Adjoint Optimization Approaches to Urban Climate Modeling

Many urban areas constitute an urban heat island (UHI, Fig. 1), i.e. they experience elevated temperatures compared to their rural surroundings. The annual mean air temperature of an UHI is approximately 2K warmer than its surrounding and the temperature difference can exceed 10K on a clear, calm night. Though the phenomenon decreases as the city size decreases, even smaller cities will create future heat islands –where public spaces are warmer than human comfort levels tolerate– with the more frequent occurrence of hot & dry heatwaves due to global warming. The associated summer health problems are expected to increase significantly in the future. Humans adjust to excess heat through their physiological heat adaptation which tends to collapse when temperatures surpasses 36-38C. Urban dwellers therefore face a severe risk for heat stress in the coming decades if no countermeasures are taken. Ironically, urban heat stress pushes humans into air-conditioned buildings at the cost of rising heat loads and outdoor temperatures. 

Supplementary to anthropogenic waste heat from motorized transportation, industry or air-conditioning and to poor ventilation, building materials are deemed major contributors to UHI due to the large amount of heat stored in their  thermal mass. At the same time, they also represent a promising startingvpoint for passive reductions of the heat load. Hence, mitigation techniques recommend cool materials, urban vegetation, water and shading next to enhanced ventilation as solutions to moderate temperatures and increase the adaptive capacity. UHI is a complex phenomenon, not only because of the complexity of urban geometric settings (I) and weather patterns (II), but also due to the interplay between its contributing physics (III) and the range of the involved scales (IV). From an optimization point of view, its is dominated by the complexity of the interacting physics (III), the related uncertainty & variability (V) and a large number of design variables (VI). The control of UHI phenomena is based on the challenges (I)-(VI) and the specific situation of a particular city including the climate of future decades but also local contextual parameters of the urban surface fabric.

The research aims to develop a simulation-driven optimization process to reduce urban heat levels in Hamburg and involves three building blocks. The first building block addresses the second challenge (II) on high-quality predictions of climate conditions expected in the next decades. Results will be obtained from the Earth-System model ICON, including the opportunity to assess related variabilities. It will serve as input to the second building block, an ”offline-nested” urban climate simulation model used to predict the details of typical future urban summer diurnal cycles. The project will utilize an established, parallel urban climate scientific community simulation model, i.e. the PALM model. PALM is able to render complex physical interaction (III, IV) and allows spatial resolutions on a meter scale for realistic urban settings (I), which is computationally supported by an excellent parallel performance. Modeled features refer to, for example, scale-resolved turbulence transport, thermal balances for the atmosphere (air), clear-sky radiation & long- and shortwave radiative heat transfer, as well as thermal models for the entire building envelop and paving surfaces, viz. land and building surface models. Maintainance and access to sources is provided by the Leibniz Univ. Hannover.

The innovation refers to the third building block, an adjoint optimisation framework to be supplemented during this research, and –to the best of our knowledge– has not yet been used for UHI studies. Attention will be given to objective functionals that address physical properties of interest, viz. surface temperatures, air temperatures in the canopy layer and biophysical (mean radiant) temperatures as well as lower section wind speeds. We will introduce hybrid continuous adjoint optimization methods to the simulation framework, which allow to assess the sensitivities of the objective functionals to the design and the fabric of the building and paving envelop, and their governing physical properties. The latter involve the albedo, emissivity, surface roughness length, thermal conductivity and heat capacity, soil moisture, leaf area density or window parameters, respectively. Simulations will be performed for (nested) selected city fractions with a spatially limited coverage of approximately 53km to capture all scales of the urban boundary layer. In addition to general/global parameter studies already accessible by current simulations, the adjoint method offers the opportunity to impose targeted local changes to the specific urban setting. This might for example help to manage apparent contradictions of the local sensitivity, e.g. when the local temperature increases in response to a global albedo decrease due to a locally increased radiative heat transfer. Research questions will also be concerned with the potential of optimized paving materials, featuring higher moisture capacity or permeability, and suitably placed roof and facade vegetation to counteract decreased evapotranspiration in urban environments. Moreover, the roughness of urban surfaces and their heat capacity can cause tem- perature variations and stimulate local turbulence. Thus, local-targeted non-uniform urban landscapes suggested by an optimizer can stimulate city breezes and help to reduce the UHI intensity.

(Optimization) Method: Because of their unrivaled efficiency in optimizing problems under the aegis of a very large number of degrees of freedom (VI), adjoint optimization methods did receive increasing attention over the last decade. Whilst industrial applications for single-field problems, e.g. related to the optimization of structures or aerodynamic shapes, have reached an impressive level of maturity, transient and/or multi-physics studies remain in their infancy, with very few recent exceptions. Continuous adjoint formulations of PDE constraint optimization problems were formerly developed, implemented and published by the applicant for a range of practical problems using FV-based parallel procedures. Activities did consider adjoint multi-field aspects and adjoint wall-function models (III), but were not yet applied to true unsteady operations. Proposed efforts will address unsteady issues, where particular difficulties arise from the oppositely directed information transport of the primal and adjoint procedures. In a trade-off between compute and memory expenses, check-pointing strategies were previously suggested, but the related overheads often question their feasibility for practical applications. An innovative alternative refers to order reducing singular value decomposition (SVD) methods, which are often employed for reduced-order models. In the context of adjoint shape optimizations they must be implemented as time-incrementing, spatially parallel strategies to project the primal flow field into a compact formulation. Improving recent suggestions for smart field data reconstructions as regards the attainable computational efficiency and the independency of the parallelization is crucial to massively parallel transient adjoint simulations and will be one central aspect of the project. Moreover, the reconstructed data should obey to the physical realizability, e.g., adhere to plausible limits, which supports both the robustness of the optimization process and the predictive quality. The incremental SVD or related alternatives can be used as a smart ”interpolator” that avoids check-pointing in unsteady optimizations. Moreover, mode-based (ROM) optimization methods are an attractive area of research, that will provide more extensive reductions of the computational cost. Another aspect could be devoted to minimizing the standard deviation of the objective functional alongside its mean, during a stochastic optimization approach to account for variations of future climate conditions (V).

Potential PhD Topics:

• Adjoint approaches to urban climate models

• Stochastic optimization approaches to urban climate models

• Efficient model-order reducing, parallel approaches to unsteady heat island optimization

• Mitigation of urban heat islands using optimal building and surface envelopes

• Comparison of full- and reduced-order optimization approaches in urban heat modeling

In progress.