Algorithms for Estimating Trends in Global Temperature Volatility

Abstract

Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that are tailored for dense, gridded observations over both space and time. We evaluate our methods with a simulation that mimics these data's features and on a large, publicly available, global temperature dataset with the eventual goal of tracking trends in cloud reflectance temperature variability.

$$\ell _{1}$$ Common Trend Filtering

“…1 Figure 1 illustrates a continuous piecewise linear trend. The filter and its variants have been subsequently applied in various fields, including astronomy (Politsch et al 2020), climatology (Khodadadi and McDonald 2019), economics (Yamada and Jin 2013;Yamada and Yoon 2014;Winkelried 2016;Yamada 2017;Klein 2018), electronics (Suo et al 2019), environmental science (Brantley et al 2019), finance (Mitra and Rohit 2018), and geophysics (Wu et al 2018).…”

Exponential Family Trend Filtering on Lattices

“…In contrast to most other results, the theory applies without assuming boundedness of the estimated natural parameter. Khodadadi and McDonald (2019) examine computational approaches for variance estimation on spatiotemporal grids. Kakade et al (2010) discuss strong convexity of general exponential families and use the results to analyze 1 penalized maximum likelihood.…”

“…Ramdas and Tibshirani (2016) examine a fast ADMM algorithm for k > 0. Wang et al (2016) develop ADMM and Newton methods for general graphs and arbitrary k. We follow the approach of Khodadadi and McDonald (2019) for the MLE trend filter (2) and use an algorithm Algorithm 1 Linearized ADMM for the MLE trend filter 1: Input: y, φ, D, λ 1 > 0, λ 2 ≥ 0 2: Set:…”