Evaluation of Classical Statistical Methods for Estimating and Reconstructing the Daily Temperature in Iran

Introduction: Effective decision-making and management in the field of sustainable development of natural resources require access to accurate and up-to-date climatic information. This information enables the examination of the role of climate change in various issues and the formulation of effective management strategies accordingly. In this context, temperature as one of the most important climatic indicators plays a key role in environmental analyses and research. Given the fundamental role of temperature in various situations, access to precise and comprehensive temperature data is of high importance. Such data should be sufficiently detailed to provide a clear and complete picture of temperature patterns over time. Unfortunately, climatic data often faces problems such as statistical discontinuities and measurement errors, which can lead to incorrect decisions and inefficient planning. In this research, statistical methods have been employed to analyze existing temperature data and their statistical discontinuities. These methods include geographical coordinates (graphical), normal ratio, weighted correlation coefficient, and arithmetic mean, which are well-established and widely used in completing climatic data. Selecting the most appropriate method from among these can enhance the accuracy of temperature data estimation and play a pivotal role in decisions based on more comprehensive and reliable data. The objective of this research is to identify the optimal methodology for estimating data and addressing statistical discontinuities. This will assist researchers, managers, and policymakers in the field of sustainable development and in better understanding climatic conditions, enabling them to make more informed and effective decisions.
Material and Methods: In order to address the statistical gap, a number of well-known and popular classical statistical methods were evaluated for estimating Iran temperature data. These included geographical coordinates, normal ratio, weighted correlation coefficient, and arithmetic mean. In order to determine the best method for completing missing information, data from 125 stations with complete information (without any missing data) over 21 years (2000 to 2020) were used. Given the extensive and time-consuming nature of the calculations, a random selection of 10% of the stations with an appropriate spatial distribution was employed to carry out the data filling operations. The information of the selected stations was removed at each stage separately and reconstructed based on their five nearest stations. To evaluate the aforementioned methods, statistical evaluation criteria such as R-squared (R2), root mean square error (RMSE), and mean absolute deviation (MAD) were used.
Results and discussion: The results of the analysis of computational values through the normal ratio method were evaluated against observational values. It was found that all the stations under study exhibited a high correlation, indicating the acceptability of the normal ratio method to data estimation. The average values obtained from the evaluation of results indicate that the methods of normal ratio, weighted correlation coefficient, geographical coordinates, and arithmetic mean are prioritized in order, with RMSE values of 3.05, 3.28, 3.30, and 3.51 degrees Celsius, respectively. Consequently, the normal ratio method is the most suitable among the other studied methods and can be employed to address issues such as a lack of information, existing data errors, and also the expansion of the study period.
Conclusion: Among the methods reviewed, the normal ratio method is generally more acceptable and of higher quality than the other methods and is recommended for use in future research within similar study ranges. In subsequent ranks, the methods of geographical coordinates, weighted correlation, and arithmetic mean are placed, respectively. It is notable that, although the other methods are considered of secondary importance, they nevertheless demonstrate satisfactory efficacy in certain locations. Consequently, under varying circumstances, a range of methods may be employed to address data deficiencies, and the optimal approach should be selected and utilized in accordance with the specific study area.