## 1 Introduction  
In a variety of engineering and basic scientific area, the turbulent boundary layers over smooth and rough wall surfaces have long been discussed and reported. It is usually related with an increase in momentum transport, for example, see the literatures ([PERSON] [1], [PERSON] [2], [PERSON] et al. [3], [PERSON] [4], [PERSON] and [PERSON] [5], and [PERSON] and [PERSON] [6]). Depending on the shape and height of the surface roughness, the flow field could be substantially different in terms of the mean velocity and turbulence statistics (see [PERSON] et al. [7; 8] and [PERSON] et al. [9]) Regarding the details of turbulent boundary layer on the surface, there have been more literatures ([PERSON] [10], [PERSON] [11], [PERSON] [12], [PERSON] and [PERSON] [13], [PERSON] [14], and [PERSON] and [PERSON] [15]). In direct numerical simulation (DNS), all scales ranging from the smallest scales, where the dissipation of the turbulence kinetic energy into thermal energy takes place (termed the Kolmogorov length scale), up to the largest scales (typically defined by the characteristic length of the flow configuration being considered) are resolved both in space and time. Therefore, DNS requires enormous computational efforts. DNS studies are still limited to the flow problems with small Reynolds numbers and simple geometries. On the other hand, regarding large eddy simulation (LES), only the large scales are resolved, and the effects of the smallest scales are modeled. This is because the large-scale eddies are known to be largely affected by the boundary conditions and therefore should be computed, but small scales are largely independent of the flow geometry and tend to be homogeneous and isotropic, irrespective of the geometry being considered, and, therefore,can be easily modelled. Therefore, LES requires less computational effort than that for DNS, and the computational requirements of the LES remain rather high for the optimization of complicated processes where a large number of computations need to be performed. The most direct method of generating a well-developed turbulent boundary layer is to simulate a laminar inflow and allow it to develop spatially over a suitably long domain, i.e., over a hundred times the thickness of the eventual boundary layer depth of interest. However, even this \"simple\" method would present difficulties associated with ensuring the correct surface conditions, such as the length scale and wall treatment. Further, the computational cost would be very high. Alternatively, using a time-evolving large eddy simulation (LES) or direct numerical simulation (DNS) with a periodic ([PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], [PERSON] et al. [19]) or a \"modified periodic\" ([PERSON] and [PERSON] [20]) boundary condition, the inlet-outlet boundary condition can be used to generate the appropriate turbulent flow. For the latter, [PERSON] et al. [18] used a sort of \"precursor simulation\", in which the velocity field at an appropriate downstream station is stored and imposed in a suitably re-scaled form as the inflow data for the primary computation. The precursor simulation generates a realistic turbulent flow field. However, it is also expensive and has limitations, such as its applicability to simple geometries only. Therefore, it is difficult to determine the usefulness of such a method in actual urban-type scenarios. Procedures that are based on proper orthogonal decomposition ([PERSON] et al. [21], [PERSON] and [PERSON] [22], [PERSON] et al. [23]) may be less expensive than the above methods for the generation of inflow data provided that there are appropriate DNS/LES ([PERSON] and [PERSON] [22]) or experimental datasets ([PERSON] et al. [21], [PERSON] et al. [23]) available for processing in order to obtain the most energetic modes, with an appropriate set of time-dependent projection coefficients that provide the phase information. The reconstructed inflow data for later LES/DNS are \"almost realistic\".