The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall
Abstract
:1. Introduction
2. Materials and Methods
2.1. Inverse Distance Weight Matrix
2.2. Moran Index
2.3. Spatial Autoregressive Exogenous (SAR-X)
2.4. Estimation
3. Real Data Application
3.1. Data Description
3.2. RShiny Web Application for SAR-X Model
- A.
- The process of building an R script for the SAR-X model
- Importing the climate data used for the SAR-X modeling, encompassing 13 climate observation stations in the West Java region.
- Constructing vectors and matrices based on the climate data, including:
- Vector : defines the rainfall variable at each location.
- Matrix : represents the exogenous variables, such as air temperature, humidity, solar irradiation, wind speed, and surface pressure.
- Matrix : consists of location coordinate entries in latitude and longitude.
- Matrix : identity matrix with the size of as many as five exogenous variables, according to matrix .
- Matrix : the result of calculating the inverse distance weight matrix using the equation with input location coordinates (latitude and longitude).
- Kronecker : the expression obtained from the multiplication of the kronecker with the identity matrix of the five exogenous variables
- Matrix : the product of matrix , , and
- The Moran Index calculation using function “moran.test” and Moran Scatterplot using function “moran.plot”.
- The calculation of parameter estimation and , obtaining the prediction results , absolute error, and MAPE of the SAR-X model prediction with the Casetti model approach.
- The SAR-X model prediction data with the Casetti model approach in the form of
- B.
- Creating and publishing the RShiny web application with the developed script.
- Installing packages and call libraries, specifically “shiny” and “shinythemes”, to set up RShiny.
- Creating a User Interface (UI) and Server for the Web ApplicationUI scripts managed the appearance of the web, incorporating headers, images, panel tabs, and more. Furthermore, the previously crafted R script for the SAR-X model was integrated into the server script. Running the application involved clicking “Run App.” Successful execution prompted progression, while errors in the console necessitated troubleshooting.
- Publishing the RShiny Web Application
3.3. Calculation Result of Inverse Distance Weight Matrix
3.4. Calculation Result of Moran’s Index and Scatterplot Moran
3.5. Prediction Result of SAR Model
3.6. Prediction Result of SAR-X Model
3.7. Cross-Validation
4. Discussion
5. Conclusions
6. Patents
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- SAR model for predicting rainfall in Balitpa Sukamandi:
- SAR model for predicting rainfall in Lanud Atang Sanjaya Semplak:
- SAR model for predicting rainfall in LPHP Tasikmalaya:
- SAR model for predicting rainfall in SMPK Cirebon:
- SAR model for predicting rainfall in SMPK Maranginan Sukabumi:
- SAR model for predicting rainfall in SMPK Nariewattie:
- SAR model for predicting rainfall in SMPK Pacet Cianjur:
- SAR model for predicting rainfall in SMPK Pasir Sarongge:
- SAR model for predicting rainfall in Stage of Bandung:
- SAR model for predicting rainfall in Stage of Lembang:
- SAR model for predicting rainfall in Staklim Darmaga:
- SAR model for predicting rainfall in Stamet Citeko Bogor:
- SAR model for predicting rainfall in Stamet Jatiwangi:
Appendix B
- SAR-X model for predicting rainfall in Balitpa Sukamandi:
- SAR-X model for predicting rainfall in Lanud Atang Sanjaya Semplak:
- SAR-X model for predicting rainfall in LPHP Tasikmalaya:
- SAR-X model for predicting rainfall in SMPK Cirebon:
- SAR-X model for predicting rainfall in SMPK Maranginan Sukabumi:
- SAR-X model for predicting rainfall in SMPK Nariewattie:
- SAR-X model for predicting rainfall in SMPK Pacet Cianjur:
- SAR-X model for predicting rainfall in SMPK Pasir Sarongge:
- SAR-X model for predicting rainfall in Stage of Bandung:
- SAR-X model for predicting rainfall in Stage of Lembang:
- SAR-X model for predicting rainfall in Staklim Darmaga:
- SAR-X model for predicting rainfall in Stamet Citeko Bogor:
- SAR-X model for predicting rainfall in Stamet Jatiwangi:
Appendix C
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No. | Locations | Latitude | Longitude | Rainfall (mm) | Air Temperature (°C) | Humidity (%) | Solar Irradiation (W/m2) | Wind Speed (m/s) | Surface Pressure (kPa) |
---|---|---|---|---|---|---|---|---|---|
1 | Balitpa Sukamandi | −6.3 | 107.65 | 186.36 | 25.3 | 83.45 | 415.2 | 1.76 | 97.86 |
2 | Lanud Atang Sanjaya Semplak | −6.9 | 106.77 | 200.74 | 23.72 | 87.25 | 411.23 | 1.71 | 95.52 |
3 | LPHP Tasikmalaya | −7.28 | 108.16 | 228.2 | 23.68 | 89.15 | 398.29 | 2.1 | 96.46 |
4 | SMPK Cirebon | −6.72 | 108.58 | 189.71 | 27.7 | 78.58 | 418.72 | 3.67 | 100.86 |
5 | SMPK Maranginan Sukabumi | −7.25 | 106.25 | 191.42 | 25.79 | 84.61 | 415.46 | 3.12 | 98.84 |
6 | SMPK Nariewattie | −7.25 | 108 | 194.57 | 22.59 | 87.85 | 398.29 | 1.57 | 93.62 |
7 | SMPK Pacet Cianjur | −6.73 | 107 | 176.28 | 24.7 | 85.19 | 415.2 | 1.46 | 96.82 |
8 | SMPK Pasir Sarongge | −6.75 | 107 | 176.28 | 24.7 | 85.19 | 415.2 | 1.46 | 96.82 |
9 | Stage of Bandung | −6.92 | 107.6 | 203.29 | 21.41 | 88.29 | 415.2 | 1.51 | 90.93 |
10 | Stage of Lembang | −6.83 | 107.62 | 203.29 | 21.41 | 88.29 | 415.2 | 1.51 | 90.93 |
11 | Staklim Darmaga | −6.55 | 106.75 | 176.28 | 24.7 | 85.19 | 411.23 | 1.46 | 96.82 |
12 | Stamet Citeko Bogor | −6.7 | 106.93 | 176.28 | 24.7 | 85.19 | 411.23 | 1.46 | 96.82 |
13 | Stamet Jatiwangi | −6.75 | 108.27 | 181.08 | 26.45 | 80.97 | 418.72 | 2.49 | 99.66 |
No. | Climate Variable | p-Value | Description |
---|---|---|---|
1 | (Rainfall) | 0.0168 | There is spatial autocorrelation |
2 | (Air Temperature) | 0.0061 | There is spatial autocorrelation |
3 | (Humidity) | 0.0163 | There is spatial autocorrelation |
4 | (Solar Irradiation) | 0.0013 | There is spatial autocorrelation |
5 | (Wind Speed) | 0.0487 | There is spatial autocorrelation |
6 | (Surface Pressure) | 0.0044 | There is spatial autocorrelation |
No. | Parameter Estimated Value | |
---|---|---|
1 | β1 | −89.56 |
2 | β2 | −12.21 |
3 | β3 | −0.63 |
4 | β4 | 27.50 |
5 | β5 | 36.49 |
No. | Locations | y | Absolute Error | |
---|---|---|---|---|
1 | Balitpa Sukamandi | 186.36 | 214.49 | 15.09 |
2 | Lanud Atang Sanjaya Semplak | 200.74 | 215.98 | 7.59 |
3 | LPHP Tasikmalaya | 228.20 | 260.09 | 13.98 |
4 | SMPK Cirebon | 189.71 | 217.49 | 14.64 |
5 | SMPK Maranginan Sukabumi | 191.42 | 226.58 | 18.37 |
6 | SMPK Nariewattie | 194.57 | 273.16 | 40.39 |
7 | SMPK Pacet Cianjur | 176.28 | 189.40 | 7.44 |
8 | SMPK Pasir Sarongge | 176.28 | 189.41 | 7.45 |
9 | Stage of Bandung | 203.29 | 250.93 | 23.44 |
10 | Stage of Lembang | 203.29 | 250.81 | 23.38 |
11 | Staklim Darmaga | 176.28 | 196.39 | 11.41 |
12 | Stamet Citeko Bogor | 176.28 | 192.96 | 9.46 |
13 | Stamet Jatiwangi | 181.08 | 228.85 | 26.38 |
No. | Parameter Estimated Value | |
---|---|---|
1 | −539.33 | |
2 | −96.53 | |
3 | 2.93 | |
4 | 139.34 | |
5 | 207.11 | |
6 | −33.57 | |
7 | −5.94 | |
8 | 0.17 | |
9 | 8.96 | |
10 | 12.86 |
No. | Locations | Parameter Estimated Value of | ||||
---|---|---|---|---|---|---|
1 | Balitpa Sukamandi | −215.93 | −45.51 | 58.56 | −21.52 | −0.73 |
2 | Lanud Atang Sanjaya Semplak | −31.14 | −116.44 | −2.56 | 120.40 | 43.66 |
3 | LPHP Tasikmalaya | 0.16 | −20.48 | −42.76 | 29.06 | 16.71 |
4 | SMPK Cirebon | 86.59 | 3.91 | −112.28 | −1.67 | 24.16 |
5 | SMPK Maranginan Sukabumi | 80.12 | −0.91 | 38.00 | −0.32 | 11.79 |
6 | SMPK Nariewattie | 137.49 | 36.36 | 14.27 | −49.03 | −1.14 |
7 | SMPK Pacet Cianjur | 32.06 | 5.04 | −1.21 | 71.15 | 24.35 |
8 | SMPK Pasir Sarongge | −1.75 | 343.87 | 20.79 | 20.24 | −12.06 |
9 | Stage of Bandung | −4.98 | 68.96 | −17.38 | −1.40 | 6.13 |
10 | Stage of Lembang | −55.57 | −2.87 | 48.79 | 12.41 | 8.65 |
11 | Staklim Darmaga | 295.90 | −58.45 | 16.20 | −30.12 | −1.05 |
12 | Stamet Citeko Bogor | 60.51 | −134.81 | −1.27 | −50.76 | 29.39 |
13 | Stamet Jatiwangi | −2.62 | 285.08 | 18.01 | −1.64 | −5.17 |
No. | Locations | y | Absolute Error | |
---|---|---|---|---|
1 | Balitpa Sukamandi | 186.36 | 189.49 | 1.68 |
2 | Lanud Atang Sanjaya Semplak | 200.74 | 200.78 | 0.02 |
3 | LPHP Tasikmalaya | 228.20 | 222.30 | 2.59 |
4 | SMPK Cirebon | 189.71 | 190.80 | 0.57 |
5 | SMPK Maranginan Sukabumi | 191.42 | 193.36 | 1.01 |
6 | SMPK Nariewattie | 194.57 | 202.01 | 3.82 |
7 | SMPK Pacet Cianjur | 176.28 | 175.13 | 0.65 |
8 | SMPK Pasir Sarongge | 176.28 | 176.62 | 0.19 |
9 | Stage of Bandung | 203.29 | 193.78 | 4.68 |
10 | Stage of Lembang | 203.29 | 210.81 | 3.70 |
11 | Staklim Darmaga | 176.28 | 171.90 | 2.48 |
12 | Stamet Citeko Bogor | 176.28 | 179.17 | 1.64 |
13 | Stamet Jatiwangi | 181.08 | 176.87 | 2.32 |
No. | Locations | Latitude | Longitude | Rainfall (mm) | Solar Irradiation (W/m2) | Wind Speed (m/s) |
---|---|---|---|---|---|---|
1 | Bandung City | −6.91486 | 107.6082 | 203.29 | 415.2 | 1.511 |
2 | Bekasi City | −6.24159 | 106.9924 | 172.32 | 411.2 | 2.492 |
3 | Cirebon City | −6.73725 | 108.5507 | 189.71 | 418.7 | 3.674 |
4 | Sukabumi City | −6.9237 | 106.9287 | 200.74 | 411.2 | 1.706 |
5 | Tasikmalaya City | −7.31956 | 108.203 | 228.2 | 398.3 | 2.099 |
6 | Pangandaran Regency | −7.61506 | 108.4988 | 210.14 | 1.816 | 398.3 |
7 | Bogor Regency | −6.59504 | 106.8166 | 176.28 | 411.2 | 1.456 |
8 | Majalengka Regency | −6.83638 | 108.2274 | 194.57 | 418.7 | 1.575 |
9 | Indramayu Regency | −6.32758 | 108.3249 | 181.08 | 418.7 | 2.495 |
10 | Purwakarta Regency | −6.53868 | 107.4499 | 186.36 | 415.2 | 1.76 |
11 | Kuningan Regency | −7.01381 | 108.5701 | 184.64 | 398.3 | 1.781 |
No. | Parameter Estimated Value | |
---|---|---|
1 | −0.08 | |
2 | 4.04 | |
3 | −0.01 | |
4 | 0.35 |
No. | Locations | Parameter Estimated Value of | |
---|---|---|---|
1 | Bandung City | 0.11 | −0.06 |
2 | Bekasi City | 2.72 | 0.08 |
3 | Cirebon City | 0.03 | 3.88 |
4 | Sukabumi City | 5.48 | 0.10 |
5 | Tasikmalaya City | 0.08 | 3.26 |
6 | Pangandaran Regency | 3.79 | 0.03 |
7 | Bogor Regency | 0.12 | 5.51 |
8 | Majalengka Regency | 2.48 | 0.07 |
9 | Indramayu Regency | 0.16 | 4.32 |
10 | Purwakarta Regency | 1.14 | 0.12 |
11 | Kuningan Regency | 0.20 | 2.59 |
No. | Locations | y | Absolute Error | |
---|---|---|---|---|
1 | Bandung City | 203.29 | 206.08 | 2.79 |
2 | Bekasi City | 172.32 | 177.63 | 5.31 |
3 | Cirebon City | 189.71 | 203.23 | 13.52 |
4 | Sukabumi City | 200.74 | 201.40 | 0.66 |
5 | Tasikmalaya City | 228.20 | 223.60 | 4.60 |
6 | Pangandaran Regency | 210.14 | 140.21 | 69.93 |
7 | Bogor Regency | 176.28 | 191.01 | 14.73 |
8 | Majalengka Regency | 194.57 | 203.28 | 8.71 |
9 | Indramayu Regency | 181.08 | 183.86 | 2.78 |
10 | Purwakarta Regency | 186.36 | 190.22 | 3.86 |
11 | Kuningan Regency | 184.64 | 211.11 | 26.47 |
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Falah, A.N.; Ruchjana, B.N.; Abdullah, A.S.; Rejito, J. The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall. Mathematics 2023, 11, 3783. https://doi.org/10.3390/math11173783
Falah AN, Ruchjana BN, Abdullah AS, Rejito J. The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall. Mathematics. 2023; 11(17):3783. https://doi.org/10.3390/math11173783
Chicago/Turabian StyleFalah, Annisa Nur, Budi Nurani Ruchjana, Atje Setiawan Abdullah, and Juli Rejito. 2023. "The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall" Mathematics 11, no. 17: 3783. https://doi.org/10.3390/math11173783
APA StyleFalah, A. N., Ruchjana, B. N., Abdullah, A. S., & Rejito, J. (2023). The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall. Mathematics, 11(17), 3783. https://doi.org/10.3390/math11173783