Supplementary Material
Appendix 1: Variables and equations used.
Variables
d
inverse Earth-sun distance
G
ground heat flux [MJ m-2 day-1]
J
day of the year
L
latent heat flux [MJ m-2 day-1]
m
month of the year
N
day length [hours]
P
pressure [kPa]
q
specific humidity [kg kg-1]
Re
extraterrestrial radiation [MJ m-2 day-1]
Rl
longwave radiation [MJ m-2 day-1]
Rn
net radiation [MJ m-2 day-1]
Rs
shortwave radiation [MJ m-2 day-1]
S
sensible heat flux [MJ m-2 day-1]
T
air temperature [°C]
u
zonal wind velocity [m s-1]
v
meridional wind velocity [m s-1]
vpd
vapor pressure deficit [kPa]
ws
wind speed [m s-1]
γ
psychrometric constant [kPa °C-1]

declination [radians]
Δ
slope of saturation vapor pressure curve [kPa °C-1]
λ
latent heat of vaporization [MJ kg-1]

latitude [radians]

sunset-hour angle [radians]
1
Hamon PET [mm day-1] (Lu et al. 2005)
17.26939∗T
)
𝑁
216.7 ∗ 6.108 ∗ 𝑒 ( 𝑇+237.3
𝑃𝐸𝑇 = 0.1651 ∗ ( ) ∗
(𝑇 + 273.3)
12
Priestley-Taylor PET (mm day-1) (Shuttleworth 2007)
1.26
Δ
(𝑅𝑛 − 𝐺) ∗ (
𝑃𝐸𝑇 =
)
𝜆
Δ+𝛾
Penman PET (mm day-1) (Shuttleworth 2007)
1
Δ
𝛾
6.43 ∗ 𝑣𝑝𝑑 ∗ (1 + 0.563𝑤𝑠)
𝑃𝐸𝑇 = (𝑅𝑛 − 𝐺) ∗ (
)+ (
)∗(
)
𝜆
Δ+𝛾
γ+Δ
𝜆
Thornthwaite PET (mm day-1) (Shaw and Riha 2011)
if T < 26.5ºC
𝑁 10𝑇 𝑎
𝑃𝐸𝑇 = 1.067 ( ) (
)
24
𝐼
𝑎 = 6.75 ∗ 10−7 𝐼 3 + 7.71 ∗ 10−5 𝐼 2 + 0.0170𝐼 + 0.4921
12
𝑇𝑚 1.514
𝐼= ∑( )
5
𝑚=1
if T > 26.5ºC
𝑃𝐸𝑇 = −27.7 + 2.15𝑇 − 0.029𝑇 2
Oudin PET (mm day-1) (Shaw and Riha 2011)
𝑅𝑒 𝑇 + 5
𝑃𝐸𝑇 =
(
)
𝜆 100
 is taken as 2.45
Earth-sun Distance (Allen et al. 1998)
2𝜋
𝑑 = 1 + 0.033cos (
𝐽)
365
Ground Heat Flux [MJ m-2 day-1]
𝐺 = 𝑅𝑛 − (𝐿 + 𝑆)
2
Day length [hours] (Allen et al. 1998)
24
𝑁= 𝜋𝜔
Extraterrestrial Radiation [MJ m-2 day-1] (Allen et al. 1998)
24 ∗ 60
𝑅𝑒 = (
) ∗ 0.082𝑑[𝜔 sin(𝜑) sin(𝛿) + cos(𝜑) cos(𝛿) sin(𝜑)]
𝜋
Net Radiation [MJ m-2 day-1]
𝑅𝑛 = 𝑅𝑠 ↓ −𝑅𝑠 ↑ +𝑅𝑙 ↓ −𝑅𝑙 ↑
Downward and upward arrows indicate incoming and outgoing radiation
Vapor Pressure Deficit [kPa] (WMO 2008; Wallace and Hobbs 2006)
17.62∗𝑇
𝑞∗(1−𝑞)−1
𝑣𝑝𝑑 = 0.6112 ∗ 𝑒 243.12+𝑡 − 𝑃 ∗ 0.622+𝑞∗(1−𝑞)−1
Wind Speed [m s-1]
𝑤𝑠 = √𝑢2 + 𝑣 2
Psychrometric Constant (kPa °C-1) (Shuttleworth 2007)
0.0016286𝑃
𝛾=
𝜆
Declination [radians] Allen et al. (1998)
2𝜋
𝛿 = 0.409sin (
𝐽 − 1.39)
365
Slope of Saturation Vapor Pressure Curve (kPa °C-1) (Allen et al. 1998)
17.27𝑇
0.6180𝑒 237.3+𝑇
𝛥 = 4098 ∗
(𝑇 + 237.3)2
Latent Heat of Vaporization (MJ kg-1) (Shuttleworth 2007)
𝜆 = 2.501 − 0.002361𝑇
Sunset-hour Angle [radians] (Allen et al. 1998)
𝜔 = 𝑐𝑜𝑠 −1 [− tan(𝛿) tan(𝜑)]
3
Supplementary Figure Captions
Supp Fig 1 Comparison of changes in Priestley-Taylor and Penman potential evapotranspiration
in terms of statistical significance, sign and consistency between models. White areas indicate
qualitative agreement between methods. Pale yellow denotes areas where one method does not
show a consistent statistically significant change, and the other method suggests a statistically
significant change in at least half of the models. Gold shading represents areas where one method
shows no consistent statistically significant change, while the other suggests that there is a
statistically significant change, but that models disagree about the sign of that change. Orange
areas indicate that one method finds a statistically significant change with a high degree of model
agreement, and the other method a statistically significant change, but model disagreement. Red
denotes areas where the two methods find robust and statistically significant trends of opposite
signs.
Supp Fig 2 Change in Priestley-Taylor potential evapotranspiration (PET) minus the change in
Penman PET (mm day-1) where at least five models show a statistically significant (p ≤0.05)
increase in PET by both methods. Stippling indicates that the values are significantly different (p
≤ 0.05). White areas denote that fewer than five models showed a statistically significant change
in PET by both methods.
Supp Fig 3 Changes in cloud cover (%) between 2002-2011 and 2079-2098 under the A1B
scenario. Colors show the mean change in cloud cover across all models. Stippling indicates that
at least 80% of the models projecting a significant (p ≤ 0.05) change agree in sign. White areas
4
indicate that although at least half of the models project a significant change in cloud cover, they
do not agree on the direction of change. Lack of stippling over colored areas of the map indicated
that less than 50% of models projected a significant change in cloud cover.
Supp Fig 4 As in Supp Fig 3, but for vapor pressure deficit (kPa)
Supp Fig 5 As in Supp Fig 3, but for Thornthwaite PET (mm day-1)
Supp Fig 6As in Supp Fig 3, but for Oudin PET (mm day-1)
Supp Fig 7 Number of models (out of 17) indicating a statistically significant (p ≤ 0.05)
decreased in Priestley-Taylor PET.
Supp Fig 8 As in Supp Fig 7, but for Penman PET.
Supp Fig 9 As in Supp Fig 7, but for Hamon PET
5