Global Navigation Satellite System (GNSS) polarimetric radio occultation (PRO) observations sense the presence of hydrometeor particles along the ray path by measuring the difference of excess phases in horizontally and vertically polarised carrier waves. As a first step towards using these observations in data assimilation and model diagnostics, a forward operator for the GNSS-PRO observable

The speed of light is slowed down when radio waves pass through the air, and this “retardation” is larger when the air is heavier and more humid. Because of this, as radio waves travel through stratified atmosphere from an emitter on a Global Navigation Satellite System (GNSS) satellite to a receiver on board a low-Earth-orbit (LEO) satellite, they undergo bending (or refraction) to minimise the travel time along the ray. In radio occultation (GNSS-RO) observations, this bending is retrieved from continuous measurement of the phase of the radio waves. As the refraction depends on the density of dry air and the amount of water vapour, measurements of bending can inform us about the thermodynamic properties of the atmosphere along the ray paths. GNSS-RO observations are routinely assimilated at most major numerical weather prediction (NWP) centres and are recognised as an indispensable component of modern NWP systems (e.g.

The carrier waves employed in GNSS are circularly polarised to minimise the impact of receivers' antenna alignment on the accuracy and stability of positioning. Because the carrier waves are polarised, it should be possible, in principle, to obtain information on properties of hydrometeors along the rays, just like polarimetric phase-shift measurement from dual-polarised weather radars (e.g.

Such polarimetric measurement of GNSS-RO observations, which we shall call PRO hereafter, has not been explored until recently but was enabled by the sensor deployed for Radio Occultation and Heavy Precipitation (ROHP) mission on board the Spanish PAZ satellite

PRO observation complements the standard RO measurements of a bending-angle profile, which is sensitive to the thermodynamic variables (temperature, pressure and humidity) of the atmosphere, with additional information on the vertical profile of heavy precipitation. Such additional information is provided by measurement of the differential phase shift at each vertical level of the ascending/descending rays, which in turn is enabled by measuring the phase delay at two orthogonal (horizontal and vertical) polarisations.

The promise of PRO measurements is already established by recent studies.

An important benefit that is unique to PRO observations is that because the regular RO (or bending) measurement and the newly available PRO measurement are carried out simultaneously, profiles of thermodynamic and cloud-related properties can be observed at the same time. Hence, if an accurate observation operator is available that can simulate PRO measurements from state variables of a NWP model, PRO observations can potentially be of great diagnostic value to modelling of physical processes.

As a first step towards PRO assimilation and model validation with PRO measurements, we develop an offline forward operator of PRO measurement for the Integrated Forecasting System (IFS) model of the European Centre for Medium-Range Weather Forecasts (ECMWF).

The paper is structured as follows. Section 2 describes the specification and the main components of the forward operator, clearly presenting the assumptions we made and their potential limitations. Section 3 describes the data and the model used in this study, along with the cases examined. Section 4 presents the results including those from several sensitivity experiments, followed by discussion and conclusions in Sect. 5.

The main observable of GNSS-PRO is the differential phase shift

The main components to computing Eq. (

We develop the PRO forward operator by extending the operational two-dimensional (2D) forward operator for RO bending angles

The ray tracing follows “Approach 2” of

Once the 2D slice is set up, the forward operator computes the ray path, starting from the tangent point by integrating the ray equations in both directions (towards the receiver on board the LEO satellite and towards the transmitter on board the GNSS satellite). The numerical integration of the ray equations is based on the second-order Runge–Kutta method (

During an occultation event, the horizontal position of the tangent point drifts as the ray ascends or descends. While the operational 2D operator for bending angles has accounted for such “tangent-point drift” (see Sect.

We remark that the ray tracing implemented in our 2D operator relies on the position of tangent points and the impact parameter provided from the RO data processing centres, but the tangent-point position can only be determined after ray tracing has been done. In this sense, our ray tracing is dependent on externally performed estimation of the ray path. The accuracy of this tangent-point estimation may impact the performance of our ray tracing.

Specific differential phase shift,

In IFS, hydrometeors represented with the resolved (or large-scale) microphysics scheme can be categorised into the following four different kinds: non-precipitating liquid water, non-precipitating ice water, precipitating liquid water (or rain) and precipitating ice water (or snow). We denote the water content of these categories, respectively, by LWC, IWC, RWC and SWC. In addition to these resolved-scale variables, the deep-convection parametrisation scheme also represents precipitating rain and snow separately. We denote the rainwater content and snow water content that are attributable to the deep-convection scheme, respectively, by RWCconv and SWCconv.

To determine

The main approximating assumptions behind the formula relating

It is relevant to note that

We also note here that the orientation of the ice/snow particles are situation dependent, and hence the axis ratio (ar) would better be allowed to vary. For example,

The formula for liquid water (LWC, RWC and RWCconv) should be different from Eq. (

In IFS, the amount of hydrometeor is represented (and archived) differently for the resolved (large-scale) scheme and for the parametrised convection scheme. In the resolved microphysics, LWC, IWC, RWC and SWC are directly available as specific water content (in units of kg kg

The forecast data used to simulate

List of the examined atmospheric river (AR) cases (provided by Ramon Padullés). RO ID is an identification code given following the UCAR convention for each occultation event; time (UTC) is the time at which the occultation begins; and latitude and longitude are those of the “occultation point”, where the excess phase exceeds 500 m for the first time during the occultation event.

As in Table

The model fields are available at an hourly interval in time. The forecast fields at two adjacent time steps are ingested to the forward operator, which are then linearly interpolated to the start time of the occultation event. The mass flux variables are archived as time accumulation from the beginning of the forecast integration; for these variables, we take the difference of forecast fields at two adjacent time steps that contain the time of occultation event and divide the difference by 3600 s as if it is an instantaneous value, assuming that their values are constant over the 1 h time interval.

We use the version V06 of PAZ Level-1B data processed and calibrated at the Spanish Institute of Space Sciences ICE-CSIC/IEEC

The

Using the forecast model and the observed data described above,

We first examine the overall agreement of the simulated and observed

Comparison of the observed (blue) and simulated total (purple)

For the AR cases (Fig.

We have seen that the simulated

Estimates of the uncertainty in simulated

Figure

Uncertainty of simulated total

The results shown so far have been computed by fully taking into account the effect of tangent-point drift (i.e., by changing the horizontal position of the tangent point for each tangent-point height). In practice, this can be prohibitively expensive because, each time the tangent-point position changes, the 2D slice has to be re-generated. It is thus desirable to reduce the frequency of tangent-point position updates to minimise the number of 2D slices to be created as long as the accuracy is not too degraded.

Here, in addition to the “full drift” approach shown above, we explored two more approaches: “no drift”, in which the drift of tangent point is not accounted for, and “11-batch”, in which 11 neighbouring tangent-point heights are grouped into a batch which shares the same 2D slice. In the 11-batch approach, rays in each batch are assumed to share the same tangent-point horizontal position, which is the sixth point of the 11 tangent points within the batch. The ECMWF's operational system uses the 11-batch approach to assimilate bending angles.

Profiles of

Impact of different approaches to account for tangent-point drifts. Profiles of

Most global NWP centres rely on a one-dimensional (1D) forward operator in simulating and assimilating RO bending angles. A 1D forward operator computes bending-angle observables by only using the atmospheric profile at the tangent point, assuming that atmospheric thermodynamic fields within the occultation slice can be regarded horizontally uniform, and hence an identical atmospheric profile can be used for all the columns in the 2D slice. It is thus interesting to see how a 1D operator would perform in simulating the PRO observable

Our 2D operator can easily operate in “1D mode” to emulate a 1D operator. To do this, we just set the derivative of the horizontal ray position to zero when integrating the ray equation (which is equivalent to assuming zero horizontal gradient of refractivity within the 2D slice). For simplicity, the tangent-point drift is ignored in our 1D computation.

The results of 1D computation are summarised in Fig.

As in Fig.

To understand why, cross-sections of resolved-scale snow water content (SWC), which is the dominant contributor to

Resolved-scale snow water content (in g m

The poor fit of the simulated and observed

A forward operator for the GNSS-PRO observable

In contrast to the success with AR cases, we found TC cases to be much more challenging, with the simulated

From the results in Fig.

This finding is in line with previous findings by

In the weather radar community, it is widely accepted that

The geometry of GNSS-PRO may be a factor contributing to the high sensitivity of

Another factor that may explain this apparent contradiction would be the difference in carrier wave frequencies of GNSS and weather radars. In GNSS, the L-band is chosen as the carrier frequency since radio waves at these frequencies are less prone to attenuation by hydrometeors, thus allowing for signals to propagate in all sky conditions. In the L-band, the frequency is

In Sect.

Consider, for example, a scenario where the observed

Apart from the sparsity of observations, correcting displacement of the background fields is also difficult because it is known to induce non-Gaussianity in the probability distribution of the background errors (e.g.

In this study, we have assumed a linear relation between

In our forward operator we assumed that the axis ratio (ar) is constant at the arbitrarily chosen value of 0.5. While this choice resulted in

We found that, unlike the successful

At the moment ECMWF is the only operational NWP centre to perform 2D ray tracing in assimilating GNSS-RO observations operationally. Our results suggest that, when other centres start investigation on GNSS-PRO assimilation, they would need to start by first extending their RO forward operator to adopt 2D ray tracing. Depending on how the code is parallelised, this alone can be non-trivial work.

This study investigated characteristics of our implementation of a forward operator for the GNSS-PRO observable

The key challenge in assimilating PRO observations would be to account for displacement error of the background, and this will be particularly important for smaller-scale phenomena such as tropical cyclones. While the currently operational 4DVar is known to be able to correct position errors in the background by assimilating dense observations like all-sky microwave radiances (e.g.

The linear relation between

In this study we focused on simulating the polarimetric differential phase shift

The PAZ data are available for download from

DH contributed to the conceptualisation, investigation, methodology, software, visualisation and writing. KL contributed to the conceptualisation, methodology, writing and software. SH contributed to conceptualisation, software, interpretation and writing.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The authors thank Estel Cardellach and Ramon Padullés of ICE-CSIC/IEEC in Spain and Joe Turk of NASA/JPL for kindly providing PAZ data and for guiding us on the use and interpretation of their data. Michael Murphy and Jennier Haase are also acknowledged for selecting the AR cases examined. The authors also thank Peter Bechtold, Alan Geer, Robin Hogan and a number of other colleagues at ECMWF for their support. The authors thank Josep M. Aparicio and Joe Turk for their careful review of the manuscript and for constructive comments. This study is an outcome from a collaboration between ECMWF and Japan Meteorological Agency (JMA). The authors acknowledge the financial support of the Space-related Overseas Fellowship Program offered by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the government of Japan.

This research has been supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the government of Japan.

This paper was edited by Peter Alexander and reviewed by Joe Turk and Josep M. Aparicio.