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\begin{document}

\title{Long-term modelling of runoff formation processes at remote mountainous
permafrost basin using historical data of short-term special
observations (Suntar-Khayata Ridge, Eastern Siberia).}



\author[1]{Nataliia Nesterova}%
\author[1]{Olga Makarieva}%
\affil[1]{Melnikov Permafrost Institute of the Siberian Division of the Russian Academy of Sciences}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\selectlanguage{english}
\begin{abstract}
The study investigates the possibility to parameterize a hydrological
model for remote high-altitude permafrost basin based on the data of
historical short-term observations conducted in 1957-1959 at the
Suntar-Khayata research station (Eastern Siberia) and simulate the
changes of runoff observed in recent decades in the region. The
Hydrograph model is applied as it has the advantage of using observed
physical properties of landscapes as its parameters. The developed
parametrization of the goltsy landscape is verified by the results of
simulations of variable states of snow and frozen ground. Continuous
simulations of streamflow with daily time step are conducted for the
period of 1957-2012 at the Suntar River basin (area 7680 km2, altitude
828-2794 m) with average and median values of Nash-Sutcliff criteria
reaching 0.58 and 0.67 respectively. The results of simulations have
shown that the largest part of runoff (about 70\%) is formed in the
high-altitude area which takes only 44\% of the Suntar River basin area.
Simulated series of streamflow reproduce the patterns of recently
observed changes, including the increase of low flow, by magnitude of
trends and their change period, suggesting that the increase of the
increase of liquid precipitation share in autumn months due to air
temperature rise can be important factor of streamflow changes in the
region. The data presented in the paper are unique for the vast
mountainous parts of North-Eastern Eurasia which play important role in
general climate circulation. The results indicate that if the assessment
of hydrological model parameters is based on observation data instead of
calibration, the models can be used in the tasks of studying the
response of river basins to climate change with more confidence.%
\end{abstract}%



\sloppy


\textbf{Title:} Long-term modelling of runoff formation processes at
remote mountainous permafrost basin using historical data of short-term
special observations (Suntar-Khayata Ridge, Eastern Siberia)

\textbf{Short running title:} Modelling in mountainous permafrost basin

\textbf{Author names:} Nataliia Nesterova\textsuperscript{1,2*}, Olga
Makarieva\textsuperscript{1}

\textbf{Authors institutional affiliations:}

\textsuperscript{1}North-Eastern Permafrost Station, Melnikov Permafrost
Institute, Portovaya St., 16, Magadan, Russia 685000

\textsuperscript{2}Saint Petersburg State University, Institute of Earth
Sciences, 7/9 Universitetskaya nab, St. Petersburg, Russia 199034

*corresponding author:\emph{nnesterova1994@gmail.com}

\textbf{Acknowledgements:}

The study was carried out with the support of the RFBR (the research
project 19-35-90090). The authors are grateful to Tatiana Vinogradova
and David Post for the discussion of the study results and English
language reviewing.

\textbf{Keywords:} remote high-altitude permafrost basin, hydrological
model Hydrograph, short-term observations, parametrization, goltsy,
climate change, Suntar River, streamflow, state variables

\textbf{Long-term modelling of runoff formation processes at remote
mountainous permafrost basin using historical data of short-term special
observations (Suntar-Khayata Ridge, Eastern Siberia)}

\textbf{Abstract.} The study investigates the possibility to
parameterize a hydrological model for remote high-altitude permafrost
basin based on the data of historical short-term observations conducted
in 1957-1959 at the Suntar-Khayata research station (Eastern Siberia)
and simulate the changes of runoff observed in recent decades in the
region. The Hydrograph model is applied as it has the advantage of using
observed physical properties of landscapes as its parameters. The
developed parametrization of the goltsy landscape is verified by the
results of simulations of variable states of snow and frozen ground.
Continuous simulations of streamflow with daily time step are conducted
for the period of 1957-2012 at the Suntar River basin (area 7680
km\textsuperscript{2}, altitude 828-2794 m) with average and median
values of Nash-Sutcliff criteria reaching 0.58 and 0.67 respectively.
The results of simulations have shown that the largest part of runoff
(about 70\%) is formed in the high-altitude area which takes only 44\%
of the Suntar River basin area. Simulated series of streamflow reproduce
the patterns of recently observed changes, including the increase of low
flow, by magnitude of trends and their change period, suggesting that
the increase of the increase of liquid precipitation share in autumn
months due to air temperature rise can be important factor of streamflow
changes in the region. The data presented in the paper are unique for
the vast mountainous parts of North-Eastern Eurasia which play important
role in general climate circulation. The results indicate that if the
assessment of hydrological model parameters is based on observation data
instead of calibration, the models can be used in the tasks of studying
the response of river basins to climate change with more confidence.

\textbf{Keywords:} remote high-altitude permafrost basin, hydrological
model Hydrograph, short-term observations, parametrization, goltsy,
climate change, Suntar River, streamflow, state variables

\textbf{1. Introduction}

The Arctic regions are experiencing unprecedented changes of climate
(IPCC, 2014). Mountainous areas of the Arctic are the remotest, less
studied but provide the largest share of Arctic runoff (Hinzman et al.,
2005; Viviroli et al., 2011). Recent studies have shown that due to
climate warming Arctic runoff is changing too (Makarieva et al. 2019a;
Rawlins et al., 2010; Stuefer et al., 2017; Tananaev et al., 2016) but
the mechanisms behind observed changes are not fully understood.

The lack of data can partly be compensated by hydrological modelling.
Models are also used for projections of future states of hydrological
system in the Arctic (Krogh \& Pomeroy, 2018; Pohl et al., 2006; Rasouli
et al., 2014).

The problematic issue of future projections is that large-scale,
relatively simple, conceptual hydrological models are being calibrated
against streamflow series in gauging stations of large rivers (Hudson \&
Thompson, 2019; Nijssen et al., 2001), while more process-based ones,
require detailed observational information for their parametrization and
are usually applied for well-studied research basins (Changing Cold
Regions Network project, Improving Processes \& Parameterization for
Prediction in Cold Regions Hydrology project; Marsh et al., 2020; Zhang
et al.. 2008). It is not very often that hydrological models are tested
if they are really able to reproduce currently observed changes before
issuing the future projections. These problems undermine the ability of
hydrological community to deal with Arctic warming challenge.

The study advocates the approach to hydrological modeling presented in
earlier papers (Semenova \& Beven, 2015; Semenova et al., 2013;
Vinogradov et al., 2011) which suggest a priori or based on expert
judgement estimation of model parameters and extensive verification of
models and the sets of their parameters as the tool of comprehension of
hydrological process in ungauged basins.

The tasks of the study are:

* Compile the database of available historical observations (1957-1959)
for remote mountainous river basin located in the zone of continuous
permafrost with long-term streamflow series and pronounced changes of
hydrological regime in recent decades.

* Describe runoff generation processes; parameterize the hydrological
model using compiled data and the results of previous regionalization of
the model parameters.

* Verify the model based on available observations of variable states of
snow and frozen ground.

* Verify the model by streamflow for the continuous period of
observations (1956-2012).

* Assess the ability of the model to reproduce the recent changes of
streamflow.

* Investigate the factors of streamflow changes using the hydrological
model.

The novelty of the study is the approach that allow for continuous
long-term simulations of streamflow and active layer dynamic in remote
basin with complicated mountainous permafrost environment based on
process understanding and scarce data of short-term observations
conducted more than 60 years ago.

\textbf{2. Research area and study basin}

The Suntar River basin at the Sakharyniya river mouth (basin area 7680
km\textsuperscript{2}) was selected as the object of the study (Fig. 1).
This river belongs to the Indigirka river basin and drains from the
Suntar-Khayata Ridge which is a continuation of the Verkhoyansk mountain
system (Eastern Siberia). In the central parts of the south it is
adjacent to the Ugamskiy Ridge. Together, they form triple headwaters
between the Indigirka basin in the northeast, the Aldan basin in the
west, and the rivers of the Okhotsk sea basin in the south. The slopes
of the Suntar-Khayata Ridge are very divers: high peaks (the Mus-Haya
mountain, 2959 m a.s.l.) are combined with deep river valleys.

The climate of the region is extremely continental with altitudinal
zonation and air temperature inversions in the cold season. Average
annual temperature is -13.8 and -14.1 \selectlanguage{ngerman}º\selectlanguage{russian}С (in July +6.4 and +17.5 \selectlanguage{ngerman}º\selectlanguage{russian}С, in
January -28.0 and -39.6 \selectlanguage{ngerman}º\selectlanguage{russian}С) at the stations of Suntar-Нayata (2068 m
a.s.l.) for the period 1957-1964 and Agayakan (776 m a.s.l.) for the
period 1957-2012 correspondingly. Annual average precipitation at the
Vostochnaya (1966--2012) is 280 mm and at the Suntar-Нayata (1957-1964)
is about 690 mm. Most precipitation occurs in summer (Vostochnaya,
1966--2012).

The studied territory is situated in the region of continuous
permafrost, its thickness within the mountain ranges is about 400-600 m,
and under river valleys it is 200-300 m (Geocryology of the USSR, 1989).
However, permafrost can be interrupted in fractured zones by taliks
associated with intrapermafrost and suprapermafrost water flow (Grave et
al., 1964).

The study area belongs to the northern taiga climate zone which is
affected by altitude and aspects of mountain slopes. According to
(Landscape map of the USSR, 1985) the following landscape units can be
found within the study region. They are 1) lowland plains, sometimes
swampy, with larch woodlands or larch forests in combination with
hummock and moss tundra; 2) the plateaus with gentle slopes with
stony-lichen and shrub tundra and larch woodlands; 3) ridge mountains
with stony and stony-lichen tundra and areas of larch woodlands in the
valleys.

The tundra areas are located from the absolute altitudes of 1500-1550 m
(from 1400 m under the glaciers). The main feature of the overlying
high-altitude zone (1600-2100 m) is the predominance of lichens and
almost complete absence of shrubs and flowering plants.

The average altitude of the Suntar river basin is 1410 m a.s.l. from
2794 m a.s.l. to 828 m a.s.l. Therefore, the basin covers the landscapes
from upper reaches of the mountains to the lowland plains in the river
valley.

The Suntar river regime is characterized by high spring freshet and rain
summer-autumn floods. In winter, the Suntar River freezes completely.
Maximum streamflow is observed in the summer months. Snow cover is
formed in September. Usually a spring freshet begins in the third week
of May. Average annual flow for the Suntar river is about 180 mm, with a
maximum recorded daily discharge of 1900 m\textsuperscript{3}/s
(1957-1964). Water levels at the gauge range from 198 cm (1964) to 781
cm (1980) (Fig. 2) with the variation of river depth up to 6 m. Daily
streamflow data (1956-2015) for hydrological gauge originate from the
publications of the Hydrological Yearbooks (Hydrological Yearbooks,
1936-1980; State Water Cadastre, 1981-2007) and are available for the
period 2008-2015 on the website of the Automated information data system
for state monitoring of water bodies (AIS SMWB) (URL:
https://gmvo.skniivh.ru, reference date: 01.03.2018).

About two dozen small glaciers with areas from 0.05 to 2.7
km\textsuperscript{2} and total area of 14.7 km\textsuperscript{2} are
located within the upstreams of the Suntar River (GLIMS and NSIDC, 2005,
updated 2017) (Fig.1). This accounts for 0.2\% of the Suntar River basin
area. There are no direct estimates of glacier streamflow for the Suntar
River basin, but according to Grave et al. (1964), specific rate of flow
of all the glaciers of the Suntar-Khayata Ridge in 1957, 1958 and 1959
was about 17, 13 and 22 ls\textsuperscript{-1}km\textsuperscript{2},
respectively. The glaciers' contribution to river streamflow in the
catchments with higher glacier areas can be significant. Grave et al.
(1964) assessed the values for the neighboring basin of the Agayakan
river, where glaciers cover over 2.2\% of the catchment. In 1957, which
was average by hydrological conditions, the glaciers contribution
exceeded 3.8\% of the overall annual flow and reached 6.1\% of flow in
July and August.

In the last decades, a steady decreasing trend of the Suntar-Khayata
Ridge glacierization has been observed (Lytkin, 2016) which sums up to a
reduction in area of about 20\% over the period 1945 to 2003
(Ananicheva, 2005). In this study we assume that the contribution of the
glaciers in the Suntar river flow is likely to be smaller than the
precipitation assessment error and cannot really be accounted for
explicitly due to a lack of information.

There are numerous aufeis fields that are formed at mountain ranges, in
submountain and intermountain depressions in the study region. In the
Suntar river basin, the aufeis cover up to 0.76\% of basin area
(Makarieva et al., 2018c; 2019b). In the last 70 years the amount of
aufeis fields at the Suntar river basin has increased from 45 to 53, and
their total area has decreased from 75 km\textsuperscript{2} to 60
km\textsuperscript{2} (Fig.1) (Makarieva et al., 2018c). The aufeis flow
contribution is most significant in May-June (Sokolov, 1975). Following
the approach by Sokolov (1975) we estimated that the share of aufeis
runoff for the Suntar river basin may reach 9.2 \% (17.4 mm).

Perennial snow fields and rock glaciers are widespread within the
Suntar-Khayata Ridge (USSR surface waters resources, 1966). They, along
with the ice of the active layer and summer atmosphere precipitation,
may represent a significant source of streamflow, however in this
respect they have barely been studied (Lytkin, 2016; Zhizhin et al.,
2012).

\textbf{3. Special observations}

The high-altitude Suntar-Khayata Station was operating in the Suntar
River basin in 1957-1959 under the program of the International
Geophysical Year (Dodds et al., 2010). Glaciological, geomorphological,
geocryological and hydrological observations were carried out (Grave et
al., 1964). The Station was located at an altitude of 2067 m in a rocky
talus (goltsy) landscape and the observations are unique for the
high-mountain areas of Eastern Siberia and the North-East of Russia.

We systematized the observations from the Station, which included
meteorological data, snow measurements, evaporation data, the
descriptions of soils and landscapes, the data on typical active layer
depth, ground temperature at various depths, etc. (Grave, 1959; Grave et
al., 1964; Grave \& Koreisha, 1957, 1960; Koreisha, 1963).

According to the results of the Station studies and descriptions, the
high-altitude landscapes zoning of the Suntar River basin was
elaborated:

\begin{itemize}
\tightlist
\item
  Goltsy (or rocky-talus, completely bare landscape) is located in the
  altitude range 1900 to 2700 m a.s.l. (average height is 2040 m), its
  share accounts for 7\% of the Suntar river basin. Ground profile
  consists of argillite broken stone with admixed loam materials,
  cemented together with ice and the layers of clean ice up to 2 m
  depth. Vegetation is absent. Despite significant amount of
  precipitation and its irregular distribution, the upper layer of
  diluvia is characterized by low moisture content and its barely
  visible variations during the warm season. It is explained by the high
  permeability of broken rocks. Unevaporated water easily infiltrates
  deep down and flows along the frozen bedrock. The unsuccessful
  experience of experimental runoff site construction had shown that the
  bedrock has deep splits and hollows, and even though their temperature
  is below zero, they are not fully filled with ice (Grave, 1959).
\item
  Mountain tundra is located within the altitudes of 1450-1900 m a.s.l.
  (1630 m on average) and takes 37 \% of the Suntar River basin. It has
  tight and depressed layer of grass and moss with bushes under which
  there is rock formation with some ice with admixtures.
\item
  Sparse larch forest (1100-1450 m a.s.l., 1310 m on average) consists
  of sparse growth of larch forest at north slopes and larch forest at
  south slopes, and covers 42\% of the basin.
\item
  Swampy sparse larch forest is spread within the river valleys and
  floodplains (828-1100 m a.s.l., 1060 m on average) and covers 14\% of
  the basin.
\end{itemize}

The active layer depth within the study territory is very variable.
Table 1 shows some data on maximum active layer depth, obtained in 1958.
In the high mountainous area of the altitude 1700 m and above, the depth
of thawing of rocky talus sediments ranges from zero under glaciers and
perennial snowfields to 70-90 cm at the foot of the slopes at the
alluvial cone, folded by gravelly loam. Observed values at the
Suntar-Khayata Station reached 75 cm in 1958 and 90 cm in 1959 (Grave et
al., 1964). On steep slopes with southern exposure, the depth of
penetration of positive temperature into the ground is expected to be
greater. In similar landscapes with the same conditions, large-scale
crushed stone thaws up to 55-60 cm during the season, and crushed loam
thaws up to 80-85 cm. Observations show that large-scale sediments at
the time when the snow comes down are firmly cemented by ice, which
fills all the pores between the material. The data indicates that the
variation of active layer depth in the high-altitude area is
significantly variable over individual years. The depth of the seasonal
thaw layer is more stable in the mid-mountain region. The maximum depth
of thawing is observed in coarse-grained rocks this region. In
sand-gravel-pebble ground at an altitude of about 1400 m, the depth of
seasonal thawing reaches 120-150 cm and in loam soils ranges from 25 to
30 cm, depending on the moisture content (Grave et al., 1964).

\textbf{4. Hydrograph model}

The Hydrograph model is a distributed process-based hydrological
modelling system (Vinogradov et al., 2011). It describes all components
of the land hydrological cycle, including precipitation and its
interception; snow accumulation and melting; evaporation from snow,
soil, and vegetation cover; surface \selectlanguage{english}flow and in\selectlanguage{english}filtration; soil water
dynamics and \selectlanguage{english}flow; heat dynamics and phase change in soil layers;
underground \selectlanguage{english}flow formation, slope and channel \selectlanguage{english}flow transformation. The
model requires the following atmospheric variables as its input: air
temperature and humidity, the amount of precipitation. The output are
flow hydrographs, water balance and state variables of basin elements.
The model can be run at time steps from minutes and hours to daily.

The concept of runoff elements used in the Hydrograph model for spatial
discretization of basins is a key concept. The catchment area consists
of runoff elements of different levels -- surface, soil and underground.
The concept proposes the system of runoff elements characteristics, such
as outflow time which include the time and intensity of outflow from
elements, depending on the water storage (Vinogradov et al., 2011).

Within the discretization procedure, the basin territory is divided into
several conditionally homogeneous parts called runoff formation
complexes (RFC). It is assumed that the characteristics of soil,
vegetation, topography, and other components of the landscape are
constant within each RFC, while the runoff formation process is uniform.
The main parameters of the model are the physical properties of the
landscapes that may be observed in nature and are classified according
to the types of soil (specific weight, specific heat capacity of soil
particles, specific heat conductivity of dry soil particles, porosity,
maximum water holding capacity, wilting point, ice impedance factor,
infiltration coefficient, hydraulic parameter of subsurface system of
runoff elements), vegetation (seasonal shadiness by vegetation cover,
landscape albedo, interception storage capacity, coefficient of
evaporation from the interception storage during the maximum development
of vegetation cover, parameter of heat supply from atmosphere to soil
surface, phenological dates) and other characteristics (Vinogradov et
al., 2011; Semenov et al., 2013).

The method for simulating thermal dynamics in the upper layer of ground
is incorporated in the Hydrograph model. It is based on several
techniques that simplify the differential equation of thermal
conductivity in the soil profile and allows bringing the system of
differential equations to a system of linear algebraic equations without
losing the quality of the simulation results (Lebedeva et al., 2015;
Semenova et al., 2015).

The Hydrograph model has been successfully applied to simulate the river
runoff formation in cold regions with a lack of ground-based observation
data (Semenova et al., 2013; Semenova et al., 2015; Vinogradov et al.,
2011). Here we present the results of parameterization and verification
of the Hydrograph model for mountainous landscapes of the North-East of
Russia based on the data of short-term special observations. For
modeling, the Suntar River basin is presented as a hexagonal grid, with
32 representative points (RP) (Fig. 1). Each RP has its own set of point
characteristics, which include the coordinates, latitude, elevation,
slope aspect, slope inclination and lag time.

\textbf{5. Model parameterization and input data}

\textbf{5.1 Parameterization}

The parametrization of the Hydrograph model was performed based on joint
analysis of available field descriptions of ground hydrothermal regime
and corresponding patterns of runoff formation in typical landscapes
(Vinogradov et al., 2011). According to altitudinal zonation, the
catchment of the Suntar river is divided into 4 RFCs which are presented
above: goltsy (RFC \#1), mountain tundra (RFC \#2), sparse larch forest
(RFC \#3), swampy sparse larch forest at waterlogged soils (RFC \#4)
(Fig. 1). For each RFC, a schematization of the vertical profile is
developed that considers vegetation, soil composition, snow accumulation
features and runoff formation processes. In the Hydrograph model the
soil column is divided into computational soil layers (CSL), which may
have different depths but it is usually taken to be equal to 10~cm, and
the total depth of the calculated soil profile should exceed the maximum
active layer depth, if the model is applied to the permafrost zone. In
this study the calculation depth of the ground column was taken as 2
meters (20 CSL by 10 cm). This value is assigned from the assumption of
maximum possible active layer depth (150 cm) (Grave, 1964).

RFC \#1

The parametrization of goltsy landscape was developed with the use of
observational data from the Suntar-Khayata Station (Grave, 1959; Grave
\& Koreisha, 1957, 1960; Koreisha, 1963).

The set of the model parameters representing physical properties of the
soil (ground) column was elaborated based on the detailed description of
goltsy landscape, its ground profiles (Grave \& Koreisha, 1957) and
physical properties of ground column at different depths, such as
density, porosity, water capacity, heat conductivity (Table 2) (Grave,
1959; Grave \& Koreisha, 1960; Grave et al., 1964; Koreisha, 1963).

Assigned values of specific density and porosity for all 20 CSL are 2700
kg/m\textsuperscript{3} and 42\%. Maximum water holding capacity is
0.12; maximum ice holding capacity is 0.22-0.32 according to Grave
(1959) and is taken as an average value of 0.26. Specific heat capacity
of ground particles in dry condition accounts for 840 J/kg \selectlanguage{ngerman}°\selectlanguage{russian}С, and
specific heat conductivity -- 1.5 W/m \selectlanguage{ngerman}°\selectlanguage{russian}С. The infiltration coefficient
(assigned as 10, 5, 1 and 0.1 mm/min for the ground layers 10, 20, 30 cm
and below 30 cm, respectively) was not determined at the Suntar-Khayata
Station and is adopted from (Semenova et al., 2013) for similar
landscape of the Kolyma water balance station.

The hydraulic parameters of the runoff elements (1) in ground profile
(Semenova et al., 2013; Vinogradov et al., 2011) were determined by
manual calibration using the observed hydrographs and based on the
general ideas about the runoff formation processes. For example, runoff
generation in the upper horizon of ground profile is much faster than in
the mineral layer. The value of this parameter is estimated as 10 at the
upper layer and 0.005 at the bottom layer.

The boundary conditions of the ground temperature at a constant depth
were taken from the average monthly soil temperature data at the 4 m
depth at the Suntar-Khayata Station in 1958. The minimum value of the
ground temperature reaches -11.7 \selectlanguage{ngerman}º\selectlanguage{russian}С in May, the maximum is -6.7 \selectlanguage{ngerman}º\selectlanguage{russian}С in
October.

The parameter of heat supply from the atmosphere to soil surface may be
treated as the heat transfer coefficient between atmosphere and soil
surface under conditions of instantaneous energy withdrawal from the
surface of contact. Depending on the vegetation density above the soil
surface, the value of the parameter changes with increasing vegetation
height/density from 1.0 (RFC \#1) to 3.0 (RFC\#3-4) (Semenova et al.,
2014).

RFC \#2-4

Assuming that runoff formation processes in mountainous regions of the
Kolyma river upstreams and in the Suntar river basin are similar, the
parameters for RFC \#2-4 were adopted from (Lebedeva et al., 2014;
Makarieva et al., 2020; Semenova et al., 2013), who assessed them based
on detailed data from the Kolyma water-balance station (Makarieva et
al., 2017, 2018a).

\textbf{5.2 Meteorological information}

Daily air temperature and humidity, precipitation totals from
meteorological stations of hydrometeorological network within or nearby
the basin were used as meteorological input for hydrological modelling.
Four of them, Suntar-Khayata, Nizhnyaya Baza, Vostochnaya and Agayakan,
were used for the period 1957-1964 and two, Agayakan and Vostochnaya,
for the period 1966-2012 (Table 3, Fig. 1). Input data from
meteorological stations are interpolated to each RP. The interpolation
is based on the triangulation method, when ideally each RP is inside a
triangle, in the corners of which there are weather stations. Linear
interpolation is conducted between the stations, if only two are
available.

\textbf{5.2.1 Distribution of air temperature and humidity with
elevation}

The study area is characterized by temperature inversions. Annual
average monthly temperature and air saturation deficit lapse rates were
estimated using the data from the Suntar-Khayata and Agayakan
meteorological stations (the range of elevation is 1292 m), they change
from +1.1 \selectlanguage{ngerman}º\selectlanguage{russian}С and +0.01 mbar per 100 m elevation increase in January to
-1.3 \selectlanguage{ngerman}º\selectlanguage{russian}С and -0.35 mbar per 100 m in June. The estimated values were used
to correct interpolated temperature and saturation deficit from
meteorological stations to RP depending on the difference of elevation.

\textbf{5.2.2 Distribution of precipitation with elevation}

The data of four meteorological stations (Suntar-Khayata, Nizhnyaya
Baza, Vostochnaya and Agayakan) from Reference book (1968) and the
information of snow surveys at high mountain elevation (Grave, 1960)
were used to analyze the distribution of precipitation at different
altitudes for warm (May -- August) and cold (September -- April) periods
of the year.

Annual precipitation at the Suntar-Khayata Station exceeds the
precipitation amount observed at foothills by more than twofold.
Precipitation gradient at the altitude range 777 to 1350 m a.s.l. is 7
mm (5-7\%) per 100 m, and at the altitude range 1350 to 2068 m a.s.l. it
exceeds 35 mm (15-16\%). Snow survey data for 1957-1959 (Grave, 1960)
had demonstrated that altitudinal gradients of precipitation increase
are steady and equal on average to 35 (5-8\%) and 30 (4-5\%) mm per 100
m for the altitude ranges of 2068-2257 and 2257-2477 m a.s.l.
correspondingly.

Solid precipitation share at 777 m a.s.l. is approximately 25\% of the
annual total, and at 2068 m a.s.l. it increases to 60\%. Mean annual
precipitation from 1957 to 1964 at the Suntar-Khayata Station according
to the rain gauge data is 555 mm.

Correct estimation of precipitation is difficult in mountainous areas,
significant biases occur especially for winter precipitation under
effect of the wind on snowfall (Groisman et al., 2014). There are
several methods for precipitation corrections. They are mainly based on
the coefficient on wind speed and wind protection, air temperature and
precipitation type (WMO Report no. 67, 1998; Yang \& Goodison, 1995). In
Reference Book (1968) some adjustments are recommended for wind
underestimation and wetting loss, which can reach up to 1.7 times (1.6
on average in cold season) for solid precipitation, and 1.3 times (1.16
times on average in warm season) for liquid precipitation, which leads
to the annual precipitation amounts of 688 mm at 2068 m a.s.l.
(Reference Book, 1968), and 800 mm at the mountains peaks (Vasiliev \&
Torgovkin, 2002).

Corrected values of precipitation at meteorological stations were used
to develop the dependencies between both liquid and solid precipitation
amount and terrain elevation in the basin. Precipitation amount for each
RP is assessed according to those dependencies based on its elevation
and interpolated daily solid and liquid sums of precipitation are
normalized.

\textbf{6. Hydrograph model verification based on special observation}

We used available observational data from the Suntar-Khayata Station to
verify the model parameterization for the goltsy landscape.

\textbf{6.1 Ground temperature}

Geothermal measurements were carried out at the Suntar-Khayata Station
site in three boreholes at depths down to 10-20 m in 1958. Temperature
measurements were made 4 times a day at depth horizons to a depth of 1
m, once a day to a depth of 5 m and once every five days on deeper
horizons. Average monthly ground temperatures at numerous horizons were
published in Grave (1959). We used these data to verify ground
temperature modeling which was conducted on a daily time step at
different depths using thermal-physical soil properties. Mean absolute
deviations between simulated and observed monthly temperatures accounted
for 1.1 \selectlanguage{ngerman}º\selectlanguage{russian}С, 0.7 \selectlanguage{ngerman}º\selectlanguage{russian}С, 0.2 \selectlanguage{ngerman}º\selectlanguage{russian}С and 0.3 \selectlanguage{ngerman}º\selectlanguage{russian}С, and their maximum values -- +3.6
\selectlanguage{ngerman}º\selectlanguage{russian}С (December), +4.0 \selectlanguage{ngerman}º\selectlanguage{russian}С (November), +2.4 \selectlanguage{ngerman}º\selectlanguage{russian}С (June) and -1.7 \selectlanguage{ngerman}º\selectlanguage{russian}С (January)
at 5, 50, 100 and 200 cm depths correspondingly in 1958 (Table 4).
Overall, modelled soil temperature values at different depths provide a
good fit to the observed values (Fig. 3).

\textbf{6.2 Active layer depths}

Ground thaw starts in mid-June and continues to mid-September. According
to Grave (1964) maximum active layer thickness (ALT) reaches 75 cm at
the goltsy landscape and 30-45 cm at the swampy landscape (Table 1).

For simulating ALT at the goltsy landscape we varied two types of
initial conditions: 1) with lenses of ground ice in upper part of soil
profile and 2) without ground ice. In the first case (with ground ice)
the average simulated ALT (1957-1964) is 32 cm with the range from 20 cm
(1958) to 42 cm (1960) at RFC \#1 (Fig. 4). The same values are 33 cm
for the period 1966-2012 with maximum 70 cm in 1968 and minimum 2 cm in
1979. In the second case (without ground ice) simulated ALT varies in
the range of 50-80 cm for the period 1957-2012.

The average simulated depth of the active layer (1966-2012) at the RFC
\#2 is 180 cm, at the RFC \#3 is 122 cm, at the RFC \#4 is 67 cm. In
general simulated ALT exceed observed values in those landscapes for
which the model parameters were adopted from the study at the Kolyma
water-balance station (Makarieva et al., 2018a).

For example, mean ALT values in tundra and rocky talus landscapes are
about 1.5 m there, reaching 2.5 m at steep southern slopes due to higher
air temperatures and longer freeze-free period (about 130 days compared
to 55 days at the Suntar-Khayata Station).

It is important to mention that there are no statistically significant
increasing trends of simulated ALT values in long-term period.

\textbf{6.3 Snow cover}

Snow measurements were conducted at the meteorological site of the
Suntar-Khayata Station at the altitude of 2070 m. The triangle plot with
the sides of 12 m was instrumented with three rails installed in the
corners where snow height and volume weight were measured each 10 days
(Koreisha, 1963). The snow data are available only for two years
(1958-1959).

At the altitude of the Suntar-Khayata Station, snow cover is formed in
early September and melts only in the second part of June -- early July.
The snow-free period lasts about 2 months, (on average 56 days in
1957-1959).

Snow water equivalent (SWE) varies greatly from year to year. Maximum
observed SWE reached 348 mm in 1958 and only 153 mm in 1959. Maximum
simulated SWE amounted to 363 mm in 1958 and 171 mm in 1959. Mean
simulated SWE by the end of winter for the period of 1957-1964 was 251
mm.

Mean deviation value between simulated and observed daily SWE is 18.4
mm. The maximum deviation value reached 43 mm on November 20th, 1958.
The absolute error of simulated maximum SWE is 5-12\% during 1958-1959.
Mean simulated SWE by the end of winter for the period of 1966-2012 was
213 mm and range from 114 mm (1983) to 379 (1967). The height of snow
changed from 44 cm to 99 cm and the mean value was 70 cm.

The comparison of simulated and observed values of SWE during winter
seasons 1958-1959 is presented in Fig. 4 and shows general model
adequacy. It is noteworthy that modelling results show that the snow
cover formed within 5 days from 5 to 10 August 1957 and then melted
(Fig. 4). The modelling results of the same variable state at the
Canadian Rocky Mountains watersheds shows that overestimation or
underestimation of the peak SWE ranged from 2.4 to 16\% for the upper
watershed landscapes (Fang et al., 2013).

Also snow surveys were conducted at the territory adjacent to the
Suntar-Khayata Station along the 3-km long route with elevation range
over 400 m (2068-2477) in 1957-1959. Spatial variation coefficient of
snow redistribution was calculated based on the data as 0.60. A normal
distribution (Vinogradov et al. 2011) was used to statistically account
for snow redistribution in the goltsy landscape based on this
estimation. In general, this value is consistent with the data on snow
variation for mountainous landscapes in the Yukon River Basin (SWE
variation is 0.69 by McCartney et al. (2006), 0.48 by Pomeroy et al.
(2004) and 0.69-0.84 in the upstreams of Kolyma River based on the data
by Makarieva et al. (2018a).

\textbf{6.4 Evapotranspiration}

Assessment of evapotranspiration (ET) is the very problematic for this
region due to the lack of the data. Annual values of ET for goltsy
landscape at the Morozova Creek watershed (altitude range 1100-1700 m
a.s.l.) was estimated based on the water balance data of the Kolyma
water balance station (KWBS) in the range from 70 mm (Lebedeva et al.,
2017) to 92 mm (Makarieva et al., 2018a). In the Upper Wolf-Creek
catchment (part of the southern headwaters of the Yukon River, Canada)
with tundra and shrub-tundra environment and elevation reaching 2250 m
annual value of ET reached 135 mm (Janowicz et al., 2004). The
assessment for the Upper Kuparuk (elevation range of 698-1464 m) and
Imnavait River basins (elevation range from 844 to 960 m) (Alaska) from
tundra landscape was about 140 and 178 mm respectively (Schramm et al.,
2007). In the the Tana River Basin (Finnish Tenojoki), with the mean air
temperature -6\selectlanguage{english}@C at the highest mountain tops (1010 m), annual values of
snow sublimation and evapotranspiration was estimated as 90 and 58 mm
respectively (Dankers \& Chrisrensen, 2005). The assessment of total
annual evaporation at the Axel Heiberg Island at the Canadian Arctic
Archipelago was about 140 mm (Ohmura, 1982).

The observations of ET from the ground surface at the Suntar-Khayata
station were carried in 1958 (Grave, 1959). Two land evaporimeters
GGI-500 were used (Makarieva et al., 2018a). The evaporimeters were
installed in early June 1958, when the snowpack was continuous, had not
started melting yet, and ground temperature was below zero. Evaporation
tanks were filled with soil from the Suntar-Khayata Station site and
left under snow until it completely melted at the site on July 20-27,
1958. The observations continued throughout August 1958. Evaporation
tanks were weighted every 5 days, precipitation was registered daily in
direct proximity to them (Grave, 1959). In August 1958 observed values
of precipitation accounted for 77 mm, infiltration rate -- 36 mm, ET --
44 mm (about 1.4 mm per day).

Compared to the ET assessments for the KWBS watersheds where free-snow
season lasts twice longer and mean summer values of air moisture deficit
are 1.5 times higher than at the Suntar-Khayata Station, we question
this single result of observations and suggest that the value of 44 mm
is significantly overestimated.

In the Hydrograph model the amount of ET is calculated taking into
account the potential evaporation, initial amount of moisture in soil
layers, maximum water holding capacity of the soil, the fraction of
contribution of a given soil layer to total evaporation, the value of
which depends on soil and vegetation type (Semenova et al., 2013). To
estimate ET we adopted the evaporation coefficient parameter from the
modelling studies conducted for the Kolyma water-balance station
(Semenova et al., 2013; Makarieva et al., 2020). Its value for goltsy
landscape is 9*10\textsuperscript{-10} m (hPa*s)\textsuperscript{-1}.
Simulated ET values were 19 mm in August, 1958 and 43 mm on average
during snow free season for the whole period of simulations. Adding 11
mm of snow evaporation it gives us about 54 mm of annual total
evaporation at the goltsy landscape.

\textbf{7. Results of streamflow modeling}

Continuous runoff modeling with daily temporal resolution was carried
out for the Suntar river basin for the period 1957-1964, using input
meteorological data from four meteorological stations (Suntar-Khayata,
Nizhnyaya Baza, Vostochnaya and Agayakan); and for the period 1966-2012
using the data from two stations (Vostochnaya and Agayakan). Water
balance components distribution for these periods are presented in Table
5, and the comparison of observed and calculated streamflow hydrographs
-- in Fig. 5, Fig. 6.

Calculated mean annual precipitation for the Suntar river basin is 344
mm for the 1957-1964 period. Estimated streamflow is 199 mm, which is
10\% higher than the observed value (180 mm). Estimated ET from the
whole basin equaled 143 mm.

Maximum precipitation and streamflow annual values for the entire
simulation period reached 486 and 348 mm in 1959, while minimum values
were 259 mm in 1958 and 136 mm in 1963 for the Suntar River basin. The
coefficient of variation of annual streamflow is 0.30.

Here we compare the water balance distribution with other research basin
in the region, the KWBS station, the Kontakovy creek watershed (area
21.3 km\textsuperscript{2}, average altitude 1070 m). The value of ET
for the KWBS is assessed within the range from 114 to 137 mm (Lebedeva
et al., 2017; Zhuravin, 2004). Mean annual precipitation and streamflow
reached 420 and 280 mm for the period 1948--1997.

The average and median Nash-Sutcliffe efficiency (NS) for the Suntar
River amounted to 0.75 in 1957-1964. The same value for the period of
1966-2012 is lower (average 0.58, median 0.67 with maximum and minimum
values of 0.88 and -0.90, respectively). We attribute this decrease of
efficiency to the lack of meteorological data in the second period.
Overall, despite some overestimation of streamflow, the calculated
streamflow hydrographs match the observed ones quite satisfactorily,
both in phases and absolute discharge values. Overestimation of
simulated streamflow during spring freshet may be associated with the
spread of underchannel taliks. In spring dry alluvial deposits in the
river channels are filled with snowmelt water and delay the start of
freshet and decrease its magnitude (Grave et al., 1964). Such phenomena
are also described by Mikhaylov (2013).

We also compared simulated and observed maximum discharges. The maximum
simulated and observed discharges were 1200 and 1659 respectively during
1957-1964 and 1905 and 1910 during 1966-2012 for the Suntar River basin
(Table).

Based on the simulation results, the contribution of each runoff
formation complex (RFC) into total streamflow of the Suntar River was
evaluated (Table 6, Fig. 7). Goltsy complex that covers only 7\% of the
basin provides 20\% of the total streamflow, and the runoff coefficient
reaches 0.91. Tundra is the largest contributor to the runoff formation
at the Suntar river catchment -- 49\% of the total runoff, with a runoff
coefficient of 0.74. The total streamflow from the taiga and sparse
forest landscapes, which take 56\% of the territory, is about 31\%. The
contribution of the goltsy landscape increases in dry years and may
reach up to 28\% (for example, in 1963 the total annual streamflow was
only 130 mm, while the streamflow from the goltsy complex was simulated
as 513 mm).

\textbf{8. Simulated streamflow trends}

Studying the mechanisms of runoff regime transformation changes in the
Arctic basins in current and future climate conditions is important
research task. In general, river streamflow in Northern Eurasia and
North America is increasing (Shiklomanov \& Lammers, 2013). Most of the
rivers exhibit the increase of winter base flow (Makarieva et al. 2019a;
Spence et al., 2011; Tananaev et al., 2016) and there are different
hypothesis about the factors of such changes. The analysis of monthly
streamflow data in the basins of the Yana and Indigirka Rivers
(1936-2015) has shown the presence of statistically significant (p
\textless{}0.05) positive trends in May and autumn period (Makarieva et
al., 2019a). The values of trends for the Suntar River are the
following: 6.8 mm or 103 \% in May, 9.9 mm or 49 \% in September, 3.3 mm
or 70\% in October and 0.43 mm or 52\% in November (Makarieva et al.,
2019a). There is a decrease in precipitation in winter (minus 8 to 13
mm) and the absence of significant changes in other seasons. The rise of
annual air temperature by +2,0\selectlanguage{ngerman}°C led to an increase in the amount of
liquid precipitation and streamflow in September by about 12 mm. The
revealed dependences of monthly streamflow on the amount of liquid
precipitation in September for small catchments, as well as the single
period (1991-1996), when the changes of these hydrometeorological
characteristics are simultaneously observed, indicate that the phase
state of precipitation can be among main factors affecting the increase
of low flows of studied rivers.

According the Mann-Kendall and Spearman rank-correlation tests (Kendall,
1975; Mann, 1945) and Pettitt's test (Pettitt, 1979) significant
positive trends of simulated streamflow was in May (1.3 mm or 118 \%),
September (10.2 mm or 38.1\%), in October (1.3 mm or 33.3\%) and
November (0.35 mm or 35.9\%) (Nesterova et al., 2019). Thus, the
simulated trends do coincide with the observed trends of stream flow
values (Table 7). The share of liquid precipitation increased by an
average of 10 \% or 13.6 mm, which corresponds to the observed value of
12 mm. The change point in the autumn season coincides with the observed
data and refers to the period 1993-1996 (Fig. 8).

\textbf{9. Discussion and conclusion}

The ongoing increase of air temperatures, changes in precipitation and
permafrost degradation affect the hydrological cycle via seasonal
redistribution of water balance elements, changes in soil wetness and
ALT, intensification of ground and surface water runoff exchange
(Makarieva, 2019a; Rawlins et al., 2010; Shiklomanov \& Lammers, 2013;
Tananaev et al., 2016; Walvoord \& Kurylyk, 2016).

However, the research is complicated by the lack of observed data and
the inaccessibility of the study area of the most of the Arctic (Bennett
et al., 2015). In the conditions of insufficient information, typical
for the high-altitude mountain permafrost regions, the main tool for
studying the processes is the method of mathematical modeling. The
Arctic places increased demands on hydrological models. The vast
majority of hydrological models, well-established in areas with a
temperate climate, cannot be used in the permafrost zone. The main
requirements are the physical validity of models to natural processes,
their versatility in terms of use, both in different landscapes and
spatial and temporal scales, and most importantly, the ability to assess
the parameters of the model based on the measured properties of
landscapes.

Stationary observations in small research catchments are the main source
of information on the physical mechanisms of runoff formation and
changes of hydrological cycle. But such observations are often expensive
to maintain (especially in hard-to-reach regions), require large number
of specialists, and are difficult to perform without additional support
from the state or other interested stakeholders. In these conditions,
the information for improving the models can also be integrated from
short-term studies at certain landscapes and watersheds. The concept of
such studies was proposed by Vinogradov (1988), he called it
``nonstationary research watersheds and plots''. The idea was further
developed by Vinogradova and Vinogradov (2014) and Gartsman and Shamov
(2015) who called this approach ``mobile watershed''. According to this
approach, one or several indicative watersheds or plots are selected in
the study area. The research visits are short-term (approximately from
2-3 weeks to 2 months) and last for several years. The observations are
vaster and less detailed.

Conducting short-term intensive observations on specially selected
representative watersheds, despite their fragmentation, allow
formulating a general idea of \selectlanguage{english}\selectlanguage{english}the conditions of runoff formation and
hydrological phenomena of the territory in question, and most
importantly, approximate quantitative assessment of the parameters of
mathematical models of hydrological processes (Vinogradov \&
Vinogradova, 2014). However, not having in their basis the tasks of
model development and parametrization, or refining existing methods for
calculating the flow characteristics, such observations lose most of
their value and do not justify the investment.

The three-years extensive observations at the Suntar-Khayata Station can
be regarded as the good example of such approach. Among the others
expeditions to remote regions we may mention historical studies at the
Putorano Plateau in 1988-1990 (Reports\ldots{}, 1988-1990), recent
studies at Chukotka (Tregubov et al., 2020) and the Lena River delta
(Tarbeeva et al., 2020). We emphasize the need for open access to the
detailed hydrometeorological data of such research sites which can
provide the opportunity for multi-criteria assessment of hydrological
models in different conditions of permafrost zone (e.g. Fang et al.,
2018; Makarieva 2017, 2018a; Rasouli et al., 2019).

In this research, based on the observation data at the high altitude
Suntar-Khayata Station (the Indigirka river upper reaches) under the
program of the International Geophysical Year in 1957-1959, the
parameters of the hydrological model Hydrograph were developed, which
describe the runoff formation processes in the high mountain goltsy
landscape of the Suntar river basin. Variable states of snow cover and
heat dynamics in ground profile in the goltsy zone were simulated, as
well as runoff formation process and its changes in recent time
throughout the whole catchment of the Suntar river. Modeling results are
considered acceptable.

Model calculations have allowed evaluation of long-term average annual
values of water balance for different landscapes, their contribution to
runoff formation in the mountain river outlet. It is established that
the runoff formation occurs mainly in the high-altitude region of goltsy
and tundra (about 70\%).

The model reproduced observed trend values and change point of
streamflow during the study period supporting the hypothesis that the
increase of liquid precipitation in autumn due to climate warming could
be the main factor of streamflow changes in the autumn-winter period in
this permafrost region.

Currently, in the mountain regions of the Yana, Indigirka and Kolyma
rivers basins no hydrological research stations are left to perform a
comprehensive study of runoff formation processes. Therefore,
development and verification of methods for hydrological processes
modeling which may successfully utilize short-term, extremely scarce
data, become more of great current interest. The presented study has
demonstrated that the Hydrograph model and its further development may
become a foundation for solving scientific and practical issues in the
research region.

\textbf{Data Availability Statement}

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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