# 20. Glossary¶

- analysis
It is the optimal state estimated through a data assimilation or optimization procedure.

- APosterioriCorrelations
Keyword to indicate the correlation matrix of

*a posteriori*analysis errors.- APosterioriCovariance
Keyword to indicate the covariance matrix of

*a posteriori*analysis errors.- APosterioriStandardDeviations
Keyword to indicate the standard errors diagonal matrix of

*a posteriori*analysis errors.- APosterioriVariances
Keyword to indicate the variances diagonal matrix of

*a posteriori*analysis errors.- background
It is a part (chosen to be modified) of the system state representation, representation known

*a priori*or initial one, which is not optimal, and which is used as a rough estimate, or a “best estimate”, before an optimal estimation.- BMA
The acronym means

*Background minus Analysis*. It is the difference between the background state and the optimal state estimation, corresponding to the mathematical expression .- boundary conditions
These are particular input and control variables of the simulator, which characterize the description of the system’s behavior at the border of the simulation spatial domain.

- case
One ADAO case is defined by a set of data and of choices, packed together through the user interface of the module (in TUI as in GUI). The data are physical measurements that have technically to be available before or during the case execution. The simulation code(s) and the data assimilation or optimization method, and their parameters, has to be chosen, they define the execution properties of the case.

- CostFunctionJ
Keyword to indicate the minimization function, noted as .

- CostFunctionJb
Keyword to indicate the background part of the minimization function, noted as .

- CostFunctionJo
Keyword to indicate the observation part of the minimization function, noted as .

- CurrentState
Keyword to indicate the current state used during an optimization algorithm procedure.

- digital simulator
All the numerical relationships and equations characterizing the physical system studied.

- initial conditions
These are specific simulator input and control variables that characterize the description of the system’s behavior at the initial edge of the simulation time domain.

- innovation
Difference between the observations and the result of the simulation based on the background state, filtered to be compatible with the observation. It is similar with OMB in static cases.

- iteration (internal)
An (internal) iteration takes place when using iterative optimization methods (e.g. for the 3DVAR algorithm). Internal iterations are performed within each iterative optimization operation. The iterative behavior is fully integrated into the execution of the iterative algorithms, and is only apparent to the user when his observation is explicitly requested using “

*Observer*” attached to computational variables. See also step (of assimilation).- MahalanobisConsistency
Keyword to indicate the Mahalanobis parameter measuring the consistency of the data assimilation optimal state estimation. Its value can be compared to 1, a “good” estimation leading to a parameter “close” to 1.

- numerical simulation
Computational implementation of the set composed of the numerical simulator and a particular set of all the input and control variables of the simulator. These variables enable the digital simulator to be able to numerically represent the system’s behavior.

- observation operator
It is a transformation of the simulated state into a set of quantities explicitly comparable to the observations.

- observations or measurements
These are quantities that come from measuring instruments and characterize the physical system to be studied. These quantities can vary in space or time, can be punctual or integrated. They are themselves characterized by their measurement nature, size, etc.

- OMA
The acronym means

*Observation minus Analysis*. It is the difference between the observations and the result of the simulation based on the optimal state estimation, the analysis, filtered to be compatible with the observation, corresponding to the mathematical expression .- OMB
The acronym means

*Observation minus Background*. It is the difference between the observations and the result of the simulation based on the background state, filtered to be compatible with the observation, corresponding to the mathematical expression .- physical system
This is the object of study that will be represented by numerical simulation and observed by measurements.

- SigmaBck2
Keyword to indicate the Desroziers-Ivanov parameter measuring the background part consistency of the data assimilation optimal state estimation. Its value can be compared to 1, a “good” estimation leading to a parameter “close” to 1.

- SigmaObs2
Keyword to indicate the Desroziers-Ivanov parameter measuring the observation part consistency of the data assimilation optimal state estimation. Its value can be compared to 1, a “good” estimation leading to a parameter “close” to 1.

- step (of assimilation)
An assimilation step takes place when a new observation, or a new set of observations, is used, for example to follow the temporal course of a dynamic system. Remark: a

*single step*of assimilation can contain by nature*several iterations*of optimization when the assimilation uses an iterative optimization method. See also iteration (internal).