Understanding biases in Tropical Cyclone Intensity Forecast Error

Transcription

1 Understanding biases in Tropical Cyclone Intensity Forecast Error John L. McBride, Wei Na, Zhang Xing-Hai, Duan Yi-Hong Bureau of Meteorology (retired/emeritus) And Chinese Academy of Meteorological Sciences (CAMS)

2 24-hour error in intensity forecast (y-axis) versus subsequent 24 hour intensity change (x-axis) Large negative correlation (-.77, -.77, -.68 ) The large negative errors (under-forecast) when there is a large positive intensity change. Large positive errors (over-forecast) when the system is rapidly weakening) Top right and bottom left quadrants are empty (a) (b) (c)

3 Data Official intensity forecasts, and best track data Northwest Pacific Basin (WP): Chinese Meteorological Agency North Atlantic Basin (NA): National Hurricane Center, USA. East Pacific Basin (EP): National Hurricane Center, USA.

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7 Aim of this study is to understand this diagram Understand the cause of this behaviour? Is it a function of our tropical cyclone forecast models? Or, is it due to the nature of the intensity change processes of the tropical cyclones? (a) (b) (c)

8 Strategy: Use a very simple objective forecast model ---- see if the simple model exhibits the same behavior : large negative correlation between forecast error and intensity change.

9 The simple forecast model: Trend Persistence Model (TPM) By definition, this model forecasts the 24-h intensity change to be equal to the observed intensity change over the preceding 24 hours. Thus, TPM T+24h =I T +(I T -I T-24h )

10 Intensity Forecast time Intensity change over previous 24 hours Time

11 Intensity Trend Persistence Model (TPM) Forecast Intensity change over previous 24 hours Time

12 The Trend Persistence Model (simplest possible objective forecast) shows the same behaviour: large negative correlation between forecast error and 24-hour intensity change ( )

13 Our hypothesis: This implies the large negative correlation between forecast error and intensity change is a function of the behaviour or life-cycle of the tropical cyclones, rather than a function of our forecast models

14 Intensity Trend Persistence Model (TPM) Forecast error Observation Forecast Intensity change over previous 24 hours Time

15 Intensity Error is forecast observation Equals 24 hour change minus forecast 24 hour change Equals{ I (t+24) I(t) minus I(t) I(t-24)} Equals minus (finite difference expression for d 2 I/dt 2 ) Observation Forecast Intensity change over previous 24 hours Time

16 TPM-E = -ΔT 2 d 2 I/dT 2 where the derivative is approximated by its finite difference form, and ΔT is the time step, which is 24 hours. So: For the Tendency Persistence Model (TPM), we can understand the reason for the behaviour of the errors. Because we have an analytical expression for the error. The forecast error is exactly equal to the finite difference formulation of the second derivative ΔT 2 ( d 2 I/dT 2)

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18 This diagram is actually a climatology: The y-axis (TPM error) is a climatology of intensity-time curve curvature: d 2 I/dt 2

19 For the TPM the reason for the negative correlation between error and intensity change is completely understood. It is simply a function of the climatological characteristics of the cyclones intensity change. Large positive and negative intensity changes almost always occur in the presence of a strongly concave upwards or concave downwards intensity-time graph, respectively.

20 It is contended that the same aspect of the climatology is the underlying reason for the presence of the negative OFE-intensity change correlation. In nature large intensity changes occur only in the presence of large positive or negative values of d 2 I/dT 2; so that the official forecast is attempting to predict a rapidly changing or accelerating state, which is inherently difficult.

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22 It is contended that the same aspect of the climatology is the underlying reason for the presence of the negative OFE-intensity change correlation. In nature large intensity changes occur only in the presence of large positive or negative values of d 2 I/dT 2; so that the official forecast is attempting to predict a rapidly changing or accelerating state, which is inherently difficult. Take home message: The intensity forecast error is equal to d 2 I/dt 2 Or the curvature of the intensity-time curve.

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