D EFINITIONS OF DERIVED VARIABLES

At the synoptic scale, climate variability in the study region is largely governed by the behavior of the polar jet stream and the relative intensity of several

semi-permanent pressure systems. Variations in the intensity of these pressure systems and the tracking and intensity of synoptic scale phenomena in the study region have been linked to larger pressure oscillations (or teleconnection patterns), specifically the North Atlantic Oscillation (NAO) and Pacific North American (PNA) pattern. Both the NAO and PNA are prominent hemispheric-scale modes of climate variability that are strongly linked to surface temperature and precipitation at least partly via synoptic scale circulation

patterns. For example, the NAO accounts for 31% of the variance in mid-latitude winter mean surface air temperatures (Hurrell 1996) and the PNA is closely linked with both thermal and hydrologic regimes within the Ohio Valley (Coleman and Rogers 2003;

Sheridan 2003), accounting for as much as 40% of the variance in surface air temperature during winter season (Leathers et al. 1991).

The NAO and PNA teleconnection indices describe patterns of mean sea level pressure (MSLP) and tropospheric height variability, respectively, and hence represent the steering patterns of synoptic scale phenomena (Leathers et al. 1991; Hurrell 1995).

They are used here both as an evaluation tool for GCMs and to explain differences in the synoptic scale climate in the study region across time or data sets. Both the NAO and PNA exhibit variability on a range of temporal scales. Stephenson and Pavan (2003) show that the NAO signal is dominated by short-term (i.e., year to year) variations and state that more than 70% of the NAO variance is explained by fluctuations with periods of less than a decade. Likewise, the PNA teleconnection varies on all timescales from days to decades (Blackmon et al. 1984; Yarnal and Leathers 1988).

3.1.1.1 The North Atlantic Oscillation (NAO)

The NAO describes a redistribution of atmospheric mass between the Arctic and the subtropical Atlantic, typically characterized by winter sea-level pressure anomalies associated with the Azores high and the Icelandic low (Walker 1924; Walker and Bliss 1932). During the positive phase of the NAO, both of these pressure centers are stronger than average and shifted to the northeast (Glowienka-Hense 1990), resulting in stronger westerlies in the mid-latitude Atlantic Ocean. Although it is centered east of North America, the positive phase of the NAO is generally associated with higher temperatures and increased moisture content in the Midwestern USA in response to the strengthening of the flow around the subtropical Atlantic high generating southerly flow over the eastern USA (Dickson and Namias 1976; Yarnal and Leathers 1988; Yin 1994).

There is no unique way to define the spatial structure of the NAO (Hurrell et al.

2003). It has been defined in terms of pressure differences between point locations, area weighted pressure extremes or in terms of principal components of pressure fields (see Osborn et al. 1999; Hurrell et al. 2003). In this study, the NAO index is computed as the difference in standardized (i.e., transformed to have a mean of zero and variance of one by subtracting the mean and dividing by the standard deviation) SLP between grid points near the NAO “centers of action” or:

Iceland Azores SLP SLP

NAO= − 3.1 where SLPAzores is the standardized SLP at Ponta Delgada, Azores (37.7°N, 25.7°W) and SLPIceland is the standardized SLP at Stykkisholmur, Iceland (65.1°N, 22.7°W).

3.1.1.2 The Pacific/North American (PNA) pattern

The mean flow over the Pacific-North American sector is characterized by a trough in the east-central North Pacific, a ridge over the Rocky Mountains, and a trough over eastern North America (Leathers et al. 1991; Kang et al. 2002). The PNA

teleconnection index reflects deviations from this mean flow, suggesting more meridional (positive phase) or zonal (negative phase) flow over North America. During the positive phase, negative geopotential height anomalies are located south of Alaska and in the southeastern United States, while positive geopotential height anomalies are located near Hawaii and over the Rocky Mountains resulting in meridional flow over North America.

During the negative PNA phase, the anomalies at the pressure centers are reversed and the flow over North America is more zonal.

The PNA index used in this study is computed using the equation of Wallace and Gutzler (1981):

[

]

4

1 Z N W Z N W Z N W Z N W

PNA= ^{o o} − ^{o o} + ^{o o} − ^{o o} 3.2

where Z are standardized (by season within the study period) 500 hPa geopotential height values.

3.1.2 Geostrophic flow and vorticity component definitions

Several studies have identified geostrophic flow and vorticity components as useful downscaling predictors (Wilby 1998; Wilby 1998b). These derived variables can be estimated for any regular grid from sea level pressure fields using the method of Dessouky and Jenkinson (1975). Specifically, given the hypothetical grid shown in Figure 3.1, the flow and vorticity components are computed as follows.

Figure 3.1 Hypothetical 2.5° × 2.5° grid for demonstration of geostrophic flow and vorticity calculations.

The westerly component of surface geostrophic wind, GEOW, at the central point (P3,3) is where P is the mean sea-level pressure (SLP) and the subscript denotes the grid point.

The southerly component of the surface geostrophic wind, GEOS, at the central grid point (3,3) is given by:

latitude which accounts for the relative difference in grid spacing in the north-south and east-west directions.

The resultant geostrophic flow, GEOWS, at the central grid point (3,3) is then computed as:

GEOWS = W² +S² 3.5 The westerly component of shear vorticity, GEOZW, at the central grid point (3,3) is given by:

where c2 is a constant equal to

. Both constants account for the relative difference in grid spacing

in the north-south and east-west directions.

The southerly component of shear vorticity, GEOZS, at the central grid point (3,3) is given by:

latitude , again to account for the relative differences in north-south and east-west grid spacing.

The total shear vorticity, GEOZT, is taken as the sum of GEOZW and GEOZS. The units for the geostrophic flow variables are hPa per 10° of latitude at the grid point latitude. The vorticity variables are expressed in units of hPa per 10° of latitude at the grid point latitude, per 10° of latitude.