Recent developments for a forward operator for GPS RO

Lidia Cucurull

NOAA GPS RO Program Scientist

NOAA/NWS/NCEP/EMC

NCU, Taiwan, 16 August 20101

Introduction

3-term Refractivity expression

Bending angle

Effects of including compressibility factors (Yu-Chun Chen)

Summary and future work

Outline

2

Radio Occultation concept

LEO

Occulting GPS

Ionosphere

Neutral atmosphere

Earth

Raw measurement: change of the delay (phase) of the signal path between the GPS and LEO during the occultation. (It includes the effect of the atmosphere)

GPS transmits at two different frequencies: ~1.6 GHz (L1) and ~1.3 GHz (L2).

An occultation occurs when a GPS (GNSS) satellite rises or sets across the limb wrt to a LEO satellite A ray passing through the atmosphere is refracted due to the vertical gradient of refractivity (density) During an occultation (~ 3min) the ray path slices through the atmosphere

3

s1, s2,

1, 2

N

T, Pw, P

Raw measurements of phase of the two signals (L1 and L2)

Bending angles of L1 and L2

(neutral) bending angle

Refractivity

Ionospheric correction

Abel transfrom

Hydrostatic equilibrium,eq of state, apriori information

Clocks correction,orbits determination, geometric delay

choice of ‘observations’

Atmospheric products

4

Choice of observation operatorsC

ompl

exit

y

L1, L2 phase

L1, L2 bending angle

Neutral atmosphere bending angle (ray-tracing)

Linearized nonlocal observation operator (distribution around TP)

Local refractivity, Local bending angle (single value at TP)

Retrieved T, q, and P

Not practical

Not good enough

Possible choices

5

Introduction At microwave wavelengths (GPS), the dependence of N on atmospheric

variables can be expressed as:

€

N = 77.6P

T+ 3.73 ×105 Pw

T 2− 40.3 ×106 ne

f 2+ O(

1

f 3) +1.4 ×Ww + 0.6 ×W i

Hydrostatic balance

P is the total pressure (mb)

T is the temperature (K)

Scattering terms

Ww and Wi are the liquid

water and ice content (gr/m3)

MoisturePw is the water vapor pressure (mb)

Ionospheref is the frequency (Hz)ne electron density(m-3)

– important in the troposphere for T> 240K

– can contribute up to 30% of the total N in the tropical LT.

– can dominate the bending in the LT.

Contributions from liquid water & ice to N are very small and the scattering terms can be neglectedRO technology is almost insensitive to clouds.

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Forward Model for refractivity

(1) Geometric height of observation is converted to geopotential height. (2) Observation is located between two model levels. (3) Model variables of pressure, (virtual) temperature and specific humidity

are interpolated to observation location. (4) Model refractivity is computed from the interpolated values. The assimilation algorithm produces increments of

– surface pressure– water vapor of levels surrounding the observation– (virtual) temperature of levels surrounding the observation and all levels below the

observation (ie. an observation is allowed to modify its position in the vertical)

Each observation is treated independently and we account for the drift of the tangent point within a profile

€

N = 77.60P

T+ 3.73 ×105 Pw

T 2

7

€

H (obs) = H (k1)+Rd

2G

⎛

⎝ ⎜

⎞

⎠ ⎟x[T (obs)+T (k1)]x[ln P(k1)− ln P(obs)]

k1

k1-1

surface

k2

k1-2€

H (k1) = H (k1−1)+Rd

2G

⎛

⎝ ⎜

⎞

⎠ ⎟x[T (k1)+T (k1−1)]x[ln P(k1−1)− ln P(k1)]

€

H (k1−1) = H (k1− 2)+Rd

2G

⎛

⎝ ⎜

⎞

⎠ ⎟x[T (k1−1)+T (k1− 2)]x[ln P(k1− 2)− ln P(k1−1)]

€

H (1) = H (surf )+Rd

2G

⎛

⎝ ⎜

⎞

⎠ ⎟x[T (1)+T (1)]x[ln P(surf )− ln P(1)]

obs

Pre-operational implementation run

PRYnc (assimilation of operational obs ),

PRYc (PRYnc + COSMIC refractivity)

We assimilated around 1,000 COSMIC profiles per day

Anomaly correlation as a function of forecast day (geopotential height)

rms error(wind)

9

•Dashed lines: PRYnc•Solid lines: PRYc (with COSMIC)

•Red: 6-hour forecast•Black: analysis

Pre-operational implementation run (cont’d)

10

More accurate forward operator for refractivity– Three term expression

– Analysis of different sets of refractive indexes Update of the quality control procedures

– More observations (in particular in tropical latitudes) Optimal observation error characterization (Desroziers 2005)

– Smoother normalized differences

– No empirical tuning Changes resulted in an improvement in model skill in SH (mass fields) and

reduction of the low- and high-level tropical wind errors These changes were implemented operationally at NCEP in Dec 2009 Detailed description of the changes and results can be found in Cucurull 2010,

WAF, 25,2,769-787

Improved algorithms for N

3-term Forward Operator for refractivity

(1) Geometric height of observation is converted to geopotential height. (2) Observation is located between two model levels. (3) Model variables of pressure, (virtual) temperature and specific humidity

are interpolated to observation location. (4) Model refractivity is computed from the interpolated values. The assimilation algorithm produces increments of

– surface pressure– water vapor of levels surrounding the observation– (virtual) temperature of levels surrounding the observation and all levels below the

observation (ie. an observation is allowed to modify its position in the vertical)

Each observation is treated independently and we account for the drift of the tangent point within a profile

€

N = 77.60Pd

T+ 70.4

Pw

T+ 3.739 ×105 Pw

T 2

12

13

original (ops) QC & error modified QC & error

(O-B)/O_err

Errors too smallMany more

Observations !! Very few observations

NH

TR

SH

Impact with COSMIC

AC scores (the higher the better) as a function of the forecast day for the 500 mb gph in Southern Hemisphere

40-day experiments:– expx (NO COSMIC)

– cnt (old RO assimilation code - with COSMIC)

– exp (ops

– - with COSMIC) COSMIC provides 8 hours of gain in model forecast skill starting at day 4 !!!

Cucurull 2010 (WAF)

Forward Model for bending angle

Make-up of the integral:– Change of variable to avoid the singularity

– Choose an equally spaced grid to evaluate the integral by applying the trapezoid rule

€

x = a2 + s2

)(

)(

ln2)(

2/122

nrx

dxax

dxnd

aaa

=

∫ −−=

∞

16

Compute model geopotential heights and refractivities at the location of the observation

Convert geopotential heights to geometric heights Add radius of curvature to the geometric heights to get the radius: r Convert refractivity to index of refraction: n Get refractional radius (x=nr) and dln(n)/dx at model levels and evaluate them

in the new grid. We make use of the smoothed Lagrange-polynomial interpolators to assure the continuity of the FM wrt perturbations in model variables.

Evaluate the integral in the new grid.

Each observation is treated independently and we account for the drift of the tangent point within a profile

Forward Model for bending angle (cont’d)

17

QC

18

NH

TR

SH

NH

TR

SH

QC (model level)

19

NH

TR

SH

NH

TR

SH

N vs BA (single case, T62L64)

20

N

BA

21

N

BA

22

N

BA

Assimilation algorithm

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0:gps 82761 9.1646957113037395E+04 1.1070:gps 83635 5.1683558671757288E+04 0.6180:gps 83705 5.1001526772670179E+04 0.609

0:gps 49970 7.7231250467998078E+04 1.5460:gps 50934 2.8707346020729292E+04 0.5640:gps 51138 2.7751283896612065E+04 0.543

Counts J J/counts

N

BA

Experiments setup Case: 2010/02/01 12ZCTRL: no compressibility factor, old coefficient for N

EXP0: Compressibility Factor + old coefficient for N

EXP1: Compressibility Factor + Rueger’s Coefficient for N

EXP2: (Compressibility Factor + Rueger’s Coefficient for N) for GPS only

)1994,(3739004000.706000.772

BevisT

P

T

p

T

pN wwd

)2002,(3754632952.716890.772

RuegerT

P

T

p

T

pN wwd

EXP0 V.S. CTRL EXP1 V.S. CTRL Northern Hemisphere

Yu-Chun Chen

CTR

Lanl V

.S. E

XP1

anl

CTR

Lanl V

.S. E

XP2

anl

EXP1anl V.S. EXP2anl

Small differences 0.3%~0.7%

Summary

NCEP’s operational assimilation algorithm for GPS RO makes use of a three-term forward operator for refractivity

Current work focuses on the use of a (local) bending angle operator

Compressibility factors will be further evaluated and tested in a future parallel run

Future work should address the horizontal gradients of refractivity (non-local operators)

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