The scientific core

The methods behind the tools

Every number a tool on this site produces traces back to a published method listed here — with its real validity domain, and an explicit verdict on whether it transfers to the ephemeral wadis of arid regions. Almost all classical river equations were calibrated on perennial temperate rivers; this library says so out loud.

33 methods, and growing with every new tool.

Valid in arid regionsUse with caution in wadisNot transferable to wadis / arid regions

Classification frameworks

Whole-river typologies. No framework is objectively best (Buffington & Montgomery 2022) — run several and compare.

Rosgen Level II 1994

Use with caution in wadis

What it gives you: Deterministic stream types (A–G + bed material) from entrenchment ratio, W/D, sinuosity, slope and D50.
Validity domain: Descriptive, form-based. Documented critiques: form ≠ process (Simon 2007); observer variance; bankfull-identification error propagates into ER.
Arid / wadi verdict: Form types occur in wadis, but bankfull stage — the anchor of the whole key — is notoriously ambiguous in ephemeral channels. Treat outputs as descriptive labels only.

Montgomery & Buffington 1997 / 2022

Use with caution in wadis

What it gives you: Process-based reach types (cascade, step-pool, plane-bed, pool-riffle, dune-ripple, braided) from slope bands, w/h and relative submergence.
Validity domain: Calibrated in Pacific-Northwest mountain streams; slope bands overlap regionally — present probabilistically, not as hard cut-offs.
Arid / wadi verdict: Morphologies exist in arid mountains too, but supply-/capacity-limited behaviour differs where flow is episodic and sediment pulses dominate. Regional recalibration advised.

Schumm 1963/1985

Valid in arid regions

What it gives you: Suspended-/mixed-/bed-load channel types from silt-clay index M; empirical F=255·M⁻¹·⁰⁸ and P=0.94·M⁰·²⁵.
Validity domain: Built largely on Great Plains (semi-arid US) rivers; sand-bed alluvium.
Arid / wadi verdict: One of the few classics with genuinely semi-arid roots — among the safer starting points for wadi work, within sand-bed alluvial settings.

Church 2006

Use with caution in wadis

What it gives you: Regime classes (Jammed → Threshold → Transitional → Labile) from bankfull Shields number τ*bf.
Validity domain: Physics-anchored and broadly applicable where a meaningful bankfull stage exists.
Arid / wadi verdict: The physics carries over; the reference "bankfull" state does not — in ephemeral channels pick the effective (formative) discharge explicitly instead.

River Styles 2005

Valid in arid regions

What it gives you: Open-ended, expert-led typology: confinement → planform → bed material → geomorphic units; plus condition and recovery potential.
Validity domain: No fixed thresholds by design; strength is process narrative, weakness is expert dependence.
Arid / wadi verdict: Framework-level thinking transfers well; Australian origins include extensive dryland rivers.

REFORM / Gurnell et al. 2016

Use with caution in wadis

What it gives you: EU multi-scale hierarchy (catchment → reach → unit) with a 22-type extended planform typology; sinuosity ≥1.5 meandering, BI > 1.5 multithread.
Validity domain: Designed for EU WFD rivers (predominantly perennial, often regulated).
Arid / wadi verdict: Hierarchy and metrics are usable; the type catalogue under-represents ephemeral and flash-dominated forms.

MQI — Rinaldi et al. 2013+

Valid in arid regions

What it gives you: Morphological Quality Index: 28 indicators (function, artificiality, channel adjustment) → MQI = 1 − Stot/Smax, five classes.
Validity domain: Type-adaptive scoring; global adaptations exist — including Iran (Jajrood, 2025).
Arid / wadi verdict: Explicitly designed for regional adaptation, with a documented Iranian application — a defensible assessment backbone for wadi corridors.

Planform prediction

Meandering, braided, or anabranching? From classic slope–discharge lines to the stream-power framework (κ up to 0.95).

Leopold & Wolman 1957

Not transferable to wadis / arid regions

What it gives you: Braided/meandering discriminator S = 0.013·Q_bf^(−0.44).
Validity domain: Ignores grain size; κ = 0.48 on the 134-river benchmark — historical baseline, not a decision tool.
Arid / wadi verdict: Calibrated on perennial temperate rivers with a stable bankfull; ephemeral wadis violate both assumptions.

Lane 1957

Not transferable to wadis / arid regions

What it gives you: K = S·Q_m^0.25 pattern thresholds (SI: meandering ≤ 7.0e-4; braided ≥ 4.1e-3).
Validity domain: Sand-bed rivers only; uses mean (not bankfull) discharge.
Arid / wadi verdict: "Mean discharge" is close to zero in ephemeral regimes, so K collapses — the formula is structurally unfit for wadis.

Henderson 1961

Not transferable to wadis / arid regions

What it gives you: Grain-aware threshold S = 0.64·D^1.14·Q^(−0.44) (ft/cfs).
Validity domain: Imperial units; constants flagged [CHECK] pending source verification.
Arid / wadi verdict: Same perennial-bankfull lineage as L&W; no ephemeral data behind it.

Bledsoe & Watson 2001

Use with caution in wadis

What it gives you: Probabilistic p(braided) = logit(b₀ + b₁·log₁₀(S·Q^0.5) + b₂·log₁₀D50); 85–94% correct.
Validity domain: US sand (n=109) and gravel datasets; the best basis for probabilistic outputs.
Arid / wadi verdict: The probabilistic form is exactly right for data-poor wadis, but the fitted coefficients are temperate — refit before operational use.

van den Berg 1995

Not transferable to wadis / arid regions

What it gives you: Potential specific stream power ω_pot = ρ·g·Q_ef·S_v/W_r with W_r = α√Q_ef; braiding threshold ω_bm = 900·D50^0.42.
Validity domain: By its own title: perennial, equilibrium rivers, Q ≥ 10 m³/s, D50 0.1–100 mm.
Arid / wadi verdict: Ephemeral channels are excluded by the method’s own definition; applying it to a wadi is outside the published domain, full stop.

Kleinhans & van den Berg 2011

Not transferable to wadis / arid regions

What it gives you: Four stability fields (laterally stable / scroll-bar meandering / chute–moderately braided / braided) between ω_ia = 90·D50^0.42 and ω_bm = 900·D50^0.42; κ = 0.95 when read as lower bounds.
Validity domain: Inherits van den Berg’s domain (perennial, equilibrium). Sinuosity is a descriptor, not a predictor.
Arid / wadi verdict: The strongest perennial predictor we have — and still not transferable to ephemeral wadis without redefining the formative discharge and re-validating.

Candel et al. 2021

Use with caution in wadis

What it gives you: Adds bank silt+clay (SC%) as a third axis: critical shear τ_c(SC) separates inactive/tortuous/meandering; 87% correct (n=70).
Validity domain: K&vdB lines stay valid for SC below ~25%. Perennial dataset.
Arid / wadi verdict: Bank-strength physics is exactly what wadi prediction is missing — promising direction, but the calibration set contains no ephemeral rivers yet.

Parker 1976

Use with caution in wadis

What it gives you: Stability criterion ε = S_c·√(g·H·W⁴)/Q_bf; braided ≥ 1. κ = 0.69.
Validity domain: Theory-based; needs W/H, so it discriminates existing channels rather than predicting new ones.
Arid / wadi verdict: Physics is regime-agnostic; the practical inputs (a stable W/H at a formative stage) are what get shaky in flash regimes.

Fredsøe 1978

Use with caution in wadis

What it gives you: Linear-stability braiding threshold near W/H ≈ 50. κ = 0.63.
Validity domain: Theoretical; same discriminator-not-predictor caveat as Parker 1976.
Arid / wadi verdict: As with Parker 1976 — the theory travels, the formative-stage inputs do not.

Crosato & Mosselman 2009

Use with caution in wadis

What it gives you: Bar mode m² = 0.17·g·(b−3)·√((ρs−ρ)/(ρ·D50))·(W³·S_c)/(C·Q_bf); m=1 alternate bars, m≥3 braided.
Validity domain: Valid to W/H ≈ 100; use for bar mode, not as a five-class pattern classifier.
Arid / wadi verdict: Physics-based and unit-consistent — usable in wadis if a defensible formative discharge is supplied; the burden shifts to that choice.

Millar 2000

Use with caution in wadis

What it gives you: Vegetation-aware pattern threshold S* = 0.0002·D50^0.61·φ′^1.75·Q^(−0.25); φ′ 40°→~80°.
Validity domain: Gravel rivers; coefficients flagged [CHECK]. Vegetation alone can flip braided ↔ single-thread.
Arid / wadi verdict: In sparse-vegetation wadis φ′ sits near its lower bound, collapsing the method toward unvegetated thresholds — informative, but with little discriminating power there.

Eaton, Millar & Davidson 2010

Use with caution in wadis

What it gives you: Dimensionless discriminator S_c = 0.56·BI^0.43·μ′·Q*^(−0.43): stable single-thread / stable anabranching / unstable braided.
Validity domain: Gravel-bed; relative bank strength μ′ ∈ [1, 3.4] must be judged.
Arid / wadi verdict: μ′ was conceived around vegetation and cohesion; for wadi banks (often weakly cohesive, unvegetated) its calibration is untested.

Hydraulic geometry & regime

What width, depth and slope does a stable channel take? Empirical, regime and extremal answers.

Leopold & Maddock 1953

Not transferable to wadis / arid regions

What it gives you: Power-law hydraulic geometry W∝Q^b, d∝Q^f, v∝Q^m; downstream bankfull b ≈ 0.50 — the square-root-of-discharge law.
Validity domain: The most robust empirical result in fluvial geomorphology — for perennial rivers.
Arid / wadi verdict: In ephemeral streams transmission losses make discharge DECREASE downstream, inverting the very relations this law encodes. Do not extrapolate.

Lacey (regime) 1930

Not transferable to wadis / arid regions

What it gives you: Regime relations (P = 4.75√Q, silt factor f = 1.76√d50 …) for stable alluvial canals.
Validity domain: Indian irrigation canals: sand 0.1–0.6 mm, steady flow, sediment load < 500 ppm.
Arid / wadi verdict: Steady canal flow is the exact opposite of a flash-flood wadi; sediment loads in wadi floods routinely exceed the 500 ppm ceiling by orders of magnitude.

Simons & Albertson 1963

Not transferable to wadis / arid regions

What it gives you: Regime geometry by three boundary classes (sand/sand, sand/cohesive, cohesive/cohesive): P = C₁Q^0.512, R = C₂Q^0.361.
Validity domain: Canal-derived; steady formative flow assumed; R < 7 ft conversions.
Arid / wadi verdict: Same steady-flow lineage as Lacey — structurally mismatched with episodic wadi hydrology.

Millar (extremal) 2005

Use with caution in wadis

What it gives you: Dimensionless regime set W* = 28.1·Q*^0.50·C^-1.12·μ′^-1.66 (+ depth, slope forms) with bank strength μ′ explicit.
Validity domain: Mobile gravel-bed with stable banks; μ′ ∈ [1, 3.4].
Arid / wadi verdict: Rational closure travels better than pure empiricism, but μ′ for unvegetated wadi banks is essentially unconstrained by data.

UBCRM — Eaton, Church & Millar 2004+

Use with caution in wadis

What it gives you: Full rational regime model (trapezoidal, Ferguson resistance, bank-stability closure) — the only regime model that also predicts the number of stable threads.
Validity domain: Gravel-bed; vegetation effect fades above Q_bf ≈ 400 m³/s.
Arid / wadi verdict: Structurally the most promising for wadis (physics, not curve-fits) — provided formative discharge and bank cohesion are set honestly for the ephemeral case.

Julien & Wargadalam 1995 / 2006

Use with caution in wadis

What it gives you: All-purpose geometry: h ≈ 0.2·Q^0.33·D50^0.17·S^-0.17; W ≈ 1.33·Q^0.44·D50^-0.11·S^-0.22 (SI).
Validity domain: Calibrated on 1,485 measurements, sand through gravel.
Arid / wadi verdict: The broadest calibration base of any geometry set — yet ephemeral rivers remain a minority in it; expect wider error bands in wadis, not different physics.

Parker et al. 2007

Not transferable to wadis / arid regions

What it gives you: Quasi-universal gravel relations: B̃ = 4.63·Q̂^0.0667, H̃ = 0.382, S = 0.101·Q̂^-0.344; inverse Q_bf estimator included.
Validity domain: Q 2.7–5,440 m³/s; D50 27–167.5 mm; single-thread temperate gravel. Slope predicts worst (×14.8 band).
Arid / wadi verdict: “Quasi-universal” means universal across temperate single-thread gravel rivers — the paper’s own dataset bounds exclude wadi regimes.

Hey & Thorne 1986

Not transferable to wadis / arid regions

What it gives you: W = a·√Q with a set by bank vegetation density (4.33 grassy → 2.34 heavily treed).
Validity domain: UK gravel rivers; vegetation classes are the whole method.
Arid / wadi verdict: A vegetation-indexed method has nothing to index on sparse wadi banks; the coefficient choice becomes arbitrary.

Sediment transport

Transport capacity formulas — each with a hard validity window that screening must enforce.

Wong & Parker (MPM corrected) 2006

Use with caution in wadis

What it gives you: Bedload transport for gravel — the corrected MPM to be preferred over the 1948 original.
Validity domain: Flume domain: gravel 0.4–29 mm, slope < 2%.
Arid / wadi verdict: Steep wadi reaches routinely exceed both bounds (our own real-data test tripped exactly these flags). Inside the window it remains a sound gravel baseline.

Engelund & Hansen 1967

Use with caution in wadis

What it gives you: Total-load transport for sand-bed, suspension-dominated rivers.
Validity domain: Uniform sand 0.19–0.93 mm.
Arid / wadi verdict: Applicable in sandy wadi reaches within the size window — but hyperconcentrated wadi flows leave the dilute-flow assumptions of all classical formulas.

Recking 2013

Valid in arid regions

What it gives you: Reach-averaged bedload for gravel and mountain streams — best uncalibrated performer in comparative tests.
Validity domain: Gravel/mountain, including steep slopes where MPM-family formulas fail.
Arid / wadi verdict: The most defensible default for steep gravelly wadis precisely because it was built for steep, wide-ranging field data rather than mild flumes.

Screening & segmentation

Network-scale first looks: stream power balance and automatic reach segmentation.

ST:REAM — Parker, Thorne & Clifford 2015

Valid in arid regions

What it gives you: GIS-ready Lane balance: ω(reach)/ω(upstream) ratios flag reaches prone to erosion or deposition; drives automatic segmentation.
Validity domain: Screening, not prediction — ESPL 2023 showed weak correlation of stream-power indices with observed adjustment.
Arid / wadi verdict: Ratio-based and unit-free, so the framework itself transfers; feed it a wadi-appropriate design discharge rather than a mean-annual flow.

Effective discharge — Biedenharn et al. 1960 / 2000

Valid in arid regions

What it gives you: The formative discharge as the peak of (flow frequency × sediment rating); USACE 25-bin procedure.
Validity domain: Needs ≥10 years of daily flow; the Q1.5 shortcut is a temperate convention.
Arid / wadi verdict: Williams (1978) showed return periods from <1 to 32 years — the fixed-Q1.5 assumption is explicitly invalid in arid/flashy regimes, and THIS procedure is the honest replacement. Central to everything else on this page.

Channel evolution

Where an incised channel is heading — stage models for trajectory, not just state.

CEM / SEM 1984 / 2014

Valid in arid regions

What it gives you: Stage models of incised-channel evolution (incision → widening → aggradation → quasi-equilibrium); SEM adds Stage 0 and cyclicity with habitat scores.
Validity domain: Developed on incised, disturbance-driven channels (US Southeast, semi-arid West).
Arid / wadi verdict: Incision–widening trajectories are common in arid channels after flash events; the stage lens fits wadi post-flood assessment well.