Follow a cold spell
Begin with bare ground at −20 °C air temperature. Watch the 25 cm trace first, then 1 m and 4 m. Which depth notices the cold last?
FIELD NOTE 07 / GROUND HEAT LAB
The ground remembers.
Change the air. Watch the cold travel below your feet.
Day 0.0
Inside the landscapeAir −15 °C
DEEP-GROUND RESERVOIR8 °C held at 10 m
No net heat transfer at the lower boundary.
Blue is lake water; the pale surface sheet is floating ice. The dashed blue soil contour and white ice underside measure different things; they need not meet at the shore. The house is enlarged and horizontal spacing is schematic.
Why does deep lake water stay near 4 °C?
Fresh water is densest near 4 °C. As the lake cools toward that temperature, denser surface water sinks. Further cooling leaves lighter, colder water above it, beneath the floating ice. The ice and snow slow heat loss, so deep water can remain near 4 °C while the surface freezes. This is a tendency, not a thermostat: the model never pins lake water to 4 °C. Explore the lake science ↓
≤−30 °C0≥30 °C
- Open-ground frost depth
- 0.00 m
- Frost beside basement
- 0.00 m
- Lake ice equivalent
- 0.00 m
Open ground · 1.00 m deep · 8.0 °C
The dotted probe line marks the selected location. Each plot colour follows one depth.
Temperature through time · Open ground
°C · elapsed daysAir25 cm50 cm1 m2 m4 m
Press Play or +7 days to build the traces. All locations are recorded together, so switching location keeps their full histories.
Read current temperatures as a table
| Depth | Open ground | Beside basement | Lake |
|---|
Freezing through time
Metres · elapsed daysOpen-ground frostFrost beside basementLake ice equivalent
Frost depth is the deepest subzero soil, including any frozen layer left beneath a thawed surface. Lake ice equivalent adds the frozen fraction through the lake column and is drawn as a floating surface sheet. It excludes freezing expansion and is not an ice-strength estimate.
Try a change
Ready. Soil and water begin at 8 °C. Press Play to follow the heat.
Make a prediction. Change one thing. See what happens.
Model notes & references ↗FOLLOW THE SCIENCE
The weather changes.
The warmth takes longer.
A thermometer in the air responds to a cold spell long before one buried a metre underground. Heat must move through the ground, and each layer stores energy. Deeper temperature changes are usually smaller and arrive later. This delay gives the ground a kind of thermal memory.
The house and lake change that story locally. A warm basement supplies heat through its buried walls and floor. Water stores considerable energy, and freezing releases additional energy that must escape before more ice can form.
A FEW QUESTIONS TO TRY
Let’s see what happens.
Give the ground a blanket
Add 30 cm of snow while winter is underway. Does the ground warm instantly, or does the rate of heat loss change first?
Let spring arrive
After frost develops, remove the snow and raise the air to 12 °C. Compare thawed soil above buried frost with lake ice that floats at the surface as it thins.
These buttons change the conditions from this moment onward. Use Reset when you want to compare separate runs from the same initial temperature.
Insulation changes the pace.
A BLANKET OF SNOW
Keeping warmth in.
Snow contains air between its ice grains. Its resistance to heat flow can keep soil warmer than exposed ground under the same cold sky. It slows heat transfer in both directions; it does not create heat. NSIDC: the science of snow ↗
A BASEMENT WALL
A warmer neighbour.
The basement is a maintained heat source when it is warmer than the surrounding soil. More wall insulation reduces that transfer. Compare the ground beside it with the open-ground probe, using the same depths and the same weather.
Can the ground supply heat from below?
Yes. Soil stores energy, so warmer layers can transfer heat toward colder layers above them. Near the surface, much of the seasonal warmth comes from energy absorbed during warmer weather. Earth’s interior also provides a geothermal contribution. NRC Canada: ground temperatures ↗
Here, soil and water begin at 8 °C and the lower boundary stays at 8 °C. It acts as a large reservoir that can supply or absorb heat as the model evolves. The arrows and the readout show the actual heat transfer across that boundary. This represents deep-ground thermal storage; an additional geothermal heat flux is not imposed.
Why is the deep water near 4 °C?
Fresh water is densest near 4 °C. Cooling surface water can sink and mix while it is warmer than that; colder water can remain above denser water below. Ice forms at the top, where energy is leaving. It is less dense than liquid water, so a freely floating ice cover stays at the surface as it thins. Unlike buried frozen soil, it does not remain suspended between layers of liquid water during a thaw. USGS: water density ↗
Once the surface cools below about 4 °C, that water becomes less dense and stays above the deeper water. The resulting winter stratification has cold water near the ice and often warmer water near 4 °C below. Ice and snow reduce further heat loss. The deeper water is not held at 4 °C: its temperature still responds to heat exchange, mixing, lake depth and its initial stored energy. The model calculates that temperature; only the deep-ground boundary is held at a prescribed temperature.
Should the ice be thinner at the shore?
A warm bank can supply heat from the side and accelerate melting at the ice edge. A cold bank can instead help ice grow, so shore ice does not always start thinner or disappear first. Real shores also respond to shallower water, sunlight, runoff and currents.
Here, heat flows between the bank and lake through their shared boundary. The shoreline is a simplified vertical bank, with 6 m of water immediately beside it; shallow shelves, solar heating and runoff are not simulated. The dashed blue soil line marks 0 °C, while the white lake line marks the underside of the floating ice. Their depth difference is not a gap in heat transfer. Soil has much less water per unit volume than the lake, and its buried frost stays in place while lake ice floats.
Temperature is only part of the energy story.
Freezing 1 kg of water releases about 333.5 kJ. That energy has to go somewhere. In the soil, pore water freezes over a range of temperatures, so a probe can linger near 0 °C while the frozen fraction keeps changing. PTB / BIPM: heat of fusion ↗
The mathematics, assumptions & references
Following energy from cell to cell
∂H / ∂t = ∇ · (k ∇T)
q = −k ∇T · α = k / C
q = −k ∇T · α = k / C
H is energy per unit volume, including sensible heat and latent heat; k is thermal conductivity; C is volumetric heat capacity. The 40 m × 10 m cross-section uses 80 × 40 finite-volume cells. Each internal face transfers equal and opposite amounts of energy between its neighbours. Explicit time steps are at most one hour. Depth readings interpolate cell-centre temperatures within the same material.
Outside the freezing interval, H changes by C ΔT. Within it, a linearly varying liquid fraction adds the latent-energy term. The soil uses a teaching freezing interval of −1 to 0 °C; lake water uses −0.1 to 0 °C as a numerical approximation to freezing at 0 °C. On land, the dashed blue line is the interpolated 0 °C contour, not a sharp boundary between completely liquid and completely frozen soil. On the lake, the white line marks the base of the surface ice sheet using the column’s ice equivalent; thin ice is drawn at its fractional-cell thickness. The 25 cm vertical cells limit front resolution. Landscape view uses natural material colours and temperature labels; Temperature map uses the numerical colour scale. Both views show the full 10 m domain, with the same computed fronts, phase fractions and probe values. The illustration enlarges the house and compresses horizontal distances; interior details do not alter the model geometry.
| Material | k, W/(m·K) | C, MJ/(m³·K) | Latent energy, MJ/m³ |
|---|---|---|---|
| Soil: thawed → frozen | 1.6 → 2.1 | 2.4 → 1.8 | 73.37 (22% water by volume) |
| Lake: liquid → frozen | 0.6 → 2.2 | 4.18 → 1.93 | 333.5 |
| Prescribed snow | 0.20 | Not a stored-energy layer | Not modelled |
The boundaries matter
qsurface = (Tair − Tcell) / [1/h + dsnow/ksnow + Δz/(2k)]
The air exchange coefficient h is 10 W/(m²·K). Snow adds resistance on exposed land and where the top lake cell is at least 95% frozen. Manual snow depth stays fixed until you change it. Regional snow depth follows the interpolated station averages as the calendar advances. Both are prescribed insulating layers: snow mass, compaction and the energy of snowmelt are not simulated. The station’s ground snow depth is also applied to formed lake ice as a simplification; real lake snow can differ because of wind and drifting. Surface radiation, evaporation, rainfall, flowing groundwater and frost heave are omitted.
Soil and water start uniformly at 8 °C; the 10 m lower boundary stays at 8 °C. This is a prescribed-temperature reservoir, not a specified geothermal heat-flux boundary. Its heat transfer can reverse direction; the displayed W/m² value is the instantaneous average across the full 40 m lower boundary. Side boundaries are insulated. The basement occupies x = 6–12 m and reaches 2.5 m down. Its temperature is maintained, with the selected resistance on buried walls and slab; the above-ground building envelope is outside this model. The lake begins at x = 28 m and is 6 m deep, representing a simplified slice of a larger body of water.
After each heat-transfer step, a buoyancy adjustment gathers the lake’s frozen material into a surface sheet and moves liquid beneath it. Phase parcels keep their relative order and carry their stored energy as they are remapped onto the grid. This conserves column enthalpy and total water amount; contact within a boundary cell can redistribute sensible and latent heat. Soil cells stay fixed. Fully liquid lake layers then mix vertically if the upper layer is denser, conserving their combined energy. A simple density ordering ρ ≈ 1000 − 0.008(T − 4)² gives a maximum at 4 °C. Stable stratification remains.
The ice is treated as a freely floating, drained sheet. Surface melt ponds, ice held to the shore or lake bed, breakup, wind mixing, currents, solar penetration and salinity are omitted. Freezing expansion and the small height of ice above the waterline are not resolved. Lake ice equivalent is frozen water volume per unit area on this fixed grid; the illustration uses that same equivalent thickness.
Regional climate averages
In Annual Cycle, choose one of eight Canadian locations to drive the air boundary with ECCC’s published 1991–2020 monthly daily-average temperatures. Regional snow uses Average Snow Depth (cm), not snowfall totals or month-end snow depth. The source table preserves those monthly values. Choose Set snow manually to isolate the effect of snow insulation while keeping the regional temperature cycle.
The source records are composite stations, often airports, representing their location rather than every part of a city or region. ECCC’s coverage codes describe the underlying record: A meets its 30-year standard; B has at least 25 years, C at least 20, and D at least 15. The temperature and snow elements can have different coverage. The controls show that coverage and link to the original station tables. Locations with missing monthly values were excluded; blanks were not replaced with zero.
For a continuous model input, straight lines connect monthly means at the midpoint of each month, including December to January. This interpolation does not recreate observed daily weather or exactly preserve each calendar month’s mean. Snow stays nonnegative. The selected start month places day 0 on its first day, and the cycle repeats on a 365-day calendar. Changing region, start month or snow source keeps the model time and stored heat. The date readout is a model calendar, not a historical replay.
Monthly averages smooth away cold snaps, storms and intermittent snow. Because freezing and snow insulation are nonlinear, a run driven by averages is not itself an observed average frost depth. The same soil, lake geometry, 8 °C initial state and 8 °C boundary at 10 m are used for every region. Local geology, permafrost, lake depth and measured deep-ground temperatures are not calibrated here. The second cycle reduces some startup effects but does not guarantee equilibrium. ECCC: Canadian Climate Normals & calculation information ↗
Seasons and delayed responses
Tair(t) = Tmean − A sin(2πt / 365 days)
δ = √(2α / ω) · amplitude at depth z ∝ e−z/δ
δ = √(2α / ω) · amplitude at depth z ∝ e−z/δ
The custom annual curve starts at its mean and cools first. In a uniform, nonfreezing half-space, a sinusoidal surface temperature is attenuated and delayed with depth; δ is its characteristic penetration depth. The landscape model adds boundaries and freezing, so it does not follow that simple solution exactly. These are controlled experiments, not local weather or calibrated frost-depth predictions. The first cycle also reflects the uniform initial temperature. Runs stop at 730 days.