diff --git "a/CNAzT4oBgHgl3EQfTvwq/content/tmp_files/load_file.txt" "b/CNAzT4oBgHgl3EQfTvwq/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/CNAzT4oBgHgl3EQfTvwq/content/tmp_files/load_file.txt" @@ -0,0 +1,933 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf,len=932 +page_content='Deep Learning for bias-correcting comprehensive high-resolution Earth system models Philipp Hess1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Stefan Lange2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' and Niklas Boers1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 1Earth System Modelling,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' School of Engineering & Design,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Technical University of Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Germany 2Potsdam Institute for Climate Impact Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Member of the Leibniz Association,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Potsdam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Germany 3Global Systems Institute and Department of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' University of Exeter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Exeter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' UK Key Points: A generative adversarial network is shown to improve daily precipitation fields from a state-of-the-art Earth system model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Biases in long-term temporal distributions are strongly reduced by the generative adversarial network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our network-based approach can be complemented with quantile mapping to fur- ther improve precipitation fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' –1– arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='01253v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='ao-ph] 16 Dec 2022 Abstract The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The complex cross-scale interactions of processes that produces precipi- tation are challenging to model, however, inducing potentially strong biases in ESM fields, especially regarding extremes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' State-of-the-art bias correction methods only address errors in the simulated frequency distributions locally, at every individual grid cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Improving unrealistic spatial patterns of the ESM output, which would require spatial context, has not been possible so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Here, we show that a post-processing method based on physically constrained generative adversarial networks (GANs) can correct biases of a state-of-the-art, CMIP6-class ESM both in local frequency distributions and in the spatial patterns at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' While our method improves local frequency distributions equally well as gold-standard bias- adjustment frameworks it strongly outperforms any existing methods in the correction of spatial patterns, especially in terms of the characteristic spatial intermittency of precipita- tion extremes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 1 Introduction Precipitation is a crucial climate variable and changing amounts, frequencies, or spatial distributions have potentially severe ecological and socioeconomic impacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' With global warming projected to continue in the coming decades, assessing the impacts of changes in precipitation characteristics is an urgent challenge (Wilcox & Donner, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Boyle & Klein, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' IPCC, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Climate impact models are designed to assess the impacts of global warming on, for example, ecosystems, crop yields, vegetation and other land-surface characteristics, infrastructure, water resources, or the economy in general (Kotz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022), using the output of climate or Earth system models (ESMs) as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Especially for reliable assessments of the ecological and socioeconomic impacts, accurate ESM precipitation fields to feed the impact models are therefore crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' ESMs are integrated on spatial grids with finite resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The resolution is limited by the computational resources that are necessary to perform simulations on decadal to centennial time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Current state-of-the-art ESMs have a horizontal resolution on the order of 100km, in exceptional cases going down to 50km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Smaller-scale physical processes that are relevant for the generation of precipitation operate on scales below the size of individual grid cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' These can therefore not be resolved explicitly in ESMs and have to included as parameterizations of the resolved prognostic variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' These include droplet interactions, turbulence, and phase transitions in clouds that play a central role in the generation of precipitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The limited grid resolution hence introduces errors in the simulated precipitation fields, leading to biases in short-term spatial patterns and long-term summary statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' These biases need to be addressed prior to passing the ESM precipitation fields to impact mod- els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In particular, climate impact models are often developed and calibrated with input data from reanalysis data rather than ESM simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' These reanalyses are created with data assimilation routines and combine various observations with high-resolution weather models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' They hence provide a much more realistic input than the ESM simulations and statistical bias correction methods are necessary to remove biases in the ESM simulations output and to make them more similar to the reanalysis data for which the impact models are calibrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Quantile mapping (QM) is a standard technique to correct systematic errors in ESM simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' QM estimates a mapping between distributions from historical sim- ulations and observations that can thereafter be applied to future simulations in order to provide more accurate simulated precipitation fields to impact models (D´equ´e, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Tong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Gudmundsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' State-of-the-art bias correction methods such as QM are, however, confined to address errors in the simulated frequency distributions locally, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', at every grid cell individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' –2– Unrealistic spatial patterns of the ESM output, which would require spatial context, have therefore so far not been addressed by postprocessing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For precipitation this is particularly important because it has characteristic high intermittency not only in time, but also in its spatial patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Mulitvariate bias correction approaches have recently been developed, aiming to improve spatial dependencies (Vrac, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Cannon, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' However, these approaches are typically only employed in regional studies, as the dimension of the input becomes too large for global high-resolution ESM simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Moreover, such meth- ods have been reported to suffer from instabilities and overfitting, while differences in their applicability and assumptions make them challenging to use (Fran¸cois et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Here, we employ a recently introduced postprocessing method (Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022) based on a cycle-consistent adversarial network (CycleGAN) to consistently improve both local frequency distributions and spatial patterns of state-of-art high-resolution ESM precipita- tion fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Artificial neural networks from computer vision and image processing have been successfully applied to various tasks in Earth system science, ranging from weather forecast- ing (Weyn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Rasp & Thuerey, 2021) to post-processing (Gr¨onquist et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Price & Rasp, 2022), by extracting spatial features with convolutional layers (LeCun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Generative adversarial networks (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2014) in particular have emerged as a promising architecture that produces sharp images that are necessary to capture the high-frequency variability of precipitation (Ravuri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Price & Rasp, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' GANs have been specifically developed to be trained on unpaired image datasets (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This makes them a natural choice for post-processing the output of cli- mate projections, which – unlike weather forecasts – are not nudged to follow the trajectory of observations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' due to the chaotic nature of the atmosphere small deviations in the initial conditions or parameters lead to exponentially diverging trajectories (Lorenz, 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' As a result, numerical weather forecasts lose their deterministic forecast skill after approximately two weeks at most and century-scale climate simulations do not agree with observed daily weather records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Indeed the task of climate models is rather to produce accurate long-term statistics that to agree with observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We apply our CycleGAN approach to correct global high-resolution precipitation simu- lations of the GFDL-ESM4 model (Krasting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2018) as a representative ESM from the Climate Model Intercomparison Project phase 6 (CMIP6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' So far, GANs-based approaches have only been applied to postprocess ESM simulations either in a regional context (Fran¸cois et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021), or to a very-low-resolution global ESM (Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We show here that a suitably designed CycleGAN is capable of improving even the distributions and spatial patterns of precipitation fields from a state-of-the-art comprehensive ESM, namely GFDL- ESM4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In particular, in contrast to rather specific existing methods for postprocessing ESM output for climate impact modelling, we will show that the CycleGAN is general and can readily be applied to different ESMs and observational datasets used as ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In order to assure that physical conservation laws are not violated by the GAN-based postprocessing, we include a suitable physical constraint, enforcing that the overall global sum of daily precipitation values is not changed by the GAN-based transformations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' es- sentially, this assures that precipitation is only spatially redistributed (see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' By framing bias correction as an image-to-image translation task, our approach corrects both spatial patterns of daily precipitation fields on short time scales and temporal distributions aggregated over decadal time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We evaluate the skill to improve spatial patterns and temporal distributions against the gold-standard ISIMIP3BASD framework (Lange, 2019), which relies strongly on QM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Quantifying the “realisticness” of spatial precipitation patterns is a key problem in current research (Ravuri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We use spatial spectral densities and the fractal dimension of spatial patterns as a measure to quantify the similarity of intermittent and un- paired precipitation fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We will show that our CycleGAN is indeed spatial context-aware and strongly improves the characteristic intermittency in spatial precipitation patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We –3– will also show that our CycleGAN combined with a subseqeunt application of ISIMIP3BASD routine leads to the best overall performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2 Results We evaluate our CycleGAN method on two different tasks and time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' First, the correction of daily rainfall frequency distributions at each grid cell locally, aggregated from decade-long time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Second, we quantify the ability to improve spatial patterns on daily time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our GAN approach is compared to the raw GFDL-ESM4 model output, as well as to the ISIMIP3BASD methodology applied to the GFDL-ESM4 output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='1 Temporal distributions 10 6 10 5 10 4 10 3 10 2 10 1 100 Histogram a 0 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='94 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='98 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='993 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='997 W5E5v2 precipitation percentiles W5E5v2 GFDL-ESM4 ISIMIP3BASD GAN GAN (unconstrained) GAN-ISIMIP3BASD 0 25 50 75 100 125 150 Precipitation [mm/d] 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 Absolute error b Figure 1: Histograms of relative precipitation frequencies over the entire globe and test period (2004-2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (a) The histograms are shown for the W5E5v2 ground truth (black), GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), unconstrained GAN (orange), and the constrained-GAN-ISIMIP3BASD combination (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (b) Distances of the his- tograms to the W5E5v2 ground truth are shown for the same models as in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Percentiles corresponding to the W5E5v2 precipitation values are given on the second x-axis at the top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Note that GFDL-ESM4 overestimates the frequencies of strong and extreme rainfall events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' All compared methods show similar performance in correcting the local frequency distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' –4– We compute global histograms of relative precipitation frequencies using daily time series (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GFDL-ESM4 model overestimates frequencies in the tail, namely for events above 50 mm/day (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7th percentile).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our GAN-based method as well as ISIMIP3BASD and the GAN-ISIMIP3BASD combination correct the histogram to match the W5E5v2 ground truth equally well, as can be also seen in the absolute error of the histograms (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Comparing the differences in long-term averages of precipitation per grid cell (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2 and Methods), large biases are apparent in the GFDL-ESM4 model output, especially in the tropics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The double-peaked Intertropical Convergence Zone (ITCZ) bias is visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The double-ITCZ bias can also be inferred from the latitudinal profile of the precipitation mean in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Table 1 summarizes the annual biases shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2 as absolute averages, and addi- tionally for the four seasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GAN alone reduces the annual bias of the GFDL-ESM4 model by 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The unconstrained GAN performs better than the physically constrained one, with bias reductions of 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' As expected, the ISIMIP3BASD gives even better results for correcting the local mean, since it is specifically designed to accurately transform the local frequency distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' It is therefore remarkable that applying the ISIMIP3BASD procedure on the constrained GAN output improves the post-processing further, leading to a local bias reduction of the mean by 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='6%, compared to ISIMIP3BASD with 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For seasonal time series the order in which the methods perform is the same as for the annual data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Besides the error in the mean, we also compute differences in the 95th percentile for each grid cell, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' S1 and as mean absolute errors in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Also in this case of heavy precipitation values we find that ISIMIP3BASD outperforms the GAN, but that combining GAN and ISIMIP3BASD leads to best agreement of the locally computed quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Table 1: The globally averaged absolute value of the grid cell-wise difference in the long- term precipitation average, as well as the 95th percentile, between the W5E5v2 ground truth and GFDL-ESM4, ISIMIP3BASD, GAN, unconstrained GAN, and the GAN-ISIMIP3BASD combination for annual and seasonal time series (in [mm/day]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The relative improvement over the raw GFDL-ESM4 climate model output is shown as percentages for each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Season Percentile GFDL- ESM4 ISIMIP3- BASD % GAN % GAN (unconst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=') % GAN- ISIMIP3- BASD % Annual 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='535 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='217 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='328 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='532 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='247 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='6 SON 95th 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='689 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='495 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='741 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='592 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='366 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2 –5– Figure 2: Bias in the long-term average precipitation over the entire test set between the W5E5v2 ground truth (a) and GFDL-ESM4 (b), ISIMIP3BASD (c), GAN (d), uncon- strained GAN (e) and the GAN-ISIMIP3BASD combination (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2 Spatial patterns We compare the ability of the GAN to improve spatial patterns based on the W5E5v2 ground truth, against the GFDL-ESM4 simulations and the ISIMIP3BASD method applied to the GFDL-ESM4 simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' To model realistic precipitation fields, the characteristic spatial intermittency needs to be captured accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We compute the spatial power spectral density (PSD) of global precipitation fields, averaged over the test set for each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' GFDL-ESM4 shows noticeable deviations from W5E5v2 in the PSD (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our GAN can correct these over the entire range of wave- –6– W5E5v2 mean [mm/d] GFDL-ESM4 a b N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0° S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0 ISIMIP3BASD GAN N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0° 60°S GAN (unconstrained) GAN-ISIMIP3BASD e f N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0° S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 120°W 60°W 0 60°E 120°E 120°W 60°W 0° 60°E 120°E 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0 -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0 Bias [mm/d]80 S 60 S 40 S 20 S 0 20 N 40 N 60 N 80 N Latitude 0 1 2 3 4 5 6 7 Mean precipitation [mm/d] W5E5v2 GFDL-ESM4: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='241 ISIMIP3BASD: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='120 GAN: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='226 GAN (unconstrained): MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='102 GAN-ISIMIP3BASD: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='068 Figure 3: Precipitation averaged over longitudes and the entire test set period from the W5E5v2 ground truth (black) and GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), unconstrained GAN (orange) and the GAN-ISIMIP3BASD combination (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' To quantify the differences between the shown lines, we show their mean absolute error w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='t the W5E5v2 ground truth in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' These values are different from the ones shown in Table 1 as the average is taken here over the longitudes without their absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GAN-ISIMIP3BASD approach shows the lowest error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' lengths, closely matching the W5E5v2 ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Improvements over ISIMIP3BASD are especially pronounced in the range of high frequencies (low wavelengths), which are responsible for the intermittent spatial variability of daily precipitation fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Adding the physical constraint to the GAN does not affect the ability to produce realistic PSD distribu- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' After applying ISIMIP3BASD to the GAN-processed fields, most of the improvements generated by the GAN are retained, as shown by the GAN-ISIMIP3BASD results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For a second way to quantifying how realistic the simulated and post-processed pre- cipitation fields are, with a focus on high-frequency spatial intermittency, we investigate the fractal dimension (Edgar & Edgar, 2008) of the lines separating grid cells with daily rainfall sums above and below a given quantile threshold (see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For a sample and qualitative comparison of precipitation fields over the South American continent see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The daily spatial precipitation fields are first converted to binary images using a quantile threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The respective quantiles are determined from the precipitation distribution over the entire test set period and globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The mean of the fractal dimension computed with box- counting (see Methods) (Lovejoy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Meisel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Husain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021) for each time slice is then investigated (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Both the GFDL-ESM4 simulations themselves and the results of applying the ISIMIP3BASD post-processing to them exhibit spatial patterns with a lower fractal dimension than the W5E5v2 ground truth, implying too low spatial intermittency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In contrast, the GAN translates spatial fields simulated by GFDL-ESM4 in a way that results in closely matching fractal dimensions over the entire range of quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 3 Discussion Postprocessing climate projections is a fundamentally different task from postprocessing weather forecast simulations (Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In the latter case, data-driven postprocess- ing methods, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' based on deep learning, to minimize differences between paired samples –7– 128 256 512 1024 2048 4096 8192 Wavelength [km] 10 6 10 5 10 4 10 3 10 2 PSD [a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='u] W5E5v2 GFDL-ESM4 ISIMIP3BASD GAN GAN (unconstrained) GAN-ISIMIP3BASD Figure 4: The power spectral density (PSD) of the spatial precipitation fields is shown as an average over all samples in the test set for the W5E5v2 ground truth (black) and GFDL- ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan, dashed), unconstrained GAN (orange, dashed-dotted) and the constrained-GAN-ISIMIP3BASD combination (blue, dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GANs and W5E5v2 ground truth agree so closely that they are indistinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In contrast to ISIMIP3BASD, the GAN can correct the intermittent spectrum accurately over the entire range down to the smallest wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' of variables such as spatial precipitation fields (Hess & Boers, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Beyond time scales of a few days, however, the chaotic nature of the atmosphere leads to exponentially diverging trajectories, and for climate or Earth system model output there is no observation-based ground truth to directly compare to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We therefore frame the post-processing of ESM projec- tions, with applications for subsequent 195 impact modelling in mind, as an image-to-image translation task with unpaired samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' To this end we apply a recently developed postprocessing method based on physically constrained CycleGANs to global simulations of a state-of-the-art, high-resolution ESM from the CMIP6 model ensemble, namely the GFDL-ESM4 (Krasting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=" O' Neill et al." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We evaluate our method against the gold-standard bias correction framework ISIMIP3BASD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our model can be trained on unpaired samples that are characteristic for climate simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' It is able to correct the ESM simulations in two regards: temporal distributions over long time scales, including extremes in the distrivutions’ tails, as well as spatial patterns of individual global snap shots of the model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The latter is not possible with established methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our GAN-based approach is designed as a general framework that can be readily applied to different ESMs and observational target datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This is in contrast to existing bias-adjustment methods that are often tailored to specific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We chose to correct precipitation because it is arguably one of the hardest variables to represent accurately in ESMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' So far, GANs have only been applied to regional studies or low-resolution global ESMs (Fran¸cois et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GFDL-ESM4 model simulations are hence chosen in order to test if our CycleGAN approach would lead –8– 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='9 Quantile 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='7 Fractal dimension W5E5v2 GFDL-ESM4: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='048 ISIMIP3BASD: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='037 GAN: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='002 GAN (unconstrained): MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='002 GAN-ISIMIP3BASD: MAE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='004 Figure 5: The fractal dimension (see Methods) of binary global precipitation fields is com- pared as averages for different quantile thresholds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Results are shown for the W5E5v2 ground truth (black) and GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), un- constrained GAN (orange, dashed), and the GAN-ISIMIP3BASD combination (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GAN can accurately reproduce the fractal dimension of the W5E5v2 ground truth spatial precipitation fields over all quantile thresholds, clearly outperforming the ISIMIP3BASD basline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' to improvements even when postprocessing global high-resolution simulations of one of the most complex and sophisticated ESMs to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In the same spirit, we evaluate our ap- proach against a very strong baseline given by the state-of-the-art bias correction framework ISIMIP3BASD, which is based on a trend-preserving QM method (Lange, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Comparing long-term summary statistics, our method yields histograms of relative pre- cipitation frequencies that very closely agree with corresponding histograms from reanalysis data (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The means that the extremes in the far end of the tail are accurately cap- tured, with similar skill to the ISIMIP3BASD baseline that is mainly designed for this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Differences in the grid cell-wise long-term average show that the GAN skillfully reduces bi- ases (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' in particular, the often reported double-peaked ITCZ bias of the GFDL-ESM4 simulations, which is a common feature of most climate models (Tian & Dong, 2020), is strongly reduced (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The ISIMIP3BASD method - being specifically designed for this produces slightly lower biases for grid-cell-wise averages than the GAN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' we show that combining both methods by first applying the GAN and then the ISIMIP3BASD procedure leads to the overall best performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Regarding the correction of spatial patterns of the modelled precipitation fields, we compare the spectral density and fractal dimensions of the spatial precipitation fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Our results show that indeed only the GAN can capture the characteristic spatial intermittency of precipitation closely (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4 and 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We believe that the measure of fractal dimension is also relevant for other fields such as nowcasting and medium-range weather forecasting, where blurriness in deep learning-based predictions is often reported (Ravuri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021) and needs to be further quantified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' –9– Post-processing methods for climate projections have to be able to preserve the trends that result from the non-stationary dynamics of the Earth system on long-time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We have therefore introduced the architecture constraint of preserving the global precipitation amount on every day in the climate model output (Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We find that this does not affect the quality of the spatial patterns that are produced by our CycleGAN method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' However, the skill of correcting mean error biases is slightly reduced by the constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This can be expected in part as the constraint is constructed to follow the global mean of the ESM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Hence, biases in the global ESM mean can influence the constrained GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This also motivates our choice to demonstrate the combination of the constrained GAN with the QM- based ISIMIP3BASD procedure, since it can be applied to future climate scenarios, making it more suitable for actual applications than the unconstrained architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' There are several directions to further develop or approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The architecture employed here has been built for equally spaced two-dimensional images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Extending the CycleGAN architecture to perform convolutions on the spherical surface, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' using graph neural net- works, might lead to more efficient and accurate models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Moreover, GANs are comparably difficult to train, which could make it challenging to identify suitable network architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Using large ensembles of climate simulations could provide additional training data that could further improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Another straightforward extension of our method would be the inclusion of further input variables or the prediction additional high-impact physical variables, such as near-surface temperatures that are also important for regional impact models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4 Methods 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='1 Training data We use global fields of daily precipitation with a horizontal resolution of 1◦ from the GFDL-ESM4 Earth system model (Krasting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2018) and the W5E5v2 reanalysis prod- uct (Cucchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' WFDE5 over land merged with ERA5 over the ocean (W5E5 v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0), 2021) as observation-based ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The W5E5v2 dataset is based on the ERA5 (Hersbach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2020) reanalysis and has been bias-adjusted using the Global Precipitation Climatology Centre (GPCC) full data monthly product v2020 (Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2011) over land and the Global Precipitation Climatology Project (GPCP) v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 dataset (Huffman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 1997) over the ocean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Both datasets have been regridded to the same 1◦ horizontal resolution using bilinear interpolation following (Beck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We split the dataset into three periods for training (1950-2000), validation (2001-2003), and testing (2004-2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This corresponds to 8030 samples for training, 1095 for validation, and 4015 for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' During pre-processing, the training data is log-transformed with ˜x = log(x+ϵ)−log(ϵ) with ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0001, following Rasp and Thuerey (2021), to account for zeros in the transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The data is then normalized to the interval [−1, 1] following (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2 Cycle-consistent generative adversarial networks This section gives a brief overview of the CycleGAN used in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We refer to (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022) for a more comprehensive description and discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Generative adversarial networks learn to generate images that are nearly indistinguishable from real-world examples through a two-player game (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In this set-up, a first network G, the so-called generator, produces images with the objective to fool a second network D, the discriminator, which has to classify whether a given sample is generated (“fake”) or drawn from a real-world dataset (“real”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Mathematically this can be formalized as G∗ = min G max D LGAN(D, G), (1) –10– with G∗ being the optimal generator network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The loss function LGAN(D, G) can be defined as LGAN(D, G) = Ey∼py(y)[log(D(y))] + Ex∼px(x)[log(1 − D(G(x)))], (2) where py(y) is the distribution of the real-world target data and samples from px(x) are used as inputs by G to produce realistic images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The CycleGAN (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017) consists of two generator-discriminator pairs, where the generators G and F learn inverse mappings between two domains X and Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This allows to define an additional cycle-consistency loss that constraints the training of the networks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Lcycle(G, F) = Ex∼px(x)[||F(G(x)) − x||1] (3) + Ey∼py(y)[||G(F(y)) − y||1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' It measures the error caused by a translation cycle of an image to the other domain and back.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Further, an additional loss term is introduced to regularize the networks to be close to an identity mapping with, Lident(G, F) = Ex∼px(x)[||G(x) − x||1] (4) + Ey∼py(y)[||F(y) − y||1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In practice, the log-likelihood loss can be replaced by a mean squared error loss to facilitate a more stable training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Further, the generator loss is reformulated to be minimized by inverting the labels, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' LGenerator = Ex∼px(x)[(DX(G(x)) − 1)2] + Ey∼py(y)[(DY (F(y)) − 1)2] (5) + λLcycle(G, F) + ˜λLident(G, F), where λ and ˜λ are set to 10 and 5 respectively following (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The corresponding loss term for the discriminator networks is given by LDiscriminator = Ey∼py(y)[(DY (y) − 1)2] + Ex∼px(x)[(DX(G(x)))2] (6) + Ex∼px(x)[(DX(x) − 1)2] + Ey∼py(y)[(DY (F(y)))2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (7) The weights of the generator and discriminator networks are then optimized with the ADAM (Kingma & Ba, 2014) optimizer using a learning rate of 2e−4 and updated in an alternating fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We train the network for 350 epochs and a batch size of 1, saving model checkpoints every other epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We evaluate the checkpoints on the validation dataset to determine the best model instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 Network Architectures Both the generator and discriminator have fully convolutional architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The gen- erator uses ReLU activation functions, instance normalization, and reflection padding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The discriminator uses leaky ReLU activations with slope 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2 instead, together with instance normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For a more detailed description, we refer to our previous study (Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The network architectures in this study are the same, only with a change in the number of residual layers in the generator network from 6 to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The final layer of the generator can be constrained to preserve the global sum of the input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' by rescaling ˜yi = yi �Ngrid i xi �Ngrid i yi , (8) –11– where xi and yi are grid cell values of the generator input and output respectively and Ngrid is the number of grid cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The generator without this constraint will be referred to as unconstrained in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The global physical constraint enforces that the global daily precipitation sum is not affected by the CycleGAN postprocessing and hence remains identical to the original value from the GFDL-ESM4 simualtions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This is motivated by the observation that large-scale average trends in precipitation follow the Clausius-Clapeyron relation (Traxl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021), which is based on thermodynamic relations and hence can be expected to be modelled well in GFDL-ESM4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='4 Quantile mapping-based bias adjustment We compare the performance of our GAN-based method to the bias adjustment method ISMIP3BASD v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='1 (Lange, 2019, 2022) that has been developed for phase 3 of the Inter- Sectoral Impact Model Intercomparison Project (Warszawski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Frieler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' This state-of-the-art bias-adjustment method is based on a trend-preserving quantile mapping (QM) framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' It represents a very strong baseline for comparison as it has been developed prior to this study and used not only in ISIMIP3 but also to prepare many of the climate projections that went into the Interactive Atlas produced as part of the 6th assessment report of working group 1 of the Intergovernmental Panel on Climate Change (IPCC, https://interactive-atlas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='ipcc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='ch/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In QM, a transformation between the cumulative distribution functions (CDFs) of the historical simulation and observations is fitted and then applied to future simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The CDFs can either be empirical or parametric, the latter being a Bernoulli-gamma distribution for the precipitation in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The CFDs are fitted and mapped for each grid cell and day of the year separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' For bias-adjusting the GFDL-ESM4 simulation, parametric QM was found to give the best results, while empirical CDFs are used in combination with the GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' To evaluate the methods in this study we define the grid cell-wise bias as the difference in long-term averages as, Bias(ˆy, y) = 1 T T � t=1 ˆyt − 1 T T � t=1 yt, (9) where T is the number of time steps, ˆyt and ˆyt the modelled and observed precipitation respectively at time step t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='5 Evaluating spatial patterns Quantifying how realistic spatial precipitation fields are is an ongoing research question in itself, which has become more important with the application of deep learning to weather forecasting and post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In these applications, neural networks often achieve error statistics and skill scores competitive with physical models, while the output fields can at the same time show unphysical characteristics, such as blurring or excessive smoothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Ravuri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (2021) compare the spatial intermittency, which is characteristic of precipitation fields, using the power spectral density (PSD) computed from the spatial fields;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' in the latter study, the PSD-based quantification was complemented by interviews with a large number of meteorological experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We propose the fractal dimension of binary precipitation fields as an alternative to quantify how realistic the patterns are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' We compute the fractal dimension via the box-counting algorithm (Lovejoy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Meisel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' It quantifies how spatial patterns, for example coastlines (Husain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2021), change with the scale of measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The box-counting algorithm divides the image into squares and counts the number of squares that cover the binary pattern of interest, Nsquares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The size of the squares, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' the scale of measurement, is then reduced iteratively by a factor s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The fractal dimension Dfractal can then be determined from the slope of the resulting log-log scaling, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', –12– Dfractal = log(Nsquares) log(s) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (10) Competing interests The authors declare no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Data availability The W5E5 data is available for download at https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='48364/ISIMIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='342217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The GFDL-ESM4 data can be downloaded at https://esgf-node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='llnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='gov/projects/ cmip6/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Code availability The Python code for processing and analysing the data, together with the PyTorch Lightning (Falcon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=', 2019) code is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='com/p-hss/earth system model gan bias correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='git.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The ISIMIP3BASD code in (Lange, 2022) is used for this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Acknowledgments NB and PH acknowledge funding by the Volkswagen Foundation, as well as the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Re- search and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' acknowledges funding by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 820970 and under the Marie Sklodowska-Curie grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 956170, as well as from the Federal Ministry of Education and Research 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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Unpaired image-to-image translation using cycle-consistent adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' In Proceedings of the IEEE international conference on computer vision (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2223–2232).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' –15– Supporting Information for ”Deep Learning for bias-correcting comprehensive high-resolution Earth system models” Philipp Hess1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Stefan Lange2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' and Niklas Boers1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='3 1Earth System Modelling,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' School of Engineering & Design,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Technical University of Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Germany 2Potsdam Institute for Climate Impact Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Member of the Leibniz Association,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Potsdam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Germany 3Global Systems Institute and Department of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' University of Exeter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Exeter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' UK Contents of this file 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Figure S1 to S2 January 4, 2023, 1:28am arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='01253v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='ao-ph] 16 Dec 2022 X - 2 : Figure S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Bias maps as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' 2 but with the 95th percentile instead of the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Global mean absolute errors (MAEs) are given in the respective titles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Combining the GAN with ISIMIP3BASD achieves the lowest error compared to the other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' January 4, 2023, 1:28am W5E5v2 95th percentile [mm/d] GFDL-ESM4: MAE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='264 b a N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0° S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0 25 50 120°W 60°W 0° 60°E 120°E 120°W 60°W 0° 60°E 120°E ISIMIP3BASD: MAE = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='073 GAN: MAE = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='415 d N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 0° S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='09 120°W 60°W .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='0 60°E 120°E 60°W 0° 60°E 120°W 120°E GAN (unconstrained): MAE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='213 GAN-ISIMIP3BASD: MAE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content='945 = e 2 120°W 60°W 0° 60°E 120°E 120°W 60°W 0° 60°E 120°E 20 -i5 -i0 -5 0 5 10 15 20 Differences in the 95th percentile [mm/d]: X - 3 a 50°S 25°S 0° 100°W 75°W 50°W 25°W W5E5v2 c 50°S 25°S 0° 100°W 75°W 50°W 25°W ISIMIP3BASD b 50°S 25°S 0° 100°W 75°W 50°W 25°W GFDL-ESM4 d 50°S 25°S 0° 100°W 75°W 50°W 25°W GAN-ISIMIP3BASD 5 10 15 20 25 30 35 Precipitation [mm/d] Figure S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' Qualitative comparison of precipitation fields at the same date (December 21st 2014) over the South American continent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' The region is used for a comparison of the fractal dimension in binary precipitation patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'} +page_content=' January 4, 2023, 1:28am' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNAzT4oBgHgl3EQfTvwq/content/2301.01253v1.pdf'}