Simulation of a former ice field with Parallel Ice Sheet Model – Snežnik study case

Abstract

In this paper, we present a reconstruction of climate conditions during the Last Glacial Maximum on a karst plateau Snežnik, which lies in Dinaric Mountains (southern Slovenia) and bears evidence of glaciation. The reconstruction merges geomorphological ice limits, classified as either clear or unclear, and a computer modelling approach based on the Parallel Ice Sheet Model (PISM). Based on extensive numerical experiments where we studied the agreements between simulated and geomorphological ice extent, we propose using a combination of a high-resolution precipitation model that accounts for orographic precipitation combined with a simple elevation-based temperature model. The geomorphological ice extent can be simulated with climate to be around 6 °C colder than the modern day and with a lower-than-modern-day amount of precipitation, which matches other state-of-the art climate reconstructions for the era. The results indicate that an orographic precipitation model is essential for the accurate simulation of the study area, with moist southern winds from the nearby Adriatic Sea having a predominant effect on the precipitation patterns. Finally, this study shows that transforming climate conditions towards wetter and warmer or drier and colder does not significantly change the conditions for glacier formation.

Full text

Clim. Past, 20, 1471–1488, 2024
https://doi.org/10.5194/cp-20-1471-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
Simulation of a former ice field with Parallel Ice Sheet Model –
Snežnik study case
Matjaž Depolli1, Manja Žebre2, Uroš Stepišnik3, and Gregor Kosec1
1Department of Communication Systems, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
2Geological Survey of Slovenia, Dimiˇ
ceva ulica 14, 1000 Ljubljana, Slovenia
3Faculty of Arts, University of Ljubljana, Aškerˇ
ceva cesta 2, 1000 Ljubljana, Slovenia
Correspondence: Matjaž Depolli (matjaz.depolli@ijs.si)
Received: 23 February 2024 – Discussion started: 27 February 2024
Accepted: 20 May 2024 – Published: 10 July 2024
Abstract. In this paper, we present a reconstruction of cli-
mate conditions during the Last Glacial Maximum on a karst
plateau Snežnik, which lies in Dinaric Mountains (southern
Slovenia) and bears evidence of glaciation. The reconstruc-
tion merges geomorphological ice limits, classified as either
clear or unclear, and a computer modelling approach based
on the Parallel Ice Sheet Model (PISM). Based on extensive
numerical experiments where we studied the agreements be-
tween simulated and geomorphological ice extent, we pro-
pose using a combination of a high-resolution precipitation
model that accounts for orographic precipitation combined
with a simple elevation-based temperature model. The geo-
morphological ice extent can be simulated with climate to be
around 6 °C colder than the modern day and with a lower-
than-modern-day amount of precipitation, which matches
other state-of-the art climate reconstructions for the era. The
results indicate that an orographic precipitation model is es-
sential for the accurate simulation of the study area, with
moist southern winds from the nearby Adriatic Sea having a
predominant effect on the precipitation patterns. Finally, this
study shows that transforming climate conditions towards
wetter and warmer or drier and colder does not significantly
change the conditions for glacier formation.
1 Introduction
The Last Glacial Maximum (LGM) in Europe was dominated
by the Fennoscandian Ice Sheet, which was one of the ma-
jor global ice masses during the last glacial cycle. A rela-
tively large ice mass was also the Alpine ice sheet over the
European Alps. Other, much smaller, mountain glaciers ex-
isted in Iberia, the Pyrenees, the Apennines, and the Balkans
(Hughes et al., 2013). These smaller ice masses, being iso-
lated from larger ice sheets, have a well-defined linkage be-
tween their areas of origin and the areas they affect, which
simplifies the task of reconstructing their past extents and
behaviours. Additionally, their tendency to react quickly to
climate change makes them valuable proxies for deducing
historical climate conditions.
Past glaciations in the northern Dinaric Mountains at the
interface between the Alpine ice sheet and Balkan Mountain
glaciers are well-documented geomorphologically (e.g. Že-
bre et al., 2013, and Žebre and Stepišnik, 2016), but there is
lack of knowledge about climate–glacier dynamics based on
the modelling approach. The northern Velebit mountains in
Croatia are the only formerly glaciated mountains in this re-
gion where an empirical reconstruction has been compared
with computer-based simulations under different palaeocli-
mate forcings (Žebre et al., 2021). In southern Slovenia, only
a few kilometres to the north of Velebit, lies Snežnik, one of
the northernmost mountain plateaux in the northern Dinaric
Mountains. Snežnik was glaciated during the LGM, although
the exact timing is still ambiguous (Marjanac et al., 2001; Že-
bre et al., 2016). Moraines that mark the farthest extent of the
glacier have been attributed to the LGM, for which the max-
imum ice area was estimated to be at least 40 km2(Žebre
and Stepišnik, 2016). Although the formerly glaciated area
is very small compared to the large Alpine ice sheet (esti-
mated to be 163 000 km2by Seguinot et al., 2018), detailed
knowledge of it can still aid in deciphering the regional past
climate conditions. There have been only a few attempts to
Published by Copernicus Publications on behalf of the European Geosciences Union.

1472 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
model the palaeo-ice field on the Snežnik mountain either
only on the limited area around the small Snežnik summit
(Žebre and Stepišnik, 2016) or as part of a larger Alpine area
(Seguinot et al., 2018). In the first case, a simple steady-state
model that assumes a perfectly plastic ice rheology was ap-
plied (Benn and Hulton, 2010), while in the second case, the
Parallel Ice Sheet Model (PISM) was used (the PISM au-
thors, 2023). However, modelling small palaeoglaciers like
the one on Snežnik is challenging, especially due to the need
for high-resolution climate data and proxy-based palaeocli-
mate forcings – but also due to insufficient knowledge of
pre-ice topography and ice flow.
In this work, we focus on amending the geomorphologi-
cal knowledge with a computer model focused on the whole
Snežnik ice field. We aim to discover the climatological con-
ditions required for the ice field to form to an extent that is
evident from the field observations. We approach the mod-
elling challenge using the PISM on lidar-based topography
with 50 m resolution and with a standard glacier modelling
approach (Bueler and Brown, 2009) and custom climate-
forcing models. Near-surface air temperature and precipita-
tion are used as climate-forcing inputs in PISM, and we have
developed custom models for using the available topology,
single weather station data, and the knowledge of current
wind patterns in the broader area. We present and explore
several climate-forcing models ranging from simple to com-
plex. In the case of Snežnik, the main challenge is achieving
ice distribution according to the geomorphological evidence,
which is skewed counter-intuitively, i.e. towards the well-
insolated southern slopes of the plateau. The inability of the
simulations to achieve an ice cover extent skewed similarly
to the estimated extent can be attributed to inaccuracies in
many of the used models, including sliding laws, basal con-
ditions, and climate forcing. In this work, we chose to only
address the latter, since a plethora of climate data are avail-
able that could lead to simulation improvement if integrated
into the computer models.
Through the use of orographic precipitation coupled with
a simple elevation-based temperature model, we manage to
simulate ice field distributions that conform better to the ge-
omorphological evidence. We find optimal overall precipita-
tion and temperature offsets relative to modern values to be
a close match to the established estimates of local precipita-
tion and temperature in the LGM, thus giving more evidence
for these estimates. We are, however, unable to credibly sim-
ulate the finer details of the ice field, such as smaller outlet
glaciers.
As a part of the study, we set up a framework for an auto-
matic quantitative assessment of the conformance of the sim-
ulated ice area to the given geomorphologically determined
ice bounds. This framework is novel in its ability to work
with two types of bounds, clear and unclear, and evaluates
the accuracy using two criteria. We also provide a simplifi-
cation that combines these two criteria into one which can
then be used as an objective within the task of optimising
computer model parameters.
2 Study area
Snežnik (45°3405300 N, 14°2505300 E) is a wide karst plateau
with an area of roughly 100 km2in the northern part of Di-
naric Mountains in Slovenia. The highest summit is Veliki
Snežnik (1796 m a.s.l.).
2.1 Glacial geomorphology
Geomorphology of the area has been studied well, with stud-
ies realising the ice extent appearing as early as 1959 (Šifer,
1959). More recent works largely confirmed the previous
findings (Žebre and Stepišnik, 2016) but also focused on de-
tailed geomorphology, geochronology, and glacial–karst in-
teraction (Žebre et al., 2016, 2019). These found that most
glacial deposits are present between 900 and 1200 m a.s.l.
They form characteristic glacial depositional features which
stand out from the surrounding karstic area, whereas typical
glacial erosional features are not common for the area. In-
stead, the area is dissected by glaciokarst depressions which
are most likely formed by a combination of karst processes
and subglacial erosion, e.g., as described in Smart (1987);
Žebre and Stepišnik (2016). The maximum geomorphologi-
cal ice extent in Snežnik was estimated, based on the overall
position of glacial features, and which was subsequently di-
vided into clear and unclear ice boundaries. The first were de-
lineated based on end-moraines and outwash fans, while the
latter were drawn over areas that only show suggestive ev-
idence for glaciation. The geochronological data (Marjanac
et al., 2001; Žebre et al., 2019), although still scarce, point
to a maximum ice extent during the last glacial maximum
(LGM), i.e. 30–17 ka (Lambeck et al., 2014).
Southeast of Snežnik lies the Gorski Kotar mountain
range, which was also glaciated. Geomorphological mapping
suggests that the Gorski Kotar ice field was approximately
twice as large as that of Snežnik (Žebre and Stepišnik, 2016).
Despite the close proximity of the two areas, there is no evi-
dence to suggest that the two ice fields were connected (Že-
bre et al., 2016). Because of that and for computational rea-
sons, the Gorski Kotar area was not included in our mod-
elling domain.
2.2 Climate
Plateau declines to the south and the southwest towards the
Adriatic Sea that starts around 25 km away. With the prox-
imity of Adriatic Sea, the plateau is provided with above-
average precipitation for the area. Snežnik receives between
2000 and 3000 mm of precipitation annually, with a strong
annual cycle, as reported by ARSO (2023). There are two
major drivers of precipitation, namely the Genoa low cy-
clone and the regular moist wind blowing from the south–
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1473
southeast, which are intensified by the orographic topology.
The mean annual air temperature at the meteorological sta-
tion in Mašun (period 1971–1986), NW of Snežnik, is around
7 °C and average air temperatures for winter and summer are
−3 and 15 °C, respectively. The rise in the specified tem-
peratures at Mašun, relative to the pre-industrial era, can be
estimated from the average of Slovenia published by Urad
za meteorologijo, hidrologijo in oceanografijo (2021) and is
0.4 °C relative to pre-industrial era. Global temperature at the
LGM was 3 to 6 °C lower than in pre-industrial times (An-
nan and Hargreaves, 2013), whereas the LGM temperature
offset over the Alps has been recently simulated to about
−6.6 °C (Del Gobbo et al., 2023). As for the precipitation
in the LGM, the same research suggests the Alps were over-
all drier (by ≈16 %) than in pre-industrial times. Del Gobbo
et al. (2023) found a similar LGM temperature and precipita-
tion offset for the northern Dinaric Mountains in general but
allowed up to ≈30 % drier climate around Snežnik. (Fig. 3 in
Del Gobbo et al., 2023). During the last glacial cycle, the sea
level in the Adriatic was 100–130m lower than at present
(Spratt and Lisiecki, 2016; Gowan et al., 2021), position-
ing Snežnik much further from the coastline, and associated
moisture source, at a distance of 150–200 km.
3 Methods
3.1 PISM setup
PISM 2.0 was used throughout the experiments. The mod-
elling parameters of PISM were set identically to those de-
scribed in Žebre et al. (2021), where a larger mountain range
just to the south of Snežnik was simulated, and similar to
those in (Canda¸s et al., 2020), where a similarly sized moun-
tain in the Republic of Türkiye was simulated. In this sec-
tion, we list all the parameters that require an explicit setting,
along with some of those that were left at their default values
but were being analysed in preliminary testing and sensitiv-
ity analysis. Model selection is listed first in Table 1, and the
parameters that either depend on the model selection or are
general are listed in Table 2. Finally, the various settings that
do not translate to PISM parameters directly are listed in Ta-
ble 3.
3.2 Model domain
The source of the topographical data for the domain is the
digital elevation models (DEMs) provided by EU-DEM v1.1
in 50 m resolution from (European Environmental Agency,
2016). To simulate the glacier, a rectangular domain is used
that covers the area of about 266km2. For preliminary simu-
lations, the resolutions of either 200 or 150 m had been used,
and most of the results presented in the paper have been com-
puted with the resolution of 100 m and in a single case 50 m.
Vertically, the ice thickness is limited to 1000m, and the
number of layers is set to 21, resulting in the vertical grid size
of the computational box of 50 m. There are also five layers
of simulated bedrock, and the total height of the simulated
bedrock is 100 m. We experimented also with higher vertical
resolutions but observed only a minuscule effect on the simu-
lation results, accompanied with a noticeable increase in ex-
ecution time. For both the number of ice and bedrock layers,
we selected the values based on maximal performance with a
satisfactory level of detail, which we determined during pre-
liminary experimentation.
We used grid sequencing, an approach used to decrease the
time complexity of steady-state simulations, which is sup-
ported by PISM. The simulation is started on a coarse grid
for a large portion of simulation time or until a relevant met-
ric, such as the ice volume, converges. Then the grid is re-
fined, and the simulation continues on the finer grid; i.e. the
last state of the simulation is interpolated to the finer grid
(regridded) and taken as input into the next simulation stage.
In the presented study, we used the following setup for grid
sequencing, which is based on the empirical values derived
from preliminary experiments. Simulations were started on a
400 m grid for 500 years, then continued on a 200 m grid for
1000 years, and finally on a 100 m grid for 1500 years. The
final resolution of these simulations was therefore 100 m, as
are the resolution of results, while lower resolutions are only
used to form rough ice coverage from the initial no-ice con-
ditions.
3.3 Quantitative validation
The main goal of the presented work is to create a com-
puter model that can describe the steady-state ice field under
LGM climate conditions. Since the general computer model
for ice fields already exists, but the climatic conditions on
a microscale are only roughly known, this goal has been
translated to a more immediate goal of determining the cli-
matic conditions under which the geomorphological shape of
glacier can exist. This goal can be achieved through an opti-
misation task – a set of input parameters which include the
climate forcing has to be continuously tuned (optimised) for
the simulations based on them to produce results of increas-
ing quality. The quality of the results can be characterised
by how closely the simulated glacier extent aligns with its
observed geomorphological form. To provide an objective
validation of the simulation result quality, two quantitative
metrics have been implemented.
First, a function to determine whether any given coordi-
nate lies inside or outside of the geomorphological glacier
area is constructed using both the clear (observed) and un-
clear glacier boundaries which, used together, bound two
separate geographical areas within the domain (see Fig. 1).
This function is used to divide the domain into the geomor-
phological glacier area and the ice-free area. Then, only the
clear glacier boundaries are used to generate two artificial
border areas, with one bounded by the observed boundary on
one side and extending away from the ice field and another
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1474 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
Table 1. PISM models used in the study.
Model Value PISM option
Stress balance SIA +SSA -stress_balance ssa +sia
SIA flow law (rheology) Glen–Paterson–Budd–Lliboutry–Duval law -ssa_flow_law gpbld
Sliding law Pseudo-plastic power law model -pseudo_plastic
Surface mass and energy process Positive degree days (PDDs) -surface pdd
Atmospheric annual cycle Scalar precipitation and temperature offset -atmosphere given, delta_T, delta_P
Subglacial hydrology Undrained plastic bed -hydrology null
Ocean models Disabled -dry
Table 2. PISM parameters that do not depend on the domain size and resolution.
Parameter Value PISM option
Number of vertical layers in the ice 21 -Mz 21
Calculation box height 1000 m -Lz 1000
Number of vertical layers in the bedrock 5 -Mbz 5
Bedrock calculation depth 100 -Lbz 100
Prevailing wind direction∗150° -atmosphere.orographic_precipitation.wind_direction 30
Scaling factor for precipitation 1 -atmosphere.orographic_precipitation.scale_factor 1
Latitude for calculating Coriolis effect 45° -precipitation atmosphere.orographic_precipitation.coriolis_latitude 45
True background precipitation 1946 mm a−1-atmosphere.orographic_precipitation.background_precip_post 1946
Pre-applied background precipitation 0 mm a−1-atmosphere.orographic_precipitation.background_precip_pre 0.0
q0 -pseudo_plastic_q 0
uthreshold 100 m a−1-pseudo_plastic_uthreshold 100
Till compressibility coefficient 12 -till_compressibility_coefficient 0.12
Till reference void ratio 1 -till_reference_void_ratio 1
Effective overburden pressure of till 0.02 -till_effective_fraction_overburden 0.02
Till reference effective pressure 1000 -till_reference_effective_pressure 1000
Till water decay rate 1 -hydrology_tillwat_decay_rate 1
Till water maximum level 2 -hydrology_tillwat_max 2
φplastic 10 -plastic_phi 10
Till cohesion 0 -till_cohesion 0
Degree day factor for ice 0.00879121 mK−1d−1-surface.pdd.factor_ice 0.00879121
Degree day factor for snow 0.0032967 mK−1d−1-surface.pdd.factor_snow 0.0032967
Refreeze for degree day 0.6 -surface.debm_simple.refreeze_ice_melt 0.6
∗Note that the wind direction in PISM seems to ignore the coordinates supplied with DEM and instead assumes some default orientation of the supplied data. We supplied the data
oriented differently; therefore, the wind direction had to be remapped.
Table 3. Parameters of custom models and other settings.
Parameter Value
Total simulation length 3000 years
Grid sequencing Three steps (see Sect. 3.2
for details)
Insolation effect amplitude AS1
bounded by the observed boundary on one side and extend-
ing towards the interior of the ice field. These border areas
thus represent an area that we are certain was ice-free and an
area that we are certain was covered with ice. The simulation
should cover the latter with ice but not the former. There-
fore, hereafter we name the two border areas forbidden and
required, respectively.
The exact procedure to generate the two border areas is as
follows. The clear limits are offset perpendicularly to them-
selves in both directions (outwards and inwards), creating the
boundaries of a singular border area. This is then compared
to the geomorphological glacier area, i.e. the area bordered
by both clear and unclear geomorphologically reconstructed
limits. The intersection of the border area and the geomor-
phological glacier area then forms the required area, while
their difference forms the forbidden area. Since both clear
and unclear limits are used in the operation, it is assured that
the forbidden area cannot extend into the geomorphological
ice field area – even in cases when offsetting the borders of
clear limits does so, e.g., in nearby parallel outlet glaciers
that exist to the northeast of the presented domain.
The optimisation task for the simulated glacier should
minimise the ice coverage of the forbidden area and max-
imise the ice coverage of the required area. While covered
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1475
Figure 1. General location of the plateau Snežnik (a) and the domain in a resolution of 25 m (b). The geomorphologically reconstructed
glacier extent is plotted with dashed (unclear/estimated) and solid lines (clear/observed). The reference weather station and the highest
summit of the plateau are marked with a dot and a cross, respectively.
surface areas for border areas could be used in an optimi-
sation procedure directly, we first transform them to relative
metrics that are both to be maximised. Therefore, we define
two performance metrics, sensitivity Sen and specificity Spe,
based on surface areas of the two border areas Arequired and
Aforbidden:
Sen =Arequired,covered
Arequired ,
Spe =1−Aforbidden,covered
Aforbidden .
When performing the validation of results, sensitivity and
specificity are calculated and represent two objectives to be
maximised. To illustrate how the metrics are related to the
results, we define a simple model of glaciation, where the
existence of ice is a function of elevation. Areas above the
threshold elevation hare covered with ice, while the others
are not, forming an ice field that is highly nonconforming
with the geomorphological ice field shape. The relation of
the metrics to the thus-defined glaciation is shown in Fig. 2.
The amount by which borders are extended inwards and
outwards to generate forbidden and required areas is by a pa-
rameter that we shall name the width of the respective area
hereafter. For simplicity, we shall keep the widths of both
areas equal. The presented metrics are a function of width,
and thus the metrics can be tuned by adjusting the width,
as shown in columns of Fig. 2. As the figure illustrates,
a nonconforming ice field shape covers almost indiscrimi-
nately both the required and forbidden areas. By increasing
the size of a nonconforming shape, both border areas get cov-
ered more; therefore, the sensitivity increases but the speci-
Figure 2. Illustration of the behaviour of quantitative performance
metrics, demonstrated on three examples of ice coverage simulated
by a simple model, where ice forms above the threshold elevation
hbut not below. Topology is used in full resolution of 25m. The
metrics are calculated for a varying width of forbidden and required
areas w(parameter of the metric) and a varying threshold elevation
h(parameter of the simulation).
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1476 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
ficity decreases. The converse is true when the nonconform-
ing shape decreases in size. To truly optimise the shape, one
has to find ways to increase both the sensitivity and speci-
ficity, which is only possible by transforming the simulated
ice field into a more conforming shape.
An optimisation in which there are multiple criteria (or ob-
jectives) to be optimised, and these criteria are generally con-
flicting, is called a multi-objective optimisation (Collette and
Siarry, 2004). The problem at hand is a multi-objective prob-
lem with two conflicting objectives, and it must be solved
as such. We use the “naive” approach (Collette and Siarry,
2004) to solving a multi-objective problem and combine the
two objectives into one; we construct the single objective Obj
by multiplying the sensitivity and specificity as follows:
Obj =Sen ·Spe.(1)
Then we solve the simpler, single-objective problem by
searching for the parameters of simulation that maximise the
value of the single objective. Such a combined objective is
near zero when one of the factors is near zero; it is higher for
balanced than for imbalanced factors (even if their sum is the
same), and it increases with the increase in each factor. As
such, Obj serves well for optimising the simulated ice field
shape to the prescribed form.
So far we have not picked the value for the width – the
parameter of both border areas that was shown to greatly in-
fluence the resulting sensitivity and specificity. We attempt to
optimise the value for width in the following way. To use the
presented metrics for quantitative result validation, the width
should be large enough to cover the majority of the simu-
lated ice field borders and thus maximise the ability to assign
a different numerical value to different results. For exam-
ple, consider the setting in which the forbidden area extends
only 1 km away from the clear boundary. Then, if a simulated
glacier extends 2 km over the boundary, it will cause the same
drop in the objective function as if it extended only 1km over
the boundary; the results of a clearly different quality will not
be discernible through the proposed metrics. Thus, large val-
ues of width should be preferred. On the other hand, since
the geomorphologically bound ice field is irregularly shaped,
increasing the width will result in border areas spreading in
such a way that the unclear limits will play an increasingly
large part in bounding them. This is not desired; the border
area near unclear limits should be minimised to minimise the
effect of errors that are likely present in unclear limits.
Three values for the width ware displayed in Fig. 2 for
an elevation-based glaciation model, and more were tested in
preliminary experiments. The optimal width of border areas
takes into account both the preference for large values and
the desire to minimise the effect of unclear limits, and ac-
cording to the scale of the major glacial features on the target
area, it seems to be ≈1000 m. From the same figure, trends
in sensitivity and specificity as functions of overall ice field
extent (characterised by simulation parameter h) can be ob-
served. For all tested values of w, the trends are similar, indi-
Figure 3. Climate data for Mašun weather station (45°3704100 N,
14°2105900 E; 1025 ma.s.l.). The values are averaged for years 1971
to 1986.
cating that the exact value of wmight not be important in the
context of optimisation. Optimisation works by analysing the
difference between the objective values of several simulation
results and not on their absolute values. Therefore, optimisa-
tion is robust relative to the selection of wand we do not try
to fine tune wany further.
3.4 Climate forcing
Climate forcing is implemented through temperature and
precipitation models. Both provide location-dependent
monthly mean values that are kept constant throughout all the
simulated years. Several different models were tested to gain
insight into which aspects of climate influence the glacier
formation the most and to see how much detail is required for
simulations with high fidelity. Within this study, temperature
and precipitation models are treated separately, with one hav-
ing no influence on the other. In this section, two temperature
and three precipitation models are presented.
The climate-forcing models are initially tuned to match
the modern conditions for which a reference weather station
is chosen. This weather station is located in a nearby Mašun,
which lies within the area of the Snežnik plateau but outside
of the geomorphological area of glaciation (45°3704100 N,
14°2105900 E) on 1025 ma.s.l. The station was active between
the years 1971 and 1986, and data are available for 97% of
this time range. Monthly mean temperature and precipitation
for the station are shown in Fig. 3.
In the second step, the models are adjusted to shift the
climate towards the LGM. The temperature model output is
offset to lower its output by several degrees, while the pre-
cipitation model output is multiplied by a factor to cause a
relative reduction or amplification, which is then expressed
in percentages. The adjustment to temperature and precipita-
tion models is uniform across the domain; i.e. both the tem-
perature offset and precipitation factor are not functions of
location. The temperature offset and precipitation factor that
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1477
form conditions for the optimal ice field are important results
of the presented study.
3.4.1 Temperature
The baseline temperature model used in this study – we
shall name it the lapse-rate model – comprises a reference
point from the reference weather station and the lapse rate
for standard atmosphere (Atmosphere, 1975) (6.5 °C km−1)
from which temperatures for all grid points can be calculated
as follows:
T(x, y)=(h(x , y )−href)
1000 ·6.5+Tref,
where h(x, y) is the elevation of each point in DEM, href is
the elevation of the reference weather station, and Tref is the
mean temperature recorded at the reference weather station.
The second is an insolation-adjusted lapse-rate model
which extends the lapse-rate model with a proxy for the ther-
mal radiation received from the Sun per surface area of the
Earth (insolation). The insolation extension is a simplified
version of the topographic shading model introduced by Ol-
son and Rupper (2019). It calculates the relative proportion
of solar insolation hitting each grid element by projecting
the Sun radiance vector to the grid element normal, which
is calculated numerically as a pair of symmetric differences
through the xand yaxis. Therefore, the slopes perpendicular
to the incoming radiation from the Sun receive the full rela-
tive insolation (value of 1), while slopes parallel to it receive
no relative insolation (value of 0). The model of relative inso-
lation Sis represented by the following equations (Burrough
et al., 2015):
"∂h
∂x
∂h
∂y #= ∇h(x,y),∀(x, y)∈DEM,
α=π
2−arctan
s∂h
∂x
2
+∂h
∂y
2
,
β=π
2−arctan −∂ h
∂x
∂h
∂y !,
S=sin(ψ)·sin(α)+cos(ψ)·cos(α)·sin(β),
where ψis the angle of the Sun above the horizon, αis the
angle of the slope relative to the horizon, and beta is the as-
pect angle; i.e. the angle between south and the direction fac-
ing the steepest descent from the given coordinates.
Relative insolation Sis then multiplied by the insolation
effect amplitude ASto form the equivalent difference in sur-
face air temperature TS:
TS=ASS.
The argument for such a mapping is that a fully insolated
area is equivalent to a fully shaded area that is exposed to a
higher surface air temperature. This is reflected in the equi-
librium line altitude (ELA); i.e. a boundary between the ac-
cumulation and ablation areas of the glacier that is very sensi-
tive not only to avalanching, snow drifting, glacier geometry,
and debris-cover but also to shading (Nesje, 2014). Geomor-
phological studies in the nearby Trnovo Forest Plateau by
Kodelja et al. (2013) and by Žebre et al. (2013) found out
that the difference between the ELA of the sun-facing south-
ern slopes and the shady northern slopes was at least 150 m,
while Evans and Cox (2005) set the theoretical boundary of
ELA difference at 320 m. The latter limit is usedto derive the
maximal insolation effect amplitude from the standard atmo-
sphere lapse rate as follows:
AS,max ≈320 m
1000m 6.5°C =2.08 °C.
Note that the calculation of AS,max should be taken as a rough
estimate.
For our further experiments, we used a smaller value of
AS=1°C, which matches the observed ELA difference bet-
ter than the upper theoretical boundary. The comparison of
temperature fields generated by the models is visualised in
Fig. 4. The difference (the insulation part of the model) can
be seen to be small and local.
Finally, temperatures produced by any of the tempera-
ture models are offset (decreased) by a constant value, since
the present climate is warmer than the simulated past. The
preliminary experiments were used to tune the temperature
offset to −5.6 °C from the reference average of 1971–1986
to match the simulated glaciation extent with the estimated
extent well. This is close to the value of the temperature
drop for the larger Alpine area during LGM estimated by
Del Gobbo et al. (2023).
3.4.2 Precipitation
Three precipitation models were explored in the presented
study. The precipitation fields generated by the three pre-
sented models are visualised in Fig. 5 to demonstrate the
great difference they produce for the simulation input.
First is the baseline precipitation model, which assumes
uniform precipitations across the domain. The value of the
precipitation is taken from the reference weather station and
is 1946 mm a−1. Although this is the simplest of models and
not appropriate for large areas, it could work in the presented
case, since the simulated area is very limited. Note that the
used precipitation value also seems low with regard do the
larger Snežnik area, with precipitations up to 3000 mm a−1.
The reason for this is that the elevation of the station is rela-
tively low, far below the ELA, while the precipitation is ex-
pected to increase with elevation. The precipitation pattern
generated by this model is shown on the left in Fig. 5.
We shall refer to the second model of precipitation as the
WorldClim model, since it originates in an existing global
climate model. We use the WorldClim (Fick and Hijmans,
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1478 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
Figure 4. Comparison of the air surface temperature models calculated in the full resolution of 25 m. The generated temperature fields are
in panels (a) and (b), while the insolation term of the insolation-adjusted lapse-rate temperature model (which equals the difference between
the model outputs) is in panel (c). The geomorphological glacial limits are plotted as black lines.
Figure 5. Comparison of the precipitation fields generated by the three described precipitation models. The first two models are pre-
calculated as input to PISM and are in the full resolution of 25 m, while the orographic precipitation model is generated by PISM in its
working resolution, which was set to 100 m in this case. The field-based estimates of the glacial limits are plotted as black lines.
2017) model of global climate as the source, reduce its cov-
erage to the area of the domain, and interpolate (with Lanc-
zos resampling) the mean monthly precipitation component
on a 50 m resolution grid (all of the above was done in
the software package GDAL). We considered using a lo-
cal model (Odprti podatki Slovenije, 2023) instead which
is based on data gathered by the Slovenian Environment
Agency (ARSO) in time interval 1981–2010. We found that
the local model did not offer any better resolution, while it
failed to cover the whole domain, since a considerable part
of the presented domain extends across the national bor-
der. The two models also differ notably in their prediction
over the selected geographical area, which is clearly observ-
able by the mean annual precipitation over the area enclosed
by the geomorphologically determined ice field bounds. For
the WorldClim model, the precipitation ranges from 1582 to
1955 mm a−1, with the mean of 1827 mm a−1, which is in
contrast to the range from 1950 to 2534 mm a−1, with mean
of 2294 mm a−1, for the local model. Thus, the local model
prescribes a significantly higher (25 %) precipitation over the
critical area for ice field formation. The performed experi-
ments show that the precipitation from the WorldClim model
needs to be increased by a small factor for the resulting ice
field to be comparable in the ice area to those of other models
(the details are available in Sect. 4.4). Therefore, we assume
that the WorldClim global climate model underestimates pre-
cipitation of the observed geographical area.
The main problem of the climate-model-based precipita-
tion model is that its resolution is far from comparable to the
target resolution for the simulations. The best approach to get
a better resolution would be to downscale the climate model
to the microscale, as there are multiple possible methods for
doing so (Maraun et al., 2010); however, even state-of-the-
art solutions can only reach resolutions of ≈1 km (Karger
et al., 2023), which is still far from the required 100 m. In
addition, a downscaling operation would require extensive
amounts of data, some of which are only available through
proxies and simulations, e.g. palaeoclimate. Therefore, for
the purposes of glacial simulation, we currently consider
downscaling to the microscale as infeasible. Instead, we per-
form purely mathematical interpolation of the input precipi-
tation field down to the target grid, which is determined by
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1479
the target resolution for the simulation at hand. While the in-
terpolated WorldClim model is likely more accurate than the
uniform precipitation model, it does not take enough of the
local topography details into account and actually leads to
a simulation result very similar to the uniform precipitation
model (see Fig. 5 for a comparison).
The third precipitation model is based on a physical model,
with the measurements only used to estimate some of its pa-
rameters. This is the model of orographic precipitation mixed
with a uniform precipitation background. Orographic precip-
itation occurs when moist air is lifted as it moves over a
mountain range. As the air rises, it adiabatically cools, and
orographic clouds form to serve as the precipitation source.
Precipitation then mostly falls upwind of the slope that
caused the air lifting. Present-day Snežnik experiences heavy
orographic precipitation caused by the south–southeastern
moist winds that transport air mass from the nearby Adri-
atic Sea. Since not all of the precipitation is expected to be of
orographic nature, this model mixes it with uniform precip-
itation across the domain. The main input to the orographic
precipitation model is the DEM of the area; thus, the model
output can be of the same resolution as the DEM without
having to invent the high-resolution details by interpolation.
On the other hand, the physics of the model are simplified,
and several model parameters have to be invented instead.
To simulate orographic precipitation, the model integrated
in PISM is used, which is an implementation of the model
by Smith and Barstad (2004) and some of its modifications
by Smith et al. (2005). Besides the fixed topology, the main
driver of orographic precipitation is wind, which is set up
in the model using two parameters – speed and direction.
Both parameters are set up as scalar values; the model there-
fore calculates precipitation for singular weather conditions,
which is likely different from the average precipitation. Since
the past climate is poorly understood, we do not attempt to
set up these two singular parameters from observational and
palaeoclimatological data but rather derive them experimen-
tally.
Wind direction is the parameter that influences glacier
shape the most; therefore, it represents the first step of the
study. First, PISM is set up with the insolation-adjusted
lapse-rate temperature model, the uniform precipitation
model, and other parameters in a way that results in a glacier
of a slightly lesser extent compared to the geomorphologi-
cal. Then, the simulations are performed with the PISM setup
changed to include the orographic precipitation with a vary-
ing wind direction by 30°, a constant default wind speed
of 10 m s−1, a uniform offset of +3500 mm precipitation (a
background precipitation level that can be locally lowered by
the orographic precipitation model), and a precipitation fac-
tor of 0.5 (which uniformly scales values of individual grid
cells of the model output). The listed PISM parameter values
can be understood as the background, and orographic precip-
itation shares being at 50 %, which is our first approximation.
Figure 6. Influence of the prevailing wind direction on glacier for-
mation. Wind direction is marked in the top-right corners, along
with wind roses. The resulting ice coverage pattern is calculated
with the presented orographic precipitation model in combination
with the adjusted lapse-rate temperature model for non-optimised
precipitation and temperature offsets. The resolution of the output
is 100 m. The field-based estimates of the glacial limits are plotted
as black lines.
Simulation results are then analysed by comparing their
final ice cover, as shown in Fig. 6. The quantitative results
of ice coverage comparison are listed in Table 4 and plot-
ted in Fig. 7. Since both sensitivity and specificity should
be maximised, the optimal wind angle appears to be 150°
(measured clockwise from north), which results in the best
trade-off between second-highest sensitivity and very high
specificity. Such an angle also seems the best from a visual
comparison of the results (which is admittedly a subjective
measure) and is furthermore consistent with the direction of
the modern precipitation bearing winds.
As the wind direction is selected, other parameters could
be optimised further, starting with the most influential ones,
namely the wind speed and the ratio between orographic and
background precipitation. We feel that a thorough optimisa-
tion would be counter-productive though, since a large error
is already being made by considering a single wind direction
and speed. It should be stressed again that the orographic pre-
cipitation model does not consider the wind angle and speed
as the mean values but rather as the exact and permanent
values. Consider, for example, how the uniformly distributed
winds between 120 and 180° instead of the single 150° (the
average) wind would generate a very different precipitation
field. The same would hold even more so for wind speeds,
which are in reality likely to be distributed over a much wider
range of values than the wind angle. Therefore, we keep the
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1480 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
Table 4. Ice coverage as a function of wind direction.
Wind angle 0 30 60 90 120 150 180 210 240 270 300 330
Sensitivity 0.56 0.47 0.42 0.37 0.53 0.78 0.79 0.75 0.56 0.30 0.33 0.51
Specificity 0.56 0.47 0.59 0.80 0.65 0.62 0.54 0.52 0.58 0.70 0.63 0.58
Sensitivity ·specificity 0.30 0.22 0.25 0.30 0.34 0.47 0.42 0.39 0.32 0.21 0.21 0.30
Figure 7. Quantitative metrics for the simulation results of the wind
direction parameter sweep. The highest value of sensitivity multi-
plied by specificity is for a wind angle of 150°.
default wind speed of 10 m s−1and other parameters of the
model (details in Table 2).
Selection of the relative magnitudes of background and
orographic precipitation terms was done as follows. Back-
ground precipitation was set to equal the measurement at the
weather station Mašun (1946 mm a−1), since the latter lies in
an area where orographic precipitation does not generate any
additional precipitation, and it therefore depends on back-
ground precipitation only (see Fig. 5). Then the orographic
precipitation was added (unmodified) from the model, result-
ing in average increase of 323mm a−1and a maximum in-
crease of 1526 mm a−1across the domain. The resulting pre-
cipitation is then 2270 mm a−1on average, with a maximum
of 3475 mm a−1, which is in line with the estimated mod-
ern precipitation of up to 3000 mm a−1on average for the
Snežnik plateau. Therefore, we treat the precipitation field
generated in the way described above as satisfactory and do
not optimise it further.
To summarise, the orographic precipitation model as-
sumes a prevailing wind originating from 150°, a wind speed
of 10 m s−1, 1946 mm a−1of background precipitations, and
an orographic precipitation model with default parameters as
provided by PISM.
In a final note regarding the orographic precipitation
model, we should acknowledge that the model was created
with a different setting in mind. That is, in the direction from
which the wind blows there should preferably be a body of
water, or it should at least have uniform elevation and as
such also uniform starting moisture content. These two as-
sumptions are a gross oversimplification in our case. The do-
main could be extended in the direction of the wind to dilute
the effect of this error because of the increased distance be-
tween the area of interest and the wind origin, but that would
increase the error caused by other model assumptions and
simplifications. We have performed a preliminary study of
how the domain size influences the precipitation pattern over
the area of interest. Although the details of the preliminary
study are beyond the scope of this study, its results show that
changing the domain extent significantly alters the precipita-
tion pattern, but the pattern does not converge when increas-
ing the domain size. Therefore, we use the orographic pre-
cipitation model on the presented domain as a demonstration
that orographic precipitation is a likely candidate for the ob-
served glacier shape, but we cannot claim so with certainty,
nor can we claim that we discovered the exact palaeoclimatic
parameters.
From Fig. 5, the orographic precipitation model can be
seen to stand out with highest variability across the domain.
The patterns of other two models are quite similar within the
geomorphological ice field area, which causes the simulation
results to be also quite similar, as will be shown later in the
paper.
3.4.3 Annual cycles
The above-described climate models are all used to model
annual mean temperature and precipitation. The exception
may be the WorldClim precipitation model, which can be
built to model precipitation at any scale supported by the
WorldClim dataset. PISM is adaptable in the way climate
data are supplied and can easily work with annual mean
data; however, we found in preliminary experiments that
simulation results differed greatly when more detailed data,
e.g. monthly means, were used instead of the annual data.
The likely reason is the monthly variability in the precipita-
tion, which peaks in early winter, as shown in Fig. 3. Con-
sequently, we opted to use monthly means for climate data
inputs, and to that end, we apply an annual cycle model on
top of previously described models.
The annual cycle model averages monthly values of tem-
perature and precipitation from the reference weather sta-
tion data and applies them on the temperatures and precipi-
tation modelled by previously described models. The excep-
tion is the WorldClim precipitation model, which we con-
structed from 12 monthly precipitation fields instead of the
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1481
annual field for the domain, and therefore, it is able to pro-
vide monthly values implicitly.
The following procedure is applied to build the annual
cycle model. First, the monthly means of temperature and
precipitation are taken from the raw weather station data
(Fig. 3). Then the monthly mean temperatures are converted
into monthly offset from annual mean and monthly precipi-
tations into monthly factor of annual mean. Finally, temper-
ature offsets are applied on the selected temperature model
output using PISM’s “temperature offsets” and precipita-
tion factors on the selected precipitation model output using
PISM’s “precipitation scaling”.
4 Results
In this section, we present the results in several forms. First,
we confirm that the ice field volume converges, and we pro-
vide a time estimate for the convergence to complete. Then
we explore how different temperature and precipitation mod-
els influence the simulation results, and we comment on
which models seem best to use on the presented area. Finally,
we present the climate under which we find the optimal con-
ditions for the growth of an ice field in the form that was
geomorphologically established.
4.1 Climate setup
The primary objective of this study is to identify the climatic
parameters that would allow an ice field atop the Snežnik
plateau to align with the extents determined by geomorpho-
logical evidence. While this goal will be reached after a
large set of experiments have been performed and analysed,
a similar goal is set for the first step of experimentation. To
even start experimenting with different computational mod-
els, since glaciers are not present in the area today, favourable
conditions for the formation of glaciers on the domain need
to be established first. In other words, the first goal is to set up
climatic conditions that would allow for the formation of an
ice field similar to the geomorphologically estimated extent.
Using the simplest two models – the lapse-rate tempera-
ture model and the uniform precipitation model – a set of
simulations has been performed to find suitable starting con-
ditions for further exploration. In Fig. 8, the results of a small
grid search with air temperature spacing by 0.5 °C and pre-
cipitation spacing of 10 % are shown.
From the figure it is clear that a decrease in temperature
of 0.5 °C coupled with a 10 % decrease in precipitation does
not significantly alter the extent of the ice field. While these
are just human-friendly numbers that were used to set up the
parameter scan experiments, we can nevertheless write this
observation in a general form:
I(T , P )≈I(T−kT,kP·P),
kT≈0.5°C,
kP≈0.9,(2)
Figure 8. The effect of climate forcings is shown as a matrix of
results. The results of the simulations on a uniform precipitation
model and a simple temperature model are presented in the reso-
lution that was used for simulations (i.e. 100 m). The field-based
estimates of the glacial limits are plotted as black lines. Both pa-
rameters can be used to either decrease or increase glacier extent.
Furthermore, the results indicate that the parameters are not inde-
pendent, and the increase in temperature is equivalent to a decrease
in precipitation, at least for the range of values shown.
where Iis the ice field that depends on surface air temper-
ature and precipitation fields Tand P, respectively, and kT
and KPare the coefficients representing an approximately
0.5 °C increase in temperature and a 10 % decrease in pre-
cipitation. We shall refine the parameters in further experi-
ments, after the confirmation of simulation convergence and
the selection of best climate models.
4.2 Convergence
Although various models for temperature and precipitation
were used in the preliminary experiments, we only noticed
the insignificant influence of the model selection to the con-
vergence of ice volume and ice extent. Therefore, the same
settings were used for all the simulations, including the se-
lection of simulated time limits and the number and resolu-
tion of simulations within grid sequencing. Figure 9 shows
the progression of the ice volume from several experiments
that was used to determine the required simulation time and
the optimal resolution for further simulations. Note that the
shown lengths of the simulation on each individual grid size
are different from the values specified in Sect. 3.2, which
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1482 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
were selected based on the simulation shown here and other
similar experiments, to optimise for the low execution time
and satisfactory resolution of the resulting ice cover. From
this figure the convergence of solutions towards a steady-
state glaciation can be seen, depicting both the time needed
for ice accumulation (about 2500 years) and the final volume
after it converges (about 2.6×1010 m3). It can be noted that
the resolution of 400 m is not detailed enough, while other
tested resolutions all converge to the same volume of ice. A
switch from 400 to 200 m could also be done sooner, at 500
to 1000 years, to allow for faster overall convergence. Also,
the variation in the ice volume after it has converged can be
clearly seen. This means that all further analyses of ice fields
that have been performed on a snapshot of the simulation in
its final time step will not be perfect, since it is likely that
those will focus on slightly different points within the range
of the natural variation.
4.3 Temperature models
In this subsection, the previously defined temperature models
(the lapse-rate model and the insolation-adjusted lapse-rate
model; see Sect. 3.4.1) are visually and quantitatively com-
pared, based on simulation results. Experimental simulations
are set up to mimic modern precipitation levels, and −6 °C
are offset from modern temperatures. Figure 10 shows part
of the sensitivity study for the insolation-adjusted tempera-
ture model. Only for values of five or greater, which seem
unrealistic and are thus not shown in the figure, do the result-
ing ice field shifts towards the north appear noticeably. Value
AS=0 makes the model behave identically to the lapse-rate
model, since the insolation adjustment is multiplied by zero.
Then the value AS=1 represents the case where the solar
insolation amplitude is set to mimic the observed ELA dif-
ference of 150 m between the insolated and shaded slopes.
Finally, the value AS=3 represents an overvalued effect of
insolation.
We experimented more with the insolation adjustment than
is shown in Fig. 10 but found no significant effect until the
ASis raised very high, e.g. about 5 times its expected value.
Similarly, the effect is entirely hidden in the noise if the
objective function is observed instead of observing the re-
sults visually. Therefore, while our analysis indicates that se-
lecting either of models would suffice for our use case, as
they cause only minimal differences in simulation results, we
selected the more realistic one; i.e. the insolation-adjusted
lapse-rate model with its amplitude parameter ASset to its
most likely value of 1 for further simulations.
4.4 Precipitation models
In this subsection, the differences between the implemented
precipitation models (see Sect. 3.4.2) are explored. Selec-
tion of the right precipitation model proved to be the most
significant one regarding the overall shape of the simulated
glacier. Comparison of the simulation results obtained using
uniform, WorldClim, and orographic precipitation models is
shown in Fig. 11. All three models are set up to mimic mod-
ern precipitation levels, and −6°C are offset from modern
temperatures.
While the quantitative analysis does not show large dif-
ference, both constant and WorldClim models cause the ice
to grow askew towards the north compared to the geomor-
phological extent. Under these two precipitation models, the
variation in precipitation is very low, and the existence of ice
is determined primarily by the temperature model, which in
turn is driven by domain elevation. The domain elevation is
skewed towards the north compared to the geomorphologi-
cal ice field position and, thus, so are the simulation results.
It should be stressed that the observed north–south imbalance
is in addition to and much larger than the one caused by the
insolation-adjusted lapse-rate temperature model. Only the
orographic precipitation model transfers the distribution of
ice southward via precipitation redistribution.
Unlike the visual inspection, the value of the objective is
only slightly higher for the orographic model (0.32) than for
the other two models (0.26 and 0.31). The larger ice field
located to the southeast is partially responsible, which cov-
ers the largest part of forbidden area in the simulation with
orographic precipitation model. The ice field to the southeast
is part of an area otherwise known as Gorski Kotar (Žebre
and Stepišnik, 2016), and is expected to glaciate in simula-
tions, but was not a part of the performed study. The isolation
of the two ice fields is clear from the performed geomor-
phology studies. Its proximity, however, makes the analysis
of Snežnik in isolation more demanding. This case therefore
highlights a disadvantage in the presented quantitative mea-
sure – the unmarked proximal ice fields may have a signifi-
cant impact on the accuracy of the qualitative measure.
Nevertheless, orographic model is best both visually and
quantitatively and is selected as the base precipitation model
to be used for further simulations of this geographical area.
4.5 Climate conditions for Snežnik
In this subsection, we present the results that to some extent
address the goal of the study – improving our understanding
of the past climate–glacier dynamics at the Alps–Dinarides
junction. There are two main results. First, we establish that
the problem is underdetermined, and we can provide optimal
climate conditions for the formulation of an ice field on the
Snežnik plateau only as a linear relation. Second, we find one
set of climate conditions that respect both the linear relation
from the first result and the state-of-the-art global climate es-
timates. We present the modelled ice field under such climate
conditions on the domain with a resolution of 50 m.
First, an experiment has been prepared to obtain one set of
climate conditions under which the simulated extent matches
the geomorphological extent the best. Since the tempera-
ture and precipitation have been found to be related, a fine-
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1483
Figure 9. Convergence of the ice field characterised by the ice volume. Presented are four experiments, all using a grid-sequencing approach
for faster execution, starting with a resolution of 400m. The label in the legend specifies the experiment’s final resolution. Above the x
axis, the grid-sequencing resolutions are specified, and times when resampling potentially occurs are marked with vertical dashed blue lines.
Experiments are only resampled to higher resolutions at the resampling times if they have not reached the experiment’s final resolution yet.
For example, the 200m experiment starts at 400 m resolution, refines to 200m resolution at 1500 a, but then remains at that resolution until
4000 a is reached and the simulation is stopped.
Figure 10. Comparison of the simulation results that use the two presented temperature models and the orographic precipitation model. The
geomorphological area of the glacier is outlined in black. The results were obtained using the insolation-adjusted lapse-rate model with three
values of AS, as depicted above the plots. The model with AS=0 equals a pure lapse-rate model, since the insulation adjustment in that case
equals 0 everywhere on the domain. The results are plotted in the resolution used by PISM, which was 100m in this case, and are contrasted
to the field-based estimates of the glacial limits, which are outlined in black lines.
grained grid search has been performed on air temperature
only, with the precipitation fixed to modern values. The main
results are summarised in Fig. 12 in the form of the objective
values for all performed simulations and in Fig. 13 in form of
ice extents of the nine best-performing simulations. Visually,
the shown extents are difficult to order by quality. Some of
the ice field features, e.g. termini, are better covered at higher
temperature, while others are covered at a lower temperature.
Looking at the value of the objective, small differences can
be made out, and the objective value peaks at the −5.6 °C
surface air temperature offset, although the differences com-
pared to other offsets are small. The result would be perfectly
acceptable if the air temperature is either increased or de-
creased up to 0.2 °C with only a different trade-off between
sensitivity and specificity.
Using the obtained set of best climate conditions, the sim-
ulated ice field extent is examined in more detail. The res-
olution of 50 m is computationally too expensive to be used
for the exploration of the climatic conditions while provid-
ing results that are only marginally better then those ob-
tained by 100 m resolution. It has been selected for the final
simulation along with the climate conditions defined above,
since it provides some additional detail, especially in the ice
flux. Ice flux in the final state of the simulation is shown
in Fig. 14. The simulation shows that the ice flow patterns
on Snežnik are largely controlled by the subglacial topogra-
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1484 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
Figure 11. Comparison of the results of simulations that use the three presented precipitation models. Values of the objective for uniform,
WorldClim, and orographic models are 0.26, 0.31, and 0.32, respectively. All results are plotted in the resolution of PISM, which was 100m
in this case, and the field-based estimates of the glacial limits are outlined in black lines.
Figure 12. Value of the objective for the fine-grained sweep over
the temperature with a fixed precipitation value. The highest value
of the objective (sensitivity multiplied by specificity) is at −5.6 °C.
phy. The glaciated area is composed of two plateaux above
1300 m that behaved as accumulation areas from where the
ice was flowing almost radially downstream. The ice from the
northern and southern plateau joined in a large karst depres-
sion in between them; from there, it was drained by an outlet
glacier flowing towards south/southeast. This is in agreement
with the geomorphological evidence, despite some discrep-
ancies between the simulated and geomorphological ice ex-
tent.
Last, we look into the relationship between temperature
and precipitation. As seen in Fig. 8 and described in Eq. (2),
any increase in precipitation can be countered by a decrease
in temperature to keep the conditions for simulated glacier
formation about the same. Using the best temperature and
precipitation models, we have performed additional exper-
iments to improve the approximations for coefficients of
Eq. (2) and found that the values of kT=0.45 and kP=0.9
are nearly optimal. Based on the Eq. (2) and the experimen-
tally discovered optimal coefficient values, the final equation
describing the optimal conditions can be written with xbeing
Figure 13. A fine-grained sweep over a single parameter – near-
surface air temperature. The objective measure for the ice cover is
given in Fig. 12. All results are plotted in the resolution of PISM,
which was 100 m in this case, and the field-based estimates of the
glacial limits are outlined in black lines.
the free parameter:
T= −5.6 °C −x·0.45°C,
P=1946mm a−1·0.9x,
x∈Rand xis small.(3)
Clim. Past, 20, 1471–1488, 2024 https://doi.org/10.5194/cp-20-1471-2024

M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1485
Figure 14. Streamlined plot of the ice flux (arrows) overlaying the
ice thickness and the geomorphological ice field outline (thick lines
for the clear outline and dashed lines for the unclear outline). The
experiment was performed on a domain with a 50 m resolution.
Figure 15. Relation between the free parameter of Eq. (3) and
the objective value. The shaded areas represent solutions where the
value of objective function is within 90% and 95 % of the maximum
obtained value.
To confirm that climate conditions that conform to Eq. (3)
result in similar ice fields, we have designed an additional
experiment. For a limited set of values x, the ice field is sim-
ulated, and the results are compared to the results simulated
at x=0 according to the defined objective. The results of the
experiment are presented in Figs. 15 and 16. Besides con-
firming the equation, the described experiment also gives a
range of valid values for x, where Eq. (3) holds.
The range of xseems to be based on the interval [−3,+8]
from the selected reference point. Therefore, one can take a
valid value of x=3.11, which is within this interval, to get
the temperature offset of −7 °C and a precipitation factor of
0.66 relative to modern conditions. Adjusting the tempera-
ture offset by the previously mentioned 0.4°C of difference
between our modern reference interval and the pre-industrial
era, the temperature offset exactly matches the results of
Figure 16. Outlines of simulated ice fields for the values of x∈
[−3,+8], for which the value of objective function is within 90%
of the maximum obtained value plotted with black lines. All simu-
lations for this figure were calculated with the PISM resolution set
to 100 m.
Del Gobbo et al. (2023), who reconstructed the LGM tem-
perature to be offset by −6.6 °C relative to pre-industrial era.
The precipitation of 0.66 relative to the modern reference in-
terval is also close to the reconstructions by Del Gobbo et al.
(2023), where the precipitation for the general area is esti-
mated to lie between −10 % and −30 % relative to the pre-
industrial.
5 Discussion and conclusions
Several results of the presented study are summarised and
discussed below. First, a qualitative metric of the simula-
tion quality was developed, which can take clear and unclear
geomorphologically deduced ice boundaries into account.
Second, the relation between precipitation and temperature
was quantified. Third, several simulations resulting in an ap-
propriately sized ice field were successfully performed us-
ing climatic forcing compatible with LGM conditions. Last,
the factor with the largest effect on the simulation results
was found to be the precipitation pattern. Global precipita-
tion models, such as the one provided by WorldClim, were
found to be insufficient for simulation of accurately shaped
ice fields. On the other hand, even the simplest temperature
https://doi.org/10.5194/cp-20-1471-2024 Clim. Past, 20, 1471–1488, 2024

1486 M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case
models, such as one based entirely on elevation and lapse
rate, were sufficient for our use case.
This research has successfully established a quantitative
framework for the assessment of palaeoglacial simulations
that integrates both definitive and provisional geomorpho-
logically deduced ice boundaries to improve the accuracy of
model results. The developed qualitative metrics help deter-
mine the agreement between the model-derived ice extents
and those derived from geomorphological field data.
The framework alleviated the difficult task of sorting the
simulation results by quality but did not eliminate visual
checks entirely. The reason lies in its shortcomings, which
we list here. First, its parameters are required to be set up,
which in turn requires experimenting. In the presented case,
the experimenting was light but could have proven more diffi-
cult for a more demanding ice field shape. Second, the frame-
work is missing a methodology for ignoring neighbouring
glaciated areas. We expect that neighbouring glaciations can
often be a problem since the simulator requires the domain
to be rectangular and to be somewhat larger than the area of
interest. Thus, it is likely for most studies to find that their
domains contain some glaciers that are outside of the focus
and require special treatment in the analysis. Finally, the pro-
posed framework is very specific in its demands for at most
two types of limits – clear and unclear. There is currently no
room for quantifying the clarity nor for including more limit
types. While this framework would work if only clear limits
were given, such cases could also make use of simpler anal-
ysis methods.
The framework, along with visual analysis, aided in decid-
ing on the best climate models and in optimising ice field re-
constructions towards conformity with the geomorphological
bounds. The reconstructions resulted in the demonstration of
the relation between air temperature and precipitation when
it comes to the size of glaciers. These two factors affect each
other in a way that creates a balance within the simulations
causing different combinations of temperature and precipi-
tation to result in similar glacier extent. This interplay pre-
cludes the determination of exact climatic conditions based
on glacier morphology alone and suggests a broader frame-
work of possible past climates that are consistent with the ob-
served glacier extent. This study formulates the interplay as a
pair of equations with a single independent variable. Further-
more, it quantifies the parameters of equations and bounds
them to a range of values beyond which the interplay gradu-
ally loses its effect.
The presented relation between temperature and precipita-
tion presents a degree of freedom that can only be resolved by
additional external data. The latest reconstructions of LGM
climate (Del Gobbo et al., 2023) are a great source for exter-
nal data, and the proposed relation between temperature and
precipitation matches this particular data point well. Simula-
tions carried out under the climatic conditions of the LGM
suggest an ice field that is broadly consistent with empirical
geomorphological reconstructions. The consistency is lim-
ited to the ice field size, however, as the simulations fail to
reproduce all the bounds of the geomorphologically recon-
structed ice field. Although the established framework aided
in the optimisation of the unbound parameters in climate
models, some systematic biases remain in the simulations.
These could be resolved in the future by more detailed cli-
mate models. The precipitation model was a key component
in the presented study and remains a candidate for further
improvements.
Another area where improvements should be sought is in
optimising the values of various unmentioned model param-
eters. Within the preliminary analysis of climate models, we
explored the sensitivity of the simulated ice field area and
volume with varying modelling parameters such as those re-
lated to the domain grid, ice rheology, stress balance, basal
sliding, and till properties. Our findings are consistent with
those from studies published by Žebre et al. (2021) and Can-
da¸s et al. (2020). Specifically, the simulated glaciation extent
and volume are as sensitive to choices related to parameter-
isation of other models, as they are to climate models. This
sensitivity suggests that small variations in parameters can
lead to significant differences in the results. Given this, along
with the lack of local measurements to aid in parameter ad-
justments, the presented results should be interpreted with
due caution. For future work, a methodology to set up or op-
timise all the major model parameters should be developed.
Another finding of this research is the disproportionate in-
fluence of precipitation patterns on the simulation results. It
was found that the spatial distribution of precipitation, es-
pecially when influenced by orographic factors, is crucial
for the accurate representation of glacier extent. It has been
shown that global precipitation models such as WorldClim
do not have the necessary resolution nor the orographic sen-
sitivity to accurately simulate the shape of ice fields. This
inadequacy requires the integration of high-resolution topo-
graphic data and locally refined precipitation data to capture
the complex interactions between topography and climate.
We must bear in mind that the orographic precipitation model
is based on assumptions about wind patterns that may not ac-
curately reflect the complex interactions between topography
and climate, especially given the lack of palaeoclimatic data
on wind direction. As a phenomenon that is underrepresented
in models but has a demonstrated high influence on results,
wind should represent an area of additional research in the
future.
Conversely, the adequacy of elementary temperature mod-
els relying solely on lapse rates and elevation data reveals the
relative insensitivity of the studied ice field extent to the tem-
perature data. This observation points to a potential area of
computational optimisation in modelling efforts where high-
resolution temperature data are not readily available.
Although advanced, the presented climate models used
may still be an oversimplification of actual past conditions.
The temperature model could be improved using mountain
shading, in addition to insolation adjustment, and a oro-
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M. Depolli et al.: Simulation of a former ice field with PISM – Snežnik study case 1487
graphic precipitation model could be extended to include a
set of most typical wind conditions. There is also the option
of extending the till and hydrology models based on addi-
tional field observations to better simulate the karst condi-
tions of the researched geographical area. On the other hand,
the existing simulations can be used to find additional evi-
dence of glaciation in the field to better constrain the next
iteration of the simulation. While a larger area of Snežnik
has already been mapped, and every standard-sized landform
has been mapped, there is still much that is unknown when
it comes to the sediment filling of karst depressions. The ex-
isting best-fit simulations could potentially help locate points
of interest for further research, e.g., to plan drilling into the
sediments trapped in karst depressions close to the simulated
ice boundary.
Code and data availability. Code and data will be made avail-
able upon request to the corresponding author.
Author contributions. GK conceptualised and supervised the
work. MŽ and US performed geomorphological investigation, col-
lected resources, and performed the validation. MD provided the
methodology and software and performed the visualisation and soft-
ware investigation. The whole team participated in writing the pa-
per.
Competing interests. The contact author has declared that none
of the authors has any competing interests.
Special issue statement. This article is part of the special issue
“Icy landscapes of the past”. It is not associated with a conference.
Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims made in the text, pub-
lished maps, institutional affiliations, or any other geographical rep-
resentation in this paper. While Copernicus Publications makes ev-
ery effort to include appropriate place names, the final responsibility
lies with the authors.
Financial support. This research has been supported by the Javna
Agencija za Raziskovalno Dejavnost RS (grant nos. P1-0419, P2-
0095, P6-0229, and J1-2479).
Review statement. This paper was edited by Atle Nesje and re-
viewed by Ethan Lee and one anonymous referee.
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