及图 ERBE Tp-of-Atrospl ere Net Radiaticn 10 SW LW 0 40 warming 40 cooling cooling -0 Atmosphere 10 10 30 C1m30 动力输送 Ftop 1∂ rad 2xa>cos f(φ) meridional energy transport Surface by atmosphere and oceans 授课教师：张洋3
授课教师：张洋 3 Atmosphere Surface SW LW 动⼒输送 f() meridional energy transport by atmosphere and oceans warming cooling cooling Ftop rad = 1 2⇡a2 cos @ @f()
及金 ERBE Tp-of-Atrospl ere Net Radiaticn 10 SW LW 40 warming 0 40 cooling cooling ptop.. 1 -0 rad f代) 2πa2c0sb0b Atmosphere 10 —4mD-hBA37 了 10 0 30 6300 6 RT (ERBE) 动力输送 NCEP OT NCEP AT atmosphere E 0 - 吉 ocean -2 Total Surface f(Φ) 80 60 40 20 20 40 60 80 Lotitude N Wunsch(2005),J.Climate 授课教师：张洋4
授课教师：张洋 4 Total atmosphere ocean Wunsch (2005), J. Climate Atmosphere Surface SW LW 动⼒输送 warming cooling cooling Ftop rad = 1 2⇡a2 cos @ @f() f()
及 Ftop 1 ∂ 2maP cos SW LW rad Atmosphere: Ftop 1 rad - Fr+FLH+FsH= 2xa2cos Ocean: Atmosphere Fsfe -FLH-FSH= rad d2 coso0dfo() 6 RT (ERBE) 动力输送 NCEP OT Rad.LH+SH NCEP AT f(φy atmosphere E 、fA( 0 ocean f.(oy Surface Total 80 60 40 20 EQ 20 4060 80 Lotitude Wunsch(2005),J.Climate 授课教师：张洋5
Ftop rad = 1 2⇡a2 cos @ @f() 授课教师：张洋 5 Total atmosphere ocean Wunsch (2005), J. Climate Atmosphere Surface SW LW 动⼒输送 Rad. LH+SH Ftop rad Fsf c rad + FLH + FSH = 1 2⇡a2 cos @ @fA() Atmosphere: Fsf c rad FLH FSH = 1 2⇡a2 cos @ @fo() Ocean: fo() f() fA()
Simple energy balance climate models ERBE Tp-of-Atrospl ere Net Radiaticn 10 SW LW 0 40 warming 40 cooling ptop. 1 cooling -0 rad 2πa2c0sb0b Atmosphere 10 -Arna DeN 56-87 了 10 0 30 6300 6 动力输送 RT (ERBE) NCEP OT NCEP AT atmosphere E 0 ocean-》 Surface Total 80 40 20 EQ 2040 60 80 Latitude N Wunsch(2005),J.Climate 授课教师：张洋 6
授课教师：张洋 6 Total atmosphere ocean Wunsch (2005), J. Climate Atmosphere Surface SW LW 动⼒输送 Simple energy balance climate models warming cooling cooling Ftop rad = 1 2⇡a2 cos @ @f()
Simple energy balance climate models Simplest models in which the interactions between SW radiation and dynamic heat transport can be considered. Assumptions are made below: One-dimensional,only latitude dependences are considered; Atmosphere Global energy budgets are assumed to be expressed in Tsur; Only annual mean conditions are considered; OT(x,t) 动力输送 solar radiation-infrared cooling Ot -divergence of heat flux x=sinΦ，whereΦis latitude. Surface aT(x,t) 1 a t 授课教师：张洋7
C @T(x, t) @t = Ftop rad 1 2⇡a2 @ @x f(x) 授课教师：张洋 7 Simple energy balance climate models n Simplest models in which the interactions between radiation and dynamic heat transport can be considered. n Assumptions are made below: n One-dimensional, only latitude dependences are considered; n Global energy budgets are assumed to be expressed in Tsur ; n Only annual mean conditions are considered; Atmosphere Surface SW LW 动⼒输送 x = sin , where is latitude. C @T(x, t) @t = solar radiation infrared cooling divergence of heat flux
Simple energy balance climate models C T(x,t) SW solar radiation-infrared cooling 8t -divergence of heat flux sin o,where o is latitude. Atmosphere solar radiation =Qs(x)A(T) s(x)-latitudinal distribution of SW,whose integral from 动力输送 the equator to pole is unity cOT(,t)=Qs()A(T)-I(T)+F(T) Ot In equilibrium, Surface Qs(x)A(T)-I(T)+F(T)-0 授课教师：张洋8
授课教师：张洋 8 Simple energy balance climate models Atmosphere Surface SW LW 动⼒输送 s(x) latitudinal distribution of SW, whose integral from the equator to pole is unity solar radiation = Qs(x)A(T) x = sin , where is latitude. C @T(x, t) @t = solar radiation infrared cooling divergence of heat flux In equilibrium, Qs(x)A(T) I(T) + F(T)=0 C @T(x, t) @t = Qs(x)A(T) I(T) + F(T)
Simple energy balance climate models In equilibrium, SW Qs(x)A(T)-I(T)+F(T)=0 ↓企 The snow line case: Atmosphere Made assumptions below: Planetary albedo is assumed to depend primarily on snow /ice cover; 动力输送 Surface A(T)= a, for TTsnow 授课教师：张洋9
授课教师：张洋 9 Simple energy balance climate models Atmosphere Surface SW LW 动⼒输送 In equilibrium, Qs(x)A(T) I(T) + F(T)=0 The snow line case: n Made assumptions below: n Planetary albedo is assumed to depend primarily on snow /ice cover; A(T) = ↵, for T Tsnow
Simple energy balance climate models In equilibrium, SW Qs(x)A(T)-I(T)+F(T)=0 ↓ The snow line case: Atmosphere Made assumptions below: Planetary albedo is assumed to depend primarily on snow /ice cover; 动力输送 The infrared cooling I=A+BT Surface A(T)= a, for TTsnow 授课教师：张洋10
授课教师：张洋 10 Simple energy balance climate models Atmosphere Surface SW LW 动⼒输送 In equilibrium, Qs(x)A(T) I(T) + F(T)=0 The snow line case: n Made assumptions below: n Planetary albedo is assumed to depend primarily on snow /ice cover; n The infrared cooling I = A + BT A(T) = ↵, for T Tsnow
Simple energy balance climate models In equilibrium, SW Qs(x)A(T)-I(T)+F(T)=0 ↓ The snow line case: Atmosphere Made assumptions below: Planetary albedo is assumed to depend primarily on snow /ice cover; 动力输送 The infrared cooling I=A+BT The primary feature of the heat transport is that it carries heat from warmer to colder regions.F(T)=C(T-T) Surface A(T)= for T Tsnow Note:F(T)is the or B, for T>Tsnow divergence of heat flux 授课教师：张洋11
A(T) = ↵, for T Tsnow 授课教师：张洋 11 Simple energy balance climate models Atmosphere Surface SW LW 动⼒输送 In equilibrium, Qs(x)A(T) I(T) + F(T)=0 The snow line case: n Made assumptions below: n Planetary albedo is assumed to depend primarily on snow /ice cover; n The n The primary feature of the heat transport is that it carries heat from warmer to colder regions. infrared cooling I = A + BT F(T) = C(T¯ T) Note: F(T) is the divergence of heat flux
Simple energy balance climate models In equilibrium, SW Qs(x)A(T)-I(T)+F(T)-0 ↓企 One-dimensional,only latitude dependences are considered; Atmosphere Global energy budgets are assumed to be expressed in Tsur Planetary albedo is assumed to depend primarily on snow /ice cover; 动力输送 Only annual mean conditions are considered; The primary feature of the heat transport is that it carries heat from warmer to colder regions. Surface Budyko,M.I.(1969).The effect of solar radiation variations on the climate of the earth.Tellus 21,611-619. 授课教师：张洋12
授课教师：张洋 12 Simple energy balance climate models Atmosphere Surface SW LW 动⼒输送 In equilibrium, Qs(x)A(T) I(T) + F(T)=0 Budyko, M.I. (1969). The effect of solar radiation variations on the climate of the earth. Tellus 21, 611-619. n One-dimensional, only latitude dependences are considered; n Global energy budgets are assumed to be expressed in Tsur ; n Planetary albedo is assumed to depend primarily on snow /ice cover; n Only annual mean conditions are considered; n The primary feature of the heat transport is that it carries heat from warmer to colder regions