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\begin{document}

\title{Stochastic representation of the microscale spatial variability in thaw
depth in permafrost boreal forests}



\author[1]{Taro Nakai}%
\author[2]{Tetsuya Hiyama}%
\author[2]{Ayumi Kotani}%
\author[3]{Yoshihiro Iijima}%
\author[2]{Takeshi Ohta}%
\author[4]{Trofim C Maximov}%
\affil[1]{National Taiwan University}%
\affil[2]{Nagoya University}%
\affil[3]{Mie University}%
\affil[4]{Institute for Biological Problems of Cryolithozone}%


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  \date{May 25, 2024}


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\begin{abstract}
In this study, a simple stochastic representation of the microscale
spatial variability in thaw depth in permafrost regions was proposed.
Thaw depth distribution measured in the two larch-type forests in
eastern Siberia, Spasskaya Pad and Elgeeii, showed different spatial,
seasonal, and interannual variability, respectively. Minor year-to-year
variation in active-layer thickness was observed in Spasskaya Pad, where
a transient layer may constrain further thawing. A gamma distribution
accurately represented the thaw depth spatial variability in both sites
as the cumulative probability. Thus, a simple model illustrating the
spatiotemporal variation in thaw depth as a function of the mean thaw
depth was developed using the gamma distribution. A hierarchy of models
was introduced that sequentially considered the constant state,
linearity, and non-linearity in the dependence of the rate parameter of
the gamma distribution for the mean thaw depth. Although the
requirements of the model levels differed between Spasskaya Pad and
Elgeeii, the proposed model successfully represented the spatial
variability in thaw depth at both sites during different thaw seasons.%
\end{abstract}%



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