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ID:(1633, 0)

Description

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To study the transfer of CO2 at the ocean surface, it is necessary to carefully observe the concentration changes in both the air and the water.

In the air, CO2 enters the water, creating a zone of low concentration where it decreases from $C_a$ to $C_{a,0}$. This layer has a thickness ranging from 0.1 to 1 mm.

The CO2 that enters the water initially accumulates at the surface, creating a concentration $C_{w,0}$, which then diffuses into the interior, reaching a lower concentration of $C_w$.

The concentration reduction allows us to define two zones: a very thin one, ranging from 0.02 to 0.2 mm, where the concentration decreases rapidly, and a second zone, spanning from 0.6 to 2 mm, where the concentration decreases more gradually until it reaches the concentration within the water.

Ocean-Atmosphere Interactions of Gases and Particles, Peter S. Liss, Martin T. Johnson (eds.), Springer-Verlag Berlin Heidelberg

ID:(12244, 0)

Equation

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The concentration jump between the air concentration $C_{a,0}$ and the water concentration $C_{w,0}$ depends on the solubility of the gas, $\alpha$. Therefore, we have the following relationship:

$ C_{w,0} = \alpha C_{a,0} $

Conditions

Variables

$\alpha$

Coeficiente flujo CO2 agua a aire

$1/J$

$C_w$

Concentración del CO2 en el agua

$1/m^3$

$C_a$

Concentración del CO2 en el aire

$1/m^3$

Relation

ID:(12235, 0)

Equation

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If we consider Fick\'s law:

we recognize that the term

$\displaystyle\frac{D}{dx}$

corresponds to a transfer velocity. Therefore, we have:

$ k_a = \displaystyle\frac{ D }{ \delta }$

Conditions

Variables

$D$

Constante de difusión en masa acuosa

$m^2/s$

$\delta_c$

Grosor de la capa superficial

$m$

$k_u$

Velocidad de transferencia aire a agua de CO2

$m/s$

Relation

ID:(12227, 0)

Equation

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The transport velocity of the gas, denoted as kw, can be modeled based on measured data. Firstly, it depends on the rate at which the system removes carbon from the air-water interface, making the transport velocity proportional to the relative velocity between the two mediums.

Secondly, there is an effect of ion mobility, which can be described by the Schmidt number, representing the ratio of momentum diffusion to particle diffusion. However, this dependence is non-linear and influenced by a factor n ranging between -1/2 and -2/3, depending on the surface roughness.

Lastly, the transport velocity also depends on a constant that, in turn, is determined by the level of surface roughness.

Taken together, the gas transport velocity kw can be described as follows:

$ k_w = u_* \beta Sc ^ n $

Conditions

Variables

$n$

Exponente de Schmidt

$-$

$\beta$

Factor beta del transporte aire a agua de CO2

$-$

$Sc$

Numero de Schmidt

$-$

$k_u$

Velocidad de transferencia aire a agua de CO2

$m/s$

$u_a$

Velocidad del aire

$m/s$

Relation

ID:(12215, 0)

Equation

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The resistance to CO2 diffusion in the atmosphere is defined as the inverse of the transfer velocity in that medium. This can be expressed as follows:

$ R_a = \displaystyle\frac{1}{ k_a } $

Conditions

Variables

$R_a$

Resistencia en aire CO2

$s/m$

$k_u$

Velocidad de transferencia aire a agua de CO2

$m/s$

Relation

ID:(12236, 0)

Equation

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The resistance to CO2 diffusion in the ocean is defined as the inverse of the transfer velocity in that medium. This can be expressed as follows:

$ R_w = \displaystyle\frac{1}{ k_w } $

Conditions

Variables

$R_w$

Resistencia en agua CO2

$s/m$

$k_w$

Velocidad de transferencia agua aire de CO2

$m/s$

Relation

ID:(12237, 0)

Equation

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The resistance to CO2 diffusion from the atmosphere to the ocean is defined as the inverse of the transfer velocity of the system. This can be expressed as follows:

$ R_{tw} = \displaystyle\frac{1}{ k_{tw} } $

Conditions

Variables

$R_{tw}$

Resistencia de transferencia agua a aire de CO2

$s/m$

$k_{tw}$

Velocidad de transferencia total agua aire de CO2

$m/s$

Relation

ID:(12238, 0)

Equation

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The resistance to CO2 diffusion from the ocean to the atmosphere is defined as the inverse of the transfer velocity of the system. This can be expressed as follows:

$ R_{ta} = \displaystyle\frac{1}{ k_{ta} } $

Conditions

Variables

$R_{ta}$

Resistencia de transferencia aire a agua de CO2

$s/m$

$k_{ta}$

Velocidad de transferencia total aire a agua de CO2

$m/s$

Relation

ID:(12239, 0)

Equation

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The total resistance for the case of the atmosphere and the ocean includes first the resistance of the water $R_w$, then the evaporation $1/\alpha$, and once CO2 has passed into the air, the resistance of the water $R_a$ itself.

$ R_{ta} = R_a + \displaystyle\frac{1}{ \alpha } R_w $

Conditions

Variables

$\alpha$

Coeficiente flujo CO2 agua a aire

$1/J$

$R_{ta}$

Resistencia de transferencia aire a agua de CO2

$s/m$

$R_w$

Resistencia en agua CO2

$s/m$

$R_a$

Resistencia en aire CO2

$s/m$

Relation

ID:(12240, 0)

Equation

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The total resistance for the atmosphere-ocean case includes, first, the resistance of the air $R_a$, then the solubility $\alpha$, and once the CO2 has penetrated into the water, the resistance of the water $R_w$ itself.

$ R_{tw} = R_w + \alpha R_a $

Conditions

Variables

$\alpha$

Coeficiente flujo CO2 agua a aire

$1/J$

$R_{tw}$

Resistencia de transferencia agua a aire de CO2

$s/m$

$R_w$

Resistencia en agua CO2

$s/m$

$R_a$

Resistencia en aire CO2

$s/m$

Relation

ID:(12241, 0)

Equation

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The relationship between the transfer resistance between the atmosphere and the ocean can be written in terms of the transfer velocities in both media as the inverse of the total transfer velocity.

$ \displaystyle\frac{1}{ k_{tw} } = \displaystyle\frac{1}{ k_w } + \displaystyle\frac{ \alpha }{ k_a } $

Conditions

Variables

$\alpha$

Coeficiente flujo CO2 agua a aire

$1/J$

$k_w$

Velocidad de transferencia agua aire de CO2

$m/s$

$k_u$

Velocidad de transferencia aire a agua de CO2

$m/s$

$k_{tw}$

Velocidad de transferencia total agua aire de CO2

$m/s$

Relation

Development

The relationship between the transfer resistance between the atmosphere and the ocean, given by the sum

$ R_{tw} = R_w + \alpha R_a $

with the resistance in the atmosphere

$ R_a = \displaystyle\frac{1}{ k_a } $

and the resistance in the ocean

$ R_w = \displaystyle\frac{1}{ k_w } $

provides us with the relationship for the total transfer velocity from the atmosphere to the ocean:

$ \displaystyle\frac{1}{ k_{tw} } = \displaystyle\frac{1}{ k_w } + \displaystyle\frac{ \alpha }{ k_a } $

where $k_{tw}$ represents the total transfer velocity.

ID:(12243, 0)

Equation

>Top, >Model

The relationship between the transfer resistance between the ocean and the atmosphere can be expressed in terms of the transfer velocities in both media as the inverse of the total transfer velocity.

$ \displaystyle\frac{1}{ k_{ta} } = \displaystyle\frac{1}{ k_a } + \displaystyle\frac{1}{ \alpha k_w } $

Conditions

Variables

$\alpha$

Coeficiente flujo CO2 agua a aire

$1/J$

$k_w$

Velocidad de transferencia agua aire de CO2

$m/s$

$k_u$

Velocidad de transferencia aire a agua de CO2

$m/s$

$k_{ta}$

Velocidad de transferencia total aire a agua de CO2

$m/s$

Relation

Development

The relationship between the transfer resistance between the atmosphere and the ocean, given by the sum

$ R_{ta} = R_a + \displaystyle\frac{1}{ \alpha } R_w $

with the resistance in the atmosphere

$ R_a = \displaystyle\frac{1}{ k_a } $

and the resistance in the ocean

$ R_w = \displaystyle\frac{1}{ k_w } $

provides us with the relationship for the total transfer velocity from the atmosphere to the ocean:

$ \displaystyle\frac{1}{ k_{ta} } = \displaystyle\frac{1}{ k_a } + \displaystyle\frac{1}{ \alpha k_w } $

ID:(12242, 0)