# Difference between revisions of "Differences of Calculated Results"

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imported>Lang Guenther (→Computational rules: text added) |
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# <math>r_i</math> (short for <math>r(x,y,z,t_i)</math>) as well as <math>f_i</math> (short for <math>r(x,y,z,t_i)</math>) must be valid data for the same instant <math>i</math> in time; otherwise the dervied results will become invalid. | # <math>r_i</math> (short for <math>r(x,y,z,t_i)</math>) as well as <math>f_i</math> (short for <math>r(x,y,z,t_i)</math>) must be valid data for the same instant <math>i</math> in time; otherwise the dervied results will become invalid. | ||

− | ==Computational | + | ==Computational results== |

− | The | + | Program [[NCDELTA]] can be used to compute all subsequent results. Locations of <math>r</math> are not required to coincide with those of <math>f</math>. Values <math>r</math> are interpolated to locations of <math>f</math>, as long as the geographical distance between the different locations does not exceed <math>R^\max</math>. In case the distance ''exceeds'' that limit, no results will be computed. In such a situation an ''invalid'' result value will be generated. The follwing results can be computed using [[NCDELTA]]. |

− | === | + | ===Ordinary differences=== |

+ | |||

+ | ====Difference==== | ||

+ | |||

+ | A result is computed for all times (one value for time-independent data) at all locations <math>(x,y,z)</math>: | ||

+ | # The difference between <math>f_i</math> and <math>r_i</math> is calculated in case <math>V(r_i,f_i)</math> returns .T.: | ||

+ | #:<math>d_i = f_i - r_i</math>, if <math>V(r_i,f_i)</math>; | ||

+ | # Result will be ''invalid'', if <math>V(r_i,f_i)</math> returns .F.: | ||

+ | #:<math>d_i = \rm{invalid}</math> if <math>\lnot V(r_i,f_i)</math>. | ||

+ | Results are computed for data belonging to categories '''K0''', '''K1''', '''KC''' und '''KN''', which means for all types of data. | ||

+ | |||

+ | ===Data for a Taylor diagram=== | ||

+ | |||

+ | ===Median=== | ||

+ | |||

+ | ===Percentiles=== | ||

---- | ---- |

## Revision as of 06:57, 6 May 2015

## Introduction

For data generated by

- mathematical models (model results), or
- analysis of calculated results (characteristic numbers), or
- measured data (observational data)

Various differences can be computed. Input data can be typically categorized as follows:

**Category K0**: , time-independent quantities;**Category K1**: , time-dependent quantities, one time step;**Category KC**: , time-dependent quantities, several discrete time steps, constant time step ;**Category KN**: , time-dependent quantities, several discrete time steps, varying time step .

For geophysical data categories K1, KC and KN are of significance. Examples:

- Category K1: topography/bathymetry for a specific instant in time;
- Category KC: water level at discrete times with constant time step, e. g. computed by a mathematical model;
- Category KN: tidal high water for times at
*non-equidistant*time intervals, e.g. derived from a water level time serie.

## Definitions

**reference data**: with respect to various*deviations*for can be evaluated. Typical data are either observational data or computational as well as analysis results for a specific (reference) state (situation);**variant data**: can be also either observational data or computational as well as analysis results, for which deviations shall be computed with respect to the reference state. Typically variant data are given for a different period in time (natural variation) or a different state of the system under study.**valid operator 1**: returns .T. or .F., in dependence whether is valid or invalid. Can be also applied to .**valid operator 2**: returns .T. or .F., in dependence whether is valid or invalid.

## Requirements for the computation of differences

The following requirements must be fulfilled by and :

- and must belong to the same category (see above);
- the number of times must be identical for and ;
- for data belonging to category KC constant time steps must coincide for and ;
- (physical) dimension as well as meaning must be equivalent for and ;
- (short for ) as well as (short for ) must be valid data for the same instant in time; otherwise the dervied results will become invalid.

## Computational results

Program NCDELTA can be used to compute all subsequent results. Locations of are not required to coincide with those of . Values are interpolated to locations of , as long as the geographical distance between the different locations does not exceed . In case the distance *exceeds* that limit, no results will be computed. In such a situation an *invalid* result value will be generated. The follwing results can be computed using NCDELTA.

### Ordinary differences

#### Difference

A result is computed for all times (one value for time-independent data) at all locations :

- The difference between and is calculated in case returns .T.:
- , if ;

- Result will be
*invalid*, if returns .F.:- if .

Results are computed for data belonging to categories **K0**, **K1**, **KC** und **KN**, which means for all types of data.

### Data for a Taylor diagram

### Median

### Percentiles

back to Pre- and Postprocessing