L1 ⚛ L1-419 ⊙ Testnet

Ocean Circulation Inverse Modeling

Environmental Science · Physical oceanography

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⬇ L1-419.md

# ⚛ L1 Principle — Ocean Circulation Inverse Modeling **ID:** `L1-419` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Physical oceanography* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D ocean state > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555238 --- ## 🧠 1. Introduction **Ocean Circulation Inverse Modeling** is a **nonlinear inverse problem** whose unknown lives in **3D ocean state** space, within the **Physical oceanography** sub-domain of **Environmental Science**. Measurements consist of N/A via a **ocean state estimation** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · adjoint · ocean 4dvar operator; O · cost · ECCO objective operator. Observations are corrupted by observation gaussian. Existence of the recovered 3D_ocean_state 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 ~= 10000.0); forcing_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → S · adjoint · ocean 4dvar → O · cost · ECCO objective → **y** (detector). ``` y = `O.cost.ECCO_objective` `S.adjoint.ocean_4dvar` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.adjoint.ocean_4dvar` | S · adjoint · ocean 4dvar operator | | `O.cost.ECCO_objective` | O · cost · ecco objective operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Physical oceanography | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | 3D_ocean_state | | Noise model | observation_gaussian | | Integration axis | ocean_volume | | Difficulty delta | 5 | | L dag | 5.5 | ## 📡 4. Measurement Model Existence of the recovered 3D_ocean_state 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 ~= 10000.0); forcing_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | temperature_RMSE_K | | Secondary | salinity_RMSE_psu | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `ocean_state_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N argo profiles | — | 3000 | | N vertical levels | — | 50 | | Assimilation years | — | 26 | | Horizontal resolution deg | deg | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N argo profiles | — | 100 – 30000 | | N vertical levels | — | 20 – 100 | | Assimilation years | — | 1 – 50 | | Horizontal resolution deg | deg | 0.1 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.3 temperature_RMSE_K | Metric | Range | |---|---| | Temperature rmse k | 0.05 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **temperature_RMSE_K**, with κ = `10000000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x64489e5c8efdb930e166acd34023b5de942d4c3385db14e23129ac22e48aaceb` - **Chain tx hash:** `0xfb6067cf84b4003ed0daf4a9b0e6ea41b055d1b7033d95214912755206747a22` - **Chain block:** `41555238` --- ## File Mapping This bundle consists of: `L1-419.md`, `L1-419.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-419.md` | Source of truth — edit this | Human or LLM | | `L1-419.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 `L1-419`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-419.md).
Regenerate L1-419.json so every field matches the Markdown.
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L2-419-001 Ocean Circulation Inverse Modeling — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555238,
  "chain_hash": "0x64489e5c8efdb930e166acd34023b5de942d4c3385db14e23129ac22e48aaceb",
  "chain_tx_hash": "0xfb6067cf84b4003ed0daf4a9b0e6ea41b055d1b7033d95214912755206747a22",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000000.0,
    "metric": "temperature_RMSE_K",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
    "metric": "temperature_RMSE_K",
    "regime": "Existence of the recovered 3D_ocean_state 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 ~= 10000.0); forcing_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "salinity_RMSE_psu"
  },
  "physics_fingerprint": {
    "L_DAG": 5.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "ocean_volume",
    "noise_model": "observation_gaussian",
    "primitives": [
      "D.space",
      "S.adjoint.ocean_4dvar",
      "O.cost.ECCO_objective"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "ocean_state_estimation",
    "solution_space": "3D_ocean_state",
    "sub_domain": "Physical oceanography",
    "title": "Ocean Circulation Inverse Modeling"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ocean_state_estimation"
    ],
    "allowed_omega_dimensions": [
      "N_vertical_levels",
      "horizontal_resolution_deg",
      "assimilation_years",
      "N_Argo_profiles"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.3 temperature_RMSE_K",
      "forward_operator": "ocean_state_estimation",
      "input_format": "measurement_only",
      "omega": {
        "N_Argo_profiles": 3000,
        "N_vertical_levels": 50,
        "assimilation_years": 26,
        "horizontal_resolution_deg": 1.0
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "temperature_RMSE_K": [
        0.05,
        1.0
      ]
    },
    "omega_bounds": {
      "N_Argo_profiles": [
        100,
        30000
      ],
      "N_vertical_levels": [
        20,
        100
      ],
      "assimilation_years": [
        1,
        50
      ],
      "horizontal_resolution_deg": [
        0.1,
        2.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Physical oceanography",
  "title": "Ocean Circulation Inverse Modeling"
}

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