Keywords:     Error statistics, quality control,
              data selection, mass and wind analysis,
              humidity analysis, analysis of surface fields,
              interpolation methods, normal mode
              initialization

                             RESEARCH MANUAL 1
                          ECMWF DATA ASSIMILATION
                          SCIENTIFIC DOCUMENTATION

                         ECMWF Research Department

2/84 Original Version
10/87 2nd Edition
3/92 3rd Edition



CONTENTS

                                             CHAPTER 1
                                             Overview

1.1   INTRODUCTION

1.2   DATA ASSIMILATION

1.3   ANALYSED VARIABLES AND COORDINATE SYSTEMS

1.4   JOB AND FILE STRUCTURE


                                             CHAPTER 2
                                       Mass and Wind Analvsis


2.1   INTRODUCTION

2.2   DESCRIPTION OF THE METHOD

    2.2.1     Statistical interpolation
    2.2.2     Super-observation formation
    2.2.3     Observation checking
    2.2.4     Grid point analysis
    2.2.4(a)  Grid point analysis by re-use of matrix inverse
    2.2.4(b)  Grid point analysis by solution of linear system

2.3   FIRST-GUESS STATISTICS

    2.3.1     General considerations
    2.3.2     Height error model
    2.3.3     Thickness error model
    2.3.4     Wind error model
    2.3.5     Practical generation of height thickness and wind covariance
    2.3.5(a)  Details on implementation
    2.3.5(b)  Data sources
    2.3.6     Modification of first-guess errors for each analysis
    2.3.7     Functional representation of horizontal and vertical correlations
    2.3.7(a)  Horizontal correlation model
    2.3.7(b)  Vertical covariance model

2.4   OBSERVATIONS AND OBSERVATION ERROR STATISTICS

    2.4.1     The analysis observation file
    2.4.2     Processing of observed data
    2.4.2(a)  Interpolation of first-guess
    2.4.2(b)  Multi-level observations
    2.4.2(c)  Upper-air single layer observations
    2.4.2(d)  Surface observations
    2.4.2(e)  Types of observations
    2.4.3     Observation error statistics
    2.4.3(a)  Error variances
    2.4.3(b)  Error correlation
    2.4.3(c)  Adjustment to off-time data

2.5   QUALITY CONTROL OF DATA

    2.5.1     Introduction
    2.5.2     Data flags
    2.5.3     Checks performed in mass and wind analysis
    2.5.3(a)  Interpretation of data flags
    2.5.3(b)  Comparison with first-guess
    2.5.3(c)  Multi-level check
    2.5.3(d)  Stability check
    2.5.3(e)  Wind direction check
    2.5.3(f)  Comparison with nearby observations
    2.5.3(g)  Comparison with analysis
    2.5.3(h)  SHIP blacklist

2.6   SELECTION OF DATA

    2.6.1     Introduction
    2.6.2     Pre-analysis data organisation
    2.6.2(a)  Discarding of observations
    2.6.2(b)  Reduction of data redundancy
    2.6.2(c)  Interface to main analysis
    2.6.3     Data selection in main analysis
    2.6.3(a)  Definitions
    2.6.3(b)  Construction of box tree
    2.6.3(c)  Details of implementation
    2.6.3(d)  Rejection of data

2.7   ORGANISATION OF THE COMPUTATION

    2.7.1     Overview
    2.7.2     Horizontal overlapping of analysis increments
    2.7.3     Computation of model level increments
    2.7.4     Analysis overlap in the vertical


                                              CHAPTER 3
                                           Humidity Analysis

3.1   INTRODUCTION

3.2   OBSERVATIONS AND THEIR USE

    3.2.1     Radiosondes
    3.2.2     Surface observations
    3.2.3     Satellite precipitable water observations


3.3  ANALYSIS TECHNIQUE

    3.3.1      Forecast errors
    3.3.2      "Super-observation" formation
    3.3.3      Quality control of data
    3.3.4      Data selection

3.4  TRANSFORMATION OF VIRTUAL TEMPERATURE AND RELATIVE HUMIDITY
     TO DRY TEMPERATURE AND SPECIFIC HUMIDITY


                                              CHAPTER 4
                                     Analysis of Surface Fields

4.1  INTRODUCTION

4.2  SEA SURFACE TEMPERATURE (SST)

4.3  SNOWDEPTH

    4.3.1      Snowfall analysis
    4.3.2      Snow depth first guess field creation
    4.3.3      Snow depth analysis


                                              CHAPTER 5
                                        Interpolation Methods

5.1  HYBRID TO PRESSURE TRANSFORMATION

    5.1.1      Height
    5.1.2      Horizontal wind
    5.1.3      Humidity
    5.1.4      10 metre wind
    5.1.5      2 metre temperature
    5.1.6      2 metre specific humidity


                                              CHAPTER 6
                                      Normal Mode Initialization

6.1  INTRODUCTION

6.2  COMPUTATION OF THE NORMAL MODES

6.3  THE INITIALIZATION PROCESS



                                              CHAPTER 7
                         Monitoring of Observation and Analysis Ouality

7.1   USE OF ASSIMILATION STATISTICS

7.2   STATISTICS ARCHIVES


REFERENCES