L1 ⚛ L1-421 ⊙ Testnet

River Hydraulics Shallow Water Inversion

Environmental Science · Hydrology

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⬇ L1-421.md

# ⚛ L1 Principle — River Hydraulics Shallow Water Inversion **ID:** `L1-421` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Hydrology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** Manning roughness bathymetry > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **River Hydraulics Shallow Water Inversion** is a **parameter-estimation problem** whose unknown lives in **Manning roughness bathymetry** space, within the **Hydrology** sub-domain of **Environmental Science**. Measurements consist of N/A via a **water level discharge measurement** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; O · least squares · rating curve operator; S · fdm · flood routing operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered Manning_roughness_bathymetry is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); bank_overflow_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → O · least squares · rating curve → S · fdm · flood routing → **y** (detector). ``` y = `S.fdm.flood_routing` `O.least_squares.rating_curve` ∇ x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `O.least_squares.rating_curve` | O · least squares · rating curve operator | | `S.fdm.flood_routing` | S · fdm · flood routing operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Hydrology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | Manning_roughness_bathymetry | | Noise model | gaussian | | Integration axis | river_reach | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered Manning_roughness_bathymetry is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); bank_overflow_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | water_level_RMSE_m | | Secondary | discharge_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `water_level_discharge_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N gauges | — | 5 | | Roughness n | N | 0.035 | | Reach length km | km | 50 | | Discharge peak m3 s | s | 1000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N gauges | — | 2 – 50 | | Roughness n | N | 0.01 – 0.1 | | Reach length km | km | 1 – 1000 | | Discharge peak m3 s | s | 10 – 100000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.10 water_level_RMSE_m | Metric | Range | |---|---| | Water level rmse m | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **water_level_RMSE_m**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x52599914468dae4784412df2a6ba1035a0b0b4c83e90b5818a9a0b7e13d04bdc` - **Chain tx hash:** `0xd4ecbe5745af85f060529b3b07df29d4aba36cf21b9c0e4ae5aa46bb59214c26` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-421.md`, `L1-421.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-421.md` | Source of truth — edit this | Human or LLM | | `L1-421.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-421`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-421.md).
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L2-421-001 River Hydraulics Shallow Water Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Environmental Science",
  "hardness_fn": {
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    "integration_axis": "river_reach",
    "noise_model": "gaussian",
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    "sensing_mechanism": "water_level_discharge_measurement",
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    "sub_domain": "Hydrology",
    "title": "River Hydraulics Shallow Water Inversion"
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      "discharge_peak_m3_s": [
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      "reach_length_km": [
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      "roughness_n": [
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        0.1
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Hydrology",
  "title": "River Hydraulics Shallow Water Inversion"
}

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