After sunset the ground radiates heat to the cold sky faster than the soil can bring it up from below. Change soil, moisture, cloud, wind and mulch and see when the surface freezes while the air thermometer still reads above zero.
Re-runs four days of weather with your current settings, changing one thing, and compares the coldest ground temperature on the fourth night with the radiative limit (no soil heat, no wind).
The science
Heat in the soil. Temperature obeys the diffusion equation C ∂T/∂t = ∂/∂z (k ∂T/∂z) with volumetric heat capacity C (J m⁻³ K⁻¹) and conductivity k (W m⁻¹ K⁻¹). It is solved on 34 layers (0.4 cm at the top growing by 10 % per layer to about 1 m) with the unconditionally stable backward-Euler scheme, so even a 10-minute step does not blow up. The bottom is held at the annual-mean temperature.
Soil properties. C is the volume-weighted sum of mineral grains, water and air. Conductivity follows Johansen (1975): k = kdry + (ksat − kdry) Ke with kdry = (0.135 ρb + 64.7)/(2700 − 0.947 ρb) and ksat = ks1−φ 0.57φ; Ke rises with the logarithm of saturation. Dry sand is a good insulator (k ≈ 0.23), wet soil conducts about ten times better, so wet ground refills the cold surface with heat from below. The mineral conductivities, porosities and the peat values are typical textbook values, not measurements of a particular soil.
Surface energy balance. The skin takes in sunshine S, longwave sky radiation ε εsky σ Ta⁴, and exchanges sensible heat H = h (Ta − Ts) with the air, while radiating ε σ Ts⁴. The sum is the heat flowing into the soil. Ground emissivity ε = 0.97; clear-sky emissivity is Brutsaert's 1.24 (e/Ta)1/7 (e in hPa, T in K) from the dew point, blended with 0.96 for overcast; the transfer coefficient is the simple wind law h = 5.7 + 3.8 u (W m⁻² K⁻¹, u in m/s). With no wind and no soil flux the skin would settle at Ts = εsky1/4 Ta, the “radiative limit” used in the experiment.
Sun. Solar elevation comes from latitude 52° N, day of year and clock time; direct beam uses Meinel's 0.7AM0.678 with a 10 % diffuse allowance, and cloud cuts it by 1 − 0.75 c3.4 (Kasten–Czeplak).
What is simplified. The air temperature follows a prescribed cosine (minimum around 03:00) and is not cooled by the ground, so real air frosts and cold-air pooling in hollows are not modelled. There is no evaporation or dew/frost latent heat (which would slow cooling near 0 °C and warm the surface at dawn), no snow, no water movement, one uniform soil, a fixed solar albedo of 0.2, and mulch is a dry layer with k = 0.06 W m⁻¹ K⁻¹ and C = 0.3 MJ m⁻³ K⁻¹ (illustrative). Expect the right direction and rough size of effects, not a forecast for your garden.