L1 ⚛ L1-418 ⊙ Testnet

Numerical Weather Prediction Data Assimilation

Environmental Science · Weather forecasting

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⬇ L1-418.md

# ⚛ L1 Principle — Numerical Weather Prediction Data Assimilation **ID:** `L1-418` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Weather forecasting* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** atmospheric state vector > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41555238 --- ## 🧠 1. Introduction **Numerical Weather Prediction Data Assimilation** is a **nonlinear inverse problem** whose unknown lives in **atmospheric state vector** space, within the **Weather forecasting** sub-domain of **Environmental Science**. Measurements consist of N/A via a **4dvar data assimilation** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · 4dvar · adjoint method operator; O · cost function · background observation operator. Observations are corrupted by observation gaussian. Existence of the recovered atmospheric_state_vector 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 ~= 100000.0); model_error_during_window 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 · 4dvar · adjoint method → O · cost function · background observation → **y** (detector). ``` y = `O.cost_function.background_observation` `S.4dvar.adjoint_method` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.4dvar.adjoint_method` | S · 4dvar · adjoint method operator | | `O.cost_function.background_observation` | O · cost function · background observation operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Weather forecasting | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | atmospheric_state_vector | | Noise model | observation_gaussian | | Integration axis | analysis_time_window | | Difficulty delta | 10 | | L dag | 5.5 | ## 📡 4. Measurement Model Existence of the recovered atmospheric_state_vector 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 ~= 100000.0); model_error_during_window dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | analysis_error_RMSE_K | | Secondary | forecast_skill_score_S1 | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `4dvar_data_assimilation` **Center point:** | Parameter | Unit | Value | |---|---|---| | Window hours | — | 6 | | N observations | — | 1000000 | | Obs error ratio | — | 1 | | Model resolution km | km | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Window hours | — | 3 – 12 | | N observations | — | 100000 – 5000000 | | Obs error ratio | — | 0.5 – 5.0 | | Model resolution km | km | 2 – 50 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 analysis_error_RMSE_K | Metric | Range | |---|---| | Analysis error rmse k | 0.1 – 2.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **analysis_error_RMSE_K**, with κ = `100000000.0` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xbb6021636ae13b8f1afba0e4fc64fa62d247e24d3001f82167ad4751c0cdf882` - **Chain tx hash:** `0xb8ced1f3cbe6efb9a0a8c653bd86bca006f8f80f92272759fa0eef1261ed82a1` - **Chain block:** `41555238` --- ## File Mapping This bundle consists of: `L1-418.md`, `L1-418.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-418.md` | Source of truth — edit this | Human or LLM | | `L1-418.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 `L1-418`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-418.md).
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L2-418-001 Numerical Weather Prediction Data Assimilation — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555238,
  "chain_hash": "0xbb6021636ae13b8f1afba0e4fc64fa62d247e24d3001f82167ad4751c0cdf882",
  "chain_tx_hash": "0xb8ced1f3cbe6efb9a0a8c653bd86bca006f8f80f92272759fa0eef1261ed82a1",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 10,
    "kappa": 100000000.0,
    "metric": "analysis_error_RMSE_K",
    "type": "epsilon_fn"
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    "metric": "analysis_error_RMSE_K",
    "regime": "Existence of the recovered atmospheric_state_vector 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 ~= 100000.0); model_error_during_window dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "forecast_skill_score_S1"
  },
  "physics_fingerprint": {
    "L_DAG": 5.5,
    "carrier": "N/A",
    "difficulty_delta": 10,
    "domain": "Environmental Science",
    "integration_axis": "analysis_time_window",
    "noise_model": "observation_gaussian",
    "primitives": [
      "D.space",
      "S.4dvar.adjoint_method",
      "O.cost_function.background_observation"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "4dvar_data_assimilation",
    "solution_space": "atmospheric_state_vector",
    "sub_domain": "Weather forecasting",
    "title": "Numerical Weather Prediction Data Assimilation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "4dvar_data_assimilation"
    ],
    "allowed_omega_dimensions": [
      "N_observations",
      "window_hours",
      "model_resolution_km",
      "obs_error_ratio"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.5 analysis_error_RMSE_K",
      "forward_operator": "4dvar_data_assimilation",
      "input_format": "measurement_only",
      "omega": {
        "N_observations": 1000000,
        "model_resolution_km": 10,
        "obs_error_ratio": 1.0,
        "window_hours": 6
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "analysis_error_RMSE_K": [
        0.1,
        2.0
      ]
    },
    "omega_bounds": {
      "N_observations": [
        100000,
        5000000
      ],
      "model_resolution_km": [
        2,
        50
      ],
      "obs_error_ratio": [
        0.5,
        5.0
      ],
      "window_hours": [
        3,
        12
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Weather forecasting",
  "title": "Numerical Weather Prediction Data Assimilation"
}

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