## 2 Data and Method
### AutoML Algorithm  
The AutoML algorithm was developed from traditional ensemble models [21] by automatically performing model selection and optimizing parameterization. For example, in traditional ensemble models, several base models with fixed user-determined parameters were combined into a meta-model to improve the performance of each single model [22], as shown in the following equation:  
\[Y=M_{m}(M_{b1}(X),M_{b2}(X),M_{b3}(X),\dots,M_{bn}(X)), \tag{1}\]  
where \(Y\) and \(X\) are, respectively, the response and explanatory data and \(M_{m}\) and \(M_{bi}\) (\(i=1,2,\dots,n\)) are, respectively, the meta-model and the \(i\)-th base model. The base model outputs were fed into the meta-model, which automatically determined the weights of the base models according to predefined metrics (i.e., RMSE, NME). Generally, the base models with lower error levels had larger contribution weights in the final ensemble model. However, many experiments and trials are normally needed to determine a set of suitable base models and their parameter settings. For example, to use a random forest model (RF) as a base model, loss functions, the sampling approach, the number of trees, and other parameters must be determined. Parameter tuning is an even bigger problem for popular neural network models, which have many parameters that must be determined. Traditionally, their model parameters are generally defined and decided through manual tests or experienced expertise, which could be biased or limited in selecting the best potential models.  
To solve this problem, an AutoML model was developed based on an ensemble learning framework by automatically optimizing the parameters of a group of pre-defined alternative base models [23]. These candidate base models include an RF model, gradient booster models (GBM), and a multiple layer perceptron model. The RF and GBM models are both composed of a group of relatively simple classifiers (trees) to construct competitive regression or classification capabilities, while they use different training strategies of bagging and boosting, respectively. In the AutoML model selection and training procedure, the automatic learning process achieved by the grid-search technique was implemented to optimize the hyperparameters of the base models [24; 25]. The grid-search optimization technique used an exhaustive automatic \"trial-and-error\" method to select the best parameters from a pre-defined hyperparameter space. In other words, each hyperparameter within a model was tested with a group of candidate configurations. The hyperparameters  
Figure 2: Stations in the UCS area used in this study. The bold polylines refer to city boundaries. The normal polylines refer to county boundaries.  
and corresponding model with best performances were determined as the final trained AutoML model.  
To combine these base models, a stacking ensemble method was used to merge the selected base models to form an AutoML model. As shown in Figure 3, a previously fitted historical dataset was used to train the AutoML model before the model was used to post-process raw meteorological forecasts. Equation (2) shows how the temperature and relative humidity forecasts were post-processed:  
\[Y_{p}=M_{m}\Big{(}M_{b1}\Big{(}RH_{f},\ T_{f}\Big{)},M_{b2}\Big{(}RH_{f},\ T_{f} \Big{)},\dots,M_{bm}\Big{(}RH_{f},\ T_{f}\Big{)}\Big{)}, \tag{2}\]  
where \(M_{m}\) and \(M_{bi}(i=1,\ 2,\ 3\dots,n)\) have same meaning as in Equation (1). The \(RH_{f}\) and \(\ T_{f}\) are input explanatory variables of the raw forecasts of relative humidity and temperature, respectively, and \(Y_{p}\) is a post-processed meteorological variable, such as relative humidity or temperature. In the AutoML model used in this study, the number of base models was determined to be 15 after testing different numbers of base models to balance efficiency and accuracy.