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Using GPS RO to determine the probability density of free tropospheric relative humidity

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Using GPS RO to determine the probability density of free tropospheric relative humidity and constrain how it is controlled E. R. Kursinski1, S. Sherwood2, W. Read3 – PowerPoint PPT presentation

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Title: Using GPS RO to determine the probability density of free tropospheric relative humidity


1
Using GPS RO to determine the probability density
of free tropospheric relative humidity and
constrain how it is controlled E. R.
Kursinski1, S. Sherwood2, W. Read3 1University
of Arizona, 2Yale, 3JPL
GPS Conference August 2005
2
Outline
  • Motivation
  • Accuracy of relative humidity from GPS RO
  • Improving the RH estimates via deconvolution of
    errors
  • Evaluation of simple RH distribution model
  • Stochastic model explanation
  • GPS MLS comparisons with model
  • Single cell model
  • Summary and conclusions

3
Motivation for Moisture Observations
  • Water is crucial to energy transport and
    circulation within the Earth weather and climate
    system through latent heat exchange
  • Precipitation largely controls the extent and
    type of continental biosphere
  • Water vapor is the most important greenhouse gas
    important throughout the troposphere and into the
    stratosphere
  • Clouds strongly affect the radiation budget
    through reflection scattering of shortwave
    radiation and emission and absorption of IR
  • Water cools the surface in the form of clouds in
    daytime, warms the surface through the greenhouse
    effect as both a gas and as clouds and cools the
    surface via evaporative cooling

4
Motivation Evaluation of a Simple Model
  • The tropics are where the magnitude and sign
    water vapor feedback is generally believed to be
    the most uncertain
  • We want as simple as possible an explanation of
    how the water vapor distribution is controlled in
    the tropics
  • Steve Sherwood has proposed a very simple model
  • We evaluate it using GPS and MLS relative
    humidity observations

5
Testing a simple relative humidity model with
observations
  • Model evaluation requires
  • Relative humidity histograms to establish how
    frequently each relative humidity range occur in
    free troposphere
  • Global water vapor observations with good
    vertical resolution independent of conditions
    (especially clouds).
  • Inadequate observations
  • Global analyses Unknown model humidity biases
  • Radiosondes Poor spatial sampling, biases
  • IR sounders Unknown biases associated with
    clouds
  • Nadir passive microwave Inadequate vertical
    resolution
  • Best available observations
  • GPS RO Good for 2 to 9 km alt. in tropics
  • MLS Good in upper troposphere, some sensitivity
    to clouds

6
GPS - ECMWF Specific Humidity Profile Comparisons
GPS (solid), ECMWF (dotted), saturation (dashed)
from July 2001 (g/kg)
7
Subtropical Moisture Estimates
OLR
  • GPS ECMWF comparison July 1995 10oS-25oS

Mean
Mode
8
Deriving Relative Humidity from GPS RO
  • Two basic approaches
  • Direct method use N T profiles and hydrostatic
    B.C.
  • Variational method use N, T q profiles and
    hydrostatic B.C. with error covariances to update
    estimates of T, q and P.
  • Direct Method
  • Theoretically less accurate than variational
    approach
  • Simple error model
  • (largely) insensitive to NWP model humidity
    errors
  • Variational Method
  • Theoretically more accurate than simple method
    because of inclusion of apriori moisture
    information
  • Sensitive to unknown model humidity errors and
    biases
  • Since we are evaluating a model we want water
    vapor estimates as independent as possible from
    models
  • gt We use the Direct Method

9
Direct Method Solving for water vapor given N
T
(1)
  • Use temperature from a global analysis
    interpolated to the occultation location
  • To solve for P and Pw given N and T, use
    constraints of hydrostatic equilibrium and ideal
    gas laws and one boundary condition

Solve for P by combining the hydrostatic and
ideal gas laws and assuming temperature varies
linearly across each height interval, i
(2)
where z height, g gravitation
acceleration, m mean molecular mass of moist
air T temperature R universal gas constant
10
Solving for water vapor given N T
  • Given knowledge of T(h) and pressure at some
    height for a boundary condition, then (1) and (2)
    are solved iteratively as follows
  • 1) Assume Pw(h) 0 or 50 RH for a first guess
  • 2) Estimate P(h) via
  • 3) Use P(h) and T(h) in (1) to update Pw(h)
  • 4) Repeat steps 2 and 3 until convergence.

11
Solving for Water Vapor given N T
  • To produce consistent statistics for the latitude
    versus height histograms, we begin all of the
    water vapor profiles in a given lat-hgt bin at
    the same height determined as the height where
    the average profile temperature first exceeds 240
    K
  • Relative humidity U e/es(T) is calculated for
    each profile with the saturation vapor pressure
    over liquid used above freezing temperature and
    over ice below the freezing temperature.

12
Estimating GPS water vapor error
  • The error in relative humidity, U, due to changes
    in refractivity (N), temperature (T) and pressure
    (P) from GPS is

where L is the latent heat and Bs a1TP / a2es.
  • The temperature error is particularly small in
    the tropics where we are focusing (1 - 1.25 K)
  • Refractivity error Based on simulations, the
    refractivity error is approximated as

13
Estimated GPS Relative Humidity Error (Tropics)
  • Resulting GPS U error

14
Negative U and Error Deconvolution
  • Problem The Direct Method U estimate can be
    negative
  • gt produces an unphysical, negative tail in
    the U histograms
  • Simplest correction is to push all negative U
    values to the minimum positive U bin.
  • Systematically increases the mean (bad)
  • Error deconvolution is theoretically better
    approach
  • Model the measured Umeasured as Utrue eU
  • Measured histogram (PDF) is convolution of the
    true PDF and the error PDF
  • Such that PDFUmeas PDFUtrue PDFe
  • IF we understand the error PDF we can in theory
    deconvolve it from the measured PDF to recover
    the true PDF

15
U error deconvolution (work in progress)
  • Represent the error convolution in matrix form, Y
    A X
  • X is truth,
  • A represents the convolution with the error PDF,
  • Y is measured PDF
  • Use negative tail to optimize the estimate of
    error PDF
  • Assume PDFe is symmetrical
  • Include 2 additional constraints
  • Total Probability is conserved
  • Mean of distribution is conserved (gt error has
    zero mean)
  • Add these as entries in Y and rows in A
  • Least squares problem because of entries in Y gt
    X

16
Error Deconvolution (contd)
  • Finding the best PDFe is a trial and error
    approach based upon which PDFe best matches the
    observed
  • Found that a PDFe that is a linear combination of
    gaussian and exponential works well
  • Summary
  • Choose trial PDFe gt A
  • (using lin. combination of gaussian
    exponential)
  • Calculate least squares Xls solution
  • Smooth Xls if necessary
  • Forward calc YA Xls
  • Choose A which minimizes the variance of Y-Y
  • Approach yields both better estimate of X as well
    as refined understanding and estimates of errors

17
Deconvolution example
  • Histogram of GPS relative humidity data
    between 30oS and 20oS latitude and between 2 and
    3 km altitude for July 2002. Dotted line is
    histogram of measurements. Solid line is
    sharpened histogram after deconvolving the errors.

18
Data Sets for Moisture Variability Study
  • 2000 occultations each from CHAMP in January,
    April, July, October period
  • GPS canonical transform data smoothed to 200 m
    vertically courtesy of Chi Ao at JPL
  • Interpolate the nearest ECMWF 12 hour, 22 level
    global analysis to each occultation profile
  • Bin the data into a 2-D latitude vs. height grid
  • Every 10 degrees in latitude
  • Every 0.5 km in height (2 to 9 km altitude)

19
Now on to the Model
20
Stochastic Model Summary
  • Parcels leaving a convective system possess some
    initial relative humidity, R0, 100 established
    by cloud physics.
  • leaving a convective system we define as
    reaching a distance from the convective cores
    where the advection becomes approximately
    conservative.
  • Afterward, the Clausius-Clapeyron relation and
    no-source assumption dictate increases in
    saturation mixing ratio, qs, following a parcel
    according to

21
Change in parcel RH as it descend
  • Define tdry as
  • The relative humidity of the air parcel after a
    descent time, t, is
  • t is the parcel age, the time since the last
    moistening event
  • tdry is a few days and is shorter in the upper
    troposphere
  • Assume volume of air that is saturated is small
    fraction of total atmospheric volume

22
Moistening Time Scale
  • To define a probability density of relative
    humidity, we need the probability distribution of
    the time between moistening events
  • Proposal parcels are remoistened by
    encounters that occur randomly with a fixed
    probability per unit time independent of previous
    history (a Poisson process)
  • The decay constant, tmoist, is now equal to the
    mean remoistening time

23
Stochastic Model RH Probability Distribution
  • Assume the troposphere is very deep with constant
    w, tdry and tmoist at all heights above the
    interval being considered.
  • Combining the last 2 equations yields
  • where r tdry / tmoist
  • Integrating yields a cumulative distribution

24
Stochastic Model RH Probability Distribution
  • This equation is a bit astonishing in its
    simplicity
  • One free parameter is needed to define the RH
    distribution the ratio between tdry and tmoist.
  • r 1 uniform dist.,
  • r lt 1 dist. is peaked at low R
  • So lets assess the model with GPS RO and MLS
    data

25
GPS vs. Stochastic Model Cumulative RH
Distribution TROPICS
Agreement is surprisingly good! Some
disagreement at large R
  • Cumulative distributions of R at three levels in
    the lower and middle troposphere from GPS data
    (symbols) and from the stochastic parcel model
    with three values of r (lines), where r decreases
    as the curves shift to the lower right.

26
UARS MLS vs. Stochastic Model RH Distribution
TROPICS
  • Agreement is good at 215 and 464 hPa
  • Not as good at 326 hPa
  • Same as previous Fig, except data is from the
    UARS MLS for the upper troposphere.

27
Comparison of UARS and EOS MLS Results
  • UARS 215 hPa agrees better with model while EOS
    316 hPa agrees better with model

28
Mid-latitudes GPS UARS MLS vs. Stochastic
Model RH Histograms
  • Same as previous Fig., except data from 30S-60S
    and 30N-60N.

29
Seasonal Cumulative Distribution (GPS-Tropics)
Jan
Jul
Apr
Oct
30
Zonal Mean Humidity June 21-July 4 1995
  • Derived from GPS/MET using temperatures from
    ECMWF and NCEP

ltqgt
ltUgt
31
2D Cell Model
  • The model grid contains 10 horizontal and 200
    vertical locations, equally spaced in distance
    and pressure respectively, with the vertical grid
    ranging from 850 to 150 hPa.
  • Idealized, tropical clear-sky cooling profile is
    also specified, equal to -1.25 K/day up to 300
    hPa, then linearly decreasing with pressure to
    zero at 150 hPa
  • Subsidence, w(p), is diagnosed to balance the
    clear-sky energy budget away from convection
    (Sarachik 1978, see also Folkins et al. 2002)
  • Net Mass detrainment
  • QR is radiative heating rate, T temperature, Q
    potential temperature

32
2D Model RH distribution vs. Observations
  • Vertical Processes
  • Upwelling to match subsidence
  • EVAP of hygrometeors
  • MIX diffusion
  • Horizontal Processes
  • Advection
  • Diffusion
  • Dissipation relaxation mixing

33
Summary Conclusions
  • Estimated GPS RH errors imply RH is useful for
    temperatures warmer than 245K up to 9km in the
    Tropics.
  • Deconvolution can remove negative humidities and
    improve the estimate of RH PDF (but challenging)
  • Deconvolution can improve our estimates of the
    Direct Method humidity errors which constrain a
    combination of analysis temperature and GPS
    refractivity errors
  • GPS and MLS moisture estimates are quite
    complementary in their vertical coverage
  • Relative lack of high RH in GPS results may
    indicate high RH regions in middle troposphere
    are small in horizontal extent

34
Conclusions
  • Remarkably simple, one free parameter stochastic
    model apparently explains observations
  • Model predicts broad distribution of RH even as r
    changes
  • Simple 2D model captures much of the behavior but
    seems to be missing a low altitude source and is
    too moist at high altitudes
  • Data shows and 2D model predicts minimum in RH
    near 400 mb
  • where tDry is relatively small in middle
    troposphere up to 300 mb
  • due to decreasing dry static stability, and
  • drying per unit warming decreases strongly with
    decreasing temperature due to the
    ClausiusClapeyron equation

35
Conclusions (contd)
  • Radiation controls the relative humidity
    distribution
  • Model assumes area taken up by convection is
    effectively 0 and therefore may not be important
  • Need to understand the physics of tmoist to
    predict future climatic evolution
  • RH dist. may change in the future if r changes.
  • Changes in cloud cover that reduce atmospheric
    cooling will elevate relative humidity (slower
    descent gt increase tdry gt increase r ).
  • Changes in organization that allow convective
    moisture to rapidly spread to all parts of the
    global atmosphere will reduce tmoist and increase
    relative humidity,
  • Changes that further isolate convective systems
    from other parts of the atmosphere will increase
    tmoist and decrease relative humidity.
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