Markov chain modeling and ENSO influences on the rainfall seasons of Ethiopia
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Markov chain modeling and ENSO influences on the rainfall seasons of Ethiopia By Endalkachew Bekele from NMSA of Ethiopia [email protected] Banjul, Gambia December 2002
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Markov chain modeling and ENSO influences on the rainfall seasons of Ethiopia. By Endalkachew Bekele from NMSA of Ethiopia [email protected] Banjul, Gambia December 2002. INTRODUCTION. - PowerPoint PPT Presentation
Transcript of Markov chain modeling and ENSO influences on the rainfall seasons of Ethiopia
Markov chain modeling and ENSO influences on the rainfall
seasons of Ethiopia
By Endalkachew Bekele
from NMSA of Ethiopia
Banjul, Gambia
December 2002
INTRODUCTION
• The seasonal rainfall predictions issued by the NMSA of Ethiopia are mainly the results of ENSO analogue methodologies.
• Hence, it is good to study the existing relationship between the ENSO episodic events and the Ethiopian rainfall.
• The Markov Chains approach can be useful in this regard.
INTRODUCTION (continued)
• If we provide a statistician with historical data of rainfall and ask him to tell us the probability of having rainfall on 9 December, he may go through simple to complex computations:
• Simple:- If he computes the ratio of number of rainy days on December 9 to the total number of years of the historical data.
• Complex:- If he considers the Markov Chain processes
INTRODUCTION (continued)
• Markov Chain Processes w.r.t. daily rainfall:Previous days’ event Today’s event Order
- wet zero
wet wet firstdry wet first
wet wet wet seconddry wet wet secondwet dry wet seconddry dry wet second
• By applying such simple to complex statistical methods (Markov chain modeling) to the daily rainfall data obtained from three meteorological stations in Ethiopia, the following results were obtained:
Over All Chances of Rain at A.A.
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D A T E
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Over All Chances of Rain atKombolcha
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Dire Dawa
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First-Order Markov Chain at A.A.
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p_dr p_rr f_dr f_rr
First-Order Markov Chain atKombolcha
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Diredawa
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Second-Order Markov Chain at A.A.
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f_rdd f_rdr f_rrd f_rrr
Second-Order Markov Chain at Kombolcha
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Mean rain per rainy days (mm) at A.A.
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Mean rain per rainy days (mm) atKombolcha
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rain
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Dire Dawa
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Ra
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Why Modeling?
• It is the best tool in describing the characteristics rainfall in Tropics (Stern et al)
• It leads to simulation of long-years daily rainfall data
• By using the simulated data, it would be simple to compute:– Start and end of the rains– Study the effects of ENSO events– Dry-spells etc…
What next?• The available rainfall data were categorized under:
– Warm (El Nino)----1965,1966,1969,1972…
– Cold (La Nina) -----1964,1971,1973,1974…and
– Normal episodes-----1967,1968,1970, 1976….
(based on: http:/www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyear.htm
• Then hundred years of daily rainfall data were simulated for each episodic events(El Nino and La Nia).
How the simulation is done?
• The frequency distribution of daily rainfall amount is assumed to have a form of Gamma distribution:
• Where, all parameters in F(x) are obtained while fitting curves of the appropriate Markov Chain model (mean rain per rainy day and conditional probabilities).
)(
)()(
1
k
k
xF
kx
k ekx
How the simulation is done?
• For example, for the simulation done on the Addis Ababa r/f data:
– 0-order mean rain per rainy days– 2nd order Markov chain for chances of rain and– K (El Nino) = 0.942 and K (La Nina) = 0.963
were used
What next?• Hundred years of daily rainfall data were
simulated for each episodic years
• Monthly and seasonal rainfall amounts were computed from the simulated data
• The following cumulative probability curves were produced from the the monthly and seasonal summaries:
Cumm. Prob. Of Belg rainfall during ENSO episodic years
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Rainfall (mm)
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El Nino La Nina
• The less the slope of the curves (if they become more horizontal) means the higher the inter-annual variability in seasonal rainfall amount.
• The higher the gap between the two curves means the higher the effect of the episodic events.
Cumm. Prob. Of Belg (Feb. to May) rainfall during ENSO episodic years
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Rainfall (mm)
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El Nino La Nina
• In 80% of the years the seasonal rainfall is as high as 200mm during El Nino events, while it is less than 100mm (only about 90mm) during La Nina events.
• Hence, an agricultural expert can make his decision, if he is provided with such useful information.
Cumm. Prob. Of Belg rainfall during ENSO years atKombolcha (Belg)
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Dire Dawa (Belg)
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Cumm. Prob. Of Kiremt (June to September) rainfall during ENSO
episodic years at Addis Ababa
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Cumm. Prob. Of Kiremt rainfall during ENSO years atKombolcha (Kiremt)
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Dire Dawa (Kiremt)
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Dry-spells• The same simulated data can be used to
study various other events such as:– Start and end of the rains– Dry-spells etc…– The dry spell condition computed for each
episodic years are summarized in the following way:
Prob. Of ten days dry-spell length during ENSO years at A.A.
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•La Nina increases the chances of having 10 days dry-spell in the small rainy season, while El Nino decreases that risk.
Prob. Of ten days dry-spell length during ENSO years atKombolcha
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Dire Dawa
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Conclusion• Markov chain modeling is a good tool for
studying the daily rainfall characteristics.• Its application doesn’t necessarily need long-years
data.• It summarizes large data records into equations of
few curves and few k values.• It can be used best in the study of the effects of
ENSO on Ethiopian rainfall activity.• The results obtained from this approach can be
best used for agricultural planning in Ethiopia.
Thank you
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