## 2 Materials and Methods
### Modeling Development Using Random Forest Technique  
Data from the temperature collection and the urban landscape metrics derived through geoprocessing of primary sources were organized to create a comprehensive ESRI File Geodatabases per urban area. The geodatabases allowed the development of spatial RF models, which were applied on a spatial resolution of one square meter per study area and time period (afternoon, evening, and night). The models basically took the collected temperature point data as the dependent variable while using the derived urban neighborhood morphometric data variables surrounding the points as independent variables to develop spatial models that estimated urban temperatures at those urban locations where no temperatures were recorded. Although several techniques can be used to create such models and to analyze and predict urban temperature patterns, the most common methods found in the reviewed literature were MLR, CART, RF, and sometimes a combination of multiple methods in the same study. However, recent studies utilizing mobile devices for temperature data collection showed that RF significantly outperformed MLR and CART [17; 18; 23; 24]. Recent advances in spatial statistical modeling techniques have been built into embedded tools in the software ArcGIS Pro (3.0.1). Thus, for this study, ArcGIS Pro was used for most of the steps in both the pre-processing of dependent and independent variables and also in spatial modeling. The forest-based classification and regression (nomenclature utilized by ArcGIS Pro for RF algorithm) model built into the Spatial Statistics toolbox in ArcGIS Pro was chosen for air temperature modeling. Random forest is a supervised machine learning method developed by [PERSON] and [PERSON] [36]. Random forests are a non-parametric and nonlinear machine learning technique and are a \"combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest\" [37] (p. 1). Models generated using a random forest algorithm not only provided the predicted temperature in areas where temperature data was not collected but also indicated the most influential independent variables that explain temperature patterns throughout each individual study area. A workflow of the process to derive the necessary raster datasets used as independent variables used in the random forest model can be seen in Figure 3. Ellipsoids represent functions and geoprocessing tools, rectangular red-filled objects represent the input datasets, rectangular white-filled objects represent the outcome files necessary to generate the final independent variables used in the random forest modeling, and rectangular blue-filled objects represent the generated independent variables and final outcome (predictive models). The parameters set in RF for all models consisted of 1000 randomized trees built from all effective focal distance raster datasets to predict the air temperature in each urban area in the afternoon, evening, and pre-dawn. A 70/30 hold-out method for model evaluation was used to assess the accuracy of all models. This technique separates the temperature measurements into two sets (training set and testing set) and was set as the percentage of data excluded for validation (=30%) before running each one of the models. Finally, only one number of runs was used as a validation option. The ArcGIS Pro Forest-based Classification and Regression tool accepted the inputted dependent variable as a Geodatabase Feature Class with each point holding the measured air temperature while  
Figure 3: Workflow to derive urban morphometric independent variables and application of the random forest algorithm. each independent variable came in the form of a 1 m\({}^{2}\) rasters (39 independent variables described below). Additional parameters such as number of data available per tree (100%) and number of runs for validation (1) were kept the same for all urban areas and times of the day.