Linear theory of the urban heat island cirulation

Abstract

linear time-dependent model of the urban heat island circulation is developed for use in situations with a marked inversion. It has the external and first-internal gravity wave modes as basic dynamic ingredients (the inversion is treated as a `free' surface). The background wind field may vary with height and in time, and the Coriolis acceleration, though not important in most cases, is taken into account. The model equations are formulated in two-D (horizontal) Fourier space, permitting a fully implicit scheme to be used. Large time steps can then be employed, so that the external mode is implicitly in balance, while the internal mode slowly evolves. The value of the model lies in its efficiency: with 1600 two-D Fourier components and a 1-h time step, a 10-h integration typically takes 20 s of central processor time on a Cyber 175. The model is thus suitable for use in connection with operational air quality models running on smaller computers. Another advantage over more complete mesoscale atmospheric models is that initialization is very simple. Various examples are discussed to illustrate the performance of the model.