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) ( Rossow and Schiffer 1999 ). In our analysis the correlation between low-cloud fraction and lower-tropospheric stability is not as strong, and the slope of the regression is somewhat weaker: 5% cloud fraction per kelvin in our case, as compared to 6% per kelvin reported by KH93 . Differences may have a number of origins: (i) low-cloud fraction is measured differently by ISCCP than it was by KH93 , who used the cloud climatology derived from the surface observer network; (ii) the ISCCP low
) ( Rossow and Schiffer 1999 ). In our analysis the correlation between low-cloud fraction and lower-tropospheric stability is not as strong, and the slope of the regression is somewhat weaker: 5% cloud fraction per kelvin in our case, as compared to 6% per kelvin reported by KH93 . Differences may have a number of origins: (i) low-cloud fraction is measured differently by ISCCP than it was by KH93 , who used the cloud climatology derived from the surface observer network; (ii) the ISCCP low
–Southern Oscillation (ENSO) and the Arctic Oscillation (AO) ( Griffiths and Bradley 2007 ; Leathers et al. 2008 ). While a comprehensive analysis of the effect of such mechanisms is beyond the scope of this study, an exploratory analysis was performed. Leathers et al. evaluated the association between teleconnection patterns and temperature/precipitation values using significant variables obtained from a stepwise, multiple linear regression (MLR). Six teleconnection patterns were investigated: the Arctic
–Southern Oscillation (ENSO) and the Arctic Oscillation (AO) ( Griffiths and Bradley 2007 ; Leathers et al. 2008 ). While a comprehensive analysis of the effect of such mechanisms is beyond the scope of this study, an exploratory analysis was performed. Leathers et al. evaluated the association between teleconnection patterns and temperature/precipitation values using significant variables obtained from a stepwise, multiple linear regression (MLR). Six teleconnection patterns were investigated: the Arctic
identify how the conditions vary regionally across the ice sheet. In this study, the daily MEaSUREs dataset is examined in relation to concurrent conditions using a simple linear regression analysis. The conditions are examined regionally by using defined GrIS basins. Atmospheric general circulation and cloud conditions are described using the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). Section 2 provides a description of the datasets used and the regression
identify how the conditions vary regionally across the ice sheet. In this study, the daily MEaSUREs dataset is examined in relation to concurrent conditions using a simple linear regression analysis. The conditions are examined regionally by using defined GrIS basins. Atmospheric general circulation and cloud conditions are described using the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). Section 2 provides a description of the datasets used and the regression
). In a first step, the framework of graphical models is used to detect the existence of (Granger) causal interactions yielding the interaction time delays, while in a second step a certain partial correlation and a regression measure are introduced that allow one to specifically quantify the strength of an interaction mechanism in a well interpretable way. We will demonstrate that our approach goes beyond the pure graphical models analysis of Ebert-Uphoff and Deng (2012a) and enables us to
). In a first step, the framework of graphical models is used to detect the existence of (Granger) causal interactions yielding the interaction time delays, while in a second step a certain partial correlation and a regression measure are introduced that allow one to specifically quantify the strength of an interaction mechanism in a well interpretable way. We will demonstrate that our approach goes beyond the pure graphical models analysis of Ebert-Uphoff and Deng (2012a) and enables us to
-biennial oscillation (QBO) in lower-stratospheric equatorial winds, but not when the full dataset was used in their analysis. Since then several other observational studies have been performed. In a regression analysis using 18 years (1980–97) of Stratospheric and Microwave Sounding Units(SSU/MSU) temperature data corrected and compiled by the National Centers for Environmental Prediction (NCEP)–Climate Prediction Center (CPC), Hood (2004) , referred to hereafter as H2004 ) found a vertical three-cell pattern of
-biennial oscillation (QBO) in lower-stratospheric equatorial winds, but not when the full dataset was used in their analysis. Since then several other observational studies have been performed. In a regression analysis using 18 years (1980–97) of Stratospheric and Microwave Sounding Units(SSU/MSU) temperature data corrected and compiled by the National Centers for Environmental Prediction (NCEP)–Climate Prediction Center (CPC), Hood (2004) , referred to hereafter as H2004 ) found a vertical three-cell pattern of
and Greenland Seas and the Sea of Okhotsk, and decrease in the Labrador and Bering Seas) for late winter. Hence, only these PCs are included in the analysis discussed below. In total, 12 oceanic explanatory variables or regressors are considered. They are not independent and the associated SST anomalies extend much beyond their domain of definition. This is illustrated for August–October (ASO) in Fig. 3 (left), where the SST pattern a j associated with j th regressor is obtained from the
and Greenland Seas and the Sea of Okhotsk, and decrease in the Labrador and Bering Seas) for late winter. Hence, only these PCs are included in the analysis discussed below. In total, 12 oceanic explanatory variables or regressors are considered. They are not independent and the associated SST anomalies extend much beyond their domain of definition. This is illustrated for August–October (ASO) in Fig. 3 (left), where the SST pattern a j associated with j th regressor is obtained from the
. Background—Evaluation of regional climate trends Among a range of statistical approaches to assess the time series of past climate records and differentiate the anthropogenic changes from the climate variability, often referred as “exploratory data analysis” ( Schneider and Held 2001 ), conventional linear regression remains as the mostly used approach. It is worth noting that the various statistical approaches may have different definitions of climate variability and the results for underlying trend are
. Background—Evaluation of regional climate trends Among a range of statistical approaches to assess the time series of past climate records and differentiate the anthropogenic changes from the climate variability, often referred as “exploratory data analysis” ( Schneider and Held 2001 ), conventional linear regression remains as the mostly used approach. It is worth noting that the various statistical approaches may have different definitions of climate variability and the results for underlying trend are
, we will develop a descriptive model aiming at clarifying the relationship between wind predictability and statistical properties (i.e., standard deviation and kurtosis) of wind component fluctuations in an idealized conceptual framework. Note that statistical predictability of wind components is not directly related to the mean vector wind, as the regression analysis considers fluctuations around the mean. It follows that the apparent relationship between the orientation of the mean wind and
, we will develop a descriptive model aiming at clarifying the relationship between wind predictability and statistical properties (i.e., standard deviation and kurtosis) of wind component fluctuations in an idealized conceptual framework. Note that statistical predictability of wind components is not directly related to the mean vector wind, as the regression analysis considers fluctuations around the mean. It follows that the apparent relationship between the orientation of the mean wind and
in favor of should conclusions conflict for reasons illustrated in the next section. It remains to derive results 3 and 4, which is done in the appendix. This task is important since the asymptotic distribution depends on the presence/absence of a trend. One would have to perform yet another derivation for regression structures employing sinusoidal, quadratic, or exponential terms. Sinusoidal terms, for example, could arise in the analysis of daily or monthly series. This said, the derivations
in favor of should conclusions conflict for reasons illustrated in the next section. It remains to derive results 3 and 4, which is done in the appendix. This task is important since the asymptotic distribution depends on the presence/absence of a trend. One would have to perform yet another derivation for regression structures employing sinusoidal, quadratic, or exponential terms. Sinusoidal terms, for example, could arise in the analysis of daily or monthly series. This said, the derivations
and masked to match the spatial and temporal data availability of that dataset on a grid-box basis. The models used in this analysis are listed in Table 1 . Table 1. List of modeling groups and models [including expansions and institute identification (ID)] used in this analysis. 4. Zonal patterns of precipitation change Zonal-mean change in precipitation is calculated by applying a linear least squares regression to precipitation averaged across each zonal band and is expressed as the
and masked to match the spatial and temporal data availability of that dataset on a grid-box basis. The models used in this analysis are listed in Table 1 . Table 1. List of modeling groups and models [including expansions and institute identification (ID)] used in this analysis. 4. Zonal patterns of precipitation change Zonal-mean change in precipitation is calculated by applying a linear least squares regression to precipitation averaged across each zonal band and is expressed as the
