# Local definition 9: Singular vectors and ensemble perturbations

## Local definitions

- Local definition 1
- Local definition 2
- Local definition 3
- Local definition 4
- Local definition 5
- Local definition 6
- Local definition 7
- Local definition 8
- Local definition 9
- Local definition 10
- Local definition 11
- Local definition 12
- Local definition 13
- Local definition 14
- Local definition 15
- Local definition 16
- Local definition 17
- Local definition 18
- Local definition 19
- Local definition 20
- Local definition 21
- Local definition 22
- Local definition 23
- Local definition 24
- Local definition 25
- Local definition 26
- Local definition 27
- Local definition 28
- Local definition 29
- Local definition 30
- Local definition 31
- Local definition 32
- Local definition 36
- Local definition 37
- Local definition 38
- Local definition 39
- Local definition 49
- Local definition 50
- Local definition 190
- Local definition 191
- Local definition 192

Octets | Key | Type | Contents |

41 | localDefinitionNumber | unsigned | ECMWF local GRIB use definition identifier. 9 = Singular vectors and ensemble perturbations. |

42 | class | codetable | Class |

43 | type | codetable | Type |

44-45 | stream | codetable | Stream |

46-49 | experimentVersionNumber | ksec1expver | Version number or experiment identifier. (4 ASCII characters, right justified) |

50-51 | forecastOrSingularVectorNumber | unsigned | If type 60, the perturbed forecast number. If type 62 or 63, the singular vector number. |

52-92 | These elements are set to zero for type = 60. Otherwise: | ||

52-53 | numberOfIterations | unsigned | Number of iterations. |

54-55 | numberOfSingularVectorsComputed | unsigned | Number of singular vectors computed. |

56 | normAtInitialTime | unsigned | Norm used at initial time. |

57 | normAtFinalTime | unsigned | Norm used at final time. |

58-61 | multiplicationFactorForLatLong | unsigned | Multiplication factor to convert latitude/longitude and accuracy from real to integer. |

62-65 | northWestLatitudeOfLPOArea | signed | Latitude in degrees of north-west corner of LPO area multiplied by KSEC1(47). |

66-69 | northWestLongitudeOfLPOArea | signed | Longitude in degrees of north-west corner of LPO* area multiplied by KSEC1(47). |

70-73 | southEastLatitudeOfLPOArea | signed | Latitude in degrees of south-east corner of LPO* area multiplied by KSEC1(47). |

74-77 | southEastLongitudeOfLPOArea | signed | Longitude in degrees of south-east corner of LPO* area multiplied by KSEC1(47). |

78-81 | accuracyMultipliedByFactor | unsigned | Accuracy multiplied by KSEC1(47). |

82-83 | numberOfSingularVectorsEvolved | unsigned | Number of singular vectors evolved. |

- | Ritz numbers. RITZ = KSEC1(55)*EXP( LOG(10.0*KSEC1(54) ) Thus: | ||

84-87 | NINT_LOG10_RITZ | signed | NINT( LOG10(RITZ)-5 ) |

88-91 | NINT_RITZ_EXP | signed | NINT( RITZ/( EXP(LOG(10.0*KSEC1(54) ) |

92 | Spare (set to zero) |

( 1) LPO = Local Projection Operator, an operator applied during the singular vector computation to confine the area where the final time norm is computed (eg Northern Hemisphere extra-tropics).

( 2) A negative Ritz number or a negative latitude/longitudes value is stored as positive number and its the most significant bit is set to 1.