The GNSS-RO technique is based on measuring the refraction of GNSS radio signals as they propagate on near-horizontal paths through the atmosphere1. RO instruments on board satellites in low-Earth orbit observe GNSS radio signals rising or setting at the Earth’s limb (Fig. 1). A single instrument observes many hundred occultation events per day, quasi-randomly distributed across the Earth and unaffected by clouds and the underlying surface. These data provide a source of observational information with high vertical resolution and long-term stability2,3,4, extending from near the surface to the upper stratosphere. They are becoming increasingly useful for climate monitoring and climate model testing as the RO measurement time series becomes longer.

During an occultation event a vertical profile of refraction, or “bending”, angles of the GNSS radio signal is measured. The bending angles are converted to a vertical profile of the refractive index, which is followed by retrieval of temperature and pressure profiles (see Methods). Bending angle is the variable closest to the raw measurement and is essentially bias-free up to the upper stratosphere. This property, unique to measurements of the atmosphere, is exploited in numerical weather prediction (NWP)5. Most NWP centres now assimilate bending-angle profiles, rather than any of the retrieved geophysical variables, as these can be used without bias correction (referred to as “anchor measurements”). This characteristic also makes them useful for climate reanalyses6, and the consistency of the major global temperature reanalyses in the stratosphere has improved since the number of RO measurements increased dramatically in 20067,8. Combined with the all-weather capability of RO and the long-term stability across successive satellite missions, bending-angle data are clearly well-suited for climate monitoring. We stress that the RO bending angle is a more fundamental quantity than the RO geophysical retrievals (refractive index, temperature, pressure), requiring fewer assumptions and less a priori information, and is therefore suitable when small observational biases throughout the stratosphere is a priority.

Here we use monthly mean, zonally averaged bending-angle data provided by the EUMETSAT RO Meteorology Satellite Application Facility (ROM SAF), and extending from 2002 to the present4, to examine atmospheric trends over the last two decades. The trends are computed by ordinary linear regression of monthly mean anomaly time series at each latitude-height grid point. We show that the bending-angle trends are consistent both with well-understood responses of the UTLS region to long-term global warming9,10,11 and with predictions made with the HadGEM1 climate model almost 15 years ago12.

The observed trends in bending-angle anomalies as a function of latitude and height (Fig. 2a) correspond to widespread lower-stratospheric cooling over time, which extends across the tropics and sub-tropics and into the mid and high latitudes in the Northern Hemisphere. A consistent pattern is seen in the atmospheric refractivity trends (Fig. 2c), directly reflecting the trends in air density (see Methods), while the associated trends in temperature (Fig. 2d) show tropospheric warming and a transition to stratospheric cooling across a relatively sharp vertical gradient in the tropopause region. We note that the UTLS region, where we find a clear signal of climate change, is also where we find the largest beneficial impacts of RO measurements in operational NWP systems5.

The observed bending-angle trends at low- and mid-latitudes (shown in Fig. 2a) are remarkably similar to those predicted in the modelling study of Ringer and Healy [2008]12 which used the version of the Met Office Hadley Centre climate model (HadGEM1) dating from 200613 and a plausible IPCC emissions scenario for the 21st century. These model results are reproduced in Fig. 2b. The model and observation data sets differ near the poles, consistent with the higher variability at high latitudes. The climate model projections highlighted how the expected atmospheric responses to increased greenhouse gas concentrations—a warming of the upper troposphere and cooling of the lower stratosphere with a sharp gradient at the tropopause; a general upward expansion of the atmosphere which is manifested as an increase of the pressure at fixed altitudes—would lead to well-defined consequences for the distribution of the bending angles. In addition, they suggested that the bending-angle signal in the equatorial lower to middle stratosphere would be clearly identifiable by the 2020s, while that at higher latitudes was more variable and not clearly established until the 2040s.

We also note that not only are the observed bending-angle trends at low- and mid-latitudes structurally very similar to the HadGEM1 model projections but they also have similar magnitudes. For example, the observed trends are around three-quarters of those predicted by the model in the lower stratosphere. The main differences with the model are at high latitudes, in line with the expectation that those trends are likely to be more uncertain.

The time it takes to detect trends depends on the noise characteristics of the time series. Where natural variability is large—due to either unpredictable events, such as volcanic eruptions, or more predictable ones like sudden stratospheric warmings in the polar regions and the Quasi-Biennial Oscillation (QBO) in the equatorial stratosphere—the trend detection times become longer. The observational RO climate data records have been shown to contain accurate information on QBOs14, and are expected to provide realistic estimates of the natural variability in the low-latitude stratosphere. Based on the HadGEM1 climate model, Ringer and Healy [2008] suggested that climate trends in the tropical stratosphere bending angles would be clearly detected from 11–16 years of data, and demonstrated how the model trends converged towards their final value in accordance with that analysis. Figure 2e shows the evolution of the observed bending-angle trends as the time series becomes longer. After 19 years the trend values have largely converged and become stable, indicating that the current length of the time series is sufficient for trends to be detected with some confidence. Unrealistically low natural variability in climate models may lead to underestimation of the detection times even though the trends themselves are accurately described, a point noted by Ringer and Healy [2008]. Subsequent development of climate models, in particular higher vertical resolution, has led to significant improvements in the representation of variability over time, e.g. in the representation of the QBO15.

To conclude, analysis of the now 20-year record of GNSS-RO measurements suggests the following: climate trends consistent with our understanding of the response to global warming are clearly identified in the observed monthly mean RO bending angles (Fig. 2a) and in the geophysical variables (Fig. 2c, d) retrieved from the bending angles; these climate signals are seen in regions where the information content of the RO measurements is largest and where the value of RO in both NWP and climate reanalyses is firmly established; the observed bending-angle trends match predictions made with the HadGEM1 climate model a decade and a half ago (Fig. 2b), implying that both the observed signals and models are grounded in robust, well-understood physics. This final point is analogous to that made by Stouffer and Manabe [2017] in relation to projections of surface temperature change made with earlier generations of climate models16. It confirms the expected capabilities of RO data expressed two decades ago17, and suggests that the satellite-derived bending angles provide a valuable observational data source for climate model development and evaluation.

Methods

Processing of atmospheric profiles

During an occultation event (Fig. 1) the time delay (phase shift) and amplitude of the GNSS radio signal are measured and transformed into a vertical profile of refraction angles, or bending angles, α. Under the assumption of local spherical symmetry around the occultation point, we can use the Abel transform to compute a vertical profile of refractive index, n, from the bending angles

$$\ln n(x) = \frac{1}{\pi }\mathop {\int}\limits_x^\infty \frac{{\alpha (a)}}{{\sqrt {a^2 - x^2} }}$$
(1)

where a is the impact parameter and x = nr, with r being the radius of a point on the radio signal ray path1. The microwave refractive index is a function of pressure, p, temperature, T, and water vapour partial pressure, e,

$$N = \left( {n - 1} \right)10^6 = k_1\frac{p}{T} + k_2\frac{e}{T} + k_3\frac{e}{{T^2}}$$
(2)

where N is referred to as refractivity. For a dry atmosphere, refractivity is directly proportional to air density, and a pressure profile can be retrieved by vertical integration of the refractivity profile under the assumption of hydrostatic equilibrium. The corresponding temperature profile is obtained from an equation of state, e.g. for an ideal gas. This so-called “dry” approximation is a valid assumption in the upper troposphere and throughout the stratosphere18.

We emphasise that the successive steps in this processing chain involve the use of a priori information. The retrieval of refractivity requires the bending-angle profile in Eq. (1) to be extrapolated to infinity, while hydrostatic integration of a refractivity profile requires an assumption about the pressure at high altitude. Bending angle is the least biased RO variable in the stratosphere, regarded as essentially bias-free, and is the preferred variable for use in NWP5 and atmospheric reanalysis6. The RO measurements, including the retrieved geophysical variables (refractivity, temperature, pressure), are most precise and accurate at altitudes between 8 and 30 km2,3,4, in the upper troposphere lower stratosphere (UTLS), where they also have the stability required for climate studies.

Monthly mean gridded data and anomaly time series

RO data from four satellite missions were combined to form a continuous data record covering 2002–20204. After quality screening and interpolation of the vertical profiles onto an equidistant 200 m height grid, zonally gridded monthly means were computed within 5° latitude bands and calendar months. Estimates of sampling errors were obtained from reanalysis short-term forecast data (by subtraction of true model monthly means from monthly means based on sub-sampled model data) and subsequently subtracted. Finally, anomalies are computed by subtracting a mean seasonal cycle at each latitude and height bin. The trends are computed by ordinary linear regression of the monthly mean anomaly time series at each grid point.