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Tingley, Martin

Part I presented a Bayesian algorithm for reconstructing climate anomalies in space and time (BARCAST). This method involves specifying simple parametric forms for the spatial covariance and temporal evolution of the climate field as well as ``observation equations?? describing the relationships between the data types and the corresponding true values of the climate field. As this Bayesian approach to reconstructing climate fields is new and different, it is worthwhile to compare it in detail to the more established regularized expectation? maximization (RegEM) algorithm, which is based on an empirical estimate of the joint data covariance matrix and a multivariate regression of the instrumental time series onto the proxy time series. The differing as- sumptions made by BARCAST and RegEM are detailed, and the impacts of these differences on the analysis are discussed. Key distinctions between BARCAST and RegEM include their treatment of spatial and temporal covariance, the prior information that enters into each analysis, the quantities they seek to impute, the end product of each analysis, the temporal variance of the reconstructed field, and the treatment of uncertainty in both the imputed values and functions of these imputations. Differences between BARCAST and RegEM are illustrated by applying the two approaches to various surrogate datasets. If the assumptions inherent to BARCAST are not strongly violated, then in scenarios comparable to practical applications BARCAST results in reconstructions of both the field and the spatial mean that are more skillful than those produced by RegEM, as measured by the coefficient of efficiency. In addition, the uncertainty intervals produced by BARCAST are narrower than those estimated using RegEM and contain the true values with higher probability.

Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a calibration interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage.

A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as observation equations describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series.

This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.

Variations in extreme daily temperatures are explored in relation to changes in seasonal mean temperature using 1218 high-quality U.S. temperature stations spanning 1900–2012. Extreme temperatures are amplified (or damped) by as much as ±50% relative to changes in average temperature, depending on region, season, and whether daily minimum or maximum temperature is analyzed. The majority of this regional structure in amplification is shown to follow from regional variations in temperature distributions. More specifically, there exists a close relationship between departures from normality and the degree to which extreme changes are amplified relative to the mean. To distinguish between intraseasonal and interannual contributions to nonnormality and amplification, an additional procedure, referred to as z bootstrapping, is introduced that controls for changes in the mean and variance between years. Application of z bootstrapping indicates that amplification of winter extreme variations is generally consistent with nonnormal intraseasonal variability. Summer variability, in contrast, shows interannual variations in the spread of the temperature distribution related to changes in the mean, especially in the Midwest. Changes in midwestern temperature variability are qualitatively consistent with those expected from decreases in evapotranspiration and are strongly correlated with a measure of drought intensity. The identified patterns of interannual variations in means and extremes may serve as an analog for modes of variability that can be expected at longer time scales.

Historical observations of temperature underpin our ability to monitor Earth’s climate. We identify a pervasive issue in archived observations from surface stations, wherein the use of varying conventions for units and precision has led to distorted distributions of the data. Apart from the original precision being generally unknown, the majority of archived temperature data are found to be misaligned with the original measurements because of rounding on a Fahrenheit scale, conversion to Celsius, and re-rounding. Furthermore, we show that commonly used statistical methods including quantile regression are sensitive to the finite precision and to double-rounding of the data after unit conversion. To remedy these issues, we present a Hidden Markov Model that uses the differing frequencies of specific recorded values to recover the most likely original precision and units associated with each observation. This precision-decoding algorithm is used to infer the precision of the 644 million daily surface temperature observations in the Global Historical Climate Network database, providing more accurate values for the 63% of samples found to have been biased by double-rounding. The average absolute bias correction across the dataset is 0.018 ◦C, and the average inferred precision is 0.41 ◦C, even though data are archived at 0.1 ◦C precision. These results permit better inference of when record temperatures occurred, correction of rounding effects, and identification of inhomogeneities in surface temperature time series, amongst other applications. The precision-decoding algorithm is generally applicable to rounded observations–including surface pressure, humidity, precipitation, and other temperature data–thereby offering the potential to improve quality-control procedures for many datasets.

The relationship between the mean and spatial variability of Northern Hemisphere surface temperature anomalies over the last 1200 years is examined using instrumental and proxy records. Nonparametric statistical tests applied to 14 well-studied, annually resolved proxy records identify two centuries roughly spanning the Medieval Climate Anomaly as characterized by increased spatial variability relative to the preinstrumental baseline climate, whereas two centuries spanning the Little Ice Age are characterized by decreased spatial variability. Analysis of the instrumental record similarly indicates that the late and middle twentieth century warm intervals are generally associated with increased spatial variability. In both proxy and instrumental records an overall relationship between the first two moments is identified as a weak but significant positive correlation between time series of the spatial mean and spatial standard deviation of temperature anomalies, indicating that warm and cold anomalies are respectively associated with increased and reduced spatial variability. Insomuch as these historical patterns of relatively heterogeneous warming as compared with cooling hold, they suggest that future warming will feature increased regional variability

High temperature extremes during the growing season can reduce agricultural production. At the same time, agricultural practices can modify temperatures by altering the surface energy budget. Here we identify centennial trends towards more favourable growing conditions in the US Midwest, including cooler summer temperature extremes and increased precipitation, and investigate the origins of these shifts. Statistically significant correspondence is found between the cooling pattern and trends in cropland intensification, as well as with trends towards greater irrigated land over a small subset of the domain. Land conversion to cropland, often considered an important influence on historical temperatures, is not significantly associated with cooling. We suggest that agricultural intensification increases the potential for evapotranspiration, leading to cooler temperatures and contributing to increased precipitation. The tendency for greater evapotranspiration on hotter days is consistent with our finding that cooling trends are greatest for the highest temperature percentiles. Temperatures over rainfed croplands show no cooling trend during drought conditions, consistent with evapotranspiration requiring adequate soil moisture, and implying that modern drought events feature greater warming as baseline cooler temperatures revert to historically high extremes.

The fidelity of inferences on volcanic cooling from tree-ring density records has recently come into question, with competing claims that temperature reconstructions based on tree-ring records underestimate cooling due to an increased likelihood of missing rings or overestimate cooling due to reduced light availability accentuating the response. Here we test these competing hypotheses in the latitudes poleward of 45◦N, using the two eruptions occurring between 1850 and 1960 with large-scale Northern Hemisphere climatic effects: Novarupta (1912) and Krakatau (1883). We find that tree-ring densities overestimate postvolcanic cooling with respect to instrumental data (Probability≥0.99), with larger magnitudes of bias where growth is more limited by light availability (Prob.≥0.95). Using a methodology that allows for direct comparisons with instrumental data, our results confirm that high-latitude tree-ring densities record not only temperature but also variations in light availability.

Seasonal forecast models exhibit only modest skill in predicting extreme summer temperatures across the eastern US. Anomalies in sea surface temperature and monthly-resolution rainfall have, however, been correlated with hot days in the US, and seasonal persistence of these anomalies suggests potential for long-lead predictability. Here we present a clustering analysis of daily maximum summer temperatures from US weather stations between 1982–2015 and identify a region spanning most of the eastern US where hot weather events tend to occur synchronously. We then show that an evolving pattern of sea surface temperature anomalies, termed the Pacific Extreme Pattern, provides for skillful prediction of hot weather within this region as much as 50 days in advance. Skill is demonstrated using out-of-sample predictions between 1950 and 2015. Rainfall deficits over the eastern US are also associated with the occurrence of the Pacific Extreme Pattern and are demonstrated to offer complementary skill in predicting high temperatures. The Pacific Extreme Pattern appears to provide a cohesive framework for improving seasonal prediction of summer precipitation deficits and high temperature anomalies in the eastern US.