L1 ⚛ L1-468 ⊙ Testnet

Satellite Radar Altimetry

Geodesy · Sea surface height

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⬇ L1-468.md

# ⚛ L1 Principle — Satellite Radar Altimetry **ID:** `L1-468` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Sea surface height* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 1D sea surface height > **📡 Carrier:** RF · **🌫 Noise:** thermal gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555298 --- ## 🧠 1. Introduction **Satellite Radar Altimetry** is a **parameter-estimation problem** whose unknown lives in **1D sea surface height** space, within the **Sea surface height** sub-domain of **Geodesy**. Measurements consist of RF coil signals (typical of MRI) via a **radar altimetry nadir** sensing mechanism. The forward operator applies, in order: S · altimeter · retracker brown operator; operator inherits structure from a graph (mesh, network); O · least squares · retrack operator. Observations are corrupted by thermally-driven Gaussian fluctuations. Existence of the recovered 1D_sea_surface_height 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 ~= 30); rain_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · altimeter · retracker brown → Structured graph operator → O · least squares · retrack → **y** (detector). ``` y = `O.least_squares.retrack` G `S.altimeter.retracker_brown` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.altimeter.retracker_brown` | S · altimeter · retracker brown operator | | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `O.least_squares.retrack` | O · least squares · retrack operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Sea surface height | | Carrier | RF | | Problem class | parameter_estimation | | Solution space | 1D_sea_surface_height | | Noise model | thermal_gaussian | | Integration axis | range_surface | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered 1D_sea_surface_height 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 ~= 30); rain_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | SSH_RMSE_cm | | Secondary | SWH_bias_cm | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `radar_altimetry_nadir` **Center point:** | Parameter | Unit | Value | |---|---|---| | Swh m | m | 2 | | N gates | — | 128 | | Mispointing deg | deg | 0.1 | | Noise sigma percent | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Swh m | m | 0.0 – 10.0 | | N gates | — | 64 – 512 | | Mispointing deg | deg | 0.0 – 1.0 | | Noise sigma percent | — | 1.0 – 20.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 SSH_RMSE_cm | Metric | Range | |---|---| | Ssh rmse cm | 0.5 – 20.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **SSH_RMSE_cm**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9ad6cd94a55549fd9138ab92df0b45a76970484232800376df163cb6c8a8395a` - **Chain tx hash:** `0xe7c4f2cab5f62505f2ec421104771d1695e61a991dd5ec0a53b7eee09d87e32d` - **Chain block:** `41555298` --- ## File Mapping This bundle consists of: `L1-468.md`, `L1-468.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-468.md` | Source of truth — edit this | Human or LLM | | `L1-468.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 `L1-468`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-468.md).
Regenerate L1-468.json so every field matches the Markdown.
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L2-468-001 Satellite Radar Altimetry — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555298,
  "chain_hash": "0x9ad6cd94a55549fd9138ab92df0b45a76970484232800376df163cb6c8a8395a",
  "chain_tx_hash": "0xe7c4f2cab5f62505f2ec421104771d1695e61a991dd5ec0a53b7eee09d87e32d",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "SSH_RMSE_cm",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "SSH_RMSE_cm",
    "regime": "Existence of the recovered 1D_sea_surface_height 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 ~= 30); rain_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.",
    "secondary": "SWH_bias_cm"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "RF",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "range_surface",
    "noise_model": "thermal_gaussian",
    "primitives": [
      "S.altimeter.retracker_brown",
      "G.structured",
      "O.least_squares.retrack"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "radar_altimetry_nadir",
    "solution_space": "1D_sea_surface_height",
    "sub_domain": "Sea surface height",
    "title": "Satellite Radar Altimetry"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "radar_altimetry_nadir"
    ],
    "allowed_omega_dimensions": [
      "N_gates",
      "SWH_m",
      "mispointing_deg",
      "noise_sigma_percent"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0 SSH_RMSE_cm",
      "forward_operator": "radar_altimetry_nadir",
      "input_format": "measurement_only",
      "omega": {
        "N_gates": 128,
        "SWH_m": 2.0,
        "mispointing_deg": 0.1,
        "noise_sigma_percent": 5.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "SSH_RMSE_cm": [
        0.5,
        20.0
      ]
    },
    "omega_bounds": {
      "N_gates": [
        64,
        512
      ],
      "SWH_m": [
        0.0,
        10.0
      ],
      "mispointing_deg": [
        0.0,
        1.0
      ],
      "noise_sigma_percent": [
        1.0,
        20.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sea surface height",
  "title": "Satellite Radar Altimetry"
}

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