Retrieval of Moisture from GPS Slant-path Water Vapor Observations using 3DVAR and its Impact on the

Prediction of Convective Initiation and Precipitation

EMC seminar04/17/2007

Haixia Liu1,2 and Ming Xue2

1 NCEP/EMC2 SoM and CAPS, University of Oklahoma

Accurate characterization of 3D water vapor is important.

for the forecast of CI and subsequent storm evolution for QPF

Water vapor is under-sampled for convection processes.

GPS can potentially provide water vapor measurements at high spatial and temporal resolutions under all weather conditions.

One form of GPS measurements is the slant-path water vapor (SWV) derived from slant-path total delay.

Because of the integrated nature of the SWV data, their analysis is non-trivial and require advanced methods.

This study develops a 3DVAR system for analyzing SWV data.

Examines the impact of SWV data on CI and QPF (preliminary results)

Introduction

Outline

• 3DVAR method

• GPS observation system

• Moisture retrieval from SWV data with spatial filters

• Numerical simulation of 12 June, 2002 IHOP case

• Impact of GPS data on CI and QPF within OSSE framework

1

1

1 1

2 21

2

1

2 2 2

sfc sfc

b bswv swv swv

Tb b

sfc v sfc sfc v

b b b b

c

J H H

H H

W

v v Β v Βv x SWV R Βv x SWV

Βv x q R Βv x q

Βv x Βv x Βv x Βv x

so as to exclude the inverse of B in the definition of J and to use explicit filter to replace B.

3DVAR System with Explicit Filter

1bv = B x - xA new control variable is defined as vx qHere,

(Liu and Xue 2006 MWR)

3DVAR System with Recursive Filter

1

1

New control variable defined as:

1 1( )

2 21

2

1

2 2 2

sfc sfc

b

T

TTswv b swv swv b

T

sfc b v sfc sfc b v

T

b b b bc

J H H

H H

W

J

v

v x x x Dv

DD B

v v v x Dv SWV R x Dv SWV

x Dv q R x Dv q

x Dv x Dv x Dv x Dv

v

1

1

v, only applied when q is < 0

T Tswv swv swv swv

T Tsfc sfc sfc sfc c

Tc c b

J

J W

v

v

D H R H Dv d

D H R H Dv d

D x Dv

(Liu, Xue, Purser and Parrish 2007 MWR)

Background Error Covariance B

B is crucial to the successful analysis because:

variances determine the relative weights for the background and observations;

spatial covariance determine the spatial spreading or smoothing of observational information;

for multivariate analysis, cross-covariances reflect balance properties among fields.

The flow-dependent B is formulated directly in terms of the error field

given a physically meaningful correlation function form.

22

2 exp exp , based on Riishøjgaard (1998)ij i jij b

r f

r f fb

L L

Flow-dependent Anisotropic B

22

2exp .ij

ij br

rb

L

An important difference is the analysis background field is used as the f in his case. In our case, f, is defined as the error field.

The flow-independent B is often assumed to be Gaussian:

Obs=14.72 g kg-1 Bg = 0 g kg-1 Ana=14.69 g kg-1

Analysis increments from a single sfc observation

Lr = 4 grid intervalsLf = 2 g/kg

Isotropic B Anisotropic B

single sfc ob.

Dryline

This test is general – not related to SWV.Did it use EF or RF?

GPS Observation SystemGPS Observation System

Control segment Ground-based receiverSpace segment

.

The GPS-Met network consists of 386 sites.

http://gpsmet.fsl.noaa.gov/jsp/index.jsp

Ground-based GPS Network

Total atmospheric delay

Ionospheric delayEstimate from dual frequency observations

Neutral delay

Hydrostatic delayEstimate from surface pressure measurements

Wet Delay (SWD)

Ground-based GPS Data

, 0.15SWV SWD where

PW ZWD pw: precipitable water in a column in vertical directionZWD: zenith wet delay

3D Moisture Retrieval/Analysis with 3DVAR from GPS SWV and Surface

Station Data using Spatial Filters

Observation System Simulation

truth

qv field valid at 2000, 19 June, 2002

km

(km)

kmGPS receiver

GPS satellite

,

th

th

j satellite

ij v

i receiver

SWV q ds

Hypothetical GPS Network

give number of sat and ground station spacing

Analysis background

Explicit filter

•Anisotropic B based on true error field

22

2 exp expij i jij b

r f

r f fb

L L

truth-background analysis increment

A B

ISO•Isotropic B

UB(Updated B)

•Anisotropic B

•But the f field is the ISO analysis increment

•This is a two-step iterative procedure

2

2 exp ijij b

r

rb

L

analysis v.s. truth (solid) analysis increment

A B

A B

22

2 exp expij i jij b

r f

r f fb

L L

Explicit Filter

List of Analysis Experiments

Experiment anisotropic Filter

RMSE (g kg-1) CC CC with EF

ISO_RF No 0.35 0.84 0.83*

ANISO_RF Yes 0.28 0.91 0.93

UB_RF Yes 0.34 0.86 0.83

*Lr = 4, in unit of grid point, which is optimal, for ISO_RF experiment while Lr = 3 is optimal for ISO experiment using explicit filters.

ISO_RF: Isotropic B

analysis increment truth-background

A B

CC=0.84; RMSE=0.35 g kg-1

Recursive Filter

ANISO_RF:Anisotropic B based on truth

A B

UB_RF:(covariance-updated)

Anisotropic B based on the analysis with isotropic B

A B

CC=0.91; RMSE=0.28 g kg-1

CC=0.86; RMSE=0.34 g kg-1

analysis increment xz cross-section along AB

Recursive Filter

Sensitivity to Lr & Lf

RMSE (g/kg) w.r.t. Lr

ISO is the worstISO is more sensitive to Lr

UB with different Lf is in between

ANISO is the best (impossible for practical application)

optimal Lrs

22

2 exp expij i jij b

r f

r f fb

L L

Summary 1

• Our 3DVAR system incorporating background error through an isotropic Gaussian filter properly recovers 3D meso-scale moisture structure in a dryline case.

• The use of flow-dependent background error covariances realized through an anisotropic spatial filter improves the analysis.

• The two-step iterative procedure to estimate The two-step iterative procedure to estimate BB proposed proposed ((covariance-updatedcovariance-updated) improves upon the result of isotropic analysis.) improves upon the result of isotropic analysis.

• Compared to EF, the biggest advantage of RF is the computational Compared to EF, the biggest advantage of RF is the computational efficiency.efficiency.

• The quality of analyses using RF is in general comparable to or The quality of analyses using RF is in general comparable to or better than those obtained with EF in terms of CC.better than those obtained with EF in terms of CC.

• Isotropic analysis is more sensitive to geometric de-correlation Isotropic analysis is more sensitive to geometric de-correlation scale, scale, LrLr , than anisotropic analysis. , than anisotropic analysis.

(Results reported in Liu and Xue 2006; Liu et al. 2007 MWR)