6e86d5dd-f02b-4c87-959a-bf073e653bbc 1701 2 5 false false 1 decimal

Design: Eng. N.D.T.M. Amarasekera - Feb. 2020

RAIN FALL ANALYSIS - Standardized Precipitation Index (SPI)

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Station Name: Millawana-Estate

Type: Precipitatiom

Data Interval: Daily

Unit: Millimeters

Period 1960/01/01 to 2018/12/31

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4 appVersion 0.99.7251.32800

Project Millawana Estate 11 mat :

t.start 0 time :

1. Select period

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t1 0 time :

Assume 30 day month

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Input Matrix. You can extend 
or reduce the size of matrix input.1 3 Months 330 * 4 Months 430 * 6 Months 630 * 9 Months 930 * 12 Months 1230 * 18 Months 1830 * 62 mat :

"3 Months"
"4 Months"
"6 Months"
"9 Months"
"12 Months"
"18 Months"

Select Period

nn_day

Output nn_day 9012018027036051 mat

For use in results months nn_day 30 / : 34691251 mat

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 gaps.

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

MyFile MyDirectory rainfall\005F\KalaOyaBAsin.xlsx concat :

Read daily rainfall data file. Define correct cell range (in this case B3:B21552

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RF_DATA MyFile Sheet1 B3 B21552 importData.XLSX :

RF_DATA rows 21550

RF_DATA cols 1

n.DATA RF_DATA length : 21550

0 time t1 - 0.47 s *

3. Find 'n' day totals for a a single duration

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Program 4: Finds 'p' day Avg. of an Array :

Super Fast:

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t1 0 time :

period.tot n.DATA 360 / round yr * :

Program 1: To find "p" day TOTAL. q p n_day_Tot q q eval : j 1 q rows p / trunc range : PT j el q n el n 1 j 1 - (p * + j p * sum : eval PT 41 line :

period.tot yr 60

Only to demonstrate how Program 1 works n_day nn_day 1 el : 90

Apply Program 1 with appropriate variables X RF_DATA n_day n_day_Tot : 557.36 549.82 992.27 848.58 634.75 457.57 705.05 878.01 395.09 91 mat

X max 1643.35

X min 17.6

n X rows : 239

RF_DATA rows n_day / 239.4444

n.bal RF_DATA rows n_day / n - (n_day * : 40

n n_day * n.bal + 21550

0 time t1 - 0.22 s *

4. Find 'n' day totals for multiple durations

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Program 2:  For a range of 'p' day totals of vector 'A' . 
Calls Program 1 repeatedly for  each 'nn_day' array element. A p nn_day_total j 1 p rows range : B j el A p j el n_day_Tot : eval 21 line :

Input Array nn_day 9012018027036051 mat

t1 0 time :

Calls Program 2 XX RF_DATA nn_day nn_day_total :

Input Array passed to Program 2 to find XX

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0 time t1 - 0.97 s *

X 557.36 549.82 992.27 848.58 634.75 457.57 705.05 878.01 395.09 456.94 225.98 919.66 897.09 505.92 284.32 151 mat

XX 1 el 557.36 549.82 992.27 848.58 634.75 457.57 705.05 878.01 395.09 456.94 225.98 919.66 897.09 505.92 284.32 151 mat

XX 2 el 966.21 1082.64 899.18 726.71 1054.48 894.19 600.02 350.72 1046.91 1118.93 555.27 1313.66 543.19 567.52 671.38 151 mat

XX rows 5

XX cols 1

Compare

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XX 1 el Max 1643.35

XX 1 el Min 17.6

XX 1 el rows 239

XX 2 el rows 179

XX Max vectorize 1643.35 2163.81 2185.43 2646.56 2987.86 51 mat

XX Min vectorize 17.6 23 287.14 711.64 1125.56 51 mat

XX rows vectorize 239179119795951 mat

5. Find logarithms of a single XX vector

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XX Min vectorize 17.6 23 287.14 711.64 1125.56 51 mat

No zeros or -ve

values in XX

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t1 0 time :

{rogram 3: To deal with zero values. for  "ln(X)" M LNX j 1 M rows range : B j el 0 M j el 0 ≡ M j el ln cases : eval 21 line :

XX 1 el LNX 6.32 6.31 6.9 6.74 6.45 6.13 6.56 6.78 5.98 6.12 5.42 6.82 121 mat

XX 2 el LNX 6.87 6.99 6.8 6.59 6.96 6.8 6.4 5.86 6.95 7.02 6.32 7.18 121 mat

XX LNX rows vectorize 239179119795951 mat

6. Find logarithms of an array of XX vectors

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Program 4: Calls Program 3.
Vectorize function used all_LNX XX LNX vectorize eval :

Calls Program 3

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all_LNX 1 el 6.32 6.31 6.9 6.74 6.45 6.13 6.56 6.78 5.98 6.12 5.42 6.82 6.8 6.23 5.65 7.17 161 mat

all_LNX 2 el 6.87 6.99 6.8 6.59 6.96 6.8 6.4 5.86 6.95 7.02 6.32 7.18 6.3 6.34 6.51 6.24 161 mat

all_LNX rows vectorize 239179119795951 mat

0 time t1 - 0.17 s *

6. Find Means of XX array and Means of LNX arrays

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t1 0 time :

All_XX.mean XX Mean vectorize eval : 490.32 653.04 977.54 1452.48 1934.61 51 mat

All_LNX.mean all_LNX Mean vectorize eval : 5.97 6.32 6.81 7.24 7.54 51 mat

7. Gamma PDF and CDF

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A All_XX.mean ln All_LNX.mean - vectorize : 0.22 0.16 0.08 0.04 0.03 51 mat

α 14 A * / 114 A 3 / * + sqrt + (* vectorize eval : 2.42 3.25 6.43 12.09 16.64 51 mat

β All_XX.mean α / vectorize eval : 202.64 200.65 151.91 120.09 116.24 51 mat

Eqn for Gamma function PDF x j g 1 β j el α j el^α j el Gamma * / x α j el 1 -^* e x β j el / -^* :

1 β / vectorize 0.0049 0.005 0.0066 0.0083 0.0086 51 mat

Eqn. 1

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Eqn for Gamma function CDF x_val j G 1 β j el α j el^α j el Gamma * / x α j el 1 -^e x β j el / -^* x 0 x_val int * :

Eqn. 2

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β α^vectorize 381413.15 31153938.77 1.09 1014^* 1.42 1025^* 2.37 1034^* 51 mat

α 1 - 1.42 2.25 5.43 11.09 15.64 51 mat

α Gamma vectorize 1.26 2.56 256.29 50346333.06 7.73 1012^* 51 mat

Some Examples

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X 1 el 1 g 0.0011

X 2 el 1 g 0.0011

XX 1 el 1 el 1 g 0.0011

0 time t1 - 0.03 s *

7.1 PDF

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t1 0 time :

Ptogtam 5 x# n# PDF j 1 x# rows range : B j el x# j el n# g : eval 21 line :

Program 6: Calls Program 5 x# All_PDF j 1 x# rows range : B j el x# j el j PDF : eval 21 line :

X 557.36 549.82 992.27 848.58 634.75 457.57 705.05 878.01 395.09 456.94 225.98 919.66 897.09 505.92 284.32 1300.52 161 mat

XX 3 el 1107.18 1840.85 1092.31 1583.07 852.02 1145.63 1403.02 1584.85 685.67 1096.42 904.84 1503.01 1129.55 1197.32 806.25 846.36 161 mat

X XX 1 el - 0000000000000000161 mat

A1 XX 1 el 1 PDF : 0.0011 0.0011 0.0003 0.0005 0.0009 0.0013 0.0007 0.0004 0.0014 0.0013 0.0015 0.0004 0.0004 0.0012 141 mat

A1 sum 0.2561

Ans1 XX All_PDF eval :

Ans1 1 el 0.0011 0.0011 0.0003 0.0005 0.0009 0.0013 0.0007 0.0004 0.0014 0.0013 0.0015 111 mat

Ans1 2 el 0.0005 0.0004 0.0006 0.0009 0.0004 0.0007 0.0012 0.0012 0.0004 0.0004 0.0012 111 mat

Ans1 1 el sum 0.2561

Ans1 2 el sum 0.1607

Ans1 rows vectorize 239179119795951 mat

0 time t1 - 0.2 s *

7.2 CDF

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Program 7 x# n# CDF j 1 x# rows range : B j el x# j el n# G : eval 21 line :

Program 8: Calls Program 7 x# All_CDF j 1 x# rows range : B j el x# j el j CDF : eval 21 line :

t1 0 time :

G XX All_CDF :

0 time t1 - 5.44 s *

X 1 CDF 0.6618 0.6538 0.9257 0.8738 0.736 0.5441 0.7912 0.8866 0.4583 0.5433 0.2003 0.9026 0.8942 0.6043 0.2901 0.9776 0.4763 0.2802 181 mat

G 1 el 0.6618 0.6538 0.9257 0.8738 0.736 0.5441 0.7912 0.8866 0.4583 0.5433 0.2003 0.9026 0.8942 0.6043 0.2901 0.9776 0.4763 0.2802 181 mat

Compare

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t1 0 time :

8. Calculation of SPI values and Probabilities

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Program 9: Returns Inv. Cumulative 
Normal Distribution values F.inv.normal G ICDF.Normal vectorize :

Extract 2 nd column of ICDF Z F.inv.normal 2 col vectorize :

F.inv.normal 1 el 0.6618 0.4175 0.6538 0.3956 0.9257 1.4444 0.8738 1.1445 0.736 0.631 0.5441 0.1108 0.7912 0.8107 0.8866 1.2084 0.4583 0.1048 - 0.5433 0.1088 0.2003 0.8406 - 0.9026 1.2965 0.8942 1.2491 0.6043 0.2644 0.2901 0.5531 - 152 mat

Z 1 el 0.4175 0.3956 1.4444 1.1445 0.631 0.1108 0.8107 1.2084 0.1048 - 0.1088 0.8406 - 1.2965 1.2491 0.2644 0.5531 - 151 mat

Z 2 el 0.9357 1.1734 0.7904 0.3806 1.1175 0.7793 0.0365 0.8224 - 1.1023 1.2441 0.0966 - 1.6007 0.1338 - 0.0595 - 0.2357 151 mat

Z rows vectorize 239179119795951 mat

Z sum vectorize 0.1317 0.4357 0.0602 - 0.0506 - 0.0022 - 51 mat

0 time t1 - 0.14 s *

t1 0 time :

Program 10: Rounding data to 2 decimals. 
Jean's method revised: Very handy data Rounded collects index list j 1 data rows range : a j el P data j el : 2 round vectorize eval : 31 line :

Rounding necessary as the Condition Matrix has 2 decimals. See 8.1 below

ZZ Z Rounded :

ZZ rows 5

0 time t1 - 0.06 s *

ZZ 1 el 0.42 0.4 1.44 1.14 0.63 0.11 0.81 1.21 0.1 - 0.11 0.84 - 1.3 121 mat

ZZ 2 el 0.94 1.17 0.79 0.38 1.12 0.78 0.04 0.82 - 1.1 1.24 0.1 - 1.6 121 mat

ZZ rows vectorize 239179119795951 mat

ZZ 1 el rows 239

ZZ 2 el rows 179

After rounding ZZ sum vectorize 0.16 0.47 0.05 - 0.07 - 0.02 51 mat

Before rounding Z sum vectorize 0.1317 0.4357 0.0602 - 0.0506 - 0.0022 - 51 mat

8..1 Condition Matrix to calculate SPI & Probabilities

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Condition Matrix

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t1 0 time :

Program 11: All conditions in a Matrix, where each element represents a specific condition x All_Conds x 2.0 ≥ x 1.5 1.99 lele x 1.0 1.49 lele x 0.99 - 0.99 lele x 1.49 - 1.0 - lele x 1.99 - 1.5 - lele x 2.0 - ≤ 71 mat :

Program 12: SPI for a single vector x# SPI_Single x# All_Conds vectorize sum eval 11 line :

B j el P x# j el All_Conds : (:

First vector of ZZ AA ZZ 1 el :

For a Single Array (ZZ₁)

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3 appVersion 0.99.7251

Program 13: For AA, find number of occurences 
satisfying each condition (TRUTH TABLE) SPI1 ZZ 1 el SPI_Single : 51324161229571 mat

Program 14: Probability vector for AA Pr1 SPI1 SPI1 sum / 100 * : 2.1 5.4 10 67.4 9.2 3.8 2.1 71 mat

SPI1 sum 239

Pr1 sum 100

For a Nested Array (ZZ)

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t1 0 time :

Program 15: Find All SPI vectors using Vectorize fumction: Very handy S1 ZZ SPI_Single vectorize transpose : 51324161229571 mat 3917126136571 mat 341479124371 mat 4175394171 mat 0553955071 mat 15 mat

Program 16: Sum of each SPI vector S2 S1 vectorize sum : 239179119795915 mat

0 time t1 - 0.14 s *

Program 17: Similarly, find All Probability vectors P1 S1 S2 / vectorize 100 * : 2.1 5.4 10 67.4 9.2 3.8 2.1 71 mat 1.7 5 9.5 70.4 7.3 3.4 2.8 71 mat 2.5 3.4 11.8 66.4 10.1 3.4 2.5 71 mat 5.1 1.3 8.9 67.1 11.4 5.1 1.3 71 mat 0 8.5 8.5 66.1 8.5 8.5 071 mat 15 mat

Program 18: Sum of each Prob vector P2 P1 vectorize sum : 10010010010010015 mat

Program 19:Add headers to S1  & S2 S1S2 S:'SPI S1 S2 stack vectorize : S:'SPI 51324161229523991 mat S:'SPI 3917126136517991 mat S:'SPI 341479124311991 mat S:'SPI 417539417991 mat S:'SPI 055395505991 mat 15 mat

Program 20: Add headers to P1 & P2 P1P2 S:'Pr P1 P2 stack vectorize : S:'Pr 2.1 5.4 10 67.4 9.2 3.8 2.1 10091 mat S:'Pr 1.7 5 9.5 70.4 7.3 3.4 2.8 10091 mat S:'Pr 2.5 3.4 11.8 66.4 10.1 3.4 2.5 10091 mat S:'Pr 5.1 1.3 8.9 67.1 11.4 5.1 1.3 10091 mat S:'Pr 0 8.5 8.5 66.1 8.5 8.5 010091 mat 15 mat

Program 21 : Very useful feature to bring relevant matrices together All_SP S1S2 P1P2 augment vectorize :

All_SP S:'SPI S:'Pr 5 2.1 13 5.4 2410161 67.4 22 9.2 9 3.8 5 2.1 23910092 mat S:'SPI S:'Pr 3 1.7 9517 9.5 126 70.4 13 7.3 6 3.4 5 2.8 17910092 mat S:'SPI S:'Pr 3 2.5 4 3.4 14 11.8 79 66.4 12 10.1 4 3.4 3 2.5 11910092 mat S:'SPI S:'Pr 4 5.1 1 1.3 7 8.9 53 67.1 9 11.4 4 5.1 1 1.3 7910092 mat S:'SPI S:'Pr 005 8.5 5 8.5 39 66.1 5 8.5 5 8.5 005910092 mat 15 mat

MTH months transpose : 34691215 mat

months 34691251 mat

Program 22 : Create header for Months hd1 MTH num2str M concat vectorize : 3 M 4 M 6 M 9 M 12 M 15 mat

0 time t1 - 0.16 s *

t1 0 time :

Description of SPI definitions & ranges Des S:'RF S:'Period'/'Category S:'mm S:'Wet'/'Dry 2.0+ Extremely Wet 1.5 to 1.99 Very Wet 1.0 to 1.49 Moderately Wet -0.99 to +0.99 Near Normal -1.0 to -1.49 Moderately Dry -1.5 to -1.99 Severely Dry ≤ -2.0 Extremely Dry Σ Total 102 mat :

Convert to a single matrix Des Des 11 mat : S:'RF S:'Period'/'Category S:'mm S:'Wet'/'Dry 2.0+ Extremely Wet 1.5 to 1.99 Very Wet 1.0 to 1.49 Moderately Wet -0.99 to +0.99 Near Normal -1.0 to -1.49 Moderately Dry -1.5 to -1.99 Severely Dry ≤ -2.0 Extremely Dry Σ Total 102 mat 11 mat

Click on dotted region & Drag to rigth to view entire expression

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Program 23 : Stack with "hd1" All_SP2 hd1 All_SP stack vectorize : 3 M 3 M S:'SPI S:'Pr 5 2.1 13 5.4 2410161 67.4 22 9.2 9 3.8 5 2.1 239100102 mat 4 M 4 M S:'SPI S:'Pr 3 1.7 9517 9.5 126 70.4 13 7.3 6 3.4 5 2.8 179100102 mat 6 M 6 M S:'SPI S:'Pr 3 2.5 4 3.4 14 11.8 79 66.4 12 10.1 4 3.4 3 2.5 119100102 mat 9 M 9 M S:'SPI S:'Pr 4 5.1 1 1.3 7 8.9 53 67.1 9 11.4 4 5.1 1 1.3 79100102 mat 14 mat

All_SP3 Des All_SP2 augment : S:'RF S:'Period'/'Category S:'mm S:'Wet'/'Dry 2.0+ Extremely Wet 1.5 to 1.99 Very Wet 1.0 to 1.49 Moderately Wet -0.99 to +0.99 Near Normal -1.0 to -1.49 Moderately Dry -1.5 to -1.99 Severely Dry ≤ -2.0 Extremely Dry Σ Total 102 mat 11 mat

0 time t1 - 0

All_SP3 All_SP2 Des hd1 MTH All_SP P1P2 S1S2 P2 P1 S2 S1 SPI_Single Rounded All_CDF CDF All_PDF PDF g LNX nn_day_total n_day_Tot period.tot t1 t.start Project All_SP3 Des Pr1 SPI1 AA SPI_Single All_Conds ZZ Rounded Z F.inv.normal G All_CDF CDF Ans1 A1 All_PDF PDF g β α A All_LNX.mean All_XX.mean all_LNX LNX XX nn_day_total X n_day_Tot period.tot RF_DATA months nn_day t1 t.start Project g period.tot t1 t.start

All_SP3
mat("S:RF","S:Period/Category","S:mm","S:Wet/Dry","2.0+","Extremely Wet","1.5 to 1.99","Very Wet","1.0 to 1.49","Moderately Wet","-0.99 to +0.99","Near Normal","-1.0 to -1.49","Moderately Dry","-1.5 to -1.99","Severely Dry","≤ -2.0","Extremely Dry","Σ","Total",10,2)	mat("3 M","3 M","S:SPI","S:Pr",5,2.1,13,5.4,24,10,161,67.4,22,9.2,9,3.8,5,2.1,239,100,10,2)	mat("4 M","4 M","S:SPI","S:Pr",3,1.7,9,5,17,9.5,126,70.4,13,7.3,6,3.4,5,2.8,179,100,10,2)	mat("6 M","6 M","S:SPI","S:Pr",3,2.5,4,3.4,14,11.8,79,66.4,12,10.1,4,3.4,3,2.5,119,100,10,2)	mat("9 M","9 M","S:SPI","S:Pr",4,5.1,1,1.3,7,8.9,53,67.1,9,11.4,4,5.1,1,1.3,79,100,10,2)	mat("12 M","12 M","S:SPI","S:Pr",0,0,5,8.5,5,8.5,39,66.1,5,8.5,5,8.5,0,0,59,100,10,2)
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Millawana Estate
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0 time t.start - 9.9 s *