European Geosciences Union, General Assembly 2009 NH 1.4 Extreme Events Induced by Weather and Climate Change: Evaluation, Forecasting and Proactive Planning European Geosciences Union, General Assembly 2009 Vienna, Austria, 19 – 24 April 2009 RECURRENCE QUANTIFICATION ANALYSIS IN MAXIMUM MONTHLY PRECIPITATION BASED ON ATMOSPHERIC CIRCULATION Dionysia Panagoulia Eleni Vlahogianni National Technical University of Athens School of Civil Engineering Dept of Water Resources and Environmental Engineering Athens, Greece

Scope and Objectives The surface precipitation depends on large-scale atmospheric circulation and local factors that both influence it in a highly non-linear and complicated way. The relationship between atmospheric circulation and point precipitation observation can be quantified via circulation patterns (CPs). The spatial interpolation can be obtained from point data by using external drift kriging. The objective of this research is to reveal the complex non-stationary precipitation patterns via the analysis of the recurrent behavior in the maximum monthly precipitation time series.

Methodological Approach The automated objective classification method of daily circulation patterns based on optimized fuzzy rules (Bárdossy et al., 2002, Panagoulia et al., 2006). The recurrence quantification of sequential precipitation patterns (Zbilut & Webber, 1992).

Classification method The fuzzy-rules based approach combined with the simulated annealing algorithm consists of : pressure data transformation over a grid resolution of 5o X 5o. definition of fuzzy rules for defining high and low pressure anomalies , and classification of observed data.

Precipitation Dynamics Temporal precipitation patterns A sequence of N precipitation states Precipitation as a dynamical system let d state variables forming a d – dimensional vector space at time t (State-Space) Not all observable  reconstruction of an equivalent space from m observations of precipitation

Reconstructing Precipitation Dynamics Every time-series is described by a vector of the form: Precipitation patterns τ : time delay m : dimension of the reconstructed State-Space (m-1)τ : temporal window of information

Visualizing Precipitation Dynamics Recurrence Plot A symmetric matrix of Euclidean distances by computing distances between all pairs of embedded vectors

Visualizing Precipitation Dynamics RP Patterns Statistical Analogies Homogeneity Stationary process Fading Non-stationarity (trend) Disruptions Non-stationarity; transitional behavior Periodic Patterns cyclicities in the process Single Isolated Points heavy fluctuation in the process; random process Diagonal Lines similar evolution of states at different times; sign of deterministic process Vertical and Horizontal lines/clusters some states do not change or change slowly for some time (laminarity)

Identifying Precipitation Dynamics Behavior of a sequence of observation in a time window of study Relationship between sequential observations (patterns structure) Evolution of structure in time Recurrence of states Isolated states (stochasticity and randomness) Deterministic states (diagonal lines) Of a certain duration in the State-Space (length of diagonal lines)

Identifying Precipitation Dynamics Recurrence Quantification Analysis (in a specific time window) %REC = The recurrence rate corresponds to the probability that a specific state will recur Determinism and non-linearity %DET = ratio of recurrent states that form specific structures in the State-Space (parallel trajectories) to the total number of recurrent states  %DET  deterministic structure  %DET  stochasticity Maximum duration of deterministic structure in a time window  Lmax  Lmax  high non linear behavior

Study catchment and observed data (1) The Mesochora catchment drained by Acheloos’ river was selected for this study. The catchment with an area of about 633 km2 lies in the central mountain region of Greece. Digital Elevation Map of Mesochora catchment.

Mesochora catchment Elevation contour map and meteorological stations of Mesochora catchment

Study catchment and observed data (2) Mean normalized distributions of 700 hPa geopotential height of CP01 (left) and CP10 (right). (CPs are precipitation-optimized over 1982-1992 with 700 hPa data in the window 20o - 65o N, 20o W- 50o E for 12 stations of Mesochora catchment).

Recurrence Plot Maximum Monthly Precipitation Patterns τ=1, m=12  We study the dynamics of precipitation in patterns of 1 year in a 10 year time window updated every 1 month

Statistical Characteristics : Windowed RQA analysis of precipitation patterns (sliding 10 year time window) Statistical Characteristics : Increasing 10-year average maximum daily precipitation Decreasing recurrent behavior until 1986 Specific features: Variable deterministic behavior Sharp change observed in 1/1986, 5/1987 Decreasing deterministic structure and nonlinear behavior in the period 1090-1992  stochasticity in the temporal evolution of precipitation.

Conclusions Identification of precipitation temporal patterns via RQA Maximum Daily Precipitation Evolution Patterns detected and visualized Evolution of patterns statistically characterized Determinism Nonlinearity

Conclusions Basic outcomes: Variable deterministic and non-linear behavior Gradual decrease of recurrent behavior Stochasticity observed in the recent years Non-linear behavior and variable determinism denote periodic to chaotic and chaotic-to-chaotic transitions Results may be used to improve the process of constructing efficient predictors Choose the optimum modeling approach (neural networks, autoregressive stochastic models and so on) to match the statistical characteristics of precipitation

References Bárdossy, A., Stehlík, J., Caspary, H.J., 2002. Automated optimized fuzzy rule based curculation pattern classification for precipitation and temperature downscaling. Clim. Res., 22, 11-22. Panagoulia, D., Grammatikogiannis, A, and Bárdossy, A., 2006, An automated classification method of daily circulation patterns for surface climate data downscaling based on optimized fuzzy rules, Global NEST Journal, 8(3), 218-223. N. Marwan, M. C. Romano, M. Thiel, J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5–6), 237–329 (2007). E. I. Vlahogianni, M. G. Karlaftis, J. C. Golias: Statistical methods for detecting nonlinearity and non-stationarity in univariate short-term time-series of traffic volume, Transportation Research C: Emerging Technologies, 14(5), 351–367 (2006).

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