Hybrid EMD-RF Model for Predicting Annual Rainfall in Kerala, India
Abstract
:1. Introduction
2. Methodologies and Dataset
2.1. ARMA
- (i)
- AR part indicates the autocorrelation between present and past values.
- (ii)
- MA part indicating the autocorrelation between present and past values of the error term.
- (iii)
- Integrated part (I), denoting the level of differencing required to make the time series stationary.
Algorithm 1: Auto ARIMA prediction model |
The algorithm for prediction using Auto ARIMA is given below:
|
2.2. Random Forest Regression
Algorithm 2: Random Forest for Regression |
|
2.3. RF–IMF
2.3.1. Empirical Mode Decomposition
- (i)
- Only one extreme between zero crossings;
- (ii)
- Mean value of IMF is zero;
- (iii)
- The number of extremes are either equal or differs by a maximum of one.
- 1.
- Initialization
- 2.
- Locate all local maximum and local minimum values of the input signal .Find the upper envelope by connecting all the local maxima by a spline curve; do the same with all the local minima and find .
- 3.
- Calculate the local mean
- 4.
- Find the difference between the input signal and the mean
- 5.
- If the stopping criteria are satisfied by then
- 6.
- 7.
- The sifting process is stopped if the residual signal becomes a monotonic or residue function (). The original signal can be written as the summation of all IMFs and residue function:
2.3.2. RF–IMF
Algorithm 3: RF–IMF prediction model |
The algorithm for prediction using RFIMF is given below:
|
2.4. Dataset
2.5. Assessment Indicators for Predicting Performance
- (i)
- Mean absolute error (MAE): It represents the mean of the absolute difference between the actual and forecasted values.
- (ii)
- Mean squared error (MSE): It is defined as the average of the squared difference between the actual and predicted values, or, in other words, it is the measurement of the variance.
- (iii)
- Root mean square error (RMSE): It is the square root of the MSE or it is the measurement of standard deviation.
- (iv)
- Mean absolute percentage error (MAPE): It is the percentage equivalent of MAE. This can easily be interpreted and explained.
- (v)
- Coefficient of determination or R2: R-squared represents the proportion of variance in the dependent variable. It indicates how well a model fits the given dataset or it analyses how well a variable predicts another one. It lies between 0 and 1 and a larger value indicates a better fit between the predicted and actual value. R-squared value explains the strength of linear relationship between two variables. It can be used for evaluating trend analysis [27].
3. Annual Rainfall Prediction
3.1. Auto ARIMA
3.2. Random Forest Regression Model
3.3. RF–IMF Prediction Model
4. Performance Evaluation and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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x(t) | imf1 | imf2 | imf3 | imf4 | imf5 | imf6 | |
---|---|---|---|---|---|---|---|
x(t) | 1.00 | 0.77 | 0.36 | 0.28 | 0.18 | 0.23 | 0.03 |
imf1 | 0.77 | 1.00 | 0.11 | −0.03 | −0.05 | −0.08 | −0.05 |
imf2 | 0.36 | 0.11 | 1.00 | 0.09 | 0.00 | 0.00 | 0.03 |
imf3 | 0.28 | −0.03 | 0.09 | 1.00 | 0.03 | −0.10 | 0.00 |
imf4 | 0.18 | −0.05 | 0.00 | 0.03 | 1.00 | 0.08 | 0.00 |
imf5 | 0.23 | −0.08 | 2.00 | −0.10 | 0.08 | 1.00 | 0.17 |
imf6 | 0.03 | −0.0 | 0.00 | 0.00 | 0.03 | 0.17 | 1.00 |
Year/Model | Actual Rainfall (cm) | ARMA (0,0,2) (cm) | RF (cm) | RF–IMF (cm) |
---|---|---|---|---|
2001 | 263 | 272 | 281 | 261 |
2002 | 260 | 292 | 280 | 294 |
2003 | 231 | 280 | 247 | 232 |
2004 | 271 | 280 | 270 | 259 |
2005 | 230 | 268 | 269 | 253 |
2006 | 316 | 274 | 299 | 265 |
2007 | 313 | 296 | 283 | 290 |
2008 | 240 | 280 | 282 | 266 |
2009 | 258 | 274 | 257 | 244 |
2010 | 309 | 286 | 303 | 307 |
2011 | 278 | 288 | 281 | 267 |
2012 | 208 | 258 | 242 | 225 |
2013 | 319 | 283 | 281 | 293 |
2014 | 297 | 299 | 296 | 302 |
2015 | 256 | 275 | 274 | 265 |
2016 | 184 | 280 | 278 | 202 |
2017 | 267 | 271 | 264 | 264 |
2018 | 352 | 295 | 292 | 337 |
2019 | 312 | 291 | 271 | 294 |
2020 | 335 | 276 | 284 | 291 |
Evaluation Metrics | ARMA (0,0,2) | RF | RF–IMF |
---|---|---|---|
MAE (cm) | 31.45 | 26.65 | 19.70 |
MSE (cm2) | 38.80 | 26.65 | 24.60 |
RMSE (cm) | 6.16 | 5.16 | 4.90 |
MAPE (%) | 12.35 | 11.00 | 7.00 |
R2 | 0.28 | 0.38 | 0.76 |
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Jayasree, A.; Sasidharan, S.K.; Sivadas, R.; Ramakrishnan, J.A. Hybrid EMD-RF Model for Predicting Annual Rainfall in Kerala, India. Appl. Sci. 2023, 13, 4572. https://doi.org/10.3390/app13074572
Jayasree A, Sasidharan SK, Sivadas R, Ramakrishnan JA. Hybrid EMD-RF Model for Predicting Annual Rainfall in Kerala, India. Applied Sciences. 2023; 13(7):4572. https://doi.org/10.3390/app13074572
Chicago/Turabian StyleJayasree, Asha, Santhosh Kumar Sasidharan, Rishidas Sivadas, and Jayan A. Ramakrishnan. 2023. "Hybrid EMD-RF Model for Predicting Annual Rainfall in Kerala, India" Applied Sciences 13, no. 7: 4572. https://doi.org/10.3390/app13074572