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RAIN FALL ANALYSIS - Standardized Precipitation Index (SPI)

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Station Name: Angoda Mental Hospital

Type: Precipitatiom

Data Interval: Daily

Unit: Millimeters

Period 1960/01/01 to 2016/12/31

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4 appVersion 0.99.7251.32800

Climate\0020\Data\0020\Guide\0020\SPI\002E\pdf SPEI.pdf

1. Select period

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Assume 30 day months input.1 1 Month 30 2 Months 60 3 Months 90 4 Months 120 5 Months 150 6 Months 180 7 Months 210 8 Months 240 9 Months 270 10 Months 300 11 Months 330 12 Months 360122 mat :

Select how many Months

n_day

Starting time t.0 0 time :

n_day 30

2. Import rainfall data from EXCEL file

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NOTE : SMATH treats blanks in EXCEL as zeros. Hence, in case of

missing data, first use a suitable method to fill in such data.

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MyDirectory DocumentDirectory : F:\0001. Training ID\0001. IRESH Irrig. Dept\Final Gamma Results\

MyFile MyDirectory Rainfal_Data.xlsx concat :

Read daily rainfall data file. Define correct cell range (in this case B7:B20826

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RF_DATA MyFile Sheet1 B7 B20826 importData.XLSX :

RF_DATA rows 20820

RF_DATA cols 1

n.DATA RF_DATA length : 20820

Find 'p' day Total of rainfall series

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Program 1: To find 'p' day totals of vector 'A' A p n_day_total Find 'p' day total of raw data r 1 A rows p / trunc range C r el A 1 r 1 - (p * + (r p * (range el sum : for C 31 line :

period.tot n.DATA 360 / yr * :

period.tot yr 58

ΔT 0 time t.0 - : 0.5 s *

Apply Program 1 with appropriate variables X RF_DATA n_day n_day_total : 30.4 278.7 63.9 387.1 330 187.3 495.9 18 163.3 128.8 795.3 111 mat

X max 983.6239

X min 0

n X rows : 694

RF_DATA rows n_day / 694

n.bal RF_DATA rows n_day / n - (n_day * : 0

n n_day * n.bal + 20820

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3. Dealing with zero values

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ΔT 0 time t.0 - : 3.4 s *

Program 2: To deal 
with ln(0) n.zero 0 : j 1 X rows range X j el 0 ≤ LNX j el 0 : n.zero n.zero 1 + : pos n.zero el j : 31 line LNX j el X j el ln : if for n.zero 0 ≡ pos Undefined : pos pos : if 31 line

ln(x) values LNX 3.41 5.63 4.16 5.96 5.8 5.23 6.21 2.89 5.1 4.86 6.68 4.14 3.8 3.88 141 mat

Index of the LNX 
array where LNX = 0 pos 99148172196197221245269300301320328331131 mat

LNX 28 el 5.0907

j 694

Clear j from memory j Clear 1

X.mean X sum n / : 202.7543

LNX.mean LNX sum n / : 4.768

ΔT 0 time t.0 - : 3.4 s *

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4. Gamma PDF and CDF

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Number of 
zero values n.zero 29

Prob of zero values Pr.zero n.zero n / : 0.0418

A X.mean ln LNX.mean - : 0.544

α 14 A * / 114 A 3 / * + sqrt + (* : 1.063276612

β X.mean α / : 190.68821559

x Γ x Gamma :

α Gamma 0.9672

5 Gamma 24

Gamma PDF x g 1 β α^α Γ * / x α 1 -^e x β / -^* * :

12 / Gamma 1.7725

π sqrt 1.7725

Eqn. 1

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0 g 0

CDF x G 1 β α^α Γ * / u α 1 -^e u β / -^* u 0 x int * :

Eqn. 2

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0 G 0

x Q u g u 0 x int :

j 1 X rows range G1 j el X j el G eval : Q1 j el X j el Q eval : 21 line for

G1 0.1271 0.7456 0.2567 0.8525 0.8035 0.597 0.914 0.0752 0.5455 0.4601 0.9775 0.2516 0.1853 131 mat

Q1 0.1271 0.7456 0.2567 0.8525 0.8035 0.597 0.914 0.0752 0.5455 0.4601 0.9775 0.2516 0.1853 131 mat

X G vectorize 0.1379 1.4541 0.3037 2.0621 1.7403 0.953 2.6834 0.079 0.8237 0.64 4.4342 0.2967 0.2087 131 mat

ΔT 0 time t.0 - : 24.7 s *

To find 90th percentile P.90 0.90 768 ICDF.Normal : 86.25

Reverse P.90 768 CDF.Normal 0.9

50th percentile is Mean P.50 0.50 768 ICDF.Normal : 76

Reverse P.50 768 CDF.Normal 0.5

Mean