As a first step toward achieving full physics urban weather simulation capabilities within the resident-GPU large-eddy simulation (LES) FastEddy® model, we have implemented and verified/validated a method for explicit representation of building effects. Herein, we extend the immersed body force method (IBFM) from Chan and Leach (2007, https://doi.org/10.1175/2006JAMC1321.1) to (i) be scale independent and (ii) control building surface temperatures. Through a specific drag-like term in the momentum equations, the IBFM is able to enforce essentially zero velocities within the buildings, in turn resulting in a no-slip boundary condition at the building walls. In addition, we propose similar forcing terms in the energy and mass conservation equations that allow an accurate prescription of the building temperature. The extended IBFM is computationally efficient and has the potential to be coupled to building energy models. The IBFM exhibits excellent agreement with laboratory experiments of an array of staggered cubes at a grid spacing of (Formula presented.) mm, demonstrating the applicability of the method beyond the atmospheric scale. In addition, the IBFM is validated at atmospheric scale through simulations of downtown Oklahoma City ((Formula presented.) m) using data collected during the Joint Urban 2003 (JU03) field campaign. Our LES IBFM results for mean wind speed, turbulence kinetic energy, and SF₆ transport and dispersion compare well to observations and produce turbulence spectra that are in good agreement with sonic anemometer data. Statistical performance metrics for the JU03 simulations are within the range of other LES models in the literature.

The microphysical aspects of the relationship between radar reflectivity Z and rainfall rate R are examined. Various concepts discussed in the literature are integrated into a coherent analytical framework and discussed with a focus on the interpretability of Z-R relations from a microphysical point of view. The forward problem of analytically characterizing the Z-R relationship based on exponential, gamma, and monodisperse raindrop size distributions is highlighted as well as the inverse problem of a microphysical interpretation of empirically obtained Z-R relation coefficients. Three special modes that a Z-R relationship may attain are revealed, depending on whether the variability of the raindrop size distribution is governed by variations of drop number density, drop size, or a coordinated combination thereof with constant ratio of mean drop size and number density. A rain parameter diagram is presented that assists in diagnosing these microphysical modes. The number-controlled case results in linear Z-R relations that have been observed for steady and statistically homogeneous or equilibrium rainfall conditions. Most rainfall situations. however, exhibit a variability of drop spectra that is facilitated by a mix of variations of drop size and number density, which results in the well-known power-law Z-R relationships. Significant uncertainties are found to be associated with the retrieval of microphysical information from the Z-R relation coefficients, but even more so with shortcomings of the measurement of rainfall information and the subsequent processing of that data to obtain a Z-R relation. Given a proper consideration of the uncertainties, however, valuable microphysical information may be obtained, particularly as a result of long-term monitoring of rainfall for fixed observational settings but also through comparisons among different climatic rainfall regimes.

The controls on the variability of raindrop size distributions in extreme rainfall and the associated radar reflectivity-rain rate relationships are studied using a scaling-law formalism for the description of raindrop size distributions and their properties. This scaling-law formalism enables a separation of the effects of changes in the scale of the raindrop size distribution from those in its shape. Parameters controlling the scale and shape of the scaled raindrop size distribution may be related to the microphysical processes generating extreme rainfall. A global scaling analysis of raindrop size distribution, corresponding to rain rates exceeding 100 mm h^-1, collected during the 1950s with the Illinois State Water Survey raindrop camera in Miami, Florida, reveals that extreme rain rates tend to be associated with conditions in which the variability of the raindrop size distribution is strongly number controlled (i.e., characteristic drop sizes are roughly constant). This means that changes in properties of raindrop size distributions in extreme rainfall are largely produced by varying raindrop concentrations. As a result, rainfall integral variables (such as radar reflectivity and rain rate) are roughly proportional to each other, which is consistent with the concept of the so-called equilibrium raindrop size distribution and has profound implications for radar measurement of extreme rainfall. A time series analysis for two contrasting extreme rainfall events supports the hypothesis that the variability of raindrop size distributions for extreme rain rates is strongly number controlled. However, this analysis also reveals that the actual shapes of the (measured and scaled) spectra may differ significantly from storm to storm. This implies that the exponents of power-law radar reflectivity-rain rate relationships may be similar and close to unity, for different extreme rainfall events, but their prefactors may differ substantially. Consequently, there is no unique radar reflectivity-rain rate relationship for extreme rain rates, but the variability is essentially reduced to one free parameter (i.e., the prefactor). It is suggested that this free parameter may be estimated on the basis of differential reflectivity measurements in extreme rainfall.

The intrastorm variability of raindrop size distributions as a source of uncertainty in single-parameter and dual-parameter radar rainfall estimates is studied using time series analyses of disdrometer observations. Two rain-rate (R) estimators are considered: the traditional single-parameter estimator using only the radar reflectivity factor (Z) and a dual-polarization estimator using a combination of radar reflectivity at horizontal polarization (Z_n) and differential reflectivity (Z_DR). A case study for a squall-line system passing over the Goodwin Creek experimental watershed in northern Mississippi is presented. Microphysically, the leading convective line is characterized by large raindrop concentrations (> 500 drops per cubic meter), large mean raindrop sizes ( > 1 mm), and wide raindrop size distributions (standard deviations >0.5 mm), as compared to the transition region and the trailing stratiform rain. The transition and stratiform phases have similar raindrop concentrations and mean raindrop sizes. Their main difference is that the distributions are wider in the latter. A scaling-law analysis reveals that the shapes of the sealed spectra are bent downward for small raindrop sizes in the leading convective line, slightly bent upward in the transition zone, and strongly bent upward in the trailing stratiform rain. The exponents of the resulting Z-R relationships are roughly the same for the leading convective line and the trailing stratiform rain ( ≈ 1.4) and slightly larger for the transition region ( ≈ 1.5), with prefactors increasing in this order: transition ( ≈ 200), convective ( ≈ 300), stratiform ( ≈ 450). In terms of rainfall estimation bias, the best-fit mean R(Z_H, Z_DR) relationship outperforms the best-fit mean R(Z) relationship, both for each storm phase separately and for the event as a whole.