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\begin{document}

\title{Extratropical Cyclone Response to Projected Reductions in Snow Extent
over the Great Plains}



\author[1]{Ankur Desai}%
\author[2]{Ryan M Clare}%
\author[2]{Jonathan E Martin}%
\author[3]{Michael Notaro}%
\author[1]{Steve Vavrus}%
\affil[1]{University of Wisconsin Madison}%
\affil[2]{University of Wisconsin-Madison}%
\affil[3]{Nelson Center for Climatic Research}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
Extratropical cyclones are major contributors to consequential weather
in the mid-latitudes and tend to develop in regions of enhanced
cyclogenesis and progress along climatological storm tracks. Numerous
studies have noted the influence that terrestrial snow cover exerts on
atmospheric baroclinicity which is critical to the formation and
trajectories of such cyclones. Fewer studies have examined the explicit
role which continental snow cover extent has in determining cyclones
intensities, trajectories, and precipitation characteristics. While
several examinations of climate model projections have generally shown a
poleward shift in storm tracks by the late 21st century, none have
determined the degree to which the coincident poleward shift in snow
extent is responsible. A method of imposing 10th , 50th , and 90th
percentile values of snow retreat between the late 20th and 21st
centuries as projected by 14 Coupled Model Intercomparison Project Phase
Five (CMIP5) models is used to alter 20 historical cold season cyclones
which tracked over or adjacent to the North American Great Plains.
Simulations by the Advanced Research version of the Weather Research and
Forecast Model (WRF-ARW) are initialized at 0 to 4 days prior to
cyclogenesis. Cyclone trajectories and their central sea level pressure
did not change substantially, but followed consistent spatial trends.
Near-surface wind speed generally increased, as did precipitation with
preferred phase change from solid to liquid state. Cyclone-associated
precipitation often shifted poleward as snow was removed. Variable
responses were dependent on the month in which cyclones occurred, with
stronger responses in the midwinter than the shoulder months.%
\end{abstract}%



\sloppy


\textbf{Title}

Extratropical Cyclone Response to Projected Reductions in Snow Extent
over the Great Plains

\textbf{Author information}

Ryan M. Clare\textsuperscript{1,2,3}, Ankur R.
Desai\textsuperscript{1,2,*}, Jonathan E. Martin\textsuperscript{1},
Michael Notaro\textsuperscript{2}, Stephen J. Vavrus\textsuperscript{2}

\textbf{Affiliation}

\begin{enumerate}
\tightlist
\item
  \emph{Department of Atmospheric and Oceanic Sciences, University of
  Wisconsin--Madison, Madison, Wisconsin, USA}
\item
  \emph{Nelson Center for Climatic Research, University of
  Wisconsin-Madison, Madison, Wisconsin, USA}
\item
  \emph{Now at: Marine Meteorology Division, U.S. Naval Research
  Laboratory, Monterey, CA}
\end{enumerate}

*Corresponding author: Ankur R Desai, UW-Madison AOS, 1225 W Dayton St,
AOSS 1549, Madison, WI 53706 USA +1-608-520-0305, desai@aos.wisc.edu

\emph{This} ~Work~\emph{has not yet been peer-reviewed and is provided
by the contributing Author(s) as a means to ensure timely dissemination
of scholarly and technical} ~Work~\emph{on a noncommercial basis.
Copyright and all rights therein are maintained by the Author(s) or by
other copyright owners. It is understood that all persons copying this
information will adhere to the terms and constraints invoked by each
Author's copyright. This} ~Work~\emph{may not be reposted without
explicit permission of the copyright owner.}

\textbf{Abstract}

Extratropical cyclones are major contributors to consequential weather
in the mid-latitudes and tend to develop in regions of enhanced
cyclogenesis and progress along climatological storm tracks. Numerous
studies have noted the influence that terrestrial snow cover exerts on
atmospheric baroclinicity which is critical to the formation and
trajectories of such cyclones. Fewer studies have examined the explicit
role which continental snow cover extent has in determining cyclones'
intensities, trajectories, and precipitation characteristics. While
several examinations of climate model projections have generally shown a
poleward shift in storm tracks by the late
21\textsuperscript{st}century, none have determined the degree to which
the coincident poleward shift in snow extent is responsible. A method of
imposing 10\textsuperscript{th}, 50\textsuperscript{th}, and
90\textsuperscript{th} percentile values of snow retreat between the
late 20\textsuperscript{th} and 21\textsuperscript{st} centuries as
projected by 14 Coupled Model Intercomparison Project Phase Five (CMIP5)
models is used to alter 20 historical cold season cyclones which tracked
over or adjacent to the North American Great Plains. Simulations by the
Advanced Research version of the Weather Research and Forecast Model
(WRF-ARW) are initialized at 0 to 4 days prior to cyclogenesis. Cyclone
trajectories and their central sea level pressure did not change
substantially, but followed consistent spatial trends. Near-surface wind
speed generally increased, as did precipitation with preferred phase
change from solid to liquid state. Cyclone-associated precipitation
often shifted poleward as snow was removed. Variable responses were
dependent on the month in which cyclones occurred, with stronger
responses in the mid-winter than the shoulder months.

\textbf{Introduction}

\emph{The influence of snow cover}

Northern hemisphere snow cover is, at its seasonal maximum, the largest
component of the terrestrial cryosphere and exerts considerable
influence on the mid-latitude atmospheric circulation through a diverse
set of mechanisms which have a general cooling effect (e.g. Leathers et
al. 1995; Vavrus 2007; Dutla 2011). Near the surface, the presence of
snow cover typically lowers air temperature due to the snow's high
albedo (Baker et al. 1992) and its properties as an effective sink of
sensible and latent heat (Grundstein and Leathers 1999), which
contribute to an increase in static stability (Bengtsson 1980) and a
reduction of moisture flux into the atmosphere (Ellis and Leathers
1999). This inhibition of upward moisture flux may be responsible for
the negative correlation between snow cover and precipitation observed
by Namias (1985) and modelled by Walland and Simmonds (1996) and
Elguindi et al. (2005).

Studies have also shown that continental snow cover extent (SCE) is
sometimes responsible for modulating upper-level circulation (e.g.
Namias 1962; Walland and Simmonds 1996; Cohen and Entekhabi 1999;
Gutzler and Preseton, 1997; Notaro and Zarrin, 2011) and that accurately
initializing snow cover can improve subseasonal forecast skill
considerably (Jeong et al. 2013; Thomas et al. 2016). It is because of
this apparent relationship between snow cover and atmospheric
circulation that determination of the regional dependence and the
temporal scales at which snow cover drives responses in the atmosphere
is of fundamental importance to both short- and long-term forecasting.

Observations and hypotheses about the influence of established SCE on
the characteristics of ensuing synoptic weather systems may have begun
with Lamb (1955). However, one of the first analyses of this
relationship was provided by Namias (1962) who hypothesized that the
abnormally extensive North American (NA) snow cover of the winter of
1960 had contributed to the more frequent and intense cyclone
development observed along the Atlantic coast by enhancing baroclinicity
between the continent and the much warmer ocean. Dickson and Namias
(1976) subsequently showed that periods of great continental warmth or
cold in the American Southeast had a direct influence on the strength of
the baroclinic zone near the coast and would affect the average
frequency and positions of extratropical cyclones, drawing them further
south when the region was colder. Likewise, Heim and Dewey (1984) showed
that extensive NA snow cover contributed to a greater frequency of
cyclones in the southern Great Plains and Southeast and a reduction in
the amount of cyclones tracking further north. From 1979-2010 in NA, a
greater frequency of cold season mid-latitude cyclones was observed in a
region 50-350 km south of the southern snow extent boundary (snow line)
by Rydzik and Desai (2014) who noted a similar distribution of low-level
baroclinicity relative to the snow line.

Modeling studies have indicated a similar relationship between snow
extent and extratropical cyclone statistics. Ross and Walsh (1986)
studied the influence of the snow line on 100 observed North American
cyclone cases which progressed approximately parallel to the baroclinic
zone within 500-600 km of the snow line. By measuring forecast error
from a barotropic model, they were able to determine that the
baroclinicity associated with the snow boundary was an important factor
in cyclone steering and intensity. Walland and Simmonds (1997) performed
global climate model (GCM) experiments with forced anomalously high and
low extents of realistic snow cover distributions, ultimately finding a
reduction in NA cyclone frequency when snow cover was more extensive,
with cyclones frequently occurred further south, similar to the
observations of Heim and Dewey (1984). Elguindi et al. (2005) used a
25-km-resolution nested domain over a portion of the Great Plains in the
Penn State-National Center for Atmospheric Research (NCAR) Mesoscale
Model (MM5) and simulated eight well-developed cyclone cases with snow
cover added throughout the domain, initializing 48 hours prior to each
cyclone's arrival to the inner domain. All perturbed cyclone case
simulations underwent an increase in central pressure and decrease in
total precipitation with slight shifts in the cyclone trajectory which
were highly variable and inconsistent. However, this study only used a
limited number of cases and only perturbed simulations by adding snow to
the entirety of the inner domain rather than altering the position of
SCE.

In North America, the net effects of snow cover are nowhere more
pronounced than the Great Plains region, which has the highest local
maximum of snow albedo (Robinson and Kukla 1985; Jin et al. 2002) and
where the strongest correlation between snow cover and negative
temperature anomalies has been observed in NA (Heim and Dewey 1984;
Robinson and Hughes 1991). The Great Plains region represents one of the
largest disparities between local maximum snow albedo and background
land surface albedo on the continent, indicating the greatest albedo
gradient across a snow line (Figure 1). The land surface is
characterized by high inter- and intra-annual snow cover variability
(Robinson 1996) and low surface roughness. Winter cyclones track over
the Great Plains with high frequency due in part to areas of enhanced
cyclogenesis in the lee of the Rocky Mountains (Reitan 1974; Zishka and
Smith 1980). The two most prolific cyclogenetic zones over the NA
landmass account for the two types of cyclone tracks studied here: the
Alberta Clipper track, which typically begins in Alberta, Canada and
proceeds to the southeast (Thomas and Martin 2007), and the Colorado Low
track, which starts near southeast Colorado and often proceeds northeast
toward the Great Lakes region (Zishka and Smith 1980). Because of their
spatial extent and great frequency in the region, extratropical cyclones
contribute substantially to the hydrology of the Great Plains,
accounting for greater than 80\% of the total winter (December through
February) precipitation throughout much of the region (Hawcroft et al.
2012).

\emph{The scope of this study}

Typically, simulations of projected future climate states are
implemented with global climate models (GCMs) which are limited by
expansive resolutions over a global domain and, as a result, do not
allow the models to adequately resolve the fine details necessary to
accurately reproduce phenomena like precipitation and the diurnal cycle.
Harding et al. (2013) demonstrated that dynamically downscaling Coupled
Model Intercomparison Project Phase Five (CMIP5) simulations to 30 km
resolution in the NCAR WRF model improved simulation of precipitation,
especially extreme precipitation events, in the Central U.S. Many
modeling studies have applied global and regional climate models to
study the projected behavior of extratropical cyclones in the late
21\textsuperscript{st} century (e.g. Maloney et al. 2014 and Catto et
al. 2019), but few if any have examined the contribution made solely by
the projected changes in SCE. While many observational and modelling
studies have analyzed the effects of extensive distributions of snow
cover on cyclone behavior (e.g. Namias 1962; Heim and Dewey 1984;
Elguindi et al. 2005), few have explicitly studied the effects of
reductions in snow cover besides Walland and Simmonds (1984), who did
not experiment with projected SCEs. A few studies have suggested the
importance of the snow extent boundary to cyclone behavior (e.g. Ross
and Walsh 1986; Rydzik and Desai 2014), but there haven't been modelling
studies that experiment with shifts explicitly applied to these
boundaries. While the pronounced effects of snow cover in the Great
Plains has long been well understood and while regional modelling with
snow forcing has been applied to the area (e.g. Elguindi et al. 2005),
regional climate studies in the Great Plains focusing on projected snow
extent retreat have not been performed. Finally, the greatest deficiency
in all such regional, case-oriented modelling studies performed to date
is the dependence on a small number of simulations. Examining several
simulations across greater numbers of cases not only provides the
statistical robustness of a large dataset but also the chance to examine
the seasonality of the snow-cyclone relationship.

Snow retreat is of particular relevance given the likely changes in
projected snow cover under anthropogenic climate change (Brown and Mote
2008; Peacock 2012; Notaro et al 2014; Krasting et al 2013). All studies
point to reductions in North American persistent snow cover extent
duration. However, there are also areas of increased snow cover and
varying sensitivities depending on both temperature and precipitation
trends. Simulations of climatological snow cover redistribution
consistent with GCMs and studies of its impact on subsequent
extratropical cyclones has not been done.

The purpose of this study was to determine whether changes in underlying
snow cover on the Great Plains result in consistent, discernable
influence on cyclone steering, intensity, and precipitation by
conducting a broad survey of numerous cyclone simulations with snow
cover perturbed up to 96 hours prior to cyclogenesis. Snow cover was
perturbed with varying degrees of areal extent reductions and at
multiple initialization times in order to determine if there is any
spatial or temporal relationship between snow cover perturbation and
changes in cyclone intensity or track. The analysis attempted to broadly
define what direct effect, if any, North American snow cover reductions
due to future climate change will have on extratropical cyclone events.
This particular study did not intend to examine individual cases and
outliers to explain dynamical relationships between the surface boundary
conditions and the air aloft. An in-depth investigation of two
simulations from this study is presented in Breeden et al. (submitted).

We hypothesize that, because cyclones preferentially track along the
margin of snow extent (Ross and Walsh 1986; Rydzik and Desai 2014),
cyclone trajectories in simulations with poleward-shifted snow lines
will deviate poleward in kind. Because as much as 30\% of the moisture
in extratropical cyclones is obtained by surface evaporation (Trenberth
1998) and local precipitation recycling is significant in the Great
Planes (Bagley et al. 2012), it is also expected that the removal of
snow from the domain will result in appreciable increases in cyclone
precipitation.

\textbf{Methods}

\emph{Experimental design and data}

In order to test the effect of snow line position on extratropical
cyclones, 20 cold season NA cyclones (Fig. 2) between 1986-2005 were
simulated using the Advanced Research core of the NCAR Weather Research
and Forecasting model (WRF-ARW) version 4.0.3 (Skamarock et al., 2019)
with perturbed SCE. Four cyclone cases were subjectively selected from
each of the months from November through March based on manual
observational evaluation of all mid-latitude cyclones identified by
low-pressure centers through this period in daily surface and
upper-level weather charts. The criteria of selected cases required
storm trajectories over or adjacent to the Great Plains study area which
resemble either the Alberta Clipper track or that of the Colorado Low
with lifetimes of at least 2 days, based on presence of well-defined
central minimum pressure. Cases were chosen until a sufficient variety
of differences in the lifetime minimum sea-level pressure (SLP) and
magnitude of upper level forcings in the form of 500 hPa height
curvature and vorticity advection by the thermal wind were found. Cases
were simulated with observed initial conditions and validated against
observations using the 32-km spatial resolution North American Regional
Reanalysis (NARR; Mesinger et al. 2006) to ensure that WRF could
accurately simulate each case.

Alterations to the SCE of each case were made by applying average
poleward snow line retreat (PSLR) from the 20-year periods of 1986-2005
(historical) to 2080-2099 (projected) for each of the five months
examined in this study. Projected PSLR was determined by examination of
the grid cell snow mass change in 14 models of the
5\textsuperscript{th}phase of the Coupled Model Intercomparison Project
(CMIP5; Taylor et al. 2012) wherein daily snow mass data were available
and experiments were conducted with two Representative Concentration
Pathway forcings: RCP4.5 and RCP8.5 (van Vuuren et al. 2011)(Table 1).
Grid cells were identified as snow-covered if their simulated snow mass
was at least 5 kg m\textsuperscript{-2}, which corresponds to typically
5 cm of snow depth (assuming a 10:1 snow to water ratio), sufficient to
cover the surface. We did test other thresholds and did not find a
strong sensitivity to this choice in the projected snow cover maps. The
southernmost such grid cells were considered to comprise the snow line
if the 5 degree span to the north of a cell had an average snow mass
exceeding that threshold. This search radius was employed in order to
exclude outlying isolated southern patches of snow. To limit artifacts
that arise from small-scale variability in snow cover, a 600 km moving
window average was then applied to all derived southern extent of snow
cover, hereafter referred to as the ``snow line''. For each month, the
20-year average snow line of the historical and projected periods was
calculated, and the amount of projected PSLR was determined from west to
east in 30 km-wide bins across North America. Different iterations,
realizations, and physics options belonging to experiments of the same
model were combined in a ``one model, one vote'' scheme. With PSLR
calculated for both RCP forcings for each of the 14 models, each month
contained 28 PSLR values from which the 10\textsuperscript{th},
50\textsuperscript{th}, and 90\textsuperscript{th} percentiles were
determined (Table 2).

The modeling effort involved simulating each of the 20 mid-latitude
cyclone cases with five degrees of snow line perturbation, each at five
different initialization times, from zero to four days prior to
cyclogenesis, yielding a total of 500 distinct simulations. One hundred
simulations were generated without changes made to snow cover (control).
The remaining 400 runs imposed projected snow line changes of varying
magnitude (10\textsuperscript{th}, 50\textsuperscript{th}, and
90\textsuperscript{th} percentiles; \emph{P\textsubscript{10}}
,\emph{P\textsubscript{50}} , \emph{P\textsubscript{90}} ) or complete
snow removal across the domain in order to determine the degree to which
the position of the snow line influences storms as opposed to that
attributable solely to snow removal. Snow lines for perturbed
simulations were determined by applying values of PSLR to corresponding
30 km bins of the snow lines, as determined based on the method above,
for each case and removing all snow south of the new snow line except at
altitudes greater than 2,000 m, where snowpack may persist even in
warmer climates, based on conclusions by Rhoades et al. (2018). It
should be noted that the removal of all snow south of the assigned snow
line creates a discontinuous step function in snow depth, a hard margin
which is not necessarily characteristic of real snow extent boundaries.

\emph{WRF model configuration}

WRF-ARW simulations were executed in a domain comprising the continental
United States (CONUS), central and southern Canada, northern Mexico, and
much of the surrounding oceans. The WRF-ARW has previously been shown to
be reliable in simulating seasonal temperature and precipitation
dynamics over the United States (Wang and Katamarthi 2014), with biases
in line with other mesoscale numerical weather models (Mearns et al
2012). We ran WRF-ARW with 30 km horizontal resolution to best capture
synoptic scale transport, a 150 km buffer zone on each side, and 45
vertical levels (Fig. 3). Initial and lateral boundary conditions were
derived from 3-hour NARR data provided in grib format by NOAA/OAR/ESRL
PSD, Boulder, Colorado, USA, at https://www.esrl.noaa.gov/psd/. Version
4.0 of WRF offers a ``CONUS'' suite of physics options which was used in
this experiment, and appears to accurately reproduce large-scale
circulations (Hu et al. 2018). The NOAH Land Surface Model (Noah LSM;
Mitchell et al. 2001) was altered to reduce surface snow accumulation to
zero during simulation in order to avoid snow deposition prior to the
arrival of the cyclone of interest into the area without removing
precipitation in the atmosphere. The Noah LSM uses a single layer snow
model and calculates snow albedo according to the method developed by
Livneh et al. (2010), which calculates the albedo of the snow-covered
portion of a grid cell as

\begin{equation}
\alpha_{\text{snow}}=\ \alpha_{\max}A^{t^{B}}\nonumber \\
 \end{equation}

where \selectlanguage{greek}\emph{α\textsubscript{max}}\selectlanguage{english} is the maximum albedo for fresh snow
in the given grid cell (established by data from Robinson and Kukla,
1985), \emph{t} is the age of the snow in days, and \emph{A} and\emph{B}
are coefficients which are, respectively, 0.94 and 0.58 (0.82 and 0.46)
during periods of accumulation (ablation). Coefficients\emph{A} and
\emph{B} were set to accumulation phase for simulations in every month
except for March, when the snow was considered to be ablating. Sensible
and latent heat fluxes are calculated from surface and snow using an
energy balance approach based on snow pack temperature and moisture
input.

\emph{Analytical methods}

A number of tracking methods have been proposed for cyclones, as
reviewed in Rydzik and Desai (2014). Here, cyclones are tracked by
defining the center as the local SLP minimum and following it as the
cyclone proceeds. Because each cyclone case was known in advance from
subjective selection, identifying the genesis of each cyclone involved
searching a known area at a known time for SLP minima. Recording changes
in storm trajectory between two simulations of the same cyclone case is
done by calculating the mean trajectory deviation (MTD), which is the
sum of the absolute north-south deviation distance between the two storm
centers (perturbed-control) at each corresponding time step divided by
the number of time steps. Because each model time step is 3 hours, MTD
is expressed in km (3h)\textsuperscript{-1}.

Examination of precipitation amount and type involved isolating storm
associated precipitation using the method introduced by Hawcroft et al.
(2012). For each time step, it is assumed that precipitation
attributable to any cold season cyclone simulation occurs within a 12\selectlanguage{ngerman}°
radial cap of the storm center. Analyzing the precipitation quantity of
a cyclone's lifetime required determining precipitation amounts and
types from within the radial cap at each time step and ignoring those
values outside of it.

To study broad changes in wind speed, we determined the integrated
kinetic energy (IKE) of each simulated cyclone using a variant of the
method first proposed by Powell and Reinhold (2007). IKE is determined
by integration of the KE in the volume (\emph{V} ) of the bottom model
layer based on wind speeds (\emph{U} ) and assuming a constant air
density (\selectlanguage{greek}\emph{ρ} \selectlanguage{english}) of 1 kg m\textsuperscript{-3},

\begin{equation}
IKE=\ \int_{V}{\frac{1}{2}\rho U^{2}\text{dV}}\nonumber \\
 \end{equation}

As with storm associated precipitation, IKE is only calculated within a
12\selectlanguage{ngerman}° radius of the storms' pressure minima. \selectlanguage{greek}Δ\selectlanguage{english}IKE represents the
normalized ratio of control to corresponding perturbed simulations.

\textbf{Results}

\emph{Snow cover trends}

Before snow extent changes could be applied to model initialization data
for perturbation experiments, it was necessary to conduct a survey of
the 14 selected CMIP5 models to determine mean PSLR from the 1986-2005
period to 2080-2099 in the span east of the Rocky Mountains and west the
Atlantic coast of North America (105 West to 55 West). The mean PSLR of
both RCP experiments for each of the models is shown for each of the
cold season months in Figure 4. The results show snow retreat
differences among models is large although some trends are clear. All
models for both experiments in all months show a projected poleward
shift in snow cover extent, with a minimum average retreat in January of
51 km and a maximum in November of 1,025 km. The models show that the
shoulder months of November, December and March experience greater PSLR
than those in the middle of winter.

Generally, simulations of the RCP8.5 experiment yielded greater PSLR
than RCP4.5, although all months have multiple exceptions. According to
the Student's t-test, RCP8.5 PSLR is greater than RCP4.5 within the
99.9\% confidence interval except in March, when the confidence level
shrinks to 99\%. February has the lowest standard deviation of PSLR
across models at 175 km, which is comparable to January and March with
185 km and 183 km, respectively. The early winter months have the higher
standard deviations at 219 km and 210 km for December and November,
respectively.

\emph{Cyclone trajectory}

All control cases were selected to those where the control run well
depicted observed cyclone trajectory and net precipitation. The 400
perturbation cases were then compared to these 100 control runs. Cyclone
shifts in response to imposed snow cover extent (SCE) shifts, expressed
as mean trajectory deviation (MTD), were quite small, often less than
the domain grid spacing of 30 km (55\% of the time), and only
infrequently did they exceed two entire grid spaces (12\%), indicating
that cyclones in perturbed simulations followed their control
counterparts faithfully with only minor exceptions. The different in
cyclone track in the perturbed snow cover cases relative to the control
was modest, usually smaller than the mean difference of the control case
to observed cyclone tracks in reanalysis and not related to cyclone typo
(e.g., Alberta clipper and Oklahoma panhandle cyclone). Although the
simulated responses of these cyclones to short-term reductions in snow
extent may be regarded as minute, they are not always devoid of
significance.

Plotted together according to total area of snow removed (Fig. 5a), the
400 MTDs of each perturbed simulation cyclone present a mild but
significant positive linear relationship (\emph{R\textsuperscript{2}} =
0.232, \emph{p} \textless{} 0.01). The strength of the relationship
increases when limited to simulations initialized at least two days out
(\emph{R\textsuperscript{2}} = 0.292, \emph{p} \textless{} 0.01), which
implies an adjustment timescale for cyclone dynamics to respond to SCE
changes. Perturbed simulations initialized at the time of cyclogenesis
or one day prior have diminished MTDs when compared to the magnitude of
the responses for simulations initialized two days out and greater where
the signal stabilizes, with gradual increases in the mean at three and
four days prior (Fig. 5b). Figure 5c also reveals this relationship by
calendar month, thereby summarizing the MTD response according to
initialization time as well as perturbation degree. There was some
seasonality to the results with weaker responses in the late autumn to
early winter (Nov-Dec, average MTD (\selectlanguage{greek}μ\selectlanguage{english})=29.6 km 3
hr\textsuperscript{-1}), the strongest responses in mid-winter (Jan-Feb,
\selectlanguage{greek}μ\selectlanguage{english}=36.1), and moderate responses in late winter to spring (Mar, \selectlanguage{greek}μ\selectlanguage{english}=32.7),
implying albedo was not the dominant mechanism driving changes.

Despite the prevalence of cyclone trajectory deviation among perturbed
simulations, except for a few outliers, poleward deflection across cases
in response to a retreating snow line was not substantial (Fig. 5d). The
mean values and quartiles for each month never exceeded a single grid
space, even when only initialization times greater than 2 days out are
considered. Mean poleward deviation was nearly as likely to be negative
as positive for most cases. Another way to examine cyclone steering is
by calculating the tendency of trajectories to deviate toward the
perturbed snow line, which may lie to the south of the cyclone
trajectory. This method, however, also falls short of producing a robust
signal. Like the poleward shift, the snow line oriented shift only
indicated a positive signal a little over half the time and rarely with
substantial quantities.

\emph{Storm center SLP}

Across all simulations, 70\% of perturbed simulation cyclones decreased
average lifetime central low SLP compared to the corresponding control
simulation, however slightly, and every perturbed simulation cyclone
experienced a significant difference in central SLP compared to control
at some point in their lifetime. Most central SLP differences present in
perturbed simulations, like those in the analysis of the MTDs, are
small. The magnitude of mean cyclone lifetime central SLP change never
exceeded 2.2 hPa, though maximum differences could exceed 10 hPa. Figure
6a summarizes lifetime mean central SLP changes averaged for each month
according to perturbation degree and initialization time. There is a
robust dependence on perturbation degree for the latter three months of
the cold season, with exceptional responses in the no snow simulations.
November and December cyclones have a much weaker, if at all
discernable, response to the degree of PSLR. For all perturbed
simulations, November and December cyclones only undergo a mean lifetime
deepening 53\% of the time, while mean lifetime deepening occurs 81\% of
the time for the latter three months. In these latter months, responses
become more pronounced when simulations are initialized 2-4 days prior
to cyclogenesis, although responses within this period are similar.
Cyclones in transit over the region where snow had been removed
deepened, on average, 2.5 times as much as others and nearly 4 times as
much as those which remained over snow (\emph{p \textless{} 0.01} ).

The maximum instance of deepening for cyclones in perturbed simulations
decreased almost 6 hPa (Fig. 6b), although the deepening was more
strongly responsive to initialization time and also tended to stabilize
at greater than two days out. The dependence on month is not as great
for percentile-based snow removals, although it is stark in the no snow
simulations with the same latter months have a much greater response.
Maximum deepenings are more robustly correlated with MTD (Fig.
6c,\emph{R\textsuperscript{2}} = 0.395, \emph{p} \textless{} 0.01). The
relationship is notably less robust when examining mean lifetime
pressure change (\emph{R\textsuperscript{2}} = 0.209,
\emph{p}\textless{} 0.01), although still statistically significant.

\emph{Kinetic energy}

Across all 400 perturbed simulations, 72\% of perturbed simulations
experienced a positive mean intensification over their lifetime compared
to the control runs. Figure 7a shows that, like the other previously
examined variables, changes in integrated kinetic energy (IKE) relative
to control caused by perturbation of the snow fields in the vicinity of
cyclones is highly subject to both initialization time and perturbation
degree. One notable difference regarding IKE is that there is an
exceptional tendency for it to abate at the higher perturbation degrees,
particularly in the shoulder months. At the
90\textsuperscript{th}percentile of snow cover reduction, almost all
November storms experience a mean reduction in IKE, and November storms
undergo an average 1\% decrease in IKE when initialized 4 days prior to
cyclogenesis. The fact that those very same cyclones experience a nearly
equivalent increase in IKE when initialized three days out indicates a
nonlinear relationship between IKE and initialization time. For no snow
simulations, short spin-up times generally reduced IKE, although
simulations with one day of spin-up or greater increased IKE
substantially. The December cyclones appear to be the only exception to
these observations.

The seasonality of changes to IKE are made more apparent in Figure 7b,
which shows that, on average, December simulations experienced a small
decrease in intensity, although some outliers decreased intensity by
over 3\%. Simulations in every other month intensified on average,
though the signal was considerably weaker in November than in the
mid-winter and spring months. Some outliers in February and March
intensified by over 9\% when all snow was removed, and those months
still had dramatic intensifications in the 50\textsuperscript{th} and
90\textsuperscript{th} percentile experiments.

\emph{Precipitation}

Among perturbed simulations, 86\% of cases experiences an increase in
domain-integrated precipitation (Fig. 8a). Of the variables examined in
this study, precipitation had the strongest response to removed snow
cover and the greatest sensitivity to initialization time. Precipitation
in perturbed simulations had weak responses when no spin-up time was
allowed except in no snow simulations. Once again, December cases had
the weakest responses to the snow cover perturbations with the lowest
mean change in domain-integrated precipitation (Fig. 8b). While January
cases had the highest mean response in precipitation, the November cases
had the highest total increases in precipitation within individual cases
and the greatest spread among cases. In many perturbed simulations, the
phase of the precipitation changed from snow to rain, in southern
latitudes and often near the original snow line. While grid cells with
such phase changes never exceed 2\% of the cells in the study domain,
the overall increase in precipitation across the domain contributed to a
substantial generation of new rain in perturbed simulations.

Changes in the volume of precipitation were very regionally dependent.
In response to a poleward retreating snow line, cyclone-associated
precipitation increased substantially across regions where snow was
removed and across northern latitude regions downstream of the Great
Plains, while southern regions experienced decreases in total
precipitation (Fig. 9). The locations and amounts of enhanced
precipitation appear to have been largely dependent on whether snow had
been removed in that area, but new precipitation was often generated
over snow near the perturbed snow line. Removing all snow from the
domain resulted in significant quantities of new precipitation,
particularly in the latitudes north of the U.S.-Canada border with the
province of Quebec receiving an average of 1 mm of extra precipitation
per grid cell and the Southeast United States (Virginia, North Carolina,
South Carolina, Georgia, Florida, Alabama) experiencing an average
decrease of 0.05 mm per grid cell.

\textbf{Discussion}

The retreat of southern snow extent calculated by comparing averages of
historical (1986-2005) and late twenty-first century (2080-2099) snow
lines is substantial. Surprisingly, applying it to historical cyclone
cases for simulations with spin-up times of 4 days or less fails to
result in striking changes to cyclone trajectory or central minimum SLP,
notwithstanding the conclusions of other studies which would suggest a
more direct and influential relationship. The changes made to underlying
snow cover did, however, produce noteworthy responses to cyclones' total
kinetic energy and the storm-associated precipitation within a broad
radius of the storm center.

Storm-associated precipitation had the most robust positive relationship
to snow removal with the highest percentage of perturbed simulations
yielding greater amounts of either solid or liquid precipitation. Even
simulations with decreased domain-wide precipitation had relatively
little reduction relative to increase. This outcome agrees with a large
number of previous works which find an increase in precipitation amount
and intensity in the Northern Hemisphere by the late
21\textsuperscript{st} century (e.g. Catto et al. 2019). This study,
however, does not find this result due solely to the Clausius-Clapeyron
relationship whereby a warming climate drives increases in airborne
water vapor but primarily due to the removal of snow from the surface
and its effect on atmospheric thermodynamics. This finding supports
observations made by previous authors (e.g. Namias 1962 and Elguindi et
al. 2005) that snow cover suppresses precipitation from overhead
extratropical cyclones. This may be due to the lack of moisture flux
(Trenberth 1998 and Ellis and Leathers 1999), the increase of static
stability (Bengtsson 1980), or more likely both. We can therefore
reasonably assume that the increases in precipitation shown here
represent only a portion of the increased precipitation for which
climate change will be responsible and that the poleward migration shown
is likely to be more intense.

The cyclone integrated kinetic energy (IKE), a measure of 10 m wind
speed associated with the storm, also had noteworthy responses to snow
removal. A large majority of cyclones in perturbed simulations
intensified and there exists a positive relationship between IKE and
snow removal area, suggesting that it may be related to surface energy
budget. These results contradict those of GCM studies such as Ulbrich et
al. (2009) and Seiler and Zwiers (2015) which find reductions in
extratropical cyclone wind speed by the late
21\textsuperscript{st}century. These results may differ due to changes
in upper level baroclinicity caused by climate change or even due to the
differences in our determination of intensity.

In contrast to our original expectations, trajectory deviations were
minimal. MTD measures the amount of deviation from control in perturbed
simulation cyclone trajectories and averages over the cyclones'
lifetimes. Because the majority of cyclones in perturbed simulations did
not deviate from control for most of their courses, most MTDs are
measured as less than the length of the domain grid spacing of 30 km and
only 49 of the 400 perturbed cyclone simulations deviated by an average
of more than two grid spaces. Directional MTDs considering deflection
toward the North Pole or the perturbed snow line were inconsistent and
notably minimal with few outliers. The fact that both of these metrics
often yielded such minor results indicates that many perturbed
simulation cyclones deviated primarily stochastically from the control
trajectory.

The study by Elguindi et al. (2005) wherein snow was added to a Great
Plains nested domain two days prior to cyclone arrival generated similar
trajectory outcomes with deviations in perturbed cases only rarely
exceeding 100 km. The trajectory deviations in these tests, like our
own, varied substantially and defied any discernable trend. It is
reasonable to infer that differences in trajectories between control and
perturbed cyclones in both studies are likely chaotic reactions to
considerable energy disturbances caused by step changes to surface
conditions over extensive areas, rather than functional responses to the
specific positioning of snow cover. This conclusion is unexpected, given
the significant cyclone responses to snow anomalies found by multiple
observational studies (e.g. Dickson and Namias 1976; Heim and Dewey
1984; Rydzik and Desai 2014) as well as modelling done by Ross and Walsh
(1986) and Walland and Simmonds (1997). The most obvious distinction
here is temporal scale, hinting that a similar study conducted at the
seasonal timescale may reveal a more robust relationship.

Like MTDs, changes to cyclones' central low SLP due to a retreating snow
line were minimal. This, however, differed from the results of Elguindi
et al. (2005) who found an average positive difference of 4 hPa in
response to expanded snow cover, a threshold which only seven
simulations in this whole study exceeded, all of which as part of the no
snow sensitivity experiment. Perhaps this can be attributed to the fact
that they added snow as opposed to removing it or to the physics of the
MM5 model compared to WRF-ARW. Even with the disparity in the magnitude
of pressure changes, their discovered trend of central pressure
increasing when snow is added is complemented by the findings of this
study where snow removal generally contributed to a decrease in central
pressure. The enhanced frequency of central low SLP decreasing while in
transit over regions where snow had been removed corroborates the
conclusion of Elguindi et al. (2005) that snow cover prevents the
deepening of mid-latitude depressions by reducing warm sector
temperature and moisture gradients, weakening surface convergence and
fronts. The relationship shown between MTD and pressure changes
indicates that, while the two may not be directly linked, they do
respond similarly to perturbed simulations.

\emph{Seasonality}

We find consistent trends across all examined variables affirming that
cyclone responses to poleward-shifted snow lines depend upon when in the
cold season the cyclones occur. Generally, responses of virtually every
investigated variable are greater in the mid-season months of January
and February and weaker in the shoulder months, although there are often
greater responses in March than in November or December. This is
counter-intuitive from an inspection of PSLR as seen in Figure 4. If
anything, there appears to be an inverse relationship between amount of
mean PSLR and response of cyclones to the correspondingly-shifted snow
lines. However, it has been shown that the surface temperature effect of
snow cover is strongest in late winter (Walsh et al. 1982) and March
snow cover has reduced efficacy due to its properties during ablation
(Livneh et al. 2010).

December consistently has the most abnormal responses, even
contradicting consistent trends in other months; for example, December
is the only month with a mean reduction in IKE but is also the month
with the weakest solar radiation, implying a weaker albedo gradient
effect. Still, it is not entirely understood why December in particular
has these properties, although the apparent problem in attempting to
make determinations about the seasonality of the data is that each month
represents only four separate cyclone cases which are then averaged
together.

\textbf{Conclusions}

Twenty cold season extratropical cyclones over or near the North
American Great Plains were generated in a series of simulations in order
to gauge the dependence of their trajectories, intensities, and
associated precipitation on underlying snow cover. When a realistic
retreat of snow cover consistent with climate warming scenarios was
applied to these cases, a majority of cyclones experienced an average
decrease in pressure and increases in precipitation, but only limited
changes in trajectory and modest increases in kinetic energy. These
results contradict expectations gained from observational studies such
as that of Namias (1962) and Rydzik and Desai (2014) but reflects the
results of modelling done by Elguindi et al. (2005), reflecting a
continued disagreement among models and observations.

It is yet unknown why the cyclone trajectories did not adhere more
closely to shifted snow lines, as the findings of other studies would
have suggested. Weaker responses to the removal of snow cover at the
time of cyclogenesis suggest that the presence or absence of the snow
margin has a minor, though not entirely imperceptible, immediate effect.
There is little to imply that the effect on trajectory deviation,
pressure change, or precipitation plateaus for simulations initialized
at four or more days out and so the question of the full extent of the
snow margin's influence cannot be answered until longer case study
simulations are executed.

Lingering questions remain on mechanisms of snow cover on sea-level
pressure, differences among cases in surface energy-balance and
radiative properties and its influence on cyclone dynamics, and
upper-level dynamics. Some of these, especially upper-level dynamics,
are studied in individual cases in detail in a companion paper by
Breeden et al. (submitted). The simulation model outputs provide a rich
data set for future evaluation and a provided at the archive below for
public access.

\textbf{Acknowledgements}

The authors acknowledge support for this project by the University of
Wisconsin Office of the Vice Chancellor for Research and Graduate
Education Fall Research Competition and the National Science Foundation
(NSF AGS-1640452). Specialized computing resources have been provided by
the University of Wisconsin Center for High Throughput Computing. We
also thank contributions by and discussions with G. Bromley of Montana
State University, M. Rydzik of Commodity Weather Group, and H. Miller of
University of Kentucky. Data from cyclone simulations are in process of
being archived and assigned a DOI at the Environmental Data Initiative
prior to manuscript acceptance. Reviewers can access model output at:
http://co2.aos.wisc.edu/data/snowcover/ .



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Zishka, K. M. and P. J. Smith, 1980: The climatology of cyclones and
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\textbf{Tables}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Modeling Center (or Group)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Institute ID\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Model Name\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Horizonal Res. (\selectlanguage{ngerman}°lon × °lat)\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
No. Vertical Levels\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Commonwealth Scientific and Industrial Research Organization (CSIRO) and
Bureau of Meteorology (BOM), Australia\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CSIRO-BOM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
ACCESS1.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.875 \selectlanguage{ngerman}× 1.25\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
38\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
National Center for Atmospheric Research\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NCAR\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CCSM4\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.25 \selectlanguage{ngerman}× 1.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
26\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Centre National de Recherches M\selectlanguage{ngerman}étéorologique/Centre Européen de
Recherche et Formation Avancée en Calcul Scientific\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CNRM-CERFACS\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CNRM-CM5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.4 \selectlanguage{ngerman}× 1.4\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
31\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Commonwealth Scientific and Industrial Research Organization in
collaboration with Queensland Climate Change Centre of Excellence\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CSIRO-QCCCE\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CSIRO-Mk3.6.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.8 \selectlanguage{ngerman}× 1.8\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
18\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NASA Goddard Institute for Space Studies\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NASA GISS\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
GISS-E2-H, GISS-E2-R\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.5 \selectlanguage{ngerman}× 2.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
40\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Met Office Hadley Centre\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MOHC\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
HadGEM2-CC, HadGEM2-ES\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.8 \selectlanguage{ngerman}× 1.25\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
60\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Institute for Numerical Mathamatics\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
INM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
INM-CM4\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.0 \selectlanguage{ngerman}× 1.5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
21\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Atmosphere and Ocean Research Institute (The University of Tokyo),
National Institute for Environmental Studies, and Japan Agency for
Marine-Earth Science and Technology\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MIROC\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MIROC5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.4 \selectlanguage{ngerman}× 1.4\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
40\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Max Planck Institute for Meteorology\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MPI-M\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MPI-ESM-LR\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.9 \selectlanguage{ngerman}× 1.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
47\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Meteorological Research Institute\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MRI\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MRI-CGCM3\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1.1 \selectlanguage{ngerman}× 1.1\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
48\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Norwegian Climate Centre\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NCC\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NorESM1-M, NorESM1-ME\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.5 \selectlanguage{ngerman}× 1.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
26\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 1.} CMIP5 models used in this study and their attributes

(see http://cmip-pcmdi.llnl.gov/cmip5/).\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Month & \emph{P\textsubscript{10}} & \emph{P\textsubscript{50}} &
\emph{P\textsubscript{90}}\tabularnewline
\midrule
\endhead
Nov & GISS-E2-R, RCP4.5 & CNRM-CM5, RCP4.5 & ACCESS1.0,
RCP8.5\tabularnewline
Dec & INM-CM4, RCP4.5 & HadGEM2-ES, RCP4.5 & CSIRO-Mk3.6.0,
RCP8.5\tabularnewline
Jan & GISS-E2-R, RCP4.5 & MIROC5, RCP4.5 & MIROC5, RCP8.5\tabularnewline
Feb & MRI-CGCM3, RCP8.5 & ACCESS1.0, RCP4.5 & ACCESS1.0,
RCP8.5\tabularnewline
Mar & MRI-CGCM3, RCP8.5 & CNRM-CM5, RCP8.5 & MIROC5,
RCP8.5\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Models and RCP experiments which were used to
determine 10\textsuperscript{th}, 50\textsuperscript{th}, and
90\textsuperscript{th} percentile values for late twentieth to late
twenty-first century snow line retreat.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figures}

\textbf{Figure 1.} Difference between grid point maximum snow albedo
(determined by Robinson and Kukla, 1985) and background surface albedo
calculated by the WRF Preprocessing System with input from the WRF
vegetation parameter lookup table. In principle, these values represent
the maximum albedo gradient across a hypothetical local snow line. The
large region of enhanced albedo difference in the center of the
continent represents the Great Plains study area.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} Observed cyclone trajectories for the 20 cases tested
in this study. Coloring refers to the mean central minimum SLP value
during each 3-hour segment of the cyclone trajectory.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} The domain utilized for WRF-ARW simulations. The 30
km grid spacing is shown with the black grid and the five grid cell
buffer zone is left uncovered.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4.} The distributions of average late twentieth to late
twenty-first century poleward snow line retreat (in km) east of the
Rocky Mountains for each month as determined by 14 CMIP5 models (Table
2). Values for RCP4.5 experiment are plotted in blue and RCP8.5 values
are shown in red. Solid black horizontal bars indicate the median value,
while dotted bars indicate the 10\textsuperscript{th} and
90\textsuperscript{th} percentile values. RCP4.5 and RCP8.5 retreat
values are significantly distinct (\emph{p} \textless{} 0.01).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5.} Mean trajectory deviation (MTD) in km
3h\textsuperscript{-1} for all perturbed simulations according
to\textbf{a.)} the total area of all removed snow with coloring
indicating the degree of perturbation as a percentile or all snow
removed according to key; \textbf{b.)} initialization time shown as a
number of days prior to cyclogenesis (T) with means (\selectlanguage{greek}µ\selectlanguage{english}), and average,
interquartile range, 2-\selectlanguage{greek}σ, \selectlanguage{english}and outliers depicted by box and whisker for
all cases;\textbf{c.)} MTDs for cases averaged for each month and
displayed in cells for each perturbation degree {[}top{]} with amount of
spin-up days on the x-axes {[}bottom{]}; \textbf{d.)} mean poleward
shift of all cyclone trajectories in perturbed simulations according to
degree of perturbation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6} . a.) Mean lifetime SLP change for perturbed
simulation cyclone centers averaged for each month as with Fig. 5c. b.)
Maximum deepening during cyclone lifetime averaged for each month as
with Fig. 6a. c.) Maximum deepening and MTD for all simulations and
distinguished by perturbation degree.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 7.} Normalized changes to integrated kinetic energy
within a 12\selectlanguage{ngerman}° radius of the cyclone center a.) averaged for each month
and shown at each initialization time for each perturbation degree and
b.) shown with all perturbed cases by month.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Figure 8.} Domain-integrated precipitation a). averaged for each
month and shown at each initialization time for each perturbation degree
and b.) shown with all perturbed cases by month for initialization times
[?] 3 days out only.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Figure 9.} Sum total of precipitation difference for all 20
cyclone cases for initialization times [?] 3 days out (T-\emph{n} ) and
all perturbation degrees.

\selectlanguage{english}
\FloatBarrier
\end{document}

