Temporal downscaling of precipitation from climate model projections using machine learning

Abstract

Increased greenhouse gas concentration in the atmosphere has led to significant climate warming and changes in precipitation and temperature characteristics. These trends, which are expected to continue, will affect water infrastructure and raise the need to update associated planning and design policies. The potential effects of climate change can be addressed, in part, by incorporating outputs of climate model projections into statistical assessments to develop the Intensity Duration Frequency (IDF) curves used in engineering design and analysis. The results of climate model projections are available at fixed temporal and spatial resolutions. Model results often need to be downscaled from a coarser to a finer grid spacing (spatial downscaling) and/or from a larger to a smaller time-step (temporal downscaling). Machine Learning (ML) models are among the methods used for spatial and temporal downscaling of climate model outputs. These methods are more frequently used for spatial downscaling; fewer studies explore temporal downscaling. In this study, multiple ML models are evaluated to temporally downscale precipitation time-series (available at 3-h time steps) generated by several regional climate models of the North American Regional Climate Change Assessment Program (NARCCAP) under a high-carbon-emission projection. The temporally downscaled time-series for 2-h, 1-h, 30-min, and 15-min durations are intended for subsequent statistical analysis to generate current- and future-climate IDF curves for Maryland. In this study, the behavior of the ML models is explored by assessing performance in predicting large target response quantities, identifying systematic trends in errors, investigating input/output relationships using response functions, and leveraging conventional performance metrics.

Appendix: Parameterization of the models

1.1 Artificial neural network

To develop an ANN model, a number of parameters need to be specified to determine the architecture of the network, including: (1) the type of network, (2) the number of neurons and hidden layers, (3) the number of epochs, (4) the training algorithm and transfer function, and (5) the data division. In this study, the type of the network is multilayer feedforward back-propagation, which consists of an input layer, hidden layer(s), and an output layer (Jain et al. 1996; MathWorks). The ANN architecture is determined through an iterative process. The number of hidden layers is chosen as one layer with ten neurons. The number of neurons in the hidden layer was tested across the range 7 to 12, but it was ultimately set up at ten based on the performance of the model in terms of Mean Squared Error (MSE). The training algorithm that is used for this study is Levenberg–Marquardt (Levenberg 1944; Marquardt 1963). This method, which is also known as damped least-squares, has primary application in least-squares curve-fitting problems. Bayesian regularization back-propagation (MacKay 1992; Foresee and Hagan 1997; MathWorks) is used in developing the network to solve the problem of overfitting. In this framework, the weight and bias values based on Levenberg–Marquardt optimization are updated. The transfer function is Sigmoid in the hidden layer and linear in the output layer as default. The input data in the ANN model is standardized by centering the predictor and target values using their mean and standard deviation.

1.2 Ensemble methods (Boosted Trees and Random Forest)

RF and BT are both ensemble methods that use decision trees as the learner algorithm (Breiman 1996, 2001). Modeling choices associated with these two models were selected based on the options that yielded the best performance in terms of smaller MSE. The modeling selections were initially optimized via a Bayesian optimization algorithm (MathWorks). The optimized parameters did not provide the highest accuracy throughout all the analyses performed in this study. However, they were used as a starting point to find the set of parameters that worked the best for different parts of the analysis and when applied to NARCCAP models. Further manual experiments were performed to refine parameter selections.

For the BT model, the following parameters were defined:

• minimum leaf size: 1

• number of variables to sample: 4

• ensemble aggregation method: Least-squares boosting

• number of learning cycles: 100

• learning rate: 0.09.

For the RF model, the following parameters were defined:

• minimum leaf size: 30

• ensemble aggregation method: Bootstrap aggregation

• number of learning cycles: 30.

The BT and RF models do not require data standardization.

1.3 Support Vector Regression

Modeling choices associated with the SVR model were selected based on the options that yielded the best performance in terms of $MSE$. In an SVR model, some of the key factors that can be designated in the modeling process are (1) Kernel function, (2) Kernel scale, and (3) standardization. The Kernel function is selected as Gaussian (radial basis function). The Gaussian Kernel is chosen in the current study because it provided the highest accuracy among other Kernels, including Polynomial and Linear. The Kernel scale is set as “auto” which allows the software (MathWorks 2018) to determine an appropriate value using a heuristic procedure. The SVR model is set up to standardize the data by centering the predictor and target values using their mean and standard deviation.

As a sensitivity case, a series of analyses were performed in which the SVR modeling selections were optimized via a Bayesian optimization algorithm. However, the computational expense was significantly higher for the optimized model but did not always result in better performance (in terms of $MSE$). For this reason, the non-optimized model was selected and used.