# Analysis and Modeling of Rainfall Events ```obability that a given rainfall will occur. The parameters
f the graph are:
in hrs)
in mms/hr)
y (Return Period) (in yrs)
. Formulas for rainfall intensities of long durations, Transactions
ty of Civil Engineers, 96, 592-624
R. (1984). A model fitting analysis of daily rainfall data, Journal
l Society. Series A(General), 147, 1-34.
. (1998). A mathematical framework of studying rainfall
uency relationships, Journal of Hydrology, 206, 118-135
plication of Rainfall Frequency Analysis on studying rainfall
stics of Chia-Nan plain area in southern Taiwan, Crop,
ormatics, 2, 31-38
C. (2006). Statistical Analysis of Indiana rainfall data, Joint
rch Program, Final Report
intensity is estimated by I =
𝑐
.
𝑏
𝐷+𝑎
1−𝐹(𝑟)
Parameters a and b are usually similar for a given loca
use 𝐼 =
𝐾𝑇𝑟 𝑑
𝐷+𝑎
𝑏
.
Graph 1
Model estimation
Intensity-Duration-Frequency curves
8
10
Parameters of the m
Equations of the Model
Tr=2 years
Tr=5 years
Tr=10 years
Tr=20 years
6
Rainfall duration (in hrs)
 (D) Event duration (in hrs)
 (I) Average intensity (in mm/hrs)
Table 1: Descriptive statistics of rainfall events.
Graph 1: Duration-Intensity scatter plot, inverse propor
1
Model: For every return period 𝑇𝑟 =
, the relation
12
 Table 2: Parameter e
confidence intervals
 Return period 𝑇𝑟 = 2 years (R=2.1mm)
𝟒. 𝟔𝟗
𝑰=
𝑫 − 𝟎. 𝟒𝟕 𝟎.𝟑𝟕
 Return period 𝑇𝑟 = 5 years (R=10mm)
𝟏𝟐. 𝟗𝟖
𝑰=
𝑫 − 𝟎. 𝟐𝟗 𝟎.𝟕𝟑
 Return period 𝑇𝑟 = 10 years (R=15mm)
𝟏𝟓. 𝟑𝟗
𝑰=
𝑫 − 𝟎. 𝟑𝟔 𝟎.𝟔𝟐
 Return period 𝑇𝑟 =20 years (R=25mm)
𝟐𝟏. 𝟖𝟔
𝑰=
𝑫 − 𝟎. 𝟐𝟔 𝟎.𝟔𝟗
Table
 Graph 2: IDF curves
Graph 2
Exploration of the model
appear to be optimal for every chosen return
overall correctly identified.
ion of model parameters.
0.3534
0.3534
0.3533
0.3533
0.3533
0.353
0.7791
0.779
0.779
0.3531
0.353
0.3531
0.353
R Squared
0.3531
0.7791
0.3532
R Squared
0.3532
R Squared
R Squared
0.3532
0.7789
0.7788
0.3529
0.3528
-0.5
0.3529
-0.45
a
0.3528
-0.4
0.7789
0.7788
0.3529
0.3528
0.35 0.4 0.45
b
4
4.5
c
0.7787
-0.4
5
-0.3
a
0.7787
-0.2
0.9885
0.9301
0.9301
0.9301
0.9884
0.9884
0.9299
0.9298
0.9297
-0.6
0.93
0.9299
0.9298
-0.4
a
-0.2
0.9297
0.4
0.93
0.9299
0.9298
0.6
b
0.8
0.9297
14
𝑻𝒓 =10 years
R Squared
0.9885
R Squared
0.9302
R Squared
0.9302
R Squared
0.9302
0.93
0.7 0.8
b
𝑻𝒓 =5 ye
𝑻𝒓 =2 years
R Squared
ere is a chance that estimation methods can
imates of the parameters. This can happen when
2
e try to maximize (here 𝑅 ) gets stuck in a local
ined for the selected model.
et of parameters is the optimal (the global
hed), an analysis using a Monte Carlo type
to investigate parameters’ behaviour.
𝑇𝑟 , we create 10000 random samples 𝑎𝑖 , 𝑏𝑖 , 𝑐𝑖 ,
𝑚 for different choices of intervals and each time
vector with the largest 𝑅2 .
repeated 100 times.
0.3534
R Squared
s:
0.9883
0.9882
0.9881
16
c
18
0.988
-0.4
Graph 3
0.9883
0.9882
0.9881
-0.2
a
0
0.988
0.7
b
𝑻𝒓 =20
```