1. 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

2. 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.

3. 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).

4. 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.

5. 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

6. 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

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

8. 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)

9. 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)

10. 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

11. 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.

12. Mesochora catchment
Elevation contour map and meteorological stations of Mesochora catchment

13. 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 with 700 hPa data in the window 20o - 65o N, 20o W- 50o E for 12 stations of Mesochora catchment).

14. 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

15. 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  stochasticity in the temporal evolution of precipitation.

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

17. 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

18. References
Bárdossy, A., Stehlík, J., Caspary, H.J., Automated optimized fuzzy rule based curculation pattern classification for precipitation and temperature downscaling. Clim. Res., 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),
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).

19. Thank you for your attention