Predictability and Chaos

1. Predictability and Chaos EPS and Probability Forecasting

2. Objectives of this session • Appreciate that NWP is not the complete answer • State reasons for uncertainties in weather prediction • Understand how the principle of chaos effects predictability of the atmosphere • Appreciate how ensemble forecasts help to account for chaos

3. Two 36-hour forecasts

4. Deterministic versus Probabilistic forecasts • Deterministic forecast - A forecast in which a single answer is given • It will snow this afternoon • Temperatures will reach 4C today • Probabilistic forecast – A forecast in which a numerical estimate of the certainty of the forecast is given • 30% chance of a shower

5. Typical deterministic forecast chart

6. Why is there uncertainty in weather forecasting? • The variability of ‘local’ weather • Exactly where will a shower fall? • Analysis errors • NWP models sensitive to errors in initial state • Systematic errors in NWP models • Assimilation, parametrization

7. Displacement Small differences here Time

8. BIG differences here Displacement Small differences here Time

9. 51 plots of height of a pressure level

30. Predictability • Errors in initial conditions have different effects • Why is the atmosphere predictable on some occasions, not on others? • Chaos Theory !

31. Definition of Chaos Dictionary Definition: Lack of form or systematic arrangement Scientific Definition: Processes that are not random but look random • Random - toss a coin • Chaotic - a pin ball machine

32. Edward Lorenz • 1963 Massachusetts Institute of Technology • Used 3 equations in a simple model • Truncating numbers produced different results • Introduced concept of “attractors” to describe the state of dynamical systems • certain states will never occur

33. A simple non-chaotic attractor 1 0 2 0 4 3 0

34. Why is the atmosphere chaotic? • Weather patterns are not totally random • e.g. seasonal variation is regular … but they can appear so. • Climate is the Attractor • Set of patterns that have at least some chance of occurring • Heat-wave in Arctic, snow in Sahara do not occur

35. The Lorenz Attractor

36. Predictable evolution

37. Predictable then unpredictable evolution

38. Implications of chaos theory • There is no one single solution to find • There is a time limit beyond which deterministic forecasts of daily weather become unpredictable • The outcome of all forecasts could be a set of probabilities • The predictability of the atmosphere will vary depending upon its initial state

39. Climatology The forecast Predictability range NWP SYSTEM Deterministic solution

40. Climatology Better model: Reduce the error Predictability range NWP SYSTEM Deterministic solution

41. Climatology Run the model more: Explore the range NWP SYSTEM

42. Climatology Bad day to be on duty: Lots of uncertainty NWP SYSTEM

43. Climatology Good day to be on duty? NWP SYSTEM

44. Coping with chaos: EPS Ensemble forecasting at ECMWF: • 51 forecasts run from similar initial conditions • Use a lower resolution model (T399) • Used for guidance beyond 3-4 days • Generates a lot of data!

45. Ensemble: Postage Stamps T+120

46. Probability of surface wind > 10 m/s

47. EPS Plumes

48. EPSgram

49. Extreme Forecast Index

50. Interpreting Ensemble Data • The presentation of results is important • Need to reduce the different solutions to something manageable • Clustering - grouping solutions that are similar • Probability forecasting