Discussion of “An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models” by F. Battaglia and M. K. Protopapas

The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations

Long memory and the aggregation of AR(1) processes

Granger (1980) found that the aggregation of m short-memory AR(1) processes yields a long-memory process. Thereby he assumed m -> ∞, Gaussian shape and betadistributed AR(1) parameters over (0; 1). To test hypotheses that long memory in climate time series comes from aggregation, the finding of Granger (1980) cannot be directly applied. First, the number of \'microclimatic\' processes to be aggregated is finite. Second, climatic processes often produce right-skewed data. Third, the AR(1) parameters of the microclimatic processes could be restricted to a narrower interval than (0; 1). We therefore perform Monte Carlo simulations to study aggregation in climate time series under realistic conditions. The long-memory parameter, H, is estimated by fitting an ARFIMA model to various types of aggregations. Our results are as follows. First, for m above a few hundred, H approaches saturation. Second, the distributional shape has little influence, as noted by Granger (1980). Third, the upper limit of the interval for the AR(1) parameter has a strong influence on the saturation value of H, as noted by Granger (1980).Granger (1980) fand heraus, dass die Summe von m schwach seriell abhängigen AR(1)-Prozessen einen stark seriell abhängigen Prozess ergibt. Er nahm dabei an, dass m -> ∞ geht, die Verteilungen Gaußsch sind und die AR(1)-Parameter beta-verteilt über (0; 1) sind. Um die Hypothese zu testen, daß starke serielle Abhängigkeit in Klimazeitreihen von dieser \'Aggregation\' rührt, kann das Ergebnis von Granger (1980) jedoch nicht direkt angewendet werden. Erstens: die Anzahl \'mikroklimatischer\', zu summierender Prozesse is endlich. Zweitens: Klimaprozesse erzeugen oft rechtsschief verteilte Daten. Drittens: die AR(1)-Parameter der mikroklimatischen Prozesse mögen auf ein engeres Intervall begrenzt sein als (0; 1). Wir f¨uhren deshalb Monte-Carlo-Simulationen durch, um die Aggregation in Klimazeitreihen für realistische Bedingungen zu studieren. Der Parameter H, der die starke serielle Abhängigkeit beschreibt, wird geschätzt durch die Anpassung eines ARFIMA-Modelles an unterschiedliche Aggregations-Typen. Unsere Ergebnisse sind wie folgt. Erstens: für m oberhalb einiger hundert erreicht H S¨attigung. Zweitens: die Verteilungsform hat geringen Einfluß, wie von Granger (1980) bemerkt. Drittens: die obere Grenze des Intervalles für den AR(1)-Parameter hat einen starken Einfluß auf den Sättigungwert von H, wie von Granger (1980) bemerkt

XTREND: A computer program for estimating trends in the occurrence rate of extreme weather and climate events

XTREND consists of the following methodical Parts. Time interval extraction (Part 1) to analyse different parts of a time series; extreme events detection (Part 2) with robust smoothing; magnitude classification (Part 3) by hand; occurrence rate estimation (Part 4) with kernel functions; bootstrap simulations (Part 5) to estimate confidence bands around the occurrence rate. You work interactively with XTREND (parameter adjustment, calculation, graphics) to acquire more intuition for your data. Although, using “normal” data sizes (less than, say, 1000) and modern machines, the computing time seems to be acceptable (less than a few minutes), parameter adjustment should be done carefully to avoid spurious results or, on the other hand, too long computing times. This Report helps you to achieve that. Although it explains the statistical concepts used, this is generally done with less detail, and you should consult the given references (which include some textbooks) for a deeper understanding

Effects of dating errors on nonparametric trend analyses of speleothem time series

A fundamental problem in paleoclimatology is to take fully into account the various error sources when examining proxy records with quantitative methods of statistical time series analysis. Records from dated climate archives such as speleothems add extra uncertainty from the age determination to the other sources that consist in measurement and proxy errors. This paper examines three stalagmite time series of oxygen isotopic composition (δ<sup>18</sup>O) from two caves in western Germany, the series AH-1 from the Atta Cave and the series Bu1 and Bu4 from the Bunker Cave. These records carry regional information about past changes in winter precipitation and temperature. U/Th and radiocarbon dating reveals that they cover the later part of the Holocene, the past 8.6 thousand years (ka). We analyse centennial- to millennial-scale climate trends by means of nonparametric Gasser–Müller kernel regression. Error bands around fitted trend curves are determined by combining (1) block bootstrap resampling to preserve noise properties (shape, autocorrelation) of the δ<sup>18</sup>O residuals and (2) timescale simulations (models StalAge and iscam). The timescale error influences on centennial- to millennial-scale trend estimation are not excessively large. We find a "mid-Holocene climate double-swing", from warm to cold to warm winter conditions (6.5 ka to 6.0 ka to 5.1 ka), with warm–cold amplitudes of around 0.5‰ δ<sup>18</sup>O; this finding is documented by all three records with high confidence. We also quantify the Medieval Warm Period (MWP), the Little Ice Age (LIA) and the current warmth. Our analyses cannot unequivocally support the conclusion that current regional winter climate is warmer than that during the MWP

Trends and oscillations in the Indian summer monsoon rainfall over the last two millennia

Observations show that summer rainfall over large parts of South Asia has declined over the past five to six decades. It remains unclear, however, whether this trend is due to natural variability or increased anthropogenic aerosol loading over South Asia. Here we use stable oxygen isotopes in speleothems from northern India to reconstruct variations in Indian monsoon rainfall over the last two millennia. We find that within the long-term context of our record, the current drying trend is not outside the envelope of monsoon’s oscillatory variability, albeit at the lower edge of this variance. Furthermore, the magnitude of multi-decadal oscillatory variability in monsoon rainfall inferred from our proxy record is comparable to model estimates of anthropogenic-forced trends of mean monsoon rainfall in the 21st century under various emission scenarios. Our results suggest that anthropogenic forced changes in monsoon rainfall will remain difficult to detect against a backdrop of large natural variability

Trends in extremes of temperature, dew point and precipitation from long instrumental records from central Europe

For the analysis of trends in weather extremes, we introduce a diagnostic variable, the exceedance product, which combines intensity and frequency of extremes. We separate trends in higher moments from trends in mean or standard deviation and use bootstrap resampling to evaluate statistical significances. Application to daily meteorological records from Potsdam (1893–2005) and Prague (1775–2004) reveals that extremely cold winters occurred only until mid-20th century, whereas warm winters show upward trends. These were significant changes in higher moments of the temperature distribution. In contrast, trends in summer temperature extremes (e.g., 2003 European heatwave), can be explained by linear changes in mean or standard deviation. While precipitation at Potsdam does not exhibit pronounced trends, dew point displays an enigmatic change from maximum extremes during the 1960s to minimum extremes during the 1970s.Zur Untersuchung von Trends vonWetterextremen wird ein neuartiges „Wirkungsmaß” eingeführt, das Produkt der Extremwertübertreffung, welches die beiden Aspekte „Stärke” und „Häufigkeit” miteinander verbindet. Es werden Trends in höheren Momenten von Trends in Mittelwert und Standardabweichung getrennt sowie Bootstrap-Verfahren angewendet, um die statistische Signifikanz auszuwerten. Bei der Verwendung von meteorologischen Daten in täglicher Auflösung von Potsdam (1893–2005) und Prag (1775–2004) zeigt sich, dass extrem kalte Winter nur bis Mitte des 20. Jahrhundert auftraten, wohingegen warme Winter einen Aufwärtstrend aufweisen, welche signifikante Änderungen in höheren Momenten der Temperaturverteilung darstellen. Im Gegensatz dazu kann der Trend von Sommer-Temperaturextremen (z.B. die Hitzewelle im Jahr 2003 in Europa) durch Änderungen in Mittelwert und Standardabweichung erklärt werden. Während der Niederschlag in Potsdam keine ausgeprägte Trends zeigt, weist der Taupunkt einen rätselhaften Übergang von Maximumextremen in den 1960ern zu Minimumextremen in den 1970ern auf

Trend analysis of climate time series: A review of methods

The increasing trend curve of global surface temperature against time since the 19th century is the icon for the considerable influence humans have on the climate since the industrialization. The discourse about the curve has spread from climate science to the public and political arenas in the 1990s and may be characterized by terms such as “hockey stick” or “global warming hiatus”. Despite its discussion in the public and the searches for the impact of the warming in climate science, it is statistical science that puts numbers to the warming. Statistics has developed methods to quantify the warming trend and detect change points. Statistics serves to place error bars and other measures of uncertainty to the estimated trend parameters. Uncertainties are ubiquitous in all natural and life sciences, and error bars are an indispensable guide for the interpretation of any estimated curve—to assess, for example, whether global temperature really made a pause after the year 1998. Statistical trend estimation methods are well developed and include not only linear curves, but also changepoints, accelerated increases, other nonlinear behavior, and nonparametric descriptions. State-of-the-art, computing- intensive simulation algorithms take into account the peculiar aspects of climate data, namely non- Gaussian distributional shape and autocorrelation. The reliability of such computer age statistical methods has been testified by Monte Carlo simulation methods using artificial data. The application of the state-of-the-art statistical methods to the GISTEMP time series of global surface temperature reveals an accelerated warming since the year 1974. It shows that a relative peak in warming for the years around World War II may not be a real feature but a product of inferior data quality for that time interval. Statistics also reveals that there is no basis to infer a global warming hiatus after the year 1998. The post-1998 hiatus only seems to exist, hidden behind large error bars, when considering data up to the year 2013. If the fit interval is extended to the year 2017, there is no significant hiatus. The researcher has the power to select the fit interval, which allows her or him to suppress certain fit solutions and favor other solutions. Power necessitates responsibility. The recommendation therefore is that interval selection should be objective and oriented on general principles. The application of statistical methods to data has also a moral aspect

Rampenregression - Quantifizierung von Temperaturtrends

Die Jahresmitteltemperatur-Zeitreihen dreier Stationen (Berlin, Leipzig und Stockholm) werden auf ihre langfristigen Trends im Zeitbereich 1830-1980 untersucht. Dazu wird die neuartige, parametrische Methode der Rampenregression (Mudelsee 1999a) verwendet. Die Vorteile gegenüber bisher verwendeten Verfahren sind (1) eine realistischeres Übergangsmodell und (2) Angaben des statistischen Fehlers geschätzter Übergangs-Zeitpunkte und -Niveaus. Leipzig (Erwärmung um 0.86±0.13 °C von 1889±7bis1911±7) und Stockholm (Erwärmung um 1.01±0.22 °C von 1879±23 bis 1945±21) zeigen beide einen rampenförmigen Trendverlauf, Berlin dagegen einen noch komplizierteren Trend. Im Falle von Leipzig liegt wahrscheinlich ein deutlicher Urbanisierungseinfluß vor. Die Rampenregression bietet die Möglichkeit, einen globalen Klimawechsel genauer zu quantifizieren.Timeseries of annual average temperature from three stations (Berlin, Leipzig and Stockholm) are investigated with regards to their long-term trends in the time interval 1830-1980. For that, the new, parametric method of ramp function regression (Mudelsee 1999a) is used. The advantages against other previously employed methods are (1) a more realistic transition model and (2) information about the statistical accuracy of estimated transition dates and levels. Both Leipzig (warming by 0.86±0.13 °C, from 1889±7 to 1911±7) and Stockholm (warming by 1.01±0.22 °C, from 1879±23 to 1945±21) show a ramp-form trend, whereas Berlin\''s trend is even more complicated. In the case of Leipzig a significant contribution by urbanization is likely. Ramp function regression has the potential to quantify a global climate change more accurately

Optimizing significance testing of astronomical forcing in cyclostratigraphy

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