## Introduction

With the global proportion of people living in cities expected to exceed two-thirds by 2050,1 the urban climate affects many aspects of human life, including energy demand, health and the economy. Therefore, urban climate projections that include extreme weather events, such as heat waves from climate change, are of interest, given the potentially wide range of social and scientific impacts on human activities. These projections are also important when producing strategies to mitigate urban heat and for adapting to urban climate change. For example, given that US urban temperatures are predicted to increase by 1–2 °C due to climate change, energy demand is predicted to increase by 5–25%. Therefore, effective adaptation strategies that include measures to cool the urban climate and built environment that do not result in further emissions of heat or greenhouse gases (GHGs) will need to be produced and assessed.2

Of the two main methods to obtain fine horizontal resolution projections of climate, the dynamical (rather than statistical) downscaling is used here. Several previous dynamical downscaling studies of future urban climate have used regional climate models (RCMs) with a coupled urban canopy model (UCM) (hereafter RCM/UCM). For example, Kusaka et al.3 predicted the 2070s summertime climate for three Japanese megacities using the Weather Research and Forecasting (WRF) model4 with the single-layer UCM,5,6 assuming pseudo-global warming (PGW),7,8 at a 3-km resolution. This future climate projection (dynamical downscaling) method uses reanalysis data with the climatic change component from global climate models (GCMs; see ‘Methods’ section). Similar methods have been used for cities in Asia,9,10,11 Europe,12,13 North America14,15 and Oceania.16 In these RCM/UCM studies, anthropogenic heat (QF) is an important term in the urban surface heat balance but is assumed to have a constant diurnal pattern (e.g. Fig. 3 of Kusaka et al.17). Thus QF impact on future urban temperatures is kept the same as current climate if all other factors (e.g. urban structure and human activities) do not change. This assumption may be reasonable in cities with little air-conditioning (AC) use (e.g. northern European cities); however, where AC use is already common (e.g. Asian cities), it may not.

If cities experience positive feedback from interactions between urban warming and AC use,18,19,20,21 this assumption would not hold. When air temperatures increase, energy consumption associated with AC use surges (Fig. 1a, Path 1) (i.e. increase in QF from AC use (QF, AC)). In turn, the energy released outdoors will enhance urban warming (Fig. 1a, Path 2).22 Using a simple one-dimensional mixing-layer model, Ohashi et al.23 estimated the increase in summertime air temperature from AC waste heat in Osaka City to be +0.36 to +0.72 °C. Previous studies focus on only one side of this process. Most consider impacts of urban warming on energy consumption (Fig. 1a, Path 1).24,25,26,27 Effects of QF on urban temperature (Fig. 1a, Path 2) have been studied with limited-area models.28,29,30,31,32,33 However, the amount of ‘additional warming’ from urban warming–AC feedback has yet to be assessed. Hence, the impact of this feedback process on future urban climate remains unknown.

In this study, we define the temperature difference caused by AC use as δTAC (Fig. 1b, orange):

$$\delta T_{{\mathrm{AC}}} = \delta T_{{\mathrm{AC}} \ne {\mathrm{FB}}} + \delta T_{{\mathrm{AC}} \to {\mathrm{FB}}}$$
(1)

where δTAC ≠ FB is the temperature difference caused by AC use but without AC feedback (Fig. 1b purple, without Path 2 Fig. 1a [no-QF,AC simulation], see ‘Methods’ [Model settings]). The ‘additional temperature difference’ caused by the feedback process is δTAC → FB (Fig. 1b, green, with Path 2 Fig. 1a). In this study, we use model simulations to determine the different components (Fig. 1b and ‘Methods’ provide more details).

The Salamanca et al.’s22 WRF/BEP+BEM (building effect parameterisation and building energy model)34,35,36 simulations, with and without QF,AC release, allows δTAC to be estimated (Fig. 1b, reference (R) Salamanca et al.,22 RS14). The 10-day Phoenix heat wave study obtained an extreme δTAC of 1.0 °C at night. However, as they did not separate δTAC, δTAC → FB remains unknown. Given that δTAC → FB may enhance electricity consumption (hereafter δECAC → FB), we do not have a basis for understanding these changes with climate change (Fig. 1b, red).

With increases in both global temperatures37 and AC demand,38 it is important to explore this positive feedback phenomenon and evaluate its impact on the urban climate. Projected increases in AC demand and urban expansion may increase the feedback effect enhancing future projections uncertainties, whereas improved AC performance may offset demand from a warmer ambient environment. These could be as important as other uncertainties, such as the selection of emission scenarios, RCMs, urban planning scenarios and so on. Thus the feedback process consequently affects the impact assessment results and policy decisions associated with the Paris Agreement.39

Direct feedbacks can be calculated from climate projections for cities with AC usage when the RCM/UCM is coupled to a BEM. Electricity demand and summer thermal comfort projections for Nagoya in the 2070s40 used WRF with coupled multi-layer UCM (CM)41 and BEM19 (WRF/CM+BEM42) (Fig. 1b, RT15). Impacts of urban expansion and global warming on future urban temperatures and cooling demand for the Phoenix and Tucson metropolitan areas43 explored with WRF/BEP+BEM (Fig. 1b, RT17) did not assess the ‘additional warming’ from positive feedbacks (δTAC → FB) (Fig. 1b, green) but did determine the amount of urban warming from current and future climate (ΔT) and the future electricity demand. This study addresses:

1. (1)

What is the magnitude of the impact (and associated uncertainty) associated with such a feedback (δTAC → FB and δECAC → FB) on future urban climate (Fig. 1b, green)?

2. (2)

How is δTAC → FB and δECAC → FB changed by climate change (i.e. increase/decrease, linear/nonlinear) (Fig. 1b, red)?

To address these, objectives WRF/BEP+BEM is used (‘Methods’). From the results, we propose a simple parameterisation to account for δTAC → FB and δECAC → FB in urban climate studies. We focus on Japan’s second-largest megacity, Osaka (Fig. 2, Supplementary Fig. 2), as it experiences the warmest summertime mean temperatures in Japan.44 Osaka’s humid climate (normal annual precipitation (1981–2010) is 1279 mm) results in a more significant daytime urban heat island intensity than other dry climate cities.45

## Results

### Changes in QF,AC and urban air temperature (ΔT)

The numerical model (see ‘Methods’) is verified (see Supplementary Note) for wooden detached dwellings, fireproof apartments and commercial and office buildings (hereafter simply office). Given the similarity of the results between the two dwelling types, only the fireproof apartments (hereafter simply residential) results are presented.

The mean QF,AC at 14:00 local time (LT) (i.e. close to a daily maximum of air temperature) in August is larger for office than residential areas for all seven control simulations (hereafter AC → FB) (Fig. 2a–g and ‘Methods’). QF,AC increases from current to future climates (ΔQF,AC) as ΔTGW increases, which is associated with additional AC use (Fig. 2a–g) causing a close to linear increase in both the office (ΔQF,ACTGW = 1.76 W m−2 °C−1) and residential areas (3.32 W m–2 °C–1). When ΔTGW is +3.0 °C, ΔQF,AC is 1.37 (office) to 1.81 (residential) times larger than for current climate conditions (Supplementary Table 1).

The mean August 2 m air temperature (24 h, 11 years) in Osaka is warmer than the surrounding areas in both current and future climates (Fig. 2h–n). The temperature difference between the AC → FB and the no-QF, AC case (AC ≠ FB) simulations increases along with ΔTGW (Fig. 3), indicating that urban heat will increase over time. This is caused by ΔQF,AC with larger differences in the residential than in the office areas.

The differences between simulations with (ΔTAC → FB) and without (ΔTAC ≠ FB) anthropogenic heat fluxes allows the δTAC → FB to be determined (Figs. 1a 2o–t and 3). The δTAC → FB (05:00, 11 August months) and ΔTGW increase and the δTAC → FB in Osaka’s surrounding areas are higher than those of the centre of Osaka in both current and future climates (Fig. 2o–t). The diurnal variation of the δTAC → FB in residential areas (Fig. 3b) has two main features:

1. (1)

δTAC → FB for current and future climates are relatively small during daytime (notably 09:00–18:00) but larger at night (notably 18:00–06:00), with a peak around 05:00; and

2. (2)

δTAC → FB increases gradually as ΔTGW increases (+0.5 °C to +3.0 °C) during the night, indicating that urban warmth will increase overnight.

The relatively small daytime δTAC → FB, despite the relatively large daytime QF,AC, is because of the relatively high daytime mixed layer. As QF,AC is mixed in a large volume, the impact of QF,AC on surface air temperature is reduced. At night, QF,AC is smaller, but the mixed layer height is lower. Similar results in previous work31 support this proposed mechanism.

The relation between ΔTGW and downscaled urban warming (ΔTAC → FB and ΔTAC ≠ FB) has two main features for office areas (Fig. 3d):

1. (1)

δTAC → FB tends to increase linearly with ΔTGW. This increase is from a feedback: ΔTGW modifies ΔQF,AC, contributing to additional urban warming (Fig. 1a, Path 1 → Path 2)

$$\Delta T_{GW} \to \Delta Q_{F,AC} \to {\mathrm{\delta }}T_{AC \to FB}$$
2. (2)

ΔTAC → FB has a linear trend, as does ΔTAC ≠ FB.

This is the first study to estimate the ‘additional’ positive feedback impact on future climate associated with AC. We conclude that ΔTAC → FB has an approximately linear trend (Fig. 3c–f, red). The resulting AC → FB case slope (ΔTAC → FBTGW) is 1.18 °C °C–1 for the office areas. This is larger than for the AC ≠ FB case (1.13 °C °C–1). These results suggest that it is relatively easy to estimate (parameterise) the impact of the feedback.

The two features in the monthly mean (Fig. 3d) are more evident at 05:00 (Fig. 3c) with ΔTAC → FBTGW = 1.29 °C °C–1, which is larger than for case AC ≠ FB (1.17 °C °C–1). At 14:00 feature (1), ΔTAC → FB and ΔTAC ≠ FB are essentially the same, and δTAC → FB does not increase with ΔTGW.

The daily average of normalised δTAC → FB (see ‘Methods’) is roughly constant (3–5%) and not dependent on ΔTGW for the office area (Supplementary Fig. 1a). The average of normalised δTAC → FB at 05:00 increases from 3% (+0.5 °C) to 10% (+3.0 °C) as ΔTGW increases (Supplementary Fig. 1a, Supplementary Table 1).

Results for the residential area are similar to the office area, but feature (1) is more evident, especially at 05:00 (Fig. 3e, f). The ΔTAC → FBTGW (1.38 °C °C–1) is larger than the AC ≠ FB case (1.16 °C °C–1). As AC is used 24 h per day in residential areas, this cumulatively contributes more to warming than in office areas. The daily average of normalised δTAC → FB increases slightly from +0.5 to +3.0 °C, reaching 8% (at +3.0 °C). Thus about 0.25 °C additional urban warming is caused by the feedback when ΔTGW is +3.0 °C in the residential area. The normalised δTAC → FB at 05:00 increases from 8% (at +0.5 °C) to 20% (at +3.0 °C). This means that about 0.6 °C additional urban warming is caused by the feedback when ΔTGW is +3.0 °C (Fig. 3e).

## Discussion

### Importance of the feedback in adapting to future urban climate change

The choice of emission scenario causes uncertainty in projections. For example, the 2070s August mean urban temperatures in Osaka in the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios with the A2 scenario projected 0.3 °C higher than A1b.46 Doan and Kusaka’s11 urban warming projections (current to 2050s) for greater Ho Chi Minh City based on IPCC representative concentration pathway 4.5 (RCP4.5) and RCP8.5 scenarios found different scenarios to cause urban warming differences of 0.5 °C. The feedback uncertainty (~0.25 °C for residential areas when ΔTGW = + 3.0 °C) is comparable to these emission scenario differences of 0.3 and 0.5 °C, respectively (Table 1a). Further uncertainty arises from the RCM choice. Kusaka et al.’s10 August 2050s urban temperature projections in central Tokyo, using WRF and NHRCM (non-hydrostatic model of the Japan Meteorological Agency47), had a 10-year mean temperature increase uncertainty between RCMs of ~0.2 °C (i.e. like the feedback reported here, see Table 1a).

Our work shows δTAC → FB could reach 0.25 °C in residential areas. This is comparable to the 0.3–0.5 °C century−1 estimated global warming in Japan.48 This feedback impact of 0.25 °C in residential areas is comparable to urban planning scenarios (Adachi et al.,49 Kusaka et al.10) for ‘dispersed’ (~0.34 and 0.1 °C, respectively) and ‘compact’ (~0.1 and 0.4 °C, respectively) cities and future urbanisation on temperature of 0.5 °C11 (Table 1a).

The feedback impact is small in the daytime but large nocturnally, increasing with ΔTGW (Fig. 3). The normalised δTAC → FB at 05:00 increases with ΔTGW: 10% in the office areas and 20% in the residential areas, when ΔTGW is +3.0 °C (Supplementary Fig. 1). These results suggest that mitigating the feedback process before the impact becomes large may be an effective strategy to adapt to climate change in cities as the feedback effect could be comparable to those of past global warming, affecting urban planning scenarios. For example (Supplementary Discussion), the feedback uncertainty for a ΔTGW of +2.0 °C is ~10 years (Fig. 4b, Table 1b), if we can stop the feedback technologically (e.g. improved coefficient of performance (COP), geothermal energy use) we could postpone a +2.0 °C world by about 10 years.

### Application: δTAC → FB and δECAC → FB estimates for the recent heat waves in Japan

As shown (‘Results’), ΔTAC → FB and δTAC → FB have near linear trends with ΔTGW. Also δTAC → FB and δECAC → FB are close to linear with ΔTAC → FB. This suggests that to estimate (parameterise) δTAC → FB and δECAC → FB for other future urban climates or for specific events (e.g. heat waves) is straightforward. Table 2 shows gradients (a) of linear regression (y = ax) between ΔTAC → FB (x) and δTAC → FBECAC → FB) (y). Here we estimate the δTAC → FB and δECAC → FB for the recent heat waves of July 2018 and August 2013 in Japan using our proposed linear relations to illustrate an application.

The 2013 summer was the warmest on record for Japan (statistics since 194650), with 41.0 °C recorded in western Japan (Shimanto City). In Osaka City, the August monthly mean (30.0 °C) was 0.99 °C higher than the 11-year mean (2000–2010). July 2018 was one of the hottest Julys in Japan since 1946, with Osaka’s monthly mean temperature (29.5 °C) 1.63 °C higher than the 11-year mean (2000–2010). Therefore, August 2013 and July 2018 roughly correspond to situations when ΔTAC → FB = +1.0 °C and +1.5 °C, respectively. Figure 3a, b shows a diurnal variation of the δTAC → FB for the two heat waves estimated by linear relations (Table 2a). The δTAC → FB for the two heat waves during the night to morning are higher than that for the daytime, especially in the residential areas. The 24-h mean δTAC → FB for July 2018 is 0.11 °C in the residential areas, which is higher than the 0.07 °C of August 2013. Similarly, the 24-h mean δECAC → FB for July 2018 is 0.05 W floor-m−2, which is higher than 0.03 W floor-m−2 of August 2013. Estimates of δTAC → FB and δECAC → FB could be easily assessed for other heat waves and/or future urban climates in hot cities where significant AC use is common.

### Summary

Here a positive feedback from the interaction between urban warming and AC use is identified and quantified. Analysis of simulations for current and six future climate scenarios (global warming: ΔTGW) is undertaken. For the latter, CMIP5 GCMs simulations with the highest IPCC GHG emissions scenario (RCP8.5) were used. The megacity of Osaka is analysed for August when AC use is at its greatest. From this, it is concluded that:

1. (i)

Anthropogenic heat emissions from AC use (QF,AC) are predicted to increase linearly with ΔTGW from current to future climates. Monthly total QF,AC in commercial & office and residential areas are projected to be 1.37 and 1.81 times larger than current climate conditions when ΔTGW is +3.0 °C, respectively;

2. (ii)

This represents a feedback process from current to future climate:

ΔTGW → ΔQF,AC (QF,AC increase) → δTAC → FB (‘additional’ temperature increase from the feedback)

Urban warming calculated when anthropogenic heat fluxes are permitted [case AC → FB (ΔTAC → FB)] is greater than when they are not included [case AC ≠ FB (ΔTAC ≠ FB)]. The difference between these two [ΔTAC → FB − ΔTAC ≠ FB] provides δTAC → FB. This increases almost linearly with ΔTGW suggesting urban temperatures will increase faster than global warming due to the increase of the anthropogenic heating (assuming all other characteristics of the city remain constant) in future climates. The normalised δTAC → FB at 05:00 (LT) has the larger increase with ΔTGW. This reaches 10% of ΔTGW in office areas and 20% in residential area. Thus about 0.3 °C (office) and 0.6 °C (residential) additional urban warming is caused by the feedback when ΔTGW is +3.0 °C. The δTAC → FB is expected to increase EC through a feedback process:

ΔTGW → ΔQF, AC → δTAC → FB → δECAC → FB (‘additional’ EC increase from the feedback).

The EC increase calculated by case AC → FB (ΔECAC → FB) is greater than that calculated by case AC ≠ FB (ΔECAC ≠ FB). The difference between these (ΔECAC → FB − ΔECAC ≠ FB): δECAC → FB increased linearly with ΔTGW;

3. (iii)

Uncertainty introduced by the feedback (δTAC → FB) is comparable to that introduced from selection of emission scenario, RCM and/or urban planning scenario. Thus this feedback should not be neglected in future urban climate projection, especially in hot cities where significant AC use is common; and

4. (iv)

Using linear relations proposed in this study (between ΔTAC → FB and δTAC → FB), the δTAC → FB during recent Japanese heat waves (July 2018 and August 2013) are estimated to be 0.11 and 0.07 °C, respectively. Such an approach can be used to estimate δTAC → FB for other heat waves and/or future urban climates in hot cities where significant AC use is common.

## Methods

To distinguish the difference between current and future climate Δ (e.g. ΔT) is used, and between cases with the same ∆TGW, δ is used (e.g. δT is a temperature difference between AC → FB and AC ≠ FB (explained later) at current climate or a future climate).

First, the impacts of the feedback (δTAC → FB) on future urban climate from global temperature scenarios (hereafter ΔTGW) are evaluated. Second, we explore how δTAC → FB changes in relation to ΔTGW. The urban air temperature and EC calculated by WRF/BEP+BEM were verified using detailed observational data for a year.51

### Description of the numerical model

Previously, WRF/BEP+BEM simulated urban air temperature and EC for April 2013 to March 2014 in Osaka were verified.51 The modified model reproduced current diurnal and horizontal variations of 2 m urban air temperature and EC at a 1-h temporal resolution for 12 electric power substations within Osaka City (about 1 km2 area).

At each time step, QF,AC is calculated for each grid as:19,51

$$Q_{{\mathrm{F},\mathrm{AC}}} = \left( {H_{{\mathrm{out}}} + E_{{\mathrm{out}}}} \right) + {EC} = \frac{{{\mathrm{COP}} + 1}}{{{\mathrm{COP}}}}\left( {H_{{\mathrm{out}}} + E_{{\mathrm{out}}}} \right)$$
(2)

where Hout and Eout are the sensible and latent heat supplied from the AC system for cooling (see section 2.5 of Salamanca et al.35), respectively, and COP is the coefficient of performance. The Hout and Eout are calculated from the total sensible, Hin, and latent, Ein, heat loads per floor.35 The Hin considers four physical processes: (1) solar radiation through the window and the heat exchange between the windows and the indoor air, (2) heat conduction through the walls and heat exchange between the wall, ceiling and pavement and the indoor air, (3) sensible heat exchange through ventilation, and (4) the internal sensible heat generation from equipment and occupants (Fig. 1a). Outdoor weather directly affects the Hin through processes (1–3), and the affected Hin contributes to an increase in QF,AC and EC through the Hout (Fig. 1a Path 1). Here QF,AC is split into sensible heat QF,AC,S and latent heat, QF,AC,L, as commercial and office building areas are considered52

$$Q_{{\mathrm{F},\mathrm{AC},\mathrm{S}}} = 0.722Q_{{\mathrm{F},\mathrm{AC}}}$$
(3)
$$Q_{{\mathrm{F},\mathrm{AC},\mathrm{L}}} = 0.278Q_{{\mathrm{F},\mathrm{AC}}}$$
(4)

The WRF/BEP+ BEM model system assumptions include:51 (1) individual AC units exist (using a simple parameterisation); (2) a constant COP (implications discussed in Supplemental information) occurs; (3) no QF from traffic occurs; and (4) only typical weekdays occur. Therefore, the results of this study are for these conditions (i.e. weekdays).

Although QF from traffic (QF,traffic) is important53,54 in some cities, in Osaka42,52 QF,AC is at least two times larger. As traffic is already common in Asian megacities, while AC demand is dramatically increasing38 (e.g. in Vietnam penetration rates of AC, motorcar and motorbike are 10.8%, 77.4%, and 81.8%, respectively55), QF,AC has the potential to be a big problem in the future (cf. QF,traffic) but will benefit from COP increases. Future studies will consider QF,AC and QF,traffic using models such as WRF/CM+BEM.42 However, the conclusions of this report are not impacted by QF,traffic as it is assumed to be constant and uses the single-layer UCM (SLUCM) with a static QF5,6 profile (traffic and AC) giving parallel results to urban warming without QF emissions (see next section ‘Model settings’).

### Model settings

Here the Advanced Research WRF model (ver. 3.5.1)4 was used with the same model parameters (Supplementary Table 3) and physics as previously described.51 The specific schemes used are: updated Rapid Radiation Transfer Model (RRTMG) short- and long-wave radiation schemes,56 WRF single-moment three-class (WSM3) cloud microphysics scheme,57,58 Mellor–Yamada–Janjic atmospheric boundary-layer scheme,59,60,61 Noah land surface model,62 and BEP+BEM model.34,35,36 As previously indicated, these models can accurately reproduce the diurnal variation and horizontal distribution of summertime surface air temperature and EC due to AC use.51

The model domain (Supplementary Fig. 2a) covers western Japan with 126 x and y grids in both d01 and d02 domains (horizontal resolution 5 and 1 km, respectively, and two-way nesting). As the reanalysis captures the summer synoptic-scale features (high-pressure system) around Japan,63 a larger coarse grid is not needed. The model top is 50 hPa, with 35 vertical sigma levels. The vertical resolution close to the ground (WRF atmospheric first layer height) is nearly 50 m. Therefore, 10 building layers below 50 m (5 m resolution) in BEP/BEM is used, as in previous studies,42,51 due to high model reproducibility for 2 m air temperature and EC in Osaka with the first layer at 50 m. With a mean building height of about 25 m in the office area, 50 m corresponds to the constant flux layer. The innermost domain urban grid classifications are based on the dominant building type, using land use and land cover and topographic data sets from the Geospatial Information Authority of Japan data and Osaka City GIS polygon (building footprint) data, with building use (type), building height and total floor area for each building (Supplementary Fig. 2c, d) grouped into: (i) commercial and business grids (i.e. mainly commercial and office buildings; hereafter C), (ii) residential grids with predominantly fireproof apartments (Rr), and (iii) residential grids with predominately wooden detached dwellings (Rw). The outer and inner domain urban grids outside Osaka City are classified as Rw.

For current climate simulation, initial and boundary conditions are derived from the National Center for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data64 and merged satellite and in situ global daily sea surface temperature (MGDSST) data.65 For future climate simulations, we also use a modified the NCEP–NCAR and MGDSST as initial and boundary conditions (see details in the next subsection). As previously,3 time integration is conducted from 00:00 UTC July 27 to September 1 (i.e. August with 5 days spin-up) for 11 years 2000–2010 to allow climatological discussion of the simulation results. Other studies integrate for only 1 month, several weeks or days (current and future climate), which is insufficient for climatological discussion in general. In Osaka, August is the hottest month, with more clear skies (cf. June, July and September, rainy season) and the highest EC recorded. These model settings are termed the control simulation (case AC → FB) (Fig. 1b, red arrow) for all climates, including current and six future climates (see next subsection).

The no-QF, AC simulation (case AC ≠ FB) differs from case AC → FB as QF, AC = 0 W m−2 (Fig. 1b, blue arrow); i.e. the [AC ≠ FB] − [AC → FB] difference is caused by QF, AC and it causes the feedback (δTAC → FB). Current climate conditions (August 2000–2010) and six future climates are simulated. Here δTAC → FB is estimated by ΔTAC → FB − ΔTAC ≠ FB (Fig. 1b). In the current climate case, δTAC → FB is 0 °C as we assume there is no long-term climate change (decades) (i.e. no increase in forcing temperature and ΔTAC → FB and ΔTAC ≠ FB are 0 °C). Of course, δTAC → FB may not be 0 °C in the real current climate, but it is difficult to estimate δTAC → FB from current climate only, and our objectives are to clarify δTAC → FB in relation to future urban climate and how δTAC → FB is changed by climate change (see ‘Introduction’). Therefore, here ‘δTAC → FB driven by decades of climate change’ is the focus and is estimated by a time slice experiment, including current climate simulation and six future projections. In a similar way, δECAC → FB is estimated by ΔECAC → FB − ΔECAC ≠ FB. To determine δTAC → FB and δECAC → FB, it is assumed all conditions (e.g. urban structures, human activities and AC system technology) remain constant, except for background climate change. Although AC technology will improve, it is important to know the maximum (potential) impact of the feedback driven by climate change on future urban air temperature. A constant COP scenario is used as the RCP8.5, and Shared Socioeconomic Pathway 3 scenario assumes slow technological change in the energy sector.66,67

We assume that δTAC ≠ FB is constant with ΔTGW; i.e. black dashed arrow (ΔTconst.QF) parallel to the blue arrow (ΔTAC ≠ FB) in Fig. 1b. To confirm this, the impact of QF on surface air temperature (i.e. like δTAC ≠ FB), on future climate, was conducted with simulations using SLUCM, which has a static QF5,6 (includes traffic and AC). Urban warming, when QF in the future was the same as for the current climate (ΔTconst.QF: Fig. 1b, black dashed arrow), paralleled urban warming with a no-QF emitted case, like ΔTAC ≠ FB, although different urban parameterisation was used. A reason why we used SLUCM (not BEP/BEM) to confirm black dashed arrow (ΔTconst.QF)’s gradient (ΔTconst.QFTGW) (and then compared with that of blue arrow (ΔTAC ≠ FB) by BEP/BEM) is that it is quite difficult to calculate the black dashed arrow by the BEP/BEM, because QF, AC at every time step (6 s) in future climates has to be completely same as that of current climate. To confirm the black arrow’s gradient by SLUCM is technically much easier and essentially same as that by the BEP/BEM.

### Climate projections

Six future climates, with background temperature increases (global warming: ΔTGW: +0.5, +1.0, +1.5, +2.0, +2.5, and +3.0 °C) relative to the current climate, are simulated. These are based on the ensemble mean results from four GCMs used in the Climate Model Intercomparison Project (CMIP5)68: CCSM4,69 CESM1 (CAM5),70 GFDL-CM371, and INM-CM4.72 However, the ensemble mean of only three GCMs (CCSM4, CESM1 and GFDL-CM3) is used when ΔTGW > +3.0 °C, as INM-CM4 does not reach +3.0 °C at 2100. The simulations considered the highest IPCC GHG emissions scenario (RCP8.5) (Fig. 4). CESM1 (CAM5) and CCSM4 have good model climate performance index scores73 and summertime synoptic pressure patterns around Japan perform better than other GCMs. GFDL-CM3 and INM-CM4 are selected to cover minimum to maximum uncertainties in GCM projections. By using several GCMs, the uncertainties in the GCM projections (horizontal colour bars, Fig. 4) are incorporated in the RCM. A similar GCMs selection method for future urban climate projection was used by Adachi et al.9

For future projection experiments, climate difference components between current and future are estimated by the four individual GCMs. For example, for ΔTGW = +0.5 °C, it was identified that the August mean surface air temperature difference, averaged spatially around Japan, became nearly +0.5 °C for each GCM. The other climate variables (e.g. geopotential height, horizontal wind and sea surface temperature) are extracted for each GCM for the identified years, and an ensemble mean is calculated for all variables. For ΔTGW = +0.5 °C, the ensemble mean surface air temperature difference component is +0.4725 °C (Supplementary Fig. 3) (i.e. nearly +0.5 °C). The actual ensemble mean surface air temperature differences for ΔTGW = +0.5, +1.0, +1.5, +2.0, +2.5 and +3.0 °C are +0.4725, +0.9550, +1.4750, +1.9650, +2.4450 and +2.8825 °C, respectively (Supplementary Fig. 3). For the six ΔTGW cases, the climate difference for each variable (i.e. wind components, geopotential height and temperature) are added to the NCEP–NCAR and MGDSST data (Supplementary Fig. 3), therefore changing the atmospheric variables such as long-wave radiation. Note, future climate relative humidity is assumed to be the same as the current climate.74,75,76,77,78

The PGW method7,8 was used to create regional climate projections3,10,11,21,79,80,81 and has been previously verified.80,82,83 For example, Kawase et al.82 projected East Asia’s 1960s climate by the PGW method using 1990s reanalysis data and PGW increment, calculated by the climate difference between the 1990s and 1960s. They compared the 1960s projection results with a hindcast simulation for the same period using reanalysis data. They showed that the 1960s projection could reproduce some decadal changes in the rainfall shown within the hindcast simulation, thus indicating that the PGW method could reproduce actual energy balance change using reanalysis, as precipitation is calculated in response to the atmospheric energy balance.

Yoshikane et al.83 compared PGW and direct downscaling from GCM for East Asian future climate projections and found no significant differences in temperature and precipitation (i.e. atmospheric energy balances were similar). Snowfall79,81,84 research, a process strongly influenced by atmospheric energy balance near the surface, and torrential rain85 studies, caused by atmospheric buoyancy near the surface, have also successfully used PGW methods. Therefore, the PGW method is reasonable for use in future projection research. An advantage of using the PGW method is a reduction in GCM climate bias as the method uses modified objective analysis/re-analysis data rather than GCM output.10 A disadvantage is that perturbations in meteorological variables are not considered.86 As Adachi et al.87 show, the perturbation component is equally important as the climatology component for summer precipitation, hence the PGW method is inappropriate for this. However, the perturbations do not affect near-surface air temperatures change (current to future climates) in western Japan, including Osaka during summer.87 Thus the difference in climatology projected by a GCM has a larger influence than the difference in perturbation on the downscaled temperature change and its variability in the climate projections.87 Hence, as the main contributor to the temperatures change was climate change (PGW) component, their results indicate that PGW method is appropriate for our purpose. As we focus on August, a dry period in Japan, surface air temperature is little impacted by precipitation. The PGW method is used as it enabled the study to focus on internal physical (feedback) processes in the RCM and to remove bias from individual GCMs. It also allows for direct comparison with previous PGW studies that report projected urban temperature uncertainties with selections of RCM, GHG emission scenarios and urban planning scenarios (see Table 1 and main text).

### Normalised feedback impact

Three urban land uses are selected for analysis (Supplementary Fig. 2d): commercial and office buildings, fireproof apartments, and wooden detached dwellings. These types of areas were evaluated for surface air temperature and EC model performance.48

To address the question (1), a normalised δTAC → FB (feedback impact) per future climate is determined:

$${\mathrm{Normalised}}\,\delta T_{{\mathrm{AC}} \to {\mathrm{FB}}} = \frac{{\left( {\Delta T_{{\mathrm{AC}} \to {\mathrm{FB}}} - \Delta T_{{\mathrm{AC}} \ne {\mathrm{FB}}}} \right)}}{{\Delta T_{{\mathrm{GW}}}}}$$
(5)

where ΔTAC → FB and ΔTAC ≠ FB are urban warming calculated by the AC → FB and AC ≠ FB, respectively, as explained in Fig. 1.

All times referred to are LT. Japan does not use summertime.