Regime Shift Detection Techniques for Determining the Year of Positive 0°C Crossing in the Northern Hemisphere for Late-Winter and Spring

The temperature of 0°C, the phase change point of water-ice, is among the most influential factors on the hydrology of the temperate regions that experience winter. Many cryospheric processes, such as snow and ice melt, avalanches, freshwater ice breakup, and ice jam floods, are triggered by the arrival of the above-0°C air temperatures. Moreover, such 0°C based changes can have significant cascading impacts on other parts of the physical environment as well as related socio-economic activities. This research adopts an extensive analytical approach to examine the changes in the sign of mean JFM (January-February-March) and MAM (March-April-May) air temperatures, in the 0.5° × 0.5° land grid cells of the Northern Hemisphere (20.25°N-89.75°N), during the period 1901-2009. The goal is to identify grid cells in which JFM or MAM temperatures used to be primarily below freezing, however, changed sign permanently some time during 1901-2009 due to an advancement in the arrival timing of the annual above-0°C temperature. Considering that air temperature fluctuates and can cross 0°C several times during the entire period of study, four different modelling techniques are employed to detect the shift points in the trend function as well as mean level of the time series and to determine the year when the model rises above 0°C (y₀) in a given location. Model-specific criteria are set to determine y₀ in cases of multiple positive 0°C crossings. The techniques applied include i) trend shift detection techniques: Model 2 and Model 3 (Perron and Yabu, 2009b; Kim and Perron, 2009), ii) Multivariate Adaptive Regression Splines (Friedman, 1991), and iii) the R method (Rodionov, 2004,2006). This thesis provides a thorough discussion of these techniques and reviews their strengths and weaknesses relative to the research goals. In addition to y₀, the time of the onset of warming that causes a time series to permanently rise above 0°C (y_w) is identified. The applied methods divide the entire domain of the time series into sub-regions in which the data are approximated by polynomials of degree zero or one. The segment which encompasses y₀ is termed the 'segment of interest' (S_interest). The combination of S_interest and the segment(s) with positive slope that immediately follows S_interest forms a section referred to as the 'section of total warming' (S_W_total ). The non-parametric Mann-Kendall test, following the modified trend-free pre-whitening approach (Burn et al., 2004), i