Improvement metrics for water vapour and temperature profiles retrieved fromGPS RO profiles through 1D-Var

J. K. Nielsen <jkn@dmi.dk>, Kent B. Lauritsen and Kjartan KinchDanish Meteorological Institute, Copenhagen, Denmark.

ROM SAF products and activitiesThe EUMETSAT Radio Occultation Meteorology SAF deliv-ers near real time (NRT) and offline meteorological data formeteorological production and research. The ROM SAF coreactivity is processing NRT phase shift data from the GRASinstrument (METOP A/B)

FIGURE 1: Sketch of a GPS Radio Occultation measure-ment

In addition the ROM SAF will produce an GRASS offlinearchive of meteorological data, and an gridded meteorologi-cal dataset for climate research.

Bending angle (Level 1b): obtained from the measuredphases and the positions and velocities of the two satellitesusing Doppler shift and wave optics (canonical transform)Ionosphere corrected bending angle: obtained by linear com-bination of the bending angles corresponding to the two GPSfrequencies L1 and L2Refractivity (Level 2a): obtained from the bending angle asa function of height using the Abel Transform inversion (as-suming spherical symmetry and statistical optimization)Pressure, temperature and specific humidity (water vapor)(Level 2b): obtained using ancillary temperature, humidityand, e.g., 1D-Var algorithm

Climate gridded data of bending angle, refractivity and mete-orological parameters (Level 2c).

•What would be a good way to characterize the gain ofknowledge about the sate of the atmosphere from a sin-gle occultation?•Can we identify a good measure from some examples with

known quality differrences?

We analyze the Metop-A GNSS dataset from October 2007retrieved with raw sampling, and processed with both waveoptics and geometrical optics.

1D-Var 1D-Var minimizes the costfunction:

J(x) =1

2(x− xb)TB−1(x− xb)

+1

2(yo −H(x))TO−1(yo −H(x))

Relative entropy The relative entropy (or in-formation gain) measures the departure of the pos-terior distribution p(x|y) ∝ e−J from the prior distri-bution p(x) ∝ e−0.5(x−x

b)TB−1(x−xb).

d =∫dxp(x|y) ln p(x|y)

p(x)

=1

2

(ln |BS−1|

+(xs − xb)TB−1(xs − xb)− Tr(I− SB−1)

)S−1 = B−1 +KTO−1K, where K =

∂H

∂x

1st term: Entropy difference. S(|B|) > S(|S|) Measures howmuch the prior error covariance B is reduced by 1D-Var2nd term: Solution-Background distance measured in Back-ground metrics3rd term: This term is related to the number of well measuredvariables, but it is also mean of the second term. So the sec-ond and third term in combination measures the departurefrom the expected increment of a specific retrieval.

Wave Optics Geometric Optics

Asc

ent

10/14 10/21 10/28−50

0

50

100

150

200

Time

RelativeEntropy

Entropy change WO-10–Low-Asc

Entropy DifferenceDeparture termRelative Entropy

0 50 100−50

0

50

100

150

200

Relative Entropy histogram

Number of occultations

start: 2007 10 18

end: 2007 10 27

mean: 59.8930

stdv: 25.4601

10/14 10/21 10/28−20

0

20

40

60

80

100

120

140

160

180

Time

RelativeEntropy

Entropy change GO-10–Low-Asc

Entropy DifferenceDeparture termRelative Entropy

0 50 100−20

0

20

40

60

80

100

120

140

160

180

Relative Entropy histogram

Number of occultations

start: 2007 10 18

end: 2007 10 27

mean: 61.5131

stdv: 19.2151

The 4 relative entropy diagrams corresponds to the 4 prior fraction plots on the right. The most pro-nounced difference is found between ascending and descending profiles, where the descendingprofiles track the signal deeper in the tropical troposphere. Apparently geometrical optics seemsto gain slightly more information (not necessarily correct information) about specific humidity inthe lowest troposphere. This is because the wave optical method depends on a more strict qualitycontrol.

Des

cent

10/14 10/21 10/28−50

0

50

100

150

200

250

Time

RelativeEntropy

Entropy change WO-10–Low-Des

Entropy DifferenceDeparture termRelative Entropy

0 100 200−50

0

50

100

150

200

250

Relative Entropy histogram

Number of occultations

start: 2007 10 18

end: 2007 10 27

mean: 72.2145

stdv: 28.4696

10/14 10/21 10/28−50

0

50

100

150

200

Time

RelativeEntropy

Entropy change GO-10–Low-Des

Entropy DifferenceDeparture termRelative Entropy

0 100 200 300−50

0

50

100

150

200

Relative Entropy histogram

Number of occultations

start: 2007 10 18

end: 2007 10 27

mean: 67.7866

stdv: 16.6490

Conclusions• There are differences in the retrievals between the geometric and the wave optical method.• The largest relative entropy change in this data set is found in the descending profiles processed

with wave optics.• The relative entropy measure gives high credits to the wave optical method in the descend-

ing profiles, while the prior fraction measure (for the specific humidity) favors geometric opticsmethod.

Wave Optics Geometric Optics

Asc

ent

0.2 0.4 0.6 0.8 1 1.20

10

20

30

40

50

60

Improvement (σ)/σb WO-10–Low-Asc

Prior error fraction

Altitude

start: 2007 10 18end: 2007 10 27

TemperatureHumidity

0.2 0.4 0.6 0.8 1 1.20

10

20

30

40

50

60

Improvement (σ)/σb GO-10–Low-Asc

Prior error fraction

Altitude

start: 2007 10 18end: 2007 10 27

TemperatureHumidity

Des

cent

0.2 0.4 0.6 0.8 1 1.20

10

20

30

40

50

60

Improvement (σ)/σb WO-10–Low-Des

Prior error fraction

Altitude

start: 2007 10 18end: 2007 10 27

TemperatureHumidity

0.2 0.4 0.6 0.8 1 1.20

10

20

30

40

50

60

Improvement (σ)/σb GO-10–Low-Des

Prior error fraction

Altitude

start: 2007 10 18end: 2007 10 27

TemperatureHumidity