Combined forecast impact of GRACE-A and CHAMP GPS radio occultation bending angle profiles

Transcription

1 ATMOSPHERIC SCIENCE LETTERS Atmos. Sci. Let. 8: (2007) Published online in Wiley InterScience ( Combined forecast impact of GRACE-A and CHAMP GPS radio occultation bending angle profiles S. B. Healy 1 *, J. Wickert 2,G.Michalak 2,T.Schmidt 2 and G. Beyerle 2 1 European Centre for Medium-range Weather Forecasts (ECMWF), Reading, UK 2 GeoForschungsZentrum Potsdam (GFZ), Germany *Correspondence to: S. B. Healy, European Centre for Medium-range Weather Forecasts (ECMWF), Reading, UK. sean.healy@ecmwf.int Received: 9 November 2006 Revised: 22 February 2007 Accepted: 22 February 2007 Abstract Impact experiments assimilating GRACE-A and CHAMP GPS radio occultation (GPSRO) bending angle profiles are presented. The standard deviation of the observation minus background bending angle departures above 35-km is 30% smaller for GRACE-A than CHAMP, indicating that the GRACE-A measurements are more accurate. Assimilating the GPSRO measurements improves stratospheric temperatures in the Southern Hemisphere. The combined impact of GRACE-A and CHAMP is greater than assimilating either instrument individually. Copyright 2007 Royal Meteorological Society Keywords: satellite observations; data assimilation; numerical weather prediction 1. Introduction The GPS/MET (Rocken et al., 1997) and CHAMP (Wickert et al., 2001) proof of concept Global Postioning System (GPS) radio occultation (GPSRO) missions have demonstrated that the measurement technique can provide useful temperature profile information, and there is now increasing interest in assimilating these data into operational numerical weather prediction (NWP) models. The measurements are globally distributed, have an all weather capability and good vertical resolution (e.g., see Kursinski et al., 1997). Furthermore, GPSRO measurements can be assimilated without bias correction, because they are based on the measurement of a time delay. Assimilation experiments, adding CHAMP GPSRO measurements to operational NWP systems, have produced encouraging results (Healy et al., 2005; Healy and Thépaut, 2006). These experiments demonstrated that assimilating the CHAMP measurements improved the forecast accuracy of lower stratospheric temperatures particularly, in the Southern Hemisphere over the day-1 to day-5 forecast range, despite the low number of CHAMP measurements in comparison to the number of conventional and satellite measurements that were already being assimilated. The CHAMP instrument was launched 15 July 2000 and it is now expected to provide GPSRO measurements until the end of The recent launches of the constellation of six satellites, COSMIC (Anthes et al., 2000), and the GRAS instrument on METOP- A (Loiselet et al., 2000) will increase the number of GPSRO measurements available for assimilation by roughly an order of magnitude during However, there are also other existing missions, such as GRACE-A (Tapley et al., 2004), that are potentially useful data sources. The GRACE satellites, GRACE-A and GRACE-B, were launched on 17 March 2002 and recent orbit decay calculations suggest a lifetime beyond 2012 is feasible. The accuracy and processing of GPSRO measurements made with GRACE- B have been investigated in previous work (Beyerle et al., 2005; Wickert et al., 2005). In this study, we present the first assimilation experiments with GRACE-A GPSRO bending angle profiles (GRACE- B measurements were not available for this study). It is demonstrated that the GRACE-A bending angles are more accurate than CHAMP bending angles above 35- km and that the combined impact of GRACE-A and CHAMP on stratospheric temperatures in the Southern Hemisphere is greater than the impact of either CHAMP or GRACE-A individually. The processing of the GRACE-A and CHAMP GPSRO measurements is outlined in section 2 and the NWP system used in the assimilation experiments is summarised in section 3. The results from forecast impact experiments, assimilating GRACE-A and CHAMP measurements from 13 January to 21 February 2006, are presented in section 4. The conclusions are given in section Processing of the GRACE-A and CHAMP measurements The CHAMP and GRACE-A GPSRO measurements are processed at GeoForschungsZentrum (GFZ) Potsdam. CHAMP data processing requires a space-based, single differencing technique (Wickert et al., 2002) to correct for the GPS receiver s clock error. The GRACE-A receiver clock is controlled by an ultrastable oscillator, enabling data analysis with a zerodifference method (Beyerle et al., 2005). The stability of the GRACE-A clock means that the 50 Hz clock Copyright 2007 Royal Meteorological Society

2 44 S. B. Healy et al. solution, required for the GPSRO data analysis, can be interpolated from the 30 s precise orbit determination (POD) data. In contrast, the CHAMP clock is adjusted once per second to achieve a 1 µs maximum deviation from coordinate time. These adjustments introduce discontinuities, which cannot be modelled accurately and interpolation from the 30 s POD solutions is not possible. Single differencing almost completely eliminates these clock errors, but the CHAMP clock discontinuities still introduce errors through the ionospheric correction of the reference satellite link. Monitoring at GFZ (unpublished) indicates that this additional noise contribution increases the errors of the refractivity profiles derived from CHAMP measurements above 30-km. The low earth orbit (LEO) clock solutions (for GRACE-A) and the LEO and GPS satellite positions and velocities are given by GFZ s Ultra-Rapid-Science Orbit product (USO, see König et al., 2006) with an average latency of about 3 h. The bending angles are derived from the time-derivative of the excess phase measurements using the approach described in section 4.2 of Wickert et al. (2005). This includes the use of Full Spectrum Inversion (FSI) (Jensen et al., 2003) below 15-km, to correct for multipath signal propagation in the lower troposphere. 3. The NWP system, GPSRO observation operator and assumed errors The forecast impact experiments are performed with the incremental four-dimensional variational (4D-Var) assimilation system (Rabier et al., 2000) at the European Centre for Medium-Range Weather Forecasts (ECMWF), with a 12 h assimilation window. The horizontal resolution is T511 and the model has 91 levels in the vertical, with the uppermost model level at The GPSRO measurements are assimilated as profiles of bending angles of the signal s path, α, as function of impact parameter, a, using the one-dimensional bending angle observation operator described in Healy and Thépaut (2006). Bending angles up to an impact height of 40-km are assimilated. The impact height, h, is defined as h = a R c, where a is the impact parameter and R c is the local radius of curvature at the observation location. Note that the relationship between the impact height, h, and z, the geometric height above the Earth s surface, is z h 6.3N (z) where both h and z are in metres, and N (z) is the refractivity (see Kursinski et al., 1997) at height z. For example, at the surface N (z = 0) 330, so z h The standard deviation of the combined forward model/observation errors assumed for both the GRACE-A and CHAMP measurements is characterised in terms of the impact height, h. The standard deviation of the bending angle error is assumed to be 10% of the observed value at h = 0, falling linearly with h to 1% at h = 10-km. Above 10-km, the standard deviation of the error is assumed to be 1% of the observed value until this reaches a lower absolute limit of radians (6 µrad). This error model is based on observation minus background departure statistics and detailed simulations in the domain of a mesoscale forecast model (Healy, 2001). The model is also consistent with refractivity error estimates (Kuo et al., 2004) mapped to bending angle space. The observation errors are assumed to be uncorrelated in the vertical. This assumption will be investigated in future work, but we do not believe that it introduces large errors, because the bending angle vertical weighting functions are quite sharp (Eyre, 1994). Neglecting vertical error correlations is more problematic when the weighting functions are broad and overlapping. 4. Forecast impact results The assimilation experiments are for the period 13 January to 21 February A total of 6694 CHAMP and 5228 GRACE-A GPSRO bending angle profiles are available for assimilation. Four assimilation experiments have been performed: (1) The control (CTL) experiment assimilates the set of conventional and satellite measurements that are used operationally at ECMWF. (2) The GRACE-A experiment is identical to the CTL, except that GRACE-A GPSRO bending angle profile are also assimilated. (3) The CHAMP experiment is identical to the CTL, except that CHAMP GPSRO bending angle profiles are also assimilated. (4) The CH + GR experiment is identical to the CTL, except that both CHAMP and GRACE-A GPSRO bending angle profiles are also assimilated. Figures 1 and 2 show the mean and standard deviation of the normalised observation minus background (O-B) and observation minus analysis (O-A) bending angle departures in the Northern Hemisphere (latitude >20 ), tropics (20 latitude 20 ) and Southern Hemisphere (latiude < 20 ), for the CHAMP and GRACE-A measurements, respectively. The normalisation is with respect to the assumed observation errors. The statistics are derived from the CH + GR experiment and are averaged over 40 days. Figures 1 and 2 have broadly similar characteristics. As expected, the 4D-Var minimization significantly reduces the size of the O-A departures compared with the O-B departures. The O-B standard deviations are largest in the tropopause region, and they are larger in the tropics than in the Northern or Southern Hemispheres. In general, the biases in the O-B distributions are significantly smaller than the standard deviations. In both figures, the largest bias in the bending angle departures is near the surface in the tropics. The negative normalised bending bias of 1.8 corresponds

3 Combined impact of GRACE-A and CHAMP 45 Figure 1. The mean and standard deviation of the O-B (black) and O-A (grey) normalised CHAMP bending angle departures for impact heights between 2 40-km. The statistics are derived from 40 days of data (13 January 21 February 2006). The central column gives the number of samples in the 2-km interval. The departures are normalised with respect to the assumed errors

4 46 S. B. Healy et al. Figure 2. As Figure 1 but for GRACE-A to a bias of 15% in the observed bending angle (Note that the fractional errors and biases are larger in bending angle space than refractivity space because the bending angles are related to the refractivity gradients.). The results indicate that the assumed observation errors should probably be increased in the tropical

5 Combined impact of GRACE-A and CHAMP 47 lower troposphere. In general, the GRACE-A departures are smaller than the CHAMP departures in the stratosphere, indicating that the former are more accurate measurements. This is most apparent for impact heights greater than 35-km, as shown in Figure 3, with the statistics (in µrad) summarised in Table 1. These results are after quality control, which rejects an observed bending angle if the O-B departure is greater than 30 µrad. The quality control rejects around 0.4% and 0.1% of the CHAMP and GRACE-A bending angles above 35-km, respectively, but this level of rejection does not significantly alter the main characteristics of the O-B distributions shown in Figure 3. The shape of the O-B departure distributions is broadly Gaussian for both CHAMP and GRACE-A. However, the Gaussian curves shown in Figure 3, defined by the mean and standard deviation values given in Table 1, are somewhat broader, particularly, for CHAMP. This is because there are more O-B departures in the wings of the distributions than would be expected for a Gaussians, and these increase the computed standard deviation values. The mean departures are 1 µrad, Figure 3. The O-B bending angle departures (in µrad) of CHAMP and GRACE-A in the northern hemisphere, tropics and Southern Hemisphere, for impact heights between km. The boxes and lines above each diagram indicate ± the standard deviation and the minimum/maximum values, respectively. The continuous curves are Gaussian, computed with the mean and standard deviation values given in Table 1

6 48 S. B. Healy et al. Table I. The mean and standard deviation (std) bending angle O-B departure statistics for CHAMP and GRACE-A, for impact heights from 35-km to 40-km. The data is averaged from 13 January - 21 February 2006 and the figures are given in µrad. Departures greater than 30 µrad are removed in the quality control and are not included in the statistics CHAMP GRACE-A Region Number Mean Std Number Mean Std N.Hem Tropics S.Hem but tend to be smaller for GRACE-A. To put these biases in some context, the total bending angle of a ray with a tangent point at 40-km above the surface is typically α 70 µrad, meaning that the GRACE- A biases are generally 1% of an observed value at 40-km. Further, the standard deviations of O-B departures are over 30% smaller for GRACE-A than CHAMP. These results are consistent with the statistical monitoring performed at GFZ (unpublished), comparing CHAMP and GRACE-A refractivity profiles with ECMWF analyses mapped to refractivity space, and ultimately the smaller GRACE-A errors can be attributed to the superior clock. However, comparing the O-B distributions in bending angle space is cleaner, because it reduces preprocessing of the observations, which can complicate the errors and introduce apriori information. We have investigated the forecast impact of the GRACE-A and CHAMP measurements by verifying forecasts against radiosonde observations and their own analyses. Verifying forecasts against their own analyses means, for example, that the forecasts from the GRACE-A experiment are verified against the GRACE-A experiment analyses. The forecast scores in the troposphere are broadly neutral in all regions, but assimilating the GPSRO measurements produces a clear impact in the stratosphere, particularly in the Southern Hemisphere. Figure 4 shows the root-meansquare (RMS) of the forecast fit to radiosonde temperature observations at 300, 200, 100 and 50 in the Southern Hemisphere, averaged over 40 days. The CH + GR experiment produces an improvement in the fit to the 300 and 200 radiosonde temperatures at day-1, which is found to be significant at the 0.2% level with the Student t-test, but otherwise the results are very close at these levels. The impact is much clearer at 100 and 50 where all three GPSRO experiments improve the fit to the radiosonde observations. The results from the CHAMP experiment are consistent with earlier work (Healy and Thépaut, 2006) and it is apparent that the GRACE-A measurements have a similar impact. Ideally, we would expect that assimilating both CHAMP and GRACE-A measurements would give a larger impact than assimilating either of these datasets individually, and this is clearly the case in Figure 4(c) and (d) for the day-1 to day-3 forecast range. Figure 4(c) indicates that the CH + GR experiment is poorer than both the CHAMP or GRACE-A experiments at day-4 and day-5, but this difference is not statistically significant at the 5% level. More generally, the statistical significance of the differences at 100 and 50 of the combined experiment, CH + GR, relative to the CHAMP, GRACE-A and CTL experiments is summarised in Table 2. Verification against analyses produces qualitatively similar results at 300, 200, 100 and 50, but it has the advantage of enabling verification above 50. For example, Figure 5 shows the verification of forecast temperatures up to day-10 at 10, 5, 3 and 1 against their own analysis. The statistics are based on 30 cases. It is clear that the GPSRO measurements are providing useful information at these levels. The reduction of RMS errors of the CH + GR experiment relative to the CTL experiment is generally statistically significant at the 0.1% level over the day-1 to day-10 range at the 10, 3 and 1 levels and neutral at 5. The largest reductions in the RMS errors are over Antarctica. The improvements in the combined CH + GR experiment, relative to the CHAMP and GRACE-A experiments, are generally statistically significant at the 5% level at 10, 3 and 1. It is quite surprising that the assimilation system is able to extract useful information at 3 and 1, which correspond to altitudes of approximately 40-km and 48-km, respectively. Only bending angles with tangent heights up to 40-km are assimilated because the information content of the measurements falls rapidly above this height. The positive impact at 1 is probably a result of the background error covariance matrix spreading the GPSRO information upwards. It is not clear why the impact is neutral at 5, but note that the 3 and 1 forecast errors are larger than at 5, so it is potentially easier to introduce an improvement. On the other hand, although the forecast errors are smaller at 10 than at 5, the signal to noise ratio of the bending angles with tangent heights near 10 is larger. There is some evidence of a positive impact in the tropical and Northern Hemisphere stratosphere for the Table II. The statistical significance of the change in RMS fit to the radiosonde temperature values in the Southern Hemisphere at 100 and 50. The results are for the CH + GR experiment relative to the CTL, CHAMP and GRACE-A experiments. The tabulated values are %. Only values of 5% or less are considered significant. Values greater than 5% are denotedwith Forecastday 100 CTL CHAMP GRACE-A

7 Combined impact of GRACE-A and CHAMP 49 Figure 4. The RMS fit to radiosonde temperatures at 300, 200, 100 and 50 as a function of forecast range in the Southern Hemisphere for the CH + GR, CHAMP, GRACE-A and CTL experiments. The statistics are based on 40 days of data CH + GR experiment, although the signal is smaller than in the Southern Hemisphere. To summarise the results that are statistically significant at the 5% level (Figures not shown), in the tropics the experiment improves the RMS fit to radiosonde temperature measurements at 100 for days 1, 2 and 4. At 50 there is improvement at day-1 and day-4. However, the fit is degraded at 200 for day- 4. Against the analyses, the results over the day-1 to day-10 range are generally positive on the 200, 100 and 5 levels but degraded at 3. In the Northern Hemisphere, there is a degradation of the fit to radiosondes at 300 at day-3, an improvement at day-1 and day-2 at 100 and an improvement at day-3 for 50. Against analyses, there is an improvement from day-4 to day-6 at 200 and 10, and from day-1 to day-6 at Conclusions These results illustrate that GRACE-A GPSRO bending angles are a potentially useful source of information for operational NWP. The GRACE-A and CHAMP O-B statistics above 35-km indicate GRACE- A measurements are more accurate; the GRACE-A biases are ( 0.6 µrad) and the standard deviations are 30% smaller (Table 2). This is because GRACE- A has a better clock than CHAMP, and therefore GRACE-A measurements can be processed with zero differencing (Beyerle et al., 2005). As in previous forecast impact studies with CHAMP measurements (Healy et al., 2005; Healy and Thépaut, 2006) the largest forecast impact with the GPSRO data is in the stratosphere of the Southern Hemisphere. In this work, it has been demonstrated that the data assimilation system can derive useful temperature information from the GPSRO measurements up to 1 ( 48-km). The experiments demonstrate that assimilating either GRACE-A or CHAMP measurements produce clear improvements in the forecast fit to radiosonde temperature measurements and analyses that are of comparable magnitude, when compared with the CTL experiment. Further, the verification statistics for the Southern Hemisphere show that the combined impact of GRACE-A and CHAMP is superior to assimilating either instrument individually. Acknowledgements The authors thank the CHAMP and GRACE teams, including Prof. M. Rothacher and Prof. B. Tapley, for making the occultation data from both satellites available. The figures were improved by Anabel Bowen and Rob Hine. Sean Healy is supported through the EUMETSAT/ECMWF Fellowship Programme. The GFZ work is supported by the GEOTECHNOLOGIEN research programme of the German Ministry for Education and Research within the Near Real- Time Radio Occultation (NRT-RO) project (funding code 03F0431A).

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