The main objective of the present study is to test various methods for describing the absorption spectra of coloured dissolved organic matter (CDOM) and to determine the numerical values of some optical parameters of CDOM in lakes with diverse water quality. First, the parameters of an exponential model in different spectral intervals were determined. In addition, the suitability of some other models for the approximation of CDOM spectra was estimated. Specific absorption coefficients of CDOM were calculated from the absorption coefficients and dissolved organic carbon (DOC) concentrations. The experimental initial data were differences between spectral attenuation coefficients of filtered and distilled water. Two datasets were used: 1) for 13 Estonian and 7 Finnish lakes (altogether 404 spectra between 350 and 700 nm) measured by the Estonian Marine Institute (EMI); 2) for 10 Finnish lakes (73 spectra) measured by the Finnish Environment Institute (FEI). The spectra of CDOM absorption coefficients (aCDOM) were calculated from experimental data taking into account the correction due to scattering properties of colloids in the filtered water. The total content of CDOM in natural waters of Estonian and Finnish lakes was expressed by means of aCDOM at the wavelength of 380 nm. It varied significantly, from 0.71 to 19.5 m−1, the mean value (of all the investigated lakes) being around 6.6 m−1. Slopes of the exponential approximation varied widely, from 0.006 to 0.03 nm−1. Averaged over all lakes values of slope for the interval 380-500 nm obtained from the EMI dataset are close to those obtained from the FEI dataset: from 0.014 nm−1 (without correction) to 0.016-0.017 nm-1 (with different types of correction). These results are in good correspondence with most published data. Attempts to describe the spectra in the region of 350-700 nm by means of hyperexponential functions (∽ exp(-αλη)) show that: (1) η < 1 (in the case of traditional exponential approximation η = 1); (2) a promising idea is to seek the best fit only for wavelengths λ > λ1, where λ1 will be chosen taking into account the real shape of aCDOM spectra. The mean value of the specific absorption coefficient (a*CDOM) at the wavelength 380 nm obtained in this study (0.44 L mg−1 m−1) is close to the values published in the literature, if we assume that a*CDOM (380) is calculated using the data of dissolved organic matter (DOM). The optically non-active fraction of DOM in our study was high and therefore a*CDOM (380) was considerably higher (1.01 L mg−1 m−1) than a*CDOM (380). The results of the present work could be used in the modeling of underwater light field as well as in the interpretation of radiation measurements and optical remote sensing results.

The convergence rate of histopolation on arbitrary nonuniform mesh with linear/linear rational splines of class C1 is studied. Established convergence rate depends on Lipschitz smoothness class of the function to histopolate. Corresponding numerical examples are given.

Numerical stability of the spline collocation method for Volterra integral equations is investigated. General stability conditions are obtained and applied to the most practical types of splines. Results of several numerical tests are presented.

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