Reconstruction of spatio-temporal temperature from sparse historical records using robust probabilistic principal component regression

Abstract

Abstract. Scientific records of temperature and precipitation have been kept for several hundred years, but for many areas, only a shorter record exists. To understand climate change, there is a need for rigorous statistical reconstructions of the paleoclimate using proxy data. Paleoclimate proxy data are often sparse, noisy, indirect measurements of the climate process of interest, making each proxy uniquely challenging to model statistically. We reconstruct spatially explicit temperature surfaces from sparse and noisy measurements recorded at historical United States military forts and other observer stations from 1820 to 1894. One common method for reconstructing the paleoclimate from proxy data is principal component regression (PCR). With PCR, one learns a statistical relationship between the paleoclimate proxy data and a set of climate observations that are used as patterns for potential reconstruction scenarios. We explore PCR in a Bayesian hierarchical framework, extending classical PCR in a variety of ways. First, we model the latent principal components probabilistically, accounting for measurement error in the observational data. Next, we extend our method to better accommodate outliers that occur in the proxy data. Finally, we explore alternatives to the truncation of lower-order principal components using different regularization techniques. One fundamental challenge in paleoclimate reconstruction efforts is the lack of out-of-sample data for predictive validation. Cross-validation is of potential value, but is computationally expensive and potentially sensitive to outliers in sparse data scenarios. To overcome the limitations that a lack of out-of-sample records presents, we test our methods using a simulation study, applying proper scoring rules including a computationally efficient approximation to leave-one-out cross-validation using the log score to validate model performance. The result of our analysis is a spatially explicit reconstruction of spatio-temporal temperature from a very sparse historical record.

Artificial intelligence achieves easy-to-adapt nonlinear global temperature reconstructions using minimal local data

“…To compare the deep learning climate reconstructions with a more established, linear statistical tool, we created a Principal Component Regression (PCR) reconstruction 39 , 40 trained with the MPI-GE data set. The PCR training sample size is N = 20,000.…”

An automatic robust Bayesian approach to principal component regression

“…Selection of significant PCs. The selection of pertinent PCs to be included in our robust regression model is based on model selection and in line with the methods used in [29] and [28]. Ours however differs in that we do not use the stochastic search variable selection (see [11]), which is the common tool to discriminate among a large number of (typically correlated) regressors.…”

A Two-Step Method for Missing Spatio-Temporal Data Reconstruction

“…In past decades, a large number of interpolation methods has been proposed to solve the problem of spatio-temporal missing data [4][5][6][7][8][9][10]. These methods can be roughly divided into three categories: spatial interpolation, temporal interpolation and spatio-temporal interpolation.…”

“…In recent years, a number of studies have extended single dimension interpolation methods to consider both space and time; for example, spatio-temporal probabilistic principal component regression (ST-PCR), spatio-temporal IDW (ST-IDW), spatio-temporal kriging (ST-kriging) and the spatio-temporal heterogeneous covariance method (ST-HC) [2,3,7,9,10,[20][21][22]. ST-PCR [9] is a statistical learning-based method, which takes advantage of the statistical feature of observed data. However, it often needs a strong hypothesis over the data.…”