Transcript 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

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
• 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
dry
wet
dry
wet
dry
wet
wet
dry
dry
wet
wet
wet
wet
wet
wet
wet
zero
first
first
second
second
second
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.
100
90
80
Probability
70
60
50
40
30
20
10
0
0
50
100
150
200
250
D A TE
actual
fitted
300
350
400
Over All Chances of Rain at
probabilities
Kombolcha
100
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
350
250
300
350
400
DATE
Probability
Dire Dawa
100
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
DATE
400
First-Order Markov Chain at
A.A.
100
90
80
Probability
70
60
50
40
30
20
10
0
0
50
100
150
200
250
D A TE
p_dr
p_rr
f_dr
f_rr
300
350
400
First-Order Markov Chain at
Kombolcha
100
Probability
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
350
400
250
300
350
400
Diredawa
100
Probabilities
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
Second-Order Markov Chain at
A.A.
100
90
80
Probability
70
60
50
40
30
20
10
0
0
50
100
150
200
250
D A TE
f_rdd
f_rdr
f_rrd
f_rrr
300
350
400
Second-Order Markov Chain at
Kombolcha
100
probabilities
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
350
250
300
350
400
Dire Dawa
100
Probability
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
400
Mean rain per rainy days (mm) at
A.A.
14
12
10
rain
8
6
4
2
0
0
50
100
150
200
250
DATE
atual
fitted
300
350
400
Mean rain per rainy days (mm) at
Kombolcha
16
14
rain (mm)
12
10
8
6
4
2
0
0
50
100
150
200
250
300
350
400
Dire Dawa
16
14
12
Rain
10
8
6
4
2
0
0
50
100
150
200
250
300
350
400
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:
k
( )
F ( x) 
kxk 1e

kx


( k )
• 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).
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
100
Probab.
80
60
40
20
0
0
100
200
300
400
500
Rainfall (m m )
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
100
Probab.
80
60
40
20
0
0
100
200
300
400
500
Rainfall (m m )
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 at
Kombolcha (Belg)
100
90
80
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
Dire Dawa (Belg)
100
90
80
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
Cumm. Prob. Of Kiremt (June to
September) rainfall during ENSO
episodic years at Addis Ababa
100
90
80
70
60
50
40
30
20
10
0
400
500
600
800
700
El Nino
La Nina
900
1000
Cumm. Prob. Of Kiremt rainfall during ENSO years at
Kombolcha (Kiremt)
100
90
80
70
60
50
40
30
20
10
0
0
200
400
600
800
1000
1200
1400
500
600
700
Dire Dawa (Kiremt)
100
90
80
70
60
50
40
30
20
10
0
0
100
200
300
400
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.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Jan
Feb
Mar
Apr
May
Jun
El Nino
Jul
Aug
Sep
Oct
Nov
Dec
La Nino
•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 at
Kombolcha
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Oct
Nov
Dec
Dire Dawa
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
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