Step 1: Set the surface energy balance over the diurnal cycle.
At the land surface, the net radiation \(R_n = (S_\downarrow - S_\uparrow) + (L_\downarrow - L_\uparrow)\) drives sensible (\(H\)) and latent (\(LE\)) heat fluxes and ground heat flux (\(G\)). After sunset \(S_\downarrow \approx 0\), so \(R_n<0\) due to strong longwave loss \(L_\uparrow\). Hence, \(H\) becomes negative (air is cooled by the surface), and the near‐surface layer cools continuously through the night.
Step 2: Nighttime boundary layer evolution.
Radiative cooling at the ground produces a stable surface layer (temperature increases with height). Turbulence weakens, so mixing is small and 2 m air closely follows surface cooling. This cooling proceeds monotonically through the night if sky is clear and winds are light.
Step 3: Why minimum occurs \(near\ sunrise\) and not at midnight.
Cooling continues as long as \(R_n<0\). The transition to net heating starts only after the sun rises high enough for \(S_\downarrow\) to offset longwave loss—this happens \emph{after} sunrise. Therefore the lowest 2 m temperature typically happens just before/at sunrise, with a small lag depending on clouds/wind. Midnight is earlier in the cooling period, so temperature is still dropping toward its minimum.
Step 4: Role of local factors (for completeness).
Clouds reduce longwave loss (warmer night); wind increases mixing (less cooling). Both can shift the exact timing slightly, but in tropical clear-sky land locations the canonical minimum remains just before sunrise.
Final Answer:
\[ \boxed{\text{At sunrise}} \]