## 3 Methodology  
This paper outlines the designed multidimensional meteorological data imputation framework (MMDIF) based on machine learning, which uses the predicted values of machine-learning models as the imputed values of missing data. The non-missing data in the feature to be imputed are used as the label data for training the model, and the features in the dataset that have a correlation with the feature to be imputed are used as the input data for the model. It is assumed that the dataset contains \(N\) observation values (such as temperature, humidity, wind speed, etc.), which we usually call the features of the data. Each feature has a certain percentage of randomly missing values. The MMDIF designed in this paper is as follows:  
Step 1: Choose the feature with the least missing values in the dataset as the feature to be filled in, mark it as data\", and mark the remaining features as data'.  
Step 2: Divide data' by day into layers, and replace the missing cells in each layer with the mean of the recorded cells in that layer as temporary imputation values.  
Step 3: Take the non-missing data in data\" as the label of machine learning and record the line number z where the missing value is located in data\".  
Step 4: Calculate the correlation between each feature and label in data' except for row z, and keep the features with a correlation greater than 0.2 as the machine-learning trainset (a correlation coefficient below 0.2 means that there is a very weak correlation between the two variables [42]). The correlation analysis uses the spearman correlation coefficient,  
Figure 1: Map of climatic zoning site.  
which can reflect the degree of correlation between the two variables, \(x\) and \(y\), based on Equation (1), where \(n\) represents the sample size, and \(\overline{x}\) and \(\overline{y}\) represent the sample mean:  
\[r=\frac{\sum_{i}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{\sum_{i}^ {n}{(x_{i}-\overline{x})^{2}\sum_{i}^{n}(y_{i}-\overline{y})^{2}}}} \tag{1}\]  
Step 5: Select the features consistent with trainset in data\", and select the z line as the testset. Step 6: Train the machine learning model using the label and trainset created in Steps 3 and 4. Step 7: Input the testset into the model trained in Step 6, and impute the output values of the model to the corresponding positions in data. Step 8: Check the data. If there are missing values, return to Step 1 and continue the imputation program; otherwise, exit the program.  
The MMDIF imputation process is illustrated in Figure 2. The machine-learning module depicted in the figure employs a variety of prediction mechanisms, including 20 mainstream machine-learning methods. These methods encompass linear, tree-based, instance-based, kernel-based, probability-based, and neural network-based methods. Table 1 provides a brief overview of these methods. The neural network methods are implemented using the Keras and Tensorflow modules, and the remaining methods are implemented using the scikit-learn modules. The implementation process requires setting hyperparameters for each model, and the choice of model hyperparameters greatly affects the performance of the model. In order for each model to achieve the best possible performance, in this paper, the most advantageous hyperparameter combination for the model was sought out via a grid search of the variable space [43]. Because the weight matrix initialization greatly influences the performance of neural network-based methods, we repeated these algorithms ten times on the same data and computed the mean of the results. This allowed us to compare them fairly with other machine-learning methods.  
Figure 2: MMDIF flowchart.