
ROM SAF ReportsThe GRAS SAF / ROM SAF Report series provides additional information related to scientific investigations and the underlying algorithms used in our radio occultation processing code and the ROPP software package. These documents are Copyright material. ROM SAF Report 39 Hans Gleisner 11 Sep 2020Impacts of RO mission differences on trends in multimission data records The ROM SAF CDR v1.0 COSMIC and Metop data records during 2007–2016 are characterised by a relatively constant offset between the two missions. The magnitude of the offset vary with latitude and altitude. During the same time period the weight of Metop in a combined RO data set increase from contributing less than 20% to about 70% of data. These two factors in combination (constant offset and changing data numbers) are expected to introduce a spurious trend in the multimission data record. We have investigated differences in bending angle, refractivity, and dry temperature trends amongst 10year time series (2007–2016) of RO data based on Metop, COSMIC, and the multimission data set, all of them part of the ROM SAF monthlymean gridded CDR v1.0. ROM SAF Report 38 N E Bowler 19 Aug 2020An initial assessment of the quality of RO data from COSMIC2 The COSMIC2 / FORMOSAT7 constellation of six satellites were launched in June 2019 into lowinclination orbits. These provide radiooccultation observations that are principally focussed on the tropical region. Each satellite carries a TGRS receiver that can make observations from both the GPS and GLONASS GNSS networks. The constellation provides a substantial increase in the total amount of radio occultation data available, with between 5000 and 6000 per day being expected to be provided. This is more than a 100% increase on the current operational network. The observations are generally of good quality and comparable to observations from the Metop satellites. There are some differences between the COSMIC2 and Metop constellations, with some indications that COSMIC2 is performing better in the troposphere. The design of the TGRS receiver gives a higher signaltonoise ratio compared to other receivers with the hope that this will improve the performance in lower regions of the atmosphere. Assimilation of these observations indicates that there are substantial benefits from assimilating these data, particularly to NWP forecast performance in the tropics. This study has been focussed on offline data that have been provided. These observations have recently become available in nearreal time on the Global Telecommunications System (GTS). Therefore operational assimilation of these data is something that is being actively investigated. ROM SAF Report 37 Sean B. Healy and Kent B. Lauritsen 10 Feb 20206th ROM SAF User Workshop The ROM SAF took the opportunity of the international GNSS radio occultation (GNSSRO) community meeting for the joint 6th ROM SAF User Workshop and the 7th IROWG Workshop (held jointly as ROM SAF – IROWG 2019) to formulate a set of recommendations to inform priorities for CDOP4. The four IROWG working groups were provided with a set of questions and discussion points, and asked to return written recommendations to the ROM SAF. These working group recommendations are summarised in this report. In general, there remains strong support for continuing the work of the ROM SAF. In the context of NWP, this includes continuing the nearrealtime (NRT) provision of refractivity, further development of the ROPP software package, and maintaining the NRT monitoring system. The climate recommendations include more work on the retrieval of tropospheric humidity information, improving the retrieval of temperature information in the upper stratosphere, and the provision of robust uncertainty information with all climate data records. The Space Weather group support the ROM SAF developing ionospheric products from EPSSG. They also support the development of 1DVar retrieval techniques, if the ultimate aim is to include horizontal gradient information in order to reduce retrieval errors. The Receiver Technology and Innovative Occultation Techniques group recommend that the ROM SAF starts developing forward models appropriate for the assimilation of PAZ and new LEOLEO observations. The latter is required for Observing System Simulation Experiments (OSSEs). ROM SAF Report 36 N E Bowler 23 Jun 2020An initial assessment of the quality of RO data from PAZ The PAZ satellite was launched on 22nd February 2018 into a sunsynchronous polar orbit. This satellite carries a polarimetric instrument for taking radiooccultation measurements of the atmosphere. The instrument, known as ROHPP (Radio Occultations and Heavy Precipitation with PAZ) is a variant of an earlier IGOR (Integrated GPS Occultation Receiver) instrument which has been adapted to measure horizontally and vertically polarised signals. Only one radiooccultation instrument is carried by the satellite, and therefore it is only able to measure setting occultations. Due to the dualpolarisation nature of the instrument, the calculation of bending angles follows a slightly different path from conventional instruments. Overall the performance of the bending angle data is similar to that from other operational instruments. There are differences for the bending angle data in the troposphere, but this is most likely to be due to differences between processing centres, rather than instrumental differences. The refractivity data above 35 km is more accurate than similar data from FY3C, even though the bending angle accuracy is similar at these levels. This is believed to be due to differences in the choice of climatology used in the processing. The data have recently been made available in nearrealtime. Due to problems with connection between the satellite to the ground infrastructure, the data is experiencing long delays. Improvements have been made recently, but more work in this area is still needed. ROM SAF Report 35 N E Bowler 11 Oct 2019An initial assessment of the quality of RO data from FY3D The FengYun 3D (FY3D) satellite was launched on 14th November 2017 into a sunsynchronous polar orbit. After considerable work the data were made available via the GTS on 11th January 2019. Just under 500 occultations are provided each day, so the satellite represents an important component of the (Global Navigation Satellite System  Radio Occultation) GNSSRO observing system. Both bending angle and refractivity measurements are made available. Overall the quality of this data is similar to that from FY3C. However there are two issues where the data from FY3D is noticeably worse than that from FY3C: a bias in setting occultations above 40km and a reduction in the number of observations below 20km. Work is being actively undertaken at the China Meteorological Administration (CMA) to address these issues. Tests have been run to assimilate bending angles from FY3D into the Met Office system, but excluding setting occultations above 40km. These demonstrate a small but statistically significant improvement from using the data. Therefore, it is planned to include data from FY3D into the Met Office’s operational system in early 2020. ROM SAF Report 34 N E Bowler 21 Mar 2019An initial assessment of the quality of RO data from MetopC The MetopC satellite was launched on 7th November 2018 into a sunsynchronous polar orbit. The first radio occultations from the GRAS instrument were received less than a week after this. Level 1 data (including bending angles) have been made available from EUMETSAT Secretariat from the very beginning. The ROM SAF have processed these data and calculated refractivity profiles  these profiles have been calculated for all the bending angle profiles, including the very earliest measurements. The Level 1 and Level 2 data are being disseminated via the EUMETCast system and GTS. Operational dissemination began on the 7th March 2019. Overall the quality of this data is very similar to that from MetopA and B, as might be expected from systems which use the same hardware and software. Very slight differences between the satellites exist, and these will be highlighted. ROM SAF Report 33 Sean Healy 14 Sep 2018Some science changes in ROPP9.1 ROPP9.1 is a minor release of the ROM SAF’s Radio Occultation Processing Package (ROPP). This report summarises some of the main science changes in ROPP 9.1. These include 1) modifications for GNOS processing, 2) improvements in the wave optics propagator and 3) changes to the L1/L2 bending angle forward models. Possible developments for future ROPP releases are discussed briefly. ROM SAF Report 32 N E Bowler 28 Jun 2018An initial assessment of the quality of RO data from KOMPSAT5 The KOMPSAT5 satellite was launched in 2013 into a sunsynchronous polar orbit. Recently UCAR have started processing the RO data which was being produced by this satellite. These data are made available via FTP from the CDAAC website. The observations are processed twice per day, with a delay of a few hours, which means that they are not currently suitable for operational implementation. Overall the quality of this data is excellent  approximately as good as from the COSMIC1 satellites. There is no evidence of systematic biases in the data. The standard deviation of differences between the observation and NWP model background is generally comparable to that of other satellites, except in the lowerstratosphere where they are slightly larger. Due to the orbital period the satellite produces occultations in a regular pattern across the globe. In the onemonth period considered we received 12901 observations (approx 440 per day) which compares with 16874 for MetopA and 7956 for COSMIC1 FM1. ROM SAF Report 31 Ian Culverwell 7 May 2019Sensitivity of some RO measurements to the shape of the ionospheric electron density profile This report contains brief notes on the bending angles and slantwise total electron contents that result from the use of a single, spherically symmetric ‘VaryChap’ ionosphere. This is a simple but realistic model of the ionospheric electron density distribution whose shape can be easily altered. It is used to give some insight into the sensitivity of radio occultation results to the shape of the electron density profile. ROM SAF Report 30 Ian Culverwell and Sean Healy 27 Mar 2018A first look at the feasibility of assimilating single and dual frequency bending angles The report describes the results of some numerical experiments designed to investigate the feasibility of carrying out 1D variational retrievals using dual or single frequency radio occultation bending angles, rather than the usual ionospherically corrected ‘neutral’ bending angles. A detailed analysis of the results of carrying out these experiments on two example radio occultation profiles is followed by a statistical analysis of the results of doing so on 3500 consecutive profiles observed by the GRAS instrument on MetopA. The retrieved ionospheric parameters are briefly reviewed. Further work is suggested. ROM SAF Report 29 Sean Healy and Andras Horanyi 4 Apr 2017Testing reprocessed GPS radio occultation datasets in a reanalysis system The ROM SAF plans to run two long GPS radio occultation (GPSRO) reanalyses for the period 20072015. Temporal averaging of the gridded, threedimensional reanalysis fields is an alternative way of producing level3 climatologies based on GPSRO data. In preparation for this activity, a series of experiments have been performed using the ERA5 reanalysis system. The experiments assimilate reprocessed GPSRO datasets from both UCAR and the ROM SAF, and the operational GPSRO data from the period. The impact of a subset of other measurement types has also been tested. We have found that the mean bending departure differences between the GPSRO datasets in the vertical interval between ∼ 1030 km are around 0.1 %, which is about a tenth of the assumed measurement/forward model uncertainty. Consequently, the zonally averaged temperatures computed from the reanalyses are reasonably consistent below 5 hPa. We have also found that assimilating AMSUA channel 14 radiances without bias correction is crucial for correcting large model biases around 2 hPa. Furthermore, these model biases appear to be in the GPSRO nullspace. Therefore, we conclude that AMSUA channel 14 should be included in both of the proposed ROM SAF reanalyses. It is noted that one internal (non public) ROM SAF dataset has poorer bending angle departure statistics, because quality control flags are not set correctly, but this is resolved in the later dataset. The ROM SAF data numbers tend to be lower than the operational GRAS data from the period. The reasons are understood and they will be resolved in the official version 1 (V1.0) of the ROM SAF Climate Data Record (CDR V1.0) reprocessing. ROM SAF Report 28 Sean Healy 26 Mar 2018Description of wave optics modelling in ROPP9 and suggested improvements for ROPP9.1 The physical basis of the wave optics simulation code included in ROPP9 is described. The ROPP wave optics simulation code is based on a multiple phase screen (MPS) approach which is well known, and so it is only reviewed briefly. A new method for computing the phase and amplitude at the LEO satellite, given the phase and amplitude at the final phase screen, is described in detail. More specifically, it is shown that the solution at the LEO can be computed efficiently in terms of standard Fresnel integrals. The simulations are tested by inverting the phase and amplitudes with a Full Spectrum Inversion (FSI) approach to produce bending angle profiles, and then comparing these with a onedimensional geometrical optics forward model. Some errors for large bending angle cases in the lowest 2 km are identified, and improvements for implementation in ROPP9.1 are presented. ROM SAF Report 27 Sean Healy 11 Nov 2016Recent forecast impact experiments with GPS radio occultation measurements The results from a recent set of forecast impact experiments with GPS radio occultation GPSRO) measurements are summarised. Although the main impact of GPSRO is in the uppertroposphere and stratosphere, it is shown that the data has some positive impact on tropospheric humidity and winds, particularly in the southern hemisphere. Spatial maps of GPSRO bending angle departure statistics for the lowest 2 km are presented, and it is suggested that some bias features may be related to ECMWF humidity forecast bias, rather than just observation or forward model errors. The GPSRO impact does not appear to be sensitive to increasing and reducing the assumed errors statistics in the troposphere, but increasing the assumed errors statistics in the stratosphere does have a positive impact. The relevance of these results to ongoing ROM SAF activities is discussed. ROM SAF Report 26 Sean Healy 23 Aug 2016Estimates of GNSS radio occultation bending angle and refractivity error statistics The ECMWF numerical weather prediction (NWP) system has been used to estimate the GNSS radio occultation bending angle error statistics from Metop GRAS and COSMIC measurements. These statistics have been mapped to refractivity space using a linear Abel transform. We have found that the broader vertical bending angle error correlations for rising GRAS measurements account for most of the difference between the rising and setting refractivity profile statistics. The senstivity of the refractivity results to bending angle error correlations is demonstrated and discussed. The importance of modelling the refractivity error correlations correctly is emphasised. The results also suggest that the refractivity error model used in the ROM SAF 1DVar should be revisited. ROM SAF Report 25 Estel Cardellach, Kent B. Lauritsen, Riccardo Notarpietro, Axel von Engeln 20 Feb 2017Survey on user requirements for potential ionospheric products from EPSSG radio occultation measurements This document presents the outcome of a survey that was conducted by the ROM SAF in cooperation with EUMETSAT to determine user requirements for ionospheric Radio Occultation (RO) products; thus establishing a general guideline for the potential delivery of GNSS RO observables and products at ionospheric altitudes. The main focus is on possible EUMETSAT Polar SystemSecond Generation (EPSSG) RO products, but the outcome is also relevant for other RO instruments. The document compiles the answers of the users and their concerns. It is however clearly noted that the RO instruments on EPSSG focus on the neutral atmosphere, and ionospheric sounding capabilities are an addon that do not drive the instrument or programme. Nor should suggested requirements be seen as a commitment by EUMETSAT or the ROM SAF to meet these requirements. ROM SAF Report 24 Ian Culverwell 20 Jun 2016The calculation of planetary boundary layer heights in ROPP This report concerns the Planetary Boundary Layer Height (PBLH) diagnostics that have been implemented in the ROM SAF’s Radio Occultation Processing Package, ROPP. Algorithms for calculating the PBLH are briefly described. PBLHs calculated from six different profile variables — three ‘observation fields’ and three ‘model fields’ — are compared and contrasted, both by profilebyprofile scrutiny of selected examples, and by inspection of the average of a month of occultations. PBLHs derived from forward modelled background fields are also briefly considered. Tentative conclusions are drawn before possible future work is considered. ROM SAF Report 23 Estel Cardellach and Santiago Oliveras 23 Jan 2016Assessment of a potential reflection flag product This document presents the implementation of a technique intended to identify the presence of reflected signals in GNSS radiooccultation (RO) data. Typically, the reflection occurs at the Earth surface level, or off atmospheric layers very close to the surface. The technique is based on supervised learning methods, in particular on Support Vector Machines (SVM). The report briefly describes the SVM approach, and how it is implemented for detection of reflected signals in RO data. Other aspects described in this document are the validation of the technique and computing requirements to run it. The document includes a preliminary discussion about the na ture of these reflection events, based on the statistics of occurrence over land and ocean, seasonal features, analysis of correlation with certain atmospheric or RO conditions, and comparative performance of the ECMWF model when reflections are captured or not. ROM SAF Report 22 Sean Healy 27 Aug 2015The use of the GPS radio occultation reflection flag for NWP applications A COSMIC dataset has been modified by IEEC and the Met Office to include a reflection flag. The flagged measurements are composed of a direct and reflected signal. They have been detected automatically using a technique developed by IEEC. The error statistics of the COSMIC data subsets with and without the flag activated have been computed in data assimilation experiments. It has been confirmed that the bending angle departure statistics of measurements in the troposphere with the flag activated tend to fit ECMWF forecasts more closely. However, the variability of the observations in the flagged subset is much lower, and the flag is more probable for colder, drier tropospheres. The improvement in the departure statistics varies spatially, indicating that a simple scaling of the bending error statistics used to assimilate the data when the flag is activated, is probably not appropriate. This will complicate any use of a single on/off flag in NWP applications. ROM SAF Report 21 Sean B. Healy and Andras Horanyi 27 Feb 20155th ROM SAF User Workshop on Applications of GPS radio occultation measurements ECMWF hosted EUMETSAT’s Fifth ROM SAF User Workshop (UW5) on Applications of GPS radio occultation measurements, on June 1618, 2014. The workshop was attended by around 30 international scientists, with expertise in both GPS radio occultation and climate applications. It followed the standard format of a series of presentations, followed by a day in NWP and climate working groups, and then a plenary session. The presentations and program from the 5th user workshop are available at the ECMWF workshop page. The value and continued importance of GPSRO in both operational NWP and reanalysis applications was emphasised at the plenary session. Overall, this was a useful and enjoyable workshop, which benefited greatly from the diversity of the participant’s research interests. ROM SAF Report 20 Hans Gleisner 6 Feb 2015Interpolation artefact in ECMWF monthly standard deviation plots During the development of the ROM SAF Level 3 gridded climate data processing software, a pronounced wave pattern artefact was frequently found in plots of the standard deviations of ECMWF model data. It was exclusively a problem for model data, and did not affect the observed RO data. The wave pattern was most easily discerned at low latitudes and above an altitude of 20 kilometers, and there was a seasonal variation with a tendency for the wave pattern to become stronger in the summer hemisphere. It is here shown that the wave pattern artefact is caused by the reduction of variance at the interpolation points as a result of the weighted averaging prescribed by the interpolation from model levels to intermediate points. It does not depend on the detailed choice of interpolation function. It is also shown that the dependence of the wave pattern on latitude, altitude, and season is governed by the mixing of model levels at fixed altitudes along zonal latitude bands. We propose to use logspline interpolation of refractivity as a remedy for this problem. This introduces an additional source of variability at the interpolation points, which is enough to substantially reduce the problem even though it is not fundamentally resolved. The interpolated refractivity profile is also used as input to the Abel transform, at a higher vertical resolution compared to the standard bendingangle forward model. Spline interpolation is also used to interpolate ECMWF model temperature, humidity, and geopotential heights from model levels to intermediate altitudes. The solution described in this report has been implemented in the ROM SAF Level 3 processing software, romclim1.1, used in the generation of data products GRM17,…,23, as well as plots at the ROM SAF climate monitoring web pages. The artefact described in this report, and the chosen solution, only concerns the ECMWF model data used as a reference, not the observed RO data. ROM SAF Report 19 Sean Healy 30 Apr 2014Implementation of the ROPP twodimensional bending angle observation operator in an NWP system The Radio Occultation Processing Package (ROPP) includes a twodimensional (2D) bending angle operator. This has been tested in the ECMWF numerical weather prediction system, with a view to operational implementation possibly during 2014. This report outlines how the 2D operator is implemented at ECMWF. Issues related to parallel computing architectures are discussed. We explain why problems associated with the 2D “occultation plane” spanning more than processor (or core) do not arise at ECMWF. This is because the observations are split into “pools” containing roughly equal numbers of each observation type for loadbalancing, and the forward modelling is decomposed into distinct horizontal and vertical interpolation tasks. Recent results with the 2D operator are presented showing an improvement in the bending angle departure statistics with respect to observations, indicating that the forward model errors are reduced. However, the additional computational cost during the 4DVar minimization is large. New ideas to reduce the computational cost of the ROPP 2D operator are discussed, and a new approach is suggested based on the incremental formulation of 4DVar. ROM SAF Report 18 Sean Healy 3 Mar 2014Single Frequency Radio Occultation Retrievals: Impact on Numerical Weather Prediction The impact of single frequency processing of GPS radio occultation (GPSRO) measurements on numerical weather prediction has been investigated. MetopB GRAS measurements have been degraded by adding 6 microradian and 12 microradian random Gaussian noise. The additional noise is most significant in the stratosphere, because to first order bending angle values fall exponentially with height. The degraded data have been assimilated in a system where all other GPSRO measurements are restricted to a latitude band between 40 North and 40 South. The impact of noisy data has been compared with experiments where the weight of the MetopB GRAS measurements in the stratosphere has been increased by reducing the assumed standard deviation of the observation errors to 1.5 microradians. The main forecast impact is on temperature biases in the stratosphere. The results show that the increase in noise levels will have a noticeable impact on the mean temperature analysis, particularly in polar regions and above 5 hPa. The bias corrections applied to satellite radiances are also affected. For example, the bias corrections applied to channel 13 of MetopB AMSUA differ by 0.15 K. Increasing the noise levels degrades the mean of the shortrange forecast departures with respect to radiosonde temperature measurements above 200 hPa. The rootmeansquare (RMS) temperature errors are degraded by 1% at 30 hPa for the day1 to day5 forecast range because of the additional noise. However, there is no degradation in RMS at 100 hPa. The introduction of vertically correlated errors does not affect the main results. ROM SAF Report 17 I D Culverwell and S B Healy 21 Dec 2015Simulation of L1 and L2 bending angles with a model ionosphere This report describes the modelling of the L1 and L2 bending angles by means of a simple idealised ionosphere consisting of a single Chapman layer. There are three main reasons for doing this:  The desire for an improved interpolation/extrapolation of the L1 – L2 bending angle difference where either signal (but especially L2) drops out;  The wish to make retrievals using observational data that are closer to what is observed, rather than the ionospherically corrected neutral bending angles that are usually used;  It allows the sensitivity of the observed bending angles with respect to the unknown ionospheric parameters to be assessed. Sensitivities to horizontal gradients and to the shape and size of the model ionosphere are briefly examined before calculating the bending angles induced by a single Chapman layer. The feasibility of making retrievals directly with L1 and L2, and with L1 alone, are studied in a simple ‘toy’ system, and the results are compared against retrievals made in the same system with the usual ionospherically corrected bending angles. All GRAS occultations within a five day period have their L1 – L2 bending angle differences modelled by this theory, and the derived ionospheric parameters are examined. Areas for further study are suggested. ROM SAF Report 16 Dave Offiler 3 Aug 2016Simplifying EGM96 undulation calculation in ROPP This report reviews the calculation of undulation – the difference between the (WGS84) ellipsoid and the (EGM96) geoid – in ROPP. The undulation value at the nominal RO profile location is subtracted from the Impact Height to obtain the height with respect to the geoid of any point in the profile. For practical purposes, the resulting geoid height can be considered to be the same as height above mean sea level. The current method of calculating undulations (or geoid heights in ROPP) uses a full spherical harmonic expansion which is both complex and cpuintensive. An alternative grid interpolation method has been developed which is shown to be significantly simpler in code terms and so substantially quicker to run, and without any practical loss of accuracy when compared to the present full calculation method. The interpolation method is proposed to replace the current undulation code in ROPP. ROM SAF Report 15 C. Burrows, S. Healy, I. Culverwell 13 May 2013Improvements to the ROPP refractivity and bending angle operators The current bending angle operator in the ROPP package (ROPP_FM module) is based on Healy & Thepaut (2006). This operator is also used operationally at the Met Office, ECMWF and other NWP centres. The Met Office bending angle innovation statistics have shown features which can be attributed to shortcomings in the assumption of exponentially varying refractivity between model levels when the spacing is large. However, when the level spacing is small, the exponential assumption is acceptable. Similar features can be observed in the refractivity statistics. This report aims to address these issues by proposing a more physical approximation to the refractivity as a function of height between model levels which can be used in the Abel integral to forwardmodel bending angles. Improvements in both the refractivity and bending angle biases are demonstrated, along with several approaches for implementing an improved bending angle calculation. ROM SAF Report 14 Ian Culverwell 16 Oct 2013A review of the geodesy calculations in ROPP This report reviews the geodesy calculations in ROPP, in response to concerns raised by the ROPP2.0 beta reviewer in 2008. Various expressions for the surface gravity, effective radius, radius of curvature and geopotential height are compared, and the impact of the differences in RO applications is assessed. Supporting sensitivity studies are reported. A simple model is developed that sheds light on some of the findings. GRAS SAF Report 13 H. Lewis 10 Jun 2010ROPP PP validation The Radio Occultation Processing Package (ROPP) software includes functionality for users to process radio occultation data to derive atmospheric bending angle and refractivity profiles. This report presents refractivity and bending angle profiles processed using the ROPP (v4.1) tool ropp_pp_occ_tool. This serves to illustrate the use of ROPP for occultation processing and validate its results. Note that results presented here referring to ROPP4 (v4.1) also apply to the ROPP5 (v5.0) user release distribution. GRAS SAF Report 12 P. Poli, S. B. Healy, and D. P. Dee 2 Feb 2012Assimilation of Global Positioning System Radio Occultation Data in the ECMWF ERAInterim Reanalysis This paper presents results of the assimilation of Global Positioning System (GPS) Radio Occultation (RO) bending angle data from CHAMP, FORMOSAT3/COSMIC, and MetOpA GRAS in the ECMWF global reanalysis ERAInterim. GRAS SAF Report 11 H Lewis 19 Apr 2010ROPP 1dVar validation The ROPP 1dVar processing is used to perform retrievals using one day of GRAS refractivity observations and ECMWF background data. Results illustrate the ROPP functionality and the output diagnostics generated. Tests using different configuration parameter settings and the error descriptions for optimal solutions are discussed. Results processed using COSMIC occulations and Met Office forecast model background data are also presented. GRAS SAF Report 10 H Gleisner 10 Apr 2011Latitudinal Binning and AreaWeighted Averaging of Irregularly Distributed Radio Occultation Data When forming an areaweighted mean within a latitude grid box from data given on a regular latitudelongitude grid, cosine weighting is applied in order to compensate for the meridian convergence toward higher latitudes. In the scientific literature on climate applications of RO data one can also find examples of cosine weighting being used to form gridbox means from irregularly distributed data. In this report, we point out that cosine weighting assumes that the data to be weighted have a distribution that is uniform per degree of latitude. If the data are randomly, or quasirandomly, drawn from other distributions, an error is made that may introduce a bias. For actual RO climate data, errors due to undersampling of longitudinal and temporal variability act to hide any biases caused by the use of cosine weighting. Hence, the resulting effect of using an alternative weighting strategy is mostly small. Nevertheless, the use of cosine weighting of data appears not to be appropriate for the irregularly distributed RO data. An alternative spatial averaging method is devised that provides a better approximation to the areaweighting integral with fewer assumptions concerning the latitudinal distribution of observations. GRAS SAF Report 09 S Healy 5 Oct 2009Refractivity coefficients used in the assimilation of GPS radio occultation measurements The sensitivity of ECMWF numerical weather prediction analyses to the empirical refractivity coefficients and the introduction of nonideal gas effects in the bending angle operator have been investigated. A review of the literature on the refractivity coefficients suggests that the uncertainty in the values is probably larger than has been recognised. The results reinforce the need for new measurements of the refractivity coefficients at radio frequencies. GRAS SAF Report 08 H Lewis 22 Jun 2009ROPP thinner algorithm The ropp_io module within ROPP contains routines to enable thinning of Level 1b (bending angle), Level 2a (refractivity) and Level 2b (meteorological variables) data. Thinning aims to reduce the amount of data without reducing the information content. GRAS SAF Report 01 presented some possible methods for thinning 1dimensional (profile) data. It was discussed that a typical bending angle profile does not contain more than about 250 pieces of information, and it is therefore desirable to reduce the data volume to about this number from up to 5000 measurements obtained during an occultation. A list of 247 set impact heights were defined for use in the GRAS SAF thinned BUFR productsto meet a strong user requirement for NRT data on set levels. These heights are based on the criteria of having a maximum of four points per Fresnel diameter. It is possible to perform thinning using the ROPP software for any predefined set of impact heights. This report documents the thinning algortitm as implemented in ROPP. GRAS SAF Report 07 H Lewis 1 Oct 2008Abel integral calculations in ROPP The ROPP preprocessor module ropp_pp includes routines to perform an Abel transform to derive a bending angle profile from model refractivity data and invert a corrected bending angle profile to derive refractivity. This report describes the Abel inversion and Abel transform calculations included within ROPP. The sensitivity of ropp_pp and ropp_fm results to the choice of algorithm used is discussed. GRAS SAF Report 06 H Lewis 4 Feb 2008LevenbergMarquardt minimisation in ROPP The ROPP 1dVar retrieval has been tested using the LevenbergMarquardt method (LevMarq) to solve the 1dVar minimisation problem. Results are compared with the performance of the ROPPspecific minimiser minROPP. Tests are conducted using synthetic profiles based on ECMWF background data and real observed profiles using Met Office background data. In some cases LevMarq is found to produce 1dVar solutions with smaller cost function values and which deviate more from the background profiles than minROPP for a given set of convergence criteria. The minROPP routine is typically three times faster than LevMarq however. The most suitable convergence criteria for minROPP are discussed. It is recommended that both minimisers are supported in the ROPP software, with users able to select the most appropriate algorithm for their own particular need. GRAS SAF Report 05 H Lewis 23 Jan 2008Refractivity calculations in ROPP A summary of the refractivity calculation used in the ROPP forward model is provided. Several expressions are available for calculating a refractivity profile from background pressure, humidity and temperature data. Results using an established twoterm expression (Smith and Weintraub 1956) and a more recent threeterm expression (Rueger 2002) are presented. It is recommended that the Rueger (2002) expression is implemented by users for GPSRO processing when provided in future versions of the ROPP software. GRAS SAF Report 04 H Lewis 23 Nov 2007Error function calculation in ROPP The error function erf is used in the Abel transform as part of the ROPP bending angle operator. It has been suggested that this is computed using a polynomial approximation to avoid the cost incurred by calling an external DCDFLIB library function many times while performing the 1dVar processing. This document describes the polynomial expression and the corresponding tangent linear and adjoint codes. Test results demonstrate that the approximation is a suitable replacement for the DCDFLIB function. It is strongly recommended that the polynomial approximation is implemented by users for GPSRO processing when provided in future versions of the ROPP software. GRAS SAF Report 03 H Lewis 20 Nov 2007ROPP minimiser  minROPP A new ROPPspecific minimiser minROPP has been developed as part of the GRASSAF for implementation in the 1dVar retrieval processing. A new minimiser routine ropp_1dvar_minropp} replicates the current thirdparty minimiser M1QN3 to minimise the cost function using a quasiNewton method with diagonal scaling. This document summarises the minimisation processing and outlines the new ROPminimiser. Test results demonstrate that minROPP is a suitable replacement for M1QN3. It is strongly recommended that minROPP is implemented by users for GPSRO processing when provided in future versions of the ROPP software. GRAS SAF Report 02 H Lewis 24 Oct 2007Geodesy calculations in ROPP A summary of the geodetic calculations used in ROPP to relate the geometric and geopotential height scales is provided. This document describes the most appropriate functions to use to compute height scales relative to the WGS84 reference ellipsoid. The sensitivity of results to the choice of algorithm is shown. GRAS SAF Report 01 C Buontempo 1 Mar 2007Monodimensional thinning for GPS Radio Occulation Radio occultation data tends to be oversampled in respect of the ac tual resolution and information content of the dataset. Thinning aims to reduce the amount of data without reducing the information content. A number of 1dimensional thinning algorithms are presented and their strengths and weaknesses discussed. 

