Introduction to climate dynamics and climate modelling - Water vapour and lapse rate feedbacks

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4.2.1 Water vapour and lapse rate feedbacks

According to the Clausius-Clapeyron equation, the saturation vapour pressure and the specific humidity at saturation are quasi-exponential functions of temperature. Furthermore, observations and numerical experiments consistently show that the relative humidity tends to remain more or less constant in response to climate change. A warming thus produces a significant increase in the amount of water vapour in the atmosphere. As water vapour is an efficient greenhouse gas, this will lead to a strong positive feedback (Fig. 4.9). The radiative effect of the water vapour is roughly proportional to the logarithm of its concentration, and so the influence of an increase in water-vapour content is larger in places where its concentration is relatively low in unperturbed conditions, such as in the upper troposphere (see section 1.2.1).

The most recent estimates provide a value of $λ$ _W of around 1.8 Wm^-2K^-1 (Soden and Held, 2006). This means that, in the absence of any other feedback, the surface temperature change due to a perturbation would be about 2.3 times as large as the blackbody response (see Eq. 4.11) because of this amplification associated with the water-vapour. This makes the water vapour feedback the largest of all the direct physical feedbacks.

**Figure 4.9:** Simplified signal flow graph illustrating the water vapour feedback. A positive sign on an arrow means that the sign of the change remains the same when moving from the variable on the left of the arrow to the one on the right while a negative sign implies that an increase (decrease) in one variable induces a decrease (increase) in Next one. The positive sign in a circle indicates that the overall feedback is positive.

The vertical variations of the temperature change also have a climatic effect through the lapse-rate feedback $λ$ _L. For instance, the models predict enhanced warming in the upper troposphere of tropical regions in response to an increase in the concentration of greenhouse gases. Because of this change in the lapse rate, the outgoing longwave radiation will be more than in an homogenous temperature change over the vertical. The system will then lose more energy, so inducing a negative feedback (Fig. 4.10). Moreover, at mid to high latitudes, a larger low level warming is projected as a response to the positive radiative warming, providing a positive feedback (Fig. 4.10). The global mean value of $λ$ _L thus depends on the relative magnitude of those two opposite effects. On average, the influence of the tropics dominates, leading to a value of $λ$ _L of around -0.8 Wm^-2K^-1 (Soden and Held, 2006) in recent models driven by a doubling of the CO₂ concentration in the atmosphere.

**Figure 4.10:** Schematic representation of positive and negative lapse-rate feedbacks.

The water-vapour feedback and the lapse-rate feedback can combine their effects. If the temperature increases more in the upper troposphere causing a negative lapse-rate feedback, the warming will also be associated with higher concentrations of water vapour in a region where it has a large radiative impact, leading to an additional positive water-vapour feedback. The exact changes in temperature and humidity at high altitude in response to a perturbation are not well-known. However, as the effects of the two feedbacks discussed in this sub-section tend to compensate each other, the uncertainty in the sum $λ$ _L + $λ$ _W is smaller than in the feedbacks individually. This uncertainty is estimated at about 0.1 Wm^-2K^-1, the standard deviation of the values provided by the different models presented in the 4th IPCC assessment report (Randall et al., 2007).