Theories of Monsoon Location• Plumb and Hou (1992), Emanuel (1995), Zheng (1998)

– Explained axisymmetric circulation induced by local subtropical forcing

• Rodwell and Hoskins (1995)– Rossby waves induce subsidence to the west of the

monsoon, creating east-west asymmetry• Xie and Saiki (1999)

– Hydrological feedbacks limit inland progression of the monsoon

• Chou, Neelin, and Su (2001)– Advection of low moist static energy air, hydrological

feedbacks, and Rodwell-Hoskins effect all limit poleward extent of the monsoon

Analytic theory from PH, Emanuel: this type of large scale circulation will occur if there is a strong enough local upper tropospheric temperature maximum in the subtropics. But given interactive nature of forcing in the monsoon area due to feedbacks between the flow, surface fluxes, radiation, etc, this does not tell us where the monsoon will occur.

Impact of local hb maximum over land

N

E W θv

Land

Ocean

Subcloud moist static energy, hb

S

Assume differential surface forcing over land/ocean results in subcloud h maximum over land - what circulation do we expect?Illustration of the math for a northern hemisphere case - in this diagram, subcloud h maximum results in two upper level jets, zero wind at the h maximum and easterlies equatorward of h maximum. Can be extrapolated easily to case with nonzero surface winds -subcloud h maximum coincides with region of zero shear of zonal wind throughout the troposphere.

Courtesy of Nikki Prive. Used with permission.

Resulting meridional circulation and precipitation

moist static energy

Poleward

So we need to determine and understand the distribution of h to understand the location of the monsoon.

Courtesy of Nikki Prive. Used with permission.

Factors that affect sb

• Surface heat fluxes

• Evaporation of precipitation in convective downdrafts

• Radiative cooling

• Entrainment at the top of the subcloud layer

• Advection by large-scale flow

Circulation may have a strong impact on the subcloud sbdistribution through these feedbacks.

Model Setup

THF0

∆THF

THF(φ) = LHF(TS)+ SHF(TS)THF(φ) =THF0 −∆THFsin2(φ −φ0)

NorthSouth

Over land, the surface forcing isdetermined by

16N

Use a simplified version of the atmospheric mitgcm to explore this further - we can limit the complicated feedbacks present in the real world. Use prescribed SST ocean, Newtonian cooling instead of radiation, but includes moist convection. Land coastline at 16N. Over land, the net surface heat flux is prescribed as a function of latitude as a proxy for net radiative forcing, latent and sensible heat fluxes and surface temp are interdependent. Use perpetual summer with a ‘mean summer’ distribution of forcing (ie not solstice) with maximum forcing near coastline. Run in channel 64N-64S. Start off with 2D model on latitude-height plane.

Courtesy of Nikki Prive. Used with permission.

2D Monsoon

Circulationkg/s

Zonal windm/s

1000 mb hJ/kg

Precipitationmm/day

Example of monsoonal case (THF_0 = 140) showing 100 day time mean fields for pure 2D model run (latitude-height plane). SST has max at 8N and decreases toward poles. Large cross-equatorial circulation with two ascent regions: monsoon 25-30N with precipitation peak, also ascent and peak near equator. Wind distribution - easterly jet in tropics - near zero wind good approximation for this case. 1000 mb moist static energy shows maximum at 30N (green line), which corresponds well with our theory.

Courtesy of Nikki Prive. Used with permission.

Monsoon Latitude

Shows location of monsoon precipitation maximum as a function of the strength of the surface forcing at the coastline. Although greatest surface fluxes are near coast, the monsoon moves poleward/inland with increasing surface forcing.

Courtesy of Nikki Prive. Used with permission.

Impact of flow on hb

Radiative convective equilibrium

In the presence of a meridional circulation

Why isn’t the monsoon located near the coastline, where the surface forcing is strongest? Top: Radiative convective equilibrium distribution of subcloud h: discontinuity at coastline due to forcing over land, then decreases poleward due to choice of forcing profile. When we introduce a large-scale circulation, oceanic low energy air is advected over the land. Flow travels inland and is heated by surface flux until it reaches RCE value, which is location of maximum. Far inland, RCE values are attained. Because of our choice of distribution of surface forcing (net radiative flux at surface), maximum subcloud h will occur where the inflowing air reaches the RCE value at that latitude.

Courtesy of Nikki Prive. Used with permission.

So what is going on with hb?

But why does the maximum move poleward with increased forcing? RCE energy increases over land, but not over ocean. Land heating is stronger but has to bring inflow to higher energy content. Mass flux by circulation also increases somewhat, advectingmore cool air from ocean, and with more mass to heat. Stronger forcing can’t compensate, so flow has to spend more time/travel further before reaching RCE moist static energy. Result: maximum occurs further inland, so circulation broadens and monsoon occurs further poleward.

Courtesy of Nikki Prive. Used with permission.

Expand to 3D

Now look at effect of eddies by expanding to 3D. Keep zonally uniform continental shape, ocean SST, and land forcing distribution so we can compare with 2D results.

Courtesy of Nikki Prive. Used with permission.

3D Monsoon

Circulationkg/s

Zonal windm/s

1000 mb hJ/kg

precipitationmm/day

100 day mean flow for monsoonal case with same forcing as previous figure (140 W/m^2). Large scale circulation very similar to 2D. Upper level jets are a little weaker, which is expected due to momentum transport by eddies. Double peaked precip with monsoon rain max around 22N; h maximum at 26N. Quite similar to case in 2D.

Courtesy of Nikki Prive. Used with permission.

1000 mb winds and precipitation

11 m/s

100 day mean field of 1000 mb wind and precipitation for 3D case (same as previous slide); red line indicates coastline. Flow and precipitation fields fairly symmetric (also true if you look at snapshots instead of time mean).

Courtesy of Nikki Prive. Used with permission.

Monsoon Latitude: 2D vs 3D

Comparison of location of zonal mean monsoon precipitation maximum for 2D and 3D case. 3D monsoon is closer to the coastline than 2D case for the same surface forcing. Why?

Courtesy of Nikki Prive. Used with permission.

Impact of eddies on subcloudh

Top: Red line illustrates h in RCE state as before. Eddies are going to try to smooth out this curve, shown with yellow line. So h would be raised poleward and decreased near the coast. Bottom: Inflow only needs to reach the smoothed RCE curve, with same land forcing this will occur closer to coastline.

Courtesy of Nikki Prive. Used with permission.

Introduce continental asymmetry

Introduce large scale asymmetry of forcing by restricting continent to 180 degrees.

Courtesy of Nikki Prive. Used with permission.

What happened to the monsoon?

11 m/s

100 day mean field of wind and precipitation for same forcing as previously shown cases (140). Very little precipitation over subtropical continent except for far southeastern corner and midlatitudes. No deep ascent over subtropical continent. What happened?

Courtesy of Nikki Prive. Used with permission.

Impact of advection of low hb air

11 m/s

Top shows birdseye view of 1000 mb wind and moist static energy (units of J/kg?). Bottom shows zonal mean h over land only. Now maximum in h occurs near (or slightly equatorard) of coastline instead of over land. Westerly flow carries air from cool midlatitudeoceans over continent, suppressing convection. From our theory, we don’t expect to see a monsoon over land with this h profile.

Courtesy of Nikki Prive. Used with permission.

Comparison hb distribution

11 m/s

For comparison, the 1000 mb h distribution for the case with zonally symmetric continent is shown - high valvues of h even far poleward, weak gradient of h over land.

Courtesy of Nikki Prive. Used with permission.

Subcloud hb with warm ocean

3 m/s

Explore this further with a case with warm ocean set to 302K at all latitudes. Without source of low h air, maximum occurs over land.

Courtesy of Nikki Prive. Used with permission.

Remove the source of low hb…

3 m/s

For warm ocean case, precipitation field over land which is not dissimilar from case with global continent. Easterly flow in SE corner does dampen out h a little, less precip than over rest of continent. Mention Chou, Neelin, Su (2001) - also found advection of low moist statuc energy air (they called it ventilation) to limit the poleward extent of the monsoon using the quasi-equilibrium tropical model, this adds support for their work using a gcm.

Courtesy of Nikki Prive. Used with permission.

Extension of Held-Hou to 3 Dimensions

Assume geostrophic balance:

*

1 ˆ2 sin

1 ˆ *2 sin

p

ps

kp

T k sp

αθ

θ

∂= − ×∇

∂ Ω

⎛ ⎞∂= − ×∇⎜ ⎟Ω ∂⎝ ⎠

V

Integrate upward, taking V=0 at surface:

( )1 ˆ2 sinT s T bT T k s

θ= − ×∇

ΩV

Demand that absolute vorticity at tropopause have the same sign as f:

( )2 1sin 4 sin 0sin s T bT T sθ θ

θ Ω +∇ − ∇ ≥

i