TY  - JOUR
A1  - Krämer, Hauke Kai
A1  - Marwan, Norbert
T1  - Border effect corrections for diagonal line based recurrence quantification analysis measures
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.
KW  - Recurrence plots
KW  - Recurrence quantification analysis
KW  - Shannon entropy
KW  - Dynamical invariants
Y1  - 2019
U6  - https://doi.org/10.1016/j.physleta.2019.125977
SN  - 0375-9601
SN  - 1873-2429
VL  - 383
IS  - 34
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Fahle, Marcus
A1  - Hohenbrink, Tobias Ludwig
A1  - Dietrich, Ottfried
A1  - Lischeid, Gunnar
T1  - Temporal variability of the optimal monitoring setup assessed using information theory
JF  - Water resources research
N2  - Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.
KW  - artificially drained lowland
KW  - surface water levels
KW  - hydrometric network design
KW  - Shannon entropy
KW  - shallow groundwater tables
Y1  - 2015
U6  - https://doi.org/10.1002/2015WR017137
SN  - 0043-1397
SN  - 1944-7973
VL  - 51
IS  - 9
SP  - 7723
EP  - 7743
PB  - American Geophysical Union
CY  - Washington
ER  -