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 Simulations of radio occultation bending angle profiles in transient climate experiments using a state-of-the-art global coupled climate model show a clear signal in bending angle emerging over the first half of the twenty-first century. The bending angle signal can be related to the predicted changes in the climate over this period in response to increasing greenhouse gas concentrations and is shown to be primarily a combination of three distinct effects: the changing temperature structure of the atmosphere, increased water vapor in the troposphere, and the expansion of the atmosphere due to the warming. Analysis of the predicted trends in the bending angle indicates that the climate change signal in the tropical upper troposphere and lower and middle stratosphere may become distinguishable from natural variability, i.e. “detected”, after approximately ten to sixteen years of measurements. This suggests that such observations may be one of our best prospects for monitoring the evolution of the climate over the coming decades.
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 Accurate, global, and stable long-term observations are the key to understanding the changes in climate over the coming decades predicted by the current generation of global climate models (GCMs). These observations will provide direct evidence of the climate's evolution and will also be essential to evaluate and refine the GCM predictions. GPS radio occultation (RO) measurements possess the necessary characteristics of such an observational record. In addition, their all-weather capability (the measurement is unaffected by clouds, for example), self-calibration (through their traceability to absolute standards) and high vertical resolution mean that they should be capable of providing a climate record that is free from many of the problems associated with both satellite and conventional measurements [Goody et al., 1998].
 The RO technique [e.g., Kursinski et al., 1997] is based on the fact that the path of a radio signal propagating between a GPS satellite and a receiver placed on a low earth orbit (LEO) satellite is bent or refracted by the atmosphere. The bending is caused by gradients in the refractive index of the atmosphere, which in turn can be related to gradients in the atmospheric density and water vapor. During an occultation event the motion of the satellites enables the variation of ray bending as a function of minimum ray-height above the surface to be determined. Fundamentally, the RO technique is based on the precise measurement of time-delays with atomic clocks. The bending angles are derived from these delays. Bending angle profiles can then be inverted to provide profiles of refractivity, and subsequently pressure and temperature.
 The potential of RO measurements for both climate monitoring and climate model evaluation was described by Yuan et al.  and Kursinski et al. , who noted in particular that RO observations should be able to provide useful information relating to near-tropopause temperature changes, humidity changes in the lower and middle troposphere, and the expansion of the troposphere due to global warming.
Eyre  outlined how RO data could be exploited by a global numerical weather prediction (NWP) system and concluded that direct assimilation of the bending angle was preferable to using either refractivity profiles or retrievals of temperature and humidity. The benefits of assimilating bending angle measurements in an operational framework have recently been demonstrated by Healy and Thépaut , who showed clear improvements in upper tropospheric and lower stratospheric temperatures in experiments using the ECMWF global forecasting system. An important feature of the RO measurement is that it can be assimilated without the need for bias correction. This enhances their ability to correct model biases which are otherwise difficult to rectify because other satellite data tend to be bias corrected to the assimilating model [Healy and Thépaut, 2006].
 Much work on the climate applications of RO data has focussed on the use of retrieved parameters such as temperature or geopotential heights for climate monitoring [e.g., Gobiet et al., 2007; Leroy, 1997]. Recently Leroy et al.  have considered the use of “dry pressure”, which can be derived from refractivity profiles, as a potential climate monitoring parameter. However, these derived quantities are more sensitive to structural uncertainty than bending angles [von Engeln, 2006] because of the introduction of a priori information in the additional processing steps [Eyre, 1987]. The more fundamental nature of the bending angle measurement, together with its demonstrated utility in the NWP context, suggests the use of the bending angle profile itself as a climate variable. This study therefore considers the use of the bending angle for climate monitoring. By simulating bending angle profiles in a state-of-the-art climate model we explore the climate signal over the next half-century and the information content of this signal in relation to changes in the atmosphere due to climate warming. We also estimate the time required to detect trends in the bending angle over the coming decades.
2. Climate Model Simulations and Methodology
 To investigate the climate change signal over the twenty-first century we use transient coupled model integrations of the Hadley Centre Global Environmental Model (HadGEM1) [Johns et al., 2006]. These follow the SRES A1B scenario [Nakicenovic and Swart, 2000], which specifies time-varying greenhouse gas and ozone concentrations, aerosol emissions and land use changes over the period 2000-2100. Under this scenario the global mean temperature increase by 2050, relative to the 1961–1990 mean, is approximately 2 K, rising to around 3.6 K by 2100 [Stott et al., 2006]. We also use a long control integration (employing fixed forcings) of HadGEM1 which has currently completed almost 1300 years and a simulation over the twentieth century which includes time varying forcings due to volcanic aerosols and solar irradiance changes [Stott et al., 2006].
 Bending angle profiles are calculated from monthly mean fields of temperature, pressure and humidity. Thus, for the A1B scenario integration, the profiles are calculated at each grid point, for each month over the period 2000–2055. Given the observed impact parameter, a, the bending angle, α, can be written as [e.g., Kursinski et al., 1997]
where n is the refractive index and x = nr, with r the radius value of a point on the ray path. The refractive index at radio frequencies is derived from the climate model fields using
where N is the refractivity, P is the atmospheric pressure (hPa), T is the temperature (K), Pw (hPa) is the water vapor partial pressure and c1 and c2 are 77.6 K hPa−1 and 3.73 × 105 K2 hPa−1 respectively. The bending angles are calculated at a fixed set of 110 “impact heights” (defined as the impact parameter minus the local radius of curvature, with 2 km roughly corresponding to the surface), equally spaced at 250 m intervals. This is comparable to the number of impact heights used for assimilation of the data and should be sufficient to demonstrate the information content in the climate context. Full details of the calculation of bending angle profiles from model fields are given by Healy and Thépaut .
 The annual, zonal mean bending angle profile distribution is shown in Figure 1a. The values correspond to around 0.7–1.9 degrees at the surface, decreasing to around 10−2 degrees in the middle stratosphere. Positive values of α indicate bending towards the Earth's surface. The bending angle profile depends on refractivity, which itself depends on atmospheric density: thus from the mid-troposphere upwards the primary dependence is on temperature and pressure, while in the lower troposphere water vapor also makes a significant contribution.
Figures 1b–1f show the evolution of the climate change signal in the zonal mean bending angle profiles from the present-day through to the 2050s. The signal in the tropical lower stratosphere emerges after a decade, is clearly identifiable by the 2020s and continues to intensify through to the 2050s. It is accompanied by a signal in the tropical mid-stratosphere which, though weaker initially, is of comparable size by the 2050s. The signals at polar latitudes in the mid-stratosphere are more variable over the first 20–30 years and are not clearly established until the 2040s. In the upper troposphere a signal of opposite sign emerges, the upper boundary of which follows the zonal variation of the height of the tropopause: this delineates the warming of the troposphere due to increased greenhouse gases from the cooling of the stratosphere. In the lower troposphere the increased water vapor as the climate warms dominates and the bending angle signal is positive.
 Thus by the 2050s a clear signal in the bending angle, with a well-defined geographical distribution, has emerged. We next investigate the contributions to this signal from the different effects associated with the changing climate over this period. To do this we use the tangent linear version [e.g., Hoffman et al., 1992] of the bending angle forward model. The tangent linear allows us to identify the contributions to the bending angle signal from changes in temperature, pressure and humidity: it calculates the change in the simulated bending angle values produced by pressure, temperature and humidity perturbations for a given linearization state.
 The decomposition of the 2050s minus 2000s bending angle differences is calculated with the tangent linear, using the 2000s as the linearization state (Figure 2). As expected, the contribution to the bending angle signal from the humidity change (Figure 2a) is confined to the middle and lower troposphere and is largest in tropics, where the atmospheric water vapour abundance is greatest. The temperature change contribution (Figure 2b) reflects the well-known effect of tropospheric warming and stratospheric cooling due to increasing greenhouse gas concentrations. The basic features of the temperature trends in the present simulations are consistent with the earlier Hadley Centre model study of Butchart et al. . The warming is larger in the upper troposphere than in the lower troposphere, particularly in the tropics–a consequence of the moist adiabatic lapse rate decreasing with the increasing temperatures. Also apparent is the amplification of the surface and tropospheric warming at high latitudes in the Northern Hemisphere. In the stratosphere it is the cooling which increases with altitude: in the lower stratosphere the cooling due to increased longwave emission is to a large degree offset by increased absorption of upwelling longwave radiation from the troposphere. Another feature of note is the warming signal at polar latitudes in both hemispheres at around 18 km. In the Southern Hemisphere this is partly due to the recovery of stratospheric ozone under the prescribed A1B scenario. A possible explanation for the remainder of this signal (and that in the Northern Hemisphere) is dynamical heating due to increased troposphere-stratosphere mass exchange driven by more vigorous extra-tropical tropospheric wave activity [Butchart and Scaife, 2001]. The contribution from pressure changes (Figure 2c) arises from the expansion of the atmosphere as the climate warms [Kursinski et al., 1997; Leroy et al., 2006]: this manifests itself as an increase in pressure at fixed height surfaces, with the maximum (which is around 3–4 hPa in these simulations) occurring near the tropopause.
 It can thus be seen that the total bending angle signal due to climate change can be neatly decomposed into components due to these different effects and results from their linear combination (cf. Figures 2d and 1f, which indicates that we are within the linear regime with respect to perturbations considered here). In the tropics, for example, we see four distinct maxima: a positive signal due to increasing water vapour in the lower troposphere (which dominates a negative change due to the increased temperature); a negative signal in the upper troposphere due to enhanced warming compared to the surface; a positive signal in the lower stratosphere (due predominantly to the maximum in the thermal expansion effect); and a positive signal in the mid-stratosphere arising primarily from the enhanced radiative cooling compared to the lower stratosphere. Thus, although it might initially appear to be a somewhat esoteric quantity, changes in the bending angle due to climate warming can be readily understood and interpreted in terms of more familiar geophysical variables. Given the particular qualities of the measurement this suggests that the bending angle itself is of great potential use both for climate monitoring and climate model evaluation.
 We next consider the application of bending angle measurements to detect climate trends over the coming decades. Following Weatherhead et al. , the number of years, n*, required to detect a trend of magnitude ∣ω0∣ at the 95% confidence level, with 90% probability is given by
where σN is the month-to-month variability in the noise and ϕ is the lag 1-month autocorrelation in the noise. This method has previously been applied to total column ozone data [Weatherhead et al., 2000] and to shortwave radiative flux measurements [Loeb et al., 2007].
 We consider the trends at the equator at impact heights of 12, 20 and 26 km, where maxima in the bending angle signal have been noted (Figure 1f). The least squares linear trends are calculated from the A1B scenario integration over the period 2000–2050 (Figures 3a–3c). The variability and autocorrelation in the noise are obtained from the long control integration of HadGEM1 with fixed greenhouse gases and other forcings: monthly mean bending angle profiles are calculated from a set of five fifty-year segments of the simulation and the noise characteristics derived from the monthly mean anomalies after removal of the mean seasonal cycle. The results (Table 1) indicate that the trend in the mid-stratosphere would be detectable within a decade (the trend is smallest but so too is the noise), while those in the lower stratosphere and upper troposphere would be detectable after approximately sixteen years. The 95% confidence intervals in the detection times are given by (n*e−B, n*eB), where
and M is the number of months of data [Weatherhead et al., 1998]. Alternatively, one can also consider the evolution of the trend estimate with time over the 2000–2050 period (Figures 3d–3f). Here the trend has been estimated using a weighted least squares regression, with the error covariance matrix defined by the estimates of the noise characteristics. In all three cases the trend estimate has clearly started to converge to its final value by the detection times shown in Table 1. Note that these detection times are comparable to estimates presented by Leroy et al.  based on the optimal finger-printing technique using dry pressure.
Table 1. Bending Angle Trends and Detection Times at the Equator for Three Selected Altitudes
Impact Height, km
Trend, ω0, 10−6 rads/year
Variability of Noise, σN, 10−6 rads
Autocorrelation of Noise φ
Detection Time n*, years
95% Confidence Interval, years
 As a caveat to these results it should be noted that if the model's natural variability is unrealistically low then these detection limits might be underestimated. On the other hand, it should also be noted that we have not averaged the data in either latitude or height in order to try and reduce the noise. Unpredictable events such as large volcanic eruptions also have the potential to increase the detection times. To test this we have calculated the noise characteristics for the period 1950–2000 using a HadGEM1 simulation employing anthropogenic and observed forcings, including those due to major volcanic events and solar variability. The increase in both the variability and autocorrelation of the noise (primarily due to the eruptions of El Chichón in 1982 and Pinatubo in 1991) leads to potential increases in the detection times of approximately 8–10 years.
 This study indicates that the emerging signal of climate change due to global warming over the coming decades should be clearly identifiable in radio occultation bending angle profile measurements. Moreover, the bending angle signal can be related, in a straightforward manner, to the predicted changes in the atmospheric structure as the climate warms. Analysis of the predicted trends in bending angle in the tropics suggests that it might be possible to detect climate change signals at key locations in the upper troposphere and in the lower and mid-stratosphere within ten to sixteen years. Given the many difficulties associated with establishing a temperature record of the recent past for the tropical upper troposphere and lower stratosphere [Karl et al., 2006], radio occultation measurements offer an alternative which is highly accurate and free of the calibration issues associated with both conventional observations and other satellite retrievals. Data from the CHAMP mission [Wickert et al., 2001] extend from 2001 to the present and are now being augmented by the more recent COSMIC [Anthes et al., 2000] and GRAS (J.-P. Luntama et al., EPS GRAS mission for operational radio occultation measurements, submitted to Bulletin of the American Meteorological Society, 2007) missions. The creation of a bending angle climate record from these data, which will be greatly aided by a thorough knowledge of their error characteristics gained from their use in numerical weather prediction, will provide a powerful new tool for monitoring the evolution of the climate. It will also be an important new resource for testing climate models and evaluating their predictions of climate change.
 MAR was supported by the Joint Defra and MoD Programme, (Defra) GA01101 (MoD) CBC/2B/0417_Annex C5. SBH is funded by the GRAS-SAF. The bending angle forward model used here is available as part of the ROPP software package from the GRAS-SAF homepage (http://garf.grassaf.org).