Balance

Storyboard

In a state of equilibrium the energy captured from the sun must necessarily be equal to that which the earth itself emits returned to space. The first comes primarily as visible radiation, heats the planet and this in turn emits as infrared radiation via the atmosphere returned to space.

>Model

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Radiation balance model (D1+0)

Image

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![earth016](showImage.php)

earth016

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Equilibrio termodinámico

Condition

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En general el calor fluye desde los objetos de mayor temperatura a los de menor evolucionando asi las temperaturas de todos los elementos involucrados.

Si uno espera un tiempo suficiente los sistemas alcanzan un equilibrio térmico, es decir cada cuerpo esta recibiendo la misma cantidad de calor como entrega a su entrono. En esta situación las temperaturas permanecen constantes en el tiempo y se habla de que el sistema esta en equilibrio termodinámico.

ID:(9976, 0)



Energy balance of the planet\'s surface

Equation

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The Earth\'s surface receives energy from the sun $I_{ev}$ and from the lower part of the atmosphere $I_b$. All of this energy is radiated as $I_e$ and lost through convection and conduction $I_d$ with:

$ I_{ev} - I_e - I_d + I_b =0$

$I_d$
Energy transmitted by conduction and evaporation
$W/m^2$
$I_b$
Infrared Intensity emitted by the Bottom of the Atmosphere
$W/m^2$
$I_e$
NIR intensity emitted by the earth
$W/m^2$
$I_{ev}$
VIS intensity absorbed by the ground
$W/m^2$

ID:(4692, 0)



Energy balance of the planet\'s surface, detail

Equation

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Bajo condición con de

$$



la ecuación de balance con energy transmitted by conduction and evaporation $W/m^2$, infrared Intensity emitted by the Bottom of the Atmosphere $W/m^2$, nIR intensity emitted by the earth $W/m^2$ and vIS intensity absorbed by the ground $W/m^2$

$ I_{ev} - I_e - I_d + I_b =0$



se puede reescribir con la radiación VIS absorbida por la superficie con

$$



la radiación NIR recibida de la atmósfera con

$$



la perdida por calor latente y convección con



y la emisión NIR de la propia superficie con

$$



como con

$(1-a_e)(1-\gamma_v)I_s-(\kappa_l+\kappa_c(T_e-T_b))u-\sigma\epsilon T_e^4+\sigma\epsilon T_b^4=0$

ID:(4681, 0)



Energy balance of the lower part of the atmosphere

Equation

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The energy balance equation for the lower part of the atmosphere includes the acquisition of energy through convection and conduction, denoted as $I_d$, as well as the radiation from the Earth\'s surface $I_{esa}$ and from the upper part of the atmosphere $I_t$. All of this energy is subsequently radiated by the lower part of the atmosphere $I_b$ towards both the upper atmosphere and the Earth\'s surface:

$ I_d + I_{esa} -2 I_b + I_t =0$

$I_d$
Energy transmitted by conduction and evaporation
$W/m^2$
$I_b$
Infrared Intensity emitted by the Bottom of the Atmosphere
$W/m^2$
$I_t$
Infrared Intensity emitted by the Top of the Atmosphere
$W/m^2$
$I_{esa}$
NIR intensity emitted by the earth to the atmosphere
$W/m^2$

ID:(4693, 0)



Energy balance of the lower part of the atmosphere, detail

Equation

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Bajo condición con de

$$



la ecuación de balance con energy transmitted by conduction and evaporation $W/m^2$, infrared Intensity emitted by the Bottom of the Atmosphere $W/m^2$, infrared Intensity emitted by the Top of the Atmosphere $W/m^2$ and nIR intensity emitted by the earth to the atmosphere $W/m^2$

$ I_d + I_{esa} -2 I_b + I_t =0$



se puede reescribir con la energía del calor latente y convección recibida con



la radiación NIR recibida desde la superficie de la tierra con

$$



la radiación NIR recibida desde la atmósfera superior con

$$



y la radiación emitida tanto hacia la tierra como a la atmósfera superior con

$$



con como:

$( \kappa_l + \kappa_c ( T_e - T_b )) u -2 \sigma \epsilon T_b ^4+ \sigma \epsilon T_t ^4+(1- \gamma_i ) \sigma \epsilon T_e ^4=0$

ID:(4682, 0)



Energy balance of the upper part of the atmosphere

Equation

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The upper part of the atmosphere acquires energy through the absorption of solar energy $I_{sa}$ and from the lower part of the atmosphere $I_b$. Subsequently, this energy is radiated by the upper part $I_t$ both towards the lower part of the atmosphere and towards space:

$ I_{sa} + I_b -2 I_t =0$

$I_b$
Infrared Intensity emitted by the Bottom of the Atmosphere
$W/m^2$
$I_t$
Infrared Intensity emitted by the Top of the Atmosphere
$W/m^2$
$I_{sa}$
Radiation Absorbed by the Clouds
$W/m^2$

ID:(4694, 0)



Energy balance of the upper part of the atmosphere, detail

Equation

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Bajo condición con de

$$



la ecuación de balance con infrared Intensity emitted by the Bottom of the Atmosphere $W/m^2$, infrared Intensity emitted by the Top of the Atmosphere $W/m^2$ and radiation Absorbed by the Clouds $W/m^2$

$ I_{sa} + I_b -2 I_t =0$



se puede reescribir con la radiación VIS absorbida por la atmósfera con

$$



la radiación NIR recibida de la parte inferior de la atmósfera con

$$



y la radiación NIR emitida hacia la parte inferior y al espacio con

$$



como con

$(1-a_a)\gamma_vI_s+\sigma\epsilon T_b^4-2\sigma\epsilon T_t^4=0$

ID:(4683, 0)



Numerical solution

Php

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Las ecuaciones de balance radiativo

nos permiten calcular las temperaturas sobre la superficie de la tierra $T_e$, en la parte inferior de la atmosfera $T_b$ y en la parte superior $T_t$.

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