A Question of Adequacy of Observations in Variational Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 110

ill-conditioning—an augmentation to the cost function including terms that fit the
model to the prior in accord with the representativeness and accuracy of the prior.
But as will be explored in this paper, if the number of observations is fixed but free
to be moved (in space and/or time), there is a strategy that can generally remove the
ill-conditioned nature of the problem.
We numerically test this idea of moveable observations in the context of a sim-
plified Lagrangian air/sea interaction model with relevance to air mass modification
over the Gulf of Mexico in wintertime. The strategy revolves around knowledge of
the sensitivities of the model variables to elements of control—generally obtained
by integration of equations similar to the dynamical equations of the model.
The examination of sufficiency/insufficiency of observations in variational data
assimilation will be explored through use of two schemes: Forward Sensitivity
Method (FSM) and the variational method with (negative gradient of the

cost function) serving to determine the search direction. For simplicity, we refer
to this latter method as the

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-method. In an earlier paper, Lakshmivarahan and
Lewis ( 2010 ) have proved the equivalence of these two schemes. Since little is
known about FSM, the mechanics of this scheme will be developed after rudiments
of the air/sea interaction model are presented. Numerical experiments follow and
the paper ends with conclusions and a discussion on applicability of these ideas to
the more challenging dynamics of NWP.

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5.2 Model Dynamics: Air/Sea Interaction

5.2.1 Background Physical Processes

We consider a persistent operational weather prediction problem that has plagued
modelers and weather forecasters at the National Center for Environmental Pre-
diction (NCEP)/Environmental Modeling Center (EMC) for several decades [from
the late 1980s to the present day; reviewed in Lewis ( 2007 )]. The problem occurs
in association with air mass modification over the Gulf of Mexico in the cool
season. These events occur 4-5 times per month from November to March.
The phenomenon is labeled “return flow” since air that enters the Gulf exhibits
anticyclonic turning and returns to the coast as the cold high pressure system moves
eastward. A schematic diagram of the process is depicted in Fig. 5.1 .Inthetop
portion of this figure, the cold front is shown entering the Gulf with the attendant
low/high pressure couplet to the north. As the front moves through the Gulf along
with the eastward movement of the cyclone/anticyclone couplet, low-level southerly
winds at LCH (Lake Charles, LA) and BRO (Brownsville, TX) shift to northerly
and easterly, respectively. From this wind structure it is clear that the air entering
the Gulf near LCH will move southward and then westward along an over-water
trajectory. The persistent problem faced by forecasters is bias in the numerical
prediction of low-level temperature and water vapor as the air is modified over