JuMee Ryoo, Darryn Waugh, Takeru Igusa

1
PDFs of Tropical Tropospheric Humidity
Measurements and Theory
Ju-Mee Ryoo, Darryn Waugh, Takeru Igusa Johns
Hopkins University Correspondence
jryoo1_at_jhu.edu waugh_at_jhu.edu
Introduction
Spatial variation in r and k
Generalized model parameters

• Since water vapor is the main greenhouse gas, it
  is important to know its spatial distribution and
  the processes behind this distribution.
• Here we examine the PDFs of tropospheric relative
  humidity (RH) for measurements from MLS and AIRS,
  and show that the observed PDFs can be reproduced
  by a simple theoretical model.

Non-convective Region Small r slow
remoistening Large k less randomness
Convective Region Large r rapid
remoistening Small k more randomness

• Variations in r and k characterize variations
  in the moistening processes.
• The maps of µR and sR show a strong resemblance
  to those of r and k, respectively, i.e., there is
  large µR where r is large and large sR where k is
  small.

AIRS RH 250 hPa
Generalized model parameters
r
k
PDFs of AIRS RH
Aura MLS PDFs
subtropics
PDFs of daily 215 hPa RH for several subregions
from Aura MLS data (symbol)
tropics
western Pacific (120E-140E)
k
east Asia (40E-60E)
eastern Pacific (260E-280E)

• PDFs of RH show a large variation between
  different subregions.

Aura MLS RH 215 hPa
µR
sR
a
b
c
r µR k 1/ (sR) 2
a
µR
f
e
d
eastern Pacific (260E-280E)
east Asia (40E-60E)
Aura MLS RH (Read et al. 2007), 215 hPa, 2005
2007, DJF
western Pacific (120E-140E)
sR
a
Tropics (5S-5N)
Comparison between MLS and AIRS
Theoretical Models
Subtropics (15N-25N)
a
PDFs for 3 subregions in the (a) subtropics
(15?N-25?N) and (b) tropics (5?S-5?N) for
different data set in DJF.

Basic Assumptions
Subtropics (15N-25N)

• Good agreement between different data sets
  except the tropical convective regions (5S-5N,
  120E-140E) where the PDFs from MLS are much
  broader than those from AIRS.

• Moistening by random events
• Uniform subsidence (water is conserved)

• t age (time) of Parcel since Last saturation

• In tropical dry non-convective regions, the
  range of PDFs are similar, but the peak values
  are slightly different.

Tropics (5S-5N)

• UARS MLS RH (Read et al. 2001), 215 hPa,
  1992-1994, DJF
• Aura MLS RH (Read et al. 2007), 215 hPa,
  2005-2007, DJF

Generalized version of S06 Model
Sherwood et al. (2006) Model (S06 Model)
Given uniform subsidence, RH can be approximated
as
Longitudinal variation (a, c) r, and (b, d) k for
generalized model fit to Aura MLS, UARS MLS, and
AIRS measurements.
Time since last saturation is modeled as time
between random moistening events
Time since last saturation is now modeled as
random moistening events but includes randomness
of these events (k).

• Good agreement between different data sets in
  terms of r and k.

• The general tendency of variation of k is that
  the k is larger from AIRS than MLS.

Eliminate t from above equations, yields the PDFs
of RH as
Eliminate t from above equations, yields the
generalized PDFs of RH as

• Small r (rlt1) and large k in dry regions in
  subtropics and tropical eastern Pacific.
• Large r (rgt1) and small k in tropical
  convective regions.

• Largest disagreement of k occurs in tropical
  convective regions.

where,
where,
Gamma function
is the uniform drying time by
subsidence is the time between remoistening
events.
r ratio of drying time ( ) to moistening
time ( ) k measure of randomness of
remoistening events
Generalized PDFs of RH reduces to the original
S06 distributions when k1
Conclusions
Comparison of MLS with Models

• Data can be well fit by a two parameter
  generalization of the Sherwood et al. (2006)
  model.
• The parameter r and k not only provide a simple
  way to characterize the RH distributions, but
  also provide insight into the processes
  controlling on the RH distributions.

PDFs
Large r, small k in tropical convective regions
rapid, random vertical mixing Small r,
large k in dry regions slow, more
regular lateral mixing

• Generalized model closely matches the observed
  PDFs and Cumulative Distribution Functions
  (CDFs).
• The generalized model can fit the data for all
  subregions.
• Note that the generalized model can reproduce
  some important features such as the peak, range
  and skewness of the PDF at RH.

(a) PDFs and (b) CDFs of 215 hPa RH in NH winter
(DJF) for whole tropics (30S-30N) from Aura MLS
data (symbol), fits by S06(dotted) and
generalized (solid) models.
(a)

• A more quantitative link between the different
  physical processes and the parameters r and k is
  needed. This would be performed by
  trajectory-based water vapor simulations.

(b)
Acknowledgement
In the whole tropics and tropical convective
region, AIRS PDFs show better match with model.
This work was supported by grants from NASA and
NSF. We thank Andrew Gettelman for providing the
gridded AIRS data, and Eric Fetzer, Annmarie
Eldering, Bill Read, and Steve Sherwood for
helpful conversations and advice.
References
PDFs for Tropics (5S-5N,120E-140E)
PDFs for subtropics (15-25N,120E-140E)
Fetzer, E., and Coauthors, 2003 Validation of
AIRS/AMSU/HSB core products for Data Release
Version 3.0, JPL D-26538. Read, W. G., and
Coauthors, 2001 UARS Microwave Limb Sounder
upper tropospheric humidity measurement Method
and validation, J. Geophys. Res., 106,
32,207-32,258. Read, W. G., and Coauthors, 2007
Aura Microwave Limb Sounder upper tropospheric
and lower stratospheric H2O and relative humidity
with respect to ice validation, J. Geophys. Res.,
112, D24S35, doi10.1029/2007JD008752. Ryoo,
J.-M., T. Igusa, and D. W. Waugh, 2008 PDFs of
Tropical Tropospheric Humidity Measurements and
Theory, Submitted to J. Climate (in
review). Sherwood, S. C., E. R. Kursinski, W. G.
Read, 2006 A distribution law for free
tropospheric relative humidity, J. Climate, 19,
6267-6277.
PDFs for Tropics (5S-5N,120E-140E) from AIRS
PDFs for whole Tropics (30S-30N,0E-360E) from
AIRS
Cf)