{
  "title": "Storm Lake Frost-Depth Calculator",
  "author": "Barbara Cintron",
  "location": "Storm Lake, Iowa, USA",
  "model": {
    "name": "Stefan Phase-Change Approximation",
    "equation": "D = K(m) × √(HDD)",
    "variables": {
      "D": {
        "symbol": "D",
        "name": "frost depth",
        "unit": "centimeters",
        "description": "Maximum vertical penetration of ice front into soil matrix"
      },
      "K": {
        "symbol": "K(m)",
        "name": "conductivity factor",
        "unit": "cm/(°C·day)^0.5",
        "formula": "2.2 + (m - 5) × (2.0 / 40)",
        "bounds": {
          "min": {"moisture_percent": 5, "K_value": 2.2, "soil_type": "dry sand"},
          "max": {"moisture_percent": 45, "K_value": 4.2, "soil_type": "saturated clay"}
        },
        "storm_lake_typical": {
          "moisture_percent": 22,
          "K_value": 3.82
        }
      },
      "HDD": {
        "symbol": "HDD",
        "name": "heating degree-days",
        "unit": "°C·days",
        "base_temperature": "0°C",
        "calculation": "Σ(max(0, T_base − T_daily))",
        "typical_iowa_jan_mar": {
          "min": 4500,
          "max": 6800
        }
      }
    }
  },
  "citations": [
    {
      "wikidata": "Q14524610",
      "slug": "heating-degree-day",
      "concept": "sum of temperature deficits driving phase change"
    },
    {
      "wikidata": "Q3775789",
      "slug": "stefan-problem",
      "concept": "moving boundary solution for solidification fronts"
    },
    {
      "wikidata": "Q487005",
      "slug": "thermal-conductivity",
      "concept": "material property scaling heat flux through soil matrix"
    }
  ],
  "operational_thresholds": [
    {"depth_cm": 30, "classification": "light freeze", "action": "snow cover sufficient"},
    {"depth_cm": 60, "classification": "moderate freeze", "action": "mulch perennials, 0.9m pipe depth"},
    {"depth_cm": 120, "classification": "deep freeze", "action": "biennial dormancy, 1.5m foundations"},
    {"depth_cm": 200, "classification": "critical freeze", "action": "geothermal displacement required"}
  ],
  "version": "1.0.0",
  "compiled": "2026-07-17T06:00:00Z"
}