• Anthes, R. A., and et al. , 2008: The COSMIC/FORMOSAT-3 mission: Early results. Bull. Amer. Meteor. Soc., 89, 313–333, doi:10.1175/BAMS-89-3-313.

    • Search Google Scholar
    • Export Citation
  • Ao, C. O., , and Hajj A. J. , 2013: Monitoring the width of the tropical belt with GPS radio occultation measurements. Geophys. Res. Lett., 40, 6236–6241, doi:10.1002/2013GL058203.

    • Search Google Scholar
    • Export Citation
  • Aparicio, J. M., , and Deblonde G. , 2008: Impact of the assimilation of CHAMP refractivity profiles on Environment Canada global forecasts. Mon. Wea. Rev., 136, 257–275, doi:10.1175/2007MWR1951.1.

    • Search Google Scholar
    • Export Citation
  • Cardinali, C., 2009: Monitoring the observation impact on the short-range forecast. Quart. J. Roy. Meteor. Soc., 135, 239–250, doi:10.1002/qj.366.

    • Search Google Scholar
    • Export Citation
  • Cardinali, C., , and Healy S. , 2014: Impact of GPS radio occultation measurements in the ECMWF system using adjoint-based diagnostics. Quart. J. Roy. Meteor. Soc., doi:10.1002/qj.2300, in press.

    • Search Google Scholar
    • Export Citation
  • Cucurull, L., 2010: Improvement in the use of an operational constellation of GPS radio occultation receivers in weather forecasting. Wea. Forecasting, 25, 749–767, doi:10.1175/2009WAF2222302.1.

    • Search Google Scholar
    • Export Citation
  • Davis, N. A., , and Birner T. , 2013: Seasonal to multidecadal variability of the width of the tropical belt. J. Geophys. Res. Atmos.,118, 7773–7787, doi:10.1002/jgrd.50610.

    • Search Google Scholar
    • Export Citation
  • Davis, S. M., , and Rosenlof K. H. , 2012: A multidiagnostic intercomparison of tropical-width time series using reanalyses and satellite observations. J. Climate, 25, 10611078, doi:10.1175/JCLI-D-11-00127.1.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Guo, Y., , Chang E. K. M. , , and Leroy S. S. , 2009: How strong are the Southern Hemisphere storm tracks? Geophys. Res. Lett., 36, L22806, doi:10.1029/2009GL040733.

    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., , Hajj G. A. , , Schofield J. T. , , Linfield R. P. , , and Hardy K. R. , 1997: Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res., 102, 23 42923 465, doi:10.1029/97JD01569.

    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., , Hajj G. A. , , Leroy S. S. , , and Herman B. , 2000: The GPS radio occultation technique. Terr. Atmos. Oceanic Sci., 11, 53114.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., 1997: Measurement of geopotential heights by GPS radio occultation. J. Geophys. Res., 102, 69716986, doi:10.1029/96JD03083.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , and Anderson J. G. , 2007: Estimating Eliassen-Palm flux using COSMIC radio occultation. Geophys. Res. Lett., 34, L10810, doi:10.1029/2006GL028263.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , Anderson J. G. , , and Dykema J. A. , 2006: Testing climate models using GPS radio occultation: A sensitivity analysis. J. Geophys. Res., 111, D17105, doi:10.1029/2005JD006145.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , Ao C. , , and Verkhoglyadova O. P. , 2012: Mapping GPS radio occultation data by Bayesian interpolation. J. Atmos. Oceanic Technol.,29, 1062–1074, doi:10.1175/JTECH-D-11-00179.1.

  • Liou, Y.-A., , Pavelyev A. G. , , Liu S.-F. , , Pavelyev A. A. , , Yen N. , , Fluang C.-Y. , , and Fong C.-J. , 2007: FORMOSAT-3/COSMIC GPS radio occultation mission: Preliminary results. IEEE Trans. Geosci. Remote Sens., 45, 38133826, doi:10.1109/TGRS.2007.903365.

    • Search Google Scholar
    • Export Citation
  • MacKay, D., 1992: Bayesian interpolation. Neural Comput., 4, 415447, doi:10.1162/neco.1992.4.3.415.

  • Manney, G. L., , Hegglin M. I. , , Daffer W. H. , , Santee M. L. , , Ray E. A. , , and Pa S. , 2011: Jet characterization in the upper troposphere/lower stratosphere (UTLS): Applications to climatology and transport studies. Atmos. Chem. Phys., 11, 61156137, doi:10.5194/acp-11-6115-2011.

    • Search Google Scholar
    • Export Citation
  • Mannucci, A. J., and et al. , 2006: Generating climate benchmark atmospheric soundings using GPS occultation data. Atmospheric and Environmental Remote Sensing Data Processing and Utilization II: Perspective on Calibration/Validation Initiatives and Strategies, A. H. L. Huang and H. J. Bloom, Eds., International Society for Optical Engineering (SPIE Proceedings, Vol. 6301), 630108, doi:10.1117/12.683973.

  • Randel, W., 1987: The evaluation of winds from geopotential height data in the stratosphere. J. Atmos. Sci., 44, 30973120, doi:10.1175/1520-0469(1987)044<3097:TEOWFG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Reichler, T., 2009: Changes in the atmospheric circulation as indicator of climate change. Climate Change: Observed Impacts on Planet Earth, T. M. Letcher, Ed., Elsevier, 145–164.

  • Rennie, M. P., 2010: The impact of GPS radio occultation assimilation at the Met Office. Quart. J. Roy. Meteor. Soc., 136, 116–131, doi:10.1002/qj.521.

    • Search Google Scholar
    • Export Citation
  • Schmetz, J., , Holmlund K. , , Hoffman J. , , Strauss B. , , Mason B. , , Gaertner V. , , Koch A. , , and Van De Berg L. , 1993: Operational cloud-motion winds from Meteosat infrared images. J. Appl. Meteor., 32, 12061225, doi:10.1175/1520-0450(1993)032<1206:OCMWFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Sears, J., , and Velden C. S. , 2012: Validation of satellite-derived atmospheric motion vectors and analyses around tropical disturbances. J. Appl. Meteor. Climatol., 51, 18231834, doi:10.1175/JAMC-D-12-024.1.

    • Search Google Scholar
    • Export Citation
  • Seidel, D. J., , Fu Q. , , Randel W. J. , , and Reichler T. J. , 2008: Widening of the tropical belt in a changing climate. Nat. Geosci., 1, 21–24, doi:10.1038/ngeo.2007.38.

    • Search Google Scholar
    • Export Citation
  • Steiner, A. K., , Lackner B. C. , , Ladstadter F. , , Scherllin-Pirscher B. , , Foelsche U. , , and Kirchengast G. , 2011: GPS radio occultation for climate monitoring and change detection. Radio Sci., 46, RS0D24, doi:10.1029/2010RS004614.

    • Search Google Scholar
    • Export Citation
  • Wickert, J., and et al. , 2001: Atmosphere sounding by GPS radio occultation: First results from CHAMP. Geophys. Res. Lett., 28, 32633266, doi:10.1029/2001GL013117.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Monthly averaged wind maps (m s−1) for January 2007: (a) reference winds from the ERA-Interim at 200-hPa constant kinetic pressure surface, (b) geostrophic wind map at 200-hPa constant dry pressure surface from the simulated dataset based on COSMIC ROs, and (c) the difference between the two.

  • View in gallery

    Sampling error. Difference between monthly averaged simulated geostrophic wind map and monthly averaged ERA-Interim geostrophic winds (m s−1) at constant dry pressure surface of 200 hPa for (left) January 2007 and (right) July 2007. Results for (a),(b) COSMIC geolocations with the maximum spherical harmonic basis of 14, (c),(d) COSMIC geolocations with the spherical harmonic basis of 18, and (e),(f) CHAMP geolocations with the spherical harmonic basis of 14. Sampling error RMS for COSMIC in 2007 (g) globally and (h) in a subtropical region (equatorward from ±35°). The near-equatorial region of ±10° is excluded.

  • View in gallery

    Ageostrophy error. Difference between reference ERA-interim winds and ERA-Interim-derived geostrophic winds (m s−1) at constant kinetic pressure surfaces at 200-hPa constant pressure surface for (a) January and (b) July 2007; (c) global RMS for different constant pressure surfaces in 2007; and (d) RMS in subtropics in 2007.

  • View in gallery

    Dry pressure error. Difference maps between two geostrophic wind datasets (m s−1) for January 2007 at (a) 250- and (b) 300-hPa constant pressure surfaces.

  • View in gallery

    Total error. Difference between monthly averaged simulated geostrophic wind map and monthly averaged reference ERA-Interim winds (m s−1) for (left) January 2007 and (right) July 2007 with the maximum spherical harmonic basis of 18. Results for COSMIC geolocations at (a),(b) constant pressure surface 100 hPa, (c),(d) constant pressure surface 200 hPa, and (e),(f) constant pressure surface 300 hPa. Total error RMS for COSMIC in 2007 (g) globally and (h) in a subtropical region (equatorward from ±35°). Near-equatorial region of ±10° is excluded.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 86 86 10
PDF Downloads 79 79 6

Estimation of Winds from GPS Radio Occultations

View More View Less
  • 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
  • | 2 Harvard School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts
  • | 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
© Get Permissions
Full access

Abstract

GPS radio occultations (RO) offer the possibility to map winds in the upper troposphere and lower stratosphere (UTLS) region because geopotential height is the independent coordinate of retrieval. Most other sounders do not offer this possibility because their independent coordinate of retrieval is pressure. To estimate the precision with which GPS radio occultation data can map winds, dry pressure profiles are simulated from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) at the actual locations of the Challenging Minisatellite Payload (CHAMP) and the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) soundings for the year 2007. Monthly wind maps were created by using Bayesian interpolation on subsampled ERA-Interim data in 3–5-day bins and subsequent averaging over a month. Mapping winds in this approach requires that 1) geostrophy approximates winds; 2) dry pressure approximates pressure in the UTLS; and 3) geopotential height can be mapped accurately given sparse, nonuniform distributions of data. This study found that, under these conditions, it is possible to map monthly winds near the tropopause with an accuracy of 5.6 m s−1 with CHAMP alone and 4.5 m s−1 with COSMIC alone. The dominant contributors to uncertainty are undersampling of the atmosphere and ageostrophy, particularly at the leading and trailing edges of the subtropical jet. The former is reduced with increased density of GPS RO soundings. The latter cannot be reduced even after iteration for balanced winds. Nevertheless, it is still possible to capture the general wind pattern and to determine the position of the subtropical jet despite the uncertainty in its magnitude. COSMIC radio occultation measurements from 2006 through 2011 were used to estimate monthly geostrophic winds maps in UTLS. The resultant wind dataset is posted online.

Corresponding author address: Olga P. Verkhoglyadova, Jet Propulsion Laboratory, California Institute of Technology, M/S 138-310, 4800 Oak Grove Drive, Pasadena, CA 91109. E-mail: olga.verkhoglyadova@jpl.nasa.gov

Abstract

GPS radio occultations (RO) offer the possibility to map winds in the upper troposphere and lower stratosphere (UTLS) region because geopotential height is the independent coordinate of retrieval. Most other sounders do not offer this possibility because their independent coordinate of retrieval is pressure. To estimate the precision with which GPS radio occultation data can map winds, dry pressure profiles are simulated from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) at the actual locations of the Challenging Minisatellite Payload (CHAMP) and the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) soundings for the year 2007. Monthly wind maps were created by using Bayesian interpolation on subsampled ERA-Interim data in 3–5-day bins and subsequent averaging over a month. Mapping winds in this approach requires that 1) geostrophy approximates winds; 2) dry pressure approximates pressure in the UTLS; and 3) geopotential height can be mapped accurately given sparse, nonuniform distributions of data. This study found that, under these conditions, it is possible to map monthly winds near the tropopause with an accuracy of 5.6 m s−1 with CHAMP alone and 4.5 m s−1 with COSMIC alone. The dominant contributors to uncertainty are undersampling of the atmosphere and ageostrophy, particularly at the leading and trailing edges of the subtropical jet. The former is reduced with increased density of GPS RO soundings. The latter cannot be reduced even after iteration for balanced winds. Nevertheless, it is still possible to capture the general wind pattern and to determine the position of the subtropical jet despite the uncertainty in its magnitude. COSMIC radio occultation measurements from 2006 through 2011 were used to estimate monthly geostrophic winds maps in UTLS. The resultant wind dataset is posted online.

Corresponding author address: Olga P. Verkhoglyadova, Jet Propulsion Laboratory, California Institute of Technology, M/S 138-310, 4800 Oak Grove Drive, Pasadena, CA 91109. E-mail: olga.verkhoglyadova@jpl.nasa.gov

1. Introduction

Global mapping of upper-air winds remains a challenge in meteorology and climate. The challenge arises because the direct measurement of winds is sparse, available only by rawinsonde or aircraft measurements. Atmospheric motion vectors have been estimated from satellite infrared measurements by tracking clouds and gradients in water vapor (Schmetz et al. 1993), but coverage is limited and the heights of the tracked features are difficult to estimate. Global upper-air wind fields in data gaps must be inferred from dynamics and knowledge of upper-air temperature and surface pressure. While the upper-air temperature field is densely measured by operational passive nadir sounders, surface pressure is not. In numerical weather prediction, denser observations of upper-air winds are desired because winds are undersampled, especially in oceanic regions and in regions of severe weather (Sears and Velden 2012). In climate research, global estimates of upper-air winds are important because of their relevance to projected widening of the Hadley circulation. The Hadley cell’s width is difficult to infer from existing data (Seidel et al. 2008; Davis and Rosenlof 2012; Davis and Birner 2013) because of the different data types and methods used for the estimations.

Radio occultation using the global positioning system (GPS RO; Kursinski et al. 1997, 2000) provides reliable and uniform datasets for a variety of atmospheric parameters that are being extensively used in climatological studies (e.g., Mannucci et al. 2006; Steiner et al. 2011). Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) ROs were successfully used to study the strength of wind tracks in the Southern Hemisphere (Guo et al. 2009). Recent studies by Davis and Birner (2013) and Ao and Hajj (2013) use GPS RO data to evaluate the width of the tropical belt and ultimately its widening. Leroy and Anderson (2007) used COSMIC RO data on temperature and geopotential height to study stratospheric circulation. They showed that GPS RO technique allows resolution of large-scale atmospheric eddies of about 1000 km on a daily basis.

The upper-air wind field is related to pressure gradients to first order by dynamical scale analysis. Since the retrieval of atmospheric variables from GPS RO data has geopotential height as its independent vertical coordinate (Leroy 1997), it can be used to directly infer upper-air pressure gradients. The zeroth-order winds that result from the dynamical balance of the pressure gradient and the Coriolis force are the geostrophic winds, obtained by the geostrophic wind equations [cf. Eqs. (7.6.6)–(7)] in Gill (1982). First-order correction to those winds due to cyclostrophic and self-acceleration effects can be estimated by iteration (Randel 1987), while other corrections cannot. Thus, even though GPS RO data are currently being assimilated into numerical weather prediction systems worldwide (Aparicio and Deblonde 2008; Cardinali 2009; Cucurull 2010; Rennie 2010; Cardinali and Healy 2014), GPS RO can be used independently of all other data and integrations of the equations of motion to estimate upper-air winds. In this paper we seek to discover how well GPS RO alone can be used to infer upper-air winds. We begin from the standpoint that upper-air winds can be estimated as geostrophic winds and possibly corrected upon iteration (Randel 1987). Three potential sources of error arise from 1) the differences between geopotential on surfaces of constant pressure and geopotential on surfaces of constant dry pressure, the latter of which is retrieved from GPS RO independent of outside information, giving rise to an error in geopotential; 2) undersampling of the spatial–temporal variability in geopotential yields sampling error; and 3) cyclostrophy, vertical advection of momentum, and convergence and divergence of wave momentum flux cause actual winds to depart from geostrophic winds, referred to as ageostrophy.

In the second section we explore the possibility of using geostrophic winds as an approximation of actual winds in the upper troposphere and lower stratosphere (UTLS) region and introduce the datasets. The contributions by the three sources of error mentioned above are explored and analyzed, as described in the third section. We briefly investigate a higher-order nonlinear wind (balance wind) approach. The final section summarizes the findings and provides conclusions.

2. Data and methodology of geostrophic wind estimation

Geostrophic wind is a first-order wind component determined at each constant atmospheric pressure surface by the horizontal pressure gradient and the Coriolis force. The horizontal geostrophic wind velocity is defined as
e1
where f = 2Ω sinθ is the Coriolis parameter with Ω as the sidereal spin rate of the earth and θ is the geodetic latitude, is the vertical unit vector, p is a horizontal gradient on a constant pressure surface, and Φ is geopotential energy per unit mass including the centrifugal potential. The geopotential is related to geopotential height Zg by Φ = g0Zg, where g0 = 9.806 65 m s−2 is the World Meteorological Organization (WMO) standard for gravity. We seek to answer how well these geostrophic winds approximate actual winds and what the intrinsic errors of the winds derived from GPS RO–based dataset of geopotential height are.

The Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim; Dee et al. 2011) is used as a benchmark model that supplies realistic and dynamically consistent gridded winds and geopotential defined at constant pressure surfaces. ERA-Interim is subsampled at the locations of actual GPS RO data obtained by the Challenging MiniSatellite Payload (CHAMP; Wickert et al. 2001) and COSMIC [also known as Formosa Satellite 3 (Formosat-3); Liou et al. 2007; Anthes et al. 2008] missions over the year 2007. The geopotential height data at each pressure surface are optimally interpolated with a Bayesian interpolation technique using a spherical harmonic expansion without overfitting the data (MacKay 1992; Leroy et al. 2012), providing an analytic map from which gradients can be evaluated easily.

The wet–dry ambiguity is a characteristic of GPS RO retrieval (Kursinski et al. 1997). Water vapor contributes to refractivity mostly in the lower troposphere, and thus retrievals of pressure and temperature assuming a perfectly dry atmosphere approximate kinetic pressure and temperature well in the UTLS region [see Eq. (5) and discussion in Leroy et al. 2006]. Such retrievals of pressure are called dry pressure retrievals in the GPS RO community. Because we are investigating how well GPS RO data alone can be used to infer winds, we assume knowledge of dry pressure only and proceed to apply geostrophy. Departure of dry pressure from kinetic pressure is considered a source of error for wind estimations to be quantified in this study.

We simulated a dataset by subsampling ERA-Interim Zg values on constant dry pressure surfaces at retrieved COSMIC and CHAMP RO geolocations and sounding times in the year of 2007. Dry pressure itself is calculated from the gridded temperature and humidity products of ERA-Interim using Eq. (5) of Leroy et al. (2006). The geopotential is interpolated linearly in the logarithm of dry pressure. The average monthly number of ROs for CHAMP is about 4500 and for COSMIC about 55 300. We use 6-h temporal resolution and 1.5° × 1.5° spatial resolution ERA-Interim geopotential data. The data are bilinearly interpolated in space and linearly in time to fit actual RO sounding times and geolocations. Geostrophic winds are calculated from Zg with Eq. (1) and binned in 5-day temporal bins. We use 3- or 4-day bins to account for remaining days in months in which the number of days is not divisible by 5. Bin lengths must be greater than or equal to 3 days because bin lengths shorter than 3 days will not provide enough data for the subsequent optimal mapping. Optimal mapping is accomplished using Bayesian interpolation (Leroy et al. 2012). In Bayesian interpolation, data in each temporal bin are fit without being overfit using a spherical harmonic expansion as basis functions. The fit is then expanded onto a 1.5° × 1.5° grid poleward of ±10° latitude. Based on the study by Leroy et al. (2012), we used a 14th-degree spherical harmonic expansion as the basis for CHAMP ROs derived Zg and 18th degree for COSMIC. We anticipate that higher-degree spherical harmonic expansions should reduce sampling error by better resolving stationary finescale atmospheric structures. To enable direct comparison between COSMIC and CHAMP RO data, we also used a 14th-degree spherical harmonic basis. After optimal mapping, the mapped geostrophic wind data are averaged over a month to create a simulated GPS RO dataset. We use constant dry pressure surfaces of 100, 150, 200, 250, and 300 hPa. With this approach we can use actual gridded ERA-Interim wind data defined at real pressure surfaces as the reference “perfect model” dataset. Monthly averaged gridded ERA-Interim winds and the simulated dataset (monthly averaged mapped geostrophic winds) are compared to estimate uncertainties in applying the technique.

In the error analysis, we introduce three types of gridded wind fields determined from the gridded products of ERA-Interim. The first gridded wind field is the actual wind field published and distributed in ERA-Interim, which we use as the “true” wind field. The second gridded wind field is the geostrophic wind field, which is computed using the geostrophic wind equation and horizontal gradients of geopotential on constant kinetic pressure surfaces. The third gridded wind field is the “dry pressure” geostrophic wind field, which is determined in the same way as the gridded geostrophic wind field but on surfaces of constant dry pressure. Definitions of the wind field datasets are summarized in Table 1.

Table 1.

Description of gridded wind datasets used in the study. All data are defined on 1.5° × 1.5° spatial grid and averaged over a month.

Table 1.

Figure 1a shows monthly averaged reference winds from the ERA-Interim at 200-hPa kinetic pressure for January 2007. Figure 1b shows geostrophic winds from the simulated COSMIC dataset at 200-hPa dry pressure surface, and Fig. 1c shows the difference between the two. Hereafter, the difference between two vector fields is defined as , where U is the eastward wind component and V is the northward wind component. The simulated COSMIC geostrophic wind pattern generally agrees with the ERA-Interim reference wind pattern, but there are differences up to ~10 m s−1, mostly in the tropics. In the next section, we will analyze the factors that contribute to this difference and estimate the uncertainty (or errors) of our wind estimation technique in the UTLS.

Fig. 1.
Fig. 1.

Monthly averaged wind maps (m s−1) for January 2007: (a) reference winds from the ERA-Interim at 200-hPa constant kinetic pressure surface, (b) geostrophic wind map at 200-hPa constant dry pressure surface from the simulated dataset based on COSMIC ROs, and (c) the difference between the two.

Citation: Journal of Atmospheric and Oceanic Technology 31, 11; 10.1175/JTECH-D-14-00061.1

3. Estimation of errors

a. Sampling error

We define the sampling error as the (absolute) difference between the gridded ERA-Interim geostrophic dry pressure winds and the simulated GPS RO dataset (see Table 1). The difference at 200-hPa dry pressure for January 2007 is shown in Fig. 2a. Bayesian interpolation with a 14th-degree spherical harmonic basis is used for optimal mapping. The equatorial region (±10°) is excluded from the error analysis because the geostrophic approximation is invalid near the equator. When compared to total error (Fig. 1c), sampling error is small but has maximum values of ~10 m s−1 in tropical region, which we define as within 35° north and south latitude. Figure 2b shows the difference for July 2007. It shows a larger error (up to 20 m s−1) in the tropical region.

Fig. 2.
Fig. 2.

Sampling error. Difference between monthly averaged simulated geostrophic wind map and monthly averaged ERA-Interim geostrophic winds (m s−1) at constant dry pressure surface of 200 hPa for (left) January 2007 and (right) July 2007. Results for (a),(b) COSMIC geolocations with the maximum spherical harmonic basis of 14, (c),(d) COSMIC geolocations with the spherical harmonic basis of 18, and (e),(f) CHAMP geolocations with the spherical harmonic basis of 14. Sampling error RMS for COSMIC in 2007 (g) globally and (h) in a subtropical region (equatorward from ±35°). The near-equatorial region of ±10° is excluded.

Citation: Journal of Atmospheric and Oceanic Technology 31, 11; 10.1175/JTECH-D-14-00061.1

Despite dense coverage by GPS RO near the subtropical front, the largest sampling error occurs in this region. The gradient of isobaric geopotential height at the subtropical front is nearly discontinuous, and the smoothly varying spherical harmonics used as the basis for Bayesian interpolation cannot capture the discontinuity well. Increasing the degree of the spherical harmonic basis, though, helps to reduce the sampling error near the subtropical front by better resolving the discontinuity in the gradient of the geopotential height field. Figures 2c,d show the differences between the simulated geostrophic winds, mapped with an 18th-degree (as opposed to 14th degree) spherical harmonic basis and ERA-Interim geostrophic winds at the 200-hPa dry pressure surface for January and July 2007, respectively. Sampling error for the 18th-degree basis is substantially less than for the 14th-degree basis for both months, thus demonstrating better resolution of the meridional structure of the atmosphere. Similar maps for the CHAMP-based simulated dataset, mapped with a 14th-degree spherical harmonic basis, are shown in Figs. 2e,f. There are larger sampling errors globally and in tropical regions, up to 20 m s−1, as compared to the COSMIC-based simulated dataset with the same spherical harmonic basis (Figs. 2a,b).

We introduce global and tropical root-mean-square (RMS) of the difference between two monthly averaged global velocity maps and as a quantitative measure of global error with the summations over geodetic latitude θ and longitude ϕ,
e2
on the 1.5° × 1.5° geodetic grid. Global RMS is evaluated for all latitudes outside 10° north and south latitude, and tropical RMS for all latitudes between 35° north and south but outside 10° north and south latitude. Monthly time series of RMS sampling error at four dry pressure levels for COSMIC geolocations are shown in Fig. 2g. Mapping with an 18th-degree spherical harmonic basis is used. The maximum global RMS sampling error is less than 4 m s−1 and is greatest in June 2007. Tropical RMS sampling error for COSMIC geolocations reaches 4 m s−1 (Fig. 2h). RMS sampling errors are uniform for the dry pressure range from 200 to 300 hPa but decrease for dry pressure of 150 hPa or less. Subtropical RMS sampling errors are somewhat greater than global RMS sampling error.

b. Ageostrophy error

Ageostrophic winds are computed as the difference between ERA-Interim reference winds and ERA-Interim gridded geostrophic winds on different constant kinetic pressure surfaces. Figures 3a,b show the differences between the wind maps at 200-hPa constant pressure surface in January and July 2007, respectively. The largest error is in the subtropics in the winter hemisphere. Figure 3c summarizes the global RMS ageostrophy error for different pressure surfaces. The largest global RMS error, ≈3.7 m s−1 in January–February, is at 200 hPa. Figure 3d shows subtropical RMS, which is substantially larger (≈4.5 m s−1) than the global RMS ageostrophy error. The ageostrophy error is largest around altitudes of the subtropical jet (150–250 hPa; see also Davis and Birner 2013).

Fig. 3.
Fig. 3.

Ageostrophy error. Difference between reference ERA-interim winds and ERA-Interim-derived geostrophic winds (m s−1) at constant kinetic pressure surfaces at 200-hPa constant pressure surface for (a) January and (b) July 2007; (c) global RMS for different constant pressure surfaces in 2007; and (d) RMS in subtropics in 2007.

Citation: Journal of Atmospheric and Oceanic Technology 31, 11; 10.1175/JTECH-D-14-00061.1

c. Dry pressure error

The dry pressure error is estimated as the difference between the ERA-Interim gridded geostrophic wind (on a constant kinetic pressure surface) and the dry pressure gridded geostrophic wind (on a constant dry pressure surface). Figure 4a,b show the dry pressure error for 250 and 300 hPa for January 2007. This error is important in the subtropics at 300 hPa, where it can reach 5 m s−1, and deeper in the atmosphere because of water vapor’s increasing contribution to the microwave index of refraction. The global RMS error at 200 hPa is about 0.12 m s−1. The subtropical RMS error reaches 0.2 m s−1. Our calculations show that this error is the least significant of the three in the UTLS region.

Fig. 4.
Fig. 4.

Dry pressure error. Difference maps between two geostrophic wind datasets (m s−1) for January 2007 at (a) 250- and (b) 300-hPa constant pressure surfaces.

Citation: Journal of Atmospheric and Oceanic Technology 31, 11; 10.1175/JTECH-D-14-00061.1

d. Total error

Total error is calculated as the difference between the simulated dataset of geostrophic winds on constant dry pressure surfaces and gridded ERA-Interim reference winds on constant kinetic pressure surfaces (see Table 1; Fig. 1c). Figure 5 presents results for simulated COSMIC RO data in January (left panels) and July (right panels) in 2007. The Bayesian interpolation uses an 18th-degree spherical harmonic basis. The top panels show the difference maps at 100 hPa, the middle panels at 200 hPa, and the bottom panels at 300 hPa. The largest difference is in the subtropics at 200 hPa. Figure 5g shows a monthly time series of the total global RMS error. The largest error is ≈4.5 m s−1 at 250 hPa. The error is the smallest (average of 3 m s−1) at 150 hPa. The global RMS error is uniform for between 200 and 300 hPa. In the subtropics (Fig. 5h), RMS total error is the greatest (≳5 m s−1) around 200–250 hPa.

Fig. 5.
Fig. 5.

Total error. Difference between monthly averaged simulated geostrophic wind map and monthly averaged reference ERA-Interim winds (m s−1) for (left) January 2007 and (right) July 2007 with the maximum spherical harmonic basis of 18. Results for COSMIC geolocations at (a),(b) constant pressure surface 100 hPa, (c),(d) constant pressure surface 200 hPa, and (e),(f) constant pressure surface 300 hPa. Total error RMS for COSMIC in 2007 (g) globally and (h) in a subtropical region (equatorward from ±35°). Near-equatorial region of ±10° is excluded.

Citation: Journal of Atmospheric and Oceanic Technology 31, 11; 10.1175/JTECH-D-14-00061.1

A summary of the error estimates for COSMIC RO in January and July 2007 at 200 hPa is given in Table 2 for a global estimate and a subtropical region separately. Mapping with an 18th-degree spherical harmonic basis was used because it provides better fitting for COSMIC soundings compared to a 14th-degree basis (Leroy et al. 2012). The global ageostrophy error is greater than the global sampling error. Dry pressure error can be ignored for the UTLS in comparison with other errors. The ageostrophy error is also the largest contributor to the total error in the subtropics. Detailed study showed that the sampling error and the ageostrophy error are anticorrelated, primarily near the subtropical front, leading to partial cancellation of the two sources of error.

Table 2.

Global RMS (m s−1) of main errors at 200-hPa constant pressure surface estimated for the simulated dataset based on COSMIC geolocations in January and July 2007. Mapping with a spherical harmonic basis of 18th degree is used.

Table 2.

Table 3 presents the comparison between RMS errors estimated for COSMIC and CHAMP RO at 200 hPa using a 14th-degree spherical harmonic basis for mapping rather than an 18th-degree basis as in Table 2. For COSMIC ROs the sampling and ageostrophy errors are comparable (between ≈3.2 and 3.7 m s−1). The sampling error (>4.0 m s−1) dominates the ageostrophy error (<3.7 m s−1) for CHAMP ROs. The total error for COSMIC ROs (~4.1 m s−1) is larger for a 14th-degree spherical harmonic basis when mapping than for an 18th-degree spherical harmonic basis (~3.7 m s−1; Table 2).

Table 3.

Global RMS (m s−1) of main errors at 200-hPa constant pressure surface estimated for the simulated dataset based on COSMIC and CHAMP geolocations in January and July 2007. Mapping with a spherical harmonic basis of 14th degree is used.

Table 3.

e. Balance winds

Figure 1 shows an example of geostrophic winds underestimating actual winds. Randel (1987) suggested using balance winds as a more accurate representation of actual winds than simple geostrophic winds. The balance winds are a higher-order nonlinear wind approximation derived from the full momentum equations but without time derivatives and vertical advection terms [Eqs. (4a) and (4b) in Randel 1987]. Additional terms to approximate horizontal winds beyond the geostrophic approximation are described as cyclostrophic acceleration terms, but they do not account for the convergence of momentum flux. The resulting momentum equations are solved by iteration for zonal and meridional components and converge to solutions at about the third iteration (Randel 1987). This approach is important to improve accuracy in the determination of the location of the jet stream core. Davis and Birner (2013) included one of the nonlinear terms in the balance equations, the so-called metric term u2 tan(θ)/a, where u is the meridional wind component, θ is the latitude, and a is the mean radius of the earth. They have shown that this term is ~5% of the linear term. We tested the balanced wind approach in the UTLS and estimated the differences between mapped balance winds after the first iteration and gridded monthly averaged ERA-Interim real winds on several constant pressure surfaces. The balanced wind approximation in the first iteration improved the wind estimation outside the tropics and at the upper-altitude boundary of the UTLS, but showed larger disagreements with actual winds near the subtropical front. The error maximizes between 150 and 250 hPa, near the core of the subtropical jet. Maximum differences between simulated and ERA winds in the tropics range from ≲ 10 m s−1 at 70 hPa to ≳ 20 m s−1 at 200 hPa. The balanced wind solution started to diverge at the second and third iterations, rendering this technique unsuited to mapping two-dimensional winds using RO data (see section 4).

4. Discussion

We mapped monthly winds at constant pressure surfaces from 150 to 300 hPa with geostrophic winds. Since we used simulated wind field datasets based on ERA-Interim, the total error does not include GPS RO retrieval errors. Kursinski et al. (1997) estimates an RMS uncertainty of ~0.5 K in temperature and ~10 m in geopotential height per sounding. COSMIC should be able to obtain monthly averages with sampling errors of 2 m in the tropics and 6 m in midlatitudes at 200 hPa (Leroy et al. 2012). A recent study compares the geopotential height computed from CHAMP and COSMIC ROs with several Coupled Model Intercomparison Project, phase 5 (CMIP5) models as well as ERA-Interim and Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalyses from 2002 to 2008 (Ao et al. 2014, manuscript submitted to J. Geophys. Res. Atmos.). It shows excellent agreement between GPS RO and reanalyses and good agreement between GPS RO–based results and climate models in the tropics.

Assimilating UTLS winds computed by the method described in this paper directly into an operational forecast system would be an interesting experiment. The uncertainties in UTLS winds estimated here are competitive with estimates of uncertainties in analyzed winds produced by modern data assimilation systems. It is possible that assimilating RO-derived winds directly into a forecast system should offer advantages over indirect inference of UTLS winds after assimilation of RO bending angle data, as is currently done in many forecasting centers (Aparicio and Deblonde 2008; Cardinali 2009; Cucurull 2010; Rennie 2010; Cardinali and Healy 2014). Any misconstruction of background error covariance or observation error covariance would lessen the impact of RO data on UTLS winds. Because the analysis cycle of many forecast systems is 6 h, it will be necessary to produce RO-derived winds with the same frequency; however, the density of RO data is not yet sufficient to produce RO-derived winds with that frequency. At this point, only an observational system simulation experiment can be applied to investigate the merits of directly assimilating RO-derived UTLS winds.

Study of the global circulation and its long-term variability is important for understanding climate change (Reichler 2009). Actual winds and geostrophic winds (Figs. 1a,b) show a similar global pattern with differences of ~10 m s−1 in the wind magnitude in the subtropics. This opens the possibility to determine the position of the subtropical jet despite uncertainty in its magnitude. A recent study by Ao and Hajj (2013) evaluated the use of RO data for monitoring poleward expansion of the tropical jet. They show a promising result of a statistically significant widening trend in the Northern Hemisphere consistent with ECMWF-based estimates. While RO-derived winds may be useful for climate research, the question of whether the provided uncertainties in wind estimates are good enough for climate applications will be a subject for future studies.

We have performed preliminary analysis in deriving the jet stream position from the RO wind fields. A simple algorithm of searching for the local maxima (Davis and Birner 2013) has yielded encouraging results. We suggest that a more elaborate algorithm rather than searching for a local geostrophic velocity maximum in GPS RO data could yield better accuracy in determining a jet core position. Currently, we are looking into applying well-developed techniques of jet characterization to our GPS RO–derived geostrophic wind dataset. Such techniques are widely used to study jet streams using sparse satellite measurements and to locate multiple tropopauses in the UTLS (Manney et al. 2011).

We calculated the first iteration of balance winds (Randel 1987; Davis and Birner 2013) for the simulated Zg dataset in the UTLS region. The balanced winds approach is validated for the upper stratosphere at the constant pressure surface of 10 hPa (Randel 1987). However, we found that this method did not produce better wind estimates compared with ERA winds at the first iteration. The maximum errors (up to 20 m s−1) were the largest at the constant pressure surfaces of 150 and 250 hPa. Nonlinear terms in the balance wind equations introduced numerical noise and the solution did not converge at the third iteration as expected. It is likely that a more detailed investigation into extracting balanced winds from RO data, though, may render more accurate RO-derived winds than RO-derived geostrophic winds.

5. Conclusions

We described a technique to map monthly winds at constant pressure surfaces from 150 to 300 hPa with an accuracy of 5.6 m s−1 global RMS error with CHAMP alone and 4.0 m s−1 global RMS error with COSMIC alone (Tables 2 and 3). Sampling, ageostrophy, and dry pressure errors all contribute to total error. Sampling error decreases for COSMIC RO–derived estimates when the spherical harmonic basis for mapping increases from the 14th to 18th degree (see also Leroy et al. 2012). The largest error of ~5 m s−1 occurs in the subtropics. Sampling error is the dominant error for the CHAMP dataset because only a 14th-degree spherical harmonic basis can be used for mapping the data. Ageostrophy error is the largest error for the COSMIC dataset in the subtropics and at altitudes around the subtropical jet from 200 to 300 hPa. Dry pressure error can be neglected above 300 hPa. Sampling error and ageostrophy are spatially anticorrelated. Enhanced ageostrophy is associated with exaggerated finescale structure in the geopotential fields, and coarse mapping algorithms such as Bayesian interpolation have difficulty resolving them, giving rise to sampling error.

After evaluating the above-mentioned contributors to error, we used the COSMIC–GPS RO dataset for 2006–11 to create gridded monthly geostrophic wind maps. The main steps of the proposed technique are as follows:

  • Derive geopotential height data from GPS RO measurements (Leroy 1997).
  • Combine data from individual profiles into several day bins (optimal number is from 3- to 5-day temporal bins) and bin by 17 constant pressure surfaces from 10 to 275 hPa.
  • Perform Bayesian interpolation within the bins to obtain global maps of geopotential height as an expansion of spherical harmonics (Leroy et al. 2012).
  • Calculate geostrophic winds for each constant pressure surface on 5° × 5° grid.
  • Average the gridded geostrophic wind data over a month.

The data are available at the Jet Propulsion Laboratory Global Environmental and Earth Science Information System (GENESIS) website (http://genesis.jpl.nasa.gov/genesis/) in netCDF3.0 data format. We strongly advocate further use of parameters derived from geopotential height readily available from GPS RO measurements to capture the general wind pattern and to determine the position of the subtropical jet.

Acknowledgments

The authors thank the reviewers for their useful comments. Portions of this work were done at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. S. Leroy acknowledges support from NASA Grant NNX10AK55G to Harvard University. Government sponsorship acknowledged.

REFERENCES

  • Anthes, R. A., and et al. , 2008: The COSMIC/FORMOSAT-3 mission: Early results. Bull. Amer. Meteor. Soc., 89, 313–333, doi:10.1175/BAMS-89-3-313.

    • Search Google Scholar
    • Export Citation
  • Ao, C. O., , and Hajj A. J. , 2013: Monitoring the width of the tropical belt with GPS radio occultation measurements. Geophys. Res. Lett., 40, 6236–6241, doi:10.1002/2013GL058203.

    • Search Google Scholar
    • Export Citation
  • Aparicio, J. M., , and Deblonde G. , 2008: Impact of the assimilation of CHAMP refractivity profiles on Environment Canada global forecasts. Mon. Wea. Rev., 136, 257–275, doi:10.1175/2007MWR1951.1.

    • Search Google Scholar
    • Export Citation
  • Cardinali, C., 2009: Monitoring the observation impact on the short-range forecast. Quart. J. Roy. Meteor. Soc., 135, 239–250, doi:10.1002/qj.366.

    • Search Google Scholar
    • Export Citation
  • Cardinali, C., , and Healy S. , 2014: Impact of GPS radio occultation measurements in the ECMWF system using adjoint-based diagnostics. Quart. J. Roy. Meteor. Soc., doi:10.1002/qj.2300, in press.

    • Search Google Scholar
    • Export Citation
  • Cucurull, L., 2010: Improvement in the use of an operational constellation of GPS radio occultation receivers in weather forecasting. Wea. Forecasting, 25, 749–767, doi:10.1175/2009WAF2222302.1.

    • Search Google Scholar
    • Export Citation
  • Davis, N. A., , and Birner T. , 2013: Seasonal to multidecadal variability of the width of the tropical belt. J. Geophys. Res. Atmos.,118, 7773–7787, doi:10.1002/jgrd.50610.

    • Search Google Scholar
    • Export Citation
  • Davis, S. M., , and Rosenlof K. H. , 2012: A multidiagnostic intercomparison of tropical-width time series using reanalyses and satellite observations. J. Climate, 25, 10611078, doi:10.1175/JCLI-D-11-00127.1.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Guo, Y., , Chang E. K. M. , , and Leroy S. S. , 2009: How strong are the Southern Hemisphere storm tracks? Geophys. Res. Lett., 36, L22806, doi:10.1029/2009GL040733.

    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., , Hajj G. A. , , Schofield J. T. , , Linfield R. P. , , and Hardy K. R. , 1997: Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res., 102, 23 42923 465, doi:10.1029/97JD01569.

    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., , Hajj G. A. , , Leroy S. S. , , and Herman B. , 2000: The GPS radio occultation technique. Terr. Atmos. Oceanic Sci., 11, 53114.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., 1997: Measurement of geopotential heights by GPS radio occultation. J. Geophys. Res., 102, 69716986, doi:10.1029/96JD03083.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , and Anderson J. G. , 2007: Estimating Eliassen-Palm flux using COSMIC radio occultation. Geophys. Res. Lett., 34, L10810, doi:10.1029/2006GL028263.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , Anderson J. G. , , and Dykema J. A. , 2006: Testing climate models using GPS radio occultation: A sensitivity analysis. J. Geophys. Res., 111, D17105, doi:10.1029/2005JD006145.

    • Search Google Scholar
    • Export Citation
  • Leroy, S. S., , Ao C. , , and Verkhoglyadova O. P. , 2012: Mapping GPS radio occultation data by Bayesian interpolation. J. Atmos. Oceanic Technol.,29, 1062–1074, doi:10.1175/JTECH-D-11-00179.1.

  • Liou, Y.-A., , Pavelyev A. G. , , Liu S.-F. , , Pavelyev A. A. , , Yen N. , , Fluang C.-Y. , , and Fong C.-J. , 2007: FORMOSAT-3/COSMIC GPS radio occultation mission: Preliminary results. IEEE Trans. Geosci. Remote Sens., 45, 38133826, doi:10.1109/TGRS.2007.903365.

    • Search Google Scholar
    • Export Citation
  • MacKay, D., 1992: Bayesian interpolation. Neural Comput., 4, 415447, doi:10.1162/neco.1992.4.3.415.

  • Manney, G. L., , Hegglin M. I. , , Daffer W. H. , , Santee M. L. , , Ray E. A. , , and Pa S. , 2011: Jet characterization in the upper troposphere/lower stratosphere (UTLS): Applications to climatology and transport studies. Atmos. Chem. Phys., 11, 61156137, doi:10.5194/acp-11-6115-2011.

    • Search Google Scholar
    • Export Citation
  • Mannucci, A. J., and et al. , 2006: Generating climate benchmark atmospheric soundings using GPS occultation data. Atmospheric and Environmental Remote Sensing Data Processing and Utilization II: Perspective on Calibration/Validation Initiatives and Strategies, A. H. L. Huang and H. J. Bloom, Eds., International Society for Optical Engineering (SPIE Proceedings, Vol. 6301), 630108, doi:10.1117/12.683973.

  • Randel, W., 1987: The evaluation of winds from geopotential height data in the stratosphere. J. Atmos. Sci., 44, 30973120, doi:10.1175/1520-0469(1987)044<3097:TEOWFG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Reichler, T., 2009: Changes in the atmospheric circulation as indicator of climate change. Climate Change: Observed Impacts on Planet Earth, T. M. Letcher, Ed., Elsevier, 145–164.

  • Rennie, M. P., 2010: The impact of GPS radio occultation assimilation at the Met Office. Quart. J. Roy. Meteor. Soc., 136, 116–131, doi:10.1002/qj.521.

    • Search Google Scholar
    • Export Citation
  • Schmetz, J., , Holmlund K. , , Hoffman J. , , Strauss B. , , Mason B. , , Gaertner V. , , Koch A. , , and Van De Berg L. , 1993: Operational cloud-motion winds from Meteosat infrared images. J. Appl. Meteor., 32, 12061225, doi:10.1175/1520-0450(1993)032<1206:OCMWFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Sears, J., , and Velden C. S. , 2012: Validation of satellite-derived atmospheric motion vectors and analyses around tropical disturbances. J. Appl. Meteor. Climatol., 51, 18231834, doi:10.1175/JAMC-D-12-024.1.

    • Search Google Scholar
    • Export Citation
  • Seidel, D. J., , Fu Q. , , Randel W. J. , , and Reichler T. J. , 2008: Widening of the tropical belt in a changing climate. Nat. Geosci., 1, 21–24, doi:10.1038/ngeo.2007.38.

    • Search Google Scholar
    • Export Citation
  • Steiner, A. K., , Lackner B. C. , , Ladstadter F. , , Scherllin-Pirscher B. , , Foelsche U. , , and Kirchengast G. , 2011: GPS radio occultation for climate monitoring and change detection. Radio Sci., 46, RS0D24, doi:10.1029/2010RS004614.

    • Search Google Scholar
    • Export Citation
  • Wickert, J., and et al. , 2001: Atmosphere sounding by GPS radio occultation: First results from CHAMP. Geophys. Res. Lett., 28, 32633266, doi:10.1029/2001GL013117.

    • Search Google Scholar
    • Export Citation
Save