Evaluation of Infilling Methods for Time Series of Daily Temperature Data: Case Study of Limpopo Province, South Africa
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data
2.2. Methodology
2.2.1. Arithmetic Averaging Method (AA)
- is the estimated value,
- is the observed temperature value of the neighboring station, and
- is the number of neighboring stations.
Nearest Stations (AA_D)
2.2.2. Normal Ratio Method (NR)
- is the estimated value,
- is the observed temperature value of the neighboring station,
- is annual average temperature of the neighbouring station,
- is annual average temperature of the target station, and
- is the number of neighboring stations.
2.2.3. Inverse Distance Weighting Method (IDW)
- is the estimated value,
- is the observed temperature value of the neighboring station,
- is the distance between the target station and the neighboring station,
- is a natural number, usually = 2, and
- is the number of neighboring stations.
2.2.4. Correlation Coefficient Weighted Method (CC)
- is the estimated value,
- is the observed temperature value of the neighboring station,
- r is the correlation coefficient between target station and neighboring station, and
- is the number of neighboring stations.
2.2.5. Multiple Regression Method (MR)
- is the estimated value,
- is the observed temperature value of the neighboring station,
- are regression coefficients, and
- is the number of neighboring stations.
2.2.6. The Traditional (UK) Method
- is the UK coefficient value of the neighboring station.
- is the observed temperature value of the neighboring station of month,
- is the long-term average of the observed temperature of the neighboring station of month,
- is the long-term average of observed temperature of the target station of the month.
2.2.7. Averaging the Best Correlated Stations (UK_AA_C)
- is the estimated value,
- is the UK coefficient value of the neighboring station, and
- is the number of neighboring stations.
2.2.8. Blending of UK and Correlation Coefficient (UK_CC_C)
- is the estimated value,
- is the UK coefficient value of the neighboring station,
- r is the correlation coefficient between target station and neighboring station, and
- is the number of neighboring stations.
2.2.9. Averaging of the Closest Station Estimates (UK_AA_D)
2.2.10. Blending of UK and IDW (UK_ID_D)
- is the estimated value,
- is the UK coefficient value of the neighboring station,
- is the distance between the target station and the neighboring station,
- is a natural number, usually q = 2, and
- is the number of neighboring stations.
2.3. Determination of Accuracy of Estimated Temeperature Values
2.3.1. Correlation Coefficient (r):
- is the actual value,
- is the estimated value, and
- is the mean.
2.3.2. Mean Absolute Error (MAE):
- is the actual value and
- is the estimated value.
2.3.3. Root Mean Squared Error (RMSE):
- is the actual value and
- is the estimated value.
2.3.4. Mean Bias Error (MBE):
- is the actual value and
- is the estimated value.
2.3.5. Accuracy Rate (AR):
3. Results and Discussion
3.1. Correlation Between Measured and Estimated Temperature Values
3.2. Mean Absolute Error (Mae) Values for Estimated Temperatures Values Compared with Measured Values
3.3. Root Mean Square Error (RMSE) Values for Estimated Temperatures Values Compared With Measured Values
3.4. Mean Bias Error (Mbe) Values for Estimated Temperatures Values Compared with Measured Values
3.5. Accuracy Rate (AR) Values for Estimated Temperature Values Compared With Measured Values
4. Further Discussions
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Station | Lat. | Long | Alt | Aspect | StartDate (Year-Month-Day) | EndDate (Year-Month-Day) | Years | Missing (%) | |
---|---|---|---|---|---|---|---|---|---|
Name | Number | ||||||||
Letsitele | 1 | −23.867 | 30.317 | 623 | 235 | 1974-01-01 | 2008-02-29 | 34 | 10.2 |
Polokwane | 2 | −23.836 | 29.694 | 1226 | 38 | 1984-07-01 | 2010-08-09 | 26 | 18.3 |
Mara | 3 | −23.150 | 29.567 | 894 | 43 | 1949-01-01 | 2004-03-31 | 55 | 22.7 |
Towoomba | 4 | −24.900 | 28.333 | 1143 | 108 | 1937-01-01 | 2004-03-31 | 67 | 22.7 |
Macuville | 5 | −22.267 | 29.900 | 522 | 100 | 1933-10-01 | 2004-01-31 | 70 | 24.3 |
Tshiombo | 6 | −22.801 | 30.481 | 650 | 0 | 1983-01-01 | 2006-03-31 | 23 | 28.4 |
ElandsKloof | 7 | −24.283 | 28.050 | 1215 | 62 | 1979-03-01 | 2001-09-30 | 23 | 33.6 |
Hoedspruit | 8 | −24.414 | 30.784 | 573 | 65 | 1985-07-01 | 2005-01-31 | 20 | 38.0 |
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Shabalala, Z.P.; Moeletsi, M.E.; Tongwane, M.I.; Mazibuko, S.M. Evaluation of Infilling Methods for Time Series of Daily Temperature Data: Case Study of Limpopo Province, South Africa. Climate 2019, 7, 86. https://doi.org/10.3390/cli7070086
Shabalala ZP, Moeletsi ME, Tongwane MI, Mazibuko SM. Evaluation of Infilling Methods for Time Series of Daily Temperature Data: Case Study of Limpopo Province, South Africa. Climate. 2019; 7(7):86. https://doi.org/10.3390/cli7070086
Chicago/Turabian StyleShabalala, Zakhele Phumlani, Mokhele Edmond Moeletsi, Mphethe Isaac Tongwane, and Sabelo Marvin Mazibuko. 2019. "Evaluation of Infilling Methods for Time Series of Daily Temperature Data: Case Study of Limpopo Province, South Africa" Climate 7, no. 7: 86. https://doi.org/10.3390/cli7070086