A robust method for tropopause altitude identification using GPS radio occultation data

GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L12808, doi:10.1029/2009gl039231, 2009 A robust method for tropopause altitude identification using GPS radio occultation data H. W. Lewis 1 Received 18 May 2009; accepted 27 May 2009; published 18 June 2009. [1] A robust method to determine the tropopause altitude directly from GPS Radio Occultation (RO) measurements of bending angle is presented. An objective covariance transform method is applied to identify transitions in a bending angle profile. The tropopause is identified by the maximum in the convolution of the natural logarithm of an observed bending angle profile with a gradient window function. Identification of the tropopause from bending angles is of particular value since they are directly derived from climate benchmark observations. This method avoids additional RO data processing and assumptions to derive parameters such as dry temperature, and use of subjective tropopause identification criteria. The RO tropopause altitude is compared with lapse rate and cold point criteria using dry temperatures and radiosonde temperature profiles. A longer-term tropopause altitude analysis for May to November 2008 using the RO bending angle method shows good agreement with tropopause altitudes computed from dry temperature parameters. Citation: Lewis, H. W. (2009), A robust method for tropopause altitude identification using GPS radio occultation data, Geophys. Res. Lett., 36, L12808, doi:10.1029/2009gl039231. 1. Introduction [2] Accurate and continuous observations of the tropopause on a global scale are crucial for monitoring climate change [Santer et al., 2003] and understanding stratospheretroposphere exchange [e.g., Holton et al., 1995]. Reanalyses and radiosonde observations show an increase of global mean tropopause altitude of the order of 100 m per decade during the last 25 years [Randel et al., 2000]. [3] The tropopause is conventionally identified from vertical transitions in temperature. The thermal lapse rate tropopause (LRT) is defined by the World Meteorological Organization (WMO) as the lowest level at which the lapse rate is less than 2 K km 1 and the average between this level and the next 2 km does not exceed 2 K km 1 [World Meteorological Organization, 1957]. The cold point tropopause (CPT) may be more relevant for identifying the tropical tropopause. Determining tropopause altitude using radiosonde data benefits from their high vertical resolution, but monitoring on a global scale is limited by being largely restricted to land areas with sparse coverage in the Southern Hemisphere. Interpretation of trends from radiosonde data are complicated by the need to account for changes in instrument calibration and biases due to sensor changes. Identification of the tropopause in reanalyses is limited by 1 Met Office, Exeter, UK. Published in 2009 by the American Geophysical Union. their coarser vertical resolution and model biases [Randel et al., 2000]. [4] GPS radio occultation (RO) [e.g., Kursinski et al., 1997] is an important remote sensing technique for monitoring Earth s atmosphere. Long-term stability enables data from different missions to be combined without intercalibration. The data have global coverage and high vertical resolution of the order 1 km. Refractive index gradients cause radio signals to bend as they propagate through the atmosphere, resulting in a measurable time delay relative to that for a straight line signal path between the GPS and a low earth orbit receiver. Relative satellite motion during an occultation gives profiles of bending as a function of the minimum ray-height above the centre of curvature, known as the impact parameter. The fundamental RO phase delay observation is a climate benchmark as it is traceable to the international definition of the second by independent differencing methods [Leroy et al., 2006]. [5] Bending angles, a, are derived as a function of impact parameter, x, from phase delays given precise satellite positions and velocities. Assuming spherical symmetry, bending angles can be inverted using an Abel transform to compute refractive index n as a function of geometric height h. The impact parameter for a ray with tangent radius r is x ¼ nr ¼ nðh þ R c Þ where R c is the local radius of curvature with respect to the geoid. Refractivity N =10 6 (n 1) is empirically related to atmospheric pressure, temperature and humidity [e.g., Kursinski et al., 1997]. Most tropopause studies using RO data have focused on the use of dry temperature (T dry ). Foelsche et al. [2007] estimated the error from assuming a dry atmosphere to be less than 0.5 K in the tropopause region. Schmidt et al. [2004] demonstrated this method for monitoring the tropical tropopause. Schmidt et al. [2008] used T dry profiles over a period of 80 months to estimate a global increase of tropopause altitude by between 4 and 7myr 1. [6] Given the climate benchmark nature of the RO measurement, it is desirable to identify the tropopause directly from bending angle data. Their information content has been demonstrated in the context of data assimilation [e.g., Healy and Thépaut, 2006] and examining trends in climate models [Ringer and Healy, 2008]. These data are less sensitive to uncertainties related to data processing than refractivity and T dry [e.g., Staten and Reichler, 2008]. Use of bending angles avoids inclusion of a priori information in the Abel transform, assuming hydrostatic equilibrium and use of a priori pressure in the hydrostatic integration to derive T dry. The assumption of a dry atmosphere and hydrostatic ð1þ L12808 1of5

Figure 1. Co-located radiosonde and RO profiles for contrasting tropopause cases with (top) sharp and (bottom) broad transitions. (a and e) Radiosonde temperature (solid line) and lapse rate (dashed line). (b and f) RO derived T dry (solid) and lapse rate (dashed). LRT and CPT altitudes are shown by a horizontal line and solid circle respectively and values are listed. (c and g) RO bending angle (solid) and its gradient (dashed) as a function of impact height (x R C ). (d and h) Natural logarithm of RO bending angle (solid) and its covariance transform (dashed). The tropopause impact height (geometric height) is shown by a horizontal (dashed) line, and its value listed as XT (ZT). equilibrium near the tropopause may be invalid in tropical regions during periods of strong convection [Holton et al., 1995]. [7] This study presents a robust method for determining tropopause altitude from RO bending angles. Transitions in the bending angle profile at the tropopause are identified with a covariance transform. The method is described in Section 2. The technique is tested by comparing results with LRT and CPT altitudes from radiosonde temperatures in Section 3. A RO tropopause analysis is presented in Section 4 and a summary provided in Section 5. 2. Tropopause Identification Algorithm [8] Figure 1 shows radiosonde and co-located RO observations in the troposphere and lower stratosphere with the LRT and CPT marked. The influence of humidity on T dry profiles is evident below about 8 km, but there is good quantitative agreement between the radiosonde and T dry profiles around the tropopause. [9] Figures 1c and 1g show the corresponding RO bending angle profiles, together with its gradient. Temperature and moisture gradients in the lower troposphere lead to large fluctuations in the bending angle gradient. Narayana Rao et al. [2007] proposed that the tropopause altitude coincides with a peak in the gradient of bending angle followed by a decrease for at least 1 km. Contrasting Figures 1c and 1g highlight the difficulties of defining unique detection criteria using these data, requiring a latitude-dependent lower limit on the tropopause height for example. Examination of a number of RO profiles suggests this approach is not sufficiently objective or robust for use in climate monitoring. From a sample of 282 co-located radiosonde and RO profiles examined, the tropopause height defined by a maximum in the bending angle gradient above 8 km was incorrectly diagnosed by a spike in the lower troposphere in 30% of cases. [10] In contrast, Figures 1d and 1h illustrate a clear variation of the natural logarithm of bending angle ln(a) about the tropopause. This parameter varies approximately 2of5

Figure 2. Correlation between (a) RO bending angle method tropopause and radiosonde LRT altitudes, (b) T dry and radiosonde LRT altitudes and (c) RO tropopause and T dry LRT. (d) RO tropopause and radiosonde CPT, (e) T dry and radiosonde CPT, (f) RO tropopause and T dry CPT. All altitudes are expressed as a geometric height. A line of best fit to the data is plotted for each case. linearly with height, with a distinct steepening of the gradient in the stratosphere relative to that in the tropopause. It is generally difficult to identify the exact transition point from gradients of ln(a), unless the tropopause is particularly sharp (e.g., Figure 1d). A more robust and objective method using covariance transforms offers the potential to distinguish the different behaviour of ln(a) between the troposphere and stratosphere. 3. Covariance Transforms [11] Gamage and Hagelberg [1993] described a method to identify sharp transitions in profiles of atmospheric variables by use of covariance transforms. The localised covariance transform, W f (a, b) ofdataf(z) usingabasis function h is defined as W f ða; bþ ¼ 1 a Z zt z b f ðzþh z b dz a where z b and z t are the lower and upper limits of the data profile respectively. A local maximum in W f (a, b) identifies the altitude z = b where a step in f(z) with a coherent vertical scale of a occurs. Brooks [2003] used a step function to ð2þ identify boundary layer height and found that the choice of a must be tuned to reflect the scale of the signals to be detected. [12] Figures 1d and 1h show the results of applying the covariance transform method to observed ln(a) profiles with a gradient function defined as h z b ¼ f ðzþ fðbþ; b a 2 z b þ a 2 a 0; elsewhere A transition from steep to shallower gradients with increasing height is identified by a maximum of W f (for negative f(z)). Figures 1d and 1h show a clear W f peak in the vicinity of the tropopause, allowing for unambiguous identification of the tropopause from bending angle data. [13] A gradient function width of 35 km was used. This choice for a identifies the larger scale tropopause transition and filters small scale variations associated with lower troposphere temperature and humidity gradients. This avoids the need for subjective bounds on the tropopause altitude, required if using T dry. For smaller a values, W f becomes more sharply peaked at transition points. However for a less than about 20 km the lower troposphere peaks in W f tend to be of comparable magnitude to that at the tropopause. In all ð3þ 3of5

from RO bending angles to geometric height. Figure 2 illustrates that the covariance transform approach provides a robust method to determine tropopause altitude directly from RO bending angles. The covariance transform results are well correlated with co-located radiosonde tropopause altitudes and comparable to those using T dry. Figure 3. (a) Zonal mean (5 ) and (b) standard deviation of RO derived tropopause altitudes for the period May November 2008. Results are shown for the bending angle method expressed in impact height (solid line) and in geometric height (dotted) together with LRT altitudes from derived T dry profiles (dashed). cases examined where maximum W f occurs in the tropopause region, the value of the tropopause altitude is independent of a. [14] If the tropopause transition is very broad, the computed W f profile may become broad with no distinct peak. To distinguish these cases, the relative strength of the W f maximum relative to its average in the surrounding ±5 km is calculated. A robust tropopause definition suitable for climatology is considered where the peak value exceeds 5% of the average (10% below 10 km). This check removed 14% from a sample of 282 co-located radiosonde and RO profiles examined. 4. Comparison With Radiosonde Observations [15] RO bending angle and refractivity data from a number of missions, namely CHAMP and GRACE-A, COSMIC and GRAS are analysed. Dry temperature profiles are derived from measured refractivity using the method described by Schmidt et al. [2004]. [16] The covariance transform method is tested using observations during July 2008. Results are compared with LRT and CPT altitudes identified from T dry profiles and colocated radiosonde temperature profiles from a sample of 32 globally distributed sites. A subset of 288 radiosonde temperature profiles met the co-location criteria that the radiosonde was launched within a distance of less than 300 km and within 3 hours of a RO profile. [17] Figure 2 shows the correlation between tropopause altitudes derived from co-located radiosonde and RO data. Altitudes are shown as geometric heights for consistent comparison between the different approaches. Equation (1) is used to convert tropopause impact height determined 5. May November 2008 Analysis [18] To determine global tropopause characteristics from bending angles the covariance transform method is applied to over 400,000 observed RO profiles between May and November 2008. A global tropopause altitude analysis is produced by computing averages on a 5 latitude and longitude grid. 5.1. Spatial Distribution [19] Figure 3 shows the global tropopause altitude distribution determined from RO bending angle (RO) and T dry. The distribution of RO zonal mean tropopause altitude and standard deviations are in qualitative agreement with T dry results and previous observations [Hoinka, 1998]. There is excellent quantitative agreement between altitude distributions in the extra-tropics when RO results are expressed in geometric height Z. The conversion to geometric height is only required for quantitative comparison with other observation types. Figure 3 shows it is possible to monitor spatial distributions of tropopause altitude directly in terms of impact height. [20] The RO method leads to slightly higher average tropopause altitudes than analysis of T dry within the tropics. This is because the LRT criteria identifies the lowest possible tropopause height while the RO bending angle approach identifies the most significant transition. This results in different results where multiple tropopause transitions occur in a profile and the bending angle transition at an upper layer is greater than at the lowest tropopause. This also explains the increased standard deviation of RO results about the mean within the tropics compared with T dry. The covariance transform method is a potentially important tool for detailed study of multiple tropopauses from high resolution RO data. Figure 4. Monthly zonal mean of RO derived tropopause altitudes during the period May November 2008. Results are shown as averages within 20 latitude bands for the bending angle method expressed in impact height (solid line) and geometric height (dotted) together with LRT altitudes from derived T dry profiles (dashed). 4of5

Increased standard deviations for the T dry LRT method across Antarctica supports the suggestion by Narayana Rao et al. [2007] that analysis of bending angles is more sensitive to tropopause transitions in this region than T dry. 5.2. Seasonal Variability [21] Figure 4 shows timeseries of monthly mean zonal tropopause altitudes between May and November 2008. The variation of the equatorial and 30 50 N monthly zonal means illustrate the northward shift of the tropopause height maximum during Northern Hemisphere summer. The RO method results in temporal variations of tropopause altitude in quantitative agreement at all latitudes with results using T dry and previous observations [Hoinka, 1998]. The amplitude of the seasonal cycles are the same for results using T dry and RO methods expressed in either geometric height or impact height. This result is significant for long-term climate monitoring of tropopause altitude since only bending angle data, which are directly linked to climate benchmark observations [Leroy et al., 2006], are then required to identify and monitor temporal tropopause altitude trends. 6. Summary [22] Global tropopause altitude can be determined directly from RO bending angle data. A robust method identifies the tropopause at the location of a maximum of the covariance transform of a bending angle profile with a gradient function. The use of bending angle data is of particular value for climate monitoring since bending angles are directly linked to climate benchmark observables with no need for additional processing or assumptions. This approach is more objective than previous criteria using bending angle or T dry. Note that tropopause temperature cannot be obtained from bending angle data alone. [23] Results show excellent quantitative agreement between the bending angle method and LRT and CPT derived from T dry and co-located radiosonde temperature profiles. Analysis of temporal and spatial distributions indicate it is possible to investigate global tropopause characteristics in terms of the measured impact height, without conversion to geometric height. [24] Use of bending angle profiles is potentially of particular importance for resolving multiple tropopause layers. This is because derivation of refractivity and T dry leads to vertical smoothing by the Abel transform and hydrostatic integration which may mask some multiple layers. [25] Acknowledgments. The author wishes to thank GFZ, UCAR and the GRAS SAF for providing RO data sets of GRACE and CHAMP, COSMIC and GRAS respectively. The radiosonde data were provided by the University of Wyoming. References Brooks, I. 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Healy (2008), Monitoring twenty-first century climate using GPS radio occultation bending angles, Geophys. Res. Lett., 35, L05708, doi:10.1029/2007gl032462. Santer, B., et al. (2003), Contributions of anthropogenic and natural forcing to recent tropopause height changes, Science, 301, 479 483. Schmidt, T., J. Wickert, G. Beyerle, and C. Reigber (2004), Tropical tropopause parameters derived from GPS radio occultation measurements with CHAMP, J. Geophys. Res., 109, D13105, doi:10.1029/ 2004JD004566. Schmidt, T., J. Wickert, G. Beyerle, and S. Heise (2008), Global tropopause height trends estimated from GPS radio occultation data, Geophys. Res. Lett., 35, L11806, doi:10.1029/2008gl034012. Staten, P. W., and T. Reichler (2008), Use of radio occultation for long-term tropopause studies: Uncertainties, biases, and instabilities, J. Geophys. Res., 113, D00B05, doi:10.1029/2008jd009886. World Meteorological Organization (1957), Definition of the tropopause, WMO Bull., 6, 136. H. W. Lewis, Met Office, Fitzroy Road, Exeter EX1 3PB, UK. (huw.lewis@metoffice.gov.uk) 5of5