1

Passive sub-ambient cooling:

radiative sky cooling vs. evaporative cooling

Ablimit Ailia, Xiaobo Yina,b, Ronggui Yangc,d,*

a Department of Mechanical Engineering, University of Colorado, Boulder, CO

80309, United States b Materials Science and Engineering Program, University of Colorado, Boulder, CO

80309, United States

cSchool of Energy and Power Engineering, Huazhong University of Science and

Technology, Wuhan, Hubei 430074, China

dState Key Laboratory of Coal Combustion, Huazhong University of Science and

Technology, Wuhan 430074, China

* Corresponding authors: ronggui@hust.edu.cn

Abstract

Day-and-night radiative sky cooling has emerged as a potential alternative to

conventional cooling technologies such as refrigeration-based air conditioning and

evaporative wet cooling. Both radiative sky cooling and evaporative cooling can

passively achieve sub-ambient cooling. Although both cooling methods are subject to

impacts from various weather conditions, the extents of impacts under the same

conditions are not well understood. In this work, we both experimentally and

theoretically explore how a passive radiative cooler and a passive evaporative cooler

perform when exposed to a clear night sky. We show that evaporative cooling is better

suited for high-temperature and low-humidity weather conditions, with the

measured sub-ambient temperatures of the radiative and evaporative coolers being

−13.5℃ vs. −15.0℃ at a low relative humidity of 13% and a high ambient

temperature of 26℃. On the other hand, radiative cooling is relatively more resilient

than evaporative cooling under high-humidity and/or low-temperature weather

conditions, with the measured sub-ambient temperatures of the coolers being −11.5℃

vs. −10.5℃ at a slightly higher relative humidity of 32% and a slightly lower ambient

temperature of 17℃. Depending on water availability and weather conditions, both

evaporative cooling and radiative cooler can be adopted as mutually supplemental

cooling technologies.

Keywords: passive cooling, radiative sky cooling, evaporative cooling, sub-ambient

cooling

2

1. Introduction

Developing environment-friendly, energy-efficient, and affordable sub-ambient

cooling technologies has become an increasingly important research endeavor as part

of the efforts to meet the ever-increasing energy demand,1 reduce greenhouse gas

emissions,2 combat climate change, tackle water scarcity,3 reduce thermal pollution,4

and address energy poverty.5 Conventional cooling technologies contribute to the

above-listed challenges in so many ways, directly or indirectly. For instance,

refrigeration-based air conditioning systems may directly leak hydrocarbons that are

considered harmful greenhouse gasses or ozone-depleting substances, although

refrigerants with reduced environmental damage are being developed.6 Another

drawback of current air conditioning systems is high power consumption and the

associated energy bill, which discourages households to turn on air conditioners, even

in developed countries.5 In many developing countries, a substantial number of

households have yet to install air conditioning systems because of their installation

and energy costs.7 Much more severe yet indirect impacts of air conditioning systems

come from the fact that fossil-fuel-burning thermal power plants account for most of

the electricity generation worldwide.8,9 Thermal power plants have at least three

major impacts on the environment. One is the release of greenhouse gases, mainly

CO2 into the atmosphere.10 Another impact is large water withdrawals and the

release of low-quality waste heat into water reservoirs, causing thermal pollution.4,11

Traditional one-through wet-cooled thermal power plants are often associated with

water reservoirs’ thermal pollutions.11 The third major impact is evaporative water

losses by cooling towers into the atmosphere. On one hand, the water evaporated

into the atmosphere must be resupplied by a water reservoir, which can otherwise be

used for other purposes such as agriculture and domestic applications, and especially

for alleviating water scarcity. On the other hand, this water vapor in the atmosphere

amplifies the greenhouse effect12 because it “cloaks” the atmospheric transmittance

window, trapping the outgoing thermal radiation from the Earth's surface and

increasing the downward radiation from the atmosphere.13 As the atmosphere gets

warmer, more electricity must be generated to meet the ever-growing demand for air

conditioning, thus forming a complex vicious cycle.14

Considering both cost and efficiency, evaporative cooling has been used in many

forms as an alternative to refrigeration-based air conditioning systems or to cool the

condensers in thermal power plants.15,16 The simplest form of evaporative cooling is

spraying water on surfaces, which is still widely used worldwide to cool ambient and

suppress dust on yards, roads, and construction zones. A more sophisticated form of

evaporative cooling is commercial portable swamp coolers used for space cooling.

3

Swamp coolers work best in dry seasons and regions to achieve both humidification

and cooling. High humidity however severely affects the performance of swamp

coolers as the wet-bulb temperature approaches the dry-bulb (ambient) temperature.

The most vital and widest application of evaporative cooling is thermal power plant

cooling, mostly in the form of wet cooling towers and sometimes cooling ponds. In the

US alone, nearly 6 trillion liters of withdrawn water are evaporated into the

atmosphere by thermal power plants each year.17,18 Evaporative cooling in thermal

power plants indeed brings several challenges described above.

Radiative sky cooling has been proposed as an alternative cooling method.19,20,21

Without using much electricity or evaporating any water, radiative sky cooling

passively dumps waste heat through the atmospheric window into the deep space

instead of releasing it to the ambient air as in conventional cooling systems.22,23,24

Radiative sky cooling has the potential advantage of deep sub-ambient cooling due to

the ultra-cold Universe, given that little to no solar absorption occurs and parasitic

convective loss is minimized.25,26 With advancements in materials science and

engineering, highly solar reflective radiative cooling materials have recently been

developed in the form of solid photonic structures,27,28 thin films,29 paints,30,31 and

even wood.32 Radiative sky cooling systems with the capability of sub-ambient cooling

of water and cold generation have been demonstrated.33,34,35 Widespread adoption of

radiative sky cooling is possible if low-cost materials are available even though its

power density tends to be low (~100 W/m2).

In water-stressed and hot regions, radiative sky cooling can be a potential

alternative to evaporative cooling.36,37 Even though both evaporative cooling and

radiative sky cooling are reasonably well understood, it is not clear how these two

compare in terms of performance under similar environments. The two share several

similarities and differences. In addition to being able to passively achieve sub-

ambient cooling, both are adversely affected by humidity.34,38 An increase in humidity

(strictly speaking, precipitable water) results in a less transparent and more emissive

atmospheric window, thus increasing the downward radiation from the atmosphere

and diminishing the net radiative cooling power of an emissive surface.34,39,40 An

increase in humidity also results in reduced water uptake ability of the ambient air,

thus diminishing the rate and cooling power of evaporation.38 Other conditions affect

radiative cooling and evaporative cooling differently. Convection is considered purely

parasitic for achieving sub-ambient cooling by a radiative cooling surface.22 However,

the role of convection in evaporative cooling is two-fold: partially parasitic loss and

partially advective gain.38 An increase in the ambient temperature may reduce the

net cooling power of a radiative sky cooling surface because of increased atmospheric

downward radiation and increased convective parasitic loss. On the other hand, an

4

increasing ambient temperature causes the atmosphere to uptake much more water

vapor and thus enhance the evaporative cooling power, even though convective

parasitic loss also increases. These similar yet different effects of weather conditions

on radiative sky cooling and evaporative cooling performance must be comparatively

evaluated to make an informative choice in applications.

In this work, we experimentally and theoretically compare the passive sub-

ambient cooling performances of a radiative sky cooler and an evaporative cooler. To

ensure the experiment variables were controllable, we carried out cooling tests during

the nighttime. The lack of solar irradiance, less windy ambient, as well as moderately

dynamic ambient temperature and humidity were helpful to achieve results with a

much better quality. Modeling was then used to study the effects of air heat transfer

coefficient, ambient temperature, and relative humidity on the sub-ambient cooling

performances of the coolers. Colormaps of net cooling power as a function of cooler

and ambient temperatures were created for extreme weather conditions: dry weather

with low humidity and wet weather with high humidity. Depending on weather

conditions, radiative sky cooling can perform better or worse than evaporative cooling.

Specifically, sub-ambient evaporative cooling is better suited for high-temperature

and low-humidity weather conditions, whereas sub-ambient radiative sky cooling is

more resilient than evaporative cooling under high-humidity and low-temperature

weather conditions.

2. Experiment setup

As shown in Fig. 1, a radiative cooling module and an evaporative cooling module

with an identical surface area of 0.3×0.3 m2 were made to carry out comparative

cooling experiments. On the radiative cooler (Fig. 1a), an emissive film made of

PETG with a thickness of 70 µm was laminated on a 1-mm thick aluminum plate. An

infrared transmissive PE windshield was added on the top to minimize parasitic heat

loss. On the evaporative cooler (Fig. 1b), a 70-µm thick hydrophobic film (PVDF) was

first laminated as a corrosion protection layer on an aluminum plate. A hydrophilic

cellulose fabric layer (~100 µm) was placed on top of the film to ensure the uniform

spreading of water. The initial layer thickness of water during the experiments was

around 3 mm. It was thin enough to make sure that the temperature gradient from

the water surface to the aluminum plate bottom surface was small ( Δ𝑇 = 𝑃𝑛𝑒𝑡 ∙

{𝜏𝑤 𝑘𝑤⁄ + 𝜏𝑓 𝑘𝑓⁄ + 𝜏𝑎𝑙 𝑘𝑎𝑙⁄ } ≈ 0 ~ 0.4 ℃ for the net cooling power range of 0 ~ 100 W).

The water was also sufficient to provide at least 12 hours of sub-ambient cooling

(𝑚𝑤 = 𝐴𝜏𝑤𝜌𝑤 ≈ 𝑃𝑒𝑣𝑎𝐴Δ𝑡 ℎℎ𝑓𝑔⁄ for Peva ≈ 100 W/m2). On both coolers, the back and the

four sides were insulated to ensure that heat transfer mainly occurred on the sky-

5

facing top surface. Each cooler was equipped with three thermal couples to monitor

their temperature during experiments. Two thermocouples with a tip shielded with

non-emissive aluminum tape were used to monitor the ambient temperature.

The spectral emissivity of the radiative cooling surface (PETG film) and the

evaporative cooling surface (one layer of PVDF and one layer of cellulose fabric

without water) are given in Fig. 1c. The radiative cooling surface is wavelength-

selective, i.e., it mainly emits in the atmospheric transmittance window (8 – 13 µm).

The evaporative cooling surface, on the other hand, is nearly black, with a high

emissivity at wavelengths beyond 6µm. For sub-ambient cooling, a “selective”

radiative cooler is expected to perform better than a “black” radiative cooler.34,41

However, the addition of water evaporation can enhance the sub-ambient cooling

performance of the “black” radiative cooler.

Cooling experiments were carried out during clear-sky nighttime. There are

several advantages in conducting experiments during the nighttime than during the

daytime: avoiding complications due to different degrees of solar absorption by the

radiative cooling surface and the evaporative cooling surface with water, avoiding

frequently changing windy climate during the daytime, reducing frequent

fluctuations in air temperature and relative humidity, and most importantly,

achieving controllable and easily comparable cooling performances.

Since a change in one of the weather conditions was often accompanied by changes

in other weather conditions during the experiment, we also resort to theoretical

approaches in Section 5 to elucidate how radiative cooling and evaporative cooling

are affected by a single changing weather condition while other conditions remain

constant.

6

Fig. 1. Experimental setup. (a) Passive radiative cooler. (b) Passive evaporative cooler.

On the radiative cooler, a radiative cooling film (PETG, ~70 µm thick) was laminated

on a 1-mm thick aluminum plate to ensure the surface temperature uniformity. An

infrared transmissive PE windshield was added to maximize the sub-ambient cooling

degree. On the evaporative cooler, a hydrophobic film (PVDF, ~70 µm thick) was also

laminated on an aluminum plate, and then a hydrophilic fabric (cellulose, ~ 100 µm

thick) was placed on top of the film to ensure the uniform spreading of water. The

initial water thickness during the experiment was around 3.0 mm. (c) The infrared

emissivity of the radiative cooling surface and evaporative cooling surface in its dry

form. The radiative cooling surface is “partially selective” and the evaporative cooling

surface is “nearly black”.

PE wind shield

Emissive film

Aluminum plate

Insulation

Thermocouple

Evaporative water

Hydrophilic fabric

Hydrophobic film

Aluminum plate

Insulation

Thermocouple

b

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

0.0

0.2

0.4

0.6

0.8

1.0

Em

issi

vity

Wavelength (mm)

Evap cooler

Rad cooler

Atmosphere

Radiative cooler Evaporative coolera

c

7

3. Experiment results

Fig. 2 presents the measurement results of the nighttime cooling experiments

that continued from 8:30pm to 6:30am the second day (June 16-17, 2020). The relative

humidity and the wind velocity during the experiments are given in Fig. 2a. Except

for a gust of wind, the wind velocity was mostly within 0 ~ 1.0 m/s, implying rather

calm weather. Initially, the relative humidity was quite stable within the range of 10

~ 20 %. Upon the arrival of the wind gust, the relative humidity jumped to a range of

30 ~ 35% and remained relatively constant afterward. The ambient temperature (Fig.

2b) also evolved at a mostly steady rate, except for a sudden drop with the arrival of

the wind gust, gradually decreasing from a peak of 27°C near the beginning of the

experiment to a low of 17°C near the end of the experiment. Mostly stable but

occasionally dynamic weather conditions allowed us to observe interesting and

delicate changes in the temperatures of the coolers.

Temperatures of the coolers are presented in Fig. 2b. Initially, the coolers were

placed indoors at a temperature of 23oC and covered with opaque shields. The coolers

were then moved outdoors, with the covers immediately lifted triggering rapid

temperature drops. There was a lag in the evaporative cooler temperature because of

the larger thermal mass of water. However, the evaporative cooler temperature fell

below the radiative cooler temperature in less than an hour from the start of the

experiment, and it remained as such for at least 5 hours. The arrival of a wind gust,

a sudden jump in the relative humidity, and a slightly abrupt drop in the ambient

temperature all coincided with an inversion in the trend of the cooler temperatures.

The temperature of radiative sky cooler temperature now dropped below the

evaporative cooler temperature, which is explored further in the following sections.

We also plotted the sub-ambient cooling temperatures (Ts −Tamb) of the coolers in

Fig. 2c. Throughout the measurement duration, both coolers’ temperatures were well

below the ambient temperature. Two timepoints, t1 (10:30 pm) and t2 (05:45 am)

indicated by red arrows, are used to specify the sub-ambient temperature of the

coolers. At time t1, the sub-ambient temperatures of the radiative and evaporative

coolers were −13.5℃ and −15.0℃, respectively, demonstrating the excellent passive

cooling performance of both coolers. As the ambient temperature slowly dropped, the

sub-ambient temperatures of the coolers gradually increased but were still below

−12.0℃, until a flip in trend occurred with the occurrence of the wind gust and an

abrupt increase in the relative humidity from 15 ~ 20% to 30 ~ 35%. At time t2, the

sub-ambient temperatures of the radiative cooler and the evaporative cooler were

about −11.5℃ and −10.5℃, respectively. Although both coolers saw a deterioration

in their sub-ambient cooling performance as the relative humidity increased from

8

13.0% at t1 to 32.0% at t2 and the ambient temperature decreased from 26.0℃ to

17.0℃, the degree of deterioration on the evaporative cooling was larger.

Next, we use theoretical approaches to elucidate how radiative cooling and

evaporative cooling are affected by individual changes in the convective heat transfer

coefficient, ambient temperature, and relative humidity (precipitable water).

Fig. 2. Sub-ambient cooling measurement results. (a) Relative humidity (red curve)

and wind velocity (blue curve) as a function of time. (b) Temperatures of the radiative

cooler (green curve), the evaporative cooler (blue curve), and the ambient (black curve).

(c) Sub-ambient temperatures of the radiative cooler (green curve) and the evaporative

cooler (blue curve). The two time points highlighted by red arrows, t1 = 10:30 pm and

t2 = 05:45 am, corresponds to the ambient weather conditions later used in modeling,

where Tamb-t1 = 26.0oC, RHt1 = 13, Vt1 = 0.50 m/s, and Tamb-t2 = 17.0oC, RHt2 = 32.0%,

Vt2 = 0.00 m/s.

4. Modeling

4.1. Radiative sky cooling and evaporative cooling models

On a sky-facing cooler (radiative or evaporative), the power density of upward

radiation from the cooler surface is given by

9

𝑃𝑠 = ∫ ∫ ∫ 휀𝑠(𝜆, 𝜃)𝐼𝐵(𝑇𝑠, 𝜆) sin 𝜃 cos 𝜃

𝜋2

0

𝑑𝜃2𝜋

0

𝑑𝜑∞

0

𝑑𝜆, (1)

where 𝐼𝐵 is the blackbody spectral radiance (𝐼𝐵 =2ℎ𝑝𝑐2

𝜆5

1

exp[ℎ𝑝𝑐 (𝜆𝑘𝐵𝑇)⁄ ] −1), λ is the

wavelength, and 휀𝑠(𝜆, 𝜃) is the hemispherical spectral emissivity of the cooler

surface.

The atmospheric downward radiation absorbed by the cooler surface is given by

𝑃𝑎𝑡𝑚 = ∫ ∫ ∫ 휀𝑠(𝜆, 𝜃)휀𝑎𝑡𝑚(𝜆, 𝜃, 𝑃𝑊)𝐼𝐵(𝑇𝑎𝑡𝑚, 𝜆) sin 𝜃 cos 𝜃

𝜋2

0

𝑑𝜃2𝜋

0

𝑑𝜑∞

0

𝑑𝜆, (2.1)

where 휀𝑎𝑡𝑚(𝜆, 𝜃, 𝑃𝑊) is the effective hemispherical spectral emissivity of the

atmosphere, and 𝑇𝑎𝑡𝑚 refers to the ambient temperature 𝑇𝑎𝑚𝑏 . Our analyses show

that using zenith-0o atmospheric emissivity, which is the lowest over the hemisphere,

and 𝑇𝑎𝑚𝑏, which is the highest in the densest layer of the atmosphere, gives the lowest

error when the atmosphere is treated as if it is a solid body with an effective spectral

emissivity.

The effective atmospheric emissivity is mainly a function of the atmospheric

precipitable water (PW), which itself is a function of both relative humidity and

ambient temperature. For a location with a clear sky and a given altitude (~1600 m

in this work), PW (in mm) can be estimated by34,42

𝑃𝑊 ≈ 2.15𝑅𝐻3800 exp (

17.63𝑇𝑎𝑚𝑏

𝑇𝑎𝑚𝑏 + 243.04)

𝑝𝑎𝑚𝑏− 0.82. (2.2)

The atmospheric spectral emissivity can be computed as a function of the

precipitable water by using tools such as MODTRAN.43,44

The convective parasitic power density over the cooler surface is simply given by

𝑃𝑐𝑜𝑛𝑣 = ℎ𝑎𝑖𝑟(𝑇𝑎𝑚𝑏 − 𝑇𝑠), (3.1)

where ℎ𝑎𝑖𝑟 is air convective heat transfer coefficient. For horizontal rectangular

surfaces, it may be expressed as34,45

ℎ𝑎𝑖𝑟 = 𝑎 + 𝑏𝑉 (3.2)

where V is the wind velocity, and coefficients as a and b depend on if there is a

windshield or not. Without a windshield, ℎ𝑎𝑖𝑟 ≈ 8.5 + 2.5𝑉 .46,47 With a windshield,

ℎ𝑎𝑖𝑟 ≈ 2.5 + 2.0𝑉 .34 For 𝑉 ≈ 0~1.0 𝑚/𝑠 in the experiment, we estiamte ℎ𝑎𝑖𝑟 ≈

8.5~11.0 𝑊𝑚−2𝐾−1 for the evaporative cooler, and ℎ𝑎𝑖𝑟 ≈ 2.5~4.5 𝑊𝑚−2𝐾−1 for the

radiative cooler.

10

For the evaporative cooler, the power density of evaporation is given by48

𝑃𝑒𝑣𝑎 =𝑑𝑚𝑤

𝑑𝑡∙ ℎ𝑓𝑔 = ℎ𝑚𝑎𝑠𝑠(𝜌𝑣,𝑠 − 𝜌𝑣,∞)ℎ𝑓𝑔, (4.1)

where hmass is the mass transfer coefficient, 𝜌𝑣,𝑠 and 𝜌𝑣,∞ are respectively the vapor

densities at the water surface and in the air far from the surface, and ℎ𝑓𝑔 is the latent

heat of vaporization of water.

The mass transfer coefficient is related to the convective heat transfer hair as48

ℎ𝑎𝑖𝑟

ℎ𝑚𝑎𝑠𝑠= 𝜌𝑎𝑖𝑟𝑐𝑝,𝑎𝑖𝑟𝐿𝑒1−𝑛, (4.2)

where 𝜌𝑎𝑖𝑟 is the air density, 𝑐𝑝,𝑎𝑖𝑟 is the air heat capacity, and Le is the Lewis number,

which is the ratio of the thermal and concentration boundary layer thicknesses

(𝛿𝑡 𝛿𝑚⁄ = 𝐿𝑒𝑛). For gasses, Le is on the order of unity (𝐿𝑒 ≈ 1). For the air-water

systems in this work, it is set 0.847.49 Here, the value of the exponent n is set ¼ since

the surface was horizontal and the wind velocity was small during the experiment.

The water vapor densities at the surface and in the air can be obtained from the

surface and air temperatures and the relative humidity, respectively, as

𝜌𝑣,𝑠 =𝑝𝑠𝑎𝑡

𝑅𝑣𝑎𝑝𝑜𝑟𝑇𝑠, 𝑎𝑛𝑑 𝜌𝑣,∞ =

𝑅𝐻 ∙ 𝑝𝑠𝑎𝑡

𝑅𝑣𝑎𝑝𝑜𝑟𝑇𝑎𝑚𝑏. (4.3)

Combining equations (1), (2.1), and (3.1) with their respective parameters and

properties, the net cooling power of the radiative cooler is then given as

𝑃𝑛𝑒𝑡− 𝑟𝑎𝑑 = 𝑃𝑠(𝑇𝑠,𝑟𝑎𝑑, 휀𝑟𝑎𝑑 ) − 𝑃𝑎𝑡𝑚(𝑇𝑠,𝑟𝑎𝑑 , 휀𝑠,𝑟𝑎𝑑 , 휀𝑎𝑡𝑚 )

− 𝑃𝑐𝑜𝑛𝑣(𝑇𝑠,𝑟𝑎𝑑 , 𝑇𝑎𝑚𝑏 , ℎ𝑎𝑖𝑟,𝑟𝑎𝑑). (5)

Similarly, combining equations (1), (2.1), (3.1), and (4.1) with their respective

parameters properties, the net cooling power of the evaporative cooler is then given

as

𝑃𝑛𝑒𝑡− 𝑒𝑣𝑎 = 𝑃𝑒𝑣𝑎(𝑇𝑠,𝑒𝑣𝑎, 𝑇𝑎𝑚𝑏 , 𝑅𝐻, ℎ𝑚𝑎𝑠𝑠) + 𝑃𝑠(𝑇𝑠,𝑒𝑣𝑎, 휀𝑒𝑣𝑎 ) − 𝑃𝑎𝑡𝑚(𝑇𝑠,𝑒𝑣𝑎 , 휀𝑠,𝑒𝑣𝑎 , 휀𝑎𝑡𝑚 )

− 𝑃𝑐𝑜𝑛𝑣(𝑇𝑠,𝑒𝑣𝑎, 𝑇𝑎𝑚𝑏 , ℎ𝑎𝑖𝑟,𝑒𝑣𝑎). (6)

The sub-ambient cooling temperature of the coolers at equilibrium is given by Pnet

= 0. Using the above models for radiative sky cooling and evaporative cooling, we

investigate next how air heat transfer coefficient, ambient temperature, and relative

humidity individually affect the net cooling power and the sub-ambient temperature

of the coolers.

11

4.2. Effect of air heat transfer coefficient on sub-ambient cooling

In sub-ambient cooling, convection is a purely parasitic loss on the radiative cooler

(Eq.3), where its role on the evaporative cooler is two-fold: parasitic loss (Eq.3) and

advective removal of water vapor (Eq.4.1). Fig. 3 shows net cooling power (Pnet) vs.

non-equilibrium sub-ambient temperature (Ts− Tamb) for different values of air heat

transfer coefficient at Tamb = 25℃ and RH = 30%. On the radiative cooler (Fig. 3a),

the smaller the air heat transfer coefficient, the higher the net cooling power at any

sub-ambient cooling temperature. At equilibrium (Pnet = 0), the sub-ambient

temperature of the radiative cooler drops from −4.5℃ to −14.5℃ as the air heat

transfer coefficient hair decreases from 20 W/(m2K) to 2.5 Wm-2K-1. The transition

from convective loss to convective gain occurs only at (Ts− Tamb = 0) for all heat

transfer coefficient values.

In comparison, the case for the evaporative cooler is more complicated (Fig. 3b).

At Tamb = 25℃ and RH = 30%, a low air heat transfer coefficient is beneficial to

achieve a sub-ambient cooling temperature as low as possible at equilibrium (Pnet =

0): −15.4℃ vs. −11.2℃ for hair values of 20 Wm-2K-1 vs. 2.5 Wm-2K-1, respectively. As

the sub-ambient temperature increases to around −10℃, all cooling power curves for

different hair values intersect at an inversion point, where the gain from evaporation

overtakes the parasitic loss from convection. At an even higher sub-ambient

temperature above the inversion point, the larger the air heat transfer coefficient, the

higher the net cooling power.

Based on the analyses above, to achieve a low sub-ambient temperature alone, it

is preferable to keep the air heat transfer coefficient small for both coolers, implying

a windshield is beneficial to reduce the convective loss. For practical purposes,

however, a windshield was added only to the radiative cooler during the sub-ambient

cooling experiment.

It is important to point out that when there is no sub-ambient cooling (Ts− Tamb =

0), the net cooling power densities of the radiative and evaporative coolers are 115

W/m2 vs. at least 190 W/m2, implying evaporative cooling posses a much higher

cooling potential under hot and dry climates.

12

Fig. 3. Effects of air heat transfer coefficient, hair, on the net cooling powers (Pnet), and

the sub-ambient temperatures (Ts− Tamb) of the coolers. (a) Radiative cooler and (b)

evaporative cooler. For both coolers, the lower the convective heat transfer coefficient,

the lower the sub-ambient cooling temperature at equilibrium (Pcool = 0) at the given

ambient conditions of Tamb = 25oC and RH = 30%. However, a larger convective heat

transfer coefficient is beneficial to the evaporative cooler when the sub-ambient cooling

degree is smaller than 10oC because of evaporative cooling power overcoming

convective parasitic loss.

4.3. Effects of ambient temperature and relative humidity on sub-

ambient cooling

Weather conditions such as relative humidity and ambient temperature naturally

affect the cooling performances of the radiative and evaporative coolers. As shown in

Fig.4, we separately modeled the effects of humidity and ambient temperature on

the coolers’ equilibrium sub-ambient temperatures when one of the conditions is fixed.

The specified relative humidity values, RH = 13% and 32%, as well as the two ambient

temperatures Tamb = 26℃ and 17℃, are respectively based on the weather conditions

at t1 = 10:30 pm and t2 = 05:45 am during the experiments. The air convective heat

transfer coefficients used in modeling are 4.5 Wm-2K-1 for the radiative cooler with a

windshield and 10.5 Wm-2K-1 for the evaporative cooler without a windshield, as

estimated from Eq.3.2 and the best agreement between the modeling and

experimental results. The corresponding atmospheric precipitable water (PW, Eq 2.1)

estimated from relative humidity and ambient temperature is given as the top x-axis.

The measured sub-ambient temperatures at the experimental conditions are

highlighted by open circles. The modeling and experimental results agree well with

less than 1℃ differences.

13

Fig.4. Effects of ambient temperature and relative humidity on the sub-ambient

cooling temperatures of the radiative and evaporative coolers. (a & b) Effects of

ambient temperature on the cooler sub-ambient temperatures at equilibrium, for RH

= 13% and 32%, respectively. (c & d) Effects of relative humidity on the cooler sub-

ambient temperatures at equilibrium, for Tamb = 26℃ and 17℃, respectively. The

specified relative humidity values, RH = 13% and 32%, as well as the two ambient

temperatures Tamb = 26℃ and 17℃, are respectively based on the weather conditions

at t1 = 10:30 pm and t2 = 05:45 am during the experiments. The experimental sub-

ambient temperatures at the corresponding conditions are highlighted by open circles.

The atmospheric precipitable water (PW) given as the top x-axis was estimated from

the corresponding relative humidity and the ambient temperature. The air convective

heat transfer coefficients used in modeling are 4.5 Wm-2K-1 for the radiative cooler

with a windshield and 10.5 Wm-2K-1 for the evaporative cooler without a windshield,

as estimated from Eq.3.2.

As Fig.4a&b shows, the equilibrium sub-ambient temperatures (Ts− Tamb) of the

radiative and evaporative coolers are affected by the ambient temperature differently

at the two specified humidities. The sub-ambient temperature of the radiative cooler

14

overall increases with the ambient temperature (except at low humidity and low

temperature in Fig.4a), whereas the sub-ambient temperature of the evaporative

cooler decreases with the ambient temperature. For the radiative cooler, even though

relative humidity is fixed, rising ambient temperature results in increasing

precipitable water at a growing rate (see top x-axes) and thus increasing atmospheric

emissivity. Rising ambient temperature and its consequent effect on the atmospheric

emissivity causes the atmospheric downward radiation to grow at a faster rate (Eq.2)

than the upward radiation from the cooler surface as it is only dependent on the

surface temperature (Eq.1). On the other hand, for the evaporative cooler, the

evaporative cooling power (Eq.3) is enhanced by the rising ambient temperature

much more than the convective loss (Eq.4), resulting in decreased sub-ambient

temperature.

The effect of relative humidity on the cooler sub-ambient temperatures at

equilibrium is presented in Fig.4c&d for the two specified ambient temperatures,

respectively. Both coolers are adversely affected, yet differently, by an increase in

relative humidity. The evaporative cooler sees a faster deterioration than the

radiative sky cooler. This is because the net cooling power of the radiative cooler is

only non-linearly and negatively correlated to relative humidity (Eqs.2) through the

atmospheric radiation. On the other hand, the net cooling power of the evaporative

cooler contains an evaporative term that is linearly and negatively proportional to

relative humidity (Eqs. 4) and the atmospheric radiation term that is non-linearly

and also negatively correlated to relative humidity (Eqs.2). It can be inferred further

that the radiative sky cooler may be a more resilient sub-ambient cooler under high

humidity conditions because of its relatively weaker dependence on humidity. On the

other hand, the evaporative cooler could perform better under high temperature and

low humidity conditions. In Fig.4, the measured sub-ambient temperatures (open

circles) of the radiative and evaporative coolers agree well with the modeled sub-

ambient temperatures: (−13.5℃ and −15.0℃) vs. (−13.8℃ and −15.8℃) at RH = 13%

and Tamb = 26℃, and (−11.5℃ and −10.5℃) vs. (−11.5℃ and −10.3℃) at RH = 32%

and Tamb = 17℃.

4.4. Net cooling power at low and high humidity

To investigate how extreme weather conditions, such as very low or very high

humidities, affect the passive net cooling power and the sub-ambient temperatures

of the coolers, we plotted in Fig. 5 net cooling power colormaps as functions of the

cooler and ambient temperatures for two humidity values: a low RH = 15% and a high

RH = 70%. In this figure, the regimes of sub-ambient cooling are bounded by two

15

dashed curves: the equilibrium sub-ambient cooling temperature curve at Pnet = 0 and

the net cooling power curve at Ts− Tamb = 0. The horizontal width of the highlighted

regimes represents the sub-ambient cooling temperatures of the coolers. At RH = 15%,

both coolers have a large sub-ambient cooling potential at all temperatures plotted,

although the sub-ambient temperature of the radiative cooler does not change much

at high temperatures (Fig. 5a) while the evaporative cooler sees a noticeable increase

(Fig. 5b). At RH = 70%, however, the sub-ambient cooling potential of both coolers

diminishes at all temperatures (Fig. 5c&d), which is especially significant on the

evaporative cooler. The sub-ambient temperature of the radiative cooler also becomes

significantly small at high temperatures and this specified high humidity.

Fig. 5. Net cooling power color maps as functions of the cooler surface temperature and

the ambient temperature. (a) Radiative cooler and (b) evaporative cooler. The two

figures at the top are for a high-humidity condition (RH = 70%), and the two figures

at the bottom are for a low-humidity condition. The highlighted regions represent

passively achievable sub-cooling regimes defined by Ts – Tamb = 0 and Pnet cool = 0. The

horizontal width of the sub-ambient cooling regimes represents the sub-ambient

temperatures of the coolers.

Low

Humidity

(RH = 15%)

High

Humidity

(RH = 70%)

Radiative cooler Evaporative coolera b

c d

16

The cooling power colormaps and the sizes of the sub-ambient cooling regimes

indicate that evaporative cooling is better suited for high-temperature and low-

humidity weather conditions, although radiative cooling also performs well under

these conditions. On the other hand, radiative cooling is positioned better than

evaporative cooling to work at high-humidity and low-temperature weather

conditions, where cold generation and storage for later use may be a more practical

approach. High-humidity and high-temperature weather conditions, unfortunately,

are detrimental to the performances of both coolers.

5. Conclusions

In this work, we have experimentally and theoretically investigated the passive

sub-ambient cooling performances of radiative cooling and evaporative cooling under

the same weather conditions. With sky-facing radiative and evaporative coolers with

the same surface, we experimentally observed the sub-ambient temperatures (Ts

−Tamb) of the coolers were −13.5℃ and −15.0℃, respectively, at a relative humidity

(RH) of 13% and an ambient temperature (Tamb) of 26℃. This shows the evaporative

cooler performs better than the radiative cooler at low-humidity but high-

temperature weather conditions. At a higher relative humidity of 32% and a lower

ambient temperature of 17℃, the observed sub-ambient temperatures of the

radiative and evaporative coolers were −11.5℃ and −10.5℃, respectively. This

indicates the radiative cooler is better positioned to work under low temperature or

high humidity conditions.

To elucidate the impacts of air convection, ambient temperature, and relative

humidity on the sub-ambient cooling performances of the coolers, we carried out

further theoretical analyses. We created net cooling power colormaps as functions of

the cooler and ambient temperatures for two humidity conditions: a low RH = 15%

and a high RH = 70%. The cooling power colormaps and the sizes of the sub-ambient

cooling regimes further confirm our experimental observations.

Our study validates and compares the passive sub-ambient cooling potential of

radiative cooling and evaporative cooling. In regions with high humidity or limited

water resources, radiative cooling can be a potential alternative to evaporative

cooling.

17

References

1. Mcneil, M. A., Letschert, V. E. & Org, E. Title Future Air Conditioning Energy

Consumption in Developing Countries and what can be done about it: The

Potential of Efficiency in the Residential Sector. (2008).

2. Xu, T., Sathaye, J., Akbari, H., Garg, V. & Tetali, S. Quantifying the direct

benefits of cool roofs in an urban setting: Reduced cooling energy use and

lowered greenhouse gas emissions. Build. Environ. 48, 1–6 (2012).

3. Peer, R. A. M. & Sanders, K. T. The water consequences of a transitioning US

power sector. Appl. Energy 210, 613–622 (2018).

4. Raptis, C. E., Van Vliet, M. T. H. & Pfister, S. Global thermal pollution of

rivers from thermoelectric power plants. Environ. Res. Lett. 11, 104011 (2016).

5. Thomson, H., Simcock, N., Bouzarovski, S. & Petrova, S. Energy poverty and

indoor cooling: An overlooked issue in Europe. Energy Build. 196, 21–29

(2019).

6. Lindley, A. A. & McCulloch, A. Regulating to reduce emissions of fluorinated

greenhouse gases. Journal of Fluorine Chemistry 126, 1457–1462 (2005).

7. Davis, L. W. & Gertler, P. J. Contribution of air conditioning adoption to

future energy use under global warming. Proc. Natl. Acad. Sci. U. S. A. 112,

5962–5967 (2015).

8. EIA. Annual Energy Outlook 2021.

9. Santamouris, M. Cooling the buildings – past, present and future. Energy

Build. 128, 617–638 (2016).

10. Mittal, M. L., Sharma, C. & Singh, R. Estimates of Emissions from Coal Fired

Thermal Power Plants in India. in 2012 International emission inventory

conference (2012).

11. Madden, N., Lewis, A. & Davis, M. Thermal effluent from the power sector:

An analysis of once-through cooling system impacts on surface water

temperature. Environ. Res. Lett. 8, (2013).

12. Held, I. M. & Soden, B. J. WATER VAPOR FEEDBACK AND GLOBAL

WARMING 1. (2000).

13. Allen, J. R. & Allen, J. R. Measurements of Cloud Emissivity in the 8–13 μ

Waveband. J. Appl. Meteorol. Climatol. 10, (1971).

14. Ürge-Vorsatz, D., Cabeza, L. F., Serrano, S., Barreneche, C. & Petrichenko, K.

Heating and cooling energy trends and drivers in buildings. Renewable and

18

Sustainable Energy Reviews 41, 85–98 (2015).

15. Ulpiani, G. Water mist spray for outdoor cooling: A systematic review of

technologies, methods and impacts. Applied Energy 254, 113647 (2019).

16. Xuan, Y. M., Xiao, F., Niu, X. F., Huang, X. & Wang, S. W. Research and

application of evaporative cooling in China: A review (I) - Research. Renewable

and Sustainable Energy Reviews 16, 3535–3546 (2012).

17. Cheryl A. Dieter, Molly A. Maupin, Rodney R. Caldwell, Melissa A. Harris,

Tamara I. Ivahnenko, John K. Lovelace, Nancy L. Barber, and K. S. L.

Estimated Use of Water in the United States in 2015. US Geological Survey

(2018). doi:10.3133/cir1441

18. Averyt, K. et al. Water use for electricity in the United States: An analysis of

reported and calculated water use information for 2008. Environ. Res. Lett. 8,

(2013).

19. Liang, Z., Shen, H., Li, J. & Xu, N. Microstructure and optical properties of

silicon nitride thin films as radiative cooling materials. Sol. Energy 72, 505–

510 (2002).

20. Berdahl, P., Martin, M. & Sakkal, F. Thermal performance of radiative

cooling panels. Int. J. Heat Mass Transf. 26, 871–880 (1983).

21. Granqvist, C. G. Radiative heating and cooling with spectrally selective

surfaces. Appl. Opt. 20, 2606 (1981).

22. Zhao, D. et al. Radiative sky cooling: Fundamental principles, materials, and

applications. Appl. Phys. Rev. 6, 021306 (2019).

23. Zhao, B., Hu, M., Ao, X., Chen, N. & Pei, G. Radiative cooling: A review of

fundamentals, materials, applications, and prospects. Appl. Energy 236, 489–

513 (2019).

24. Vall, S. & Castell, A. Radiative cooling as low-grade energy source: A

literature review. Renew. Sustain. Energy Rev. 77, 803–820 (2017).

25. Chen, Z., Zhu, L., Raman, A. & Fan, S. Radiative cooling to deep sub-freezing

temperatures through a 24-h day–night cycle. Nat. Commun. 7, 13729 (2016).

26. Leroy, A. et al. High-performance subambient radiative cooling enabled by

optically selective and thermally insulating polyethylene aerogel. Sci. Adv. 5,

1–9 (2019).

27. Rephaeli, E., Raman, A. & Fan, S. Ultrabroadband photonic structures to

achieve high-performance daytime radiative cooling. Nano Lett. 13, 1457–

19

1461 (2013).

28. Raman, A. P., Anoma, M. A., Zhu, L., Rephaeli, E. & Fan, S. Passive radiative

cooling below ambient air temperature under direct sunlight. Nature 515,

540–544 (2014).

29. Zhai, Y. et al. Scalable-manufactured randomized glass-polymer hybrid

metamaterial for daytime radiative cooling. Science (80-. ). 355, 1062–1066

(2017).

30. Mandal, J. et al. Hierarchically porous polymer coatings for highly efficient

passive daytime radiative cooling. Science (80-. ). 362, 315–319 (2018).

31. Li, X., Peoples, J., Yao, P. & Ruan, X. Ultrawhite BaSO4Paints and Films for

Remarkable Daytime Subambient Radiative Cooling. ACS Appl. Mater.

Interfaces 13, 21733–21739 (2021).

32. Li, T. et al. A radiative cooling structural material. Science 364, 760–763

(2019).

33. Goldstein, E. A., Raman, A. P. & Fan, S. Sub-ambient non-evaporative fluid

cooling with the sky. Nat. Energy 2, 17143 (2017).

34. Zhao, D. et al. Subambient Cooling of Water: Toward Real-World Applications

of Daytime Radiative Cooling. Joule 3, 111–123 (2019).

35. Aili, A. et al. A kW-scale, 24-hour continuously operational, radiative sky

cooling system: Experimental demonstration and predictive modeling. Energy

Convers. Manag. 186, 586–596 (2019).

36. Dyreson, A. & Miller, F. Night sky cooling for concentrating solar power

plants. Appl. Energy 180, 276–286 (2016).

37. Zeyghami, M. & Khalili, F. Performance improvement of dry cooled advanced

concentrating solar power plants using daytime radiative cooling. Energy

Convers. Manag. 106, 10–20 (2015).

38. Hisatake, K., Tanaka, S. & Aizawa, Y. Evaporation rate of water in a vessel.

J. Appl. Phys. 73, 7395–7401 (1993).

39. Dong, M., Chen, N., Zhao, X., Fan, S. & Chen, Z. Nighttime radiative cooling

in hot and humid climates. Opt. Express 27, 31587 (2019).

40. Liu, C., Wu, Y., Wang, B., Zhao, C. Y. & Bao, H. Effect of atmospheric water

vapor on radiative cooling performance of different surfaces. Sol. Energy 183,

218–225 (2019).

41. Aili, A. et al. Selection of polymers with functional groups for daytime

20

radiative cooling. Mater. Today Phys. 10, 100127 (2019).

42. Ruckstuhl, C., Philipona, R., Morland, J. & Ohmura, A. Observed relationship

between surface specific humidity, integrated water vapor, and longwave

downward radiation at different altitudes. J. Geophys. Res. Atmos. 112, 1–7

(2007).

43. MODTRAN®. Available at: http://modtran.spectral.com/modtran_home.

44. Berk, A. & Hawes, F. Validation of MODTRAN®6 and its line-by-line

algorithm. J. Quant. Spectrosc. Radiat. Transf. 203, 542–556 (2017).

45. Mirsadeghi, M., Cóstola, D., Blocken, B. & Hensen, J. L. M. Review of external

convective heat transfer coefficient models in building energy simulation

programs: Implementation and uncertainty. Appl. Therm. Eng. 56, 134–151

(2013).

46. Test, F. L., Lessmann, R. C. & Johary, a. Heat Transfer During Wind Flow

over Rectangular Bodies in the Natural Environment. J. Heat Transfer 103,

262 (1981).

47. Sharples, S. & Charlesworth, P. S. Full-Scale Measurements of Wind-Induced

Convective Heat Transfer From a Roof-Mounted Flat Plate Solar Collector.

62, 69–77 (1998).

48. Bergman, T.L., Incropera, F.P., DeWitt, D.P. and Lavine, A. S. Fundamentals

of Heat and Mass Transfer. (John Wiley & Sons, 2011).

49. Lienhard, I. V., H. J. A HeatTransfer Textbook. (Phlogiston press, 2017).