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The En4DVar method is designed to combine the flow-dependent statistical covariance information of EnKF into the traditional 4DVar method. However, the En4DVar method is still hampered by its strong dependence on the adjoint model of the underlying forecast model and by its complexity, maintenance requirements, and the high cost of computer implementation and simulation. The primary goal of this paper is to propose an alternative approach to overcome the main difficulty of the En4DVar method caused by the use of adjoint models. The proposed approach, the nonlinear least squares En4DVar (NLS-En4DVar) method, begins with rewriting the standard En4DVar formulation into a nonlinear least squares problem, which is followed by solving the resulting NLS problem by a Gauss–Newton iterative method. To reduce the computational and implementation complexity of the proposed NLS-En4DVar method, a few variants of the new method are proposed; these modifications make the model cheaper and easier to use than the full NLS-En4DVar method at the expense of reduced accuracy. Furthermore, an improved iterative method based on the comprehensive analysis on the above NLSi-En4DVar family of methods is also proposed. These proposed NLSi-En4DVar methods provide more flexible choices of the computational capabilities for the broader and more realistic data assimilation problems arising from various applications. The pros and cons of the proposed NLSi-En4DVar family of methods are further examined in the paper and their relationships and performance are also evaluated by several sets of numerical experiments based on the Lorenz-96 model and the Advanced Research WRF (ARW) Model, respectively.

The recently reported interesting behavior of the EPR spin intensity as freshly prepared CuZSM-5 is dehydrated has been confirmed, and the interpretation offered in explanation has been tested by extending the data. Magnetic susceptibility and optical diffuse reflection spectroscopy have been used to show that the anomalous EPR data correspond to changes in symmetry rather than disproportionation of [CuOH] + into Cu + and Cu 2+ Oas H 2 O is removed, as previously suggested. Moreover, the relatively small negative Weiss constants suggest that antiferromagnetic coupling through the supposedly EPR silent conventional bridge species, [Cu 2+ -O 2--Cu 2+ ] 2+ , cannot be responsible for the relatively large changes in observed EPR spin intensity on dehydration. EPR measures selectively individual paramagnetic species and ignores those of low symmetry, while magnetic susceptibility integrates over all magnetic species in the sample. The changes in the EPR intensities were much larger than those observed by magnetic susceptibility. Furthermore, those from EPR occurred as the first H 2 O was removed, before any significant change in susceptibility occurred. The EPR data reflected those expected for the decrease in symmetry accompanying dehydration. Support for these views was found in the magnetic susceptibility and optical reflectance data. Evidence for CuO formation concomitant with dehydration was obtained.

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