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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.
6
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
23
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)
27