Observer norm complement and documentation

[modules/adao.git] / doc / en / ref_algorithm_3DVAR.rst

diff --git a/doc/en/ref_algorithm_3DVAR.rst b/doc/en/ref_algorithm_3DVAR.rst
index ed3ef44e7fb6b29e017406b50775add8d70a4bb5..430b0f47f8a7366ec9a57a659137540b332430b3 100644 (file)
--- a/doc/en/ref_algorithm_3DVAR.rst
+++ b/doc/en/ref_algorithm_3DVAR.rst
@@ -33,7 +33,7 @@ Description
 This algorithm performs a state estimation by variational minimization of the
 classical :math:`J` function in static data assimilation:
 
-.. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})
+.. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-H(\mathbf{x}))^T.\mathbf{R}^{-1}.(\mathbf{y}^o-H(\mathbf{x}))
 
 which is usually designed as the "*3D-VAR*" function (see for example
 [Talagrand97]_).
@@ -165,10 +165,11 @@ The options of the algorithm are the following:
     these variables being calculated and stored by default. The possible names
     are in the following list: ["APosterioriCorrelations",
     "APosterioriCovariance", "APosterioriStandardDeviations",
-    "APosterioriVariances", "BMA", "CostFunctionJ", "CurrentOptimum",
-    "CurrentState", "IndexOfOptimum", "Innovation", "MahalanobisConsistency",
-    "OMA", "OMB", "SigmaObs2", "SimulatedObservationAtBackground",
-    "SimulatedObservationAtCurrentOptimum",
+    "APosterioriVariances", "BMA", "CostFunctionJ",
+    "CostFunctionJAtCurrentOptimum", "CurrentOptimum", "CurrentState",
+    "IndexOfOptimum", "Innovation", "InnovationAtCurrentState",
+    "MahalanobisConsistency", "OMA", "OMB", "SigmaObs2",
+    "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentOptimum",
     "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum",
     "SimulationQuantiles"].
 
@@ -283,6 +284,27 @@ The conditional outputs of the algorithm are the following:
 
     Example : ``bma = ADD.get("BMA")[-1]``
 
+  CostFunctionJAtCurrentOptimum
+    *List of values*. Each element is a value of the error function :math:`J`.
+    At each step, the value corresponds to the optimal state found from the
+    beginning.
+
+    Example : ``JACO = ADD.get("CostFunctionJAtCurrentOptimum")[:]``
+
+  CostFunctionJbAtCurrentOptimum
+    *List of values*. Each element is a value of the error function :math:`J^b`,
+    that is of the background difference part. At each step, the value
+    corresponds to the optimal state found from the beginning.
+
+    Example : ``JbACO = ADD.get("CostFunctionJbAtCurrentOptimum")[:]``
+
+  CostFunctionJoAtCurrentOptimum
+    *List of values*. Each element is a value of the error function :math:`J^o`,
+    that is of the observation difference part. At each step, the value
+    corresponds to the optimal state found from the beginning.
+
+    Example : ``JoACO = ADD.get("CostFunctionJoAtCurrentOptimum")[:]``
+
   CurrentOptimum
     *List of vectors*. Each element is the optimal state obtained at the current
     step of the optimization algorithm. It is not necessarely the last state.
@@ -309,6 +331,11 @@ The conditional outputs of the algorithm are the following:
 
     Example : ``d = ADD.get("Innovation")[-1]``
 
+  InnovationAtCurrentState
+    *List of vectors*. Each element is an innovation vector at current state.
+
+    Example : ``ds = ADD.get("InnovationAtCurrentState")[-1]``
+
   MahalanobisConsistency
     *List of values*. Each element is a value of the Mahalanobis quality
     indicator.