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Cumulative distribution function (CDF) The figures to the right illustrate the relationship between a normal distribution and its associated cumulative distribution function.The CDF is constructed from the area under the probability density function. The CDF gives the probability that a value on the curve will be found to have a value less than or equal to the corresponding value on the x-axis. For example, in the figure right, the probability for values less than or equal to X=0 is 50%. The shape of the CDF curve is related to the shape of the normal distribution. The width of the CDF curve is directly related to the value of the standard deviation of the probability distribution function. For our ensemble, the width is then related to the 'ensemble spread'. For a forecast ensemble where all values were the same, the CDF would be a vertical straight line. |
The probability distribution function of the normal distribution |
Cumulative distribution function for a normal Figure from Wikipedia
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TO BE FINISHED
Task 1: CDF for 3 locations
This exercise uses the cdf.mv icon. Right-click, select 'Edit' and then:
- Plot the CDF of MSLP for the 3 locations listed in the macroChoose 3 locations.e.g. Reading, Amsterdam, Copenhagen.
- Using 10m wind and/or wind gust data plot CDF & RMSE curves using one of the OpenIFS forecasts and the ECMWF analysis data.
- If time, change the forecast run date and compare the CDF for the different forecasts.
Q. What is the difference between the different stations and why?
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(refer to the ensemble spread maps to answer this)
Q. How does the CDF for Reading change with different forecast lead (run) dates?
Forecasting an event using an ensemble : group discussion
Ensemble forecasts can be used to give probabilities to a forecast issued to the public.
Questions:
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Her Majesty The Queen has invited Royals from all over Europe to a garden party at Windsor castle on 28th October 2013 (~20 miles west of London). Your team is responsible for the weather prediction and decision to have an outdoor party for this event. You have 3-4 days to plan for the event. You can use the data and macros provided to you to first derive probabilities of severe weather at this location (this doesn't need to be exact so use the information for Reading). i) What would your prediction for the probability of winds > 20 mph ; > 40 mph ; > 60 mph ?ii) The price of ordering the marquees and outdoor catering for the event is £100,000. Chances of the marquees falling apart when winds > 20 mph = 20% probability ; winds > 40 mph = 40% ; winds > 60 mph = 80%. Now what would the probabilities of the marquees failing be, given this new information from the rental service and the weather prediction you made |
Questions:
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Group A: The Swedish weather centre is interested in giving out useful weather warnings. They want to know the maximum precipitation and wind gusts over Scandinavia and their likelihood (more than XX m/s wind and XX mm precipitation). Would you give out weather warnings and if yes for which days and areas (1 day lead time)? Group B: The organiser of a garden party at Windsor Castle at a particular date needs to prepare for weather. The Queen will join the party and she is not amused if there are too many tents that are not necessary. However, it will take some time to prepare shelters for rain and wind or to cancel the event (two days lead time). Would you prepare for rain? Group C: The operator of a wind farm in the northern see needs to know the highest possible wind speeds to shut down turbines (at XX m/s). If the turbines are shut down too early, power production will be reduced. If they are shut down too late, they will break (6 hours lead time). Would you shut down the wind farm? |
Task 6: Creating an ensemble forecast using OpenIFS
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