Compilation of Summaries 
24 
System Nordsee 
probability of death or survival of a weather-type episode is independent of its current 
age. The GD turns out an adequate model for lifetimes as long as a week. The poor 
est agreement arises for longlived A types representing persistent blocking situations, 
which can bring to a stand the erratic course of weather evolution for time spans up 
to several weeks. The anonymized episode or, more colloquial, the weather type as 
the >thing-in-itself< was found to have a mean lifetime of 2 days. Hence, having equal 
death and survival probabilities of 0.5, the corresponding GD conforms to the run 
length distribution some weather goddess could have produced by constantly flipping 
a true coin. The fact that some weather types show greater »talent« than others, when 
it comes to survival, instead hints to 6 cheats playing the game. 
At 32 episodes, amongst them the Methuselah, who attained the great age of 18 days, 
weather type A dominated the age group > 9 days during 1971 - 2000. Otherwise this 
range was occupied only by 15 SW, 5 NW and 3 SE episodes. In 2006 and 2007 the 
same range was exclusively inhabited by 2 and 1 A episodes, of which 1 reached 11 
days in each year. The frequent occurrence of northerly (NE & NW) weather types in 
2007 also showed in long episodes within the age band 5-8 days, the frequency of 
which increased from 1 to 6 vis-à-vis 2006, while at the same time southerly episodes 
dropped from 7 to 1. Episodes attaining ages > 5 days total up to 14 for either year 
and, thus, match the climatological mean (13,6). All of these counts slightly exceed the 
expected amount of 11.4 (= 182.5x0.5 4 ) due to a GD at death probability 0.5. The cor 
responding cumulative lifetimes amount to 95 (2006), 90 (2007), 90,7 (cm), and 68,4 
days (GD). Moreover, the overall number of episodes (186, 183, and 181,1/yr), and, 
hence, the mean lifetimes of « 2 days have been conspicuously stable. 
A third way of counting applied to the 30-year time series of weather types consists 
in tallying the 6 2 distinguishable transitions from day to day. This mode of counting no 
only entails information on frequency and lifetime of weather types, but also sheds 
light on typical and untypical patterns in their sequential evolution. Within the analogue 
of a ball-game analysis these elements correspond to each players total time of ball 
possession, which is comprised of times of holding on to the ball and points in time 
of passing it. The resulting quadratic matrix of transition counts is highly asymmetric 
and most heavily occupied in the main diagonal, representing self-transitions. The first 
feature signifies that mutual passing among any 2 players is unbalanced, while the 
latter stands for each players self-regarding attitude of rather sticking to the ball than 
cooperatively passing it. Specifically, the narcissistic behavior implies high serial auto 
correlation, which together with geometrically distributed sojourn times in unchanged 
states ranks among the inherent properties of 1 st order Markov chains. 
Fitting this stochastic process to the data consists in transforming the row entries of 
the count matrix into relative frequencies with respect to each row’s sum, i. e. the in 
dividual total frequency of the weather type associated with each row. Any row vector 
of this transition matrix represents a conditional 1-step probability distribution for the 
conjoint event that any of the 6 weather types occurs tomorrow provided that today’s 
weather is of the type the row applies to. The memorylessness of the MC consists in 
the fact that the transition probabilities exclusively depend on its current state and, 
in particular, not on whatever intricate path the current state was reached. It is also 
worth noting, that the MC at hand - regardless of its initial state - converges towards 
a unique stationary distribution for stochastic forecasting periods of 1 week. Actu 
ally, this limit distribution is the climatological probability distribution of the 6 weather 
types. The rapid leveling off of the forecasting potential towards the climatological skill 
and the Markovian property of memorylessness - tantamount to the exclusive de