Impacts of the global distribution of precipitation on

Impacts of the global distribution of precipitation on the propagation of convectively coupled waves. Olivier Pauluis Juliana Dias � Center for Atmosphere-Ocean Science Courant Institute Thanks to Dargan Frierson Boualem Khouider Andy Majda Sam Stechman Banff, Canada

Outline • Introduction • Equatorial Kelvin wave propagating along a narrow ITCZ • Reflection and transmission of convectively coupled waves

Observations (Wheeler and Kiladis, JAS 1999) indicate Two distinct propagation speed: - a fast (~40 -50 m/s) dry mode - a slower (~15 m/s) coupled convective-gravity

Coupled convective-gravity waves • Convection is more intense in regions of large-scale ascent. è Latent heat release partially compensates for the adiabatic cooling. è Convection slows down the propagation of ‘coupled convective gravity waves’. 1000’s km

• But convective activity is not uniform in the tropics. There are regions of intense precipitation (warm pool, ITCZ) next to regions with little or not precipitation • How does this affect the propagation of convectively coupled waves?

Convectively coupled waves propagating along an equatorial ITCZ Equatorial Kelvin wave Equator

Idealized model U: barotropic wind U: baroclinic wind T: temperature q: humidity P: precipitation rate ‘Quasi-equilibrium’ closure:

• Statvionary solution: a Hadley-like zonally symmetric circulation is obtained the evaporation. Two control parameters allows us to control the location and width of the precipitation region

Analytic solution: • Solve for a small perturbation, e. g. • The perturbation obeys the linear shallow water equation:

Dry region Moist Region Dry region c=cd c=cm c=cd

• Matching condition: in addition, one must specified the matching condition at the interface. • The precipitation front theory (FMP 2004, PFM 2008) indicates that the solution should remain smooth, I. e the perturbation must be equal on both side of the interface. • Solutions involve both parabolic cylinder functions and confluent hypergeometric functions…

Dispersion relationship for Kelvin and Rossby waves:

Longitude-time diagram of Kelvin wave coupled with equatorial convection Colour: Tb Contour: u k=6 -8 P=4 -6 days S=10 -17 m/s Non-dispersive CT: 7 days CT: 10 days (From Yang et al. 2007)

Kelvin wave on an equatorial ITCZ

Kelvin wave on an off-equatorial ITCZ

And in the observations… (fig. from Kiladis et al. 2009)

Meridional circulation in the Kelvin wave High precip Cold c=cd Warm c=cd Low level westerlies Low level easterlies

The perturbation moves slowly within the ITCZ, where it is slowed by interactions with convection ITCZ But moves more rapidly in the dry region

We have now developed sharp temperature gradient at the interface! ITCZ This generates a secondary circulation

Warming Cooling The secondary circulation is associated with additional subsidence warming and adiabatic cooling

This pattern of cooling and warming acts to push the perturbation backward (westward) the perturbation in the dry regions, and to push it forward (eastward) in the moist regions The end result is a coherent wave that moves at a speed in between the dry and moist propagation speed. The merdional circulation plays a key role in maintaining the cohesion between the dry and moist regions.

Cold Warm The meridional circulation enhances the convergence in the ITCZ. This increases the precipitation and slows down the propagation of the disturbance.

Velocity scaling ‘Scaling 1’ assumes precipitation in the ITCZ is due to zonal flow alone ‘Scaling 2’ accounts for the additional precipitation due to the secondary meridional circulation Analytic solution

In the dry regions, water vapor and temperature are negatively correlated. High precip moist dry This implies that the ITCZ is widest after the period of maximum precipitation. Or alternatively, that high precipitation is associated with an expansion of the ITCZ.

Interactions of equatorial wave and idealized Walker circulation • Motivation: dry and moist regions can be viewed has having different refraction indices for gravity waves. From classic optic, a wave propagating from one region to another will thus be partially reflected and partially transmitted.

Reflection and transmission of convectively coupled gravity waves in 1 -D (Pauluis, Majda and Frierson, 2008) Zonal wind perturbation Moist region

Zonal wind perturbation Moist region

• And in 2 D? Precipitation front Incident moist Kelvin wave Reflected moist Rosby wave Equator Incident moist Kelvin wave

Y(1000 km) Q P u v X(1000 km)

Y (1000 km) 1 st Rossby mode - Zonal wind perturbation X(1000 km)

Time (days) 1 st Rossby mode - Zonal wind perturbation at 0 S X(1000 km)

Y (1000 km) 2 nd Rossby mode - meridional wind perturbation X(1000 km)

Time (days) 2 nd Rossby mode - Meridional wind perturbation at 0 S X(1000 km)

Y (1000 km) Equatorial Kelvin Wave - Zonal wind perturbation X(1000 km)

Time (days) Equatorial Kelvin Wave - Zonal wind perturbation at 0 S X(1000 km)

Y (1000 km) Equatorial Kelvin Wave - Humidity perturbation X(1000 km)

Time (days) Equatorial Kelvin Wave - Humidity perturbation at 0 S X(1000 km)

Conclusion • Variations of convective activity has very strong impact on the propagation of equatorial disturbance. • Convectively coupled wave can be supported by a relatively narrow ITCZ. • Kelvin wave on a narrow ITCZ show some important difference from the traditional Betaplane case, including a marked meridional circulation. • Theoretical possibility of partial reflection of Rossby and Kelvin waves by the precipitaion boundary

Dry and moist waves • In the absence of precipitation (P=0) the model has 3 characteristcis: – 2 gravity waves moving at speed cd relative to the flow and – a ‘moisture trace’ advected by the barotropic flow. • In the precipitation regions, the convectively coupled modes propagate at a lower speed cm: