Valerio Lucarini

Southern hemisphere midlatitude atmospheric variability of the NCEP-NCAR and ECMWF reanalyses

[1] We compare the representation of the Southern Hemisphere midlatitude winter variability in the NCEP-NCAR and ERA40 reanalyses by using the Hayashi spectral technique. We find important discrepancies in the description of the atmospheric waves at different spatial and temporal scales. ERA40 is generally characterized by a larger variance, especially in the high-frequency spectral region. Compared to the Northern Hemisphere, the assimilated data are relatively scarce particularly over the oceans, and they provide a weak constraint to the assimilation system even in the period when satellite data are available. In the presatellite period the discrepancies between the two reanalyses are large and randomly distributed; after 1979 the discrepancies are systematic. This study suggests that, as for the winter midlatitude variability in the Southern Hemisphere, a well-defined picture to be used in the evaluation of climate model simulations is still lacking because of the nonconsistency of the reanalyses.

Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations

In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference sample. Such experimental error brings inconsistency between phase and amplitude invoked by the causality principle. We propose a rigorous method to solve this relevant experimental problem by using an optimization method based upon singly subtractive Kramers-Kronig relations. The applicability of the method is demonstrated for measured data on an

Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities

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Testing the validity of terahertz reflection spectra by dispersion relations

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Multiply subtractive generalized Kramers–Kronig relations: Application on third-harmonic generation susceptibility on polysilane

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Verification of generalized Kramers–Kronig relations and sum rules on experimental data of third harmonic generation susceptibility on polymer

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Destabilization of the thermohaline circulation by transient changes in the hydrological cycle

Abstract Kramers–Kronig (K–K) analysis of harmonic generation optical data is usually greatly limited by the technical inability to measure data over a wide spectral range. Data inversion for real and imaginary part of χn(nω;ω,…,ω) can be more efficiently performed if the knowledge of one of the two parts of the susceptibility in a finite spectral range is supplemented with a single measurement of the other part for a given frequency. Then it is possible to perform data inversion using only measured data and subtractive K–K relations. In this paper multiply subtractive K–K relations are, for the first time, presented for the nonlinear harmonic generation susceptibilities. The applicability of the singly subtractive K–K relations are shown using data for third-order harmonic generation susceptibility of polysilane.

Kramers—Kronig Relations and Sum Rules in Nonlinear Optical Spectroscopy

Complex response function obtained in reflection spectroscopy at the terahertz range is examined with algorithms based on dispersion relations for integer powers of complex reflection coefficient, which emerge as a powerful and yet uncommon tools in examining the consistency of the spectroscopic data. It is shown that these algorithms can be used in particular for checking the success of the correction of the spectra by the methods of Vartiainen et al. [J. Appl. Phys. 96, 4171 (2004)] and Lucarini et al. [Phys. Rev. B. 72, 125107 (2005)] to remove the negative misplacement error in the terahertz time-domain spectroscopy.

Self-Scaling of the Statistical Properties of a Minimal Model of the Atmospheric Circulation

We present multiply subtractive Kramers–Kronig (MSKK) relations for the moments of arbitrary order harmonic generation susceptibility. Using experimental data on third-harmonic wave from polysilane, we show that singly subtractive Kramers–Kronig (SSKK) relations provide better accuracy of data inversion than the conventional Kramers–Kronig (KK) relations. The fundamental reason is that SSKK and MSKK relations have strictly faster asymptotic decreasing integrands than the conventional KK relations. Therefore SSKK and MSKK relations can provide a reliable optical data inversion procedure based on the use of measured data only.

Experimental mathematics: Dependence of the stability properties of a two-dimensional model of the Atlantic ocean circulation on the boundary conditions

We present an analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers–Kronig (KK) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental data of the third-harmonic generation susceptibility for different polymers: polysilane (frequency range 0.4–2.5 eV), and polythiophene (frequency range 0.5–2.0 eV). We show that, without extending the data outside their range with the assumption of an a priori asymptotic behavior, independent truncated dispersion relations connect the real and imaginary parts of the moments of the third-harmonic generation susceptibility ω2αχ(3)(3ω,ω,ω,ω),  0⩽α⩽3, in agreement with theory, while there is no convergence for α=4. We report the analysis for ω2α[χ(3)(3ω;ω,ω,ω)]2 and show that a larger number of independent KK relations connect the real and imaginary parts of the function under examination. We also compute the sum rules for the suitable moments of the real and imaginary parts, and ob...