Temperature sensing network

The temperature sensing network at the basis of this work, together with the Chicago Loop district where it is deployed, have been extensively characterized in other studies22,56. Therefore, their features are only described succinctly in this section.

Since 2019, temperature sensors have been deployed in a myriad of surface and subsurface environments in the Chicago Loop district, which is also known as “the cake” for its various levels of built environments above and below the ground surface. The aim of this endeavor has been threefold: (1) gather surface air temperature data for the downtown area of Chicago that can enrich complementary sensing endeavors for Chicagoland and Illinois57,58, (2) establish relationships between the surface air temperature and the air temperature in underground built environments in the downtown area of Chicago22, and (3) measure ground temperatures in the heart of Chicago22.

Monitored surface environments consist of green parks and streets. Monitored subsurface environments include underground streets, building basements (serving residential, commercial, and tertiary buildings), private and public parking garages (including Millennium Garages—the largest underground parking system in North America, which comprises the four parking garages called Grant Park North, Millennium Park Garage, Millennium Lakeside, and Grant Park South), subway tunnels (the blue and red lines of the Chicago Transit Authority, CTA), a subsurface railway station (operated by the Chicago Metropolitan Rail system, METRA), a vast network of freight tunnels (non-operational since the 1992 Chicago flood), and the ground.

The Loop district presents a complex surface urban morphology. Taller and denser buildings characterize the northern portion of the Loop, although buildings become more widely spaced towards its north-eastern portion. In contrast, shorter and more widely spaced buildings characterize the southern portion of the Loop. Most buildings in the considered urban area serve commercial activities, whereas only a few (about one-third) serve residential uses. Four main green areas characterize the Loop: Millennium Park and Grant Park (the largest parks in the considered district), which are located on its east side, run along most of Michigan Avenue in this area and host Millennium Garages; Lakeshore East Park, which is located on the north-eastern portion of the district; and Dearborn and Roosevelt Parks, which are located on the south-western portion of the district.

Figure 4 presents a summary of air temperature data collected to date for surface and subsurface environments with the sensing network. Sensor locations are also provided for reference. Figure 4a illustrates monthly average surface air temperature data collected across the Loop with the deployed sensing network from 2020 till the end of 2022. These data are compared with monthly maximum, minimum, and average surface air temperature data collected at Chicago O’Hare airport from 1951 till the end of 202257; monthly average water temperature data collected for Chicago River from 1951 till the end of 202257; and monthly average grass and street temperature data derived with analytical expressions59,60 from the monitored surface air temperatures. Figure 4b illustrates the relationships between surface and subsurface air temperatures for building basements, Millennium Garages, and CTA tunnels established through the sensing network from 2019 till the end of 2022.

Fig. 4: Temperature data monitored across the Chicago Loop. a Average monthly temperature trend, \(\bar{T}\), over time, \(t\) (\({\bar{T}}_{{{{{\rm{sur}}}}}}\): monthly average surface air temperature monitored by the developed sensing network and NOAA57; \({\bar{T}}_{\max }\) and \({\bar{T}}_{\min }\): maximum and minimum values of monthly average surface air temperature monitored by NOAA57; \({\bar{T}}_{{{{{\rm{water}}}}}}\): monthly average water temperature monitored by NOAA57; \({T}_{{{{{\rm{grass}}}}}}\) and \({T}_{{{{{\rm{streets}}}}}}\): grass and street temperature values determined through the analytical expression proposed by Baggs59 and the coefficients reported by Jense-Page et al.60, where \({T}_{0,g}\) is the initial undisturbed ground temperature, \({t}_{o}\) is the time in days until the time the minimum air temperature from January 1st is measured for any considered location, \({A}_{s}\) is the amplitude of the annual temperature variation measured for any considered location, and \({\alpha }_{d,g}\) is the ground thermal diffusivity); b Relationship between surface air temperature, \({T}_{{{{{\rm{sur}}}}}}\), and subsurface air temperature, \({T}_{{{{{\rm{sub}}}}}}\), for different underground built environments across the Loop (\({R}^{2}\): coefficient of determination). The 3-D view of the sensing network has been created with a baseline image provided by OpenStreetMap. Full size image

As can be noted in Fig. 4a, the monthly average surface air temperature markedly fluctuates over the year due to the harsh climate of Chicago. The recently monitored temperatures for the Loop are relatively close to the temperatures measured at Chicago O’Hare airport over the past 70 years. The monthly average temperatures determined for the water, grass, and streets in the Loop are temporally shifted and damped in magnitude compared to the average surface air temperatures.

As can be noted in Fig. 4b, the relationships between the surface and subsurface air temperatures for the monitored built environments can be described by linear functions. These functions allow for the prediction of air temperatures underground for given surface temperatures.

The gathered temperature data represent a unique resource for the study of subsurface heat islands. The reason is that they allow simulating with appropriate digital tools the waste heat emissions diffusing in the subsurface from the ground surface and underground built environments, with the promise to assess their impacts on the performance of civil infrastructure. This endeavor is performed in this study with a digital tool described in the following section.

Numerical model and simulation

The 3-D computer model of the Chicago Loop district underlying this study represents a digital twin of such an urban area. This facility has been built through an extensive characterization of the Loop from architectural, structural, hydrogeological, energy, and urban perspectives through site explorations and surveys, interactions with local companies, and the literature.

Figure 5 illustrates the 3-D model of the Loop. Such a model reproduces the myriad of underground built environments and the vast network of green spaces and streets that currently characterize the considered urban area. Based on data made available by the Illinois State Geological Survey61, the model considers a horizontal soil stratigraphy composed of layers of sand, soft clay, stiff clay, hard clay, sand and boulders, and dolomitic limestone bedrock. The sand layer extends from the ground surface down to a depth of z = 4 m and has hence a thickness of z t = 4 m. The soft clay extends between depths of 4 ≤ z < 16 m and has a thickness of z t = 12 m. The stiff clay extends between depths of 16 ≤ z < 19 m and has a thickness of z t = 3 m. The hard clay extends between depths of 19 ≤ z < 27 m and has a thickness of z t = 8 m. Sand and boulders are found between depths of 27 ≤ z < 34 m, thus having a thickness of z t = 7 m. Dolomitic limestone is found under such a layer. Groundwater is found at a depth of z = 4 m.

Fig. 5: 3-D computer model of the Chicago Loop. The different colors represent different environments characterized by specific initial and boundary conditions (T 0,g : initial ground temperature; H: hydraulic head; t: time; \(\Delta H\): change in head per unit reference length). Full size image

An analysis of historical documents and field surveys suggests that building basements penetrate the ground down to four characteristic depths: z = 4, 8.3, 12.6, and 17.2 m. On average they run at a depth of \(\bar{z}=\) 6.2 m. The depths of the parking environments that constitute Millennium Garages have been defined via the analysis of the architectural drawings of such environments, running at an average depth of \(\bar{z}=\) 10 m. The red and blue lines of the CTA subway, and the freight tunnels that run underneath almost every street in the Loop, are located at depths of \(\bar{z}=\) 11 and 12 m based on historic data55, respectively. The subway tunnels are characterized by a cylindrical cross-section with a diameter of 4 m. The freight tunnels are egg-shaped and characterized by a height of 2.3 m and a width of 1.8 m55. Although the geometry of foundation systems underneath various buildings in the Loop has been characterized through the help of local engineering firms, the model does not reproduce such information because of its massive size. The model also neglects the presence of sewer and piping systems that are renowned for running at shallow depths in the Loop because exact information about their location was not made available by local entities for liability reasons.

The developed numerical model is used to run 3-D, time-dependent, thermo-hydro-mechanical finite element simulations. As a result, not only this model allows simulation of the heat that diffuses in the ground from the surface of the Loop and its various heat-emissive built environments; this model also allows simulation of the impacts of waste heat emissions on the deformation and the groundwater regime of the subsurface. Simulations are run with COMSOL Multiphysics (v. 5.5)62.

The mathematical formulation employed for the simulation has already been presented in other studies63,64 and is capable of reproducing complex problems of heat transfer, mass transfer, and deformation similar to the one addressed in this work. Therefore, the details of such formulation are not reported here for concision. From a qualitative perspective, the formulation resolves a conductive–convective energy conservation equation to reproduce the heat transfer in the ground, which is coupled with the momentum equilibrium equation to address the mechanics of the problem and the mass conservation equation to simulate the presence and influence of groundwater flow. The idealization and assumptions governing the developed simulations are as follows48:

(i) Conduction heat transfer characterizes the ground in the shallowest 4 m of dry sand. Convection heat and mass transfers characterize the ground beyond 4 m of depth. (ii) The ground is assumed to be isotropic, homogeneous, and characterized by a linear thermo-elastic behavior. The displacements and deformations of the ground are described via a linear kinematic approach under quasi-static conditions. The materials that constitute the ground are characterized by pores filled with a fluid (e.g., water or air) and have thermo-physical properties given by the fluid and the solid phases. (iii) The master equations governing the heat transfer, mass transfer, and deformation phenomena (i.e., continuity equation, momentum equation, and energy conservation equation, respectively) are coupled numerically in a time-dependent framework.

The employed modeling approach to simulate the heat transfer, mass transfer, and deformations may be considered advanced. However, it still incorporates simplifications discussed hereafter.

Probably the most significant simplification in the simulation of the heat and mass transfers that characterize the subsurface of the Loop lies in the fact that the model refers to the current urban morphology, although simulations are run from the 1950s till the 2050s. The heat and mass transfers characterizing the subsurface of urban areas are influenced by the evolutionary features of such complex environments (e.g., the construction and demolition of built environments, the transient loads acting on such environments, the variable and heterogeneous environmental conditions at the surface, etc.), and depend on the actual, spatially non-uniform properties of the ground. However, such aspects are daunting to reproduce with digital tools, especially when considering extensive urban areas such as the Loop. Fortunately, an analysis of historical data shows that the number and location of buildings across the Loop have not significantly changed since the 1950s. New buildings have indeed been constructed in the meantime but in most cases over the footprint of previous buildings. Therefore, it is argued that the urban morphology considered in the model, while static, provides an adequate representation of buildings and underground built environments across the Loop. The close comparison between the temperature data obtained for the ground through the developed numerical simulations and the sensing network supports that the model can well reproduce the heat and mass transfer characterizing the Chicago Loop district with the considered assumptions (see “Methods, Numerical model validation”).

Probably the most significant simplification in the simulation of the deformation of the Loop lies in the employed thermo-elastic assumption. When soils are subjected to thermal, hydraulic, and mechanical loads, they can be characterized by irreversible (i.e., plastic) deformations, which are typically non-linear. The actual stress state and history of soils also crucially govern their behavior. However, strains in the ground increase as stresses increase, and linear elastic theory has been proven sufficiently accurate for scientific and engineering purposes, provided that appropriate material parameters are employed50. In this context, the availability of a substantial amount of field and laboratory test results53,65,66,67,68,69,70,71 for the soil layers beneath the Loop provides confidence in the available material parameters, thus supporting the use of a linear thermo-elastic approach that has been proven capable of capturing thermally induced deformations of civil structures and infrastructures in other studies48. By definition, this modeling approach does not account for viscous (e.g., creep) effects, which are renowned to characterize soils and construction materials and involve time-dependent surges in deformations and displacements under constant applied loads. Meanwhile, this approach appears valuable because of two reasons. First, it provides ground deformations and displacements that implicitly account for the stiffening effect of foundations, which have been neglected in the simulation because of the large size of the studied problem. Second, it provides ground deformations and displacements that appear reliable in magnitude, without representing an unjustified source of concern. The detailed resolution of the considered problem, together with the complexity of the analyses performed, further justifies using a linear thermo-elastic approach, which would incorporate undue complexity otherwise.

The material parameters used in the simulations are summarized in Tables 1–3 with corresponding bibliographic sources. The initial and boundary conditions considered in the simulations are summarized in Fig. 5.

Table 1 Thermo-physical properties of the ground underneath the Chicago Loop district. Full size table

Table 2 Thermo-mechanical properties of the ground underneath the Chicago Loop district. Full size table

Table 3 Hydrogeological properties of the ground underneath the Chicago Loop district. Full size table

Thermal initial conditions consist of a uniform ground temperature of T 0,g = 11.2 °C as per the data gathered through the deployed sensing network22. Mechanical initial conditions consist of zero initial displacements or applied forces. Hydraulic initial conditions consist of a constant hydraulic head H = 0 m.

Thermal boundary conditions consist of the following: a time-varying temperature boundary condition imposed on the uppermost surface of the model for the streets and green spaces (following the model of Baggs59 and the surface air temperature data provided by the National Oceanic and Atmospheric Administration, NOAA, from 1951 to 205157—see Fig. 4a); a time-varying temperature boundary condition for the vertical surfaces of the model (following the Chicago River water data provided by NOAA from 1951 to 205157—see Fig. 4a); a fixed constant temperature for the bottom surface of the model T 0,g = 11.2 °C; and a time-varying temperature for the interfaces between the underground built environments and the ground (following the relationships between surface and subsurface air temperatures collected through the sensing network—see Fig. 4b). These fixed temperature boundary conditions (i.e., Dirichlet boundary conditions) involve a heat transfer into/from the enclosed material volume(s) according to the imposed temperature on the surface(s) of the volume(s) and the temperature of the volume(s). These boundary conditions do not consider (by definition) any convection or radiation effects, which may characterize some underground built environments (e.g., due to airflows caused by the movement of trains in tunnels) and the ground surface (e.g., due to solar radiation). Although potentially approximate in instances, this approach is motivated by the lack of data about these phenomena over the analyzed timeframe (from the 1950s till the 2050s). Nevertheless, this approach appears acceptable for the analysis of ground temperature anomalies in the considered urban area due to the close comparison between the modeled and measured temperature data, both at shallow and relatively deep locations (see “Methods, Numerical model validation”). At shallow depths, convection and radiation effects might be present but appear negligible compared to other aspects of the problem that have been considered in the simulations. At depth, convection and radiation effects arguably characterize a minimal proportion of the underground built environments in the Loop, which mostly consist of building basements (typically not affected by airflows or extreme heat sources) and only include two train tunnels (where airflows are present). Overall, these effects thus appear negligible for the subsurface of the Loop and insignificant at the monitored locations.

Mechanical boundary conditions consist of free displacements on the top surface of the model and any surface between underground built environments and the ground. In contrast, displacements on the external vertical and bottom surfaces of the model are fixed according to the roller and pinned conditions, respectively.

Hydraulic boundary conditions consist of an imposed hydraulic gradient of \(\Delta H=\) 2.5 m/km as per field explorations72. The considered hydraulic gradient is thus minimal. For the sake of general information, simulations performed without due account of such phenomenon have yielded markedly close results to those presented in this study.

Simulations are performed over a timeframe of t = 100 years. Data are saved every month during this timeframe. All values of compressive stresses, contractive strains, downward displacements, and injected thermal powers are considered positive in this paper.

Data analysis

Data are exported with COMSOL Multiphysics (v. 5.5) and analyzed with Microsoft Excel (v. 16.68). Data are plotted with Grapher (v. 2022).

Numerical model validation

Figure 6 summarizes the validation of the modeling approach used in this study by comparing representative experimental data obtained from the field with numerical results. Figure 6a compares ground temperature data obtained through the developed simulation for Grant Park in the Loop at depths z = 0.1, 0.2, and 4 m, with field data collected at shallow depths in St. Charles at depths z = 0.1 and 0.2 m and field data gathered through the sensing network in Grant Park at a depth z = 4 m. Figure 6b illustrates the temperature trend characterizing several locations in the heart of the Loop starting from 1951 till 2051 and compares them with temperature data gathered through the sensing network from 2020 till 2022 at corresponding locations.

Fig. 6: Validation of the numerical simulation results against experimental monitoring data. a Comparison between the ground temperatures T g provided by the model in Grant Park and recorded at corresponding locations in St. Charles58 and the same Park22 (in the box plot: the center line indicates the median; the box edges indicate a 95% confidence level; the whiskers indicate maximum/minimum); b comparison between the ground temperature trends over time t provided by the model in the heart of the Loop and the sensing network. The plan views illustrating the locations of the sensors have been created with baseline images provided by OpenStreetMap. Full size image

As can be remarked from Fig. 6a, the temperature data predicted numerically and monitored experimentally for Grant Park at a depth of z = 4 m match well. The numerical and experimental temperature data referring to depths of z = 0.1 and 0.2 m are also markedly close, even though two different locations (i.e., St. Charles and the Loop) are considered. Such a result indicates comparable thermo-physical properties for the ground at the considered locations, which may derive from the relatively uniform geology of Illinois because of the glacial formation of Michigan Lake.

As can be remarked from Fig. 6b, the temperature variations predicted numerically from 1951 to date for the different ground locations beneath the Loop at a depth of z = 12 m closely match the temperature data gathered in the field through the sensing network. Such a close comparison between the numerical and experimental data, similar to that reported in Fig. 6a, holds even when slightly different depths or different thermo-physical properties (by 50%) may be considered for the ground in the numerical model, supporting the robustness of the considered simulation and its input data (e.g., material properties and boundary conditions).

Based on a sound analysis of the results of this work, it appears inappropriate to deterministically and unequivocally link the temperature variations provided by the developed simulation with exact dates in the past, present, or future due to the complexity of the considered problem. Nonetheless, it appears appropriate to argue that the developed simulation provides results representative of reality (with an accuracy of a few years for any studied date). Therefore, not only the developed numerical simulation appears capable of retrieving the temperature variations and their impacts on the subsurface of the Loop from the 1950s to current times but also of predicting the likely influence of underground climate change in such a district over the next 30 years. This highly satisfactory result strongly corroborates the representativeness of the simulations performed in this study.