Storm Lake county soil profile in midwinter. The white layer hides the depth we calculate.
STEFAN PHASE-CHANGE MODEL
Predict maximum frost penetration from accumulated degree-days and soil moisture content
PREDICTED MAXIMUM PENETRATION
0 cm
IMPERIAL EQUIVALENT
0 inches
AGRICULTURAL IMPLICATION
UNDERLYING MATHEMATICS
D = K(m) × √(HDD)
D: frost depth (cm)
K(m): conductivity factor, moisture-dependent
K = 2.2 + 0.048m, where m ∈ [5, 45]
K = 2.2 + 0.048m, where m ∈ [5, 45]
HDD: heating degree-days (°C·days)
Σ(max(0, T_base − T_daily))
Σ(max(0, T_base − T_daily))
WIKIDATA Q14524610
Heating Degree Day
Sum of temperature deficits driving phase change
WIKIDATA Q3775789
Stefan Problem
Moving boundary solution for solidification fronts
WIKIDATA Q487005
Thermal Conductivity
Material property scaling heat flux through soil matrix
OPERATIONAL NOTES — STORM LAKE COUNTY
RETURN TO HUB
The clay-loam deposits beneath our office plaza retain moisture at 22% volumetric even in drought years.
When January brings 4200 HDD and February adds 2800 more, the root zone freezes to 112 centimeters—deeper
than the taproots of turnips left to survive the winter. This is why we dig the cellar to 1.8 meters. This
is why the water pipes run south of the frost line. This is why we teach children to measure before they build.