Non-Gaussian probability of Non-Gaussian probability of observed precipitation as a observed precipitation as a motivation of the SIR filtermotivation of the SIR filter

Cosmin Barbu, Dr. I.V. Pescaru, Rodica Cosmin Barbu, Dr. I.V. Pescaru, Rodica DumitracheDumitrache

The aim of the project is to develop a prototype for a new data assimilation system for the convective scale by means of a sequential Bayesian weighting and importance re-sampling (SIR) filter

The SIR filter is a Monte Carlo approach. It uses an ensemble of very short range forecast and selects the most likely members by comparing them to observations. From selected members a new ensemble is created for the next analyses time

The 1-st stepThe 1-st step is showing that the assumption of the Gaussian the assumption of the Gaussian probability density function (pdf) isn’t justifiedprobability density function (pdf) isn’t justified for e.g. 3-hourly accumulated precipitation.

For finding out how the distribution vary in space and time it was chosen three German stations (Hamburg – coastal , Karlsruhe – Rhine valley, Kempten – near Alps). The idea is to determine how the results depend on the location of the station or the time of the year (spring, summer, autumn, winter) or the period of the day (morning, afternoon).

There was analyzed precipitation data over a period of about 50 years for each weather station. The precipitation analyses were grouped by seasons, intervals during one day (accumulated over 3 hours for each season; over 6 hours within a certain interval in summer time; over 12 hours for each season.

The first time, an equidistant The first time, an equidistant samplingsampling

was used with a bin size of was used with a bin size of variousvarious

values: values: 0.5 mm/h, 1mm/h, 5mm/h0.5 mm/h, 1mm/h, 5mm/h

The results that have been The results that have been obtained areobtained are

inconclusiveinconclusive

A new type of sampling was implement:A new type of sampling was implement:

a)a) 0.1-1, 1-5, 5-10, 10-25, 25-50 mm/h:0.1-1, 1-5, 5-10, 10-25, 25-50 mm/h:

b)b) 0.01-0.2, 0.21-1.0, 1.01-5.0, 5.01-25.0, >25.0 mm/h:0.01-0.2, 0.21-1.0, 1.01-5.0, 5.01-25.0, >25.0 mm/h:

Hamburg Karlsruhe Kempten

Hamburg

•All period (3 h-accumulated)•Seasons (3h -accumulated)• 00-12h, 12-24h•00-03h,03-06h, etc in spring, summer, autumn, winter• 06-12h, 12-18h (only in summer time)

Karlsruhe

Kempten

•All period (3 h-accumulated)•Seasons (3h -accumulated)• 00-12h, 12-24h•00-03h,03-06h, etc in spring, summer, autumn, winter• 06-12h, 12-18h (only in summer time)

•All period (3 h-accumulated)•Seasons (3h -accumulated)• 00-12h, 12-24h•00-03h,03-06h, etc in spring, summer, autumn, winter• 06-12h, 12-18h (only in summer time)

ConclusionsConclusions : :

For the 12 hours accumulated precipitation amounts log-normal For the 12 hours accumulated precipitation amounts log-normal distribution can be notice in the latter part of the day.distribution can be notice in the latter part of the day.

As a rule, it can be asserted followings the analysis of the graphs that As a rule, it can be asserted followings the analysis of the graphs that the precipitation data do not display log-normal distribution. the precipitation data do not display log-normal distribution.

Thank you !Thank you !Thank you !Thank you !