12.1. Requirements for observation or experimental measurements description¶

The whole set of measurements of the physical system we are considering are called “observations”, or even simply “an observation”. As already mentioned in [DocT] A brief introduction to Data Assimilation and Optimization, this observation is noted in the most generic way by:

$\mathbf{y}^o$

It can depend in general of the space and the time, and even of parametric variables, and this in a more or less complex way. We usually particularize the time dependence by considering that, at each instant, the quantity $\mathbf{y}^o$ is a vector of $\mbox{I\hspace{-.15em}R}^d$ (with the dimension $d$ of the space being able to possibly vary in time). In other words, an observation is a (temporal) series of (varied) measurements. One will thus speak in an equivalent way of an observation (vector), of a series or a vector of observations, and of a set of observations. In its greatest generality, the sequential aspect of the series of observations is related jointly to space, and/or to time, and/or to a parametric dependence.

We can classify the ways of representing the observation according to the uses that we have afterwards and the links with the algorithmic methods. The classification that we propose is the following, each category being detailed below:

Use of a single spatial observation
Use of a time series of spatial observations
Use of a single spatio-temporal observation
Use of a parameterized series of spatial observations

The numerical representations of the observations use all the possibilities described in the List of possible input types. We specialize their uses here to indicate different possible ways of writing this information.

12.1.1. Use of a single spatial observation¶

This refers to the use of a vector series dependent only on space. This observation is moreover used at once, i.e. being completely known at the beginning of the algorithmic analysis. This can for example be a spatial field of measurements, or several fields physically homogeneous or not.

The mathematical representation is $\mathbf{y}^o\,\in\,\mbox{I\hspace{-.15em}R}^d$ .
The canonical numerical representation is a vector.
The numerical representation in ADAO is done with the keyword “Vector”. All the information, declared in one of the following representations, is transformed into a single vector (note: lists and tuples are equivalent):
- “numpy.array” variable : numpy.array([1, 2, 3])
- “list” variable : [1, 2, 3]
- string variable : '1 2 3'
- string variable : '1,2,3'
- string variable : '1;2;3'
- string variable : '[1,2,3]'
- Python data file, with variable “Observation” in the namespace, indicated by the keyword “Script” with the condition Vector=True
- data text file (TXT, CSV, TSV, DAT), with variable pointer by name in column or row, indicated by the keyword “DataFile” with the condition Vector=True
- binary data file (NPY, NPZ), with variable pointer by name, indicated by the keyword “DataFile” with the condition Vector=True
Examples of statements in TUI interface:
- case.setObservation( Vector = [1, 2, 3] )
- case.setObservation( Vector = numpy.array([1, 2, 3]) )
- case.setObservation( Vector = '1 2 3' )
- case.setObservation( Vector=True, Script = 'script.py' )`
- case.setObservation( Vector=True, DataFile = 'data.csv' )`
- case.setObservation( Vector=True, DataFile = 'data.npy' )`

Use note: in a given study, only the last record (whether a single vector or a series of vectors) can be used, as only one observation concept exists per CADD study.

12.1.2. Use of a time series of spatial observations¶

This refers to a vector ordered series of observations, dependent on space and time. At a given instant, it is assumed that only the observations of the current and previous instants are known. The successive observations in time are indexed by $n$ , their instant of existence or of reference. This can for example be a spatial field of measurements, physically homogeneous or not, of which we consider a history.

The mathematical representation is $\forall\,n\in\{0...N\},\,\mathbf{y}^o_n\,\in\mbox{I\hspace{-.15em}R}^d$ .
The canonical numerical representation is an ordered series of vectors.
The numerical representation in ADAO is done with the keyword “VectorSeries”. The current indexing of the information is used to represent the time index when declaring in one of the following representations, and the information is transformed into an ordered series of vectors (note: lists and tuples are equivalent):
- “list” of “numpy.array” : [numpy.array([1,2,3]), numpy.array([1,2,3])]
- “numpy.array” of “list” : numpy.array([[1,2,3], [1,2,3]])
- “list” of “list” : [[1,2,3], [1,2,3]]
- “list” of string variables : ['1 2 3', '1 2 3']
- “list” of string variables : ['1;2;3', '1;2;3']
- “list” of string variables : ['[1,2,3]', '[1,2,3]']
- string of “list” : '[[1,2,3], [1,2,3]]'
- string of “list” : '1 2 3 ; 1 2 3'
- Python data file, with variable “Observation” in the namespace, indicated by the keyword “Script” with the condition VectorSerie=True
- data text file (TXT, CSV, TSV), with variable pointer by name in column or row, indicated by the keyword “DataFile” with the condition VectorSerie=True
- binary data file (NPY, NPZ), with variable pointer by name, indicated by the keyword “DataFile” with the condition VectorSerie=True
Examples of statements in TUI interface:
- case.setObservation( VectorSerie = [[1,2,3], [1,2,3]] )
- case.setObservation( VectorSerie = [numpy.array([1,2,3]), numpy.array([1,2,3])] )
- case.setObservation( VectorSerie = ['1 2 3', '1 2 3'] )
- case.setObservation( VectorSerie = '[[1,2,3], [1,2,3]]' )
- case.setObservation( VectorSerie = '1 2 3 ; 1 2 3' )
- case.setObservation( VectorSerie=True, Script = 'script.py' )`
- case.setObservation( VectorSerie=True, DataFile = 'data.csv' )`
- case.setObservation( VectorSerie=True, DataFile = 'data.npy' )`

Use note: in a given study, only the last record (whether a single vector or a series of vectors) can be used, as only one observation concept exists per CADD study.

12.1.3. Use of a single spatio-temporal observation¶

This single spatio-temporal observation is similar to the previous one in its representation as a vector series, but it imposes that it must be used in a single run, i.e. by being fully known at the beginning of the algorithmic analysis. It can therefore be represented as an indexed series, in the same way as for a Use of a time series of spatial observations.

12.1.4. Use of a parameterized series of spatial observations¶

One represents now a collection of observations parameterized by an index or a discrete parameter. This form is still similar to the previous one. It is therefore representable as an indexed series, in the same way as for a Use of a time series of spatial observations.

12.1.5. General comments on the observations¶

Warning

When the assimilation explicitly establishes a temporal iterative process, as in state data assimilation, the first observation is not used but must be present in the data description of a ADAO case. By convention, it is therefore considered to be available at the same time as the draft time value, and does not lead to a correction at that time. The numbering of the observations starts at 0 by convention, so it is only from number 1 that the observation values are used in the temporal iterative algorithms.

Observations can be provided by single time steps or by successive windows for iterative algorithms. In this case, a series of observations must be provided for each algorithmic iteration relative to a time window. In practice, for each window, we provide a series as in a Use of a time series of spatial observations.

The observation acquisition options are richer in the TUI textual interface, as not all options are necessarily available in the GUI.

For data entry via files, please refer to the description of the possibilities around the keyword “DataFile” in the Pseudo-types of digital data description.