A Genesis Potential Index for Polar Lows

Kevin Boyd aUniversity of Illinois at Urbana–Champaign, Urbana, Illinois

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Zhuo Wang aUniversity of Illinois at Urbana–Champaign, Urbana, Illinois

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John E. Walsh bUniversity of Alaska Fairbanks, Fairbanks, Alaska

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Abstract

Polar lows (PLs) are intense maritime mesocyclones that typically develop during marine cold-air outbreak events over the high latitudes. The impacts posed by these systems to humans and the broader environment demand a robust understanding of the environmental factors that promote PL formation and, in turn, skillful prediction of PL activity. We hypothesize that the variability of PL activity is associated with some key large-scale climate variables skewed toward “extreme” values, which can provide predictable information on PL activity beyond the synoptic time scale. A PL genesis potential index (PGI) is developed that relates the climatological spatial distribution of PL genesis frequency and key climate variables in a Poisson regression framework. The optimal set of predictors consists of a static stability parameter and an environmental baroclinicity parameter. The optimal predictor categories are shown to be robust across different reanalyses and PL track datasets. The observed spatial distribution and seasonal cycle of PL genesis frequency are represented well by the PGI, and the interannual variability of PL activity is captured skillfully. The effects of the Arctic Oscillation (AO), El Niño–Southern Oscillation (ENSO), and a few other climate modes on the interannual variability of PL activity are explored. Overall, our results suggest that the PGI may be used to inform skillful subseasonal to seasonal prediction of PL activity.

Significance Statement

Polar lows are intense mesocyclones over high-latitude oceans, and they have destructive impacts on coastal and island communities, and maritime and air operations. However, skillful prediction of polar lows on the subseasonal and longer time scales remains challenging. This study links polar low activity to large-scale environmental conditions in the Arctic through a statistical modeling approach. This work is based on the hypothesis that a shared statistical relationship exists between the large-scale climate variables and polar low activity across the Arctic, which enables a geographical unification of the controlling factors on polar low activity. Our results reveal two dominant factors, one related to the lower-tropospheric stratification and the other to the hydrodynamic instability of the lower-tropospheric flow. This statistical framework has potential applications to climate prediction and projection of polar low activity.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zhuo Wang, zhuowang@illinois.edu

Abstract

Polar lows (PLs) are intense maritime mesocyclones that typically develop during marine cold-air outbreak events over the high latitudes. The impacts posed by these systems to humans and the broader environment demand a robust understanding of the environmental factors that promote PL formation and, in turn, skillful prediction of PL activity. We hypothesize that the variability of PL activity is associated with some key large-scale climate variables skewed toward “extreme” values, which can provide predictable information on PL activity beyond the synoptic time scale. A PL genesis potential index (PGI) is developed that relates the climatological spatial distribution of PL genesis frequency and key climate variables in a Poisson regression framework. The optimal set of predictors consists of a static stability parameter and an environmental baroclinicity parameter. The optimal predictor categories are shown to be robust across different reanalyses and PL track datasets. The observed spatial distribution and seasonal cycle of PL genesis frequency are represented well by the PGI, and the interannual variability of PL activity is captured skillfully. The effects of the Arctic Oscillation (AO), El Niño–Southern Oscillation (ENSO), and a few other climate modes on the interannual variability of PL activity are explored. Overall, our results suggest that the PGI may be used to inform skillful subseasonal to seasonal prediction of PL activity.

Significance Statement

Polar lows are intense mesocyclones over high-latitude oceans, and they have destructive impacts on coastal and island communities, and maritime and air operations. However, skillful prediction of polar lows on the subseasonal and longer time scales remains challenging. This study links polar low activity to large-scale environmental conditions in the Arctic through a statistical modeling approach. This work is based on the hypothesis that a shared statistical relationship exists between the large-scale climate variables and polar low activity across the Arctic, which enables a geographical unification of the controlling factors on polar low activity. Our results reveal two dominant factors, one related to the lower-tropospheric stratification and the other to the hydrodynamic instability of the lower-tropospheric flow. This statistical framework has potential applications to climate prediction and projection of polar low activity.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zhuo Wang, zhuowang@illinois.edu

1. Introduction

Polar lows (PLs) are intense maritime mesocyclones that occur in the high latitudes during the winter season. Rasmussen and Turner (2003) proposed a definition for PLs that remains widely cited in the literature:

A polar low is a small, but fairly intense maritime cyclone that forms poleward of the main baroclinic zone (the polar front or other major baroclinic zone). The horizontal scale of the polar low is approximately between 200 and 1000 kilometers and surface winds near or above gale force. (p. 12)

The severe weather conditions associated with these systems, such as large-amplitude oceanic waves (Rojo et al. 2019) and heavy snow showers (Harrold and Browning 1969), have long posed a threat to maritime operations, in addition to coastal and island communities. PLs are also thought to affect deep-water formation in the North Atlantic through the associated strong surface heat fluxes, and thus may be important for the large-scale oceanic circulation (Condron and Renfrew 2013).

There has long existed contention among researchers regarding the precise physical mechanisms involved in the formation and development of PLs. The vagueness of the above definition for PLs highlights this problem: there is not a single conceptual model that clearly explains the so-called PL spectrum, which ranges from purely baroclinic PLs with comma-shaped cloud structures to convective, hurricane-like systems with spiraliform cloud structures (Rasmussen and Turner 2003). Indeed, most PLs are a hybrid between these two extremes (Bracegirdle and Gray 2008). However, in general, broadly similar environmental characteristics are present during PL development. PLs tend to form on the flanks of marine cold air outbreaks (MCAOs) from ice-covered regions or along convergence zones or shear zones imbedded in the synoptic-scale cold air mass. The MCAOs are typically associated with a synoptic-scale cyclone and accompanied by an upper-level cold trough (Businger 1985; Mallet et al. 2013; Terpstra et al. 2021). The dry, cold airflow over a relatively warm ocean results in strong surface heat and moisture fluxes, contributing to the decreasing of atmospheric static stability, along with the moistening and deepening of the boundary layer (Hartmann et al. 1997), which promotes convection and cyclone development. This process is aided by various sources of low-level vorticity, such as the aforementioned shear and convergence zones, in addition to the baroclinically generated vorticity in the vicinity of sea ice boundaries and strong SST gradients where large vertical wind shear is present (Terpstra and Watanabe 2020). Therefore, the genesis regions of PLs are often characterized by low static stability, large baroclinicity, moisture gradients, and upper-level forcing (Jonassen et al. 2020). The relationship between environmental variables and PL occurrence has been used for PL tracking (Bracegirdle and Gray 2008; Zahn and von Storch 2008; Chen and von Storch 2013; Zappa et al. 2014; Yanase et al. 2016; Stoll et al. 2018; Michel et al. 2018; Stoll 2022) or to identify favorable conditions for PL development (Kolstad 2011; Mallet et al. 2013). The most commonly used parameters are MCAO criteria in the form of the difference in temperature or potential temperature between the surface and some pressure level, such as 500 mb (1 mb = 1 hPa) (Zahn and von Storch 2008; Mallet et al. 2013; Zappa et al. 2014; Stoll et al. 2018; Stoll 2022) or 700 mb (Bracegirdle and Gray 2008; Kolstad 2011). Other commonly used parameters in PL tracking include vortex intensity criteria, such as those based on sea level pressure (Stoll et al. 2018), low-level vorticity (Zappa et al. 2014; Yanase et al. 2016; Michel et al. 2018; Stoll 2022), or low-level wind speed (Chen and von Storch 2013; Yanase et al. 2016). The large majority of these studies focus on subdaily analysis of PLs; aside from the global, objective PL climatologies developed by Stoll et al. (2018) and Stoll (2022), their spatial extents are limited to selected regions and often feature a limited time period as well.

The impacts of PLs to coastal and island communities, maritime and air operations, and the large-scale oceanic circulation demand skillful prediction and projection of PL activity. Although numerical weather prediction models have shown increasingly better performance at simulating the dynamics and structures of PLs (Stoll et al. 2020; Müller et al. 2017), the lack of observational data over the Arctic region and an underperforming data assimilation poses difficulties for these models (McInnes et al. 2011; Moreno-Ibáñez et al. 2021). The prediction of PL activity on subseasonal and longer time scales is particularly challenging due to the relatively coarse resolution of climate models and the small spatial scales, rapid development, and convective nature of PLs (Furevik et al. 2015; Stoll et al. 2020).

The objective of this study is to develop a physics-based statistical model that links PL genesis frequency to key large-scale climate variables on monthly and longer time scales. This work is based on the hypothesis that the variability of PL activity is associated with some key, large-scale climate variables skewed toward “extreme” values, which provide predictable information beyond the synoptic time scale. Although we lack the theoretical foundations from which to describe the variability of PL activity within the climate system from first principles, previous studies on the relationship between PLs and environmental conditions provide the physical basis for our study. It is worth emphasizing that we are not concerned with individual PL genesis events, but instead focus on climate mean variables relevant to PL frequency or likelihood on the subseasonal to longer time scales. Our work is thus different from the previous studies that track individual PLs using subdaily data.

This work is largely inspired by the studies of empirical relationships between tropical cyclone (TC) frequency and the large-scale climate, some of which date to several decades ago (e.g., Gray 1979; Emanuel and Nolan 2004; Tippett et al. 2011; Wang and Murakami 2020). The most directly relevant of these studies is Tippett et al. (2011), in which a skillful TC genesis potential index was constructed using a Poisson regression model. Application of a similar procedure to PLs beyond the regional scale has only recently been enabled by the developments of global, objective climatologies of PLs (Stoll et al. 2018; Stoll 2022).

The structure of the remainder of this paper is as follows: In section 2, the PL climatology and climate variables that form the basis for our investigation are introduced. The development of the PL genesis potential index (PGI) is described in section 3, and the agreement between the PGI and the observed PL climatology is examined in section 4. The PGI’s ability to represent the interannual variability of PLs and the effects on climate modes on PL frequency are examined in sections 5 and 6 respectively, followed by a discussion in section 7 and, last, a summary in section 8.

2. Data

a. The PL climatology

This research is enabled by the recent developments of global, objective climatologies of PLs (Stoll et al. 2018; Stoll 2022). The more recent climatology is based on the ERA5 reanalysis and ranges from 1979 to 2020 (Stoll 2022). Cyclone tracks were identified with a tracking algorithm based on the spatially smoothed 850-hPa relative vorticity field to focus on vortices on the meso-β and larger scales, and PL tracks were then selected by imposing a number of objectively developed constraints, known as PL identification criteria (PL-IC), which can effectively differentiate intense PLs from other cyclones. Specific details of the tracking algorithm can be found in Stoll (2022) and Watanabe et al. (2016).

This PL dataset captures the large majority of manually detected PLs from several datasets and its spatial and temporal distribution agrees well with PL climatologies reported in previous studies (Stoll 2022). Furthermore, this PL dataset is preferred over the earlier iteration due to its use of the ERA5 reanalysis, which has been shown to be superior to the ERA-Interim (herein ERA-I) reanalysis in reproducing PLs (Stoll et al. 2021). It thus provides a solid basis for further physical and statistical inquiry into the large-scale climate features influencing PL genesis frequency on climatological time scales.

We identify PL genesis as the time step when all PL-IC are first satisfied simultaneously in a PL’s track. Furthermore, we require that PL genesis locations satisfy a “distance-to-land” threshold of 75 km (one-quarter of the typical vortex diameter of PLs). The result is a total number of 10 977 (of the original 13 888) PL tracks in the Northern Hemisphere (NH). The position of PL genesis is then interpolated to the nearest grid point on a 2.5° × 2.5° longitude–latitude grid. This yields a PL genesis density function (PGF) field, which represents the frequency of PL genesis in a 2.5° × 2.5° grid cell. The PGF is thus derived from an observationally based PL track dataset, in contrast to the PGI, which is derived from a statistical model (section 3). The time period of our analysis is from 1979 to 2020, determined by the availability of the PL dataset.

b. Predictor data

The predictor fields are extracted from the ECMWF’s ERA5 reanalysis (Hersbach et al. 2020). This dataset is natively produced on a spatial grid of 30-km resolution. For the purposes of this study, all predictor fields are interpolated to a coarser spatial resolution, defined on a 2.5° × 2.5° longitude–latitude grid. Climatological monthly means of predictor fields during 1979–2020 are computed for each calendar month. We intentionally use coarse-resolution climatological monthly mean data for two purposes. First, the Poisson fitting is carried out grid point wise, and a larger grid cell effectively increases the number of PLs per grid cell and improves the robustness of the fitting. Second, our framework aims to relate PL activity to large-scale climate conditions, and developing the framework using coarse-resolution data facilitates the application of the framework to PL prediction and projection using climate model output.

The spatial domain of this study is the latitudinal band between 50° and 80°N. Since PLs occur exclusively over open water, grid points that exceed a land or sea ice fraction of 80% are removed. This fraction threshold is chosen to be conservative in order to include as many PLs as possible from Stoll’s (2022) PL climatology.

The complete predictor pool is given in Table S1 in the online supplemental material. The candidate predictors are chosen to capture dynamical or physical relationships between the large-scale environment and PL formation. The candidate predictors are broadly categorized in terms of their possible dynamical functions or roles in the formation of PLs: static-stability or MCAO indices, environmental baroclinicity, environmental moisture content, upper-level forcing, and atmospheric flow distortion.

c. Climate modes

The relationship between select climate modes and the spatiotemporal distribution of PL genesis is also investigated. The climate modes of interest are the Arctic Oscillation (AO), North Atlantic Oscillation (NAO), El Niño–Southern Oscillation (ENSO), and the Pacific–North American (PNA) mode. Monthly mean index values are obtained from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC). The oceanic Niño index (ONI) is used to represent the ENSO index (NOAA 2019a,b).

3. Methodology and development of the polar low genesis index

a. Poisson regression

Poisson regression is often used for the modeling of count-based data, where the predictand consists of only nonnegative integer values (Wilks 2011). The Poisson distribution models the probability of a random variable N with expected value (or conditional mean) μ, if N assumes the values n = 0, 1, 2, …, as follows:
P(N=n)=eμμnn!.
In this application, N is the long-term monthly mean of PL genesis frequency for each 2.5° × 2.5° grid cell. Our goal is to predict the expected value of PL genesis events μ from large-scale climate variables. The appropriate choice is to adopt a log-linear model, which ensures nonnegative predictions. In this model, the logarithm of μ is related linearly to a vector of climate predictors x by the following expression:
logμ=bTx+log(cosφ),
where b is a vector of parameter coefficients or regression coefficients; φ is the latitude, and log(cosφ) takes into account the decrease of grid cell area with increasing latitude. One of the elements of x is taken to be a constant, assuming the value of unity, and the other predictors are standardized so that the parameter coefficients represent the sensitivity of PL frequency to variability of a predictor. Standardization is based on the mean and standard deviation over all space and time (the long-term monthly means in all calendar months for all oceanic grid points).

The Poisson regression model is fit to climatological monthly means of cosine-weighted PL genesis observations and climate predictors over all oceanic grid points for all calendar months. The parameter coefficients are estimated using the method of maximum log-likelihood. They can be conceptually interpreted as sensitivities of the predictand to the predictors. The PGI thus quantifies the relationship between the climate predictors and PL genesis frequency.

Two inherent model assumptions are important for model development: 1) the variance of a Poisson distributed variable is equal to its mean, and 2) predictors are independent of each other. The distribution of PL genesis observations exhibits less variability than a Poisson distributed variable, so the first assumption is not perfectly satisfied in our application, which is often the case in practice. After further examination of our findings, we return to discuss the implications of violating this assumption. The steps used to choose independent predictors, both physically and statistically, are discussed in the next subsection.

b. Model development

The forward selection method is used to select predictors in our model development framework (Wilks 2011) from a predictor pool (see Table S1). Several metrics are used to evaluate model performance and guide predictor selection. The root-mean-square error (RMSE) and pattern correlation coefficient inform how well the model fitting represents the magnitude and spatial pattern of observations. The pseudo R-squared serves as a means of comparing the quality of model fitting (as a function of the log-likelihood) between different model configurations. Note that the pseudo R-squared is not an analog to the R-squared metric utilized in evaluation of linear regression models, as the magnitude of the former metric carries little meaning and its importance lies in comparison of model fitting skill for different models of the same predictand.

To ensure the independence of selected predictors, after a predictor is selected, all the other candidate predictors in the same category are removed from the pool for the next iteration. Additionally, pattern correlations between model predictors were examined, and predictors across different categories are found to be weakly correlated (∼0.3). Furthermore, we impose an objective stopping criterion to determine when predictor selection should no longer continue. The pseudo R-squared metric is required to increase by at least 5% of its value from the previous iteration. If this condition is not met with the addition of a predictor, then that predictor is rejected and the predictor selection process concludes.

c. The polar low genesis potential index

Following the steps described above, the PGI is developed with two climate predictors:
logPGI=b+bSS+bBB+log(cosφ)
or, equivalently,
PGI=exp[(b+bSS+bBB)]×cosφ,
where S and B are, respectively, the difference between the skin potential temperature and the 500-mb potential temperature (i.e., static stability predictor), and the magnitude of the horizontal gradient of the 800-hPa equivalent potential temperature (i.e., environmental baroclinicity predictor); b is the constant term. The model performance and parameter coefficients at each iteration are summarized in Table 1. The predictor B depends on both the temperature field and the moisture field and can be regarded as a simple proxy for moist baroclinicity. The 800-hPa pressure level was chosen to best mediate between two conflicting factors: the desirability of a predictor to represent low-level baroclinicity, and undesired orographic influences on data reliability. The selection of the predictor B indicates that reduced static stability, or MCAO, is a necessary but not sufficient condition for PL formation. This is consistent with the finding by Terpstra et al. (2021) that not all MCAOs are associated with polar mesoscale cyclones and the emphasis on moist baroclinicity in PL development by some studies (e.g., Stoll et al. 2021). In addition, upper-level PV and low-level convergence, which are suggested as triggers of PL formation, were not selected. It is possible that they do not represent a triggering mechanism for all PLs, or the transient small-scale features (in particular, low-level convergence) do not leave a clear footprint on the longer time scales. The latter possibility reflects the predictability limit of PL activity on the longer time scale.
Table 1

The selected (optimal) predictor at each iteration, accompanied by the base model statistics granted by addition of that predictor and the model parameter coefficients b1,2,3, and the constant term b. The third selected predictor (relative humidity at 925 mb) is excluded by the stopping criteria described in section 3b.

Table 1

The Poisson regression model assumes that all predictors follow a log-linear relationship with the predictand [Eq. (2)], and we investigate the validity of this assumption by constructing marginal functions (see Fig. 11 in Tippett et al. 2011) for each model predictor (Fig. 1). Marginal functions are constructed for each predictor by integrating the PGF or PGI over a range (bin) of predictor values, allowing for the visualization of their relationship. The static stability predictor closely abides the log-linear relationship, and to a lesser degree for the environmental baroclinicity predictor.

Fig. 1.
Fig. 1.

Marginal functions for each model predictor, separated by PGF (observations) and PGI (model fitting). The y axis is scaled logarithmically, and the x axis is the standardized predictor values. Underneath each predictor’s marginal function is the histogram of the predictor.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

d. Fractional contribution function

To quantify the contribution of each model predictor to the PGI, fractional contribution functions (FCFs) are computed. For example, to compute the FCF for the model predictor S, we define
FCFS=exp[(b+bSS+bBB)]×cosφexp[(b+bBB)]×cosφexp[(b+bSS+bBB)]×cosφ,
which can be further simplified
FCFS=1exp(bsS)
such that FCFS represents the relative change in the PGI (as a decimal) by removal of the S predictor. The theoretical upper limit of the FCF is 1; however, the lower limit extends to infinity in the case of extremely negative values of the model predictor. To constrain the range of the FCF to between 0 and 1, only standardized model predictor values above 0 are considered. However, values below 0 are scarcely found in major PL source regions by virtue of negative values representing nonfavorable conditions for PL formation.

4. Climatology of polar low activity

a. Spatial distribution

The climatological spatial distribution of the PGF and PGI are plotted side by side in Fig. 2. In general, the PGI tends to smooth the small-scale features of the PGF while retaining the appropriate magnitude. This is due to the simple functional form of the PGI [Eq. (4)] in conjunction with the spatiotemporal nature of the predictors, which do not capture the small-scale, high-frequency processes influencing PL formation. Nevertheless, there is a good agreement between the PGI and PGF over both the Atlantic and Pacific sectors although PL development in different regions may be associated with different preferred synoptic-scale atmospheric conditions. The agreement suggests that a unified framework exists to describe the PL developmental conditions across the Arctic.

Fig. 2.
Fig. 2.

The annual PL genesis frequency from (a),(c) observations (PGF) and (b),(d) model fitting (PGI). Grid cells with negligible PL genesis frequency (less than 0.1) are plotted equivalently as zero.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

The large parameter coefficient associated with the static stability predictor (Table 1) suggests that low static stability is likely a necessary condition for PL formation, while baroclinicity supports PL formation in such low static stability environments. This is further supported by the FCF fields (Fig. 3). Regions with large PGF are collocated with large FCF values for both predictors, reflective of the nonlinear predictor relationships inherent in the Poisson regression model. In such regions, the static stability predictor alone would be inadequate in capturing the controlling factors for enhanced PL activity (Terpstra et al. 2021). Our model thus provides a novel, simplified notion of the environmental controls on PL development, regardless of the exact dynamical forcing of the incipient PLs. Next, we will examine the regional agreement between the PGF and PGI and the contribution from individual predictors.

Fig. 3.
Fig. 3.

The fractional contribution function (FCF) for each model predictor. (a),(c) The static stability FCF and (b),(d) the environmental baroclinicity FCF. (top) The Atlantic sector and (bottom) the Pacific sector. The FCF fields are derived from climatological monthly mean predictor fields and then averaged over all calendar months.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

In the North Atlantic basin, varying degrees of influence from model predictors are found (Figs. 3a,b). In the Nordic seas, the PGF (Fig. 2a) peaks in proximity to the western coastline of Svalbard and extending down to the Tromsø Flake (located around 72°N, 15°E), collocated with climatologically reduced static stability associated with frequent, intense MCAO events and relatively large SSTs (Terpstra et al. 2021). This feature is skillfully captured by the PGI (Fig. 2b). Collocated with this feature, the largest static stability FCF across the Arctic is found, although the environmental baroclinicity predictor evidently plays an important, but relatively smaller role as compared to some other major source regions (e.g., the Irminger Sea). This suggests that PLs in the Nordic seas form, on average, in more barotropic environments compared to their North Atlantic counterparts in the Irminger Sea and Denmark Strait regions, which is in agreement with Blechschmidt et al. (2009). Extending from the Denmark Strait to the Labrador Sea, the PGF is again well represented by the PGI, but with some notable caveats. The PGF maxima over the Labrador Sea extend farther north than those of the PGI, and the PGF maxima in proximity to the southern tip of Greenland are not captured well by the PGI. The latter feature is likely associated with the so-called Greenland tip jet (Doyle and Shapiro 1999), but its relationship with PL formation is not well understood.

Moving onto the Pacific basin, the PGI (Fig. 2d) performs well at representing the spatial pattern and magnitude of the PGF (Fig. 2c), with some minor but noteworthy differences. The major source regions of PL genesis are in agreement, namely the Sea of Okhotsk, the western Bering Sea, the northwest Pacific Ocean, and the Gulf of Alaska. Note that the Sea of Japan is not included in our analysis (see section 7 for more details). The PGF reaches a basin maximum in proximity to the Kamchatka Peninsula, with large values found over the seas bordering its eastern and western coastlines. The PGF shows that PL genesis does not commonly occur in the open ocean regions of the central and southeastern Bering Sea, and rarely occurs north of the Bering Strait, where sea ice is present during the cold season. These broad features are captured by the PGI. A secondary maximum of PGF is found displaced off the coastline over the Gulf of Alaska (a feature not sensitive to the “distance-to-land” threshold), but the PGI peaks along the coastline. Examination of the FCF fields suggests that the PGI is largely controlled by the static stability predictor, and the environmental baroclinicity predictor plays a minimal role except close to the coastline (Figs. 3c,d). Both predictors work cooperatively in creating the coastal PGI maxima over the Gulf of Alaska. The PGF is more broadly dispersed across the Pacific basin (i.e., not concentrated near coastlines), suggesting that PLs form in less baroclinic environments (on the synoptic scale) in comparison to North Atlantic PLs.

b. Seasonal cycle of PL genesis

In this subsection, we assess the ability of the PGI to represent the seasonal cycle of PL genesis. As shown in Fig. 4a, the PGI shows great skill in replicating the seasonal cycle of PL genesis, with PL activity occurring over the extended winter season, frequency peaking in December and January, and the relative lull in the summer months. Inspection of the spatially averaged FCF fields (Fig. 4b) indicates that the static stability predictor largely controls the seasonal cycle of PL genesis. The PGI, however, underestimates PL frequency in March and estimates infrequent, but nonnegligible PL frequency in the summer months. The environmental baroclinicity predictor appears to be responsible for the latter result (Fig. 4b). The relative peak of PL frequency in March is further investigated by decomposing the seasonal cycle for the Arctic into three separate regions (not shown; see next section for details of regional subdivision). We find that this feature is specific to the North Atlantic, but most prominently the Nordic seas, where the largest discrepancy between the PGF and PGI is present in March. The relative peak in PL observations in March over the Nordic seas is a robust feature that has been noted in previous climatological studies (Noer et al. 2011; Smirnova et al. 2016; Stoll et al. 2018), but its physical cause is unclear. Thus, the misrepresentation of this feature is a potential limitation of our model.

Fig. 4.
Fig. 4.

(a) The seasonal cycle of the observed (PGF; solid) and fitted (PGI; dashed) PL genesis counts summed over the analysis region (units: number of PLs per month). (b) The seasonal cycle of the spatially averaged climatological monthly mean FCF fields.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

5. Interannual variability of polar low genesis

Recall that the model is developed using the long-term monthly means of the PGF and predictor fields. Thus, the annual frequency of PL genesis can be regarded as an independent dataset, and testing the model’s representation of the interannual variability of PL genesis helps assess the model performance and forecasting potential. The fitted annual PL frequency is calculated by summing monthly PGI values over a PL year, which are derived using the corresponding monthly mean predictor fields. A PL year spans from the July of the previous year to June of the concurrent year. The PL year in 1979 consists only of six months. To give each year an equal weighting, the PL frequency in each PL year is normalized by the number of months that fall into it.

The time series of observed and fitted PL genesis frequency with respect to PL year are plotted in Fig. 5 for the pan-Arctic and different basins. The Arctic is subdivided into three regions of interest: the west Atlantic, east Atlantic, and Pacific. The east and west Atlantic regions are separated by the 345°E line. The regional subdivision is based on the spatial coherence of PL genesis frequency in both basins, assessed through correlation maps (not shown).

Fig. 5.
Fig. 5.

The monthly mean observed (PGF) and fitted (PGI) PL genesis counts from 1979 to 2020 on both the hemispheric and regional scale (units: number of PLs per month). The Pearson correlation (ACC) is computed and indicated in each panel title. All correlations exceed the 99% confidence level.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

The annual frequency of PL genesis exhibits strong interannual variability during 1979–2020. Our model skillfully represents this interannual variability at both hemispheric and regional scales. At the hemispheric scale, the correlation between the PGI and PGF time series is 0.631, and at the regional scale, 0.715, 0.76, and 0.724 for the west Atlantic, east Atlantic, and Pacific, respectively, all exceeding the 99% confidence level. It is interesting to note that the correlation at the regional scale exceeds that at the hemispheric scale. This is an unexpected result, but it can be explained by a weak anticorrelation between the annual time series of PL genesis frequency in the North Atlantic and Pacific basins (significant at the 90% level). Overall, these results give confidence that our model skillfully captures the variability of PL genesis at the seasonal and annual time scales, given that the predictor fields are adequately represented.

6. Impacts of the climate modes on polar low activity

The ability of the PGI to represent the impacts of climate modes on PL genesis is examined in this section. Although some studies have investigated these relationships (Mallet et al. 2013), only relatively short temporal periods and small spatial extents were analyzed. A more extensive statistical evaluation of these relationships over a larger spatial scale and a longer time period has yet to be done.

We focus on the extended winter season, from November to March, which is the peak season for PL activity, ENSO, PNA, NAO, and AO. The correlations between the seasonal mean time series of climate indices and PL genesis frequency are shown in Table 2. In the Pacific basin, the AO and ENSO index are uncorrelated with observed and fitted PL frequency. However, the PNA index is positively correlated with both the observed and fitted PL frequency (significant at the 95% and 99% level, respectively), although the correlation with the fitted PL frequency is much stronger. Further investigation shows that there is no significant spatial structure associated with PGF anomalies in PNA index regimes (not shown), and therefore no special emphasis is placed on these relationships. Neither of the Atlantic regions are correlated with the ENSO index. A significant positive correlation exists between the PGI and the AO and NAO indices over the east Atlantic (weak) and west Atlantic (moderate to strong). However, the observed PL genesis frequency only shows a significant correlation with the AO and NAO indices over the west Atlantic. This suggests that the AO and NAO modulate the predictor fields over both subbasins, but the variability of the model predictors is not associated with corresponding changes in the PL activity in the east Atlantic. The strong impacts of the NAO on PL activity over the west Atlantic are consistent with Mallet et al. (2013), who found that the large majority of PLs within the Irminger and Labrador Sea occurred in the NAO+ phase. Moreover, the NAO and AO indices are strongly correlated, but we found better agreement between correlations of observed and fitted PL frequency and the AO index (compared to that of the NAO index) in the west Atlantic. Next, we will further investigate this relationship through inspection of the PGF, PGI, and FCF fields.

Table 2

Pearson correlations between the seasonal mean time series of climate mode indices and PL genesis frequency from PGF or PGI in different regions. The first and second numbers within parentheses represent the correlations with the PGF and PGI, respectively. Bolded values are statistically significant at the 95% level.

Table 2

Figure 6 shows the composite differences of the PGF, PGI, and FCF fields between the nine strongest positive AO years and nine strongest negative AO years. A two-sided t test is performed to assess statistical significance. Significant positive (negative) PGF anomalies occur in positive (negative) AO regimes over the Irminger Sea and Denmark Strait. Over the Labrador Sea, the PGF anomalies carry the same sign, but are weaker in comparison and insignificant. The PGI captures the broad spatial pattern of these anomalies, but the magnitude is overestimated over the Labrador Sea. Investigating the FCF anomaly fields here, both predictors are modulated by the AO, but only the static stability FCF anomalies are statistically significant. Large static stability FCF anomalies extend from the Labrador Sea to the Denmark Strait, suggesting that the AO modulates the frequency of MCAO events over these oceanic regions, which is consistent with Kolstad et al. (2009). North of the Denmark Strait, significant positive (weak) PGI anomalies are present along Greenland’s eastern coastline. This is not in agreement with the PGF anomalies, and evidently, both predictors contribute to this feature. The reason for the modulation of predictors in this region is unknown to the authors, but several possibilities might provide an explanation, such as barrier flow events correlated with the NAO (Harden et al. 2011) or the so-called Greenland Sea jet (van Angelen et al. 2011). Overall, the PGI captures the general pattern of the AO impacts on PL genesis frequency, especially in the major source regions (Irminger Sea and Denmark Strait), but overestimates the significant impacts. The overestimate may not be a surprise given that PL genesis is also modulated by high-frequency, small-scale processes, which can disrupt the relationship between PLs and the AO but are not represented by the PGI.

Fig. 6.
Fig. 6.

Composite anomalies of (a) PGF, (b) PGI, and (c),(d) FCF fields for the two model predictors during the PL season between the AO positive and negative phases. A two-sided t test is performed to compute the statistical significance of anomalies. Anomalies with less than 95% significance are hatched.

Citation: Journal of Climate 35, 24; 10.1175/JCLI-D-22-0100.1

7. Discussion

The PGI framework is developed using the PL track dataset from Stoll (2022). Several objective climatologies of PLs are now available, the majority of which are regional (Bracegirdle and Gray 2008; Zahn and von Storch 2008; Chen and von Storch 2013; Zappa et al. 2014; Yanase et al. 2016; Michel et al. 2018) while some are global (Stoll 2022; Stoll et al. 2018). These climatologies feature subtle methodological differences in identifying PL vortices, but such differences may lead to large differences in the statistics of cyclone datasets (Neu et al. 2013). Therefore, it is important to evaluate the sensitivity of the PGI formulation and performance to the PL climatology used in model development and evaluation. For this purpose, we carry out two robustness tests. In the first test, we use the same PGI formulation described in earlier sections [i.e., the same model predictors and parameter coefficients as in Eq. (4)], but the model is fed by predictor values derived from the ERA-I reanalysis (Dee et al. 2011), and the model performance is evaluated against the PL dataset developed by Stoll et al. (2018), which was developed from the ERA-I reanalysis using a different tracking algorithm from Stoll (2022). In the second test, a PGI is developed, following the steps outlined in sections 3a and 3b, using the PGF derived from Stoll et al.’s (2018) PL track dataset and predictor values derived from the ERA-I reanalysis. The purpose of the first test is to assess the robustness of the PGI [Eq. (4)] performance to evaluation datasets, and the purpose of the second test is to reassess the robustness of the PGI formulation to the training dataset used in model development. To clarify, evaluating the robustness of the PGI to model predictors derived from different reanalysis datasets is not the purpose of these tests, but this could be an interesting direction for future scientific investigations.

The PGF and predictor fields are handled in a nearly identical fashion as explained in section 2, with the exception being that the “distance-to-land” threshold on PL genesis time steps is not applied since this information is not available. Additionally, due to the lower temporal resolution (6-hourly) of the ERA-I reanalysis, we impose a minimum PL lifetime constraint of 12 h to exclude transient, uncertain events. The result is a total number of 6614 PL tracks in the NH. In both tests, the PGI is tested with respect to its representation of the interannual variability of PL genesis frequency, as done in section 5.

The first test yields the correlation coefficient of 0.534 at the hemispheric scale (significant at the 99% confidence level), and higher correlations on the regional scale (see Fig. S1 in the online supplemental material). This affirms that the PGI performance is robust with respect to data source, but with some noteworthy caveats. Since the statistical fitting was developed using the PL track dataset from Stoll (2022), which includes a larger number of PLs than Stoll et al.’s (2018) track dataset, the PGI naturally overestimates PL frequency when evaluated with respect to Stoll et al.’s (2018) track dataset.

In the second test, the following predictors are chosen from the forward selection method: 1) the potential temperature difference between the near-surface and 500 mb (2.34); 2) the vertical wind shear between 925 and 400 mb (0.39); and 3) the relative vorticity at 850 mb (0.22). The corresponding parameter coefficients are given in parentheses. In other words, the static stability and environmental baroclinicity predictors still arise from the pool. The inclusion of the relative vorticity predictor, with a smaller parameter coefficient, is likely due to the large number of orographically induced shear zones in Stoll et al.’s (2018) PL dataset, some of which may be spurious (Stoll 2022). The PGI still yields significant correlation coefficients with the observations at both the hemispheric and regional scale (Fig. S2). Overall, these results affirm the robustness of the optimal predictor categories found in this study but also indicate that uncertainties in the PL dataset may influence the exact formulation of the PGI, which motivates the continued development and improvement of PL track datasets.

The application of the PGI works under the assumption that the empirical relationship between PL genesis frequency and model predictors does not vary with respect to location or time. In some unique environments for PL formation, such as the Sea of Japan, this assumption fails. The influence of the Kuroshio is known to produce highly unstable conditions over the Sea of Japan, and the low-level environmental baroclinicity field is strongly modulated by the proximity of this region to the wintertime-mean polar front. These influences elevate the PGI in this region, but such influences are not reflected in the PGF. Thus, the Sea of Japan does not fit into the geographically unified framework proposed here and was not included in our analysis. However, the PGI has some skill in capturing the interannual variability of PL genesis over the Sea of Japan if the monthly predictor fields are standardized relative to this specific region (see Fig. S3), but skill decreases substantially whenever standardization is done relative to the broader hemispheric domain (not shown). This suggests that application of the same statistical approach to PL prediction in the Sea of Japan is still plausible under alternative conditions in model development, such as with a limited spatial domain focused on the Sea of Japan, where the fitting may yield different parameter coefficients or select different optimal predictors.

The Poisson regression model assumes the mean and variance of the predictand are equal. The PGI is developed in an underdispersion region (variance is less than the mean), so this assumption is violated (see section 3a). Underdispersion in Poisson regression models may be handled using complex statistical methods, but those methods are less desirable than the simple Poisson model because the complexity would complicate the physical interpretation of the model. Although it is challenging to fully assess the implications of this violated assumption, the good performance of the PGI suggests that this violated assumption is not a significant concern. In particular, Fig. 5 suggests that the variance of the PGI is comparable to that of the PGF (in terms of year-to-year variations).

8. Summary

Environments rich in PL formation feature large-scale climate conditions that elevate the potential for polar low (PL) genesis on climatological time scales. To exploit these relationships, we develop a polar low genesis potential index (PGI) that relates the climatological spatial distribution of PL genesis frequency and key climate variables in a Poisson regression framework. The subset of predictors that maximizes model performance includes the potential temperature difference between the near-surface and 500 mb (i.e., static stability) and the magnitude of the horizontal gradient of the 800-hPa equivalent potential temperature (i.e., environmental baroclinicity). To the knowledge of the authors, this is the first instance of an empirical relationship between PL activity and large-scale variables on the climatological time scale to be established in the literature.

In general, the PGI is in good agreement with the observed PL genesis climatology (Fig. 2). The PGI tends to smooth the smaller-scale features of the observed PL genesis climatology, while retaining the large-scale spatial pattern with comparable magnitudes. The seasonal cycle of PL genesis frequency is well represented by the PGI (Fig. 4a) and is largely controlled by the seasonality of environmental static stability (Fig. 4b).

The parameter coefficients (Table 1) are indicative of the sensitivity of PL genesis frequency to the predictors, and the fractional contribution functions (FCFs; Fig. 3) reveal the regional influence of the predictors on the PGI. It suggests that low static stability is a necessity for PL formation, while strong baroclinicity amplifies PL genesis potential in such low static stability environments. Our findings suggest that a unified framework exists to describe the environmental “ingredients” for PL genesis across the subarctic although PL development in different regions may be associated with different preferred synoptic-scale atmospheric conditions. This highlights the novelty and significance of the PGI approach to study the variability of PL activity.

The index is applied to the representation of the interannual variability of PL genesis frequency as a means of assessing its forecasting potential, where PGI calculations are made using monthly mean predictor fields from each PL year, which can be regarded as an independent dataset (Fig. 5). The PGI shows substantial skill in representing the interannual variability of PL observations, at both the regional and hemispheric scale, with all correlations exceeding the 99% confidence level. In particular, the PGI accounts for more than 50% of the interannual variance on the regional scale. We also investigated the relationship between the interannual variability of PL genesis frequency and different climate modes. The PGI captures the link between the AO and PL genesis frequency over the west Atlantic region (Table 2) but overestimates the impacts of AO on PL genesis frequency (Fig. 6). Analysis of the FCF fields suggests that AO influences PL genesis frequency in the west Atlantic by modulating the MCAO frequency. This demonstrates that the PGI is a useful diagnostic to understand and quantitatively assess the impacts of environmental conditions on the variability of PL activity.

Overall, our analysis illustrates the potential applicability of the PGI to PL prediction. The application of the PGI to subseasonal to seasonal prediction of PL activity is underway and will be reported in due course. Additionally, we will explore the applicability of the PGI on the climate change time scale, which depends on the existence of a stationary relationship between PL genesis frequency and the predictor variables.

Acknowledgments.

This study was supported by the Office of Naval Research through Grant N000141812216. We are grateful that Dr. Patrick Stoll made the global polar low track datasets (Stoll 2022; Stoll et al. 2018) publicly available, which was essential for enabling this work. This study also benefitted from discussions with Dr. Patrick Stoll. We acknowledge the NCAR Computational and Information Systems Laboratory (CISL) for providing computing resources and access to the ERA5 and ERA-Interim reanalyses.

Data availability statement.

The polar low track datasets used in this study are detailed in Stoll et al. (2018) and Stoll (2022). Both datasets are publicly available. The dataset based on ERA-Interim reanalyses (Stoll et al. 2018) is available at https://archive.norstore.no/pages/public/datasetDetail.jsf?id=945E779C-54DE-4A9D-BCF6-C767B15B8AE1. Similarly, for the dataset based on ERA-5 reanalysis is available at https://dataverse.no/dataset.xhtml?persistentId=doi:10.18710/TVZDBF.

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Supplementary Materials

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  • Blechschmidt, A.-M., S. Bakan, and H. Graßl, 2009: Large-scale atmospheric circulation patterns during polar low events over the Nordic seas. J. Geophys. Res., 114, D06115, https://doi.org/10.1029/2008JD010865.

    • Search Google Scholar
    • Export Citation
  • Bracegirdle, T. J., and S. L. Gray, 2008: An objective climatology of the dynamical forcing of polar lows in the Nordic seas. Int. J. Climatol., 28, 19031919, https://doi.org/10.1002/joc.1686.

    • Search Google Scholar
    • Export Citation
  • Businger, S., 1985: The synoptic climatology of polar low outbreaks. Tellus, 37A, 419432, https://doi.org/10.3402/tellusa.v37i5.11686.

    • Search Google Scholar
    • Export Citation
  • Chen, F., and H. von Storch, 2013: Trends and variability of North Pacific polar lows. Adv. Meteor., 2013, 170387, https://doi.org/10.1155/2013/170387.

    • Search Google Scholar
    • Export Citation
  • Condron, A., and I. A. Renfrew, 2013: The impact of polar mesoscale storms on northeast Atlantic Ocean circulation. Nat. Geosci., 6, 3437, https://doi.org/10.1038/ngeo1661.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and M. A. Shapiro, 1999: Flow response to large-scale topography: The Greenland tip jet. Tellus, 51A, 728748, https://doi.org/10.3402/tellusa.v51i5.14471.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., and D. S. Nolan, 2004: Tropical cyclone activity and global climate. Proc. 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 240241.

  • Furevik, B. R., H. Schyberg, G. Noer, F. Tveter, and J. Röhrs, 2015: ASAR and ASCAT in polar low situations. J. Atmos. Oceanic Technol., 32, 783792, https://doi.org/10.1175/JTECH-D-14-00154.1.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., 1979: Hurricanes: Their formation, structure and likely role in the tropical circulation. Meteorology over the Tropical Oceans, D. B. Shaw, Ed., Roy. Meteor. Soc., 155218.

    • Search Google Scholar
    • Export Citation
  • Harden, B. E., I. A. Renfrew, and G. N. Petersen, 2011: A climatology of wintertime barrier winds off southeast Greenland. J. Climate, 24, 47014717, https://doi.org/10.1175/2011JCLI4113.1.

    • Search Google Scholar
    • Export Citation
  • Harrold, T. W., and K. A. Browning, 1969: The polar low as a baroclinic disturbance. Quart. J. Roy. Meteor. Soc., 95, 710723, https://doi.org/10.1002/qj.49709540605.

    • Search Google Scholar
    • Export Citation
  • Hartmann, J., C. Kottmeier, and S. Raasch, 1997: Roll vortices and boundary-layer development during a cold air outbreak. Bound.-Layer Meteor., 84, 4565, https://doi.org/10.1023/A:1000392931768.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

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  • Fig. 1.

    Marginal functions for each model predictor, separated by PGF (observations) and PGI (model fitting). The y axis is scaled logarithmically, and the x axis is the standardized predictor values. Underneath each predictor’s marginal function is the histogram of the predictor.

  • Fig. 2.

    The annual PL genesis frequency from (a),(c) observations (PGF) and (b),(d) model fitting (PGI). Grid cells with negligible PL genesis frequency (less than 0.1) are plotted equivalently as zero.

  • Fig. 3.

    The fractional contribution function (FCF) for each model predictor. (a),(c) The static stability FCF and (b),(d) the environmental baroclinicity FCF. (top) The Atlantic sector and (bottom) the Pacific sector. The FCF fields are derived from climatological monthly mean predictor fields and then averaged over all calendar months.

  • Fig. 4.

    (a) The seasonal cycle of the observed (PGF; solid) and fitted (PGI; dashed) PL genesis counts summed over the analysis region (units: number of PLs per month). (b) The seasonal cycle of the spatially averaged climatological monthly mean FCF fields.

  • Fig. 5.

    The monthly mean observed (PGF) and fitted (PGI) PL genesis counts from 1979 to 2020 on both the hemispheric and regional scale (units: number of PLs per month). The Pearson correlation (ACC) is computed and indicated in each panel title. All correlations exceed the 99% confidence level.

  • Fig. 6.

    Composite anomalies of (a) PGF, (b) PGI, and (c),(d) FCF fields for the two model predictors during the PL season between the AO positive and negative phases. A two-sided t test is performed to compute the statistical significance of anomalies. Anomalies with less than 95% significance are hatched.

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