We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive limit of the strong duals, but on the other hand we show that this is indeed true if one deals with projective spectra of retractive (LB)-spaces. Finally, we apply our results to a question of Grothendieck about biduals of (LF)-spaces.
In a previous study, the topsoil and root zone ASCAT satellite soil moisture data were implemented into three multi-objective calibration approaches of the TUW hydrological model in 209 Austrian catchments. This paper examines the model parametrization in those catchments, which in the validation of the dual-layer conceptual semi-distributed model showed improvement in the runoff simulation efficiency compared to the single objective runoff calibration. The runoff simulation efficiency of the three multi-objective approaches was separately considered. Inferences about the specific location and the physiographic properties of the catchments where the inclusion of ASCAT data proved beneficial were made. Improvements were primarily observed in the watersheds with lower slopes (median of the catchment slope less than 15 per cent) and a higher proportion of farming land use (median of the proportion of agricultural land above 20 per cent), as well as in catchments where the runoff is not significantly influenced by snowmelt and glacier runoff. Changes in the mean and variability of the field capacity parameter FC of the soil moisture regime were analysed. The values of FC decreased by 20 per cent on average. Consequently, the catchments’ water balance closure generally improved by the increase in catchment evapotranspiration during the validation period. Improvements in model efficiency could be attributed to better runoff simulation in the spring and autumn month. The findings refine recommendations regarding when hydrological modelling could consider satellite soil moisture data added to runoff signatures in calibration useful.