ASSESSING THE EASTERN MEDITERRANEAN CIRCULATION BY CLUSTERING THE DAILY WEATHER

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• ASSESSING THE EASTERN MEDITERRANEAN CIRCULATION
  BY CLUSTERING THE DAILY WEATHER

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THE CONTENT PURPOSES, DATABASE, APPROACH AND
METHODOLOGY, RESULTS AND CONCLUSIONS

• PURPOSES STUDY OF WEATHER EMERGENCE AND
  MESOSCALE CIRCULATION
• DATABASE
• THE TEL AVIV UNIVERSITY WEATHER CATALOG (TAUWC)
  DAILY WEATHER, 1948-2001 (19724 days) ASSESSED
  (Alpert at al., 2004a,b) BY HAND (1991) METHOD
• APPROAC AND METHODOLOGY
• STATISTICS, STOCHASTIC AND MATHEMATICAL ASPECTS
  OF WEATHER EVOLUTION
• CLUSTERING OF DAILY WEATHER INTO SUB-BRANCHES,
  BRANCHES, SUB-CLUSTERS tc
• RESULTS
• Non-Hierarchical Clustering k-mean, seeded, SOM
• Hierarchical Clustering Non-ordered and Ordered
• Annual Distribution of Weather Types and
  Mesoscale Circulation
• Probabilities Pattern of Weather Types and
  Mesoscale
• Marcov Chain Transitional Probability of Daily
  Weather
• Relations Between

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EXAMPLE OF THE TEL AVIV UNIVERSITY WEATHER
CATALOG AND A SCHEMATIC VIEW OF THE 25 GRID
POINTS OF NCEP ANALYSIS EMPLOYED FOR THE
OBJECTIVE SYNOPTIC SYSTEMS CLASSIFICATION OVER
THE EASTERN MEDITERRANEAN (see, Alpert et al.,
2004a,b Osetinski et al, 2004, Ziv et al., 2004))

• date Class
• 01/01/48 7
• 01/02/48 7
• 01/03/48 14
• 01/04/48 14
• 01/05/48 17
• 01/06/48 10
• 01/07/48 8
• 01/08/48 3
• 01/09/48 3
• 01/10/48 3
• 01/11/48 3
• 01/12/48 8
• 01/13/48 1
• 01/14/48 8
• 01/15/48 10
• 01/16/48 1
• 01/17/48 7
• 01/18/48 10

• 3 0 35 40
• 37.5
• 35
• 32.5
• 29.5
• 27.5

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ANNUAL DISTRIBUTION OF a) WEATHER TYPES and b)
WEATHER GROUPS (AFTER, Alpert et. alL, 2004a)
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EASTERN MEDITERRANEAN AVERAGE DISTRIBUTION OF
c) MONTHLY WEATHER, b) WEATHER TYPES AND C)
SYNOPTIC GROUPS
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WHY CLUSTERING?

• A KIND OF THE MULTIVARIATE STATISTICAL ANALYSIS
• OPPOSITE TO THE DISCRIMINANT ANALYSIS THE
  CLUSTERING DOES NOT IMPOSE A PREVIOUS STRUCTURE
• IT IS SUITABLE TO CLASSIFY UNKNOWN STATES
• THE RESULTS EMERGE FROM THE DATA ITSELF
• A LARGE VARIETY OF APPROACHES, PROCEDURES,
  TECHNOQUES, METHODS ETC

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????? ?"?????" CLASSIFICATION OF STATES -

• PLANETARY CLIMATE?????? ????????
• LARGE-SCALE OSCILLATION?????? ????? ?????
• COALITIONS ??????
• MESOSCALE CIRCULATION ????? ????? ???????
• WEATHER CYCLE ????? ??? ?????-
• WEATHER BRANCH ???
• WEATHER TYPE - ??? ?????

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CLUSTERING
CLUSTERING

• SIMILARITY/DISSIMILARITY- are related to their
  inter-distance.
• APPROACHES
• (i) DIVISIVE - begins with all the cases that
  are gradually broken down into smaller and
  smaller clusters, and,
• (ii) AGGLOMERATIVE - starts with a single member
  and fused gradually until one large cluster is
  formed.
• SCHEME
• monothetic, the cluster membership is based on a
  single propriety
• polythetic the cluster is based on more
  variables.

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WEATHER DEFINITION, METHODLOGICAL CONCEPTS

• MODELING THE WEATHER TYPES
• Statistical Analysis
• the WT Vector WTi, i1,2,19724 days is examined
  trough Time Series Analysis (Spectrum Analysis
  and ANOVA)
• Stochastic Analysis
• the weather matrix M, is analyzed as a Marcov
  chain of a transitional probabilitiy (Mt x Mtl
  l0,1,2,,.NL), or by other Operational Research.
• Mathematics
• the WT record is a set of dots (or vertices) that
  connects by lines (edges) the matrix state (M) of
  discrete daily states. Three dominant
  proprieties
• - Symmetry,
• - Reflexivity and
• - Transitivity,
• suggest a quite good - not yet absolute - state
  of pre-order.

• Terminology
• weather is an equilibrium atmospheric state
  related to upper-scales lows/highs circulation,
  that evolves from the former states.
• Weather evolution
• VARIABILITY- is measured versus their K-means
• SIMILARITY - measured their close resembling
  each to other
• Operational Research
• To defines the WT preferences and
  pre-order or any stochastic relations resulting
  from their
• combinatorial,
• random and
• competitive processes.
• For example, the combination of four weather
  types possible successions 4! 1x 2x3x4 24
  possibilities

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CLUSTER VARIABILITY (DIFFERENCES BETWEEN) is
measured versus their K-means, CLUSTERS
SIMILARITY (DISSIMILARITY ) how close
resembling each to other

• HIERARHICAL
• split on the sample in an increasing number of
  nested classes of a dendogram.
• Standardized inputs (Xi-Xm)/d)
• Methods Average, Centroid, Ward, Single,
  Complete
• Ordering The INPUT is in a given TIME ORDER

• NON_HIERARCHICAL K-MEANS
• split on the sample into a pre-established number
  of clusters
• as an iterative alternative, fit the clusters
  around their centroid, by classifying the groups
  starting from seeded points and around the
  clusters means. The SOM uses clusters number as
  grids
• Methods K-MEANS

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SPEARMAN NON-PARAMETRIC CORRELATION BETWEEN THE
19 WT (EXCEPT THE AUTOCORRELATION)
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NON-HIERARCHICAL CLUSTERINGOF THE 19724 DAILY
WEATHER TYPES

• Fig.2 The Non-Hierarchical Clustering (SOM
  procedure)

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NON-HIERARCHICAL CLUSTERING OF 19724 WEATHER
BRANCHES BY K-MEAN- NORMAL MIXTURE-SELF
ORGANIZING MAP (SOM)
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HIERARCHICAL CLUSTERINGOF THE MONTHLY SUM OF
WEATHER TYPES ORGANIZED INTO THE MATRIX (648,
19)648 54 YEARS X 12 MONTHS/YEAR
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NON-ORDERED HIERARCHICAL CLUSTERING OF
(LEFT-SIDE) AVERAGE ANNUAL DAILY WT (365, 19)
and (RIGTH-SIDE) MONTHLY (648, 19)
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SCHEMATIC VIEW OF THE DENDOGRAM
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HIERARCHICAL ORDERRED CLUSTERING OF 19724 DAILY WT
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EXTENDED HIERARCHICAL CLUSTERING
(WINTER-SUMMER)- MESOSCALE CIRCULATIONS- WEATHER
CYCLE-BRANCH-SUB-BRANCH- SUB-SUB-BRANCH (RAINY OR
NOT RAINY)
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WEEKLY DAILY WEATHER BRANCHES VIEW DURING
1948-1950 ()
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WEEKLY RELATIVE VARIABILITY OF WEATHER TYPES
BRANCHES DURING 1948-1967
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WEEKLY RELATIVE VARIABILITY OF WEATHER TYPES
BRANCHES DURING 1948-2001
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COMPETITIVE RELATIONSHIPS BETWEEN DIFFERENT
CIRCULATIONS
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Fig. 6 Annual Distribution of Weekly Lows and
High Weather
Fig. 6 Annual Distribution of Weekly Lows and
High Weather
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THE STOCHASTIC APPROACH

• Stochastic Process.. Families of random variables
  (? t , t ? T), where, t, the time, cross all T
  interval.
• Whilst, the weather is a continuous dynamics
  process, its record is a discrete series of daily
  state.
• Similar to rainy/dry runs, all weather cycles
  are alternant cyclones-anticyclones crossing EM
  (Gabriel and Neumann, 1962).
• The process is called Marcovian, if, the
  realization of any event do depends on the
  anterior events, e.g., at every instant u, for
  each ?u x, all the ?t , for all t gtu does not
  depend on ?s, s lt -u.
• Otherwise, the process is considered to be
  without memory.

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EM Daily Weather as Vector and as Lattice
(1999-2000)
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EM DAILY CIRCULATION AS VECTOR AND AS LATTICE
(1999-2000)
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MARCOV TRANSITIONAL PROBABILITY OF WEATHER
TYPES WTto- WTt1 WTto-WTt3 WTto-WTt5
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SUMMARRY AND CONCLUSIONS

• KNOWN THE REGIONAL DAILY WEATHER, IS POSSIBLE TO
  ASSESS THE INTERMEDIATE STATES (WEATHER CYCLES,
  MESOSCALE CIRCULATIONS, COALITIONS ETC, BY
  APPLYING THE HIERARCHICAL CLUSTERING
• THE APPLICATION OF THE MARCOV CHAIN THEORY OPEN
  THE POSSIBILITIES TO APPLY BOOLEAN ALGEBRA IN
  SYNOPTIC CLIMATOLOGY
• THE FOLLOWING STEPS SHOULD APPLY THE RESEARCH
  OPERATIONAL DISCIIPLINES SUCH THE THEORY OF
  GRAPH, GAMES THEORY