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Marvin Lorenz, Knut Klingbeil, and Hans Burchard

Abstract

Recent studies could link the quantities of estuarine exchange flows to the volume-integrated mixing inside an estuary, where mixing is defined as the destruction of salinity variance. The existing mixing relations quantify mixing inside an estuary by the net boundary fluxes of volume, salinity, and salinity variance, which are quantified as Knudsen or total exchange flow bulk values. So far, river runoff is the only freshwater flux included, and the freshwater exchange due to precipitation and evaporation is neglected. Yet, the latter is the driving force of inverse estuaries, which could not be described by the existing relations. To close this gap, this study considers evaporation and precipitation to complete the existing mixing relations by including cross-surface salinity variance transport. This allows decomposing the mixing into a riverine and a surface transport contribution. The improved relations are tested against idealized two-dimensional numerical simulations of different combinations of freshwater forcing. The mixing diagnosed from the model results agrees exactly with the derived mixing relation. An annual hindcast simulation of the Persian Gulf is then used to test the mixing relations, both exact and approximated, e.g., long-term averaged, for a realistic inverse estuary. The results show that the annual mean mixing contributions of river discharge and evaporation are almost equal, although the freshwater transport due to evaporation is about one order of magnitude larger than the river runoff.

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Hans Burchard, Xaver Lange, Knut Klingbeil, and Parker MacCready

Abstract

The well-known Knudsen relations and the total exchange flow (TEF) analysis framework provide quantifications of exchange flow across an open boundary to the adjacent ocean in terms of bulk values (Knudsen theory: inflow and outflow volume or salinity) or with resolution in salinity space (TEF: profiles of volume and salt flux in salinity coordinates). In the present study, these theories are extended toward mixing of salinity, defined as the decay of salinity variance due to turbulent mixing. In addition to the advective fluxes, diffusive fluxes across the boundary are also considered now. These new Knudsen and TEF relations for mixing are derived by applying Gauss’s theorem to the salinity square and salinity variance equations. As a result of the analysis, four different Knudsen relations for the mixing in estuaries are derived. The first one is exact and considers nonperiodicity as well as nonconstancy of the inflow and outflow salinities. The other three formulations are approximate only, in the sense that either nonperiodicity or nonconstancy or both are relaxed. The simplest of those formulations has recently been derived by MacCready et al. and estimates the estuarine mixing as the product of inflow salinity, outflow salinity, and time-averaged river runoff. These four mixing estimates are systematically assessed by means of a number of idealized estuarine test cases. For periodic tidal flow, the simplest estimate still predicts the effective (physical plus numerical) mixing within an error of about 10%.

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Ulf Gräwe, Knut Klingbeil, Jessica Kelln, and Sönke Dangendorf

Abstract

We analyzed changes in mean sea level (MSL) for the period 1950–2015 using a regional ocean model for the Baltic Sea. Sensitivity experiments allowed us to separate external from local drivers and to investigate individual forcing agents triggering basin-internal spatial variations. The model reveals a basin-average MSL rise (MSLR) of 2.08 ± 0.49 mm yr−1, a value that is slightly larger than the simultaneous global average of 1.63 ± 0.32 mm yr−1. This MSLR is, however, spatially highly nonuniform with lower than average increases in the southwestern part (1.71 ± 0.51 mm yr−1) and higher than average rates in the northeastern parts (2.34 ± 1.05 mm yr−1). While 75% of the basin-average MSL externally enters the Baltic basin as a mass signal from the adjacent North Sea, intensified westerly winds and a poleward shift of low pressure systems explain the majority of the spatial variations in the rates. Minor contributions stem from local changes in baroclinicity leading to a basin-internal redistribution of water masses. An observed increase in local ocean temperature further adds to the total basinwide MSLR through thermal expansion but has little effect on the spatial pattern. To test the robustness of these results, we further assessed the sensitivity to six different atmospheric surface forcing reanalysis products over their common period from 1980 to 2005. The ensemble runs indicated that there are significant differences between individual ensemble members increasing the total trend uncertainty for the basin average by 0.22 mm yr−1 (95% confidence intervals). Locally the uncertainty varies from 0.05 mm yr−1 in the central part to up to 0.4 mm yr−1 along the coasts.

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Florian Lemarié, Hans Burchard, Laurent Debreu, Knut Klingbeil, and Jacques Sainte-Marie
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Knut Klingbeil, Johannes Becherer, Elisabeth Schulz, Huib E. de Swart, Henk M. Schuttelaars, Arnoldo Valle-Levinson, and Hans Burchard

Abstract

This paper presents thickness-weighted averaging (TWA) in generalized vertical coordinates as a unified framework for a variety of existing tidal-averaging concepts in seas and estuaries. Vertical profiles of resulting residual quantities depend on the specific vertical coordinate, which is held fixed during the averaging process. This dependence is demonstrated through the application to one-dimensional analytical tidal flow with sediment transport, to field observations from a tidal channel, and to model results from a two-dimensional estuary. The use of different coordinate systems provides complementary views on the residual dynamics and stresses the importance of a correct interpretation of residual quantities obtained by tidal averaging.

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