Table 1 Definitions of all the acronyms used in this study.

T_sf

soil temperature of forest, °C

E

transpiration and actual evapotranspiration, mm

T_af

air temperature of forest, °C

E_t

transpiration, mm

T_c

canopy surface temperature, °C

E_i

interception loss, mm

T_so

soil temperature of open lands, °C

U(Vz)

wind speed at height z, m s⁻¹

T_ao

air temperature of open lands, °C

ρ_a

density of air, kg m⁻³

ΔT_s

biophysical effects of forest on soil temperature, °C

K

coefficient of the energy flux into soil to total radiation, dimensionless

ΔT_a

biophysical effects of forest on air temperature, °C

f_β

an energy redistribution factor caused by the Bowen ratio (β)

ΔT_Lee

temperature difference between forest and nonforest estimated by Lee et al.²², °C

C^S

relative contributions of seasonal changes in ∅_n, R, LE, LE_understory, LE_canopy, H^*, \({H}_{{understory}}^{* }\) and \({H}_{{canopy}}^{* }\)

ΔT_Su

comprehensive biophysical effects on temperature estimated by the CAS model, °C

C^C

relative contributions of long-term variations in ∅_n, R, LE, LE_understory, LE_canopy, H^*, \({H}_{{understory}}^{* }\) and \({H}_{{canopy}}^{* }\)

\({f}_{{\rm{r}}}^{1}\)

vertical aerodynamic resistances ratio index between r_s and r_a,c

λ₀, \({\lambda }^{{\prime} }\)

sensitivity of temperature to changes in net short-wave radiation

\({f}_{{\rm{r}}}^{2}\)

vertical aerodynamic resistances ratio index between r_a,c and r_c,a

H^*

corrected H, H^*can be split into \({H}_{{\rm{canopy}}}^{* }\) and \({H}_{{\rm{understory}}}^{* }\), W m⁻²

\(\phi\)_n

short-wave radiation, W m⁻²

ΔS

changes of net short-wave radiation, W m⁻²

R

long-wave radiation, W m⁻²

u

cosine value of the solar zenith angle, θ

Rn

net radiation, W m⁻²

θ

solar zenith angle, °

\({R}_{{\rm{near}}}\)

differences between incoming and outgoing R, W m⁻²

ε_s

emissivity coefficients of the soil surface, dimensionless

R_outnear

total R, W m⁻²

ε\({\rm{sky}}\)

emissivity coefficients of sky, dimensionless

LE

latent heat flux, LE can be split into \({{\rm{LE}}}_{{\rm{canopy}}}^{* }\) and \({{\rm{LE}}}_{{\rm{understory}}}^{* }\), W m⁻²

ε_canopy

emissivity coefficients of forest canopy, dimensionless

H

sensible heat flux, W m⁻²

a

albedo, dimensionless

H_{(soil→air,understory)}

sensible heat flux between soil and understory, W m⁻²

r_a,c

aerodynamic resistances to sensible heat above canopy, s m⁻¹

H_{(air,understory→canopy)}

sensible heat flux between understory and canopy, W m⁻²

r_c,a

aerodynamic resistances to sensible heat below canopy surface, s m⁻¹

H_{(canopy→airopen)}

sensible heat flux between canopy layer to open air, W m⁻²

r_s

aerodynamic resistances to sensible heat at soil surface, s m⁻¹

G_soil

heat storage in soil, W m⁻²

σ

Stefan–Boltzmann constant, W m⁻² K⁻⁴

G_tree

heat storage in tree, W m⁻²

m_s

soil moisture, %

LAI

leaf area index, dimensionless

C

extinction coefficient, dimensionless

h_c

canopy height, m

C_cover

cloud coverage, %

VPD

vapor pressure deficit, hPa

\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\)

seasonal variations of \(\Delta {T}_{{\rm{Su}}}\), °C

C_p

specific heat capacity of air, J kg⁻¹ K⁻¹

\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\)

long-term variations of \(\Delta {T}_{{\rm{Su}}}\), °C