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Hourly Precipitation Prediction
Nithya
Agenda• Model• Variable Selection
• Correlation• Time Lagged Correlations• Simulation Result• Variable selection Vs Mean Error
• Input -Neighbor Stations Selections• Stations which can be used as good predictors• Cross Correlation Between Stations for Hourly Precipitation• Correlation Plots
• Results • Error Plot• Hourly System output
Model
Data Collection Train Network Predict Data Web Interface
Train Network
Normalize Data..
∑❑
∑❑
∑❑
∑❑∑❑
Neural Network Training Section Cubic Spline Interpolation Multiple Sections
Online Prediction and Web Section Trained Neural Network Aggregate Data∑❑
Variable Selection-Correlation
• Output• 4 hours of Probability data for
Hourly Precipitationhttp://10.39.8.247/predict/correlation.php#div-1
All VariablesTemperatureHumidityDew pointPressureWind SpeedWind Speed GustWind DirectionWind Direction DegreeDaily RainHourly Precipitation
Selected VariablesHourly PrecipitationHumidityWind DirectionDaily RainSolar RadiationTemperature
Cross Correlation Between VariablesHP Vs Humidity HP Vs Pressure HP Vs Solar Radiation
HP Vs Temperature HP Vs Wind Direction Degree HP Vs Wind Speed
*HP- Hourly Precipitation
Variable Selection-Cross Correlation
HP Vs Humidity HP Vs Pressure HP Vs Solar Radiation
HP Vs Temperature HP Vs Wind Direction Degree HP Vs Wind Speed
Selected VariablesHourly PrecipitationHumidityWind DirectionDaily RainSolar RadiationTemperature
All VariablesTemperatureHumidityDew pointPressureWind SpeedWind Speed GustWind DirectionWind Direction DegreeDaily RainHourly Precipitation
Selected VariablesHourly PrecipitationHumidityDaily RainWind Direction
CorrelationCross Correlation
Simulation –Variable Combination
HP-WD-DR-T HP-P-WD-H-DR HP-H-T T-HP-SR-P-WS-H-DR HP-P-WD HP-P-H-DR HP-SR-P-H0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Mean Absolute Error
Mea
n Ab
solu
te E
rror
1 2 3 4 5 6 7 80
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Mean Absolute Error
Number of Variables usedM
ean
Abso
lute
Err
or
• List of Selected Variables Combinations• HP-WD-H-DR• HP-WD-DR-T• HP-WD-H-DR-T• HP-P-WD-WS-DR• HP-P-WD-H-T
• Legend• T- Temperature• HP- Hourly Precipitation• WD- Wind Direction• WS- Wind Speed
• P- Pressure• H- Humidity• DR- Daily Rain• SR- Solar Radiation
• HP-SR-WD-DR• HP-P-WD-DR• HP-P-WD-WS-H• HP-P-WD-T• HP-WD-WS-H-T
Variable Selection-Simulation
HP-WD-DR-T HP-WD-WS-T HP-P-WS-DR HP-SR-WD-WS HP-WS-DR-T HP-DR HP-SR-P-WD-H-T HP-SR-WD HP-P-T0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Mean Absolute Error
Mea
n Ab
solu
te E
rror
1 2 3 4 5 6 7 80
0.0020.0040.0060.008
0.010.0120.014
Mean Absolute Error
Number of Variables used
Mea
n Ab
solu
te E
rror
Selected VariablesHourly PrecipitationHumidityWind DirectionDaily RainSolar RadiationTemperature
All VariablesTemperatureHumidityDew pointPressureWind SpeedWind Speed GustWind DirectionWind Direction DegreeDaily RainHourly Precipitation
Selected VariablesHourly PrecipitationHumidityDaily RainWind Direction
Selected VariablesHourly PrecipitationHumidityDaily RainWind Direction
CorrelationCross CorrelationSimulation
Number of Hours of input data
0 5 10 15 20 25 300
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Number of Input hours of data required
Number of hours
MAE
0 5 10 15 20 25 30 351
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Number of Neurons
Number of Neurons
MAE
• Number of Hours input data- 24• Number of hidden Neurons=7
Stations which can be used as good predictors
-18 -17 -16 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -10
5
10
15
20
25
Number of Times Rainfall occured at stations before IBSURRE21
Burna10CWWKIbccoqui5Ibcpittm3Surre10Surre6
Number Hours Ahead
Coun
t
Possible Predictor Burna 10, Coqui5, Surre6
-7 -6 -5 -4 -3 -2 -10
5
10
15
20
25
Burna10CWWKIbccoqui5Ibcpittm3Surre10Surre6
Cross Correlation Between Stations for Hourly Precipitation
SURRE21-COQUI5 SURRE21-SURRE6 SURRE21-PITTM3
SURRE21-BURNA 10 SURRE21-SURRE10
Cross Correlation Between Stations for Hourly Precipitation- Daily Rain
SURRE21-Surre10 SURRE21-Surre6
SURRE21-COQUI5 SURRE21-BURNA10
Cross Correlation Between Stations for Hourly Precipitation- Humidity
SURRE21-BURNA10 SURRE21-CWMM SURRE21-CWWK
SURRE21-COQUI5 SURRE21-SURRE6 SURRE21-SURRE10
Input Selection –Station Combination
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.50
0.02
0.04
0.06
0.08
0.1
0.12
0.14
MEAN Absolute Error
Number of Input Variables
MAE
Best CombinationSurre21,Burna 10, Ibccoqui5Surre21,Burna 10, PITM3Surre21,PITM3, Surre6
Sur21-NA10-IBC5 Sur21-NA10-IBC5-PIT3-CWWK Sur21-PIT3-CWWK Sur21-IBC5-PIT3-Sur6 Sur21-IBC5-Sur10-CWMM0
0.05
0.1
0.15
0.2
0.25
0.3
Combination Plot for Stations
Mea
n Ab
solu
te E
rror
Input Selection –Station Combination
Sur21-NA10-IBC5 Sur21-PIT3-Sur10-CWMM-CWWK Sur21-PIT3-Sur6-CWWK Sur21-NA10-IBC5-PIT3-Sur10Sur21-IBC5-PIT3-Sur10-CWMM Sur21-NA10-CWWK Sur21-NA10-IBC5-PIT3-CWMM0
0.05
0.1
0.15
0.2
0.25
0.3
Combination Plot for Stations
Mea
n Ab
solu
te E
rror
Input/output Representation• Input is 24 hour Normalized data from three stations and 3 variables
from the stations.• Output is 4 variable. Each variable indicating probability of rain for
every hour ahead.
Date Time Hour1 Hour2 Hour3 Hour4
… 0 0 0 0
…. 0 1 0 0
… 1 0 0 0
…. 0 0 0 1
• Sample Actual OutputData Used for Training• Rainfall>1(mm) ? Output=1 : Output =0
We Have 2^4= 16 different Combinations of possible Output
Distribution of Actual Output Classes2011-2013
Error PlotPr
edic
ted
Error Computed for Random Sample data 2011-2013*This data was not used for Training
Value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Output Class 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Pred
icte
d
actual actual
counts percentage
Hourly Precipitation Results
12:00 AM
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM0
102030405060708090
100
0
0.5
1
1.5
2
2.5
3
Low Rain 1/7/2014
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
2:00 AM
4:00 AM
6:00 AM
8:00 AM
10:00 AM
12:00 PM
2:00 PM
4:00 PM
6:00 PM
8:00 PM0
102030405060708090
100
00.511.522.533.54
Average Rain 1/2/2014
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
8:00 PM0
20
40
60
80
100
012345678
Heavy Rain 1/11/2014
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM0
102030405060708090
100
0
0.5
1
1.5
2
2.5
3
Snow Fall 2/22/2014
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
Hourly Precipitation – Low rain
12:00 AM
1:00 AM 2:00 AM 3:00 AM 4:00 AM 5:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 AM
11:00 AM
12:00 PM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM0
10
20
30
40
50
60
70
80
90
100
0
0.5
1
1.5
2
2.5
3
Rainfall Prediction 1/7/2014
Predict 1 Predict 2 Predict 3 Predict 4 Predict 5 Predict 6 Preict 7 Predict 8 Precipitation
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
Hourly Precipitation – Average rain
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
0
10
20
30
40
50
60
70
80
90
100
0
0.5
1
1.5
2
2.5
3
3.5
4
Rainfall Prediction 1/2/2014Predict 1 Predict 2 Predict 3 Predict 4 Predict 5Predict 6 Preict 7 Predict 8 Precipitation
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
Hourly Precipitation – Heavy rain
4:00 PM 5:00 PM 6:00 PM 7:00 PM 8:00 PM 9:00 PM 10:00 PM 11:00 PM 12:00 AM 1:00 AM 2:00 AM 3:00 AM 4:00 AM 5:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 8:00 PM0
20
40
60
80
100
0
1
2
3
4
5
6
7
8
Rainfall Prediction 1/11/2014
Predict 1 Predict 2 Predict 3 Predict 4 Predict 5 Predict 6 Preict 7 Predict 8 Precipitation
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
Hourly Precipitation – Snow Fall
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
0
10
20
30
40
50
60
70
80
90
100
0
0.5
1
1.5
2
2.5
3
Rainfall Prediction 2/22/2014Predict 1 Predict 2 Predict 3 Predict 4 Predict 5Predict 6 Preict 7 Predict 8 Precipitation
Prob
abili
ty(%
)
Prec
ipita
tion
(mm
)
Cross Correlation Plots
Hourly Precipitation Vs Humidity6-23-13
5-11-131-3-13
Hourly Precipitation Vs Pressure6-23-13
5-11-131-3-13
Hourly Precipitation Vs Solar Radiation
6-23-13
5-25-131-3-13
Hourly Precipitation Vs Temperature6-23-13
5-25-131-3-13
Hourly Precipitation Vs Wind Direction
6-23-13
5-25-131-3-13
Back time lagged correlation
Hourly Precipitation Vs Wind Direction
Back time lagged correlationNorth NNE NE
ENEEast ESE SE
SSESouth
SSW SWWSW
WestWNW NW
NNW0
50
100
150
200
250
300
350
Direction Vs Degress
Degr
ee
2013- 6 Hours Prior to Rainfall- Wind Direction Distribution
Correlation Matrix1. SURRE 21
2. CWWK
*Everything Variable with a number suffix belongs to corresponding station listed Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. SURRE6
*Everything Variable with a number suffix belongs to corresponding station listed Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. CWMM
*Everything Variable with a number suffix belongs to corresponding station listed Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. SURRE10
*Everything Variable with a number suffix belongs to corresponding station listed Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. PITM3
*Daily Rain and Wind Direction Deg are dropped, because more 80% of the data is NA Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. IBCCOQUI5
*Daily Rain and Wind Direction Deg are dropped, because more 80% of the data is NA Back To Station Correlation>>
Correlation Matrix1. SURRE 21
2. BURNA10
*Daily Rain and Wind Direction Deg are dropped, because more 80% of the data is NA Back To Station Correlation>>