The canopy layer urban heat island (UHI) effect, as manifested by elevated near-surface air temperatures in urban areas, exposes urban dwellers to additional heat stress in many cities, specially during heat waves. We simulate the urban climate of various generated cities under the same weather conditions. For mono-centric cities, we propose a linear combination of logarithmic city area and logarithmic gross building volume, which also captures the influence of building density. By studying various city shapes, we generalise and propose a reduced form to estimate UHI intensities based only on the structure of urban sites, as well as their relative distances. We conclude that in addition to the size, the UHI intensity of a city is directly related to the density and an amplifying effect that urban sites have on each other. Our approach can serve as a UHI rule of thumb for the comparison of urban development scenarios.

In this paper, we describe the PALM model system 6.0. PALM (formerly an abbreviation for Parallelized Large-eddy Simulation Model and now an independent name) is a Fortran-based code and has been applied for studying a variety of atmospheric and oceanic boundary layers for about 20 years. The model is optimized for use on massively parallel computer architectures. This is a follow-up paper to the PALM 4.0 model description in Maronga et al. (2015). During the last years, PALM has been significantly improved and now offers a variety of new components. In particular, much effort was made to enhance the model with components needed for applications in urban environments, like fully interactive land surface and radiation schemes, chemistry, and an indoor model. This paper serves as an overview paper of the PALM 6.0 model system and we describe its current model core. The individual components for urban applications, case studies, validation runs, and issues with suitable input data are presented and discussed in a series of companion papers in this special issue.

The Radiative Transfer Model (RTM) is an explicitly resolved three-dimensional multi-reflection radiation model integrated into the PALM modelling system. It is responsible for modelling complex radiative interactions within the urban canopy. It represents a key component in modelling energy transfer inside the urban layer and consequently PALM's ability to provide explicit simulations of the urban canopy at metre-scale resolution. This paper presents RTM version 3.0, which is integrated into the PALM modelling system version 6.0. This version of RTM has been substantially improved over previous versions. A more realistic representation is enabled by the newly simulated processes, e.g. the interaction of longwave radiation with the plant canopy, evapotranspiration and latent heat flux, calculation of mean radiant temperature, and bidirectional interaction with the radiation forcing model. The new version also features novel discretization schemes and algorithms, namely the angular discretization and the azimuthal ray tracing, which offer significantly improved scalability and computational efficiency, enabling larger parallel simulations. It has been successfully tested on a realistic urban scenario with a horizontal size of over 6 million grid points using 8192 parallel processes.