## 4 Conclusions  
In this paper, we proposed a novel approach for spatiotemporal missing value imputation. Furthermore, this approach was illustrated by applying it to impute rainfall data in six reference stations to compile a complete data set that could be used in building a rainfall forecasting model for a target station. The proposed approach is a hybrid approach combining MLP that captures the temporal variability and spatial interpolation (spatial kriging) that captures the spatial variations. This hybrid model was designed for imputing missing values when the missingness of reference stations was spread discontinuously and not uniformly over the given period and a few rainfall gauging stations are spatially correlated. Moreover, the results obtained by the hybrid model were compared with those resulting from spatiotemporal kriging. The study supported the claim that the proposed hybrid approach provided the lowest prediction error when estimating a sequence of missing values.  
Only a single published research study that imputes the missing rainfall values of Ratnapura gauging stations is available. The accuracy measurements of the proposed method are far better than those of said study [28].  
The availability of a few rain gauging stations around Ratnapura station and unavailability of data in some stations for a considerable period due to relocation or other reasons were the challenging limitations confronted during this study.  
In order to verify the optimality of weight estimates and the outperformance of the hybrid method, the data for an extended period need to be gathered and tested.  
While considering the aforesaid limitations, the future direction of this research will be the development of more hybrid models combining other missing value imputation methods and applying this approach to estimate missing values of spatiotemporal data obtained from other fields.  
Figure 9: The outperformance of models with respect to RMSE (**a**), MAE (**b**), and R\({}^{2}\) (**c**) values.  
**Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14030999/s1](https://www.mdpi.com/article/10.3390/app14030999/s1)]([https://www.mdpi.com/article/10.3390/app14030999/s1](https://www.mdpi.com/article/10.3390/app14030999/s1)), Table S1: Missing value imputation of substation rainfall data using DL methods; Table S2: Final optimal weights; Table S3: Comparison of prediction error of all models in validation under Section 3.4.2.  
**Author Contributions:** Conceptualization, C.T. and S.S.; methodology, S.S., C.T., P.L. and M.M.; software, S.S.; validation, S.S.; formal analysis, S.S.; investigation, C.T., M.M. and P.L.; resources, S.S.; data curation, S.S.; writing--original draft preparation, S.S.; writing--review and editing, C.T. and M.M.; visualization, S.S.; supervision, C.T., M.M. and P.L.; project administration, C.T.; funding acquisition, C.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Collaborative Research Grant of the University of Colombo, Sri Lanka, grant number AP/3/2019/CG/30.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the authors upon reasonable request.  
**Acknowledgments:** The authors wish to acknowledge the University of Colombo, Sri Lanka, for the monetary support.  
**Conflicts of Interest:** The authors declare no conflict of interest.