Variability and Confidence Intervals for the Mean of Climate Data with Short- and Long-Range Dependence

Abstract

This paper presents an adaptive procedure for estimating the variability and determining error bars as confidence intervals for climate mean states by accounting for both short- and long-range dependence. While the prevailing methods for quantifying the variability of climate means account for short-range dependence, they ignore long memory, which is demonstrated to lead to underestimated variability and hence artificially narrow confidence intervals. To capture both short- and long-range correlation structures, climate data are modeled as fractionally integrated autoregressive moving-average processes. The preferred model can be selected adaptively via an information criterion and a diagnostic visualization, and the estimated variability of the climate mean state can be computed directly from the chosen model. The procedure was demonstrated by determining error bars for four 30-yr means of surface temperatures observed at Potsdam, Germany, from 1896 to 2015. These error bars are roughly twice the width as those obtained using prevailing methods, which disregard long memory, leading to a substantive reinterpretation of differences among mean states of this particular dataset. Despite their increased width, the new error bars still suggest that a significant increase occurred in the mean temperature state of Potsdam from the 1896–1925 period to the most recent period, 1986–2015. The new wider error bars, therefore, communicate greater uncertainty in the mean state yet present even stronger evidence of a significant temperature increase. These results corroborate a need for more meticulous consideration of the correlation structures of climate data—especially of their long-memory properties—in assessing the variability and determining confidence intervals for their mean states.

Multi-Frequency Analysis of Simulated versus Observed Variability in Tropospheric Temperature

“…A key issue in our study and in trend significance assessments is whether observed low-frequency natural variability should be estimated after signal removal or from raw data. 7 One scientific perspective is that the latter strategy is preferable (Franzke 2010(Franzke , 2012aBowers and Tung 2018). This is not an unreasonable strategy when dealing with climate data at individual locations, where the true signal is poorly known and S/N ratios are lower than for global-scale spatial averages.…”

“…The indices p and q are the orders of the autoregressive and moving-average components of the model, respectively. The simplest FARIMA(0, d, 0) model has been used to describe a slowly decaying temporal autocorrelation structure in studies of long-term climate variability and trend significance (Bloomfield and Nychka 1992;Koscielny-Bunde et al 1998;Franzke 2012a,b;Imbers et al 2014;Franzke et al 2015;Bowers and Tung 2018).…”

Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

“…Moreover, because long-term records of environmental variables show often long-range memory, some other tools are usually applied. The fractionally integrated moving average models [ARFIMA (p,d,q)] have been widely used in the literature to describe meteorological variables (Yaya and Fashae, 2015;Bowers and Tung, 2018), pollutants and soil gas (Pan and Chen, 2008;Donner et al, 2015;Belbute and Pereira, 2017;Reisen et al, 2018), and hydrological time series (Montanari et al, 1997;Wang et al, 2007). This class of models is used when the longterm correlations in the data decay more slowly than an exponential form, that is, a typical shape of autocorrelation in the autoregressive moving average [ARMA(p,q)] processes (Box et al, 2015).…”

Distribution and spatio-temporal variation of temperature and precipitation in the Sierra de Otontepec Ecological Reserve, Veracruz, Mexico through GIS modelling

“…Confidence intervals (CIs) were obtained from the values of the adjusted variables using the Student's t test (α = 0.95). Considering that the CIs in the climatology are a useful resource for the identification of similar climates(Mudelsse, 2013;Bowers and Tung, 2018), and due to the existence of different microclimates in each region, if the values of temperature and precipitation extracted from the isohypsa of RESO were within the CIs determined by the group of stations, they would represent similarity conditions with a confidence level of 95%.…”