Rough surfaces are prevalent in flow-related applications due to surface degradation. The roughness topography can alter the surface skin friction and heat transfer in turbulent flows. Depending on the different mechanism of the roughness formation process, the roughness topography may exhibit anisotropic properties. The present work aims to shed light on the effect of roughness an isotropy on skin friction and heat transfer by systematically varying roughness properties in different directions and across various scales. To this end, irregular anisotropic rough surfaces are generated based on 2-D power spectrum (PS). The surfaces are generated with Gaussian height probability density functions (PDF) and with either matched surface anisotropy ratios (SAR=𝐿𝐶𝑜𝑟𝑟𝑥 ∕𝐿𝐶𝑜𝑟𝑟𝑧 ) or effective slope ratios (ESR=𝐸𝑆𝑥∕𝐸𝑆𝑧). By adjusting the 2-D PS, the degree of anisotropy is varied at different wavenumbers, some surfaces are more anisotropic at large scales and some at small scales. Direct numerical simulations are performed to study turbulent flow over these anisotropic rough surfaces at Re𝜏 = 500, 𝑃 𝑟 = 0.71. The results demonstrate that the roughness an isotropy play a pivotal role in influencing both skin friction and heat transfer of the rough surface, leading to alterations of up to more than 50% in the roughness function 𝛥𝑈 +and the temperature roughness function 𝛥𝛩+. Detailed analysis indicates that commonly used parameters, SARor ESR alone, may not be the most appropriate predictive quantities to characterize the effects of an isotropicirregular roughness. In light of this, we introduce a new roughness topographical parameter 𝜂SA= ESR/SAR that successfully correlates with the observed anisotropic effect. The suitability of this new parameter is assessed through comprehensive analysis of both the current dataset and the an isotropic roughness from literature.