Deep-learning based climate downscaling using the super-resolution method : a 2 case study over the western US

4 Xingying Huang1* 5 6 1Earth Research Institute, University of California Santa Barbara, Santa Barbara, 93106, USA 7 *Correspondence to: Xingying Huang (xingyhuang@gmail.com) 8 9 10 Abstract. Demand for high-resolution climate information is growing rapidly to fulfill the needs of both scientists 11 and stakeholders. However, deriving high-quality fine-resolution information is still challenging due to either the 12 complexity of a dynamical climate model or the uncertainty of an empirical statistical model. In this work, a new 13 downscaling framework is developed using the deep-learning based super-resolution method to generate very high14 resolution output from coarse-resolution input. The modeling framework has been trained, tested, and validated for 15 generating high-resolution (here, 4 km) climate data focusing on temperature and precipitation at daily scale from the 16 year 1981 to 2010. This newly designed downscaling framework is composed of multiple convolutional layers 17 involving batch normalization, rectification-linear unit, and skip connection strategies, with different loss functions 18 explored. The overall logic for this modeling framework is to learn optimal parameters from the training data for later19 on prediction applications. This new method and framework are found to largely reduce the time and computation 20 cost (~23 milliseconds for one-day inference) for climate downscaling compared to current downscaling strategies. 21 The strength and limitation of this deep-learning based downscaling have been investigated and evaluated using both 22 fine-scale gridded observations and dynamical downscaling data from regional climate models. The performance of 23 this deep-learning framework is found to be competitive in either generating the spatial details or maintaining the 24 temporal evolutions at a very fine grid-scale. It is promising that this deep-learning based downscaling method can be 25 a powerful and effective way to retrieve fine-scale climate information from other coarse-resolution climate data. 26 When seeking an efficient and affordable way for intensive climate downscaling, an optimized convolution neural 27 network framework like the one explored here could be an alternative option and applied to a broad relevant 28 application. 29

here, $,& ' represents the th filter's output at a location ( , ). When designing a convolution layer, the parameters for 108 stride and padding also need to be specified. The stride value controls the offset of the sliding window when moving 109 to the next sliding. Padding is used to pad extra values (usually set as 0) at the borders to gather enough data for the 110 convolution operation on the entries centered at borders.

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In this framework (Figure 1), stride value of 1 and stride value of 2 are used for different convolutional layers. For the 112 convolutional layer with stride being 1, the spatial domain size of the output is the same with the spatial size of the 113 input. For the convolutional layer with stride set as 2, the spatial size of the output is smaller (around half in each 114 dimension) than that of the input. In deep learning practices, convolutional layers with stride being 2 are used to 115 increase the receptive fields of the convolutional layers. The receptive field is defined as the area where the 116 convolutional filters can influence. Usually, the area where a single convolution filter can influence depends on its 117 kernel size (here, 3x3). The area (or receptive field) is accumulated by using more convolutional layers and having 118 stride be 2 will further accumulate the receptive field. Deep neural networks can be sensitive to the initialized values of the trainable parameters during the training process.

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To reduce such sensitivity, batch normalization layers are used as a common way to stabilize the training, which is 143 used to re-center and rescale the input and has been shown to be effective in improving the training speed, accuracy, The idea of skip connections is to concatenate the outputs from two non-consecutive layers. Previous work shows that 152 skip connections can improve some details for the output (Ronneberger et al. 2015). In this framework, two skip 153 connections (see the stacked layers in Figure 1) are used as seen fit.   In the case of precipitation downscaling, most of the entries are zeros. As a result, using L1 loss is more difficult to 177 converge to an optimal solution than using L2 loss. Therefore, the output trained with L2 loss is used as the prediction 178 for precipitation in this study. While, in the case of temperature downscaling, the input values are continuous without 179 zero values (in the unit of Kelvin). The model using L1 loss has less chance for suffering instability, and L2 loss's 180 derivative is sensitive to the scale of the difference between prediction and ground truth. Therefore, for the temperature 181 downscaling results, the model using L1 loss has a larger chance to converge more efficiently and reach a final optimal 182 solution than L2 loss. As a result, the output trained with L1 loss is used as the prediction for temperature.   The PyTorch framework is used to build deep learning models. To speed up the dataset reading, the training data has 220 been converted to HDF5 database format, which provides a faster query compared to the NetCDF format or other non-221 database files. The total trainable parameter number is ~7,500,000. The training loss curve from the finalized 222 downscaling framework is shown in the supplemental ( Figure S1). Firstly, the prediction performance for the yearly average temperature is shown (Figure 2). It can be seen that the

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Unlike temperature, precipitation is non-continuous and is involved with complex regional features, making it much 292 more difficult to downscale for very high-resolution information from a coarse-resolution input. The intrinsic 293 complication of precipitation downscaling requires a well-trained network. As described in the dataset section, 294 additional relevant supporting data to precipitation downscaling include zonal and meridional winds (U and V), 295 relative humidity (RH), and specific humidity (Q) at 850 hPa vertical level from the input are also used. However, 296 precipitation over the western US is still largely controlled by the complex topography and orographic forcings, which 297 also makes the elevation details the key supporting information to reconstruct the spatial details.

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Firstly, the yearly mean precipitation is investigated ( Figure 5). As observed, the prediction exhibits a similar spatial