A step-response approach for predicting and understanding non-linear precipitation changes

Abstract

Future changes in precipitation represent one of the most important and uncertain possible effects of future climate change. We demonstrate a new approach based on idealised CO₂ step-change general circulation model (GCM) experiments, and test it using the HadCM3 GCM. The approach has two purposes: to help understand GCM projections, and to build and test a fast simple model for precipitation projections under a wide range of forcing scenarios. Overall, we find that the CO₂ step experiments contain much information that is relevant to transient projections, but that is more easily extracted due to the idealised experimental design. We find that the temporary acceleration of global-mean precipitation in this GCM following CO₂ ramp-down cannot be fully explained simply using linear responses to CO₂ and temperature. A more complete explanation can be achieved with an additional term representing interaction between CO₂ and temperature effects. Energy budget analysis of this term is dominated by clear-sky outgoing long-wave radiation (CSOLR) and sensible heating, but cloud and short-wave terms also contribute. The dominant CSOLR interaction is attributable to increased CO₂ raising the mean emission level to colder altitudes, which reduces the rate of increase of OLR with warming. This behaviour can be reproduced by our simple model. On regional scales, we compare our approach with linear ‘pattern-scaling’ (scaling regional responses by global-mean temperature change). In regions where our model predicts linear change, pattern-scaling works equally well. In some regions, however, substantial deviations from linear scaling with global-mean temperature are found, and our simple model provides more accurate projections. The idealised experiments reveal a complex pattern of non-linear behaviour. There are likely to be a range of controlling physical mechanisms, different from those dominating the global-mean response, requiring focussed investigation for individual regions, and in other GCMs.

Appendices

Appendix 1

The coefficients (A, B and C) in Eq. 2 are derived simultaneously by least-squares regression using the multi-linear regression (Draper and Smith 1981) library routine in IDL. Three variables are supplied to the regression routine: ln(CO₂), T and ln(CO₂)T (David Stephenson, personal communication), along with the dependent variable (P). Data from the three step experiments (4x_step, 2x_step and 4x_1x_step) and the control run are combined together for the regression.

Results from the projections were withheld from the regression and used only for validation.

Appendix 2

Under the grey assumption (that optical depths do not vary with wavelength), the OLR flux F can be expressed as a function of an “effective emitting temperature” T_eff:

$$ F = \sigma T_{eff}^{4} $$

(15)

Differentiating and rearranging:

$$ \Updelta T_{eff} = \frac{{T_{eff} \Updelta F}}{4F} $$

Taking the OLR forcing from CO₂-doubling (ΔF) as around 4 W/m2, OLR (F) as 220 W/m² and T_eff as 220 K makes ΔT_eff, the cooling of the effective level of emission due to CO₂-doubling, around 1 K.

To get the change of dF/dT due to increased CO₂ (assuming that the effect of increased CO₂ is to raise the effective emission level to higher altitude and hence reduce T_eff), we differentiate again twice to give:

$$ \frac{\partial }{{\partial \ln ({\text{CO}}_{2} )}}\left( {\frac{\partial F}{\partial T}} \right) = \frac{12F}{{T_{eff}^{2} }}\frac{{\partial T_{eff} }}{{\partial \ln ({\text{CO}}_{2} )}} $$

Using the values of F and T_eff quoted above, the change of dF/dT due to CO2 doubling is around 0.05 W/m²/K.

According to our SCM fit, the 5–95 % CI of the change in dF/dT due to CO₂ doubling (Fig. 5c) is (0.125–0.175)·ln(2) = (0.08–0.12) W/m²/K.