift Zone built from about 2,800 aerial photographs and approximately 1.5 billion automatically selected common points. The preliminary mapped volume was about 0.8 cubic kilometres. After correction, USGS reported a minimum rate estimate of roughly 50–200 m³/s. Those are historical, preliminary mapping results with stated caveats, not a universal conversion between fountain height and rate; see the USGS thickness explanation.
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Methods that observe active channels
Mapped deposits describe what accumulated over an interval. To estimate more immediate output, monitoring teams can observe moving lava in an active channel.
Velocity and cross-section
If scientists measure the channel’s cross-sectional area and the lava’s mean velocity, they can estimate flux as area × velocity. Surface speed is not automatically the mean speed: a channel may have a faster centre, slower margins and a different velocity at depth. Thermal conditions, crust, turbulence and changing channel geometry must be considered.
Video, particle tracking and UAS
USGS describes repeated downward-looking unmanned-aircraft-system (UAS) video over lava channels as one way to support velocity and rate estimates. Stable video can also be analyzed with particle image velocimetry, which tracks the movement of visible surface patterns between frames. Thermal and visual imaging, photogrammetry, radar and lidar are complementary measurements used in specialist volcano-monitoring programs. The recommended capabilities report is at USGS Scientific Investigations Report 2024–5062, and an example of UAS response work is documented at the USGS Land Imaging Report Site.
These are professional operations, not consumer photography projects. Aircraft, observers and instruments must remain outside exclusion zones and comply with aviation, land-management and emergency rules.
Why estimates disagree
Every method contains assumptions. A field height can be biased if the base is hidden or the observer’s distance is wrong. A camera estimate can shift if the viewing geometry changes or analysts include isolated particles in one frame but not another. A deposit map can miss thin margins, vegetation-hidden edges or material removed after emplacement. An active-channel estimate can be wrong if surface velocity is treated as the average velocity through a three-dimensional channel.
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The 2007 review states that individual effusion-rate approaches can have errors of up to about 50%. Its authors summarize the practical issue directly: “No approach is without its problems, and all can have large error (up to ∼50%).” Agreement among independent methods, careful calibration and explicit uncertainty bounds can nevertheless produce reliable operational estimates.
How to compare two published rates fairly
- Check the averaging period. Determine whether the value is instantaneous, a ten-minute average, a daily average or an entire-eruption mean.
- Check the spatial scope. Identify whether it covers one vent, one channel, one flow unit or the whole active field.
- Identify the measurement method. A differenced elevation model, channel-flux calculation and camera-based proxy do not measure exactly the same physical quantity.
- Read the assumptions. Look for assumed thickness, channel fill, velocity profile, camera calibration, ground control and corrections for obscured areas.
- Keep units and qualifiers attached. Preserve whether a value is a minimum, preliminary estimate, corrected value or range, and note the region and eruption episode.
For example, a corrected minimum of 50–200 m³/s from a mapped 2018 flow should not be compared directly with a one-minute channel estimate unless the time window, area and method are reconciled.
What the measurements tell scientists
Fountain height is a rapid indicator of changing vent energy and can reveal pulsation when measured repeatedly. A height time series may show onset, pauses or escalation even before a complete flow map is available. Volume-based rates show how much lava is actually entering the landscape and help forecast channel reach, inundation and the likely growth of a flow field. Combining the two—along with seismic, gas, thermal and deformation observations—gives a more defensible picture than relying on either height or rate alone.
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The essential discipline is to describe the quantity precisely: what was measured, where, over what time, using which boundary and with what uncertainty. That is what makes measurements from different days, instruments and eruptions scientifically comparable.
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