As computer resources increase, mesoscale models (MMs) can be run with the spatial filter scale (Δ) corresponding to the energy-containing turbulence scale (l), although typical MMs have not been designed to run within the region of l/Δ ~ 1, the “Terra Incognita” defined by Wyngaard (2004). I attack the “Terra Incognita” issue from the convective boundary layer (CBL) perspective. The integral scale of the turbulence in the CBL is comparable to the CBL height, typically 1 km. Thus, MMs with an effective resolution much larger than 1 km employ one-dimensional ensemble-average schemes which are based on a horizontally homogeneous CBL.

By definition the CBL is directly influenced by the earth’s surface that is almost always heterogeneous on various spatial scales. I focus on the impact of the surface energy balance (SEB) on a scale from a few 10s of km to a few 100s of km on the CBL. By using large-eddy simulation (LES) with a simple sinusoidal SEB variation, I investigate the impact from two perspectives: 1) organized mesoscale motions, and 2) microscale (turbulent) fluctuations. I found several interesting features of horizontally heterogeneous CBLs. First, mesoscale horizontal flows induced by heterogeneity of the surface energy balance (SEB) are divided into quasi-stationary and non-stationary flows, with amplitudes of 100 Wm-2 and greater being non-stationary flows. The transition of the generated motions from a quasi-stationary state to a non-stationary state occurs when horizontal advection is strong enough to level out the temperature gradient on the surface heterogeneity scale. Second, when the generated motions are in quasi-stationary state, the energy provided by the SEB variation remains in organized mesoscale motions on the surface heterogeneity scale itself. However, in a non-stationary state, the energy cascades to smaller scales, with the cascade extending into the turbulence scale. Third, the microscale (turbulent) structure of the CBL in quasi-stationary state retains characteristics of mixed-layer similarity. However, in the CBL that is in non-stationary state, mixed-layer similarity is violated even after mesoscale fluctuations are filtered out. Given these findings, mesoscale models employing CBL parameterization may fail to simulate the structure of the CBL over a strongly heterogeneous surface – in particular on a scale of 10s of km.