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\begin{document}

\title{Learning to infer weather states using partial observations}



\author[1]{Jie Chao}%
\author[2]{Baoxiang Pan}%
\author[3]{Quanliang Chen}%
\author[4]{Shangshang Yang}%
\author[5]{Jingnan Wang}%
\author[6]{congyi nai}%
\author[7]{Yue Zheng}%
\author[8]{Xichen Li}%
\author[9]{Huiling Yuan}%
\author[2]{Xi Chen}%
\author[10]{Bo Lu}%
\author[2]{Ziniu Xiao}%
\affil[1]{Chengdu University of Information Technology}%
\affil[2]{Institute of Atmospheric Physics, Chinese Academy of Sciences}%
\affil[3]{Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, College of Atmospheric Science,Chengdu University of Information Technology}%
\affil[4]{Key Laboratory of Mesoscale Severe Weather Ministry of Education/School of Atmospheric Sciences, Nanjing University}%
\affil[5]{College of Computer, National University of Defense Technology}%
\affil[6]{Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences}%
\affil[7]{ClusterTech Limited, Hong Kong}%
\affil[8]{International Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences}%
\affil[9]{Key Laboratory of Mesoscale Severe Weather/Ministry of Education, and School of Atmospheric Sciences, Nanjing University, Nanjing, China}%
\affil[10]{National Climate Center, China Meterological Administration}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\begin{abstract}
Accurate state estimation of the high-dimensional, chaotic Earth
atmosphere marks a Sisyphean task, yet is indispensable for initiating
weather forecast and gauging climate variability. While much effort is
devoted to assimilating observations and forecasts to infer weather
state, the inherent low-dimensional statistical structure in atmospheric
circulation, shaped by geophysical laws and geographic boundaries, is
underutilized as informative prior for state inference, or as reference
for assessing representative of existing observations and planning new
ones. We realize these potential by learning climatological distribution
from climate reanalysis/simulation, using deep generative model. For a
case study of estimating 2 m temperature spatial patterns, the learned
distribution faithfully reproduces climatology statistics. A combination
of the learned climatological prior with few station observations yields
strong posterior of spatial pattern estimates, which are spatially
coherent, faithful and adaptive to observation constraints, and
uncertainty-aware. This allows us to evaluate each observation's value
in reducing state estimation uncertainty, and guide optimal observation
network design by pinpointing the most informative sites. Our study
showcases how generative models can extract and utilize information
produced in the chaotic evolution of climate system.%
\end{abstract}%



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