Monitoring the Melting of Snow Stored in Snow Dumps (Yuzhno-Sakhalinsk, Russia)

Abstract

This study reviews the melting rate of anthropogenic snow patches formed as a result of cleaning the territory of Yuzhno-Sakhalinsk city from snow and collecting it in designated areas known as snow dumps. Snow patches persisted at absolute altitudes of less than 50 m in the summers during the period of 2010–2022, except in 2017. The positive factor was the ratio of the relatively small area occupied by the anthropogenic snow patch and its significant height at the beginning of the melting period. The detailed observations of anthropogenic snow patch growth and melting were conducted by the authors starting in the winter season of 2017–2018. The snow volume collected in snow dumps during the winter season in Yuzhno-Sakhalinsk can reach 3000 m³. That is why it is necessary to determine how the anthropogenic snow patch will loosen the water through the warm season. Special models of anthropogenic snow patch melting do not exist. So, the authors review the ability of four glacier and snow cover melting model applications for such objects. The contribution of various parameters affecting the snow path melting rate was also determined. The collected factual data allowed for the development of empirical snow patch melting models. The largest errors resulting in the usage of reviewed models are related to the beginning (April) and ending (September–October) of the melting periods.

1. Introduction

Annually, stable snow cover occurs within most of the territory of Russia during the cold period of the year. Municipal services collect a significant amount of snow after the urbanized areas are cleared. The main method of snow handling is in its storage in designated areas known as snow dumps. Currently, Russian federal legislation does not regulate procedures related to mass snow disposal from city streets and snow dump arrangements. Problems with snow management are related to landscaping issues and are resolved by local governments.

At the same time, snow masses have a constant effect on the occupied territory, which is associated with the snow storage process in the cold period. The processing of heavy machinery makes continuous noise at the snow dump. The dump trucks transporting snow cause traffic jams. For example, about 50 dump trucks blocked one of the motor roads connecting Yuzhno-Sakhalinsk and Dolinsk cities at the snow dump entry after heavy snowfall in January 2022.

Some cases of perennial anthropogenic snow patch formation at the snow dumps are known [1,2,3]. During the warm period, the problems are related to the snow melting. Snow melting negatively affects not only the territory of the snow dump but also the adjacent territories. The effects of melting can be divided into engineering and ecological effects.

The main type of engineering effect is territories flooding. Ussuriysk city (Primorski Krai) is the most affected by this type of impact in Russia, where residential buildings were flooded on several streets at once in 2016 [4]. The cities of Kirov [5] and Yuzhno-Sakhalinsk (2018, 2020) experienced the same impacts. In 2020, the technical committee of Yuzhno-Sakhalinsk decommissioned a gantry crane located on the industrial site adjacent to the snow dump due to the crane concrete base deformation, which occurred due to a change in the physical and mechanical characteristics caused by excessive water logging of the ground with melt water from the snow dump. The distance from the gantry crane to the snow dump was 100 m.

The ecological effect is represented in the release of pollutants into the environment during snow melting, as well as the formation of the insoluble waste layer in these areas. Environmental problems associated with snow dumps are typical for many countries. For example, it has been established that soils are polluted with polycyclic aromatic hydrocarbons during snow dump melting in Finland [6]. Heavy metals and microplastics are released into the environment during snow dump melting in Sweden [7]; Pb, Cd, Zn, and Cu content increases were found in the territories adjacent to Ottawa (Canada) snow dumps [8]; and the total calculated hydrocarbon load from one snow dump is about 5.1 tons of hydrocarbons in Edmonton (Canada) [9]. According to the results of prosecutorial inspections, violations of the environmental legislation requirements were found in such large cities as Moscow, Khanty-Mansiysk [10], Kazan, and other cities in Russia.

During a multi-year research project, it was established that snow dumps in Yuzhno-Sakhalinsk are objects causing a negative impact on the environment [1]. Snow transported from the Yuzhno-Sakhalinsk territory contains pollutants that accumulate in it after snow melting reagent application and fallout from the city atmosphere. In addition, snow is not processed to speed up the melting of snow dumps, and it melts in natural conditions. Melted water from dumps is not purified, and it flows down to the territory adjacent to the dumps. As a result, pollutants accumulate in the soil [1].

The aim of this study is to investigate the snow melting dynamics of snow dumps using the example of sites located in Yuzhno-Sakhalinsk. The specific research related to the melting of natural anthropogenic objects, such as snow dumps, does not exist, in spite of the fact that many researchers note the phenomenon of pollutant accumulation in stored snow [6,7,8]. However, the rate and volumes of pollutant effluence in the environment directly depend on the melting rate.

In this study, the following terms are used: snow dumps—territories for the storage of snow, disposed after city cleaning; anthropogenic snow patch—a stationary snow amassment in the snow dump area, which persists after the melting of the surrounding snow cover and differs from the natural snow patch by the specific chemical composition, determined by the usage of snow melting reagents at urbanized territories and the incremental formation of a debris layer at the snow dump surface due to snow melting; debris layer—a layer consisting of sand, household, and construction waste, falling into removed snow during city clearing processes.

2. Study Object

The study objects are situated in Sakhalin Island, which is located on the Pacific coast of Russia. Eleven cities of Sakhalin have 13 snow dumps for snow placement during winter (Figure 1a). Two snow dumps are located in Yuzhno-Sakhalinsk, and the same situation is in Kholmsk, with the cumulative volume of stockpiled snow detailed in

Table 1. Annual volume of stored snow, hard precipitation quantity and square of Sakhalin cities, where the snow dumps are operating.

City	The Mean Volume of Stored over the Year Snow (thous. m3)	The Mean Hard Precipitation Quantity Per the Winter (mm)	Settlement Area (km2)
Yuzhno-Sakhalinsk	1500	220	160
Dolinsk	200	299	5.1
Nevel’sk	200	275	4.0
Kholmsk	200	241	8.2
Korsakov	150	191	6.0
Aniva	100	281	1.1
Tomari	100	274	1.4
Okha	100	237	2.1
Uglegorsk	100	211	7.7
Makarov	100	204	1.7
Poronaysk	100	151	8.4

. The mean volume of snow hauled to these dumps correlated with the size of the settlement area and the quantity of solid precipitation falling on its territory (Table 1). Prolonged monitoring of snow dumps in Sakhalin revealed that the volumes of snow stored are largely determined by the effectiveness of urban street cleaning operations. It is related to economic factors. Municipalities sign snow removal contracts in the summer, implying approximate snow volumes without accurate forecasts for the coming winter. In snowy winters, excess snow is stored on lawns and left in city parks, while in dry winters, this does not happen. Hence, the average volumes of snow transported to dumps (Table 1) are quite stable. There was a significant increase in snow volume during the winter season of 2017–2018, when the amount of solid precipitation exceeded the normal levels by 150%. The total volume of snow stored at dumps of Yuzhno-Sakhalinsk increased twofold and reached 3000 thous. m³.

Observations of snow dumps in Yuzhno-Sakhalinsk have been carried out since the start of their operation in 2010. During the observation period, anthropogenic snow patches at snow dump sites melted completely before the start of a new snow storage season (the end of October–November) in 2017, 2019 and 2022 only. The primary cause for the preservation of these anthropogenic snow patches involves the formation of an insulating layer on their surfaces, which consists of melted sand and trash integrated into the snow during the city street cleaning procedures.

The two largest snow dumps, by volume of stored snow, are located in Yuzhno-Sakhalinsk (administrative center) (Figure 1c). One of them is situated in the northern part of the city and the other in the southern part. These snow dumps were named according to their locations.

The Northern snow dump is the smaller of two snow dumps operating in Yuzhno-Sakhalinsk. The average annual snow volume stored in the dump is approximately 500 (thous. m³). Due to its restricted dimensions, snow is stacked vertically, leading to considerable increases in height. For example, the snow height exceeded 30 (m) in 2018. Figure 1c shows the dynamics of changes in the snow dump area size since the start of site operation in 2010, when its area was 5.5 (ha). Marginal melting is predominant in the snow patch that forms in the Northern dump territory.

The Southern snow dump, being the larger of the two snow dumps, occupies an area of 43 (ha). However, the mean height of the stored snow is 3–5 (m). As a result, the snow patch formed over the winter season is divided into numerous smaller, separated snow patches with different sizes during the early period of melting (May–beginning of June). Since the annual division of the snow patch occurs unpredictably, it was decided to study the melting process of a more stable snow patch that forms at the Northern snow dump and then extrapolate the results to the Southern snow dump.

Snow storage in the dump commences in November and terminates in mid-April. Following the cessation of snow delivery, the dumps lie dormant, allowing snow to undergo natural melting. Complete snow melting at the Northern snow dump does not occur every year. Prior to initiating a new snow storage period, machinery arrives at the dump in late October–early November to break up and redistribute the remaining snow. If it is impossible to redistribute the residual snow, snow storage starts around the existing snow patch. Over time, this remnant becomes buried beneath newly delivered snow masses removed from urban territories. Thus, an enduring anthropogenic snow patch nucleus emerges artificially, ensuring sustained growth over consecutive years.

3. Data Collection and Methods

Observations of the Northern snow dump started in 2010. As a part of observations, we have been conducting monthly aerial surveys on snow dumps since 2018. Monthly aerial surveys that were carried out made it possible to track the dynamics of the morphometric characteristics of snow dumps and build chronological 3D models. The aerial photographic survey usage allows us to reduce or avoid the risks associated with heavy equipment (excavators and dump trucks) operating on snow dumps in winter 24 h a day. In addition, in spring and summer, carrying out measuring activities on the ground poses a risk of injury due to snow melting, which leads to cracks and sink formation in the snow and ice core, as well as the risks from melted-out household waste including glass shards and metal objects.

3.1. Data Collection

3.1.1. Orthophoto Data

The measurements of snow patch volume were conducted using the aerial vehicle (UAV) DJI Pantom 4 (with the standard camera of 20 Mp), and a software system allowed us to conduct the flight missions as well as subsequent data processing. The flight task was conducted in the “Pix4Dcapture” program, enabling the setting of required flight parameters (altitude, speed, shooting frequency, as well as the percentage of photo overlap) [2].

The obtained photographs were processed using the “Agisoft Photoscan” program. The constructed 3D models of snow dumps allowed for tracking the dynamics of changes in their volumes over time and were also used to determine other morphometric parameters (e.g., height and occupied area size) (Figure 2). Moreover, the positioning of the snow dump base without snow was implemented using geodetic satellite equipment (EFT M1 GNSS) to calculate the snow dump volume.

During snow dump height determination using UAVs, the mean absolute divergence in height in comparison with our manual measurements was ±10–30 (cm), depending on the shooting date, which does not significantly affect the quality of the work performed.

3.1.2. Meteorological Data

The meteorological conditions during the annual snow patch melting seasons are presented in

Table 2. The main meteorological parameters of reviewed melting seasons.

Meteorological Parameter	Month
	April	May	June	July	August	September	October
average
Air temperature, °C	1.6	7.0	11.5	15.7	17.1	13.1	6.3
Precipitation, mm	57	69	59	86	107	103	99
Wind speed, m/s	3.1	3.4	3.0	2.6	2.3	2.5	2.3
Total cloudiness, ball	5.7	6.3	6.8	7.5	7.0	5.7	5.5
2018
Air temperature, °C	2.7	8.3	10.6	15.3	16.5	13.3	7.7
Precipitation, mm	23	61	76	96	49	63	86
Wind speed, m/s	2.4	2.5	2.9	2.5	2.0	1.9	2.1
Total cloudiness, ball	4.1	5.0	6.2	7.5	6.3	4.4	5.2
2019
Air temperature, °C	3.3	10.5	11.8	15.7	15.9	13.8	7.2
Precipitation, mm	21	42	105	53	114	57	45
Wind speed, m/s	2.1	2.6	2.4	2.3	2.1	1.7	2.0
Total cloudiness, ball	4.0	4.2	7.5	7.5	7.5	4.4	4.4
2020
Air temperature, °C	1.7	7.8	11.9	16.4	16.3	14.5	7.4
Precipitation, mm	57	56	65	66	155	76	157
Wind speed, m/s	2.6	2.6	2.9	2.2	2.2	1.8	2.0
Total cloudiness, ball	5.3	5.0	6.3	6.2	6.5	5.0	5.3
2021
Air temperature, °C	3.0	6.7	13.2	20.4	17.3	14	6.3
Precipitation, mm	69	103	51	13	95	111	81
Wind speed, m/s	2.8	3.3	2.7	2.1	1.8	1.7	2.0
Total cloudiness, ball	5.5	6.3	6.1	4.5	6.4	5.2	4.5
2022
Air temperature, °C	3.7	8.5	11	17.8	18.3	14.5	6.8
Precipitation, mm	64	101	106	52	113	106	91
Wind speed, m/s	2.8	3.0	2.6	2.5	1.9	2.0	2.1
Total cloudiness, ball	4.2	6.0	6.6	6.2	5.4	4.2	5.6

. These data were obtained at the meteorological station «Yuzhno-Sakhalinsk», located 5.9 (km) from the Northern snow dump [11]. All meteorological parameters from Table 2 were used as input parameters in the melting model, with the exception of precipitation. However, it is reasonable to assume that liquid precipitation affects the rate of snow patch melting. Therefore, the contribution of this parameter was tested in the model proposed in this study.

3.1.3. Snow Density Data

The density of snow stored in the dumps was measured using a sampling corer that was driven into the snow and then excavated for weighing. During each survey, at least seven snow samples were taken from different parts of the snow patches to which access could be gained. Additionally, snow density measurements were also conducted on exposed sidewalls along the perimeter of these snow patches, employing the same method. The obtained values were averaged for subsequent calculations. Figure 3 presents the collected data on snow density employed for calculating the melting rates of snow patches.

Manual drilling was not carried out because the snow contains household waste that may damage the equipment. Mechanized drilling was also impossible due to the difficulties in reaching the snow patches for heavy machines during the melting season.

3.1.4. Debris Layer Data

When snow melting starts, debris layer formation occurs. The layer thickness increases with debris melting from snow during the warm season. The debris distribution at the snow patch surface is irregular. Additionally, the debris layer on steeper slopes of the snow patch can become unstable, potentially causing localized denudation. Following this event, the melting rate in these areas accelerates.

The debris layer survey was conducted once at the end of every month using visual and manual measurements. The snow patch area was divided as a net with cells of 50 × 50 (m), and the mean debris thickness was measured for each cell (Figure 4). At least three manual measurements per cell were taken using a ruler. Pictures captured contemporaneously with a thermal camera assisted in visual estimations. The color gradation allowed us to evaluate how evenly the debris layer of equal thickness was distributed. It also helped us estimate the area that was only slightly covered by debris. It usually has a blue color, which is associated with negative temperatures. In Figure 5, it is shown that the temperature in the hollow area is greater than that found on elevated slopes because of debris that collects there after sliding downhill. The pictures acquired through a thermal camera facilitated the choice of areas for conducting manual measurements, thereby enabling the most correct averaging across cells (Figure 4).

3.1.5. Debris Temperature Data

Thermovision display device Testo 871 (Figure 5) and temperature recorders TR-2L (DS1922L-F5, absolute error ±0.5 (°C)) were used for the debris layer temperature surveying. Readings were taken and new sensors were installed monthly. The number of used recorders varied from 4 to 8 throughout the five-year observation period. The recorders changed their position both horizontally (from 15 to 100 cm) and vertically (from 5 to 10 cm) during the periods between the data readings. Some recorders were lost due to snow detachment at the edges of the snow patch during certain months. As a result, a total of 11 recorders were lost over the course of 5 years of observations.

The loggers were placed within the central part of the debris layer covering the snow patch. The height of logger installation varied across specific cells (Figure 4) and dates of observation. If the debris layer thickness was insufficient for placing the recorder, it was installed at the contact point of snow/debris. The thickness of the debris layer is unstable during the melting period and tends to increase. Due to the high variability in the observed object, conducting regular measurements, as implemented by other researchers [12,13], proved impossible. We used the weighted average temperature from all the working sensors to derive the T_d index for calculations with the models. An attempt was made to model the melting by segmenting the site into individual sections and applying the T_d index value from the nearest sensor to each section separately. The total monthly melt volume was determined as the sum of melt volumes over all segments. The results of calculations using the weighted average temperature and sum of segments melting differed in the range of 5%. This deviation is considered acceptable, and, further, we used only the weighted average temperature values from all the sensors.

Anthropogenic snow patches are studied insufficiently, and specific methods allowing for the calculation of their melting velocity and melt water volumes do not exist. So, the calculations of snow patch melting were implemented following the methods [14,15,16] that are used for calculations for the melting of debris-covered glaciers.

3.2. Model Methods

Table 3. Values of constants and variables used for models.

Parameters	Symbol	Unit	Value
Variables
Distribution of temperature within the morainal layer	Td	°C	1–8.5
Debris layer thickness	dz	m	0.008–0.30
Time-step	i	h	720–744
Air temperature [11]	T	°C	1.7–20.4
Albedo [11]	α	–	0.14–0.35
Incoming shortwave radiation [11]	I	Wm−2	551,390–783,330
Lag parameters accounting for the energy transfer through the debris layers	lagT	H	0–10
	lagI	h	0–11
Temperature factor [15]	TF	mm h−1 °C−1	0.0265–0.0984
Shortwave radiation factor [15]	SRF	m2mmW−1h−1	0.0001–0.0044
Average of the maximum air temperature	θmax	°C	0.7–26.2
Average of the air temperature	θave	°C	−4.5–20.4
Mean daytime air temperature	θd	°C	−3.3–22
Mean night air temperature	θn	°C	−6.4–17.3
Mean daily wind speed	υd	m/s	2.2–3.8
Mean night wind speed	υn	m/s	1.1–2.7
Total cloudiness [11]	Nt	ball	4.0–7.5
Low cloudiness [11]	Nl	ball	4.2–6.6
Cloudiness coefficient	CN	–	2–2.7
Snowmelt factor	β	–	1–40
Snow water equivalent	S	mm
Constants
Density of snow	pi	kg m−3	350–650
Latent heat of fusion of water	Lm	J kg−1	3.35 × 105
Debris thermal conductivity	kd	W m−1 K−1	2.1

presents explanations of symbols, ranges of input values and constant values from formulae used for the following calculations.

Temperature index or degree-day models are based on empirical relationships between air temperature and melting rate. Empirical models offer the advantage of reduced data requirements compared to physically grounded energy balance models (Table 3).

3.2.1. The Enhanced Temperature Index (ETI)

An intermediate step between an empirical and energy balance model is the Enhanced Temperature Index model (ETI) developed by Pellicciotti et al. [14]. In addition to the air temperature factor, the ETI model includes a shortwave radiation factor that takes into account both incoming solar radiation and albedo. The melting rate per hour (mm w.e.h⁻¹) is calculated using the formula:

$$M=TF\times T+SRF\times \left(1-\alpha \right)\times I$$

3.2.2. Debris Enhanced Temperature-Index (DETI)

Carenzo et al. [15] improved the formula of ETI and proposed a new empirical approach, taking into account the feedback of the debris thickness for the melting rate computation. The Debris Enhanced Temperature-Index (DETI) allows computation of the melting rate per hour (mm w.e.h⁻¹) using the following formula:

$$M=TF\times T\left(i-{lag}_T\right)+SRF\times \left(1-\alpha \right)\times I(i-{lag}_I)$$

3.2.3. Debris Energy-Balance Model (DEB)

The energy-balance model [16] allows computation of the energy exchange between the debris layer and the overlying atmosphere. This approach requires numerous incoming meteorological variables (shortwave and longwave radiation, wind speed, air temperature, relative humidity) and parameters of the snow patch surface, roughness, albedo and moisture content within the debris. A detailed description of the DEB model can be found in a study by Reid and Brock. The melting rate is computed through the heat transmission value at the boundary surface between the snow and debris, often assuming that the snow is at the melting point:

$$M={\displaystyle \frac{G_i{∆}_t}{p_i{L}_f}}$$

where G_i—the downward conductive heat flux at the bottom boundary of debris is calculated using the following formula:

$$G_i=k_d\left({\displaystyle \frac{d{T}_d}{dz}}\right)$$

3.2.4. The Snow Melting According to Kuzmin Model

The snow melting model published in 1961 [17] was reviewed. The formulae for the model were derived by the author based on the heat balance equation, utilizing correlations between daily variations in air temperature and radiative influx, as well as dependencies between absolute humidity and air temperature. Snow melting is calculated separately for daytime and nighttime hours because the snow cover receives heat due to radiation only during daylight hours. At night, snow melting significantly diminishes or ceases entirely due to the absence of heat from radiation.

Day melt:

$$\begin{gathered} M_d=3.1\beta \left({\theta }_{max}-{\theta }_{ave}\right)+0.675\left[C_N\left({\theta }_d+45\right)-60\right]+ \\ 0.83\left(1+0.54{\mathsf{\upsilon }}_d\right)\left({\theta }_d-0.65\right)+0.006S{\theta }_n \end{gathered}$$

Night melt:

$$M_n=0.83\left(1+0.54{\mathsf{\upsilon }}_n\right)\left({\theta }_n-0.65\right)+0.675\left[C_N\left({\theta }_n+45\right)-60\right]$$

where C_N—coefficient accounting for cloudiness, calculated using the following formula:

$$C_N=1+0.24N_l+0.12\left(N_t-N_l\right)$$

The snow melting coefficient (β) has a value of 1 prior to the formation of the debris layer and, subsequently, according to the growth of the debris layer thickness.

4. Results and Discussion

It is assumed that a difference of ±10% between factual data in melting volumes and data gathered through modeling is negligible, as the factual snow patch melting data have an accuracy that is equal to the difference.

4.1. ETI

Calculations derived using this model gave the best result (Figure 6). The debris layer thickness is the parameter that has the greatest impact on the melting rate. A significant difference between the calculated and factual data was identified at the onset and termination of the melting period. Several months were characterized by such a difference, reaching 2.6-times (April 2020, 2021). This difference is related to debris layer thickness, which was higher than usual in these years (Figure 4) and decelerated natural melting. Overvaluation of melting volume by the models can be related to the area of the snow dump that is used for calculation. The area remained unchanged throughout 2020 and 2021, but the quantity of snow transported to the snow dump was lower. However, April is the month when snow melting starts and the factual melting volume is not significant (5–6% from total volume per season). So, the derived discrepancies are compensated by the good results observed during the main snow melting period when the melting volumes are large and reach more than 50% of the annual melting volume (May, June, July occasionally). As a result, this model gives acceptable values of melting volumes per season: 2018—1%; 2019—−12%; 2020—−9%; 2021—15%; 2022—32%.

The best result for this model was obtained in the 2018 season, when the snow dump volume was maximal, 1000 thous. m³. During the other seasons, the snow volumes were less than 400 (thous. m³), which led to the model calculations exceeding the actual values at the beginning of melting (April and May) while underestimating them towards the end of melting, almost in all cases. According to the modeling results, the snow patch should have been completely melted away in both 2021 and 2022, but, in reality, it only melted away fully in 2022.

4.2. DETI

In our case, the parameters lag_T and lag_I added to the ETI formula proposed by Pellicciotti et al. [14] did not have a noticeable effect on the results. The values calculated by these models differed by 0.1–0.2% for all months. This difference is negligible compared to the annual melting volumes. Annual differences between the calculated and factual volumes in water closely agreed with the ETI (Figure 6) and were as follows: 2018—1%; 2019—−11%; 2020—−9%; 2021—15%; 2022—31%. The following values were taken from the study of [15] for modeling: lag_T, lag_I, TF and SRF.

4.3. DEB

The energy-balance model based on the calculation of the energy in the snow patch core significantly exceeded the values of snow melting volumes for several months. The temperature and thickness of the debris layer noticeably affect the final result during the calculation Gi using this model. Only 4 out of 33 monthly calculations gave a lower volume of melting snow than the factual ones (Figure 6). The rest had exceedances of 1–6-times. The annual values were also strongly exceeded: 2018—80%; 2019—115%; 2020—50%; 2021—48%; 2022—335%.

Several factors can contribute to such a significant overestimation of the melting volume values: small size of the snow patch; high air temperatures; severe requirements for debris temperature measurement that are difficult to meet.

4.4. The Model of Kuzmin

The θ_max and θ_ave parameters from the model equation are the most significant for obtaining the results. The computed values for the start of the melting season (April) exceeded the factual ones by 2-times. One can suppose that it is due to the debris layer absence on the snow patch surface in April. Therefore, we use the value 1 for the parameter β during this period, which is typical for natural snow cover. Additional albedo observations could improve the coefficient value for this period.

A distinguishing feature of this model is its tendency to reduce monthly melting volumes post-May. It is the most noticeable for the August–September period (Figure 6). The results of calculations have a significant value divergence in a range from 0.0- to 3.6-times for single months. However, the factual melting volumes are not high at the end of the warm period, similarly to the ETI model, and lowering these volumes does not contribute noticeably to the total volume of melted snow. Annual divergences from the factual values were as follows: 2018—−11%; 2019—−19%; 2020—−2%; 2021—−10%; 2022—−43%.

Over a period of snow dump melting that lasts for 7 months, the maximal melting occurs in May–June until the debris layer thickness reaches its critical value. All the models prove this, except DEB. Our investigation showed that melting processes slow down once the debris layer achieves a critical thickness value of 10 (cm). A similar result was also obtained by other researchers [18]. The exception occurred in 2021 when the peak of melting was observed in July. This may be related to unusually high air temperatures during the month. The observed average air temperature for the month was 20.3 (°C), which is 4.4 (°C) above the long-term average annual value of 15.9 (°C).

A comparison of monthly water losses showed the result of the DEB model to be the worst (Figure 6). Calculations using all models gave the worst result for the year 2022 compared to other years. In our opinion, the main reason is the debris layer thickness, which was lower than the critical value of 10 cm and changed in a range of 1–8 (cm) during the entire melting period (Figure 4).

None of the selected melt models were designed specifically for anthropogenic snow patches. However, a comparison between factual and calculated monthly water losses over a 5-year observation period (Figure 6) showed the applicability of these models with specified accuracy. The best results were obtained using the DETI and ETI methods. The closest to factual values were data obtained in 2018, when the snow volume in the snow dump reached 1000 (thous. m³). It was the maximal volume observed for this snow dump. It seems probable that the higher the initial snow volume on the dump at the start of the melting period, the closer the calculated values will be to the factual ones.

The lowering of melting volumes is observed for all models, except DEB, toward the end of the melting period (September–October). It is related to the growth of debris layer thickness that is used for calculations. This parameter is always higher than the critical 10 cm.

Analysis of factual data enabled the identification of the principal parameters influencing the melting volume (W) of anthropogenic snow patches. In a first approximation, the following parameters were highlighted: the snow dump base area (S), debris layer thickness (H), air temperature (T) and precipitation quantity (P). Changes in these parameters significantly influenced the calculated snowmelt volume. The contribution of other parameters (Table 3) is noticeably lower.

Observational data collected at the anthropogenic snow patch served as the basis for developing a characteristic melting model. Data collected during the period 2018–2021 were utilized for the development of the model. The data from 2022 were reserved for verifying the model’s accuracy. Primary analyses entailed applying the Pearson criterion to evaluate the degree of association between paired parameters (

Table 4. Correlation coefficients between the chosen parameters (excludes cases pairwise).

R	W	S	H	T	P
W (melting volume)	1.0
S (snow dump base square)	0.73	1.0
H (debris layer thickness)	−0.65	−0.81	1.0
T (average air temperature)	0.08	−0.24	0.29	1.0
P (precipitation quantity)	−0.18	−0.38	0.32	0.07	1.0

). Significant correlations were found between W and S, W and H, S and H.

A high correlation coefficient alone does not guarantee that the model accurately represents the data. Therefore, a visual revision was carried out, which validated the correspondence between the datasets (Figure 7).

We found a linear relationship between the data, using the linear regression method. The factual melting volume value (W) was taken as the dependent variable, and we increased the quantity of predictors per cycle (

Table 5. Models with different predictor quantities and associated correlation coefficients.

Model	Correlation Coefficient	Predictors Quantity	Adjusted R-Squared
W from S	0.74	1	0.5299
W from S, H	0.77	2	0.5502
W from S, H, T	0.80	3	0.5993
W from S, H, T, P	0.81	4	0.5958

). To compare models with different numbers of predictors, we used the adjusted R-squared, which allows us to assess the relevance of the added predictor to the previously available data.

As the number of added predictors was higher, the correlation coefficient increased, while the adjusted R-squared after adding P slightly decreased (Table 5). All models gave the coefficient, showing strong correlation, but we reviewed the differences in melting described by models W from S, H and W from S, H, T, P because the divergence in the calculated values was negligible. The choice of these models was made because the first combines three closely related parameters, and the second one combines all the parameters affecting melting.

The linear regression equation for W from S, H is given by:

W = k + a × S − b × H

For W from S, H, T, P:

W = k + a × S − b × H + c × T + d × P

Coefficients are listed in

Table 6. Coefficients of linear regression.

Model	Coefficients of Linear Regression
	k	a	b	c	d
W from S, H	30,205.99 ± 27,210.15	0.88 ± 0.49	−215,320.89 ± 147,591.03	–	–
W from S, H, T, P	4000.57 ± 28,990.38	1.09 ± 0.48	−216,743.27 ± 139,907.83	1290.78 ± 642.33	84.35 ± 94.14

.

Figure 8 shows a comparison of the computed and factual data. Both models give satisfactory results. The largest divergence in computed results relates to the onset of melting. Significant divergence was observed for the end of the melting periods in 2019 and 2022. During these seasons, the snow patches completely melted by the start of the new snow storage period.

The difference in annual melting volumes derived from the models for the years 2018–2021 was in the ±10% range, which is consistent with the derived factual data accuracy. For the 2022 season, the difference between the factual and modeled data by W from S, H, T, P melting volumes was 12%, by W from S, H—20%. As the data array increases, the calculation accuracy will grow.

Estimation of the three best models by W from S, H, T, P, by W from S, H and ETI for all studied periods of observation from 2018 to 2022 was implemented using the mean percentage error (MPE):

$$MPE={\displaystyle \frac{1}{n}}·\sum _{i=1}^n\left|{\displaystyle \frac{x_i–x_t}{x_i}}\right|·100\%$$

where x_i—result of i-th single measurement; x_t—predicted value; n—quantity of measurements in sample.

A set of 33 values (n) was derived for each model; values with errors greater than 100% were treated as outliers and not included in the calculations. The values related to the beginning and end of the melting period were considered as outliers. Those were October 2019 and September 2022, when the factual melting volume and the values for April in the 2020 and 2021 years were minimal (2500 and 4000 cubic meters, respectively). The result is presented in

Table 7. Mean percentage error.

Model	W from S, H	W from S, H, T, P	ETI
$MPE$	16	10	28
n	30	31	31

.

Despite the limited incoming data for melting volume predictions, the current level of accuracy is deemed acceptable for applying both models to the needs of city services. This will allow city services to plan snow dump territory cleaning and determine the necessity of snow mass breakage in cases where the expected melting volume is less than the calculated snow patch volume at the start of the melting period.

5. Conclusions

Observations revealed the occurrence of anthropogenic perennial snow patches in regions where natural snow patches and glaciers do not exist. These snow patches form from snow masses that accumulate and are stored at snow dumps following urban area clearing. Waste and sand contained in the snow removed from urbanized territories contribute to anthropogenic snow patch conservation by forming a protective layer on the snow patch surface that prevents snow melting. As the debris layer thickened during the snow melting and reached a critical thickness of 10 (cm) and higher, this facilitated the formation of perennial snow patches in the snow dump territory. Usually, such debris layer thicknesses are observed at the snow dump between late June and early July, after which the factual snow melting rate decreases.

The construction of 3D snow dump models based on aerial surveys enabled us to obtain the morphological characteristics that serve as the basis for monitoring the chronology of snow accumulation and melting. For the first time, problems related to monitoring changes in snow volumes at dumps using remote sensing methods have been solved. This technique provides an alternative method for the evaluation of snow volumes removed from urbanized areas.

Various snow melting models, differing in input parameters, were reviewed. The ETI and DETI models were found to give good results for the evaluation of the total annual melting. However, the critical point is the debris layer thickness. If this parameter does not reach a value of 10 (cm) by the end of June, models show the snow patches to be melted away completely.

The best results were obtained for the snow patch with a volume of 1000 (thous. m³). These models can be applied to snow patches with smaller volumes, but one should expect a decrease in the accuracy of the final results. It is supposed that the method of Kuzmin [17] can be also applied but after correcting the empirical coefficient that will correspond to the requirements of the anthropogenic snow patch melting calculation. We concluded that the DEB model is unsuitable for calculating melting volumes in Sakhalin’s conditions because significant of these volumes.

The ETI model [14] is recommended for the initial stage of melting evaluation when factual observation data are absent. The primary advantage of this model lies in its reduced data requirements. After collecting the factual data array, it is recommended to develop an empirical model with the same predictors according to the approach offered in this study. Such a model would describe the process of snow patches melting more accurately by accounting for local environmental conditions. For example, the melting of two snow patches closely located within one valley was reviewed in one paper [19], and the PDD model gave a difference in the ablation rate in a range of 38–46%. The empirical model calibrated by the factual data array allowed us to take into account the local environmental properties that may appear to us not to be apparent in terms of affecting the melting rate.

The derived results demonstrate the potential of scientific approaches to mitigate the engineering and ecological impacts on territories affected by snow dumps.

Yuzhno-Sakhalinsk city, as well as municipalities with similar snow disposal methods, should conduct a feasibility assessment to determine which action is environmentally responsible, economically reasonable and does not violate Russian regulations when processing the snow dumps.