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Role of Statistics in Climate Sciences
Boulder, NCAR, November 29-30, 2001 MADDEN SYMPOSIUM Role of Statistics in Climate Sciences
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Overview Randomness as a conceptual model Randomized parameterizations
Estimation in dynamical systems
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Stochasticity in climate:
ubiquity of non-linear components creates variability indistinguishable from (the mathematical construct of) statistical noise.
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Randomized Parameterization
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Randomized Parameterization
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Randomized Parameterization
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Randomized Parameterization
The role of statistics here is to first suggest a suitable distribution S then to condition the free parameters in a manner consistent with empirical evidence and dynamical wisdom. The parameters often include parameters like means, variances and lag correlations. As a result of such a „randomized parameterization“ the statistics of the state variables may change.
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Randomized Parameterization
Example: Energy Balance Model, with albedo nonlinearly dependent on the state variable (temperature) albedo temperature Transmissivity parameterized as constant temperature years
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Randomized Parameterization
Transmissivity as constant + Gaussian noise temperature Randomized Parameterization years
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Randomized Parameterization
Problem: high-frequency variations of wind speed and its effect on ocean waves 6 3 1 hour Randomized Parameterization
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Randomized Parameterization
Problem: high-frequency variations of wind speed and its effect on ocean waves Randomized Parameterization 3 days
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Estimation in dynamical systems
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Estimation in dynamical systems
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Estimation in dynamical systems
Simulation of water level along the North Sea coast in 20 x 20 km2 boxes. Simulated box-mean water level differs from water level along the shore line.
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Estimation in dynamical systems
POPs
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Estimation in dynamical systems
POPs of equatorial velocity potential at 200 hPa Estimation in dynamical systems 0o oE o oW o
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Estimation in dynamical systems
POP coefficients (= index of MJO) in 1985 Estimation in dynamical systems days
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Estimation in dynamical systems
Propagation of velocity potential and OLR pattern in winter Estimation in dynamical systems
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Estimation in dynamical systems
Propagation of velocity potential and OLR pattern in summer Estimation in dynamical systems
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Estimation in dynamical systems
Forecasting with recduced POP model Estimation in dynamical systems Logintudinal location of minimum of velocity potential
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Estimation in dynamical systems
Skill of forecasting with POP model correlation skill score Estimation in dynamical systems days
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Purpose of statistics: Combination of dynamical knowledge and limited empirical evidence to build consistent descriptions of reality
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