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# Calculationsystem

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### Calculationsystem

1. 1. Problems in the Calculation of Climate Systems by the Comenius Group of the Merianschule, Seligenstadt
2. 2. Problem: <ul><li>all assumptions regarding the future of the climate are based on calculated data </li></ul><ul><li>Only few facts are measureable (reduction of glaciers, decrease of ice in greenland) </li></ul><ul><li>Measured data like temperature have a wide fluctuation range </li></ul>
3. 3. How these Calculation Systems work
4. 4. The Equation: <ul><li>The heart of a calculation system is the </li></ul><ul><li>Equation: </li></ul><ul><li>The E. illustrates the condition of the system in the future </li></ul><ul><li>The E. includes all influences </li></ul><ul><li>The E. delivers the Database for next year </li></ul><ul><li>The E. is recalculated for every new year </li></ul>
5. 5. Easy Example: Number of fish in a lake (given in % from the max. population) X n+1 = X n r (1-X n ) Quantity of fish in the following year Growth Factor Quantity of fish in the actual year Balance factor
6. 6. Key function: the growth factor <ul><li>The growth factor defines the dimension of the population: </li></ul><ul><li>1. r < 1 : exponential decrease of the population </li></ul><ul><li>2. r > 1: stabilisation on a special level </li></ul><ul><li>3. r > 3 : periodic oszillation of the population </li></ul><ul><li>4. r > 3,57: chaotic behaviour, the population is not predictable </li></ul>
7. 7. 1. Expotentiell decrease <ul><li>r = 0,8 , 60% of the max. in the beginning </li></ul><ul><li>Extinction of the fishes in short time </li></ul>
8. 8. 2. Stabilisation on a special level <ul><li>r = 2 , 60% of the max. at the start </li></ul><ul><li>Stabilisation on a special level </li></ul>
9. 9. 3. Periodic Oszillation <ul><li>r = 3,5 , 60% of the max. in the beginning </li></ul><ul><li>Periodic Oszillation of the Population </li></ul>
10. 10. 3. Periodic Oszillation
11. 11. 4. Chaotic behaviour
12. 12. 4. Chaotic behaviour <ul><li>r > 3,57 (3,9 in the diagramm), 60% of the maximum at the start </li></ul><ul><li>Chaotic behaviour, changes in a part per thousands range of the start conditions, switches over to unpredictable quantity of fish after short time (17 years) </li></ul><ul><li>Every single value can be calculated precisely in a deterministic way !!! </li></ul><ul><li>Changes: x = 0,60000 or x = 0,60001 </li></ul>
13. 13. Conclusions <ul><li>Calculation systems need accurate initial conditions </li></ul><ul><li>Small changes can cause extensive effects </li></ul><ul><li>The equation must be constructed very carefully </li></ul><ul><li>Under special conditions the models turn into chaotic systems which are unpredictible </li></ul>