Robust flood statistics: comparison of peak over threshold approaches based on monthly maxima and TL-moments

ABSTRACT

Flood quantile estimation based on partial duration series (peak over threshold, POT) represents a noteworthy alternative to the classical annual maximum approach since it enlarges the available information spectrum. Here the POT approach is discussed with reference to its benefits in increasing the robustness of flood quantile estimations. The classical POT approach is based on a Poisson distribution for the annual number of exceedences, although this can be questionable in some cases. Therefore, the Poisson distribution is compared with two other distributions (binomial and Gumbel-Schelling). The results show that only rarely is there a difference from the Poisson distribution. In the second part we investigate the robustness of flood quantiles derived from different approaches in the sense of their temporal stability against the occurrence of extreme events. Besides the classical approach using annual maxima series (AMS) with the generalized extreme value distribution and different parameter estimation methods, two different applications of POT are tested. Both are based on monthly maxima above a threshold, but one also uses trimmed L-moments (TL-moments). It is shown how quantile estimations based on this “robust” POT approach (rPOT) become more robust than AMS-based methods, even in the case of occasional extraordinary extreme events.

Editor M.C. Acreman Associate editor A. Viglione     

Convection in the Presence of an Inclined Axis of Rotation with Applications to the Sun

Thermal convection in a horizontal fluid layer heated from below and rotating about an arbitrary axis is studied analytically with the attention focused on mean flows and drifts generated by the convection velocity field. Mean flows occur in both horizontal directions when the angle between the rotation vector and the vertical is finite but less than 90°. In the case of a hexagonal convection pattern, a wavelike drift is found in the presence of a horizontal component of rotation. Applications to solar convection are discussed. Considering the simplicity of the model the agreement with observations is surprisingly good.     

Riparian alder fens — Source or sink for nutrients and dissolved organic carbon? — 1. Effects of water level fluctuations

The biogeochemistry of riparian alder wetlands was studied from 1995 to 1997. Nutrient and DOC chemistry was related to water level changes. The spatial and temporal patterns of nutrients (P and N) and dissolved organic carbon (DOC) were measured in the surface water flowing through a riparian alder fen and in the adjacent creek. Nutrient and DOC concentrations were extremely variable temporally but not spatially within the wetland. In the wetland and the adjacent creek concentrations of NO₃-N, PO₄-P and DOC were homogenous during high-flow periods and frozen conditions. After low-flow conditions water bodies were isolated from the creek. The concentration of NH₄-N, PO₄-P and DOC in these isolated water bodies was significantly higher than in the adjacent creeks due to low oxygen levels.

Enclosures of different sizes were installed in the wetland to study possible release rates. A large enclosure experiment in the flooded alder fen showed the same concentrations as after high-flood conditions except for DOC. The DOC concentrations were enriched in the large enclosure after decomposition from leaf litter during fall season. Small enclosures with low oxygen levels confirmed data obtained from low-flow conditions. The release rates were calculated for low-flow conditions from small enclosure experiments for 2 months a year when the alder fen is not flooded. The rates for July and August were 11.6 kg/ha NH₄-N, 8.6 kg/ha PO₄-P and 57.6 kg/ha DOC. The DOC concentrations for fall estimated from the large enclosure-experiments were 168.2 kg/ha for the months September and October.

This means possible output rates of N, P and DOC during the summer and DOC during fall in the adjacent river system. This can cause eutrophication and organic pollution depending on the length of the low-flow conditions and the size of the alder fen. Water level changes must be regarded as important for the management of riparian wetlands such as alder fens. The riparian alder system may vary from a nutrient sink to a nutrient source at different times of a year depending on high or low water levels.     

Some new results on spherical dynamos

Small-scale motions in the Earth's liquid core are likely to be highly anisotropic because of the effects of rotation. Guided by physical considerations, the “-effect” described by an anisotropic tensor _ik is formulated and the corresponding boundary value problem for a sphere is solved for a variety of boundary conditions. A converged solution has been obtained only in the case of the Fermi condition of an infinitely conducting exterior of the sphere. In a second part of the paper, some remarks are made on the hypothetical upper bound on magnetic field strengths in planetary cores originally proposed by Busse (1976).     

High Prandtl number convection

The theory of convection in a layer heated from below is reviewed with particular emphasis on the limit of infinite Prandtl number. The review is restricted to qualitative properties of the problems which do not depend on special conditions. Similarities and differences between convection in a plane layer and in a spherical shell are pointed out and attention is called to the fact that two-dimensional or axisymmetric forms of convection are realized only in a small region of the parameter space.     

Toroidal flux oscillation as possible cause of geomagnetic excursions and reversals

It is proposed that convection driven dynamos operating in planetary cores could be oscillatory even when the oscillations are not directly noticeable from the outside. Examples of dynamo simulations are pointed out that exhibit oscillations in the structure of the azimuthally averaged toroidal magnetic flux while the mean poloidal field shows only variations in its amplitude. In the case of the geomagnetic field, global excursions may be associated with these oscillations. Long period dynamo simulations indicate that the oscillations may cause reversals once in a while. No special attempt has been made to use most realistic parameter values. Nevertheless some similarities between the simulations and the paleomagnetic record can be pointed out.     

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.     

A simple magnetostatic model of sunspots

An analytical solution is derived for the nonlinear magnetostatic balance between the Lorentz forces on one side and the pressure and gravitational forces induced by the magnetic inhibition of granular convection in a sunspot on the other. In order to exhibit the mathematical structure of the problem it has been reduced to the simplest case which still contains the basic physical features. Although the results of a model with a two-dimensional periodic magnetic field are not quantitatively comparable with sunspot observations the conclusion can be drawn that an upper limit on the size of sunspots exists. The results suggest that this upper limit is close to the size of observed large sunspots.