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Abstract
Most existing experiments on radiative cooling are conducted in dry climates for better performance. However, many important applications require cooling in hot and humid climates. Here we theoretically analyze the temperature reduction and cooling flux at nighttime with the ambient temperature (Tambient) ranging from 0-40 $^\circ{\textrm C}$ and the relative humidity (RH) from 0-100%. Our analysis reveals an interesting crossover: for lower (higher) RH, higher (lower) Tambient results in better cooling. Experimentally, we show that radiative cooling of 5 $^\circ{\textrm C}$ below ambient can be achieved even at Tambient = 29 $^\circ{\textrm C}$ with RH = 100%.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The radiative cooling technology, which utilizes the transparent nature of the atmosphere between the wavelength range of 8 to 13 microns to passively dump heat from the Earth into outer space, has been receiving renewed interest recently [1–9], as it addresses the important growing need for cooling and air-conditioning in an energy-efficient manner. Motivated by the initial theoretical discovery which points out that radiative cooling to sub-ambient temperatures can be achieved with a photonic structure even under direct sunlight [1], there have been a significant number of experimental demonstrations, most of which utilized the photonic design of selective emitters to simultaneously reflect the sunlight and emit through the atmospheric transparency window [2,4,7,10]. Most of the existing experiments were conducted under low humidity [2–4,8,11].
In many practical applications, however, achieving radiative cooling in hot and humid climates is of significant interest, in part because evaporative cooling, a prominent strategy for passive cooling, becomes less efficient in a humid environment. Moreover, in hot summer days, one would require more cooling in humid than dry environment, in order to reach the same comfortable level [12]. There are several theoretical and experimental works exploring the dependence of radiative cooling on humidity [9,13–16]. Qualitatively, these studies show that the more humid, the worse the radiative cooling, because water is highly absorptive [17,18], in particular in the atmospheric transparency window [13,15,19,20]. Quantitatively, however, these studies either lack experimental verifications [15], or rely on oversimplified atmospheric models [13]. Moreover, the humidity range in the experiments is rather limited [9,13,14,21–23].
Here, we theoretically investigate the cooling performance at nighttime with the relative humidity (RH) ranging from 0-100% and the ambient temperature (Tambient) from 0-40 $^\circ{\textrm C}$. This should serve as the upper bound for daytime radiative cooling under corresponding conditions. Our model reveals an interesting crossover: for lower RH, higher Tambient results in larger difference in temperatures between the cooler and the ambient; for higher RH, lower Tambient results in larger difference. Experimentally, we verify our model in Nanjing (China) with RH from 53-100% and Tambient from 27-32 $^\circ{\textrm C}$. We demonstrate that a cooling of 5 $^\circ{\textrm C}$ below ambient can be achieved even at Tambient = 29 $^\circ{\textrm C}$ with RH = 100%.
2. Theoretical analysis
Figure 1 shows the effect of RH, zenith angle (θ) and Tambient on the atmospheric transmittance tatm, calculated using ModTran [24]. Here we convert the parameter pair (Tambient, RH) to the precipitable water vapor (PWV), a more convenient input parameter to represent the humidity in ModTran [24,25] or ATran [26] (Appendix A). At a fixed Tambient, e. g. 30 $^\circ{\textrm C}$ in Fig. 1(a), tatm of the transparency window (8-13 µm) decreases as RH or θ increases. Likewise, at a fixed RH, e. g. 70% in Fig. 1(b), tatm decreases as Tambient increases. One interesting observation is that there is a second atmospheric transparency window between 16 to 25 µm [14], in which tatm decreases even more rapidly than that in the first window (8–13 µm), as RH or Tambient increases.
Fig. 1. Atmospheric transmittance, calculated using ModTran at different (a) RH and zenith angle (θ) or (b) ${T_{ambient}}$. Both the first window (8 - 13 µm) and the second window (16–25 µm) gradually close as RH, θ, or ${T_{ambient}}$ increases. Note that we use these spectral directional transmittance in our theoretical analysis.
With the atmospheric transmittance, we compute the steady-state temperature and the cooling flux of three emitters: a black emitter that emits 100% throughout the whole wavelength, a near-ideal emitter that emits 100% between 8-13 µm but 0% elsewhere [3] and a realistic emitter made of 3M Vikuiti Enhanced Specular Reflector (ESR) [27,28] whose emissivity spectrum will be shown in Fig. 4(b). We analyze the nighttime scenario that serves the upper bound of daytime cooling. The net flux of the emitter consists of three terms [3]: the emitted radiation from itself, the absorbed radiation from the atmosphere, and the parasitic heat exchange with its environment characterized by a parasitic heat transfer coefficient, h (Appendix C).
The steady-state temperature, $\; {T_{emitter}}$, is solved by setting the equation of the net flux be zero. Figure 2 shows the maximum temperature reduction, ${\Delta }T = {T_{ambient}} - {T_{emitter}}$, of the three emitters as a function of RH at ${T_{ambient}} = 0 \,^\circ{\textrm C}$ (solid lines) and $30 \,^\circ{\textrm C}$ (dashed lines), respectively, for an ideal scenario, $h = 0\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (upper row), and a practical rooftop scenario, $h = 8\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (lower row). Two general trends are worth noting. First, ${\Delta }T$ decreases as RH increase for all three emitters in both scenarios, as anticipated from Fig. 1(a). Second, the parasitic heat loss significantly reduces ${\Delta }T$ and blurs the distinction among different emitters, especially at higher RH. We emphasize an interesting crossover between the solid line (${T_{ambient}} = 0 \,^\circ{\textrm C}$) and the dashed line (${T_{ambient}} = 30 \,^\circ{\textrm C}$): for lower RH, ${T_{ambient}} = 30 \,^\circ{\textrm C}$ results in larger ${\Delta }T$; otherwise, ${T_{ambient}} = 0 \,^\circ{\textrm C}$ is better. Although more clear for the near-ideal emitter (left column), the crossover do exist for all scenarios, as shown in a zoom-in plot in Fig. 10 of Appendix D. This crossover emphasizes the two limits of ${\Delta }T = {T_{ambient}} - {T_{emitter}}$, in which Temitter decreases towards the temperature of outer space, Touter-sapce, as the precipitable water vapor (PWV) approaches 0, but increases towards Tambient as PWV approaches its maximum at which higher Tambient results in lower RH. One prominent feature is that the crossover displaces towards higher RH as h increases, because the effect of h is weakened at higher ${T_{ambient}}$, as explained in detail in Appendix D. Note that this crossover is fundamentally different from the crossover of the cooling flux between the selective and the black emitters [3,29,30].
Fig. 2. Maximum Temperature reduction, ${\Delta }T = {T_{ambient}} - {T_{emitter}}$, as a function of RH at two representative ${T_{ambient}}: 0 \,{^\circ{\textrm C}}$ (solid lines), and $30 \,^\circ{\textrm C}$ (dashed lines), for the three emitters (columns) under two scenarios, $h = 0\; \textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (upper low) and $8\; \textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (lower row). Crossovers between the solid and the dashed lines, more clear for the black emitter and ESR in a zoom-in plot in Fig. 10 of Appendix D, emphasize opposite trends: at lower (higher) RH, higher (lower) Tambient results in better cooling. These crossovers move towards higher RH as h increases.
Figure 3(a) shows the contour of the maximum temperature reduction (${\Delta }T$) of the three emitters as a function of Tambient (0 - 40 $^\circ{\textrm C}$) and RH (0 - 100%) for the two scenarios: $h = 0\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (first row) and $8\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (second row). For $h = 0\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$, the near-ideal emitter significantly surpasses the other two. For example, the ideal emitter reaches a ${\Delta }T$ of larger than 67$^\circ{\textrm C}$ at ${T_{ambient}} = 40^\circ{\textrm C}$ with RH = 5%, and a ${\Delta }T$ of larger than 4$^\circ{\textrm C}$ even at ${T_{ambient}} = 40^\circ{\textrm C}$ with RH = 90%. In contrast, the black emitter can only reach a ${\Delta }T$ of $26^\circ{\textrm C}$ and $2^\circ{\textrm C}$, at the corresponding condition, respectively. However, for $h = 8\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$, the advantage of the selective emitter disappears.
Fig. 3. Contour plots of (a) maximum temperature reduction (${\Delta }{ T} = {{ T}_{{{ambient}}}} - {{ T}_{{{emitter}}}}$), and (b) maximum cooling flux (Qcooling) as a function of RH (x-axis) and $ T_{ambient}$ (y-axis) for the three emitters (columns). The first and second rows assume ${ h} = 0\; {\ W}{{\ m}^{ - 2}}{{\ K}^{ - 1}}$ and $8\; {W}{{m}^{ - 2}}{{\ K}^{ - 1}}$, respectively. While the near-ideal emitter can achieve much higher ${\Delta }{ T}$, the black emitter has higher Qcooling.
Figure 3(b) shows the contour of the maximum cooling flux (Qcooling), which is obtained by assuming that the cooler is subject to a heating flux Qcooling in order to maintain ${T_{emitter}} = {T_{ambient}}$. All the three emitters can reach a Qcooling larger than $100\,{\textrm W}{\textrm{m}^{ - 2}}$ at high Tambient and low RH. The black emitter has a higher Qcooling than the other two, because in the infrared wavelengths the atmosphere is not exactly black outside the transparency window (8 - 13 µm). In particular, the maximum Qcooling of the black emitter surpasses $150\,{\textrm W}{\textrm{m}^{ - 2}}$at ${T_{ambient}} = 40 \,^\circ{\textrm C}$ with RH = 5%, in which the second transparency window (16 - 25 µm; see the first column of Fig. 1(a)) plays an important role. At high Tambient and high RH, however, Qcooling is significantly suppressed, regardless of the type of emitters. For example, Qcooling of all the three emitters is reduced to be less than $13\,{\textrm W}{\textrm{m}^{ - 2}}$ at ${T_{ambient}} = 40 \,^\circ{\textrm C}$ with RH = 90%.
3. Experiments
To suppress the thermal coupling between the emitter and the environment, we design an enclosure [2] whose bottom and side walls are made of polystyrene and covered with aluminized mylar (Fig. 4(a)). The enclosure is opened on top and covered with a layer of low-density polyethylene (LDPE) to ensure unhindered thermal coupling between the emitter and outer space [2]. This represents an easily-achievable thermal design, with a parasitic heat transfer coefficient, h, ranging from 1.5 to $2.4\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$, as estimated in Appendix C.
Fig. 4. Experimental demonstration. (a) Schematic and in-situ setup. Polyethylene (PE) is infrared transparent. (b) Emissivity of the ESR (blue) and the aluminized mylar (grey), as well as the transmittance of the PE film (yellow), all measured using FTIR. The atmospheric transmittance along the zero zenith angle (black), calculated using ModTran at ${T_{ambient}} = 30 \, ^\circ{\textrm C}$ with RH = 60 %, is for reference here. (c) A typical measurement under a clear night sky.
We choose the 3M VikuitiTM Enhanced Specular Reflector (ESR) film [27,28] as the emitter, which is a flexible thin film compatible for large-scale deployment. Its emissivity is measured using the Fourier Transform Infrared Spectroscopy (FTIR) in Fig. 4(b) (blue), with the mylar emissivity (grey), the atmospheric (black) and PE (yellow) transmittance as reference, all along the zero zenith angle for clarity.
Figure 4(c) shows a typical measurement under a clear night sky in Nanjing, a relatively humid area in China. The emitter is continuously cooled below the ambient by 9 $^\circ{\textrm C}$ from 6pm at night to 6am in the morning. Figure 5 summarizes the ${\Delta }T$ of our year-round measurements (points) with a wide range of RH (53% - 100%) at Tambient = 27, 29, 31 and 32 $^\circ{\textrm C}$, respectively. Note that RH is obtained from a weather station at Nanjing [31]. The x-axis error bar (${\pm} 2\,{\%}$) is estimated based on a standard humidiometer, and the y-axis error bar (${\pm} 1.6 \,^\circ{\textrm C}$) is from the datasheet of the K-type thermocouple, which is higher than the standard deviation of our repeated measurements at the same RH and ${T_{ambient}}$. These measurements are consistent in magnitude with our theoretical calculation (shaded area, with h ranging from 1.5 to $2.4\,{\textrm W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$, as estimated in Appendix C). However, the experimental results exhibit a relatively weaker RH dependence. Lacking further information, e.g. the possible formation of very thin layers of cloud even under a clear night sky according to the weather station, we cannot explain this discrepancy at this time. Most importantly, the measurements show that a radiative cooling of ${\Delta }T$ = $5.2 \,^\circ{\textrm C}$ can be achieved even at ${T_{ambient}} = 29 \,^\circ{\textrm C}$ with RH = 100% at a hot summer night.
Fig. 5. Comparison between experiments and model. Measured ΔT (points) as a function of RH at ${T_{ambient}} = 27, \,29, \,31 \,\textrm{and} \,32^\circ{\textrm C}$, respectively. The error bars are estimated based on the K-type thermocouple and a standard humidiometer. The grey shaded area represents the uncertainty of the model resulting from the uncertainty in estimating the parasitic heat transfer coefficient (for details, see Appendix C)
4. Conclusions
We have systematically calculated ${\Delta }T$ and Qcooling under a variety of ${T_{ambient}}$ (0–40 $^\circ{\textrm C}$) and RH (0–100%). We found an interesting crossover: higher ${T_{ambient}}$ results in larger ${\Delta }T$ at low RH, but smaller ${\Delta }T$ at high RH; while lower ${T_{ambient}}$ results in smaller ${\Delta }T$ at low RH, but larger ${\Delta }T$ at high RH. This finding could offer guidance of selecting better locations with more appropriate combinations of Tambient and RH to deploy cooling panels. We experimentally demonstrated nighttime radiative cooling in summer with RH from 53–100%. Even at a hot summer night at ${T_{ambient}} = 29 \,^\circ{\textrm C}$ with RH = 100%, we achieved radiative cooling of 5.2 $^\circ{\textrm C}$ below ambient. With a more sophisticated photonic design, a similar, if not better, cooling performance could be achieved in hot and humid climates at daytime.
Appendix A: From the ambient temperature (Tambient) and relative humidity (RH) to precipitable water vapor (PWV)
We use a standard commercial software, ModTran [24], to obtain the atmospheric transmittance. ModTran is that it uses PWV more conveniently, with unit of [$\textrm{gc}{\textrm{m}^{ - 2}}$], to represent the humidity of the atmosphere. Though several methods had been proposed to estimate PWV using either the dew point temperature or effective sky temperature [32,33], here we establish the mapping from the (RH, Tambient) pair to PWV.
First, we map the (RH, Tambient) pair to the absolute humidity (AH), with unit of [${10^{ - 3}}\textrm{gc}{\textrm{m}^{ - 3}}$]. Using Eqs. (20) and (22) of [34], we have
in which the saturation vapor pressure, es, with unit of [${10^{ - 3}}\textrm{bar}$], has an expression of ${e_s} = {T_{ambient}}^{{a_1}}{10^{{c_1} + {b_1}/{T_{ambient}}}}$, where the unit of Tambient is [K], and the parameters are: ${a_1} ={-} 4.9283$, ${b_1} ={-} 2937.4\textrm{K}$, ${c_1} = 23.5518$, and ${n_1} = 0.21668 \,\textrm{gKba}{\textrm{r}^{ - 1}}\textrm{c}{\textrm{m}^{ - 3}}$.Next, we establish the link between AH and PWV. ModTran divides the atmosphere along its thickness into different layers. Each layer is assigned a specific density of precipitable water vapor (DPWV), with unit of [$\textrm{gc}{\textrm{m}^{ - 2}}\textrm{k}{\textrm{m}^{ - 1}}$], according to the total PWV and a default distribution corresponding to a specific location (e.g. mid-latitude) and a specific season (e.g. summer). We can then obtain the total PWV from the first DPWV ($ = \textrm{AH} \times {10^5}$) and the default distribution for different layers.
Following the procedure above, we can finally map the parameter pair (RH, Tambient) first to AH, and then to PWV.
Using the relation among PWV, RH, and Tambient, Fig. 6 shows the relation between PWV and RH at several representative Tambient, and Fig. 7 reproduces Fig. 3(b) by replacing RH with PWV.
Fig. 6. Precipitable water vapor (PWV) as a function of relative humidity (RH) at three representative ambient temperatures: Tambient = 10 °C, 20 °C, and 40 °C, respectively.
Fig. 7. Reproduction of the contours of the maximum cooling flux in Fig. 3(b) by replacing RH with PWV. The shaded areas are inaccessible, because the corresponding RH exceeds 100% in these regimes.
Appendix B: Cooling flux as a function of the emitter temperature
In Fig. 3(b) of the main text, we report the maximum cooling flux by assuming there is no external cooling load attached to the emitter. To mimic the real application, here in Fig. 8 we plot the cooling flux as a function of the emitter temperature, Temitter, ranging from its steady temperature (intercept with the x-axis) to Tambient. Here we analyze the three emitters, the near-ideal, black, and the ESR, respectively, under two representative scenarios, ${ h} = 2\; { W}{{m}^{ - 2}}{{ K}^{ - 1}}$ for the thermal enclosure as shown in Fig. 4(a), and ${ h} = 8\; { W}{{m}^{ - 2}}{{ K}^{ - 1}}$ for rooftop setup without basic thermal design.
Fig. 8. Cooling flux (${Q_{cooling}}$) as a function of the emitter temperature ${T_{emitter}}$ for the three emitters (near-ideal, black and ESR) under two typical scenarios (h = 2 and 8 Wm-2K-1). Note that the calculation is based on a typical hot and humid climate at ${T_{ambient}} = 30 \,^\circ{C}$ with RH = 80%.
Appendix C: Estimate of the parasitic heat transfer coefficient
As shown in Fig. 9, the parasitic heat can access to the emitter through two parallel thermal paths: the upper path couples the emitter to the environment through convection and air conduction above and below the polyethylene cover; and the lower path through conduction of air and the base of the enclosure, respectively. Note here we neglect the conduction through the side walls of the enclosure because of its small cross section area and low thermal conductivity.
Fig. 9. Schematic of the enclosure used in our experiment, and the corresponding thermal circuit to analyze the parasitic heat loss.
The corresponding thermal resistors are as following:
in which R3 is modeled as the parallel resistance between the resistance of the air conduction, $\frac{{{L_{gap}}}}{k}$, and that of the radiation, ${R_{rad^{\prime}n}}$, between the back surface of the ESR and the top surface of the Al mylar. HereThe key here is to estimate the convection coefficient. We examine two limits: natural convection and forced convection with maximum wind velocity corresponding to our measurements.
In one limit, natural convection, we use Eq. (9. 32) of [35],
where $R{a_{{L_c}}} \equiv \frac{{gL_c^3}}{{\nu \alpha }}\frac{{{T_{ambient}} - {T_{PE}}}}{{{T_{ambient}}}}$ is the Rayleigh number, in which g is the gravitational constant. The modified characteristic length is ${L_c} \equiv A/P$, where A and P are the area and perimeter of the emitter, respectively.In the other limit, forced convection, we use Eq. (7. 25) of [35],
where $R{e_L} \equiv {u_{wind}}L/\nu $ is the Reynolds number of air flowing across the surface of a flat plate with characteristic length L, $Pr \equiv \nu /\alpha $ is the Prandtl number, and ${u_{wind}}$, k, $\nu $ and $\alpha $ are the wind speed, thermal conductivity, kinematic viscosity and thermal diffusivity of the surrounding air, respectively.Using Eqs. (2)–(8) we estimate the upper and lower bounds of the total parasitic thermal resistor to be ${R_{max}} = 0.67 \,{\textrm{m}^2}\textrm{K}{\textrm{W}^{ - 1}}$ and ${R_{min}} = 0.42 \,{\textrm{m}^2}\textrm{K}{\textrm{W}^{ - 1}}$, respectively. Correspondingly, the lower and upper bounds of the parasitic heat transfer coefficient are ${h_{max}} = 2.4\textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ and ${h_{min}} = 1.5\textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$, which corresponds to the lower and upper bounds of the shaded area in Fig. 5. We note that this estimate on h is different from that used in [2], because its value varies with some characteristic scales, e.g. Lgap in Fig. 9.
Note we use the following parameters: the maximum wind speed, ${u_{wind}} = 9.4\; \textrm{m}{\textrm{s}^{ - 1}}$, during the experimental period; the physical properties of air (300K): $\alpha = 2.21 \times {10^{ - 5}}\; {\textrm{m}^2}{\textrm{s}^{ - 1}}$, $\nu = 1.58 \times {10^{ - 5}} \,{\textrm{m}^2}{\textrm{s}^{ - 1}}$, $k = 2.26 \times {10^{ - 2}}\textrm{W}{\textrm{m}^{ - 1}}{\textrm{K}^{ - 1}}$. Other parameters include $g = 9.8\; \textrm{m}{\textrm{s}^{ - 2}}$, $L = 0.175\; \textrm{m},\; \; {L_c} = 0.051\textrm{m},\; \; {L_{gap}} = 0.015\textrm{m}$, ${\delta _{PS}} = 0.05\; \textrm{m}$, ${k_{PS}} = 3.5 \times {10^{ - 2}}\textrm{W}{\textrm{m}^{ - 1}}{\textrm{K}^{ - 1}}$, ${\varepsilon _{ESR}} = $ 0.67 and ${\varepsilon _{mylar}}$=0.53. In addition, according to experimental measurements, we use $\frac{{{T_{ambient}} - {T_{PE}}}}{{{T_{ambient}}}} = 0.42{\%}$ to estimate the Rayleigh number.
Appendix D: A phenomenological model to interpret the right-shift of the crossover as h increases
We explain why the crossover moves towards higher RH as h increases, which is more clear in a zoom-in plot in Fig. 10. For simplicity, we consider a black emitter, and assume an effective atmospheric emissivity ɛatm. The Energy balance on the emitter leads to
Fig. 10. Zoom-in plots of Fig. 2 of the main text to clearly show the crossovers for black emitter (left column) and ESR (right column) under two scenarios, $h = 0\; \textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (upper low) and $8\; \textrm{W}{\textrm{m}^{ - 2}}{\textrm{K}^{ - 1}}$ (lower row). The crossover moves towards higher RH as h increases. Note that the x-axis in the upper row is from 0% - 1%.
From Eq. (9), the derivative of Temitter with respect to h is obtained
in which ${\Delta }T = {T_{ambient}} - {T_{emitter}}$, and ${h_{rad^{\prime}n}}$=$4\sigma T_{emitter}^3$ is the linearized radiative heat transfer coefficient of the black emitter [36]. Re-arranging Eq. (10), we obtain the temperature reduction rateAt the crossover in Fig. 2 or Fig. 10, ${\Delta }T$ is the same for the two Tambient (solid vs. dashed lines). Thus, higher Tambient results in higher Temitter, and smaller $\left|{\frac{{d{\Delta }T}}{{dh}}} \right|$ from Eq. (11). As depicted in Fig. 11, this leads to the right-shift of the crossover as h increases. Note here we anchor the x-axis intercept of both the solid and dashed lines, because h has less effect on ${\Delta }T$ in high RH regime than in low RH regime, as evident from Fig. 2 of the main text.
Fig. 11. Graphical interpretation of the right-shift of the crossover. At the crossover in Fig. 2 or Fig. 10, ${\Delta }T$ is the same for the two Tambient (solid vs. dashed lines). Thus, higher Tambient results in higher Temitter, and smaller $\left|{\frac{{d{\Delta }T}}{{dh}}} \right|$ from Eq. (11). This leads to the right-shift of the crossover as h increases. Here we anchor the x-axis intercept of both the solid and dashed lines, because h has less effect on ${\Delta }T$ in high RH regime than in low RH regime, as evident from Fig. 2 of the main text.
Funding
National Natural Science Foundation of China (51776038); National Key R&D Program of China (2017YFB0406000); Basic Energy Sciences (DE-FG02-07ER46426).
Acknowledgements
We acknowledge Dr. Linxiao Zhu for fruitful discussions.
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