ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
Variational assimilation of radar reflectivity data
at the Met Office
Lee Hawkness-Smith1, Nicolas Gaussiat2, Helen Buttery1, Cristina Charlton-Perez1, Sue Ballard1
1Met Office, Meteorology Building, University of Reading, Reading, RG6 6BB, United Kingdom,
[email protected]
2Met Office,FitzRoy Road, Exeter, EX4 3PB, United Kingdom
(Dated: 30 May 2012)
Lee Hawkness-Smith
1. Introduction
The Met Office is currently running a convection permitting 1.5 km gridlength version of the Unified Model (UM; Davies et
al. 2005), the UKV, in a domain covering the United Kingdom. The high horizontal resolution of the atmospheric model, and
associated high resolution representation of orography, and improved physical parameterizations, allows the model to
produce mesoscale and convective features with a high degree of realism. The major challenge for the nowcasting
application, i.e. forecasting in the range 0 – 6 hours, is to support the improved realism with improved accuracy by the
optimum application of data assimilation.
The operational method of radar reflectivity assimilation used in Met Office convective scale models is Latent Heat Nudging
(LHN; Jones & Macpherson 1997), where model profiles of latent heat release are scaled by the difference between modelled
and observed precipitation. Latent heat nudging has been shown to have a beneficial impact on precipitation forecast skill,
particularly during the first three hours where its impact exceeds that of 3D-VAR (Dixon et al. 2009), however, to date,
NWP based forecasts have failed to beat advection based nowcasting systems during the first three hours. Therefore the
operational Met Office nowcasting system, STEPS, blends information from an advection based scheme and the UK 4 km
model.
With continued increases in the availability of computer resources and observations, including new data types and more
frequent observations, the Met Office has developed an NWP based nowcasting system, the nowcasting demonstration
project (NDP). This system provides 6 hour forecasts hourly, for a Southern UK domain, nested within the UKV. It uses
hourly cycling 4D-VAR data assimilation, which allows the optimum use of high temporal (5-15 minutes) resolution
observations. This system has demonstrated the ability to correctly forecast the location of a band of precipitating convective
cells which was missed by the blended UKV/advection based scheme because the operational UKV did not represent the
correct structure of the band of convection.
The Met Office is investigating the use of novel observation types in convective-scale data assimilation to provide the high
resolution information on the state of the atmosphere required to initialise forecasts. Such novel observations include radar
Doppler radial winds, refractivity, and reflectivity. The assimilation of radial winds has been introduced for the UKV
operationally, giving a 1-hour improvement in forecast skill at low rain rates.
This paper discusses research into the variational assimilation of radar reflectivity at the Met Office. Whilst latent heat
nudging of radar-derived surface rain rates is beneficial for precipitation forecasts, and may be difficult to beat by variational
assimilation methods due to the ability of latent heat nudging to add or remove precipitation from the model, there are
advantages to using radar reflectivity data within the variational assimilation system. Variational assimilation does not require
the assumption of latent heat nudging that latent heat release occurs in same column as precipitation. The use of all
observations together in a common framework should alleviate sub-optimal interactions and allow the consistent use of
complementary information. Assimilating radar reflectivity observations rather than radar derived surface precipitation
allows the use of the vertical information provided by multiple radar beams in the assimilation, and avoids the cumulative
effect of errors in deriving surface precipitation rates.
The Met Office is pursuing two approaches to the assimilation of radar reflectivity data: the indirect approach, where radar
reflectivity and model background data are used in 1D-VAR to produce relative humidity and temperature profiles, which
could be assimilated in 3D-VAR or 4D-VAR, and the direct approach, where a forward model is used to assimilate
reflectivity observations within 4D-VAR. 4D-VAR has the advantage of comparing each observation to model fields at the
time of the observation, using background error covariances which are evolved through the assimilation window. Thus 4DVAR has the potential to realise greater benefit from high time-frequency observations than 3D-VAR. 4D-VAR is
considerably more computationally expensive than 3D-VAR, however, due to the need to iterate a model and its adjoint. The
ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
particular advantage of the indirect approach is that the difficulty of handling the non-linear relationships between radar
reflectivity, rainwater mixing ratio and humidity, and the non-Gaussian probability distribution of these variables and their
covariances in a 3D or 4D-VAR assimilation is avoided.
In both approaches, it is important that the assumptions of the data assimilation method being used are fulfilled, which means
that the observations should be unbiased, and that the minimisation problem is only weakly non-linear. The radar data must
therefore be processed to remove artefacts such as clutter and anomalous propagation, and the observations selected for
assimilation must be sufficiently close to the model background to allow the assumption of approximate linearity to hold.
2. UK Radar Network
Fig. 1 UK Weather Radar Network.
The data source currently available for variational assimilation is the operational UK C-band (5.6–5.65 GHz) weather radar
network, shown in Fig.1. There are currently scans available for variational assimilation from 18 operational radars, including
two operated by Met Éireann in the Republic of Ireland, Dublin and Shannon, and one on Jersey.
The UK radar network is currently undergoing an upgrade through the Radar network renewal programme, which aims to
ensure continuity by avoiding age-related failures, to use the latest technology to increase radar capability, provide the
potential for future increases in capability, and to reduce running costs. New capabilities will include network-wide Doppler
and dual-polarization capability. Of particular relevance for the assimilation of radar data is the consistent provision of highquality data with quantifiable error characteristics, Doppler capability for the assimilation of radial winds, and the potential
for hydrometeor classification using dual-polarization channels.
Doppler-capable radars operate in two modes; a short-pulse mode for radial winds, and a long-pulse mode for reflectivity. In
long-pulse mode, reflectivity volumes are provided on 4 or 5 scan levels, at 1-degree by 300-metre resolution. The maximum
range of the scans is 250-km. The scan elevations for each radar are chosen based on local topography within the range 0° to
5°. Radar scan cycles are repeated every 5 minutes.
3. Quality Control
Radar data are subject to contamination by non-hydrometeorological targets, such as ground clutter and birds, and other
physical effects and technical artefacts can impede the correct physical interpretation of radar data, including: anomalous
propagation, partial beamfilling, range and velocity folding, poor calibration, noise, ambiguous hydrometeor type, and
attenuation, which can be due to the moist atmosphere, hydrometeors, or radome wetting. Alberoni et al. (2003) provides a
good review of radar quality issues with respect to data assimilation.
The Met Office is developing a Radar Quality Management System (RDQMS, Georgiou et al. 2011) to address issues of
radar data quality and reliability, which impact not only on data assimilation, but also hydrological applications.
ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
Data preprocessing is performed on the RADARNET server, which passes data to the Meteorological Database (MetDB) for
use in the Observation Processing System (OPS). Preprocessing includes options to average in range and azimuth, to
recalibrate, to measure the noise level for each averaged ray and perform noise subtraction, and to set flags for clutter, partial
beam blockage and speckle. The data is encoded in NetCDF and Grib2 files with all the QC information and metadata.
The OPS performs quality checks using the model background for all observations ingested into the Met Office dataassimilation system. The observations are filtered using QC flags. A forward model is used within OPS which simulates
reflectivity using the rain and ice-water content from the UM. A simple correction is made for beam bending and earth
curvature; attenuation and beam integration are not currently accounted for but will be included in future versions of OPS.
Experiments have been performed with different O-B rejection thresholds, with the aim to provide as much information to the
assimilation system as possible whilst providing a cost function which the assimilation system is able to minimize efficiently.
The final stage of preprocessing is superobbing, which is described in detail in the following section.
4. Superobbing and thinning
Meteorological variational-data-assimilation systems usually assume that observation and background errors are
uncorrelated, to make such systems computationally feasible. For high-resolution observational data such as radar data,
however, the assumption of uncorrelated observation errors is poor. Failing to account for the correlation of observation
errors could significantly limit the impact of assimilating radar data, as assimilating observations which are closer than the
observation error correlation lengthscale may be detrimental to the analysis.
Experience with assimilating satellite data has shown that assimilating higher-resolution data can lead to poorer analyses, and
therefore satellite data are routinely thinned, not only to reduce the computational cost of data processing, but also to reduce
the effect of unrepresented error correlations. Bormann et al. (2011) discussed this issue in more depth. An alternative to
thinning would be averaging, however, averaging observations could lead to meteorological features being smoothed out, and
inappropriate increments being applied. This has motivated the superobbing approach, where observation minus background
(O-B) differences, or innovations, are averaged. Radar reflectivity data are superobbed in the OPS prior to assimilation. For
each observation that passes QC a model observation is computed and an O-B innovation is calculated. These innovations are
then averaged and added to the model observation closest to the centre of the superobbing cell to provide the superob. Two
superobbing grids are available: a polar grid based on the radar gates and rays, or one based on the model grid. Following
superobbing, the superobs can be thinned horizontally.
Experience with Doppler winds and preliminary studies of direct reflectivity assimilation, have shown that using the
superobbing error as the observation error for assimilation in 4D-VAR gives too much weight to the observation, as
differences in representation between the model and observation, representativeness error, are not accounted for. The
approach taken for Doppler winds at the Met Office is to use the Hollingsworth and Lönnberg method (Hollingsworth and
Lönnberg, 1986, Lönnberg and Hollingsworth, 1986) to specify observation error, which requires statistics of innovation and
background error covariance as a function of distance. This follows the approach of Xu et al. (2007). A similar approach
may be tested for the assimilation of radar reflectivity observations at the Met Office. As a first guess, based on initial O-B
monitoring statistics, the observation error for reflectivity observations in direct assimilation has been set to 15 dBZ.
5. Variational assimilation methods
5.1 Reflectivity observation operator
The same observation operator for radar reflectivity is used in the indirect 1D-VAR retrievals, and in direct assimilation of
radar reflectivity observations in 4D-Var.
UM background fields of qrain (the rain-water mixing ratio) and qi (the cloud ice-water mixing ratio) are used to generate
simulated reflectivities. These model background values are first interpolated to the observation locations. The total
reflectivity (Zh) is computed as the sum of the rain reflectivity (ZhR) and the ice-precipitation reflectivity (Zhi), as:
Zh = ZhR + Zhi
Liquid-cloud reflectivity is negligible at C-band. Zhr can either be calculated as:
Zhr = 181.0 × ( 3600.0 × rrmod )
7.0 / 4.67
where rrmod is the model rain rate in mm h-1 or:
Zhr = 1.63E 3 × (1000.0 × ramod )
7.0 / 4.0
ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
where ramod is the model rain amount in mm3mm-3. Zhi can be calculated as:
Zhi = 10(
0.03589(Tmod − ZeroDegC ) + 3.12034 )
qi1.67742
where Tmod is the model temperature and the constant ZeroDegC=273K, that is, zero degrees centigrade in units of Kelvin.
The reflectivity is assigned a missing value if it is not above the noise level. The noise level is calculated from the noise
equivalent reflectivity at 1 km (NEZ) in this way:
Noise = 10( NEZ /10.0 )
a range correction (corrrange) is calculated as:
corrrange = 20.0 × log10 ( rangeobs )
where rangeobs is the range of the observation. The power can then be calculated as:
( Zh−corrrange )
Power = 10
10
If the power is not greater than 1.7 dB above the noise level, then the data is considered to be missing. Within the code,
logarithmic units are used for RH and reflectivity, and errors are specified in dB.
5.2 Indirect assimilation 1D-VAR + 3D-VAR or 4D-VAR
The indirect assimilation of reflectivity data involves using 1D-VAR to create a column of pseudo-observations of
temperature (T) and relative humidity (RH), combining the reflectivity data and the model background. These are then
assimilated with 3D- or 4D-VAR during the standard VAR cycle.
The OPS reads in all radar scans from the network available within the assimilation time window. Synthetic observations of
RH and reflectivity are generated from the model background at the location of the raw reflectivity observations, the
reflectivity observations being generated using the operator described in section 5. Using the synthetic observations, the OPS
performs QC on the raw reflectivity observations, and produced reflectivity superobs as described in sections 3 and 4. The
availability of multiple scan elevations and scans from multiple radars means that vertical profiles of reflectivity superobs can
be generated at model column locations. As an additional constraint, pseduo-humidity profiles are generated from these
reflectivity profiles, by assuming that the atmosphere is saturated where precipitation is observed. The reflectivity profiles,
and pseduo-humidity profiles are used together with their synthetic model background equivalent and model temperature
information in a 1D-VAR minimization process to created retrieved profiles of RH and T.
To simplify the variational microphysical adjustment, cloud-conserved thermodynamic and water content variables are used
in the minimization: the total water qt = q + qc, where q is the mixing ratio of water vapour, qc is the mixing ratio of
condensed water and ice, and the liquid water temperature Tl = T − (L/cp)qc , where L is the latent heat of sublimation, Ls, in
the frozen phase, or the latent heat of vaporisation, Lv, in the liquid phase. The step transition for qc and L from liquid to solid
phase is made smooth by using an inverse tangent hyperbolic function of the temperature. A B matrix generated by JeanFrancois Caron, is used in the minimisation process.
The retrieved profiles of RH and T are passed to VAR for assimilation.
5.3 Direct assimilation 4D-VAR
The Met Office 4D-VAR system (Rawlins et al. 2007) has an incremental formulation, where the UM is used to provide the
background, and a simplified, linear model, the perturbation forecast (PF) model, is iterated during the minimisation
procedure to provide updated values of the model guess fields through the assimilation time window. Following each run of
the PF model, its adjoint, which is used to calculate gradients for the minimisation, is run backwards through time. The model
variables are transformed into control variables which should be uncorrelated. The control variables used in the Met Office
VAR system are velocity potential, stream function, unbalanced pressure and a humidity variable which represents total
water.
Implementing assimilation of radar reflectivity within the VAR system has involved the introduction of a reflectivity
operator, and a linearization of the operator and its adjoint, and enhancements to the PF model to include a rainrate model
field, from which reflectivity is calculated. The reflectivity operator described in section 5.1, and its tangent linear, are used
in the direct assimilation method. The representation of ice is an area of continuing research, as the PF model does not
directly represent the evolution of cloud ice. In current experiments, only the rain component of reflectivity is used.
ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
Fig. 2 Comparison between precipitation for the control with no data assimilation without LHN (far left), the control with
full data assimilation without LHN (centre left), the control with full data assimilation including LHN (centre), the trial with
full data assimilation without LHN and with indirect reflectivity assimilation with errors of T=1.0K and RH=10% (centre
right), and the radar precipitation product (far right). This shows the analysis of the trial for 1500Z on 20 September 2011.
When developing the PF model, a balance must be maintained between increasing physical realism, whilst avoiding
unnecessary complexity which would make the system more non-linear and hence cause problems in minimisation. This is
particularly challenging for cloud and precipitation microphysics which are inherently non-linear.
The current representation of the rainrate field in the PF model is as a diagnostic variable which is calculated from the
condensed water increment in an autoconversion term. A set fraction of condensed water is autoconverted into precipitation
during a model timestep. There is no attempt to represent evaporation, which could potentially lead to negative water
contents in the linear framework. Improvements to this representation are currently being researched, and tested using
linearization tests, where the PF model increments are compared to UM increments. A limitation of this approach is that
where there is no rain in the model background, there is no gradient of reflectivity with respect to rain in the 4D-VAR cost
function, and hence no means by which to introduce rain. Approaches to this problem which are being pursued include using
a modified Z-R relationship with a positive gradient at zero rainrate, and using latent heat nudging in combination with 4DVAR to provide 4D-VAR with a background closer to the reflectivity observations.
6. Results
6.1 Indirect assimilation 1D-VAR + 3D-VAR
Trials have been carried out using the UK 4 km. The trials used standard operational settings, with a 3 hour 3D-VAR data
assimilation window. Various data-assimilation configurations were tested, including no data assimilation, latent heat nuding
only, and assimilation of pseudo-humidty and temperature profiles only. The 1D-VAR reflectivity derived profiles were
assimilated as pseudo-sonde ascents, using the sonde datastream.
Fig. 2 shows, for a 20 December 2011 case, a comparison between the surface precipitation in the control without data
assimilation, the control with full data assimilation but without latent heat nudging, the control with full data assimilation and
latent heat nudging, the trial with full data assimilation including reflectivity assimilation but without latent heat nudging, and
the radar derived precipitation rate. The full data assimilation controls, both with and without latent heat nudging, introduced
an area of spurious precipitation over the sea in the east of the domain, to the north of a genuine precipitation feature.
Including the 1D-VAR reflectivity derived profiles in the data assimilation removed this spurious feature. The spurious
feature resulted from the cloud assimilation scheme, and may be due to erronious thickening of the cloud layer. The ability of
the 1D-VAR profiles to remove this spurious feature is promising, however, these profiles contain information from the
model background as well as reflectivity observations, so it may be that removal of the spurious feature results from
assimilating the model background information. This highlights one potential weakness of the current method of indirect
reflectivity assimilation, which is that equal weighting is given to all levels of the pseudo humidity and temperature profiles,
regardless of the distance from an actual reflectivity observation, which leads to the model essentially assimilating itself at
many levels. A potential future improvement would be to weight the levels of the profile by a function of distance from actual
reflectivity observations.
ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
6.2 Direct assimilation 4D-VAR
Data assimilation experiments have been performed using the NDP data assimilation system. Preliminary work using single
observation tests, including simulated single observations, was used to test the performance of the data assimilation system
and ensure the accuracy of the adjoints of the reflectivity operator and PF model adjoint. Assimilation experiments using real
observations within the NDP domain have been performed for 5 April 2011. Fig 3 shows a comparison of surface rainrates
from the radar surface precipitation product, the model background, and PF model increments to the surface rainrate, valid at
09Z. For this experiment, superobs were thinned to 1 per 16 gridspaces, and the observation error was 15 dBZ. It is clear
from this figure that the model background features widespread precipitation which is not observed by the radars. The PF
model increments show an increase to surface precipitation where precipitation bands are observed, and suppression in the
area of unobserved precipitation. Thus far, the impact of assimilating the increments produced from reflectivity observations
has been limited, and research is ongoing to investigate this.
Fig. 3 Comparison between surface rainrates from the radar precipitation product (far left), an NDP model background
(centre), and the PF model increments at the observation time (far right). These figures are valid for 09Z on 5 April 2011.
7. Conclusions
Systems for the indirect (1D-VAR + 3D-VAR) and direct (4D-VAR) assimilation of radar reflectivity observations within
Met Office convective-permitting models have been developed. Experiments have demonstrated the ability of these systems
to fit the observed data, in a framework which allows consistency with the model background and other observations, within
the 1D-VAR retrievals and the 4D-VAR assimilation window respectively. At the time of writing, limited impact has been
seen in forecast trials, and research is ongoing to investigate this. The poster will highlight the latest results from assimilation
experiments.
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