5  Annotated Literature & Positioning

Seismic bedload transport on Mt. Rainier glacial rivers during the December 2025 atmospheric-river floods

Compiled June 2026. DOIs marked (unverified) must be confirmed before submission.

5.1 1. Foundational physics (forward models)

  • Burtin et al. (2008), JGR Solid Earth 113, B05301, doi:10.1029/2007JB005034 — first showed >1 Hz ambient noise along the Trisuli (Himalaya) tracks river hydrology and bedload.
  • Tsai, Minchew, Lamb & Ampuero (2012), GRL 39, L02404, doi:10.1029/2011GL050255 — bedload forward model. PSD ∝ (impact rate)·f³·m²w², i.e. linear in flux q_b, ∝ D³ in grain size (coarse tail / D₉₄ dominates). Our high-frequency band rests on this.
  • Schmandt et al. (2013), GRL 40, 4858, doi:10.1002/grl.50953 — Grand Canyon controlled flood: bedload 15–45 Hz, fluid tractions <1 Hz, air–fluid waves ~6–7 Hz are spectrally separable.
  • Gimbert, Tsai & Lamb (2014), JGR-ES 119, 2209, doi:10.1002/2014JF003201 — turbulent-flow forward model. P_water ∝ H^(7/3) S^(7/3) ∝ u*^(14/3); turbulence occupies a lower band than bedload. Through hydraulic geometry → P ∝ Q^(0.9–1.4), i.e. the ~linear “water baseline.” No analytic 5/4 exponent exists in this paper.

5.2 2. Inversion / quantification (the standard toolchain)

  • Roth et al. (2016), JGR-ES 121, 725, doi:10.1002/2015JF003782 — Erlenbach; linear spectral inversion separates turbulence/rain from bedload, validated against impact-plate geophones.
  • Dietze (2018), ESurf 6, 669, doi:10.5194/esurf-6-669-2018 — eseis R package, de-facto environmental-seismology toolbox (implements Tsai/Gimbert models). Consider porting/benchmarking against it.
  • Dietze et al. (2019), WRR 55, doi:10.1029/2019WR026072 — joint inversion of bedload flux and flow depth from spectra.
  • Bakker et al. (2020), JGR-ES 125, doi:10.1029/2019JF005416 — the key prior result for our diagnostic. Low f (~10 Hz) → exponent ~1.5 (matches turbulence ~1.4); >30 Hz → strongly nonlinear with Q but ~linear with sediment flux. Establishes “exponent rises with frequency above the turbulence baseline ⇒ bedload.” Power governed by ~D₉₅, ∝ D³.
  • Lagarde et al. (2021), WRR 57, doi:10.1029/2020WR028700 — quantifies Green’s-function and coarse-tail GSD uncertainty in inversion.
  • Nasr et al. (2024), ESurf 12, 117, doi:10.5194/esurf-12-117-2024 — hydroacoustic analogue; distributed-source inversion.

5.3 3. Recent advances (2022–2026)

  • Cook & Dietze (2022), Annu. Rev. Earth Planet. Sci. 50, 183, doi:10.1146/annurev-earth-032320-085133 — authoritative review; best single entry point.
  • Antoniazza et al. (2023), JGR-ES 128, e2022JF007000, doi:10.1029/2022JF007000 — 24-station watershed-scale network, maps where/when coarse sediment mobilizes; resolves multiple discrete pulses. Closest “array/network” precedent.
  • “Sounding out the river” / Chmiel et al. (2023/24), ESPL, doi:10.1002/esp.5940 — joint seismic + hydroacoustic bedload in a lowland alluvial river.
  • Luong et al. (2024), JGR-ES 129, doi:10.1029/2024JF007761 — modifies Tsai model for inelastic impacts + rolling/sliding; 30–80 Hz optimal bedload band; Tsai model under-predicts flux 1–2 orders at shallow flow.
  • Luong et al. (2026), WRR, doi:10.1029/2025WR040371 (recent) — hybrid empirical model: seismic power + shear stress jointly predict bedload flux. Directly relevant to our empirical-scaling approach.
  • Roth et al. (2025), Seismica (DAS, “A River on Fiber”) — distributed acoustic sensing for spatially-continuous fluvial monitoring; the emerging successor to point sensors.
  • Rickenmann et al. (2025), ESPL 50(5), doi:10.1002/esp.70059 — long-term multi-site impact-plate bedload synthesis (calibration backbone).
  • Nicoletti et al. (2026), arXiv:2604.17913 — full numerical waveform synthesis from grain-scale dynamics + turbulence.

5.3.1 Added from the June-2026 positioning survey (competitors to differentiate)

  • Shakti P.C. & Sawazaki (2021), Prog. Earth Planet. Sci. 8, 58, doi:10.1186/s40645-021-00448-1 — the key prior art for our virtual-discharge framing. Seismic noise as a virtual gage for ungauged basins; single-station power law Q=A(E-E_0)^b, validated on three floods incl. Typhoon Hagibis (Oct 2019), 1–2 Hz optimal after transient/background removal. Our distinction: a distributed multi-station field, not single-station — network density is the contribution, not the P–Q concept.
  • Gangemi et al. (2026), EGUsphere preprint egusphere-2026-1534 — the closest competitor. Opportunistic permanent stations on the braided Tagliamento; applies the single-thread Tsai/Gimbert framework qualitatively only (correlation/hysteresis/polarization) and explicitly states a braided source model “remains speculative and needs further investigation.” Cite to show the braided source-model gap is open; we occupy it with the satellite corroboration they lack. (Preprint — track toward publication.)
  • Cook et al. (2021), Science 374, 87, doi:10.1126/science.abj1227 — Chamoli: regional seismic network detected/tracked the catastrophic flow; ~min-scale downstream lead. Early-warning precedent (different mechanism: debris flow).
  • Eibl et al. (2020), Nature Comms 11, 2504 (PMC7237689) — subglacial jökulhlaup tremor leads gage stage by >20 h in all four Skáftá cases. Early-warning precedent (different mechanism: outburst). Together these cap “early warning” as a standalone novelty — deploy our ~36 h AR-flood lead as an applied payoff, not the spine.
  • McLaughlin et al. (2024/2025), JGR-ES doi:10.1029/2024JF008159 (Arroyo de los Pinos) — bedload band 30–80 Hz; bedload dominates only for r<100 m, f>30 Hz. Supports the Nyquist caveat — but note the band is grain-size/site-dependent (Taiwan typhoon systems saw bedload at 5–15 Hz), so state #3 as grain-size-conditional, not a hard universal cap.

5.4 4. Sediment pulses & hysteresis (the “tracking” theme)

  • Roth et al. (2014), EPSL 404, 144, doi:10.1016/j.epsl.2014.07.019 (unverified) — THE blocking citation. Multi-station array along Chijiawan R. (Taiwan), hysteresis metric Ψ tracks a downstream-migrating coarse sediment pulse after dam removal. Must distinguish our work from this.
  • Roth et al. (2017), JGR-ES 122, doi:10.1002/2016JF004062 — critical caveat: hysteresis arises from bedload and boundary-roughness change; seismic power often tracks stage more than measured bedload. Must defend against.
  • Schmandt et al. (2017), Geology 45, 299, doi:10.1130/G38639.1 — 76-sensor array, 700 m reach, reach-scale bedload during augmentation flood.
  • Hassan et al. (2023), WRR, doi:10.1029/2023WR035406 — flume: supply timing controls bedload hysteresis sense.
  • Nativ et al. (2025), GRL, doi:10.1029/2024GL113784 — “Stationary boulders increase river seismic frequency via turbulence.” Direct counter-mechanism: high-f power need not be bedload. Must address explicitly.
  • Hysteresis sense conventions: clockwise ⇒ supply exhaustion / proximal / armor break-up on rising limb; counter-clockwise ⇒ delayed/distal delivery, pulse arrival on falling limb (Reid 1985; Kuhnle 1992; Mao 2014).

5.5 5. Sediment-pulse physics (translation vs dispersion)

  • Lisle et al. (2001), ESPL 26, 1409 — bed-material waves evolve dominantly by dispersion, not translation.
  • Cui et al. (2003a,b), WRR 39(9), doi:10.1029/2002WR001803 / 10.1029/2002WR001805 — sediment pulses in mountain rivers; dispersion dominates at Fr > ~0.4.
  • Sklar et al. (2009), WRR 45, W08439, doi:10.1029/2008WR007346 — translation/dispersion partitioning for gravel augmentation.
  • Czuba & Foufoula-Georgiou — network structure controls pulse aggregation/dispersion en route to the sink.

5.6 6. Mt. Rainier / Puyallup / Puget Sound context

  • Czuba et al. (2011), USGS FS 2011-3083, doi:10.3133/fs20113083 — ~6.5 Mt/yr sediment to Puget Sound.
  • Czuba et al. (2012), USGS OFR 2012-1242 — aggradation 1984–2009 up to 2.3 m (Puyallup), 0.6 m (Carbon); Nisqually nr National 0.13 m/yr. Median-pulse transit times: Nisqually ~70 yr, Puyallup ~80 yr, Carbon ~300 yr, White ~60 yr. Aggradation concentrates at the confined→lowland slope break.
  • Magirl et al. (2010), USGS SIR 2010-5240 — lower Puyallup/White/Carbon conveyance loss from deposition.
  • Anderson (2025), USGS (Pierce Co.), data DOI 10.5066/P149MBYG — channel change & sediment transport through 2022 (lidar differencing); most recent aggradation update.
  • Anderson & Shean (2022), ESPL 47(2), doi:10.1002/esp.5274 — proglacial erosion rates, four Rainier basins, 1960–2017 (DOI belongs to Anderson & Shean; previously listed as Beason).
  • Hoblitt et al. (1998), USGS OFR 98-428 — Rainier lahar hazards (Osceola, Electron mudflows down the Puyallup).
  • USGS/PNSN debris-flow seismic detection at Rainier (Tahoma Creek) — detection of mass flows, not continuous bedload quantification (our distinction).
  • December 2025 AR floods (confirmed): two back-to-back atmospheric rivers ~Dec 8–12 2025; statewide emergency (Gov. Ferguson, ~Dec 10); Carbon R. nr Fairfax highest in 19 yrs; Puyallup record flooding; Mt Rainier NP closed indefinitely (debris flows, washouts). Sources: WA Mil. Dept; WA State Standard 2025-12-10; NASA SVS #5596; NPS MORA news. (News/agency only — no peer-reviewed post-event analysis yet.)

5.7 6b. Distance attenuation & the “seismic reach” (correction methods)

The central confound for a multi-station transect: high-frequency (bedload) power is attenuated with distance from the channel.

  • Physical term (Tsai 2012 Eq. 3; Gimbert 2014 ψβ(f)): amplitude \propto r^{-1/2} e^{-\pi f r/(v_u Q)}; power \propto r^{-1} e^{-2\pi f r/(v_c Q)}. e-folding distance r_e = v_c Q/(2\pi f). With Q\approx20, v_c(f)=1295\,(f)^{-0.374} m/s (Tsai): r_e\approx316 m at 5 Hz, ~210 m at the 5–15 Hz band center, ~13 m at 50 Hz. So bedload (≳30 Hz) is essentially gone beyond a few hundred metres while turbulence (1–10 Hz) survives kilometres — bedload dominates only for r<\sim100 m and f>\sim30 Hz (Gimbert 2014).
  • Solutions used in the field:
    1. Active-source / hammer calibration of the Green’s function (Bakker et al. 2020 doi:10.1029/2019JF005416; Lagarde et al. 2021 doi:10.1029/2020WR028700) — measures v_c(f), Q locally; improves spectrogram fit by ~1 order of magnitude. Not available to us.
    2. Amplitude-decay source location (ASL): A_i=A_t\,\frac{S_i}{R_i}e^{-\pi f t_i/Q}, grid-searched (Battaglia & Aki; Walter et al. 2017 nhess-17-939; Burtin et al. 2008/2010; packaged in eseis spatial_amplitude/_track, Dietze 2018). Needs ≥3–4 stations + assumed v_c,Q.
    3. Spectral-decay inversion of Q,v_c from the data (trades off strongly with grain size).
    4. Per-station normalization (what we use) — simplest, but folds site+distance+source together; not transferable.
    5. DAS (Roth et al. 2025, Seismica) sidesteps standoff by sensing in/along the channel.
  • Our first-order result (fig 9): the same-source PR cluster (PR03/PR01/PR02 at 0.19/0.71/1.9 km) shows the 5–15 Hz power ~distance-independent over 0.2–2 km — far weaker decay than the Q=20 prediction (which would give ~10⁴× drop to PR02). Interpretation: at these mid frequencies the band retains less-attenuated lower-frequency (turbulence) energy, and site response + crude channel distances preclude a data-driven Q.
  • PNW-inferred Q (adopted instead of Q=20): Q(f)=Q_0 f^{\eta}, Q_0\approx25, \eta\approx0.5 → Q(10\,\text{Hz})\approx80 (range 40–240), from Cascade coda-Q (Havskov et al. 1989 BSSA, Q_0{\approx}63 f^{0.9}), Lg-Q (Erickson et al. 2004 BSSA, 152 f^{0.76}, lower near the arc), and Mt. St. Helens edifice attenuation (Tusa et al. 2006 GJI, Q_p{\approx}30 under the crater; De Siena et al. 2016 EPSL). This gives r_e\approx780 m at the 5–15 Hz center (vs ~210 m for Q=20) — less attenuation, but bedload (30–80 Hz) still reaches only tens–hundreds of m. We restrict bedload claims to near-channel stations and treat farther ones as upper-distance bounds. A clean correction needs active-source calibration or a higher (30–80 Hz) band recorded close to the channel — which requires ≥160-sps instruments (our CC broadband stations are 50 sps, Nyquist 25 Hz; see the frequency-sampling caveat in §Methods).

5.8 7. Novelty matrix (what to claim, what to defend)

Claim Strength Blocking prior work Framing
Mountain-to-sea longitudinal transect tracking a pulse Moderate Roth 2014; Schmandt 2017; Antoniazza 2023 Claim novelty in catchment-length scale (tens of km, glacial source → lowland), not “first multi-station pulse tracking.”
Named atmospheric-river flood + debris-flow event Strong typhoon/GLOF/windstorm studies (different storm type) First Pacific AR-tied bedload seismology; argue AR hydrology (rain-on-snow, glacial melt, sustained Q) gives a distinct signature.
Cascades glacial-river bedload seismology Strong Rainier debris-flow detection (USGS/PNSN) Distinguish continuous bedload quantification from catastrophic mass-flow detection.
Frequency-dependent scaling-exponent diagnostic Weak Bakker 2020; Gimbert 2014; Tagliamento 2026 preprint Frame as field-validation/application at transect scale, not invention.

Lead framing (June-2026 survey-revised): single-thread fluvial-seismology source-model breakdown in a braided glacial-outwash reach, diagnosed by hysteresis reversibility + cross-flood baseline drift and corroborated by Sentinel-2/-1 channel-migration imagery — a seismic+satellite joint channel-change diagnosis no 2023–2026 paper has published. The distributed virtual-gage field is the network framing device (Shakti & Sawazaki 2021 owns the single-station concept); the Nyquist/bedload limit is a grain-size-conditional bounding caveat; the ~36 h lead is the applied payoff. (Superseded earlier lead: “first transect-scale bedload seismology on Cascades glacial rivers during a named AR flood” — still true, but transect/AR-first is weaker than braided-breakdown-first given Shakti & Sawazaki 2021 and the saturation of the virtual-gage and early-warning niches.)

Three reviewer objections to pre-empt: 1. “Just Gimbert 2014 + Bakker 2020.” → We add the transect, the AR/Rainier system, and a multi-station β(f) map; we field-calibrate the water baseline per station rather than assuming it. 2. “Nativ 2025: high-f can be boulder-driven turbulence, not bedload.” → Use hysteresis + temporal evolution + the negative control (lowland Snohomish, r≈0) to argue against a static-roughness origin. 3. “Roth 2017: roughness change, not bedload, makes hysteresis.” → Report hysteresis sense per event and tie to the debris-flow supply chronology, not stage alone.

Reconcile: our water baseline came out ~1 (or the measured low band), Gimbert predicts ~1.4 — state which baseline we adopt and why (empirical per-station calibration).

Methodological caveat discovered in re-analysis (2026): the 0.5–2 Hz band is the oceanic secondary microseism, not river turbulence — at PR01 it is anti-correlated with discharge (b=−0.29, r=−0.36). The turbulence baseline must be drawn from 1–5 / 2–8 Hz; 0.5–2 Hz should never be auto-selected as the flow band. Also note spatial decay: PR01 (0.71 km from channel) gives a shallower bedload exponent (b≈1.2) than PR03 (0.19 km, b≈1.66) — consistent with distance attenuation of the high-frequency bedload signal, a transect-scale prediction worth testing explicitly.

Target journal: JGR: Earth Surface (field flagship; Gimbert/Roth/Bakker/Antoniazza live there) or ESurf (open, public review, same audience). GRL if compressed to a first-detection letter; Seismica for an open methods/detection framing.