A 4D-Var Analysis System for the California Current: A Prototype for an Operational Regional Ocean Data Assimilation System - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 350

Fig. 14.3 A schematic illustrating the overlapping 8 day data assimilation cycles used in
WCRA13 and WCRA31. The starting time for cycle j is denoted as t j
0

and the mid-point and

ending times as t j and t j

0 C 4 0 C 8

respectively. As indicated, the ending time of 4D-Var analysis

j j C 1 j C 2

cycle .The

prior circulation initial condition for cycle j C 1 is taken as the posterior circulation estimate at
the mid-point of cycle

corresponds to the mid-point of cycle and the starting time of cycle

j

circulation estimate at the mid-point of the previous analysis cycle. The advantages
of overlapping cycles are two-fold. First, it is well known that the 4D-Var analysis
cycle is equivalent to a Kalman Smoother, in which case the uncertainty in the
analysis will be at a minimum at the mid-point of the cycle, hence each analysis
cycle will start from the best possible prior initial condition. Second, at each initial
analysis time, an ensemble of three circulation estimates will be available allowing
for the possibility of ensemble averaging to further minimize the uncertainty of
the posterior circulation estimate. However, with overlapping analysis cycles, the
observations collected during the first half of each cycle will be correlated with
the background circulation during the same period. Since these correlations are not
accounted for in the current 4D-Var analysis system, this may lead to overweighting
of the analysis to some of the observations.
The dual formulation of ROMS 4D-Var was chosen for the historical analyses
because of the added utility that is available in the form of diagnostic post-
processing tools. As part of the ROMS 4D-Var suite, drivers are available for
computing the a posteriori impact of each observation on different scalar measures
of the circulation via K T , the transpose of the practical gain matrix. In addition,
the adjoint of the entire dual 4D-Var algorithm is available, and the sensitivity of the
same scalar circulation indices to uncertainties in the observations can be quantified,
as well as the expected errors in each index ( Moore et al. 2011c , 2012 ).

14.4.5 Background Quality Control of Observations for WCRA

Andersson and Jarvinen ( 1999 ) describe a procedure by which suitable values
of the threshold parameter ˛ in ( 14.9 ) can be estimated from the frequency