Is the SPI gamma function consistent in time and space for ...
Is the SPI gamma function consistent in time and space for ...
Is the SPI gamma function consistent in time and space for ...
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<strong>Is</strong> <strong>the</strong> <strong>SPI</strong> <strong>gamma</strong> <strong>function</strong> <strong>consistent</strong> <strong>in</strong> <strong>time</strong><br />
<strong>and</strong> <strong>space</strong> <strong>for</strong> calculat<strong>in</strong>g extreme values of<br />
precipitation across Canada<br />
Aston C. Chipanshi, Warren Richard, Dongzhi Qi<br />
Agriculture <strong>and</strong> Agri-Food Canada, Reg<strong>in</strong>a,<br />
DRI Workshop, W<strong>in</strong>nipeg 2011
WHY <strong>SPI</strong><br />
• <strong>SPI</strong> adopted at <strong>the</strong> WMO meet<strong>in</strong>g <strong>in</strong><br />
Nebraska as “<strong>the</strong> meteorological <strong>in</strong>dex <strong>for</strong><br />
drought” (8-11-2009),<br />
• It is a s<strong>in</strong>gle variable <strong>in</strong>dex (requires pptn<br />
only),<br />
• It can be used to monitor droughts <strong>and</strong><br />
floods,<br />
• Many agencies are already us<strong>in</strong>g <strong>SPI</strong> <strong>in</strong><br />
<strong>the</strong>ir climate risk analyses (AAFC, NOAA<br />
etc),<br />
• <strong>SPI</strong> is one of 9 deliverables under<br />
EC/NOAA-MOU-AAFC lead<strong>in</strong>g <strong>the</strong> <strong>SPI</strong><br />
sub-project.<br />
2
BASIC QUESTIONS<br />
• The <strong>gamma</strong> density <strong>function</strong> is used to compare<br />
observations <strong>in</strong> near real <strong>time</strong>. <strong>Is</strong> this <strong>function</strong> valid <strong>in</strong> all<br />
climate zones<br />
• A request has been made by users (e.g. NADM) to<br />
produce <strong>SPI</strong> at shorter <strong>time</strong> frames (weekly <strong>and</strong> biweekly).<br />
<strong>Is</strong> <strong>gamma</strong> valid at <strong>the</strong>se <strong>time</strong> frames<br />
• <strong>SPI</strong> requires historical data but most stations have<br />
TYPICAL GAMMA DENSITY FUNCTIONS<br />
4
TEST SITES<br />
5
Density<br />
Density<br />
0.00 0.03 0.06<br />
0.000 0.006 0.012<br />
Density<br />
Density<br />
0.00 0.02 0.04<br />
0.000 0.015 0.030<br />
Density<br />
Density<br />
0.000 0.006<br />
0.000 0.006<br />
Density<br />
Density<br />
0.000 0.006<br />
0.000 0.004 0.008<br />
MONTHLY DISTRIBUTIONS (ARID VS HUMID)<br />
REGINA, SK<br />
ST. JOHN’S, NF<br />
0 50 100 150 200<br />
Precipitation on January (mm)<br />
0 50 100 150 200<br />
Precipitation on April (mm)<br />
0 50 100 150 200 250 300 350<br />
Precipitation on January (mm)<br />
0 50 100 150 200 250 300 350<br />
Precipitation on April (mm)<br />
0 50 100 150 200<br />
Precipitation on July (mm)<br />
0 50 100 150 200<br />
Precipitation on October(mm)<br />
0 50 100 150 200 250 300 350<br />
Precipitation on July (mm)<br />
0 50 100 150 200 250 300 350<br />
Precipitation on October(mm)<br />
6
Density<br />
0.000 0.005 0.010 0.015<br />
Sample Quantiles<br />
50 100 150<br />
Normality Test <strong>for</strong> ST. JOHN<br />
0 50 100 150 200 250 300 350<br />
Precipitation(mm)<br />
-2 -1 0 1 2<br />
Theoretical Quantiles<br />
Histogram <strong>and</strong> QQ-plot <strong>for</strong> NFLD on July from 1970 to 2009<br />
M<strong>in</strong>. 19.30 Max. 176.00<br />
Mean 86.73250 Std Deviation 34.87569<br />
Median 83.95000 Variance 1216<br />
Skewness 0.39 Kurtosis -0.19<br />
7
Density<br />
0.000 0.005 0.010 0.015<br />
Density<br />
0.000 0.010 0.020 0.030<br />
Density<br />
Density<br />
0.000 0.005 0.010 0.015 0.020 0.025<br />
0.00 0.02 0.04 0.06 0.08<br />
BI-WEEKLY PLOTS FOR VANCOUVER<br />
The 1st Semimonthly Prec on January<br />
The 1st Semimonthly Prec on April<br />
0 50 100 150<br />
Precipitation(mm)<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
The 1st Semimonthly Prec on July<br />
The 1st Semimonthly Prec on September<br />
0 20 40 60 80<br />
Precipitation(mm)<br />
0 20 40 60 80<br />
Precipitation(mm)<br />
8
Density<br />
Density<br />
0.00 0.01 0.02 0.03 0.04<br />
0.000 0.005 0.010 0.015 0.020 0.025<br />
Density<br />
Density<br />
0.00 0.01 0.02 0.03 0.04<br />
0.000 0.010 0.020 0.030<br />
BI-WEEKLY PLOTS FOR SARNIA<br />
The 1st Semimonthly Prec on January<br />
The 1st Semimonthly Prec on April<br />
0 10 20 30 40 50 60 70<br />
Precipitation(mm)<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
The 1st Semimonthly Prec on July<br />
The 1st Semimonthly Prec on October<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
9
Density<br />
Density<br />
0.00 0.05 0.10 0.15<br />
0.000 0.010 0.020 0.030<br />
Density<br />
Density<br />
0.00 0.02 0.04 0.06 0.08 0.10<br />
0.00 0.02 0.04 0.06 0.08 0.10<br />
BI-WEEKLY PLOTS FOR REGINA<br />
The 1st Semimonthly Prec on January<br />
The 1st Semimonthly Prec on April<br />
0 5 10 15 20 25<br />
Precipitation(mm)<br />
0 5 10 15 20 25 30 35<br />
Precipitation(mm)<br />
The 1st Semimonthly Prec on July<br />
The 1st Semimonthly Prec on October<br />
0 20 40 60 80 100 120 140<br />
Precipitation(mm)<br />
0 20 40 60<br />
Precipitation(mm)<br />
10
Density<br />
Density<br />
0.00 0.05 0.10 0.15 0.20<br />
0.00 0.02 0.04 0.06<br />
Density<br />
Density<br />
0.00 0.02 0.04 0.06 0.08<br />
0.00 0.05 0.10 0.15 0.20<br />
WEEKLY DISTRIBUTIONS FOR KANASKIS<br />
The 1st Week Precipitation <strong>for</strong> 1970-2009<br />
The 17th Week Precipitation <strong>for</strong> 1970-2009<br />
0 10 20 30 40<br />
Precipitation(mm)<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
The 29th Week Precipitation<br />
The 41th Week Precipitation<br />
0 10 20 30 40 50 60 70<br />
Precipitation(mm)<br />
0 10 20 30 40<br />
Precipitation(mm)<br />
11
Density<br />
Density<br />
0.000 0.010 0.020 0.030<br />
0.00 0.01 0.02 0.03 0.04<br />
Density<br />
Density<br />
0.000 0.010 0.020 0.030<br />
0.000 0.010 0.020 0.030<br />
WEEKLY PLOTS FOR HALIFAX<br />
The 1st Week Precipitation <strong>for</strong> 1970-2009<br />
The 17th Week Precipitation <strong>for</strong> 1970-2009<br />
0 20 40 60 80<br />
Precipitation(mm)<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
The 29th Week Precipitation<br />
The 41th Week Precipitation<br />
0 20 40 60 80 100<br />
Precipitation(mm)<br />
0 50 100 150<br />
Precipitation(mm)<br />
12
WHAT WE ARE LEARNING<br />
• Depend<strong>in</strong>g on climatic zone, precipitation is not always<br />
<strong>gamma</strong> distributed,<br />
• Time of year (season) appears to affect <strong>the</strong> distribution<br />
• Chang<strong>in</strong>g <strong>the</strong> period of analysis (weekly, bi-weekly <strong>and</strong><br />
monthly) may affect <strong>the</strong> distribution type<br />
13
THE NEXT STEPS<br />
• Tests will be done at stations with a longer climatology<br />
• Explore o<strong>the</strong>r density <strong>function</strong>s<br />
• Modify code to allow users select a variety of density<br />
distributions<br />
14
Thank You<br />
Aston Chipanshi<br />
Aston.Chipanshi@agr.gc.ca
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