Issues Regarding the Assimilation of Cloud and Precipitation Data

Abstract The assimilation of observations indicative of quantitative cloud and precipitation characteristics is desirable for improving weather forecasts. For many fundamental reasons, it is a more difficult problem than the assimilation of conventional or clear-sky satellite radiance data. These reasons include concerns regarding nonlinearity of the required observation operators (forward models), nonnormality and large variances of representativeness, retrieval, or observation–operator errors, validation using new measures, dynamic and thermodynamic balances, and possibly limited predictability. Some operational weather prediction systems already assimilate precipitation observations, but much more research and development remains. The apparently critical, fundamental, and peculiar nature of many issues regarding cloud and precipitation assimilation implies that their more careful examination will be required for accelerating progress.

[1]  Jean-Noël Thépaut,et al.  Simplified and Regular Physical Parameterizations for Incremental Four-Dimensional Variational Assimilation , 1999 .

[2]  Stéphane Laroche,et al.  A microphysical bulk formulation based on scaling normalization of the particle size distribution. Part II: Data assimilation into physical processes , 2005 .

[3]  Tadashi Tsuyuki,et al.  Variational Data Assimilation in the Tropics Using Precipitation Data. Part II: 3D Model , 1996 .

[4]  O. Talagrand.  Objective Validation and Evaluation of Data Assimilation , 2003 .

[5]  J. Mahfouf,et al.  One-Dimensional Variational Data Assimilation of SSM/I Observations in Rainy Atmospheres at MSC , 2007 .

[6]  Luc Fillion,et al.  Diagnosing Summertime Mesoscale Vertical Motion: Implications for Atmospheric Data Assimilation , 2007 .

[7]  Tadashi Tsuyuki,et al.  Variational data assimilation in the tropics using precipitation data part I: Column model , 1996 .

[8]  Ronald M. Errico,et al.  Examination of the accuracy of a tangent linear model , 1993 .

[9]  E. Lorenz,et al.  The predictability of a flow which possesses many scales of motion , 1969 .

[10]  Four‐dimensional variational assimilation of special sensor microwave/imager total column water vapour in the ECMWF model , 2007 .

[11]  I. M. Navon,et al.  Impact of Parameter Estimation on the Performance of the FSU Global Spectral Model Using Its Full-Physics Adjoint , 1999 .

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

[13]  J. R. Eyre,et al.  Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation. I: Theory and simulation for TOVS , 1989 .

[14]  P. Bauer,et al.  Variational retrieval of temperature and humidity profiles using rain rates versus microwave brightness temperatures , 2004 .

[15]  Martin Ehrendorfer,et al.  Singular-Vector-Based Covariance Propagation in a Quasigeostrophic Assimilation System , 2005 .

[16]  Leo J. Donner,et al.  An initialization for cumulus convection in numerical weather prediction models , 1988 .

[17]  Tristan S. L'Ecuyer,et al.  An uncertainty model for Bayesian Monte Carlo retrieval algorithms: Application to the TRMM observing system , 2002 .

[18]  P. Lopez.  The Inclusion of 3D Prognostic Cloud and Precipitation Variables in Adjoint Calculations , 2003 .

[19]  R. Errico.  What is an adjoint model , 1997 .

[20]  Peter Bauer,et al.  The assimilation of SSM/I and TMI rainfall rates in the ECMWF 4D‐Var system , 2005 .

[21]  Roberto Buizza,et al.  The Singular-Vector Structure of the Atmospheric Global Circulation , 1995 .

[22]  Ramón de Elía,et al.  Distribution-Oriented Verification of Limited-Area Model Forecasts in a Perfect-Model Framework , 2003 .

[23]  Rolf H. Langland,et al.  Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system , 2004 .

[24]  Florence Rabier,et al.  Use of the MODIS imager to help deal with AIRS cloudy radiances , 2005 .

[25]  Ronald M. Errico,et al.  An examination of the accuracy of the linearization of a mesoscale model with moist physics , 1999 .

[26]  C. Prigent,et al.  Modeling of passive microwave responses in convective situations using output from mesoscale models: Comparison with TRMM/TMI satellite observations , 2004 .

[27]  R. Errico.  Interpretations of an adjoint-derived observational impact measure , 2007 .

[28]  Adrian M. Tompkins,et al.  A cloud scheme for data assimilation: Description and initial tests , 2004 .

[29]  Qin Xu.  Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part I: Basic Issues and Heuristic Examples , 1996 .

[30]  Philippe Lopez,et al.  The capability of 4D‐Var systems to assimilate cloud‐affected satellite infrared radiances , 2004 .

[31]  L. Fillion,et al.  Tangent Linear Aspects of the Kain–Fritsch Moist Convective Parameterization Scheme , 2004 .

[32]  F. Mesinger,et al.  Four-dimensional variational assimilation of precipitation data , 1995 .

[33]  R. Errico,et al.  The spectra of singular values in a regional model , 2001 .

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

[35]  Jean-François Mahfouf,et al.  Influence of physical processes on the tangent‐linear approximation , 1999 .

[36]  J. Michael Fritsch,et al.  Improving quantitative precipitation forecasts in the warm season: A USWRP research and development strategy , 2004 .

[37]  X. Zou,et al.  Rainfall Assimilation through an Optimal Control of Initial and Boundary Conditions in a Limited-Area Mesoscale Model , 1996 .

[38]  Jean-Jacques Morcrette,et al.  Preliminary studies on the variational assimilation of cloud–radiation observations , 2002 .

[39]  J. Mahfouf,et al.  Further investigation on adjoint sensitivity of surface precipitation to initial conditions , 2007 .

[40]  Joanna Joiner,et al.  An error analysis of radiance and suboptimal retrieval assimilation , 2000 .

[41]  B. Macpherson.  Operational experience with assimilation of rainfall datain the Met Office Mesoscale model , 2001 .

[42]  Dennis Sullivan,et al.  On the iteration of a rational function: Computer experiments with Newton's method , 1983 .

[43]  Luc Fillion,et al.  Coupling of Moist-Convective and Stratiform Precipitation Processes for Variational Data Assimilation , 2000 .

[44]  Thomas J. Greenwald,et al.  An All-Weather Observational Operator for Radiance Data Assimilation with Mesoscale Forecast Models , 2002 .

[45]  David J. Stensrud,et al.  Estimation of the error distributions of precipitation produced by convective parametrization schemes , 2001 .

[46]  J. Dudhia,et al.  Four-Dimensional Variational Data Assimilation of Heterogeneous Mesoscale Observations for a Strong Convective Case , 2000 .

[47]  J. Mahfouf,et al.  Jacobians of an operational prognostic cloud scheme , 2003 .

[48]  Ionel M. Navon,et al.  Variational data assimilation with moist threshold processes using the NMC spectral model , 1993 .

[49]  The Impact of Horizontal Resolution and Ensemble Size on Probabilistic Precipitation Forecasts by the ECMWF Ensemble Prediction System. , 2002 .

[50]  K. Puri,et al.  The Use of Satellite Data in the Specification of Convective Heating for Diabatic Initialization and Moisture Adjustment in Numerical Weather Prediction Models , 1990 .

[51]  Virginie Marécal,et al.  Variational Retrieval of Temperature and Humidity Profiles from TRMM Precipitation Data , 2000 .

[52]  Roger Daley,et al.  Observation and background adjoint sensitivity in the adaptive observation‐targeting problem , 2007 .

[53]  Steven Cocke,et al.  Details of Low Latitude Medium Range Numerical Weather Prediction Using a Global Spectral Model Part II. Effects of Orography and Physical Initialization , 1984 .

[54]  P. Bauer,et al.  SSM/I Radiance Assimilation at ECMWF , 2003 .

[55]  T. Palmer,et al.  Stochastic representation of model uncertainties in the ECMWF ensemble prediction system , 2007 .

[56]  Frank S. Marzano,et al.  Error analysis of TMI rainfall estimates over ocean for variational data assimilation , 2002 .

[57]  Philippe Courtier,et al.  Sensitivity of forecast errors to initial conditions , 1996 .

[58]  V. Ducrocq,et al.  Storm-Scale Numerical Rainfall Prediction for Five Precipitating Events over France: On the Importance of the Initial Humidity Field , 2002 .

[59]  M. Tiedtke,et al.  Representation of Clouds in Large-Scale Models , 1993 .

[60]  M. Tiedtke.  A Comprehensive Mass Flux Scheme for Cumulus Parameterization in Large-Scale Models , 1989 .

[61]  Some statistical considerations associated with the data assimilation of precipitation observations , 2000 .

[62]  Ying-Hwa Kuo,et al.  Incorporating the SSM/I-Derived Precipitable Water and Rainfall Rate into a Numerical Model: A Case Study for the ERICA IOP-4 Cyclone , 2000 .

[63]  Brian F. Farrell,et al.  Small Error Dynamics and the Predictability of Atmospheric Flows. , 1990 .

[64]  T. Palmer,et al.  Singular Vectors, Metrics, and Adaptive Observations. , 1998 .

[65]  Joseph Tribbia,et al.  The Reliability of Improvements in Deterministic Short-Range Forecasts in the Presence of Initial State and Modeling Deficiencies , 1988 .

[66]  Lars Isaksen,et al.  The structure and realism of sensitivity perturbations and their interpretation as ‘Key Analysis Errors’ , 2005 .

[67]  Philippe Lopez,et al.  A convection scheme for data assimilation: Description and initial tests , 2005 .

[68]  H. Pan,et al.  Global and Regional Moisture Analyses at NCEP , 2003 .

[69]  P. Stamus,et al.  Application of a Scale-Separation Verification Technique to Regional Forecast Models , 1992 .

[70]  Joseph Tribbia,et al.  Scale Interactions and Atmospheric Predictability: An Updated Perspective , 2004 .

[71]  Albert Ansmann,et al.  Air mass modification over Europe: EARLINET aerosol observations from Wales to Belarus , 2004 .

[72]  R. Errico,et al.  Examination of the sensitivity of forecast precipitation rates to possible perturbations of initial conditions , 2003 .

[73]  J. R. Eyre,et al.  Assimilation of TOVS radiance information through one-dimensional variational analysis , 1993 .

[74]  Florence Rabier,et al.  Use of MODIS imager to help dealing with AIRS cloudy radiances , 2003 .

[75]  Stéphane Laroche,et al.  A Microphysical Bulk Formulation Based on Scaling Normalization of the Particle Size Distribution. Part I: Description , 2005 .

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

[77]  J. Mahfouf,et al.  Four-Dimensional Variational Assimilation of Total Column Water Vapor in Rainy Areas , 2002 .

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

[79]  D. Zupanski.  A General Weak Constraint Applicable to Operational 4DVAR Data Assimilation Systems , 1997 .

[80]  M. Buehner.  Ensemble‐derived stationary and flow‐dependent background‐error covariances: Evaluation in a quasi‐operational NWP setting , 2005 .

[81]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[82]  D. Baumhefner,et al.  Predictability Experiments Using a High-Resolution Limited-Area Model , 1987 .

[83]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .

[84]  Philippe Courtier,et al.  Unified Notation for Data Assimilation : Operational, Sequential and Variational , 1997 .

[85]  Erik Andersson,et al.  Influence‐matrix diagnostic of a data assimilation system , 2004 .

[86]  Ying-Hwa Kuo,et al.  The impact of Global Positioning System data on the prediction of an extratropical cyclone: an observing system simulation experiment , 1997 .

[87]  Virginie Marécal,et al.  Experiments on 4D‐Var assimilation of rainfall data using an incremental formulation , 2003 .

[88]  C. Reynolds,et al.  Nonlinear growth of singular‐vector‐based perturbations , 2003 .

[89]  R. Errico.  The Forcing of Gravitational Normal Modes by Condensational Heating , 1989 .

[90]  P. D. Thompson,et al.  Uncertainty of Initial State as a Factor in the Predictability of Large Scale Atmospheric Flow Patterns , 1957 .

[91]  Arlindo da Silva,et al.  Data assimilation in the presence of forecast bias , 1998 .

[92]  D. P. DEE,et al.  Bias and data assimilation , 2005 .

[93]  Roberto Buizza,et al.  The Impact of Horizontal Resolution and Ensemble Size on Probabilistic Forecasts of Precipitation by the ECMWF Ensemble Prediction System , 2002 .