Predicted and Observed Histograms of Free Tropospheric

Water vapor

Steven Sherwood, Yale UniversityRobert Kursinski, JPL

William Read, JPL(Also thks to A. Dessler)

CGU/AGU 05/2004

Water vapor feedback

• GCM’s show RH distributions not changing much as climate warms --> positive WVF

• Can we trust them? Why do they do this?

The “cold trap” model of Relative Humidity

1. Water vapor near saturation in small moist convective regions;

2. Water vapor mixing ratio conserved as air leaves;

3. Dynamics maintains constant (small) difference between temperatures in convective and elsewhere;

4. Horizontal extent and organization of convective regions, RH within, and transport therefrom are known (…??)

QuickTime™ and aNone decompressor

are needed to see this picture.

Simulation of vapor from known dynamics

Pierrehumbert and Roca,1998.

(See also Sherwood 1996;Salathe and Hartmann 1997)

Stochastic implementation

€

dqsdt

= qswΓ

RvT2

⎛

⎝ ⎜

⎞

⎠ ⎟

q

qs= RH ≈ RH0e

−t /τ dry ,

τ dry =RvT

2

wΓ

From Clausius Clapeyron eq:

Integrated through time:

dry is a few days.

This gives RH as a function of parcel “age” t. Parcels age until swept intoanother convective system, where t is reset to zero.

If we additionally suppose remoistening is a Poisson process, then

€

Pt (t) = τ moist−1 e

−tτ moist

Which finally gives

€

PRH (RH)∝ RHτ dry

τ moist−1

,RH < RH0

Observed distributions

• Upper troposphere: MLS (UARS) v4.9 retrievals from 450-150 hPa (FY 1993)– 3 km resolution, microwave limb emission– Partial cloud penetration

• Lower+middle troposphere: GPS (CHAMP) occulations (O ‘91, JAJ ‘92)– 200 m resolution, radio refraction– Full cloud penetration– Diffraction-corrected (C. Ao, R. Mastaler)– These data are preliminary!!

Predicted vs. observed distribution (MLS, 30S-30N) of RH

RH0

Cloudcontamination

Predicted vs. observed distribution (GPS, 30S-30N) of RH

RH0

Eulerian implementation (II)

• Prefer theory that predicts RH0, ratio, and vs. height, and that accounts for convective ceiling.

• Energy + mass conservation constrain dry

• A simple, 2-parameter model gets 3/4!:– Simple overturning circulation in energy balance– Precipitation efficiency and/or mixing constant in

convective region– Horizontal mixing constant– Still have to prescribe but results not sensitive to it.

GPS MLS

EULERIAN MODEL

Horizontal mixing rate

Mic

roph

ysic

al p

aram

eter

RH mean

RH range

Model sensitivity

Conclusions

• A comprehensible model of relative humidity does exist

• It explains observations of very dry air, convergent histograms, bimodality, and RH min at 400 hPa indicated by MLS and GPS data

• It predicts that RH distributions are not very sensitive to cloud microphysical effects, but are somewhat sensitive to how frequently air parcels encounter convection

• Further tests of the theory are needed