Unexpected Warming From Land Radiative Management

Abstract

“Land radiative management” (LRM)—deliberately increasing surface albedo to decrease temperatures—has been proposed as a form of geoengineering to mitigate the effects of regional warming. Here, we show that, contrary to expectations, LRM causes temperatures to increase in surrounding regions. The basic reason for the increase is unintended impacts on precipitation. Precipitation is suppressed over the LRM region, but this effect also extends to nearby areas unprotected by LRM. The reduction in precipitation and soil moisture in these regions leads to higher temperatures than would be expected in the absence of LRM. The resulting warming outside the LRM region is comparable to the cooling achieved inside it. This implies that, if wealthy regions unilaterally adopt LRM to cool, their neighbors may experience warming, worsening heat inequality.

Key Points

• Land radiative management (LRM) causes temperatures to unexpectedly increase in surrounding regions

• LRM decreases precipitation over its immediate surroundings, which dries the land surface and increases temperatures

• The unilateral adoption of LRM by affluent regions will exacerbate heat inequality between wealthy and poor neighborhoods

Plain Language Summary

Land radiative management (LRM), which involves artificially increasing Earth's surface albedo to mitigate regional warming, has been recognized by the Intergovernmental Panel on Climate Change as a potential solution to combat the adverse effects of climate change. Examples of LRM approaches include the adoption of white roofs and pavements. Our study challenges conventional wisdom by demonstrating that LRM can actually cause temperatures to increase, rather than decrease as intended, due to its unintended impacts on rainfall. LRM suppresses rainfall in surrounding regions, causing them to experience higher temperatures than they would in the absence of LRM. The implications of our findings are significant, as the unilateral adoption of LRM by affluent regions will exacerbate heat inequality between wealthy and poor neighborhoods.

1 Introduction

Land radiative management (LRM) aims to reduce temperatures at local and regional scales by artificially increasing surface albedo, resulting in less shortwave radiation absorption at the land surface (Seneviratne et al., 2018). Approaches to LRM include white roofs (Li et al., 2014; Mackey et al., 2012; Sharma et al., 2016; Vahmani et al., 2016) and pavements (Erell et al., 2014; Taleghani et al., 2016), no-till farming (Davin et al., 2014; Hirsch et al., 2017; Seneviratne et al., 2018; Wilhelm et al., 2015), and desert albedo enhancement (Irvine et al., 2011). While LRM is currently limited to small scales, it is conceivable that LRM will approach mesoscales $$(O(10\,\mathrm{km}))$$ in future, and has attracted growing interest (Jia et al., 2019; Seneviratne et al., 2018).

Previous modeling studies have found that LRM causes reductions in both mean (Irvine et al., 2011; Seneviratne et al., 2018) and extreme temperatures (Hirsch et al., 2017; Wilhelm et al., 2015). Those studies used general circulation models (GCMs), which neglect important storm formation mechanisms that can be significant at the smaller scales most relevant to LRM. While some regional climate model simulations have been performed at sufficiently fine resolutions to resolve mesoscale circulations (Fallmann et al., 2013; Li et al., 2014; Lynn et al., 2009; Synnefa et al., 2008), the computational expense has precluded the analysis of long simulations necessary to distinguish rainfall signal from noise. Other studies simulate the temperature and precipitation response to changes in albedo due, for example, to deforestation (Taylor et al., 2022; Wang et al., 2000). However, deforestation is, at best, an imperfect analog for LRM, since it modifies not just surface albedo, but also roughness and other factors that generate their own confounding impacts on temperature and precipitation (Cheng & McColl, 2023).

Here, we use mesoscale convection-permitting simulations and a simple theory to show that LRM causes temperatures to unexpectedly increase in surrounding regions. The fundamental reason for this surprising result is mesoscale storm formation mechanisms (Baidya Roy & Avissar, 2002; Cheng et al., 2023; Wang et al., 2000) that have been neglected in previous LRM studies.

2 LRM Causes Warming in Mesoscale Simulations

We perform idealized simulations of an LRM region using mesoscale convection-permitting models (Khairoutdinov & Randall, 2003). Rather than using a complex urban canopy model, or focusing on one specific location, we prescribe a high surface albedo anomaly in an otherwise homogeneous environment. The idealized nature of these simulations permits a clearer diagnosis of relevant mechanisms, and thus makes our findings more generalizable. A high surface albedo anomaly (21 km $${\times} $$ 50 km in horizontal $$x$$ and $$y$$ directions, respectively) is prescribed in the middle of an otherwise uniform domain (400 km $${\times} $$ 50 km in $$x$$ and $$y$$ directions, respectively) as shown in Figure 1a. The prescribed visible albedo of the land surface in the LRM region and the surrounding background region are 0.1425 and 0.0356, respectively, comparable to the albedo change caused by cropland management in Davin et al. (2014). Simulations are conducted over a wide range of conditions, with domain-averaged near-surface air temperatures varying between 11 $${}^{\circ}$$C and 41 $${}^{\circ}$$C during the day (as detailed in Tables S1 and S2, and Figure S2 in Supporting Information S1). For simulations presented in Figures 1 and 2, only the latitude of the domain center and thus top-of-atmosphere solar radiation is varied (Table S2 in Supporting Information S1). Because our simulations are of idealized land regions, the resulting climates span a much wider range than the corresponding climates of Earth at these latitudes. Further details on the numerical simulations are provided in Supporting Information S1 (Cheng et al., 2021; Cioni & Hohenegger, 2017; ECMWF, 2016; Khairoutdinov & Randall, 2003; Kiehl et al., 1998; Lee & Khairoutdinov, 2015; Monin & Obukhov, 1954). We examine the responses of both surface $$\left({T}_{s}\right)$$ and near-surface air temperatures $$\left({T}_{a}\right)$$, but focus on near-surface air temperatures since they are most directly relevant to human health (Chakraborty et al., 2022).

Figure 1

LRM causes warming in mesoscale simulations. (a) Schematic of the simulated domain. The size of the domain is 400 km $${\times} $$ 50 km, and the width of the high-albedo rectangle denoting the LRM region at the center of the domain is 21 km. The schematic is not to scale. (b) Near-surface air temperature anomaly $$\langle {T}_{a}\rangle -{T}_{{a}_{0}}$$, where $${T}_{a}$$ is near-surface air temperature (2 m above the surface) averaged between 6 a.m. and 6 p.m. from the experiment A_RCE (Table S1 in Supporting Information S1), $${T}_{{a}_{0}}$$ refers to average near-surface air temperature far from the LRM region, $$\langle \rangle $$ denotes long-term temporal averaging, and ‾ denotes spatial averaging. Each simulation is denoted by its mean daytime temperature in the legend. The thick black lines denote the mean values across simulations. See “Mesoscale convection permitting simulations” in Supporting Information S1 for further details.

Figure 2

Simulated changes in net radiation, precipitation and soil moisture associated with LRM warming. (a) LRM reduces net radiation $$\left({R}_{n}\right)$$. (b) LRM reduces precipitation $$(P)$$. $${\rho }_{w}$$ is the density of water, and $$\lambda $$ is the latent heat of vapourization. (c) LRM reduces soil moisture, and causes a discontinuity to arise at the boundary of the LRM region. The normalized change in soil saturation $$\frac{\langle s\rangle -{s}_{0}}{{s}_{0}-{s}_{H}}$$ is shown. (d) LRM changes temperature, causing it to cool inside the LRM region, and rise immediately outside it. The terms with an “$$H$$” subscript correspond to values in the LRM region, and terms with a “0” subscript correspond to values far from the LRM region. The thick black lines denote the mean values across simulations. All quantities are averaged between 6 a.m. and 6 p.m.

Inside the LRM region, the near-surface air temperature is generally lower than that over the surrounding region (Figure 1b). However, unexpected warming occurs in the immediate surroundings of the LRM region (Figure 1b). The warming is comparable to (and, typically, greater than) the cooling achieved inside the LRM region: for the experiments shown in Figure 1b, the warming is between 110% and 400% of the maximum cooling achieved inside the LRM region. A qualitatively similar response is observed in land surface temperatures (Figure S3 in Supporting Information S1).

The observed warming outside the LRM region is robust to varying different aspects of the simulations. The warming persists in additional simulations in which a mean wind was imposed parallel to the land surface (Figure S4 in Supporting Information S1, experiment A_RCE_wind), although the warming location shifts downwind. The warming is also not especially sensitive to imposed atmospheric dynamics. Rather than imposing radiative-convective equilibrium (RCE, as discussed in previous studies (Held et al., 1993; Manabe & Strickler, 1964; Miyawaki et al., 2022)), we also ran simulations that invoke the weak temperature gradient (WTG, Figure S5 in Supporting Information S1, experiment A_WTG) approximation (Sobel et al., 2001), which permits domain-averaged atmospheric subsidence or uplift and has been applied extensively over a limited domain to model the interaction between convection and large-scale forcing over a tropical land surface (Abbott & Cronin, 2021, 2023; Cheng & McColl, 2023; Raymond & Zeng, 2005). In addition, the warming remains in simulations in which the LRM region is much smaller (Figure S6 in Supporting Information S1, experiment B_WTG). Finally, we performed control simulations (A_RCE_ctl) with spatially uniform surface albedo identical to the domain-averaged surface albedo in the experiment A_RCE, and used mean temperatures from these simulations $$\left(\overline{\langle {T}_{a,\text{ctl}}\rangle }\right)$$ as references in estimating temperature anomalies, rather than the mean temperature far from the LRM region in the original simulations $$\left({T}_{{a}_{0}}\right)$$. The warming persists in these simulations, too (Figures S7 and S8 in Supporting Information S1).

3 Changes in Rainfall Cause LRM Warming

The observed warming outside the LRM region is surprising, given the goal of LRM is to reduce temperatures. To our knowledge, warming from LRM has not been previously reported. Why does LRM cause warming in surrounding regions?

Increasing surface albedo has two impacts on a region. First, it reduces surface temperatures by reflecting a greater fraction of solar radiation, as intended. Figure 2a shows surface net radiation $$\left({R}_{n}\right)$$ is substantially reduced in the LRM region in our simulations, relative to surface net radiation in surrounding regions $$\left({R}_{{n}_{0}}\right)$$. Surface net radiation is highest just outside the LRM region, but the difference with surrounding regions is ultimately small. This peak in net radiation is caused by changes in cloud cover, discussed in the next paragraph. As we will see, it is not the main cause of warming outside the LRM region.

Second, it causes mesoscale circulations to form at the boundaries of the LRM region, which suppress precipitation inside the LRM region. Figure 2b shows that precipitation $$(P)$$ is substantially reduced in the simulated LRM region, relative to precipitation in surrounding regions $$\left({P}_{0}\right)$$. The heating differential between the LRM region and its surroundings causes a thermally direct mesoscale circulation to form (Cheng et al., 2023; Physick & Tapper, 1990), analogous to a land-sea breeze (where the LRM region is the “sea” in this analogy). The mesoscale circulation causes subsidence in the LRM region, which suppresses precipitation and cloud cover. It also causes air to rise outside the LRM region, which enhances precipitation and cloud cover. The extra precipitation generated outside the LRM region is spread thinly over a larger region, and is not obviously distinguishable from internal variability in our simulations.

Reductions in precipitation dry soils in the LRM region, whereas reductions in net radiation moisten it by reducing evaporative demand. On balance, soils dry in response to LRM in our simulations (Figure 2c). In addition, a discontinuity in the soil moisture profile arises at the boundaries of the LRM region. This robust feature is observed across a wide range of simulations.

We use a parsimonious conceptual model to explain these results. The conceptual model takes profiles of net radiation (Figure 3a) and precipitation (Figure 3b) as inputs. Based on observed profiles, we use an expression based on a logistic function to represent these profiles. The profiles smoothly connect the relatively lower values of surface net radiation and precipitation in the LRM region with corresponding higher values in the surrounding environment (Equations S1 and S2 in Supporting Information S1). These profiles are used to estimate a profile of soil saturation (Figure 3c) using a recent theory (Stahl & McColl, 2022), which is then used to predict a temperature profile (Figure 3d) using a simplified model of the atmospheric boundary layer (Garratt, 1992; Porporato, 2009; Tennekes, 1973). Full details of the conceptual model are provided in Supporting Information S1 (Brutsaert & Sugita, 1992; Driedonks, 1982; Gentine et al., 2007; Koster & Mahanama, 2012; Koster et al., 2009; Seneviratne et al., 2010; Stahl & McColl, 2022).

Figure 3

A conceptual model explains the observed warming outside the LRM region. Full details of the conceptual model are provided in Supporting Information S1. Here, the conceptual model is applied to the simulation A_RCE, $$\overline{\langle {T}_{a}\rangle }=14\ {}^{\circ}$$C. (a) Prescribed net radiation anomaly profile (Equation S2 in Supporting Information S1, $${L}_{{R}_{n}}=0$$ km). (b) Prescribed precipitation anomaly profile (Equation S1 in Supporting Information S1) with atmospheric mixing and advection included (red line, $${L}_{P}=1$$ km) and excluded (black line, $${L}_{P}=0$$ km). (c) Predicted soil moisture anomaly (Equation S4 in Supporting Information S1) using prescribed profiles of net radiation in (a) and precipitation in (b). (d) Predicted near-surface air temperature anomaly using Equation S16 in Supporting Information S1 (with parameters $${\gamma }_{\theta }=8\times 1{0}^{-3}$$ K $${\mathrm{m}}^{-1}$$, $$\beta =0.2$$; other parameters obtained by fitting to the simulation A_RCE, $$\overline{\langle {T}_{a}\rangle }=14\ {}^{\circ}$$C). Note that the y-axis limits in (d) differ from those in Figure 2d.

We first use the conceptual model to consider a naive example, in which there is no unexpected warming outside the LRM region. In this example, it is assumed that turbulent mixing and advection in the atmosphere are negligible. Reductions in surface net radiation and precipitation are confined to the LRM region itself (Figures 3a and 3b, black lines). The net effect is a reduction in soil moisture inside the LRM region (Figure 3c, black line), which reduces evaporative cooling and increases temperatures, all else being equal. This conceptual model predicts that the net effect of decreases in surface net radiation and in evaporative cooling is a reduction in surface temperatures (Figure 3d, black line), with no anomalous warming outside the LRM region. Since our simulations show anomalous warming outside the LRM region, something is missing from this explanation.

The key missing mechanism is turbulent mixing and advection in the atmosphere. Unlike the land surface, the atmosphere is a turbulent, well-mixed fluid. This means that, at the boundary of the LRM region, the precipitation anomaly caused by LRM varies smoothly over some non-zero length scale $${L}_{P}$$ (Figure 3b, red line), where $${L}_{P}$$ is the length scale over which precipitation $$P$$ transitions from lower values in the LRM region to higher values outside the LRM region. In contrast, surface net radiation is largely determined by land surface properties and, thus, is discontinuous at the LRM boundary, implying $${L}_{{R}_{n}}\approx 0$$ (Figure 3a). This spreads anomalously lower soil moisture outside the LRM region (Figure 3b, red solid line), creating a region that experiences the downsides of LRM (reduced evaporative cooling) without its benefits (reduced absorption of radiation). This is the ultimate cause of the anomalous warming outside the LRM region in our simulations (Figure 3d, red solid line). The same mechanism also creates a region just inside the LRM boundary that experiences both increased evaporative cooling and reduced absorption of radiation, explaining why the greatest cooling from LRM occurs near its boundaries. Finally, including turbulent mixing and advection in the conceptual model is sufficient to reproduce the discontinuity in the soil moisture profile at the LRM boundary observed in simulations (Figure 3c).

To further test this explanation, we conducted an additional simulation in which soil moisture is fixed to be spatially uniform at its domain-averaged value (A_RCE_fixsoil, Table S1 in Supporting Information S1). In this simulation, the proposed mechanism is switched off. Some warming still occurs outside the LRM boundary in this simulation due to changes in cloud cover caused by mesoscale circulations. However, its magnitude is relatively small: less than 24$$\%$$ of the maximum cooling achieved within the LRM region (Figure S9 in Supporting Information S1), compared with 110$$\%$$ in the corresponding simulation with interactive soil moisture (Figure 2d). Thus, our explanation in terms of soil moisture appears to be the dominant reason for the anomalous warming. The conceptual model is sufficient to qualitatively reproduce the observed warming profile, but somewhat underestimates the absolute temperature values. It also does not explain why peak warming outside the LRM region typically exceeds peak cooling inside it. This is likely due, in part, to its neglect of cloud effects. While this could be addressed by adding further complexity to the conceptual model, it does not seem essential in qualitatively explaining why the unexpected warming arises.

In summary, rainfall is suppressed over both the LRM region and its immediate surroundings, drying the land surface and increasing temperatures. While the LRM region benefits from reflective cooling that more than offsets this warming, the surrounding regions do not. The net effect is warming outside the LRM region.

4 Discussion

4.1 Relation to Previous Studies

There is a vast prior literature on surface albedo impacts on temperature and rainfall (Charney et al., 1977; Physick & Tapper, 1990; Taylor et al., 2022; Wang et al., 2000). Yet, as reviewed in Cheng et al. (2023), much of that is not directly relevant to LRM, for several reasons. First, LRM would be implemented at mesoscales ($$O$$(1–10 km)), which are too small to be resolved in many prior studies based on GCMs (Charney et al., 1977). Second, while some prior studies simulate mesoscale albedo modification, they do not consider changes in albedo independently of other changes. For example, studies of deforestation impacts on temperature and precipitation modify not only surface albedo, but also roughness and other factors that are not directly relevant to LRM (Taylor et al., 2022; Wang et al., 2000), and which also cause changes in temperature and precipitation (Cheng & McColl, 2023). Third, some studies simulate the transient temperature and precipitation response, but not the long-term equilibrium response (Physick & Tapper, 1990; Wang et al., 2000). This response is most relevant to LRM, which involves a permanent modification to the landscape.

Other studies have focused specifically on LRM (Davin et al., 2014; Irvine et al., 2011; Wilhelm et al., 2015). To identify the warming mechanism, there are three basic requirements for any simulation: (a) sufficiently high spatial resolution; (b) sufficiently large domain size; and (c) sufficiently long temporal coverage. No prior study satisfies all three of these requirements. First, many previous simulations (Davin et al., 2014; Hirsch et al., 2017; Irvine et al., 2011; Wilhelm et al., 2015) are not conducted at a sufficiently fine spatial resolution to resolve the region experiencing higher temperatures around the LRM region. For example, the horizontal resolution in regional climate models (Davin et al., 2014) and GCMs (Irvine et al., 2011; Wilhelm et al., 2015) are $$O(10\,\text{km})$$ and $$O(100\,\text{km})$$, respectively. In our simulations, the region experiencing warming is $$O$$(1 km) in size. This problem is particularly acute for GCMs, which are run at such coarse resolutions that they typically do not even resolve the mesoscale circulations that are essential to the mechanism identified here.

Second, the size of the simulated domain in some prior studies is too small. Mesoscale circulations arise over land surface heterogeneities on scales of $$O$$(1–10 km) (Baidya Roy et al., 2003; Patton et al., 2005; Sakaguchi et al., 2022; Tian et al., 2022). While some prior simulations have been conducted at sufficiently high spatial resolution, the size of the simulated domain is too small to produce mesoscale circulations (Alchapar et al., 2017; Middel et al., 2015; Taleghani et al., 2016).

Third, the simulations in some prior studies do not span a sufficiently long time period. Since precipitation exhibits significant internal variability (Lehner & Deser, 2023), considerable temporal averaging is required to identify a statistically meaningful signal. Our simulations were typically run for 1,000 days to address this issue. In contrast, relevant prior simulations often only span a single day, and never more than a few months (Fallmann et al., 2013; Gilabert et al., 2021; Jacobs et al., 2018; Li et al., 2014; Lynn et al., 2009; Sharma et al., 2016; Synnefa et al., 2008; Vahmani et al., 2016).

Cheng et al. (2023) speculated that mesoscale circulations caused by LRM could cool surrounding regions, which might appear to contradict this study's main finding. However, there is no contradiction. This study focuses on a small but significant region just outside the LRM region, in which precipitation and soil moisture are reduced with respect to surrounding regions, which ultimately causes warming in that region. In contrast, Cheng et al. (2023) focused on the average response over a much larger region. While precipitation and soil moisture decrease just outside the LRM region, that does not preclude them from increasing when averaged over the larger surrounding region. Since the changes in precipitation, soil moisture and temperature averaged over this larger area are smaller than those near the LRM boundary, they are not distinguishable from internal variability in our simulations.

4.2 Limitations

Other aspects of urban environments can cause mesoscale circulations to form, which could, in principle, counteract the mechanism proposed here. For example, Cheng and McColl (2023) found that rough surfaces, such as cities, can generate mesoscale circulations and attract rainfall. If the LRM region was systematically rougher than its surroundings—for example, if an entire city was subjected to LRM, and surrounded by farmland—this may counteract the reduction in precipitation found here, and potentially eliminate temperature increases outside the LRM region. However, if the LRM region is just one neighborhood in a larger city, this mechanism is unlikely to be significant, since the difference in roughness between urban neighborhoods is much smaller than that between urban and rural landscapes.

Our proposed mechanism will only hold in regions where evaporation is sufficiently sensitive to soil moisture. Its effects may be less pronounced in especially cold or wet regions where sensitivity is low. However, the mechanism is clearly evident in our simulations, which span a wide range of climates. Similarly, our proposed mechanism requires that soil moisture is sensitive to precipitation. This sensitivity may be somewhat lower in urban areas, where some fraction of accumulated precipitation flows over paved surfaces into drainage systems rather than soil reservoirs. Future studies should investigate the magnitude of these impacts.

We cannot currently test this mechanism using observations because LRM does not yet exist at mesoscales. Natural experiments are also not available. While it might appear, for example, that the gradient between a forest and grassland, or between a city and farmland, provides a natural albedo gradient, both cases are confounded by other differences (in roughness and vegetation) that strongly impact the heating differential between the two regions (Cheng & McColl, 2023). Nevertheless, the mechanism identified here is understandable in terms of basic physical arguments, and is robust to substantial variations in the details of the simulation.

4.3 Implications

Both high-resolution simulations and simple theory show that LRM will cause temperatures to unexpectedly increase in surrounding regions. The region affected is small ($$O$$(1 km)) but significant, with potential to impact many thousands of people in urban areas. For example, if LRM is applied to a 10 km $${\times} $$ 10 km region, and warming occurs in a 1 km wide region just outside the LRM boundaries, the resulting region experiencing warming will be 44 $${\mathrm{k}\mathrm{m}}^{2}$$. For a population density equivalent to San Francisco's, this would imply roughly 300,000 people would be subject to warming caused by LRM.

How does the size of the LRM-protected region impact the results? There must be some minimum size at which LRM will not impact rainfall, resulting in no warming of surrounding regions. We speculate that this size corresponds to the size for which mesoscale circulations start to form around a land surface anomaly ($$O$$(1–10 km)) (Baidya Roy et al., 2003; Patton et al., 2005). Future studies should further investigate this. On the other hand, the unintended warming occurs in a thin band around the sides of the LRM-protected region with a width that scales with $${L}_{P}$$. If we speculate that $${L}_{P}$$ does not change much as the LRM-protected region grows larger, then the size of the impacted region will be mainly a function of the length of the boundary of the LRM-protected region. Since the surface-to-volume ratio is larger for smaller volumes, we speculate that the relative benefit of LRM schemes will be lower for smaller schemes, since relatively larger areas will be exposed to higher temperatures. A back-of-the-envelope calculation illustrates this point. Consider a square LRM domain with side lengths $${\Lambda }$$, which cools the area inside its boundaries $$\left({{\Lambda }}^{2}\right)$$ and warms the region just outside its boundaries with area $$4{L}_{P}\left({\Lambda }+{L}_{P}\right)$$. Assuming the same population density inside and outside the LRM region, more people experience cooling than warming when $${{\Lambda }}^{2} > 4{L}_{P}\left({\Lambda }+{L}_{P}\right)$$. Using the quadratic formula, this requirement simplifies to $${\Lambda } > 2(1+\sqrt{2}){L}_{P}\approx 5{L}_{P}$$. Thus, for $${L}_{P}\approx 1$$ km, as in our simulations, this implies that an LRM region should be at least 5 km $${\times} $$ 5 km in size simply to ensure that more people experience cooling than warming. In summary, these arguments suggest the ratio of population warmed to population cooled is lowest for very small schemes ($$\ll 1$$ km, for which LRM does not impact rainfall) and very large schemes ($$\gg 10$$ km). This implies that progressive construction of LRM regions from smaller to larger scales may result in extended periods in which more people suffer from higher temperatures than benefit from cooler temperatures.

If the cost of LRM results in it primarily being implemented in wealthier neighborhoods, the mechanism we identify here would not only worsen heat inequality (Chakraborty et al., 2023; Hsu et al., 2021), but worsen conditions for poorer neighbors in absolute terms. It is theoretically possible that heat inequality could increase even though heat stress declines everywhere in absolute terms (e.g., if heat stress declined to a greater extent in wealthier regions than in poorer regions). Here, however, LRM leads to higher temperatures in neighborhoods bordering the LRM region; not just in relative terms, but in absolute terms.

This study has focused on diagnosing and understanding the problem of unexpected warming caused by LRM. While possible solutions to this problem are deferred to future studies, we briefly speculate on one possible option. Our theory suggests that designing the LRM scheme in such a way that $${L}_{{R}_{n}}\approx {L}_{P}$$ would effectively mitigate the warming. This would require introducing a smaller gradient in albedo around the boundary of the LRM scheme. There are at least three challenges to doing this. First, designing and maintaining such a gradient is more logistically difficult. Second, the length scale $${L}_{P}$$ for a given LRM geometry and location is unknown a priori. Third, the presence of a mean wind will shift the region experiencing warming, and the location of the region will vary with the direction of the wind, whereas any engineered gradient would be static. All of these challenges require further study.

Acknowledgments

K.A.M. acknowledges funding from NSF Grant AGS-2129576 and a Sloan Research Fellowship. We thank Marat Khairoutdinov for providing SAM and the land model SLM. The computations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Open Research

Data Availability Statement

The data set used for this study is available for public access at the Harvard Dataverse via Cheng and McColl (2024).