Observation errors in all‐sky data assimilation

This article examines the first-guess (FG) departures of microwave imager radiances assimilated in all-sky conditions (i.e. clear, cloudy and precipitating). Agreement between FG and observations is good in clear skies, with error standard deviations around 2 K, but in heavy cloud or precipitation errors increase to 20 K. The forecast model is not good at predicting cloud and precipitation with exactly the right intensity or location. This leads to apparently non-Gaussian behaviour, both heteroscedasticity, i.e. an increase in error with cloud amount, and boundedness, i.e. the size of errors is close to the geophysical range of the observations, which runs from clear to fully cloudy. However, the dependence of FG departure standard deviations on the mean cloud amount is predictable. Using this dependence to normalise the FG departures gives an error distribution that is close to Gaussian. Thus if errors are treated correctly, all-sky observations can be assimilated successfully under the assumption of Gaussianity on which assimilation systems are based. This ‘symmetric’ error model can be used to provide a robust threshold quality-control check and to determine the size of observation errors for all-sky assimilation. In practice, however, this ‘observation’ error is being used to account for the model's difficulty in forecasting cloud, which really comes from errors in the background and in the forecast model. Hence in future it will be necessary to improve the representation of background and model error. Separately, symmetric cloud amount is recommended as a predictor for bias correction schemes, avoiding the sampling problems associated with ‘asymmetric’ predictors like the FG cloud amount. Copyright © 2011 Royal Meteorological Society

[1]  Yann Michel,et al.  Heterogeneous Convective-Scale Background Error Covariances with the Inclusion of Hydrometeor Variables , 2011 .

[2]  Marc Bocquet,et al.  Diagnosis and impacts of non-Gaussianity of innovations in data assimilation , 2010 .

[3]  P. Bauer,et al.  Direct 4D‐Var assimilation of all‐sky radiances. Part II: Assessment , 2010 .

[4]  Anthony Hollingsworth,et al.  The statistical structure of short-range forecast errors as determined from radiosonde data , 1986 .

[5]  John Derber,et al.  The Use of TOVS Cloud-Cleared Radiances in the NCEP SSI Analysis System , 1998 .

[6]  Clemens Simmer,et al.  Remote sensing of cloud liquid water , 1994 .

[7]  Dick Dee,et al.  Adaptive bias correction for satellite data in a numerical weather prediction system , 2007 .

[8]  Niels Bormann,et al.  Estimates of observation‐error characteristics in clear and cloudy regions for microwave imager radiances from numerical weather prediction , 2011 .

[9]  Peter Bauer,et al.  Direct 4D‐Var assimilation of all‐sky radiances. Part I: Implementation , 2010 .

[10]  J. Joseph,et al.  The delta-Eddington approximation for radiative flux transfer , 1976 .

[11]  P. Bauer,et al.  A Revised Cloud Overlap Scheme for Fast Microwave Radiative Transfer in Rain and Cloud , 2009 .

[12]  Peter Bauer,et al.  Implementation of 1D+4D‐Var assimilation of precipitation‐affected microwave radiances at ECMWF. II: 4D‐Var , 2006 .

[13]  Philippe Lopez,et al.  Direct 4D-Var Assimilation of NCEP Stage IV Radar and Gauge Precipitation Data at ECMWF , 2011 .

[14]  Peter Bauer,et al.  Multiple‐scattering microwave radiative transfer for data assimilation applications , 2006 .

[15]  Loïk Berre,et al.  Diagnosis and formulation of heterogeneous background‐error covariances at the mesoscale , 2010 .

[16]  Peter Bauer,et al.  Lessons learnt from the operational 1D + 4D‐Var assimilation of rain‐ and cloud‐affected SSM/I observations at ECMWF , 2008 .

[17]  Ronald M. Errico,et al.  Issues Regarding the Assimilation of Cloud and Precipitation Data , 2007 .

[18]  Keiji Imaoka,et al.  The Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E), NASDA's contribution to the EOS for global energy and water cycle studies , 2003, IEEE Trans. Geosci. Remote. Sens..

[19]  N. Roberts,et al.  Scale-Selective Verification of Rainfall Accumulations from High-Resolution Forecasts of Convective Events , 2008 .

[20]  Sungsu Park,et al.  Intercomparison of model simulations of mixed‐phase clouds observed during the ARM Mixed‐Phase Arctic Cloud Experiment. I: single‐layer cloud , 2009 .

[21]  J. Eyre,et al.  The assimilation of cloud‐affected infrared satellite radiances for numerical weather prediction , 2008 .

[22]  C. Kummerow,et al.  The Tropical Rainfall Measuring Mission (TRMM) Sensor Package , 1998 .

[23]  Peter Bauer,et al.  Assimilating Satellite Observations of Clouds and Precipitation into NWP Models , 2011 .

[24]  M. Bocquet,et al.  Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation , 2010 .

[25]  Heikki Järvinen,et al.  Variational quality control , 1999 .

[26]  Jimy Dudhia,et al.  Toward a New Cloud Analysis and Prediction System , 2011 .

[27]  A. Benedetti,et al.  Assimilation of MODIS Cloud Optical Depths in the ECMWF Model , 2008 .

[28]  N. B. Ingleby,et al.  Bayesian quality control using multivariate normal distributions , 1993 .

[29]  Grant W. Petty,et al.  Precipitation observed over the South China Sea by the Nimbus-7 Scanning Multichannel Microwave Radiometer during Winter Monex , 1990 .

[30]  Eric A. Smith,et al.  Intercomparison of microwave radiative transfer models for precipitating clouds , 2002, IEEE Trans. Geosci. Remote. Sens..

[31]  Niels Bormann,et al.  Estimates of spatial and interchannel observation‐error characteristics for current sounder radiances for numerical weather prediction. I: Methods and application to ATOVS data , 2010 .

[32]  James P. Hollinger,et al.  SSM/I instrument evaluation , 1990 .

[33]  W. Briggs Statistical Methods in the Atmospheric Sciences , 2007 .

[34]  Luc Fillion,et al.  An Examination of Background Error Correlations between Mass and Rotational Wind over Precipitation Regions , 2010 .

[35]  Paul Poli,et al.  Diagnosis of observation, background and analysis‐error statistics in observation space , 2005 .

[36]  A. Simmons,et al.  The ECMWF operational implementation of four‐dimensional variational assimilation. I: Experimental results with simplified physics , 2007 .

[37]  Ye Hong,et al.  Design and Evaluation of the First Special Sensor Microwave Imager/Sounder , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[38]  Wei Huang,et al.  Microwave Backscatter and Extinction by Soft Ice Spheres and Complex Snow Aggregates , 2010 .

[39]  Grant W. Petty,et al.  Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indices , 1994 .

[40]  A. McNally The direct assimilation of cloud‐affected satellite infrared radiances in the ECMWF 4D‐Var , 2009 .