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  • View in gallery

    The region within the black box defines the Midwest. Dots show the locations of precipitation stations, and thin lines indicate Voronoi polygons. Light gray shading indicates Voronoi polygons included in the Midwest domain, and dark gray shading denotes the Midwest polygons that were used to define a lake effect snow index.

  • View in gallery

    (a) The real and (b) the imaginary part of the first HEOF of qv prior to any phase shift.

  • View in gallery

    The real part of the following phase-shifted first HEOFs: (a) horizontal moisture transport (qv1), (b) temperature advection (TA1), (c) vorticity advection (VA1), and (d) jet stream–level wind speed (, white contours with negative values dashed and zero contour suppressed). Shading in (d) shows the real part of the phase-shifted second HEOF of jet stream–level wind speed ().

  • View in gallery

    (a) For 1–5 Dec 1989, the phase and real part of the leading HEOF of horizontal moisture transport (qv1). (b)–(d) The daily mean horizontal moisture transport vector field (qv) for 3 days during 1–5 Dec 1989.

  • View in gallery

    (a) Scatterplot of P0.25 (mm0.25) vs the real part of the phase-shifted first HEOF of 850-hPa moisture transport (qv1). (b) Correlation between qv1 and precipitation at each station in the Midwest domain.

  • View in gallery

    For days with Midwest precipitation (P0.25) greater than or equal to the 90th percentile, anomalies of (a) jet stream–level wind speed (, shading with zero contour bold) and moisture transport [qv (m s−1); arrows], (b) jet core probability (, shading with zero contour bold), and (c) temperature advection (TA, shading) and vorticity advection (VA, contoured at 0.4 × 10−9 s−2 with negative values dashed and the zero contour suppressed).

  • View in gallery

    Power spectrum of the real part of the phase-shifted first HEOF of horizontal moisture transport (qv1, bold curve). A null red noise spectrum is shown (solid curve) along with its associated 95% confidence limit (dashed curve). Vertical dotted lines bound periods from 3 to 7 days.

  • View in gallery

    For days with the lake effect snow index () greater than or equal to 0.9: composite anomalies of (a) jet stream–level wind speed (, shaded contours) and 850-hPa moisture transport (qv, arrows) and (b) vorticity advection (VA, contours) and temperature advection (TA, shading). The zero contours are bold. (c) The first HEOF of qv phase shifted to maximize the correlation between its real part and .

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Propagating Atmospheric Patterns Associated with Midwest Winter Precipitation

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  • 1 Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah
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Abstract

For winters over eastern North America, complex Hilbert empirical orthogonal function (HEOF) analysis was used to objectively identify propagating patterns in four atmospheric fields that have potential relevance to precipitation: jet stream–level wind speed, 850-hPa moisture transport (qv), temperature advection (TA), and vorticity advection (VA). A novel phase shift method was used to show the location where each propagating pattern was most correlated with Midwest precipitation, and each of the four phase-shifted HEOF patterns was compared to its respective high-precipitation composite view. The leading HEOFs of the three transport fields (qv, TA, and VA), which collectively represented the dynamics associated with a midlatitude cyclone, accounted for almost half of Midwest precipitation variability and were associated with lake effect snow when propagating downstream from the Midwest. Correlation and spectral analyses revealed how the propagating transport patterns were related to the Pacific–North American pattern and other teleconnections. The leading HEOF of jet stream–level wind speed, which represented the tendency for the jet stream to migrate equatorward over the study region during winter, accounted for only about 4% of Midwest daily precipitation variability. In contrast, the second HEOF of jet stream–level wind speed, which represented an eastward propagating trough dynamically consistent with a midlatitude cyclone, accounted for 16% of Midwest daily precipitation variability.

Corresponding author address: Courtenay Strong, University of Utah Department of Atmospheric Sciences, 135 S 1460 E, Salt Lake City, UT 84112-0010. E-mail: court.strong@utah.edu

Abstract

For winters over eastern North America, complex Hilbert empirical orthogonal function (HEOF) analysis was used to objectively identify propagating patterns in four atmospheric fields that have potential relevance to precipitation: jet stream–level wind speed, 850-hPa moisture transport (qv), temperature advection (TA), and vorticity advection (VA). A novel phase shift method was used to show the location where each propagating pattern was most correlated with Midwest precipitation, and each of the four phase-shifted HEOF patterns was compared to its respective high-precipitation composite view. The leading HEOFs of the three transport fields (qv, TA, and VA), which collectively represented the dynamics associated with a midlatitude cyclone, accounted for almost half of Midwest precipitation variability and were associated with lake effect snow when propagating downstream from the Midwest. Correlation and spectral analyses revealed how the propagating transport patterns were related to the Pacific–North American pattern and other teleconnections. The leading HEOF of jet stream–level wind speed, which represented the tendency for the jet stream to migrate equatorward over the study region during winter, accounted for only about 4% of Midwest daily precipitation variability. In contrast, the second HEOF of jet stream–level wind speed, which represented an eastward propagating trough dynamically consistent with a midlatitude cyclone, accounted for 16% of Midwest daily precipitation variability.

Corresponding author address: Courtenay Strong, University of Utah Department of Atmospheric Sciences, 135 S 1460 E, Salt Lake City, UT 84112-0010. E-mail: court.strong@utah.edu

1. Introduction

The atmospheric dynamics underlying precipitation variability over the Midwest have received increasing attention, in part because of this region’s role in the upward trend in annual precipitation over the contiguous United States (Karl and Knight 1998; Groisman et al. 2004, 2005). The Midwest lacks direct influence from tropical systems and complex terrain, and is collocated with a maximum in cyclone frequency centered over the Great Lakes (Zishka and Smith 1980; Reitan 1974; Wernli and Schwierz 2006). In winter, the maximum in cyclone frequency over the Midwest is part of two cyclone trajectories that originate in Colorado and Alberta in the lee of the Rocky Mountains and merge over the Great Lakes (Zishka and Smith 1980; Isard et al. 2000), and associated trends in cyclone count have been investigated in several studies (e.g., Angel and Isard 1998; Key and Chan 1999; Konrad 2001).

Precipitation variability in the Midwest can also be understood in the context of large-scale standing-wave teleconnections typically resolved via empirical orthogonal function (EOF) analysis (e.g., Small et al. 2010). The positive phase of the Pacific–North American pattern (PNA) depicts a wave train consisting of an anomalously strong Aleutian low, positive height anomalies over the western United States, and negative height anomalies over the southeastern United States (Wallace and Gutzler 1981). Rodionov (1994) found that composites of 700-hPa geopotential heights for low and high Great Lakes precipitation closely resembled the positive and negative phases of the PNA pattern, respectively. An inverse relationship between precipitation in winter months and the PNA index was documented for the Ohio River valley (ORV) and the Midwest in several studies (Leathers et al. 1991; Serreze et al. 1998; Coleman and Rogers 2003). Great Lakes cyclones occurred more frequently over Canada during the positive phase of the PNA and more frequently over the southwest United States in the lee of the Rockies during the negative phase. Angel and Isard (1998) found that the PNA pattern was anticorrelated with strong cyclone occurrence over the Great Lakes during November, December, and January.

Midwest precipitation is also influenced by the El Niño–Southern Oscillation (ENSO), where El Niño events, characterized by warm SST anomalies in the eastern equatorial Pacific, are associated with reduced precipitation over the Midwest, primarily in the vicinity of the ORV during winter (e.g., Gershunov and Barnett 1998; Mo and Schemm 2008; Becker and Berbery 2009; Zhang et al. 2010). Eichler and Higgins (2006) showed changes in winter storm tracks corresponding to ENSO, with the Midwest experiencing an increase in surface cyclone frequency during La Niña events. The results of Becker and Berbery (2009) revealed a relative increase in the intensity of winter daily precipitation over the upper Midwest during El Niño events and a decrease in intensity over the ORV.

Variations in moisture transport are one way that teleconnections translate into precipitation variability. EOF analysis of moisture transport over North America identified a leading standing-wave pattern that was linked to the PNA and ENSO, and its Pacific center of action markedly impacted precipitation over the west coast of the United States (Dominguez and Kumar 2005). This same leading EOF also had a circulation center over the southeastern United States that regulated moisture flux from the Gulf of Mexico into the central United States, and significantly impacted precipitation variability over the Midwest.

The objective of this study was to determine how Midwest daily winter precipitation variability depended on leading patterns of propagating atmospheric variability over eastern North America. To accomplish this objective, we performed a complex Hilbert empirical orthogonal function (HEOF) analysis on four atmospheric fields, we used correlation analysis to evaluate the importance of the HEOFs to Midwest precipitation, and we used a novel HEOF phase shift method to enable comparison of the HEOFs and high-precipitation atmospheric composites. This set of analyses revealed the role of each propagating pattern in daily precipitation variability, as well as the role of each propagating pattern in daily variability of the field from which the pattern was derived. Section 2 describes data and methods, section 3 presents the propagating patterns and their relationship with precipitation and teleconnections, and summary and discussion are given in section 4.

2. Data and methods

Data

The Midwest was defined as the area bounded by 36°–46°N and 83°–95°W (bold box, Fig. 1)—essentially the region encompassing the upper Mississippi and Midwest subregions in Groisman et al. (2004) and Groisman et al. (2005). This region had a relatively dense precipitation measurement network with data extending back to the 1950s and earlier for most stations. The Midwest daily (0000–2359 UTC) total precipitation in mm from 1 December 1957 to 28 February 2009 was obtained from the Global Historical Climate Network (GHCN) daily dataset available from the National Climatic Data Center (NCDC; http://www.ncdc.noaa.gov/). Station data was inspected to ensure that no more than 10% of the measurements were missing from any record, and a total of 150 stations within the Midwest were retained after the inspection (indicated by dots within the bold box in Fig. 1).

Fig. 1.
Fig. 1.

The region within the black box defines the Midwest. Dots show the locations of precipitation stations, and thin lines indicate Voronoi polygons. Light gray shading indicates Voronoi polygons included in the Midwest domain, and dark gray shading denotes the Midwest polygons that were used to define a lake effect snow index.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

Atmospheric fields described in section 2b were based on daily values derived from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (NNR; Kalnay et al. 1996) provided by the Physical Sciences Division (PSD) of the National Oceanic and Atmospheric Administration (NOAA) Earth Systems Research Laboratory in Boulder, Colorado (http://www.esrl.noaa.gov). Six-hourly values were developed for each field, and daily means were then calculated to align with the daily mean precipitation data.

Monthly mean values of two teleconnection indices were obtained from the Climate Prediction Center (http://www.cpc.ncep.noaa.gov): the North Atlantic Oscillation index (NAOI; Barnston and Livezey 1987) and the PNA index (PNAI; Wallace and Gutzler 1981). The NAOI and PNAI were computed from the rotated principal components (e.g., Horel 1981; Barnston and Livezey 1987) of standardized 500-hPa height anomalies based on the 3-month period centered on each month. The multivariate ENSO index (MEI; Wolter and Timlin 1993, 1998) was defined using the first unrotated principal component of combined sea level pressure, surface wind velocity, sea surface temperature (SST), surface air temperature, and cloud cover over the central Pacific. Bimonthly MEI values were obtained from the NOAA/OAR/ESRL PSD (http://www.esrl.noaa.gov).

b. Derived fields

Midwest precipitation data retained following the initial quality control procedures were area weighted based on a Voronoi diagram (Aurenhammer 1991) of the Midwest precipitation stations (Fig. 1). Each station was assumed representative of the area in its Voronoi polygon because, by definition, every point in the polygon was closer to the enclosed station than to any other station. The area-weighted precipitation for the Midwest was thus
e1
where pi was the daily total precipitation in millimeters for station i in the GHCN data, wi was the area of the polygon enclosing station i, and n = 150 was the number of Midwest stations (i.e., the number of dots shown inside the bold box in Fig. 1). The results for P presented here were robust to reasonably sized changes in the definition of the Midwest; shifting the Midwest latitude and longitude bounds by ±2.5° yielded precipitation time series correlated with P at r ≥ 0.95, where r is the Pearson correlation coefficient. The distribution of P was positively skewed, so a ¼ power transformation (denoted P0.25) was used to establish approximate symmetry (Hinkley 1977).
Additionally, a subset of stations was subjectively chosen to form a “lake effect” index (FL). The lake effect station set (L) contained stations near the eastern side of Lake Michigan downwind of the dominant northwest lake fetch (dark gray patches in Fig. 1); FL was formulated as the fraction of total Midwest precipitation attributed to stations in L:
e2
where βi was one if iL and zero otherwise, and FL was undefined on days when P = 0. Higher values of FL indicated snow in the lee of the Great Lakes with little or no snow over the remainder of the Midwest—conditions characteristic of lake effect snow because lake effect snow tended to occur in subsidence regimes following the passage of snow-producing cyclones. As done for total Midwest precipitation, a ¼ power transformation was applied to FL, yielding the transformed time series .

Jet stream–level wind speeds () were taken from the surface of maximum wind (SMW), which was defined as the surface passing through the greatest wind speed in each column from 500 hPa to the tropopause or the upper bound of tropospheric jet streams extending into the lower stratosphere (Strong and Davis 2005). Use of the SMW rather than wind speed on a constant pressure surface takes into consideration horizontal variations in jet core pressure. A jet stream core was defined as a local maximum of wind speed greater than or equal to 25.7 m s−1 based on a second derivative test along each meridian. The probability of a jet stream core is denoted .

To analyze horizontal moisture transport, the vector field qv ≡ (qu, ) was calculated at 850 hPa. The vector field qv proved to be more informative than scalar moisture advection (−v · q) because qv indicated the magnitude and direction of moisture transport. Use of vertically integrated horizontal moisture flux would have had a minimal impact on the findings because most atmospheric water vapor was concentrated in the lower troposphere.

To gain insight into the dynamics of vertical motion, 850-hPa temperature advection (TA; K s−1) and the difference in vorticity advection between 850 and 250 hPa (VA; s−2) were analyzed. The geostrophic counterparts of VA and TA are associated with large-scale vertical motion according to the traditional omega equation (e.g., Holton 2004).

c. Statistical methods

Bootstrapping (e.g., Wilks 1995) was used to test the statistical significance of all Pearson correlation coefficients (r) reported here. Bootstrapped samples were constructed by selecting n pairs of values with replacement from a sample of n pairs, and r was calculated for each bootstrapped sample. One-thousand bootstrapped samples were developed for each correlation, and results were tested for significance at the α = 0.05 level.

For the estimate of power spectra, a Hanning window was applied to each winter, and the spectral estimates for each of the m = 52 winters were averaged. The resulting spectral estimate resolved periods from 2 to 90 days, and had 2m = 104 degrees of freedom (Welch 1967). The null red noise spectrum followed Gilman et al. (1963), and the 95% confidence limit was based on the right-tail quantile of the chi-squared distribution with 2m degrees of freedom as given in Welch (1967).

Traditional EOF analysis is useful for identifying leading variability patterns within a dataset, but its inability to resolve propagating wavelike structures is a limitation (Barnett 1983). Complex HEOF analysis resolves propagating patterns by complexifying the input data so that its imaginary part is the original dataset phase shifted in time by π/2 (Barnett 1983; Horel 1984). As discussed in Hannachi et al. (2007), HEOF analysis is distinct from “complex EOF analysis” in which the two components of a vector field are cast as real and imaginary parts to enable analysis of standing-wave patterns in vector fields (e.g., Kaihatu et al. 1998).

Together, the real and imaginary parts of an HEOF provide a parsimonious representation of a propagating pattern that would otherwise appear as two degenerate patterns in quadrature in traditional EOF analysis (Hannachi et al. 2007). Here, HEOF analysis was applied separately to the detrended , qv, VA, and TA complexified fields, and the fraction of field variance accounted for by each HEOF is given in Table 1. All HEOFs reported here were well separated under the criterion of North et al. (1982). The analysis domain extended from 20° to 60°N and 60° to 110°W on the 2.5° × 2.5° NNR grid (mapped domain in Fig. 2).

Table 1.

For each HEOF (notation defined in text), the fraction of field variance accounted for by the HEOF.

Table 1.
Fig. 2.
Fig. 2.

(a) The real and (b) the imaginary part of the first HEOF of qv prior to any phase shift.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

d. HEOF phase shift formulation

Research context may render one phase of a complex HEOF more informative or convenient than another (e.g., Klink and Willmott 1989; Merrifield and Winant 1989; von Storch et al. 1988). Here, to determine the location where a propagating pattern (HEOF) was maximally related to precipitation variability over a fixed region (the Midwest), we phase shifted the HEOF so that its real part was maximally correlated with P0.25 and its imaginary part had zero correlation with P0.25. Following the phase shift, the total (modulus) correlation with P0.25 was consolidated in the real part of the HEOF, and the real part of the HEOF depicted the propagating pattern in its phase most relevant to Midwest precipitation.

Denoting the kth HEOF of some field by ηk, and its associated principal component (time series) by ζk, the corresponding phase-shifted functions were defined as
e3
e4
The desired phase shift φk arose from the complex correlation (or complex covariance) between ζk and the time series in the fixed region of interest. Denoting power-transformed Midwest precipitation in vector form as , the complex covariance between P and the (unshifted) principal component ζk was
e5
where and are n × 1 vectors containing the means of P and ζk, respectively. Differentiating the real part of (5) with respect to φk and setting the result to zero yielded the critical point
e6
and the desired phase shift was
e7

The phase shift for the first HEOF of qv is presented as an example. Prior to phase shift, the real part of the first HEOF of qv depicted a cyclonic circulation centered over the Midwest (Fig. 2a), and the imaginary part depicted northeasterly qv over the Midwest (Fig. 2b). These two patterns lacked clear relevance to Midwest precipitation dynamics, and the modulus correlation between P0.25 and this unshifted HEOF was partitioned into real and imaginary parts.

The phase shift φ1 = −0.33π [from Eq. (7)] placed the real part of the HEOF pattern optimally to account for Midwest precipitation, with a southwesterly moisture fetch associated with an upstream surface cyclonic circulation and downstream surface anticyclonic circulation (Fig. 3a). Because the imaginary part had zero correlation with P0.25 after the phase shift, it was rendered statistically irrelevant, serving only to indicate the pattern’s direction of propagation (eastward in this case; not shown).

Fig. 3.
Fig. 3.

The real part of the following phase-shifted first HEOFs: (a) horizontal moisture transport (qv1), (b) temperature advection (TA1), (c) vorticity advection (VA1), and (d) jet stream–level wind speed (, white contours with negative values dashed and zero contour suppressed). Shading in (d) shows the real part of the phase-shifted second HEOF of jet stream–level wind speed ().

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

To illustrate that the phase shift φ1 = −0.33π maximized the correlation between P0.25 and the real part of the first HEOF of qv, Fig. 4 shows how the phase and real part of the first HEOF of qv varied as a midlatitude cyclone passed through the region during 1–5 December 1989. As the system entered the west edge of the HEOF domain on 1 December 1989 (Fig. 4b), the phase of the first HEOF of qv was close to −π/2 (Fig. 4a), indicating that the system was one-quarter wavelength upstream, rendering the real part of the first HEOF of qv close to zero (Fig. 4a). When the system arrived to the study region during 3 December 1989 (Fig. 4c), the phase of the first HEOF of qv approached zero (Fig. 4a), the real part of the first HEOF of qv maximized (Fig. 4a), and qv maximized at 2.25 mm0.25 (not shown). As the system slowed, the phase of the first HEOF of qv fluctuated around zero (Fig. 4a), and the magnitude of its real part weakened (Fig. 4a) as the moisture delivery weakened (Fig. 4d). The correlation between P0.25 and the real part of the first HEOF of qv for 1–5 December 1989 was r = 0.84.

Fig. 4.
Fig. 4.

(a) For 1–5 Dec 1989, the phase and real part of the leading HEOF of horizontal moisture transport (qv1). (b)–(d) The daily mean horizontal moisture transport vector field (qv) for 3 days during 1–5 Dec 1989.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

3. Results

Over the period of analysis (1958–2009), the linear trend of P was small (order 10−2 mm decade−1), so the results section focuses on oscillatory variability rather than linear trends. In sections 3ab, the real part of propagating patterns of moisture transport (qv), temperature advection (TA), vorticity advection (VA), and jet stream–level wind speed () are shown in their phase most correlated with Midwest precipitation variability. The four presented patterns were dynamically consistent with one another, and provided complementary views of one propagating atmospheric system (section 3a). The propagating system is related to teleconnections in section 3b, and an alternate phase of the propagating pattern of qv is shown to be relevant to lake effect snow in section 3c.

a. Propagating atmospheric system

The nth HEOF of a field is denoted by the field name with a subscript n (e.g., the first HEOF of is denoted ). HEOF phase shifting (section 2d) maximized the correlation between the real part of each pattern and P0.25, meaning the real part of each pattern is shown in its phase most relevant to Midwest precipitation. In this subsection, only the real part of phase-shifted HEOFs are shown.

The first HEOF captured a meridionally propagating jet stream pattern with a predominantly monthly power spectrum (not shown). The phase-shifted pattern (white contours, Fig. 3d) positioned the jet stream near the latitude of the Great Lakes, meaning that poleward jet stream positions slightly favored precipitation []. The times series indicated a tendency for the jet stream to migrate equatorward over the spatial range of its loading pattern during winter, and short-lived poleward excursions from this equatorward motion were common during most winters.

Phase-shifted (shading, Fig. 3d) placed the Midwest under the exit sector of an upper-level trough with enhanced jet stream–level winds to the southwest. When and first HEOFs qv1, TA1, and VA1 were phase shifted, all four patterns were dynamically consistent (Fig. 3), and the four patterns collectively captured the propagating precipitation dynamics associated with an incoming upper-level trough or midlatitude cyclone. Specifically, the Midwest was below the exit sector of an upper-level trough with a jet streak to its southwest (Fig. 3d), an 850-hPa cyclonic circulation was to its west (Fig. 3a), and warm, moist advection (Figs. 3a,b) and positive vorticity advection (Fig. 3c) were present.

Of all the HEOFs analyzed, qv1 had the strongest correlation with P0.25 (r = 0.67; Fig. 5a; Table 2). Correlations between qv1 and precipitation at individual stations tended to be weaker than the correlation of qv1 and P0.25, and generally increased in strength from northwest to southeast across the study region (Fig. 5b). Various correlation and composite analyses indicated that the qv1 pattern was part of a single archetypal precipitation system. Specifically, the , TA1, and VA1 time series were each significantly correlated with P0.25 and with qv1 (Table 2). In addition, maps of the temporal correlation between the qv1 time series and the atmospheric fields TA, VA, and (not shown) closely resembled the corresponding phase-shifted HEOF patterns for TA1, VA1, and (Fig. 3).

Fig. 5.
Fig. 5.

(a) Scatterplot of P0.25 (mm0.25) vs the real part of the phase-shifted first HEOF of 850-hPa moisture transport (qv1). (b) Correlation between qv1 and precipitation at each station in the Midwest domain.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

Table 2.

Correlation matrix for daily P0.25 and five HEOFs. All nonzero values are significant at α = 0.05.

Table 2.

Finally, composites of , qv, TA, and VA for days with precipitation greater than or equal to the 90th percentile of P0.25 closely resembled the patterns in the corresponding HEOFs: the composite indicated the exit sector of an upper-level trough over the Midwest (shading, Fig. 6a), the qv composite indicated upstream cyclonic/downstream anticyclonic moisture advection at 850 hPa (arrows, Fig. 6a), the TA composite showed warm air advection over the Midwest (shading, Fig. 6c), and the VA composite showed positive vorticity advection over the Midwest (contours, Fig. 6c). Despite the similarities, some differences are apparent comparing the patterns in the phase-shifted HEOFs (Fig. 3) and the patterns in the composite fields (Fig. 6). For example, the composite eddies are tilted southwest to northeast, whereas the phase-shifted HEOFs depict eddies that are more meridionally oriented (cf. Figs. 3b,d and Fig. 6c), and such differences might be expected given the contrasting analysis methods and contrasting underlying data (upper 10% of precipitation days for composites in Fig. 6 versus all days for HEOFs in Fig. 3).

Fig. 6.
Fig. 6.

For days with Midwest precipitation (P0.25) greater than or equal to the 90th percentile, anomalies of (a) jet stream–level wind speed (, shading with zero contour bold) and moisture transport [qv (m s−1); arrows], (b) jet core probability (, shading with zero contour bold), and (c) temperature advection (TA, shading) and vorticity advection (VA, contoured at 0.4 × 10−9 s−2 with negative values dashed and the zero contour suppressed).

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

To further illustrate the role of the jet stream, Fig. 6b shows the jet streak configuration associated with the upper-level trough, indicating enhanced likelihood of jet stream cores (; section 2b) to the southwest over the central United States and to the northeast over the Great Lakes. Placement of jet streaks to the southwest and northeast of the Midwest is particularly conducive to upward vertical motion, and closely resembles configurations identified in case studies of heavy Midwest precipitation (e.g., Uccellini 1976; Hakim and Uccellini 1992). As a context for the size of the anomalies in Fig. 6b, climatological winter over the Midwest ranges from 0.10 to 0.15 (Strong and Davis 2007).

Spectral analysis of the qv1 time series revealed statistically significant energy for variations with periods from 3 to 7 days (above the dashed curve, Fig. 7), which is consistent with a midlatitude cyclone. Although almost indistinguishable from red noise at the 95% confidence level, qv1’s energy for periods longer than 10 days was nonnegligible. In the next section, some of this lower-frequency energy is shown to be tied to planetary-scale teleconnections.

Fig. 7.
Fig. 7.

Power spectrum of the real part of the phase-shifted first HEOF of horizontal moisture transport (qv1, bold curve). A null red noise spectrum is shown (solid curve) along with its associated 95% confidence limit (dashed curve). Vertical dotted lines bound periods from 3 to 7 days.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

b. Relationship with teleconnections

Because teleconnections are most often based on monthly or seasonal mean data, daily qv1 and P0.25 values were averaged over each winter ( and , respectively) for this subsection. Table 3 summarizes the relationships among , , and leading teleconnections. None of the teleconnections explained as much variance as , and more than one-third of the variance of was accounted for by (r = 0.67, Table 3). This result might be anticipated because the qv1 spatial pattern was detected locally over the eastern United States whereas the teleconnection patterns were more hemispheric in scale. In addition, teleconnections highlighted standing-wave patterns rather than propagating wave patterns, and Midwest winter precipitation is largely driven by propagating waves (midlatitude cyclones).

Table 3.

For December–February (DJF) mean values, correlations between , teleconnection indices, and . Bold values are significant at α = 0.005.

Table 3.

The NAO’s centers of action were downstream from the Midwest (not shown), and the NAO had only weak influences on eastern North America’s propagating atmospheric patterns [e.g., , Table 3] and on Midwest precipitation [, Table 3]. Tropical Pacific variations, as manifested in ENSO, had a significant impact on , which is consistent with the ability of ENSO to modulate extratropical variations over North America, including the PNA (e.g., Namias et al. 1988; Trenberth 1990; Bladé 1999; Hannachi 2001).

Of the teleconnections analyzed here, the PNA had the strongest correlation with , accounting for approximately 16% of its variance (r = −0.40, Table 3). The propagating wave and jet stream pattern associated with the phase-shifted HEOFs in Fig. 3 projected well onto the trough upstream of the Midwest defined in the negative phase of the PNA (Wallace and Gutzler 1981, their Fig. 16). This was in agreement with Strong and Davis (2008), who found that the negative phase of the second EOF of winter Northern Hemisphere extratropical jet stream probability anomalies, characterized by a merged jet stream over central North America, was associated with the negative phase of the PNA.

The moisture transport pattern in Fig. 3a has been linked to the PNA as well. In studying the PNA and monthly mean precipitation in the ORV, Coleman and Rogers (2003) found that the meridional component of 850-hPa moisture flux was significantly greater over the ORV for winters in the uppermost quintile of their ORV index of precipitation compared to winters in the lowest quintile of their ORV index; their moisture flux pattern shares similarities with the spatial pattern of qv1, featuring an axis oriented southwest–northeast extending from the Gulf of Mexico to the eastern United States.

c. Propagating pattern relevance to lake effect snow

Lake effect snow from the Great Lakes region is an important component of Midwest precipitation, accounting for at least one-third of lakeshore snow totals (e.g., Eichenlaub 1970). Lake effect snow often occurs following the passage of an upper-level trough, which typically results in low-level north or northwesterly flow over the surfaces of one or more of the Great Lakes. When the lake is unfrozen, and the surface to 850-hPa lapse rate is approximately 10°–13°C (e.g., Holroyd 1971; Niziol et al. 1995), cold advection over the lake results in upward heat and moisture fluxes, favoring the development of clouds and precipitation (e.g., Rothrock 1969; Braham 1983).

The HEOF phase shift φ1 = −0.33π (section 2d) maximized the correlation between the real part of the first HEOF of qv and Midwest precipitation, and the resulting phase-shifted qv1 pattern depicted a cyclone upstream of the Midwest (Fig. 3a). In contrast, the phase shift that maximized the real correlation between the first HEOF of qv and the lake effect snow index (section 2b) depicted a cyclone downstream from the Midwest with a dry northerly component to the flow over the Great Lakes (Fig. 8c)—a pattern conducive to cold advection over the lake surface and lake effect snow. The first HEOF of qv pattern in Fig. 8c was advanced approximately one-half wavelength downstream from the qv1 pattern in Fig. 3a, meaning the phase shift for lake effect snow in Fig. 8c was approximately φ1 + π.

Fig. 8.
Fig. 8.

For days with the lake effect snow index () greater than or equal to 0.9: composite anomalies of (a) jet stream–level wind speed (, shaded contours) and 850-hPa moisture transport (qv, arrows) and (b) vorticity advection (VA, contours) and temperature advection (TA, shading). The zero contours are bold. (c) The first HEOF of qv phase shifted to maximize the correlation between its real part and .

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0111.1

To verify the lake effect snow atmospheric pattern in Fig. 8c, we calculated composite qv anomalies for days when was greater than or equal to its 90th percentile. The resulting qv composite (Fig. 8a) showed an upstream anticyclone and downstream cyclone with a northerly component of qv over the Great Lakes region—a pattern similar to the phase-shifted first HEOF of qv (Fig. 8c) and conducive to cold air advection over the lake surface (Fig. 8b). Composite anomalies for the same set of days (Fig. 8a) showed that the upstream anticyclone and downstream cyclone configuration was associated with a jet stream pattern placing the Midwest in the entrance sector of an upper-level trough.

The modulus correlation between and the first HEOF of qv was significant at the 95% confidence level, but limited (r = 0.20) compared to the modulus correlation between Midwest precipitation and the first HEOF of qv. Some of the weakness in the correlation between and the first HEOF of qv may stem from subtle but important differences between the qv patterns in Figs. 8a,c. For example, in Fig. 8a the cyclone is farther offshore and the flow over the Great Lakes is north or northwesterly, whereas in Fig. 8c, the cyclone is depicted over land, and the flow over the Great Lakes is northeasterly. In addition, qv does not resolve the important micro- to mesoscale physics of lake effect snow noted at the beginning of this subsection.

4. Summary and discussion

Propagating patterns of atmospheric variability relevant to Midwest winter precipitation were detected over eastern North America via HEOF analysis. A novel method was used to phase shift each HEOF so its real part was maximally correlated with Midwest precipitation, meaning the real part of the HEOF showed geographically where the propagating features maximally impacted Midwest precipitation variability. The phase shift also rendered the imaginary part of the HEOF statistically irrelevant (zero correlation with Midwest precipitation), meaning it served only to indicate the pattern’s direction of propagation.

The first HEOF of captured a monthly time scale meridional jet stream propagation with only modest importance to Midwest precipitation (r = 0.19), and phase shifting positioned the jet stream at the latitude of the Great Lakes. The second HEOF of captured an eastward propagating trough of greater importance to Midwest precipitation variability (r = 0.40), and phase shifting positioned the trough’s exit sector over the Midwest with enhanced jet-level winds to the southwest. Composite analysis indicated that the incoming trough was especially conducive to above-average precipitation when jet streaks were present to the southwest or northeast of the Midwest.

The strongest predictor of Midwest precipitation was the first HEOF of qv (r = 0.67), and phase shifting positioned the qv cyclonic circulation upstream from the Midwest. The propagating qv pattern was predominantly synoptic, but had nonnegligible energy at weekly-to-monthly time scales related to hemispheric teleconnections. The propagating qv pattern’s relevance to lake effect snow was uncovered by phase shifting the pattern an additional one-half wavelength downstream.

The propagating atmospheric patterns were detected independent of precipitation, and the fact that HEOFs , qv1, VA1, and TA1 were correlated with one another and with precipitation evidenced the importance of coherent, zonally propagating atmospheric systems to Midwest winter hydrometeorology. It was interesting that the meridionally propagating first HEOF of dominated jet stream variability, but had only a modest impact on Midwest precipitation, suggesting that the jet stream supports precipitation through its dynamical linkage to leading zonally propagating eddies, rather than fundamentally driving precipitation through dominant patterns of jet stream variability.

Empirical orthogonal functions have important roles in predicting climate variability over multimonth time scales (e.g., outlooks provided by the NOAA Climate Prediction Center). The results reported here indicate that, for regions where propagating synoptic systems strongly impact precipitation, projection of forecast ensembles onto leading propagating modes (phase-shifted HEOFs) may provide forecast skill beyond analysis of standing waves detected by traditional EOF analysis. For shorter-term forecasting, the patterns identified here show statistically important propagating synoptic conditions in their phase most important for moisture and precipitation delivery to the Midwest.

The phase-shifting methods used here are applicable to other seasons and locations, but compared to Midwest winters, the association between Midwest summer precipitation variance and leading propagating patterns of atmospheric variability are relatively weak (e.g., the first HEOF of June–August qv accounted for 16% of P0.25; not presented). During Midwest summers, other processes become important including mesoscale convective complexes (e.g., Fritsch et al. 1986) and Caribbean moisture sourcing into the Central Plains low-level jet stream (Dirmeyer and Kinter 2010). In other regions of North America, the diversity of precipitation mechanisms expands further beyond the scope of classic propagating midlatitude cyclones to include monsoonal regimes and systems of tropical origin.

Acknowledgments

Comments from anonymous reviewers helped to improve the manuscript. J. Liptak was partially supported by National Science Foundation Grant ARC-1022485.

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