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 Time Small differences here

8. Displacement Time Small differences here BIG differences here

9. 51 plots of height of a pressure level

30. Day 1

31. Day 3

32. Day 6

33. Day 10

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

35. 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

36. 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

37. A simple non- chaotic attractor 0 1 0 0 2 34

38. 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

39. The Lorenz Attractor

40. Predictable evolution

41. Predictable then unpredictable evolution

42. 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

43. NWP SYSTEM Climatology Predictabilityrange The forecast Deterministic solution

44. NWP SYSTEM Climatology Better model: Reduce the error Predictabilityrange Deterministic solution

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

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

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

48. 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!

49. Ensemble: Postage Stamps T+120

50. Probability of surface wind > 10 m/s

51. EPS Plumes

52. EPSgram

53. Extreme Forecast Index

54. 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

55. Clustering Ensemble member Cluster Cluster mean

56. 26/51=51%9/51=17.5% 7/51=14%

57. Deterministic versus probabilistic forecasts Deterministic forecast - A forecast in which a single answer is given –It will rain this afternoon –Temperatures will reach 11  C today Probabilistic forecast - Forecasts in which a numerical estimate of the certainty of the forecast is given –30% chance of a shower

58. Conclusion