Progress on the assimilation of GNSS-RO at ECMWF

Transcription

1 Progress on the assimilation of GNSS-RO at ECMWF Sean Healy ECMWF/ROM SAF Many thanks to Chris Burrows, Ian Culverwell, Chris Marquardt, Sergey Sokolovskiy, the ROM SAF, Adrian Simmons, ECMWF November 7, 2016

2 Outline Set out key aspects of the assimilation problem. Review the assimilation of GPS-RO has changed since operational implementation in December Key changes to the GPS-RO observation operator (often prompted by research work elsewhere) Changes to the assumed bending angle error statistic model Results from recent assimilation experiment. Improving the forward modelling in the lower troposphere. Trying to reduce horizontal gradient errors. Understanding the impact of the horizontal gradients on the wave optics processing (FSI). Summary 2

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4 Key points We need a forward model/observation operator to map from the NWP state information, x, to observation space (bending angle) H(x). We need to estimate the observation error statistics, R. R should include a component related to the real observation errors, E, plus the forward model (representation) error statistics, F. R=E+F The observation operator we use to assimilate the data operationally is usually based on a trade-off between computational cost and the need to reduce forward model errors. EG, assimilation of bending angle vs refractivity, Wave. optics vs Geo.optics We also need a good quality control system to reject data which is not characterised by the assumed error statistics, R. (Not discussed here). 4

5 GPS-RO Assimilation in 2006 A Geometrical optics approach. We assimilate bending angles with a 1D operator. We ignore the real 2D nature of the measurement and tangent point drift and integrate ( a) 2a The forward model is quite simple: a d ln n dx 2 2 x a dx evaluate geopotential heights of model levels convert geopotential height to geometric height and radius values evaluate the refractivity, N, on model levels from P,T and Q using the Smith and Weintraub (1953) coefficients. Integrate, assuming refractivity varies exponentially between model levels. 5

6 GPS-RO Assimilation in 2006 A Geometrical optics approach. We assimilate bending angles with a 1D operator. We ignore the real 2D nature of the measurement and tangent point drift and integrate ( a) 2a The forward model is quite simple: evaluate geopotential 2akheights i N i exp of model ki ( levels xi convert geopotential height to geometric height and radius values a d ln n dx 2 2 x a evaluate the refractivity, N, on model levels from P,T and Q using the Smith and Weintraub (1953) coefficients. Integrate, assuming refractivity varies exponentially between model levels. dx x 1 a) erf k ( x a) 10 6 i i x i 6

7 But it works. Operational fit radiosondes T,Z in the SH. 7

8 But it works. Operational fit radiosondes in the SH. The GPS-RO complement the other assimilation types They have superior vertical resolution to satellite sounders. The can be assimilated without bias correction to the model. Anchor measurements. 8

9 GPS-RO and extratropical-mean temperatures from ERA-Interim and JRA-55 Values are relative to ERA-Interim means for

10 GPS-RO and extratropical-mean temperatures from ERA-Interim and JRA-55 Improved consistency between reanalyses in the stratosphere since GPS-RO have been assimilated. Values are relative to ERA-Interim means for

11 Evolution of the forward operator October 29,

12 Some key changes Introduction of the non-ideal gas effects and revision of the refractivity coefficients. Aparicio, J. M., G. Deblonde, L. Garand, and S. Laroche (2009), Signature of the atmospheric compressibility factor in COSMIC, CHAMP, and GRACE radio occultation data, J. Geophys. Res., 114, D16114, doi: /2008jd And the refractivity coefficients: Cucurull, L. (2010), Improvement in the use of an operational constellation of GPS radiooccultation receivers in weather forecasting, Weather Forecasting, 25, Healy, S. B. (2011), Refractivity coefficients used in the assimilation of GPS radio occultation measurements, J. Geophys. Res., 116, D01106, doi: /2010jd Aparicio, J. M., and S. Laroche (2011), An evaluation of the expression of the atmospheric refractivity for GPS signals, J. Geophys. Res., 116, D11104, doi: /2010jd01521 REMARK: NCEP, Environment Canada and ECMWF (ROM SAF) use slightly different refractivity coefficients in their assimilation system. October 29,

13 Dealing Maximum with sharp refractivity gradients in the close observation to ducting conditions operator in the assimilation Problem: assumption of linearity in Model levels incremental 4D-Var when close to ducting i+1 (strong refractivity niri gradients) ni1ri 1 conditions. i Bending angle In original version of the operator, it did not calculate the bending below (i+1) if However, problems arose if the separation was only a few metres. Partial derivatives can get very large eg, q Assimilation problem too non-linear.

14 In operations Solution in the ROM SAF codes Only calculate bending angles below (i+1) if ( ni 1r i1 niri ) 10(metre) Yes, it s a bit ad-hoc. Seemed to work. But the Met Office had 4D-Var convergence problems, so we put in a maximum gradient in BA integral: max max dn dx dn dr / 2 is is an example of the difference between assimilation code and simulation code. We have be agmatic sometimes to make sure the code works within the 4D-Var minimization.

15 Testing maximum N gradient at ECMWF Fit to observations ( )/ Black = dn/dx max included

16 Tangent point drift Initially Work stimulated by paper by Foelsche et al (2010) Foelsche, U. et al.: Errors in GNSS radio occultation data: relevance of the measurement geometry and obliquity of profiles, Atmos. Meas. Tech., 4, , doi: /amt , and discussions with Mike Rennie/John Eyre (Met Office). Meteo-France and NCEP already included this in EG, see: Cucurull, L. (2012), Sensitivity of NWP model skill to the obliquity of the GPS radio occultation soundings. Atmosph. Sci. Lett., 13: doi: /asl.363 I did not think this was an important source of forward model error in the stratosphere (where we were already doing a very good job!) but that was incorrect. Bending angle departure statistics are clearly improved and improved wind scores. This made ECMWF less sensitive to the precise definition of the occultation point in the BUFR header.

17 (o-b) and (o-a) bending angle departure statistics noise normalized ( )/ Black = tpd experiment Red = fixed location (Dotted line = analysis departures) COSMIC-4 GRAS

18 Z500 Reduction in 24 hr RMS errors as a result of TPD Z100

19 Improvements in the ROM SAF bending angle integration Burrows, C. P., et al : Improving the bias characteristics of the ROPP refractivity and bending angle operators, Atmos. Meas. Tech., 7, , doi: /amt , Note, the model levels are plotted on geopotential heights, not impact heights. The oscillations in bias coincide with the model levels. Close to the model levels, the magnitude of the bias is smallest.

20 Use a dry form of the reference refractivity to calculate bending angles An approximation to the dry form of the reference refractivity with height can be integrated analytically in the Abel transform (equivalent to letting the exponential decay factor k vary linearly with z within each layer). Exponential N(x) (Exponential*quadratic) N(x) approximation This reduces the oscillations considerably, so by implementing this, the increments will have smaller biases, leading to better analyses and radiance bias corrections.

21 Assimilation with the 2D forward model. Solving a set of ray path equations rather than the BA integral Interpolate 2D information to the ray path ray path Surface Tangent height of the raypath determined by the impact parameter provided with the observation,. The outer loop uses 31 profiles to describe the 1200 km occultation plane.

22 Impact of tangent point drift and the 2D operator Poli, P. and Joiner, J. (2004), Effects of horizontal gradients on GPS radio occultation observation operators. I: Ray tracing. Q.J.R. Meteorol. Soc., 130: doi: /qj

23 Error statistics: Global error model. The assimilation diagnostics provide an estimate of R Increased from 1% to 1.25 %. 23

24 We ignore measurement error correlations in the assimilation (2015) setting rising have tested them before, BUT correlations are difficult to introduce when tangent point drift includ 24

25 Some recent assimilation experiment removing GPS-RO Good Anomaly correlations so increase is good. >100 cases Dec 2014-April Clear signal in geopotential height scores and strong signal on radiosonde temperature fits, as expected (not show 25

26 Improvement in tropical winds (?) (Better short-range fc fit to obs) 26

27 Reduction in standard deviation of relative humidity errors. Some indication of GPS-RO impact on humidity. Qu: Impact limited by model biases in the lower troposphere? Good 27

28 Lower tropospheric bending angle biases (o-b)/b (%) 28

29 Compare with ECMWF operations (Aug 2016) We don t see this pattern with the Met Office NWP system. ROM SAF will routinely produce these ECMWF/Met O plots for comparison. 29

30 Improving the 2D forward model (Discussed at the last COSMIC user workshop) Based on a geometric optics picture, tried to reduce forward model errors by modelling the impact parameter variation along the ray path d( nr sin) ds n r and then correcting impact parameter at the tangent point used to assimilate the data. IE, the impact parameter we get in the BUFR file is more consistent with the (nr sinø) value at the LEO. 30

31 Aim Use the NWP forecast model state to provide a relationship between the impact parameter value at the tangent point impact parameter value provided with the observation. a f a t, H ( x ), r, v, r, b G G L v L provided want geometry

32 Why is this important (JGR, 2001) The impact parameter we get is not what we want! Interpretation The main error introduced by horizontal gradients is assigning the wrong parameter.

33 Initial results - failure Function not appropr Based on GO

34 Do horizontal gradients cause the same errors in WO and GO processing? => Sergey Sokolovskiy GO bending angle is a multivalued function of impact parameter, but this is not possible in the processing by construction (Sergey). How do I/can I forward model the WO bending angle profile?

35 Similar results with ECMWF forecast fields DIFFICULT CASE (Case 16 from the ECMWF 55 profile dataset) LEO Incoming Stationary transmit Circular LEO orbit. Wave optics forwar SLTA = -300 km FSI to bending ang 35

36 Computed with refrac gradient limit noted ea Bending angle profiles itation operator assumes bending les located at x=0. max max dn dx dn dr

37 Remove refractivity limit 37

38 Interpretation/forward modelling of lower troposphere bending angle profiles More work required here. Improving the 2D operator requires me to have a better understanding of how horizontal gradients impact the bending angle profile produced with the wave optics inversion. We now have the (wave propagator/fsi inverse) tool that we can test in the 2D operator with. H ( x ) H ( x ) 2d 2d ref 2d T F w H ( x ) FSI( WAVE( x )) ref 2d 2d 38

39 Summary Outlined some key developments in the assimilation of GPS-RO since We now run a 2D operator+tpd +non-ideal gas+better coefficients Briefly reviewed some recent impact experiments. Shown bending angle bias plots in the lower troposphere. Main issue for my current work is better understanding of the wave optics retrievals and the impact of horizontal gradients. 39

40 Feedback from Sergey