Original: Conditioned Spatial Downscaling of Climate Variables
Revised: Conditioned Spatial Downscaling of Climate Variables

Original: Abstract
Revised: Abstract

Original: Global Climate Models (GCM) play a vital role in assessing the large-scale impacts of climate change.
Revised: Global Climate Models (GCM) play a vital role in assessing the large-scale impacts of climate change.

Original: Downscaling methods can translate coarse-resolution climate information from GCM to high-resolution predictions to forecast regional effects.
Revised: Downscaling methods can translate coarse-resolution climate information from GCM to high-resolution predictions to forecast regional effects.

Original: Unfortunately, current downscaling methods struggle to fully take into account spatial relationships among variables, especially at long distances.
Revised: Unfortunately, current downscaling methods struggle to fully take into account spatial relationships among variables, especially at long distances.

Original: In this work, we propose an instance-conditional pixel synthesis generative adversarial network (ICPS-GAN), wherein conditioning on spatial information is an explicit way of providing the GAN with previous high-resolution and current low-resolution data, resulting in an enhancement of the general performance.
Revised: In this work, we propose an instance-conditional pixel synthesis generative adversarial network (ICPS-GAN), wherein conditioning on spatial information is an explicit way of providing the GAN with previous high-resolution and current low-resolution data, resulting in an enhancement of the general performance.

Original: Experimental results on precipitation forecast for US region data outperform both traditional and other learning-based methods when extrapolating in space.
Revised: Experimental results on precipitation forecast for US region data outperform both traditional and other learning-based methods when extrapolating in space.

Revised: The code is available at https://github.com/evbecker/climate-spatial-downscaling

Original:  Introduction
Revised:  Introduction

Original: Climate change has immense impacts on people’s lives and ecosystems across the world and with the exacerbation of global warming, there are more severe weather conditions now than ever before 
Revised: Climate change has immense impacts on people’s lives and ecosystems across the world, and with the exacerbation of global warming, there are more severe weather conditions now than ever before (Nicholls & Cazenave, 2010;

Original: Nicholls & Cazenave (2010); Villén-Peréz et al. ; Wang et al. Giorgi et al.
Revised: Villén-Peréz et al., 2020; Wang et al., 2020; Giorgi et al., 2019).

Original: Correctly predicting climate change can save people a lot of time, money, resources and even lives Chakraborty et al. ; Guo et al. (2018), as people will be able to take necessary precautions before some unexpected conditions based on the prediction.
Revised: Correctly predicting climate change can save people a lot of time, money, resources and even lives (Chakraborty et al., 2000; Guo et al., 2018), as people will be able to take necessary precautions before some unexpected conditions based on the prediction.

Original: However, predicting such changes in the climate is not an easy task to do.
Revised: However, predicting such changes in the climate is not an easy task to do.

Original: In recent years, researchers have been trying to apply learning-based methods to climate problems Ardabili et al. ; Kareem et al. (2021), since deep learning-based approaches are known to be good at discovering  underlying patterns and making more reliable predictions.
Revised: In recent years, researchers have attempted to apply learning-based methods to climate problems (Ardabili et al., 2019; Kareem et al., 2021), since deep learning-based approaches are known for discovering complex underlying patterns.

Original: Global Climate Models (GCMs) are decent in providing information about climate information of the Earth, and predictions based on these models have been applied in many areas, including Earth Science, engineering, economy, and risk analysis Groenke et al.
Revised: Global Climate Models (GCMs) are effective in predicting general climate conditions, and estimates based on these models have been applied in many fields, including Earth Science, engineering, economics, and risk analysis (Groenke et al., 2020).

Original: However, GCMs usually operate at a lower resolution, having a limited ability to provide regional or fine-detailed predictions, even though they are useful in analyzing the general trend globally.
Revised: However, GCMs usually operate at a lower resolution, having a limited ability to provide regional or fine-detailed predictions, even though they are useful in analyzing the general trend globally.

Original: Moreover, there are more large-scale, lower-resolution data available than lower-scale, higher-resolution data, which makes building high-resolution models more difficult.
Revised: Moreover, there are more large-scale, lower-resolution data available than lower-scale, higher-resolution data, which makes building high- resolution models more difficult.

Original: Therefore, generating higher resolution climate projections is important for precise local climate analysis.
Revised: Therefore, generating higher resolution climate projections is important for precise local climate analysis.

Original: Statistical downscaling is the process of using some global information to make local predictions.
Revised: Statistical downscaling is the process of using some global information to make local predictions.

Original: Since global climate data is easier to access, statistical downscaling is a good way to make use of the low-resolution data for high-resolution climate predictions.
Revised: Since global climate data is easier to access, statistical downscaling is a good way to make use of the low-resolution data for high-resolution climate predictions.

Original: The statistical downscaling builds the relationship between the local climate variables and global predictors and uses such a relationship to make future predictions of the local climate variables based on the global predictors Hoar & Nychka (2008).
Revised: The statistical downscaling builds the relationship between the local climate variables and global predictors and uses such a relationship to make future predictions of the local climate variables based on the global predictors (Hoar & Nychka, 2008).

Original: In this work, we build a generative deep statistical downscaling model for local climate variable predictions.
Revised: In this work, we build a generative deep statistical downscaling model for local climate variable predictions.

Revised: Our contributions are as follows:

Revised: We propose a type of instance-conditional generative adversarial network (GAN) that addresses the issue of long range spatial dependencies by explicitly conditioning on location data and previous time-steps high-resolution images.

Revised: We characterize this model’s performance on downscaling tasks between real-world US precipitation models at different resolutions, and demonstrate its improvement over standard methods.

Original:  Problem Statement
Revised:  Problem Statement

Original: Many current statistical downscaling methods formulate the downscaling problem as finding some direct mapping function from low resolution to high resolution data (e.g. some pointwise regression).
Revised: Many current statistical downscaling methods formulate the downscaling problem as finding some direct mapping function from low resolution to high resolution data (e.g. some pointwise regression).

Original: The caveat with such methods is that they lack any underlying distribution in the high resolution space (which can be helpful for computing uncertainties associated with downscaled predictions).
Revised: The caveat with such methods is that they lack any underlying distribution in the high resolution space (which can be helpful for computing uncertainties associated with downscaled predictions).

Original: Instead, we pose the super-resolution task as a problem of finding conditional distributions.
Revised: Instead, we pose the super-resolution task as a problem of finding conditional distributions.

Original: Let I ( t ) HR ∈ R ( H × W × C ) and I ( t ) LR ∈ R ( H × W × C ) be a sequence of random variables representing high-resolution (HR) and low-resolution (LR) images, respectively.
Revised: Let I ( t ) HR ∈ R ( H × W × C ) and I ( t ) LR ∈ R ( H × W × C ) be a sequence of random variables representing high-resolution (HR) and low-resolution (LR) images, respectively with height H , width W and depth C .

Original: By images, we mean one or more channels of weather data at set latitudes and longitudes (x,y) for various time steps t ∈ T .
Revised: Each image consists of one or more channels of weather data at set latitudes and longitudes (x,y) for various time steps t ∈ T .

Original: Our goal is to learn a generator that has the following mapping:
Revised: Our goal is to learn a generator that has the following mapping:

Original: [Equation]
Revised: [Equation]

Original: Here, z is some latent variable following a tractable distribution.
Revised: Here, z is some latent variable following a tractable distribution (e.g. normal).

Original: In this paper, the objective is to estimate  I ( t ) HR given an I ( t ′ ) HRand I ( t ) LR for  t ′ < t where t ′ ̸ = t .
Revised: In this paper, the objective is to estimate the high resolution image I ( t ) HR given a previous high resolution image ( I ( t ′ ) HR for some t ′ < t ) and a current low resolution image ( I ( t ) LR ).

Original: The following tuple is the training input ( I ( t ) HR , I ( t ′ ) HR , I ( t ) LR ) .
Revised: The following tuple is the training input ( I ( t ) HR , I ( t ′ ) HR , I ( t ) LR ) .

Original: For inference, the model has access to I ( t ) LR to make the prediction where that particular t has not been part of the training.
Revised: For inference, the model has access to I ( t ) LR to make the prediction where that particular time-step has not been part of the training.

Original: The metrics that will be utilized to assess model performance over the evaluation period and quantify the representation of mean properties will be based on those reported for the VALUE baseline ensemble Widmann et al. (2019) such as root mean square error (RMSE) and Pearson correlation.
Revised: The metrics that will be utilized to assess model performance over the evaluation period and quantify the representation of mean properties will be based on those reported for the VALUE baseline ensemble (Widmann et al., 2019) such as root mean square error (RMSE) and Pearson correlation.

Original:  Related Works 3.1 Traditional Methods
Revised:  Related Works 3.1 Traditional Methods

Original: In traditional methods, the spatial structure of daily values for climate impacts is an important factor to consider.
Revised: In traditional methods, the spatial structure of daily values for climate impacts is an important factor to consider.

Original: Easterling (1999); Kettle & Thompson (2004);
Revised: Easterling (1999); Kettle & Thompson (2004);

Original: Huth et al.
Revised: Huth et al.

Original: (2008) discuss the correlations between time series at different spatial locations via Perfect Prog (PP) methods and find that large-scale predictors tend to overestimate spatial correlations, while more local methods underestimate them.
Revised: (2008) discuss the correlations between time series at different spatial locations via Perfect Prog (PP) methods and find that large-scale predictors tend to overestimate spatial correlations, while more local methods underestimate them.

Original: PP methods work the well in general, but the performance drops in summer and winter Ayar et al.
Revised: PP methods work the well in general, but the performance drops in summer and winter Ayar et al.

Original: ; Huth et al.
Revised: ; Huth et al.

Original: In addition, stochastic PP methods are useful when they explicitly model spatial structures.
Revised: In addition, stochastic PP methods are useful when they explicitly model spatial structures.

Original: Cannon (2008); Wilks (2012); Hu et al.
Revised: Cannon (2008); Wilks (2012); Hu et al.

Original: (2013) find that both
Revised: (2013) find that both

Original: Nonhomogeneous Hidden Markov Models (NHMMs) and Generalized Linear Models (GLMs) are likely to underestimate the correlation, while NHMMs are better under certain circumstances.
Revised: Nonhomogeneous Hidden Markov Models (NHMMs) and Generalized Linear Models (GLMs) are likely to underestimate the correlation, while NHMMs are better under certain circumstances.

Original: Analog methods search for historical data to match the current or forecast local variables such as precipitation over an area to similar times in the past.
Revised: Analog methods search for historical data to match the current or forecast local variables such as precipitation over an area to similar times in the past.

Original: Pierce et al.
Revised: Pierce et al.

Original: (2014) performs the statistical downscaling using Localized Constructed Analogs (LOCA).
Revised: (2014) performs the statistical downscaling using Localized Constructed Analogs (LOCA).

Original: Gutmann et al.
Revised: Gutmann et al.

Original: (2014) compare several analog methods, and most methods overestimate the spatial correlation, except for the method combining bias correction for monthly fields and spatial disaggregation (BCSDm).
Revised: (2014) compare several analog methods, and most methods overestimate the spatial correlation, except for the method combining bias correction for monthly fields and spatial disaggregation (BCSDm).

Original: They think the reason why BCSDm does not overestimate the spatial correlation is that the method inherits the spatial variability from the observations, rather than from the driving model.
Revised: They think the reason why BCSDm does not overestimate the spatial correlation is that the method inherits the spatial variability from the observations, rather than from the driving model.

Original: 3.2 Learning-based Methods
Revised: 3.2 Learning-based Methods

Original: Methods based on deep learning have also been used to solve statistical downscaling.
Revised: Methods based on deep learning have also been used to solve statistical downscaling.

Original: Sun & Lan (2021) use a simple Convolutional Neural Network (CNN) to predict the daily temperature and precipitation in China.
Revised: Sun & Lan (2021) use a simple Convolutional Neural Network (CNN) to predict the daily temperature and precipitation in China.

Original: Babaousmail et al.
Revised: Babaousmail et al.

Original: (2021) apply a convolutional autoencoder on data from
Revised: (2021) apply a convolutional autoencoder on data from

Original: North Africa where the low-resolution global data is the input and the high-resolution regional data is the output.
Revised: North Africa where the low-resolution global data is the input and the high-resolution regional data is the output.

Original: Misra et al.
Revised: Misra et al.

Original: (2018) propose a Recurrent Neural Network (RNN) model with Long
Revised: (2018) propose a Recurrent Neural Network (RNN) model with Long

Original: Short-Term Memory (LSTM) to capture the spatial and temporal dependencies in local rainfall.
Revised: Short-Term Memory (LSTM) to capture the spatial and temporal dependencies in local rainfall.

Original: The study tests their model on two datasets: precipitation in the Mahanadi basin in India and precipitation in the Campbell River basin in Canada, instead of the GCMs.
Revised: The study tests their model on two datasets: precipitation in the Mahanadi basin in India and precipitation in the Campbell River basin in Canada, instead of the GCMs.

Original: Sekiyama (2020) treat the climate data statistical downscaling problem as a single-image super-resolution (SR) problem.
Revised: Sekiyama (2020) treat the climate data statistical downscaling problem as a single-image super-resolution (SR) problem.

Original: Statistical downscaling algorithms that are based on deep learning have been shown to have better empirical accuracy than traditional methods, but they are mostly like black box Jebeile et al.
Revised: Statistical downscaling algorithms that are based on deep learning have been shown to have better empirical accuracy than traditional methods, but they are mostly like black box (Jebeile et al., 2021).

Original: Accarino et al.
Revised: Accarino et al.

Original: (2021) uses a multi-scale Generative Adversarial Network (GAN) to downscale temperature fields and Chaudhuri & Robertson (2020) proposes CliGAN, a Wasserstein GAN that is used to downscale large-scale annual maximum precipitation given by simulation of multiple atmosphere-ocean global climate models.
Revised: (2021) uses a multi-scale Generative Adversarial Network (GAN) to downscale temperature fields and Chaudhuri & Robertson (2020) proposes CliGAN, a Wasserstein GAN that is used to downscale large-scale annual maximum precipitation given by simulation of multiple atmosphere-ocean global climate models.

Original: Leinonen et al.
Revised: Leinonen et al.

Original: (2020) develops a recurrent, stochastic super-resolution GAN that can generate ensembles of time-evolving high-resolution atmospheric fields given an input sequence of low-resolution images of the same field.
Revised: (2020) develops a recurrent, stochastic super-resolution GAN that can generate ensembles of time-evolving high-resolution atmospheric fields given an input sequence of low-resolution images of the same field.

Original: Vaughan et al.
Revised: Vaughan et al.

Original: encodes the low-resolution predictor to a latent variable and retrieves the local climate variable as a query of longitude, latitude, and elevation via the latent neural process utilizing ConvLNP Vaughan et al.
Revised: encodes the low-resolution predictor to a latent variable and retrieves the local climate variable as a query of longitude, latitude, and elevation via the latent neural process utilizing ConvLNP (Vaughan et al., 2022).

Original: In terms of generative model-based Super Resolution (SR) algorithms, Ledig et al.
Revised: In terms of generative model-based Super Resolution (SR) algorithms, Ledig et al.

Original: (2017) proposes
Revised: (2017) proposes

Original: SRGAN which is a GAN-based network optimized for a new perceptual loss.
Revised: SRGAN which is a GAN-based network optimized for a new perceptual loss.

Original: ESRGAN Wang et al. (2018) includes a Residual-in-Residual Dense Block (RRDB) to combine multi-level residual networks and dense connections.
Revised: ESRGAN (Wang et al., 2018) includes a Residual-in-Residual Dense Block (RRDB) to combine multi-level residual networks and dense connections.

Original: ESRGAN+ Rakotonirina & Rasoanaivo (2020) adds Gaussian noise vectors to ESRGAN after each residual along with a learned scaling factor.
Revised: ESRGAN+ (Rakotonirina & Rasoanaivo, 2020) adds Gaussian noise vectors to ESRGAN after each residual along with a learned scaling factor.

Original: In GLEAN Chan et al. (2021), to make the model more expressive, each block of the generator takes in a latent vector while also being conditioned on the output of the encoder.
Revised: In GLEAN (Chan et al., 2021), to make the model more expressive, each block of the generator takes in a latent vector while also being conditioned on the output of the encoder.

Original: Hyun & Heo (2020) proposes VarSR-Net, which is a variational inference-base SR algorithm.
Revised: Hyun & Heo (2020) proposes VarSR-Net, which is a variational inference-base SR algorithm.

Original: Lugmayr et al.
Revised: Lugmayr et al.

Original: (2020) proposes SRFlow and uses normalizing flow models for the SR problem.
Revised: (2020) proposes SRFlow and uses normalizing flow models for the SR problem.

Original: Based on SRFlow, Jo et al.
Revised: Based on SRFlow, Jo et al.

Original: (2021) include more convolutional layers to have a large receptive field in a single flow step for better results.
Revised: (2021) include more convolutional layers to have a large receptive field in a single flow step for better results.

Original:  Method 4.1 Pixel Synthesis
Revised:  Method 4.1 Pixel Synthesis

Original: Inspired by the recent work of He et al.
Revised: Inspired by the recent work of He et al.

Original: ; Anokhin et al.
Revised: ; Anokhin et al.

Original: (2020), we leverage the conditionally independent pixel synthesis generator architecture whose generative model computes climate values at individual locations, independent of others, given a random noise vector, low-resolution weather embedding, and positional embedding of its coordinates in time and space.
Revised: (2020), we leverage the conditionally independent pixel synthesis generator architecture whose generative model computes climate values at individual locations, independent of others, given a random noise vector, low-resolution weather embedding, and positional embedding of its coordinates in time and space.

Original: In addition to the latitude, longitude, and time used by He et al. (2015) to generate RGB satellite images, we also encode elevation information.
Revised: In addition to the latitude, longitude, and time used by He et al. (2015) to generate RGB satellite images, we also encode elevation information.

Original: Elevation is an important spatial feature that should allow the model to interpolate weather data more accurately across mountainous terrain.
Revised: Elevation is an important spatial feature that should allow the model to interpolate weather data more accurately across mountainous terrain.

Original: To be specific, we encode the latitude, longitude, elevation, and time stamp through a learnable embedding function f γ , parameterized by γ , s.t.[Equation]
Revised: To be specific, we encode the latitude, longitude, elevation, and time stamp through a learnable embedding function f γ , parameterized by γ , s.t.

Original: [Equation]
Revised: [Equation]

Original: where v is the embedded positional feature, x , y , h and t is the latitude, longitude, elevation, and time stamp respectively.
Revised: where v is the embedded positional feature, x , y , h and t is the latitude, longitude, elevation, and time stamp respectively.

Original: There is also a function f θ , which takes in a low-resolution image at the current time step and a high-resolution image from the previous time step and outputs the encoded image features m :
Revised: There is also a function f θ , which takes in a low-resolution image at the current time step and a high-resolution image from the previous time step and outputs the encoded image features m :

Original: [Equation]
Revised: [Equation]

Original: where I ( t ) lr is the low-resolution image at time t
Revised: where I ( t ) lr is the low-resolution image at time t

Original: and I ( t ′ ) hr is the high-resolution image at time t ′ .
Revised: and I ( t ′ ) hr is the high-resolution image at time t ′ .

Original: The generator G takes in the encoded image feature m , positional feature v , and a noise vector z to generate the predicted high-resolution image I ′ hr ( t ) :
Revised: The generator G takes in the encoded image feature m , positional feature v , and a noise vector z to generate the predicted high-resolution image I ′ hr ( t ) :

Original: [Equation]
Revised: [Equation]

Original: where X = ( x, y, h, t ) .
Revised: where X = ( x, y, h, t ) .

Original: 4.2 Instance-Conditioned Loss Function
Revised: 4.2 Instance-Conditioned Loss Function

Original: In the given work, we propose an instance-conditional pixel synthesis generative adversarial network (ICPS-GAN) where we utilize the super-resolution architecture via conditional pixel synthesis He et al. but with an alteration to its loss function.
Revised: In the given work, we propose an instance-conditional pixel synthesis generative adversarial network (ICPS-GAN) where we utilize the super-resolution architecture via conditional pixel synthesis (He et al., 2021) but with an alteration to its loss function.

Original: Instead of training the generator with a combination of the conditional GAN loss with L0 loss, we use Instance-Conditioned GAN (IC-GAN) Casanova et al.
Revised: Instead of training the generator with a combination of the conditional GAN loss with L0 loss, we use Instance-Conditioned GAN (IC-GAN) (Casanova et al., 2021):

Original: [Equation]
Revised: [Equation]

Original: where X in equation 6 is the temporal-spatial coordinate grid ( x, y, h, t ) , while G and D in equation 5 and 6 represent the Generative and Discriminator networks respectively, and z ∈ R z is the noise vector.
Revised: where X in equation 6 is the temporal-spatial coordinate grid ( x, y, h, t ) , while G and D in equation 5 and 6 represent the Generative and Discriminator networks respectively, and z ∈ R z is the noise vector.

Original: The main objective of the IC-GAN is to learn the distribution around each datapoint.
Revised: The main objective of the IC-GAN is to learn the distribution around each datapoint.

Original: Essentially, leveraging the overlapping clusters in the data manifold where each cluster is represented by a datapoint or an instance x i .
Revised: Essentially, leveraging the overlapping clusters in the data manifold where each cluster is represented by a datapoint or an instance x i .

Original: The underlying distribution p ( x ) of the data will be a mixture of conditional distributions p ( x | f ( x i )) where f is an embedding function for each instance.
Revised: The underlying distribution p ( x ) of the data will be a mixture of conditional distributions p ( x | f ( x i )) where f is an embedding function for each instance.

Original: While the original work pre-trains this embedding function on either classification or self-supervised learning tasks, we chose to incorporate this training directly into the generator updates, with the hypothesis that we will still learn encodings useful for clustering low-resolution inputs.
Revised: While the original work pre-trains this embedding function on either classification or self-supervised learning tasks, we chose to incorporate this training directly into the generator updates, with the hypothesis that we will still learn encodings useful for clustering low-resolution inputs.

Original:  Datasets
Revised:  Datasets

Original: We train and evaluate our downscaling method on daily weather data from a custom combination of ERA-iterim, CPC, and WRF datasets.
Revised: We train and evaluate our downscaling method on daily weather data from a custom combination of ERA-iterim, CPC, and WRF datasets.

Original: Our base datasets all overlap temporally for a period ofyears (2000-2006), giving us a minimum of 2,282-time samples for each type of measurement, while
Revised: Our base datasets all overlap temporally for a period ofyears (2000-2006), giving us a minimum of 2,282-time samples for each type of measurement, while

Original: ERA-iterim and CPC overlap temporally from 2000 to 2018.
Revised: ERA-iterim and CPC overlap temporally from 2000 to 2018.

Original: At each time point, measurements for a single variable will consist of a 2D image whose pixels correspond to a specific latitude and longitude coordinate pair within the United States.
Revised: At each time point, measurements for a single variable will consist of a 2D image whose pixels correspond to a specific latitude and longitude coordinate pair within the United States.

Original: For this work, we focus on daily accumulated precipitation, measured in millimeters (mm), which provides the opportunity for our model to capture complex long-range spatial and temporal dependencies across the data.
Revised: For this work, we focus on daily accumulated precipitation, measured in millimeters (mm), which provides the opportunity for our model to capture complex long-range spatial and temporal dependencies across the data.

Original: The low-resolution ERA-iterim dataset has a native resolution of approximately 0 .
Revised: The low-resolution ERA-iterim dataset has a native resolution of approximately 0 .

Original: 75 × 0 .
Revised: 75 × 0 .

Original: 75 degrees and contains global hourly measurements for weather variables such as temperature, pressure, and precipitation Berrisford et al.
Revised: 75 degrees and contains global hourly measurements for weather variables such as temperature, pressure, and precipitation (Berrisford et al., 2011).

Original: The higher resolution CPC US Unified Precipitation data is provided by NOAA.
Revised: The higher resolution CPC US Unified Precipitation data is provided by NOAA.

Original: Resolution is 0 .
Revised: Resolution is 0 .

Original: 25 × 0 .
Revised: 25 × 0 .

Original: 25 degrees and spans the continental United States (CONUS).The WRF dataset contains very high resolution data at approximately 132 × 132 degrees. Rasmussen & Liu (2017).
Revised: 25 degrees and spans the continental United States (CONUS).The WRF dataset contains very high resolution data at approximately 132 × 132 degrees (Rasmussen & Liu, 2017).

Original: Total precipitation (mm) is recorded at hourly intervals and preprocessed into daily intervals.
Revised: Total precipitation (mm) is recorded at hourly intervals and preprocessed into daily intervals.

Original: Additionally, data is stored not in a regular latitude and longitude grid but in a projected Lambert Conformal grid.
Revised: Additionally, data is stored not in a regular latitude and longitude grid but in a projected Lambert Conformal grid.

Original: As shown in figure 1, we crop five different 10 × 10 degree squares across the United States to create climate "images" that we can then feed into our network.
Revised: As shown in figure 1, we crop five different 10 × 10 degree squares across the United States to create climate "images" that we can then feed into our network.

Original: We discuss the train and test splits of these images later in the section 6.2.
Revised: We discuss the train and test splits of these images later in the section 6.2.

Original: We hope that aligning these three datasets at different resolutions will provide a flexible and reusable benchmarkfor future research.
Revised: We hope that aligning these three datasets at different resolutions will provide a flexible and reusable benchmark

Original: Additional prepossessing and feature descriptions are provided in the appendix section A.1.

Original:  Experiments and Results 6.1 Baseline Methods
Revised:  Experiments and Results 6.1 Baseline Methods

Original: BCSD For the bias correction and spatial disaggregation (BCSD) baseline, the quantile mapping from the low-resolution to high-resolution data is fit for each day using the training data.
Revised: BCSD For the bias correction and spatial disaggregation (BCSD) baseline, the quantile mapping from the low-resolution to high-resolution data is fit for each day using the training data.

Original: In Figure 2, for a fixed longitude and latitude, the precipitation is projected for the year 2005, demonstrated in orange, where the model was trained on the data represented in blue from the previous year.
Revised: In Figure 2, for a fixed longitude and latitude, the precipitation is projected for the year 2005, demonstrated in orange, where the model was trained on the data represented in blue from the previous year.

Original: Vanilla Autoencoder For the Vanilla Autoencoder (Vanilla AE), we follow the network architecture described below.
Revised: Vanilla Autoencoder For the Vanilla Autoencoder (Vanilla AE), we follow the network architecture described below.

Original: The encoder side consists of 3 layers, where each layer has two 3 × 3 convolutional layers.
Revised: The encoder side consists of 3 layers, where each layer has two 3 × 3 convolutional layers.

Original: Each convolutional layer is followed by a Leaky Rectified Linear Unit (ReLU) and batch normalization.
Revised: Each convolutional layer is followed by a Leaky Rectified Linear Unit (ReLU) and batch normalization.

Original: At the end of each layer, we downsample the feature map by max pooling.
Revised: At the end of each layer, we downsample the feature map by max pooling.

Original: There are 16, 32, and 64 filters in convolutional layers in each of the three layers, respectively.
Revised: There are 16, 32, and 64 filters in convolutional layers in each of the three layers, respectively.

Original: The decoder follows the opposite structure except that at the beginning of each layer, we upsample the feature map by bilinear interpolation.
Revised: The decoder follows the opposite structure except that at the beginning of each layer, we upsample the feature map by bilinear interpolation.

Original: Naive Version of EAD In this baseline approach, we implemented a naive version of EAD He et al. (2021), where we use the same architecture as the generator of the GAN but without the noise vector, coordinates, high-resolution image from the previous time step, and the discriminator.
Revised: Naive Version of EAD In this baseline approach, we implemented a naive version of EAD (He et al., 2021), where we use the same architecture as the generator of the GAN but without the noise vector, coordinates, high-resolution image from the previous time step, and the discriminator.

Original: Therefore, the naive version of EAD (Naive EAD) is some form of the deterministic autoencoder.
Revised: Therefore, the naive version of EAD (Naive EAD) is some form of the deterministic autoencoder.

Original: EAD For the last baseline comparison, we re-implement the EAD method by He et al.
Revised: EAD For the last baseline comparison, we re-implement the EAD method by He et al.

Original: (2021), where it takes in the spatial coordinate as well as the time stamp as an input to the network, which allows it to locate the exact spatial and temporal information of the given image.
Revised: (2021), where it takes in the spatial coordinate as well as the time stamp as an input to the network, which allows it to locate the exact spatial and temporal information of the given image.

Original: 6.2 Implementation Details
Revised: 6.2 Implementation Details

Original: For the experiments in this section, we held out the data from Northwestern, Northeastern, Southwestern, and Southeastern from 2001 as the validation set and the ones from the Midwest from the years 2001 to 2007 as a separate test of an unseen region.
Revised: For the experiments in this section, we held out the data from Northwestern, Northeastern, Southwestern, and Southeastern from 2001 as the validation set and the ones from the Midwest from the years 2001 to 2007 as a separate test of an unseen region.

Original: Due to computational limitations, the networks in this work were trained on the data from the 4 regions (Northwestern, Northeastern, Southwestern, and
Revised: Due to computational limitations, the networks in this work were trained on the data from the 4 regions (Northwestern, Northeastern, Southwestern, and

Original: Southeastern) from 2000 to 2007.
Revised: Southeastern) from 2000 to 2007.

Original: In Section 6.7, the networks used in the experiments were trained on the data from those 4 regions from 2000 to 2018.
Revised: In Section 6.7, the networks used in the experiments were trained on the data from those 4 regions from 2000 to 2018.

Original: In Section 6.5, the training was only done inregion (Northeastern) from 2002 to 2007.
Revised: In Section 6.5, the training was only done inregion (Northeastern) from 2002 to 2007.

Original: In Section 6.8, we used the CPC data as the low-resolution data with the WRF data as the high-resolution data where we resized the images to 160 × 160 , while in all the other sections in the experiments, we used ERA data as the low-resolution data and CPC data as the high-resolution data where we resized the images to 40 × 40 .
Revised: In Section 6.8, we used the CPC data as the low-resolution data with the WRF data as the high-resolution data where we resized the images to 160 × 160 , while in all the other sections in the experiments, we used ERA data as the low-resolution data and CPC data as the high-resolution data where we resized the images to 40 × 40 .

Original: For a fair comparison, the training objective for both of the deterministic methods is L1 loss.
Revised: For a fair comparison, the training objective for both of the deterministic methods is L1 loss.

Original: For the GAN-based methods, we set λ = 0 .
Revised: For the GAN-based methods, we set λ = 0 .

Original: 2 , since this is the optimal value we observe on the validation set, which is in line with the results in Section 6.5 on the test set.
Revised: 2 , since this is the optimal value we observe on the validation set, which is in line with the results in Section 6.5 on the test set.

Original: 6.3 Baseline Comparison
Revised: 6.3 Baseline Comparison

Original: The baseline quantitative comparison of the held out region can be found in Table 1.
Revised: The baseline quantitative comparison of the held out region can be found in Table 1.

Original: Our method outperforms the other methods quantitatively.
Revised: Our method outperforms the other methods quantitatively.

Original: We believe this is because our method can generalize better to the unseen region with the longitude, latitude, and elevation information.
Revised: We believe this is because our method can generalize better to the unseen region with the longitude, latitude and elevation information.

Original: The qualitative results are shown in Fig.
Revised: The qualitative results are shown in Fig.

Original: 3, where the deterministic methods fail to generate anything meaningful.
Revised: 3, where the deterministic methods fail to generate anything meaningful.

Revised: [Table]

Original: 6.4 Ablation Study
Revised: 6.4 Ablation Study

Original: We also performed an ablation study on the unseen region, which is shown in Table 2.
Revised: We also performed an ablation study on the unseen region, which is shown in Table 2.

Original: It can be observed that adding both the elevation data and conditioning the GAN on the instance improves the performance of the model while using both improves the performance the most.
Revised: It can be observed that adding both the elevation data and conditioning the GAN on the instance improves the performance of the model while using both improves the performance the most.

Original: Adding the elevation information to the network is more useful for unseen regions as it improves the Pearson Correlation[Table] by a significant factor while for unseen years the improvement is marginal.
Revised: Adding the elevation information to the network is more useful for unseen regions as it improves the Pearson Correlation by a significant factor, while for unseen years the improvement is marginal.

Original: We conclude that if the network has seen the region during training, it is more likely to implicitly figure out the elevation of the region to some extent since the longitude and latitude are explicitly given.
Revised: We conclude that if the network has seen the region during training, it is more likely to implicitly figure out the elevation of the region to some extent since the longitude and latitude are explicitly given.

Original: Therefore, explicitly telling the network the elevation information allows the network to learn the correlation between precipitation and elevation, which is shown to be useful for unseen regions.
Revised: Therefore, explicitly telling the network the elevation information allows the network to learn the correlation between precipitation and elevation, which is shown to be useful for unseen regions.

Original: Conditioning the GAN on the instance is a more direct way of giving the GAN information about the current low-resolution data and previous high-resolution data compared with normal GAN and it is shown to be an effective way of improving the general performance. 
Revised: Conditioning the GAN on the instance is a more direct way of giving the GAN information about the current low-resolution data and previous high-resolution data compared with normal GAN, and it is shown to be an effective way of improving the general performance. [Table]

Original: 6.5 Analysis on the Hyperparameter λ
Revised: 6.5 Analysis on the Hyperparameter λ

Original: We additionally analyze the effect of the hyperparameter λ in the loss function on the results.
Revised: We additionally analyze the effect of the hyperparameter λ in the loss function on the results.

Original: The λ parameter controls how much the GAN loss term L ( IC − GAN )( G,D ) and L1 loss term L L 1 ( G ) contribute to the total loss.
Revised: The λ parameter controls how much the GAN loss term L ( IC − GAN )( G,D ) and L1 loss term L L 1 ( G ) contribute to the total loss.

Original: We want to investigate how this parameter can impact the final results.[Table]
Revised: We want to investigate how this parameter can impact the final results.

Original: (from the set of 25 points in the

Original: L ( IC − GAN )( G,D ) indicates how much the generated images look like the real images, while L L 1 ( G ) determines how well the prediction is.
Revised: L ( IC − GAN )( G,D ) indicates how much the generated images look like the real images, while L L 1 ( G ) determines how well the prediction is.

Original: We conducted the same experiment 10 times where we set λ as 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10 during each trial.
Revised: We conducted the same experiment 10 times where we set λ as 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10 during each trial.

Original: The results are shown in Table 3, where we can observe that the best results occur when λ = 0 .
Revised: The results are shown in Table 3, where we can observe that the best results occur when λ = 0 .

Original: [Table]
Revised: [Table]

Original: λ = 0 .2 .
Revised: λ = 0 .2 .

Original: 91 ± 3 .0 .
Revised: 91 ± 3 .0 .

Original: 260 ± 0 .λ = 0 .2 .
Revised: 260 ± 0 .λ = 0 .2 .

Original: 94 ± 3 .0 .
Revised: 94 ± 3 .0 .

Original: 258 ± 0 .λ = 0 .2 .
Revised: 258 ± 0 .λ = 0 .2 .

Original: 94 ± 3 .0 .
Revised: 94 ± 3 .0 .

Original: 272 ± 0 .λ = 0 .3 .
Revised: 272 ± 0 .λ = 0 .3 .

Original: 03 ± 2 .0 .
Revised: 03 ± 2 .0 .

Original: 213 ± 0 .λ = 0 .3 .
Revised: 213 ± 0 .λ = 0 .3 .

Original: 04 ± 2 .0 .
Revised: 04 ± 2 .0 .

Original: 274 ± 0 .λ = 0 .2 .
Revised: 274 ± 0 .λ = 0 .2 .

Original: 93 ± 2 .0 .
Revised: 93 ± 2 .0 .

Original: 284 ± 0 .λ =
Revised: 284 ± 0 .λ =

Original: [Table]
Revised: [Table]

Original: 6.6 Analysis of Conditional Image Encodings
Revised: 6.6 Analysis of Conditional Image Encodings

Original: As discussed in section 4.2, our embedding function differs from Casanova et al.
Revised: As discussed in section 4.2, our embedding function differs from Casanova et al.

Original: (2021) in that it is not pretrained on a classification task.
Revised: (2021) in that it is not pretrained on a classification task.

Original: We ensure that our embedding still learns some representation useful for clustering by doing principal component analysis (PCA) on the encoded conditioning images.
Revised: We ensure that our embedding still learns some representation useful for clustering by doing principal component analysis (PCA) on the encoded conditioning images.

Original: By examining figures 5 and 6, it’s clear that our embedding contains information about the type of weather and region that a coordinate is experiencing.
Revised: By examining figures 5 and 6, it’s clear that our embedding contains information about the type of weather and region that a coordinate is experiencing.

Original: Expert domain knowledge would most likely be needed to understand whether the encoding is capturing more complex class information such as weather events (e.g. thunderstorms, blizzards, hurricanes).
Revised: Expert domain knowledge would most likely be needed to understand whether the encoding is capturing more complex class information such as weather events (e.g. thunderstorms, blizzards, hurricanes).

Original: 6.7 Results on the Full Dataset
Revised: 6.7 Results on the Full Dataset

Original: The results from the model trained on the full dataset are shown in Table 4.
Revised: The results from the model trained on the full dataset are shown in Table 4.

Original: However, we observe that the results are worse than the ones from the model trained on the data from 2002–2007.
Revised: However, we observe that the results are worse than the ones from the model trained on the data from 2002–2007.

Original: We hypothesize that this is because the data distribution of later years is more different than that of the early years compared to the test set, as the test set for the unseen region is from 2001 to 2007.
Revised: We hypothesize that this is because the data distribution of later years is more different than that of the early years compared to the test set, as the test set for the unseen region is from 2001 to 2007.

Original: Another possible explanation is that the model capacity was not large enough to handle a more diverse data distribution, so the performance dropped.
Revised: Another possible explanation is that the model capacity was not large enough to handle a more diverse data distribution, so the performance dropped.

Original: [Table]
Revised: [Table]

Original: 6.8 Generating WRF data based on CPC data
Revised: 6.8 Generating WRF data based on CPC data

Original: As described in the previous sections, the resolution of ERA data is so poor that it is often impossible to recover some of the higher resolution information from the data.
Revised: As described in the previous sections, the resolution of ERA data is so poor that it is often impossible to recover some of the higher resolution information from the data.

Original: Therefore, we decided to use
Revised: Therefore, we decided to use

Original: CPC data as the low-resolution data and WRF data as the high-resolution data in this experiment to test the ability of our method to recover high-resolution information based on data that could provide more information than ERA data.
Revised: CPC data as the low-resolution data and WRF data as the high-resolution data in this experiment to test the ability of our method to recover high-resolution information based on data that could provide more information than ERA data.

Original: The quantitative results on the unseen regions are shown in Table 5.
Revised: The quantitative results on the unseen regions are shown in Table 5.

Original: The qualitative results are shown in Fig.
Revised: The qualitative results are shown in Fig.

Original: 4, where our prediction looks blurry.
Revised: where our prediction looks blurry.

Original: [Table]
Revised: [Table]

Original:  Conclusion and Future Work
Revised:  Conclusion and Future Work

Original: In conclusion, we proposed an instance-conditional pixel synthesis GAN while explicitly feeding in the latitude, longitude, elevation, and time point of each pixel to perform statistic downscaling.
Revised: In conclusion, we proposed an instance-conditional pixel synthesis GAN while explicitly feeding in the latitude, longitude, elevation, and time point of each pixel to perform statistic downscaling.

Original: The qualitative analysis has shown that our method is superior in generating realistic climate patterns compared with previous methods.
Revised: The qualitative analysis has shown that our method is superior in generating realistic climate patterns compared with previous methods.

Original: The quantitative results have shown that our method has decent generalizability for unseen regions.
Revised: The quantitative results have shown that our method has decent generalizability for unseen regions.

Original: We believe if our model is trained on more regions than only 4, the performance would be even better compared to the previous methods due to the explicit modeling of the positional information.
Revised: We believe if our model is trained on more regions than only 4, the performance would be even better compared to the previous methods due to the explicit modeling of the positional information.

Original: Due to the constraints of computational resources, we have not been able to perform comprehensive studies on training with the full dataset, generating WRF data based on CPC data, and other climate variables other than precipitation.
Revised: Due to the constraints of computational resources, we have not been able to perform comprehensive studies on training with the full dataset, generating WRF data based on CPC data, and other climate variables other than precipitation.

Original: Future research in these directions would be helpful to exhibit the benefit of our proposed method.
Revised: Future research in these directions would be helpful to exhibit the benefit of our proposed method

Original: A Appendix A.1 Multi-scale Climate Dataset for the Continental United States
Revised: A Appendix A.1 Multi-scale Climate Dataset for the Continental United States

Original: In order to better facilitate future work in climate downscaling, we have aggregated and preprocessed precipitation and temperature data at three different resolutions.
Revised: In order to better facilitate future work in climate downscaling, we have aggregated and preprocessed precipitation and temperature data at three different resolutions.

Original: This combination provides training data for three possible downscaling tasks, as shown in table 6.
Revised: This combination provides training data for three possible downscaling tasks, as shown in table 6.

Original: Because of limited memory and preprocessing time, we chose to keep the maximum WRF resolution capped at 116 × 116 degrees, as well as restrict climate variables to only accumulated precipitation (mm) and maximum temperature (K) (for reference, the size of raw WRF temperature data before downsampling was roughly
Revised: Because of limited memory and preprocessing time, we chose to keep the maximum WRF resolution capped at 116 × 116 degrees, as well as restrict climate variables to only accumulated precipitation (mm) and maximum temperature (K) (for reference, the size of raw WRF temperature data before downsampling was roughly

Original: GB).
Revised: GB).

Original: [Table]
Revised: [Table]

Original: A.1.1 Preprocessing
Revised: A.1.1 Preprocessing

Original: While each of our three data sets provides data for the continental United States, their coordinates do not align exactly (ERA and CPC have a constant offset, but WRF has a non-regular grid).
Revised: While each of our three data sets provides data for the continental United States, their coordinates do not align exactly (ERA and CPC have a constant offset, but WRF has a non-regular grid).

Original: Therefore, before training, we perform nearest neighbor interpolation to a regular grid closely matching (no higher resolution than) the highest resolution dataset.
Revised: Therefore, before training, we perform nearest neighbor interpolation to a regular grid closely matching (no higher resolution than) the highest resolution dataset.

Original: Additionally, we downsample the hourly data from ERA and WRF datasets to daily measurements by taking summations and maxima for precipitation and temperature data, respectively.
Revised: Additionally, we downsample the hourly data from ERA and WRF datasets to daily measurements by taking summations and maxima for precipitation and temperature data, respectively.

Original: To increase the temporal overlap between the CPC and ERA-iterim datasets, we separately preprocess a real-time version of the CPC dataset from 2007-2018 2 and combine it with the original.
Revised: To increase the temporal overlap between the CPC and ERA-iterim datasets, we separately preprocess a real-time version of the CPC dataset from 2007-2018 2 and combine it with the original.

Original: Another attempt at increasing the number of samples is through data augmentation.
Revised: Another attempt at increasing the number of samples is through data augmentation.

Original: We takedifferent 10 × 10 degree patches of the United States: Northwestern, Northeastern, Midwestern,
Revised: We takedifferent 10 × 10 degree patches of the United States: Northwestern, Northeastern, Midwestern,

Original: Southwestern, and Southeastern (see Figure 1).
Revised: Southwestern, and Southeastern (see Figure 1).

Original: Completely randomizing the training patches and allowing for overlap may allow for a much larger multiplier on the base dataset size, at the risk of overfitting.
Revised: Completely randomizing the training patches and allowing for overlap may allow for a much larger multiplier on the base dataset size, at the risk of overfitting.

Original: While rotations of the data were also considered, the transformation may interfere with the network’s coordinate-based conditioning (rotations would result in pixels being mislabeled as the wrong coordinate) and so it was not performed.
Revised: While rotations of the data were also considered, the transformation may interfere with the network’s coordinate-based conditioning (rotations would result in pixels being mislabeled as the wrong coordinate) and so it was not performed.

Original: To generate the coordinate grids used in interpolation, we divide the five selected 10 × 10 degree regions into a regular grid according to the desired highest resolution.
Revised: To generate the coordinate grids used in interpolation, we divide the five selected 10 × 10 degree regions into a regular grid according to the desired highest resolution.

Original: We generate three differently sized image sets this way: 40 × 40 pixel images at 0 .
Revised: We generate three differently sized image sets this way: 40 × 40 pixel images at 0 .

Original: 25 degree resolution, 100 × 100 pixel images at 0 .
Revised: 25 degree resolution, 100 × 100 pixel images at 0 .

Original: 10 degree resolution, and 160 × 160 pixel images at 116 degree resolution.
Revised: 10 degree resolution, and 160 × 160 pixel images at 116 degree resolution.

Original: The details of these image collections are provided in table 7.
Revised: The details of these image collections are provided in table 7.

Original: [Table]
Revised: [Table]

Original: A.1.2 Feature Analysis
Revised: A.1.2 Feature Analysis

Original: We justify our data alignment by Figure 7, where we see that our spatially averaged ERA-iterim,
Revised: We justify our data alignment by Figure 7, where we see that our spatially averaged ERA-iterim,

Original: CPC, and WRF datasets align closely.
Revised: CPC, and WRF datasets align closely.

Original: In Figure 9, we see that our higher resolution data have larger extremes than the coarser datasets (as expected).
Revised: In Figure 9, we see that our higher resolution data have larger extremes than the coarser datasets (as expected).