Improving the Assimilation of GPS RO Data in the Tropical Lower Troposphere Bill Kuo and Hui Liu UCAR COSMIC

Outline Challenges of GPS RO observations: – Lower tropical troposphere – Stratosphere Estimation of GPS RO BA observational errors Improving the performance of GPS RO assimilation in the lower tropical troposphere through: – Physically based GPS RO data QC – Variable vertical filtering of GPS RO data

α GPS Radio Occultation

Determining Bending Angle from observed Doppler From orbit determination we know the location of source and We know the receiver orbit. Thus we know Thus we know. And compute the bending angle Earth Bending angle  Transmitted wave fronts Wave vector of received wave fronts We measure Doppler frequency shift:

Upper stratosphere and lower troposphere are regions of maximum uncertainty for GPS RO inversions In the upper stratosphere: the signal reduces below noise level in terms of the phase (Doppler) In the lower troposphere: the signal reduces below noise level in terms of the amplitude at what height to start using signal for inversion ?

Heights where GPS-RO is reducing the 24hr errors 7-35 km height interval is sometimes called the GPS-RO “core region”. Global model sees little value of GNSS RO in lower troposphere Impact in the stratosphere is small as well

Error characterization and quality control (QC) of GPS RO bending angles (BA) Different occultations have different observation errors Accurate specification of BA observation error is only possible for spherically symmetric refractivity Large amount of water vapor makes tropospheric refractivity non-spherically symmetric, introducing uncertainty in BA Some parameters based on the structure of WO-transformed RO signals can be used as a proxy for the observation error and/or for truncation of BA profiles Assimilation of each occultation with individual observation error or using zonally averaged error model

Error Characterization Based on the RO Signal Structure Voltage signal-to-noise ratio (SNR); subject to strong variations in the lower troposphere (LT); reliable estimation is made between 60 and 80 km for each occultation individually Max. bending angle lapse (BALmax); large values indicate strong inversion layers; observations may be affected by super-refraction: assimilation of BA below SR layer is ill-posed problem BA uncertainty, a proxy for RMS BA error, estimated from local spectral width (LSW) of WO-transformed RO signal (LT) or from fluctuation of the ionosphere-free excess Doppler (UT or stratosphere) Confidence parameter, based on existence of more than one strong components in local spectra of WO-transformed RO signal

Signal to noise ratio (SNR) : ranges from ~200 to ~1000 V/V Distribution of the SNR averaged between 60 ad 80 km Effects of low SNR: RO signal cannot be distinguished from noise at low obs. heights Uncertainty (in tropics): 1) If not use: negative BA bias 2) If use noise: positive BA bias

Occultations with higher SNR result in slight reduction of the standard deviation in LT and significant reduction of the negative bias below 2 km SNR < 600 V/V SNR > 700 V/V In FORMOSAT-7/COSMIC-2, on average, the SNR is expected to be doubled compared to FORMOSAT-3/COSMIC Statistical comparison of RO to ECMWF BA in tropics (-30<lat<+30 deg)

Determining the height of ABL (and other inversion layers) max. bending angle lapse (BALmax) in a sliding window max. lapse of N gradient obtained by linear regressions in two adjacent sliding windows

truncation of profiles below the height of BALmax statistics of profiles with large and small BALmax Significant differences in bias and standard deviation in stats. with ECMWF for profiles with large and small BALmax can be explained by under-estimation of the ABL depth by the model. Thus BALmax height is an important scalar parameter which can be used for "nudging" the model to change (increase) ABL depth. This is a matter of the future.

Local spectral width of WO-transformed signal as a proxy for BA uncertainty (RMS error) in the convective moist troposphere polar occultation tropical occultation bending angle from phase of WO-transformed signal sliding spectrogram of WO-transformed signal Local width of spectrogram: measure of BA uncertainty; proxy for BA error x 2

Dynamic (individual for each occ.) BA error estimation in the troposphere BA from derivative of phase of WO-transformed signal Sliding spectrogram of WO-transformed signal Local width of the spectrogram. A proxy for RMS BA error x 2. (1) Lohmann, Radio Sci., 2006: relation of the RMS BA error to the RMS fluctuation of WO-transformed amplitude. Results in very small RMS BA errors (few percents) in the moist LT. (2) Gorbunov et al., JGR, 2006: relation of the RMS BA error to the local spectral width (LSW) of WO-transformed signal. Results in larger BA errors. Depends on the definition of LSW. Following approach (2) with different definition of LSW based on the integral of local spectral power. Approach (1): peace-wise linear least squares fit Approach (2): fixed % of the integral

Structure of the proxy for BA RMS error (definition by least squares fit) The largest error in the low-latitude LT. Depends on humidity: largest over the oceans (not so large over Africa and Australia). 8km 5km 2km

Impact of Physically-based QC

A Challenge in RO data assimilation in the lower tropical troposphere In the lower tropical troposphere, RO data (refractivity and bending angles) possess substantial systematic differences compared with NWP analyses and forecasts in the lower tropical troposphere The existence of the large systematic errors is a challenge for successful RO data assimilation

Systematic negative differences of RO refractivity below 3.5km (against ECMWF 12-h forecasts) 18 COSMIC RO refractivity is substantially smaller (up to -3%) than EC forecast below 3.5km The existence of large negative differences is a challenge for successful RO data assimilation COSMIC RO Ref data is compared with ECMWF 12-h forecast near radiosondes (<3-h & 300 km) Statistics is based on RO data in global tropics, April 1-30, 2012.

Methods to deal with the systematic differences Ignore all of RO data in the lower troposphere (e.g., ECMWF) Tighten (O-B) departures check, eliminating majority of RO data (e.g., NCEP); BUT NWP background/forecast has large errors too Need smarter methods to reduce the systematic differences and their impact on assimilation with NWP A physics-based quality control of RO data using spectrum of WO-transformed RO signals is promising

Definition: CP = (P1 - P2) / P1 (%) where P1 ad P2 are powers of the 1st and 2nd max. local spectral components Local spectra of WO-transformed RO signal for tropical occultation at different impact heights: At 15 km, the spectrum basically consists of one frequency; At 5.3 km, the spectrum broadens, but the main frequency still is seen; At 4 km, the spectrum is broad and the main frequency is not seen. Confidence parameter

Structure of the confidence parameter (1st definition) Smallest confidence in the low-latitude LT. Depends on humidity: smallest over the oceans (not so small over Africa and Australia). 8km 5km 2km

Distribution RO data with confidence parameter (Spaghetti distribution for all RO profiles in Western Pacific, Sept. 8-10, 2008) CP1 = (P1-P2)/P1 (%), where P1 and P2 are powers of the 1 st and 2 nd maximum local spectral component. The RO data with CP1 < 30% are most located below 4km.

Local spectral width (LSW) of RO signals BA from derivative of phase of WO-transformed signal Sliding spectrogram of WO-transformed signal Local width of the spectrogram Gorbunov et al., JGR, 2006: relation of the RMS BA error to local spectral width (LSW) of WO-transformed signal. Depends on the definition of LSW. Definition of LSW: Piece-wise linear least squares fit to the integral of local spectral power.

Correlations of the systematic differences of RO Ref (against ECMWF forecast) with LSW and CP 24 Evident negative correlations (up to -0.52) exist with LSW, indicating that larger LSW corresponds to the large negative systematic differences The correlation with CP is less significant, except in 0-1km Height LSW CP 0-1km km km COSMIC RO Ref data is compared with ECMWF 12-h forecast near radiosondes (<3-h & 300 km) Statistics is based on the RO data in global tropics.

Connections of the systematic differences of RO Ref (against ECMWF forecast) with LSW 25 The differences grow much larger when LSW > 35% This suggests that the threshold of LSW > 35% is reasonable for truncation of RO Ref profiles COSMIC RO Ref data is compared with ECMWF 12-h forecast near radiosondes (<3-h & 300 km) Statistics is based on the RO data in global tropics.

WRF assimilations of truncated RO Ref data Cycling assimilation of COSMIC RO Ref data over equatorial Western Pacific (active moist convection) for April 16-30, 2012 CTL run: assimilate conventional observations and available COSMIC RO refractivity data QC run: Same as CTL run but rejects RO data with LSW > 35%, below 3.5km NOGPS run: Same as CTL run, but rejects all RO data below 3.5km The radiosonde Q observations are withheld in the assimilations for verification of WRF analyses

Impact of truncating RO Ref profiles on WRF 6-h forecasts of refractivity at RO locations The truncation of Ref data eliminate ~30% of bad RO data, and reduces the negative bias and RMS error in the lower troposphere CTL: Assimilation of all RO Ref data QC: Reject RO Ref data with LSW >35% below 3.5km WRF Ref 6-hour forecasts verified against COSMIC RO observations (April 16-30, 2012)

Impact of truncating RO Ref profiles (on WRF water vapor analyses) Assimilation of the truncated Ref data (QC) performs better than CTL and NOGPS in the lower tropical troposphere CTL: Assimilation of all RO Ref data NOGPS: Assimilation of NO Ref data QC: Reject RO Ref data when LSW >35% and < 3.5km WRF Q analyses verified against independent radiosonde Q observations Verified against independent radiosonde observations (April 16-30, 2012)

Impact of truncating Ref profiles on analyses biases of PW The truncation of RO Ref data produces the smallest biases of PW analyses, than CTL and NOGPS WRF PW analyses verified against independent ECMWF analyses

Conclusions RO Ref data with large local spectral width (LSW) has good correlations with the negative systematic differences against NWP forecasts in the lower tropical troposphere The truncation of RO data with a threshold of LSW > 35% below 3.5km reduces the systematic difference of RO Refractivity data to WRF 6-h forecasts and produces best WRF analyses of water vapor than CTL and NOGPS The truncation only rejects a small part (~1/3) of RO data LSW seems more effective than the confidence parameter (CP) for the truncation purpose

Vertical Variable Filtering of Bending Angle Data

Issues Associated with BA Assimilation GPS RO bending angles (BA) can have sharp and complex structures in the lower tropical troposphere, where moist convection exists Current operational NWP models can not resolve such sharp structures, resulting in substantial representativeness errors Large representativeness errors may lead to large systematic errors due to nonlinearity associated with: – Observation error specification in percentage (%) – Flow-dependent background errors – Sequential ensemble assimilation techniques Vertical variable filtering, consistent with model vertical resolution, may reduce representativeness errors, and improves the BA assimilation performance

Representativeness Errors Heights (km) WRF intervals (m) EMCWF internals (m) BUFR intervals (m)200 AtmPrf (m)20 Raw GPS RO data are available at much higher resolution (20 m) than the model. Significant vertical variation of moisture can cause large vertical variation of bending angles, not resolvable by the model. BUFR filtering – reduce the observation data from about 20 m to 200 m. It is model independent. GPS RO BA observational errors are typically provided in terms of %. The actual value depends on the observations. Analysis increments depends on observations and the background, and the specification of observation errors, and are therefore ‘nonlinear’.

Assessment of Representativeness Error 1.Smooth COSMIC RO refractivity data from CDAAC AtmPrf profiles to have similar vertical resolutions as the NWP models. 2.Sample the refractivity data at the model vertical grids and forward model bending angles from the refractivity data using a local bending angle operator. 3.Compare the modeled bending angles with the raw bending angles (at their native levels) to estimate the representativeness errors. Steps for calculation of representativeness errors:

BA representativeness error for a WRF grid: one profile Modeled BA can not resolve the sharp structures of raw BA The Bufr format filtering is not strong enough to smooth out the sharp structures of raw BA The stronger vertical variable filtering eliminates most of the sharp structures of raw BA, and fits much closer to the modeled BA Raw: COSMIC BA with 100m resolution Modeled: BA modeled from RO refractivity sampled at a typical WRF grid (45 levels below 20 hPa) Bufr: Bufr-format filtered BA VVF: BA with vertical variable filtering 25.7S, 176.0W, April 11, 2012

BA Representativeness Errors for a WRF grid The BA representativeness error can reach ~7.5% in the lower tropical troposphere The vertical variable filtering of BA reduces the error to <2% Raw: COSMIC BA with 100m resolution Modeled: BA modeled from RO refactivity sampled at a typical WRF grid VVF: BA with ertical variable filtering Bufr : Bufr-format filtered BA Errors are defined as deviation from the modeled BA RMS Errors 25N – 25S April 16-30, 2012 VVF Bufr Raw

BA Representativeness Errors for a WRF grid RMS Representativeness Errors at 2.5 km, averaged over 25N – 25S VVF Raw Bufr Raw: COSMIC BA with 100m resolution Modeled: BA modeled from RO refactivity sampled at a typical WRF grid VVF: BA with ertical variable filtering Bufr : Bufr-format filtered BA

WRF assimilations of raw and filtered BAs Cycling assimilation experiments over equatorial Western Pacific (active moist convection) for April 16-30, km, 45 level WRF, DART ensemble data assimilation, 64 members; IC BC are from ECMWF global analysis NOBA run: assimilate conventional observations only BA run: assimilate conventional observations and raw BA BAF run: Same as BA run but assimilate the BA with vertical variable filtering The radiosonde Q observations are withheld in the assimilations for verification of WRF analyses

Locations of available RO BAs and Radiosonde data There were ~ 30 radiosonde observations available for WRF analyses verification Open circle: radiosondes Solid dots: COSMIC RO BA data

Means of Analysis Increments of Refractivity at RO Locations The mean of refractivity analyses increments of BAF is systematically more positive than that of BA below 7km. This indicates that the assimilation of raw BA data introduces systematic negative differences to the analyses increments. BAF: Assimilation of filtered BA data BA: Assimilation of raw BA data Averaged over April 2012 BAF BA BAF “O” is defined as the filtered refractivity

Impact of Vertical Filtering of RO BA profiles 41 Assimilation of raw BA data performs worse than no assimilation of BA data in the lower tropical troposphere Vertical variable filtering of BA data improves the performance, and gives the best results throughout the troposphere BAF: Assimilation of filtered BA data BA: Assimilation of raw BA data NOBA: No assimilation of BA data Verified against independent radiosonde observations

Bias in 850 hPa Q Verified against EC Analysis BAF: Assimilation of filtered BA data BA: Assimilation of raw BA data NOBA: No assimilation of BA data WRF analyses of BA have dry biases over the ocean The filtering of raw BA data reduces the biases

Bias in PW Verified against EC Analysis BAF: Assimilation of filtered BA data BA: Assimilation of raw BA data NOBA: No assimilation of BA data WRF analyses of BA have dry biases over the ocean The filtering of raw BA data reduces the biases

Conclusions The BA representative errors can be very large, up to 7.5%, for a common WRF configuration in the lower tropical troposphere; The vertical variable filtering of BA reduces the errors to < 2% The representativeness errors introduce noticeable systematic differences to WRF analyses increments Filtering of BA data, consistent with the WRF’s vertical resolution, reduces the biases of moisture analyses