# Modelling of Surface Runoff on the Yamal Peninsula, Russia, Using ERA5 Reanalysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}with the length from south to north 750 km and the width 140–240 km [1]. It extends along the longitudes 67–73° E between the Arctic Circle (66.56° N) and the latitude 73° N (Figure 1). Despite the severe climate, fragile forestless tundra landscape and deep permafrost, this land is the territory of active industrial development as it contains several rich fields of natural condensed gas and oil. The main reason is that the world energy budget cannot be closed without this source of hydro-carbonates [2,3,4,5,6].

^{2}[7,8,9].

^{2}here [10]. Therefore, the natural environment or constructions can be potentially damaged by gully erosion and the cost of such damage is high. The potential of gully erosion can be estimated with the existing models [10,11,12,13,14], but all these models require the estimates of the surface runoff. In the situation of a nearly complete absence of measurements of the surface runoff, the only way to obtain such information for the entire Yamal peninsula is the hydrological modelling on the base of meteorological data.

## 2. Materials and Methods

#### 2.1. Climatic and Hydrological Characteristics of Yamal

#### 2.1.1. Climatic Characteristics

#### 2.1.2. Hydrological Characteristic

^{2}occurs 4–5 days after the beginning of snow thaw. The surface runoff during the summer rains with low intensity can be negligible. After a few days with low intensity rains, the rain with 10–20 mm daily depth often follows. Such rain produces the surface runoff volume practically equal to the volume of rainfall for a catchment, with the maximum runoff 1–3 h after the maximum rainfall [40].

#### 2.2. Data

#### 2.2.1. Station Data and ERA5 Reanalysis

#### 2.2.2. Hydrological Model Description

#### The Period of Snow Thaw

_{j}and t

_{j+}

_{1}(at time t

_{j+}

_{1/2}). Here index “s” means “snow”, index “w”–“water”, “w_in_s”–water in snow, “w_to_s” and “s_to_w”–exchange by water and snow in the snow pack.

_{sm}:

_{j}= 0

#### The Period of Summer Rains

_{fill}and evaporated from them during the periods between rainfalls. The algorithm of calculating the losses with the formula of Popov [48] is as follows:

_{fill}exceed its maximum value H

_{f}

_{max}, the excess form the surface runoff.

#### 2.2.3. The Model Calibration

_{sm}was calibrated upon the measurements of the spring periods of 1992–1993, when both snow pack depth distribution and runoff were measured [8]. For k

_{sm}= 1.25 × 10

^{−4}the measured and calculated runoff depths were quite similar (Figure 6).

_{wc}was taken equal to 0.163 after Vinogradov [45] and the coefficient of water freezing k

_{f}was taken equal to 1.85 × 10

^{−5}after Komarov [44]. The error of estimate of daily runoff (in terms of standard deviation σ

_{E}is about ±10 mm, this measure of an error will be used further in model sensitivity analysis.

## 3. Results

#### 3.1. Evaluation of ERA5 Reanalysis Quality

#### 3.1.1. Surface Air Temperature

#### 3.1.2. Precipitation

#### 3.1.3. Snow Cover

#### 3.2. Model Sensitivity Analysis

#### 3.2.1. Snow Thaw Period

_{s}, maximum daily runoff depth X

_{s_max}and by the parameters of daily runoff probability functions. The calculations of these characteristics according to Equations (1)–(17) are controlled by snow pack depth (water equivalent) at the beginning of thaw period H

_{s}, precipitation P, air temperature T, evaporation E and model coefficients of water content in snow k

_{wc}, of water freezing k

_{f}and melt coefficient k

_{sm}. Additionally, the spatial distribution of snow pack depth is controlled by the parameters of gamma-distribution (Equation (18)) α and β (Table 1). The estimates of sensitivity of model output to temporal variation of these characteristics (in terms of coefficient of variation C

_{v}= standard deviation/mean) were performed for the node of ERA5 70.25 N and 68.25 E and for the period 1986–2019.

#### The Input Characteristics Variability

_{sa}is equal to the snow water equivalent at the beginning of thaw period H

_{s}plus precipitation P and minus evaporation E during this period. The mean error of this budget σ

_{M}is 8.7 mm with σ

_{ER}= 2.4 mm. Therefore, the temporal variability of input H

_{s}is directly transformed into the variability of output X

_{sa}with nearly the same C

_{v}. The variability of input characteristics, such as water content in snow and air temperature, changes the daily runoff, the shape of hydrograph, the maximum daily runoff X

_{s_max}and the date when it occurs.

_{s}was varied within the range 10–350 mm (see Table 1). The maximum daily runoff X

_{s_max}in general increases with input H

_{s}. When H

_{s}is less than 50 mm, X

_{s_max}increases with H

_{s}nearly linearly with the coefficient 0.46. When H

_{s}is more than 50 mm, the rate of increase of in X

_{s_max}decreases, and the coefficient of regression is 0.14: the model dampens the maximum daily runoff. The variability Cv of the maximum daily runoff X

_{s_max}is related to variability of input H

_{s}in even more complicated manner. When C

_{v}of H

_{s}and X

_{sa}is less than 0.2, temporal variability of X

_{s_max}is nearly constant and vary in the range 0.23–0.3. This additional variability is produced by the differences in air temperature regimen during the snow thaw period in different years. At higher C

_{v}of H

_{s}and X

_{sa}the model dampens the variability of maximum daily runoff, C

_{v}of which decreases nonlinearly from 100 to 60–65% of the variability of input H

_{s}(Figure 13). The timing of this maximum can vary significantly, shifting in the range of 0–16 days in different years mostly due to differences in air temperature regimen during the snow thaw period.

_{s}is well approximated by the exponent with correlation R in the range 0.97–1.0

_{s_max}variability. The module of parameter B, which shows the rate of exponential decrease of X

_{s}duration, rapidly increases with an increase of X

_{s_max}variability (Figure 14).

_{s_max}values. As expected, in the conditions of lower air temperatures, the maximum of daily runoff shifted to later dates (Figure 15). With the increase of T the maximum of daily runoff shifted to earlier dates. Its value varies from year to year, but the mean is higher than in initial conditions (Figure 16). X

_{s_max}decreases with an increase in T. When the temperatures increased above the “natural”, the values of X

_{s_max}are nearly stable with some trend to increase with increasing T. The mean duration of the snow thaw period changes with the air temperature in the opposite direction to the daily runoff maximum (Figure 16).

#### The Model Coefficients Variability

_{wc}, of water freezing k

_{f}, of melt coefficient, and of the parameters of gamma-distribution α and β on the total surface runoff during the snow thaw period is negligible due to the model conservativeness. Therefore, only variability of X

_{s_max}, A, and B is affected by changes in these coefficients.

_{sm}was changed in the range 3.5 × 10

^{−5}~2.35 × 10

^{−4}. To this rather broad range corresponds the range of X

_{s_max}36–64 mm, so calculations with the model dampen the C

_{v}of k

_{sm}= 0.46 to C

_{v}of X

_{s_max}= 0.16. The variability C

_{v}of exponential distribution parameters A and B is also dampened by the model to 0.22.

_{s_max}can vary significantly, shifting in the range of 0–16 days for different years, mostly due to differences in air temperature regimen during the snow thaw period. There are two main varieties of these regimes: a gradual rise of air temperature, as in 1993, and several maximums of daily temperatures, as in 1986. These two modes correspond to two types of shifting the date of X

_{s_max}in response to increase of k

_{sm}. The first type is a gradual shift of the date of X

_{s_max}to the earlier time; the second one is an abrupt shift of this date for several days, also to the earlier time (Figure 17).

_{f}was changed in the range 1.85 × 10

^{−6}~−3.7 × 10

^{−5}. To this rather broad range corresponds the narrow range of X

_{s_max}46.7–49.9 mm, so calculations with the model dampened the C

_{v}of k

_{f}= 0.56 to C

_{v}of X

_{s_max}= 0.02. The variability of parameters dropped to almost zero. In the calculation, the timing of X

_{s_max}was stable for 28 years of 35. It changed within 1–4 days with displacement of X

_{s}_

_{max}to the later date in the years with the first type of temperature change regimen. In the years with the second type of temperature changes, an abrupt shift for 6–16 days to the later date can occur.

_{wc}. Its value was varied in the range 0.0163–0.326. The range of calculated X

_{s_max}was 45.6–54.1 mm, the range of A—20–24 days, and of −B—0.07–0.09. In the calculation, the timing of X

_{s_max}was stable for 25 years of 35, and in other years, the date of the maximum changed in the same way as with the variations of the previous coefficient.

_{s_max}, A, and B, the standard deviation σ

_{γ}of gamma-distribution was changed in the calculation from 0.1 to 0.9. This numerical experiment showed the changes of X

_{s_max}within the range 36.8–52.1 mm, of A—17–20 days, and of B from −0.06 to −0.1. In the calculations, the timing of X

_{s_max}was stable for 25 years of 35, and in other years, the date of maximum changed by 1–8 days, shifting to the earlier dates with σ

_{γ}increase.

#### 3.2.2. The Period of Summer Rains

#### 3.3. Spatial Distribution of the Hydrological Characteristics on the Yamal Peninsula

#### 3.3.1. Mean Maximum Depth of Snow Cover and Surface Runoff Depth during the Snow Thaw Period

_{s}(Figure 20) is rather uniform, with the maximum value of 210 mm of water equivalent in the central Yamal peninsula, and with the general trend to decrease both to the south and to the north. The bands of low values of H

_{s}along the shores of the Ob Gulf and of the Kara Sea, as well as around large lakes, are artefacts of all reanalyses, where H

_{s}values are taken equal to zero in the open water (see Table S1). These bands were excluded from further analysis.

_{v}and skewness C

_{s}were calculated only for annual sequences without trend.

_{v}changes are within 0.1–0.2 except for the areas south of the Baidaratskaya Bay. C

_{s}spatial pattern is more complicated: four bands of high and low skewness values are alternating in latitudinal direction, showing probability distributions of H

_{s}from highly asymmetrical to nearly symmetrical normal functions.

_{sa}is equal to the water equivalent in snow at the beginning of thaw period H

_{s}plus precipitation P and minus evaporation E during this period. Therefore, the spatial distribution of mean annual runoff during the snow thaw period X

_{sa}and its statistical characteristics are similar to those of H

_{s}(Figure 22). Mean annual X

_{sa}spatial pattern is rather uniform, with the maximum value of 250 mm at the central Yamal, with a general trend to decrease both to the south and to the north. C

_{v}changes within 0.1–0.15 except of the areas south of the Baidaratskaya Bay. The skewness is close to zero, changing in the range −0.5~0.5 and showing nearly symmetrical normal distributions of X

_{sa}.

#### 3.3.2. Daily Surface Runoff Depth During the Snow Thaw Period

_{s_max}and its statistics are in general similar to those of mean annual values (Figure 23). The pattern is also rather uniform, with the maximum value of 50–55 mm in the central Yamal peninsula, and with a general trend to decrease both to the south and to the north. Temporal variability of X

_{s_max}is nearly the same for the entire Yamal peninsula, and C

_{v}changes within 0.2–0.25, except for the areas south of the Baidaratskaya Bay. The spatial pattern of skewness is more complicated. 5–6 bands of high and low C

_{s}values are alternating in the south-north direction, showing probability distributions of X

_{s_max}from highly asymmetrical to nearly symmetrical one.

_{d}, is well approximated with Equation (20). The parameter A reflects the duration of snow thaw period, and parameter B shows the rate of exponential decrease of X

_{s}duration.

#### 3.3.3. Mean Surface Runoff Depth of the Summer Rain Period

_{ra}are not significant (Student’s p is more than 20% for all nodes of ERA-5) for both periods under investigations 1985–2019 and 1985–2013; the latter period is used further. X

_{ra}decreases from south to north of the Yamal peninsula from 250 to 120 mm, and variability of its values (C

_{v}) in general increases in the same direction from 0.2 to 0.3 (Figure 25). The skewness shows more complicated spatial pattern. Four latitudinal bands of high and low C

_{s}values alternate in the north-south direction, showing probability distributions of annual surface runoff X

_{r}from highly asymmetrical to nearly symmetrical.

_{r_max}for the period of summer rains show in general the same spatial pattern. The mean maximum decreases from south to north from 24 to 15 mm. Variability of this maximum is greater than that of the mean X

_{ra}values, increasing in the same direction from 0.24 to 0.5 (Figure 26). The skewness also shows four alternating bands of high and low C

_{s}values.

_{r}duration. The module of parameter B increases from south to north from 0.25 to 0.35 (Figure 27).

## 4. Discussion

#### 4.1. Statistical Characteristics of the Sequences with the Trends

_{v}and of skewness C

_{s}averaged with moving 10-year intervals, is subjected to longwave temporal changes (Figure 28). Then, for different time intervals, linear trends are different.

#### 4.2. Types of Probability Density Functions Used for Different Characteristics of Surface Runoff

_{s}= 2C

_{v}. For the Yamal peninsula over 80% of empirical distributions of annual snow pack depth fit this ratio within only 20% confident intervals for C

_{v}and C

_{s}. The spatial distribution of the C

_{s}/C

_{v}ratio demonstrates a regular pattern with high values of this ratio in the northern and central parts of the peninsula (very positively asymmetric functions) and with low values characteristic of the gamma function with median asymmetry and for the normal distribution (Figure 29). Distributions with skewness less than 0.17 should be described with other types of probability distribution functions, but such C

_{s}values are rare. The main types of curves described with Equation (21) within Cv-Cs box, characteristic for Yamal, are shown in Figure 30.

_{s}/C

_{v}ratios for the sequences of mean and maximum surface runoff during the snow thaw period are in general similar to those of annual maximum snow pack depth H

_{s}(see Figure 29), with greater spatial variability of this ratio.

_{d_min}is negligibly small and parameter n = 1, Equation (23) is similar to Equation (22).

#### 4.3. Effects of Errors in ERA5 Data on the Results of Runoff Calculations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{s}during the years 1985–2019 with trend; during the years 1985–2019 with linear trend excluded; during the years 1985–2013 with linear trend excluded. The mean values differ slightly for the last two tests only at the southern part of the peninsula. Variability for first two tests varies within 5% for the main part of the peninsula, where Student’s p is more than 20%. At the southern part of the peninsula the C

_{v}values of de-trended sequence are 10–15% lower (Figure A1, left). The C

_{v}values of second two tests differ more significantly, especially at the central part of the peninsula (Figure A1, right). Variability of de-trended sequences during the years 1985–2013 is lowermost due to exclusion both of linear trend and influence of long temporal waves, therefore the statistics of this period were described in the Results section. Despite rather significant differences in C

_{v}values for these three tests, this difference is still mostly within Student’s 10% confidence interval for standard deviation (Figure A2). The maximum differences show the skewness, mostly at the southern part of the peninsula. Here spatial distributions of the ratios of Cs values for different tests show great patchiness and significant magnitude. Despite rather significant differences in Cs values for these three tests, this difference is still mostly within 10% confidence interval according to T-test (Figure A3). For first two tests, 82% of Cs values of de-trended sequence during the years 1985–2019 are within the confident limits of this sequence with the trend. For the last two tests, 88% of skewness values for the shorter sequence of the years 1985–2013 are within the confident limits of de-trended sequence of the years 1985–2019.

**Figure A1.**Ratios of C

_{v}values for different types of sequences of annual maximum snow pack depth. The

**left**is C

_{v}for the years 1985–2019 with linear trend excluded divided on C

_{v}for the years 1985–2019 with trend; the

**right**is C

_{v}for the years 1985–2013 divided on C

_{v}for the years 1985–2019, both sequences with the linear trend excluded.

**Figure A2.**Student’s 10% confidence interval for standard deviation (shown by arrows) for the sequences of annual maximum snow pack depth Hs during the years 1985–2019 with trend (

**A**); during the years 1985–2019 with linear trend excluded (

**B**) and during the years 1985–2013 with linear trend excluded (

**C**). The blue lines show the variation in standard deviation of sequences.

**Figure A3.**10% confidence interval for skewness (according to 2-sigma T-test, shown by arrows) for the sequences of annual maximum snow pack depth H

_{s}during the years 1985–2019 with trend (

**A**); during the years 1985–2019 with linear trend excluded (

**B**) and during the years 1985–2013 with linear trend excluded (

**C**). The blue lines show the variation in skewness of sequences.

## References

- Dobrinski, L.N. (Ed.) Nature of Yamal (Priroda Yamala); Nauka: Ekaterinburg, Russia, 1995; p. 435. (In Russian) [Google Scholar]
- Litvinenko, V. The Role of Hydrocarbons in the Global Energy Agenda: The Focus on Liquefied Natural Gas. Resources
**2020**, 9, 59. [Google Scholar] [CrossRef] - Paltsev, S. Scenarios for Russia’s natural gas exports to 2050. Energy Econ.
**2014**, 42, 262–270. [Google Scholar] [CrossRef] - Henderson, J.; Yermakov, V. Russian LNG: Becoming a Global Force. Working Paper; Oxford Institute for Energy Studies: Oxford, UK, 2019; p. 37. [Google Scholar]
- IGU. Global Gas Report 2019; International Gas Union: Barcelona, Spain, 2020. Available online: https://media-publications.bcg.com/SNAM-2019-GGR.pdf (accessed on 6 June 2020).
- IGU. World LNG Report 2020; International Gas Union: Barcelona, Spain, 2020. Available online: https://www.igu.org/sites/default/files/node-document-field_file/2020%20World%20LNG%20Report.pdf (accessed on 6 June 2020).
- Novikov, S.M. Hydrology of the Wetlands of the Permafrost Zone of Western Siberia (Gidrologiya Zabolochennykh Territoriy Zony Mnogoletney Merzloty Zapadnoy Sibiri); VVM Publicaiton House: St. Petersburg, Russia, 2009; p. 536. (In Russian) [Google Scholar]
- Bobrovitskaya, N.N.; Baranov, A.V.; Vasilenko, N.N.; Zubkova, K.M. Hydrological Conditions. In Erosion Processes at the Central Yamal (Erozionnyye Protsessy Tsentral’Nogo Yamala); Sidorchuk, A., Baranov, A., Eds.; RNII KPN: St. Petersburg, Russia, 1999; pp. 90–105. (In Russian) [Google Scholar]
- Sidorchuk, A. Gully erosion in the cold environment: Risks and hazards. Adv. Environ. Res.
**2015**, 44, 139–192. [Google Scholar] - Sidorchuk, A. The potential of gully erosion on the Yamal peninsula, West Siberia. Sustainability
**2020**, 12, 260. [Google Scholar] [CrossRef][Green Version] - Patton, P.C.; Schumm, S.A. Gully erosion, northwestern Colorado: A threshold phenomenon. Geology
**1975**, 3, 83–90. [Google Scholar] [CrossRef] - Vandaele, K.; Poesen, J.; Govers, G.; van Wesemael, B. Geomorphic threshold conditions for ephemeral gully incision. Geomorphology
**1996**, 16, 161–173. [Google Scholar] [CrossRef] - Garrett, K.K.; Wohl, E.E. Climate-invariant area–slope relations in channel heads initiated by surface runoff. Earth Surf. Process. Landforms
**2017**, 42, 1745–1751. [Google Scholar] [CrossRef] - Sidorchuk, A. Dynamic and static models of gully erosion. Catena
**1999**, 37, 401–414. [Google Scholar] [CrossRef] - Sagintayev, Z.; Sultan, M.; Khan, S.D.; Khan, S.A.; Mahmood, K.; Yan, E.; Milewski, A.; Marsala, P. A remote sensing contribution to hydrologic modelling in arid and inaccessible watersheds, Pishin Lora basin, Pakistan. Hydrol. Process.
**2012**, 26, 85–99. [Google Scholar] [CrossRef] - Cole, S.J.; Moore, R.J. Distributed hydrological modelling using weather radar in gauged and ungauged basins. Adv. Water Resour.
**2009**, 32, 1107–1120. [Google Scholar] [CrossRef][Green Version] - Lindsay, R.; Wensnahan, M.; Schweiger, A.; Zhang, J. Evaluation of seven different atmospheric reanalysis products in the Arctic. J. Clim.
**2014**, 27, 2588–2606. [Google Scholar] [CrossRef][Green Version] - Liu, Z.; Liu, Y.; Wang, S.; Yang, X.; Wang, L.; Baig, M.H.A.; Chi, W.; Wang, Z. Evaluation of spatial and temporal performances of ERA-Interim precipitation and temperature in mainland China. J. Clim.
**2018**, 31, 4347–4365. [Google Scholar] [CrossRef] - Lader, R.; Bhatt, U.S.; Walsh, J.E.; Rupp, T.S.; Bieniek, P.A. Two-meter temperature and precipitation from atmospheric reanalysis evaluated for Alaska. J. Appl. Meteorol. Climatol.
**2016**, 55, 901–922. [Google Scholar] [CrossRef] - Timmermans, B.; Wehner, M.; Cooley, D.; O’Brien, T.; Krishnan, H. An evaluation of the consistency of extremes in gridded precipitation data sets. Clim. Dyn.
**2019**, 52, 6651–6670. [Google Scholar] [CrossRef][Green Version] - Albergel, C.; Munier, S.; Bocher, A.; Bonan, B.; Zheng, Y.; Draper, C.; Leroux, D.J.; Calvet, J.-C. LDAS-Monde Sequential Assimilation of Satellite Derived Observations Applied to the Contiguous US: An ERA5 Driven Reanalysis of the Land Surface Variables. Remote Sens.
**2018**, 10, 1627. [Google Scholar] [CrossRef][Green Version] - Gampe, D.; Ludwig, R. Evaluation of gridded precipitation data products for hydrological applications in complex topography. Hydrology
**2017**, 4, 53. [Google Scholar] [CrossRef][Green Version] - Essou, G.R.; Brissette, F.; Lucas-Picher, P. The use of reanalyses and gridded observations as weather input data for a hydrological model: Comparison of performances of simulated river flows based on the density of weather stations. J. Hydrometeorol.
**2017**, 18, 497–513. [Google Scholar] [CrossRef] - Raimonet, M.; Oudin, L.; Thieu, V.; Silvestre, M.; Vautard, R.; Rabouille, C.; Le Moigne, P. Evaluation of gridded meteorological datasets for hydrological modelling. J. Hydrometeorol.
**2017**, 18, 3027–3041. [Google Scholar] [CrossRef] - Beck, H.E.; Vergopolan, N.; Pan, M.; Levizzani, V.; Van Dijk, A.I.; Weedon, G.P.; Brocca, L.; Pappenberger, F.; Huffman, G.J.; Wood, E.F. Global-Scale Evaluation of 22 Precipitation Datasets Using Gauge Observations and Hydrological Modelling. In Satellite Precipitation Measurement; Springer: Cham, Switzerland, 2020; pp. 625–653. [Google Scholar]
- Mahto, S.S.; Mishra, V. Does ERA-5 outperform other reanalysis products for hydrologic applications in India? J. Geophys. Res. Atmos.
**2019**, 124, 9423–9441. [Google Scholar] [CrossRef] - Nkiaka, E.; Nawaz, N.R.; Lovett, J.C. Evaluating global reanalysis datasets as input for hydrological modelling in the Sudano-Sahel region. Hydrology
**2017**, 4, 13. [Google Scholar] [CrossRef][Green Version] - Fuka, D.R.; Walter, M.T.; MacAlister, C.; Degaetano, A.T.; Steenhuis, T.S.; Easton, Z.M. Using the Climate Forecast System Reanalysis as weather input data for watershed models. Hydrol. Process.
**2014**, 28, 5613–5623. [Google Scholar] [CrossRef] - Essou, G.R.; Sabarly, F.; Lucas-Picher, P.; Brissette, F.; Poulin, A. Can precipitation and temperature from meteorological reanalyses be used for hydrological modelling? J. Hydrometeorol.
**2016**, 17, 1929–1950. [Google Scholar] [CrossRef] - Ayzel, G.; Varentsova, N.; Erina, O.; Sokolov, D.; Kurochkina, L.; Moreydo, V. OpenForecast: The First Open-Source Operational Runoff Forecasting System in Russia. Water
**2019**, 11, 1546. [Google Scholar] [CrossRef][Green Version] - Lauri, H.; Räsänen, T.A.; Kummu, M. Using reanalysis and remotely sensed temperature and precipitation data for hydrological modelling in monsoon climate: Mekong River case study. J. Hydrometeorol.
**2014**, 15, 1532–1545. [Google Scholar] [CrossRef] - Nguyen, T.H.; Masih, I.; Mohamed, Y.A.; Van der Zaag, P. Validating Rainfall-Runoff Modelling Using Satellite-Based and Reanalysis Precipitation Products in the Sre Pok Catchment, the Mekong River Basin. Geosciences
**2018**, 8, 164. [Google Scholar] [CrossRef][Green Version] - Krogh, S.A.; Pomeroy, J.W.; McPhee, J. Physically based mountain hydrological modelling using reanalysis data in Patagonia. J. Hydrometeorol.
**2015**, 16, 172–193. [Google Scholar] [CrossRef][Green Version] - Jing, W.; Song, J.; Zhao, X. Validation of ECMWF Multi-Layer Reanalysis Soil Moisture Based on the OzNet Hydrology Network. Water
**2018**, 10, 1123. [Google Scholar] [CrossRef][Green Version] - Kottek, M.; Grieser, J.; Beck, C.; Rudolf, B.; Rubel, F. World map of the Köppen-Geiger climate classification updated. Meteorol. Z.
**2006**, 15, 259–263. [Google Scholar] [CrossRef] - Vikhamar-Schuler, D.; Hanssen-Bauer, I.; Førland, E.J. Long-Term Climate Trends of the Yamalo-Nenets AO, Russia; Norwegian Meteorological Institute: Oslo, Norway, 2010; pp. 1–51. [Google Scholar]
- Bulygina, O.N.; Veselov, V.M.; Razuvaev, V.N.; Aleksandrova, T.M. Description of the Dataset of Observational Data on Major Meteorological Parameters from Russian Weather Stations. Database State Registration Certificate No. 1 49 2014. Available online: http://meteo.ru/data (accessed on 12 June 2020). (In Russian).
- Vasiliev, A.A.; Gravis, A.G.; Gubarkov, A.A.; Drozdov, D.S.; Korostelev, Y.V.; Malkova, G.V.; Oblogov, G.E.; Ponomareva, O.E.; Sadurtdinov, M.R.; Streletskaya, I.D.; et al. Permafrost degradation: Results of the long-term geocryological monitoring in the western sector of Russian Arctic. Kriosf. Zemli
**2020**, 24, 15–30. (In Russian) [Google Scholar] [CrossRef] - Borodulin, V.V.; Gryazeva, L.I. The results of hydrological studies of the Yamal rivers. Meteorol. Hydrol.
**1993**, 3, 86–94. (In Russian) [Google Scholar] - Sidorchuk, A. Gully Thermoerosion on the Yamal Peninsula. In Geomorphic Hazards; Slaymaker, O., Ed.; Wiley: Chichester, UK, 1996; pp. 141–153. [Google Scholar]
- Hersbach, H.; Dee, D. ERA5 reanalysis is in production. ECMWF Newsl.
**2016**, 147, 7. [Google Scholar] - Rango, A.; Martinec, J. Revisiting the Degree-day Method for Snowmelt Computations. J. Am. Water Resour. Assoc.
**2007**, 31, 657–669. [Google Scholar] [CrossRef] - Pistocchi, A.; Bagli, S.; Callegari, M.; Notarnicola, C.; Mazzoli, P. On the Direct Calculation of Snow Water Balances Using Snow Cover Information. Water
**2017**, 9, 848. [Google Scholar] [CrossRef][Green Version] - Komarov, V.D.; Makarova, T.T.; Sinegub, E.S. Calculation of the hydrograph of floods of small lowland rivers based on thaw intensity data. Proc. Hydrometeorol. Cent. USSR
**1969**, 37, 3–30. (In Russian) [Google Scholar] - Vinogradov, Y.B. Mathematical Modelling of Flow Formation Processes (Matematicheskoye Modelirovaniye Protsessov Formirovaniya Stoka); Gidrometeoizdat: Leningrad, Russia, 1988; p. 312. (In Russian) [Google Scholar]
- Vinogradov, Y.B.; Vinogradova, T.A.; Zhuravlev, S.A.; Zhuravleva, A.D. Mathematical modelling of hydrographs from the unstudied river basins on the Yamal peninsula. Bull. St. Petersburg State Univ.
**2014**, 7, 71–81. (In Russian) [Google Scholar] - Gelfan, A.N. Model of Formation of River Flow during Snowmelt and Rain. In Erosion Processes at the Central Yamal (Erozionnyye Protsessy Tsentral’Nogo Yamala); Sidorchuk, A., Baranov, A., Eds.; RNII KPN: St. Petersburg, Russia, 1999; pp. 205–225. (In Russian) [Google Scholar]
- Popov, Y.G. Analysis of River Flow Formation (Analiz Formirovaniya Stoka Ravninnykh Rek); Gidrometeoizdat: Leningrad, Russia, 1956; p. 131. (In Russian) [Google Scholar]
- Bosilovich, M.L.G.; Chen, J.; Robertson, F.R.; Adler, R.F. Evaluation of global precipitation in reanalyses. J. Appl. Meteorol. Climatol.
**2008**, 47, 2279–2299. [Google Scholar] [CrossRef] - Donat, M.G.; Sillmann, J.; Wild, S.; Alexander, L.V.; Lippmann, T.; Zwiers, F.W. Consistency of temperature and precipitation extremes across various global gridded in situ and reanalysis datasets. J. Clim.
**2014**, 27, 5019–5035. [Google Scholar] [CrossRef] - Recalculation of Coordinates. Available online: https://geobridge.ru/proj#null (accessed on 12 May 2020).
- Sood, A.; Smakhtin, V. Global hydrological models: A review. Hydrol. Sci. J.
**2015**, 60, 549–565. [Google Scholar] [CrossRef] - Her, Y.; Yoo, S.; Cho, J.; Hwang, S.; Jeong, J.; Seong, C. Uncertainty in hydrological analysis of climate change: Multi-parameter vs. multi-GCM ensemble predictions. Sci. Rep.
**2019**, 9, 4974. [Google Scholar] [CrossRef][Green Version] - Gleick, P.H. Water in Crisis: A Guide to the World’s Fresh Water Resources; Oxford University Press: Oxford, UK, 1993; p. 473. [Google Scholar]
- Hurlimann, A.; Wilson, E. Sustainable Urban Water Management under a Changing Climate: The Role of Spatial Planning. Water
**2018**, 10, 546. [Google Scholar] [CrossRef][Green Version] - Versini, P.-A.; Pouget, L.; Mcennis, S.; Custodio, E.; Escaler, I. Climate change impact on water resources availability—Case study of the Llobregat River basin (Spain). Hydrol. Sci. J.
**2016**, 61, 2496–2508. [Google Scholar] [CrossRef] - Bodian, A.; Diop, L.; Panthou, G.; Dacosta, H.; Deme, A.; Dezetter, A.; Ndiaye, P.M.; Diouf, I.; Vischel, T. Recent Trend in Hydroclimatic Conditions in the Senegal River Basin. Water
**2020**, 12, 436. [Google Scholar] [CrossRef][Green Version] - Deng, W.; Song, J.; Bai, H.; He, Y.; Yu, M.; Wang, H.; Cheng, D. Analyzing the Impacts of Climate Variability and Land Surface Changes on the Annual Water–Energy Balance in the Weihe River Basin of China. Water
**2018**, 10, 1792. [Google Scholar] [CrossRef][Green Version] - Krogh, S.A.; Pomeroy, J.W. Impact of future climate and vegetation on the hydrology of an Arctic headwater basin at the tundra–taiga transition. J. Hydrometeorol.
**2019**, 20, 197–215. [Google Scholar] [CrossRef] - Sidorchuk, A.Y.; Matveeva, T.A. Periglacial gully erosion on the east European plain and its recent analog at the Yamal peninsula. Geogr. Environ. Sustain.
**2020**, 13, 183–194. [Google Scholar] [CrossRef][Green Version] - Thompson, S.A. Hydrology for Water Management, 1st ed.; Balkema Publication: Rotterdam, The Netherlands, 1999; p. 380. [Google Scholar]
- Meylan, P.; Favre, A.-C.; Musy, A. Predictive Hydrology: A Frequency Analysis Approach; Taylor & Francis Inc.: Abingdon, UK, 2012; p. 212. [Google Scholar]

**Figure 2.**Mean surface (2 m) air temperature (°C) (

**a**,

**c**) and linear trend (per decade) (

**b**,

**d**) in January (

**top**) and in July (

**bottom**) based on ERA5 Reanalysis for 1985–2019.

**Figure 3.**Averaged seasonal cycle of surface air temperature (2 m) for four meteorological stations.

**Figure 4.**Meteorological stations (

**red dots**) and nearest to them ERA5 reanalysis grid points (

**blue dots**) used in the study. The black squares show the position of State Hydrological Institute measurements in 1985–1997, the star shows the position of State Hydrological Institute and Moscow State University measurements in 1990–1993.

**Figure 6.**The comparison of the surface runoff depth calculated with the model, taking the melt coefficient k

_{sm}= 1.25 × 10

^{−4}and measured daily runoff depth Xs (mm) during snow thaw periods of the years 1992 and 1993 (

**a**) at the headwaters of the Anthropogenic gully on the Yamal peninsula (

**b**). The lower figures show the calculated (blue lines) and measured (red lines) hydrographs for the years 1992 (

**c**) and 1993 (

**d**).

**Figure 7.**2m air temperature at seven stations (

**red**) and at the nearest grid points of ERA5 reanalysis (

**blue**) for the periods of snow thaw (

**a**) and summer rains (

**b**). Boxes indicate the lower and upper quartile. Horizontal line in each box represents the median t2m air temperature. “Whiskers” extending from each box represent the minimum and maximum temperature recorded for each station.

**Figure 8.**Error statistics (ERA5 versus observational data) for daily t2m: root mean square error (RMSE) (

**a**), correlation coefficient (

**b**), the ratio of the standard deviations (STD) of the ERA5 reanalysis and observed values (

**c**) for seven stations and the nearest grid points of ERA5 reanalysis for snow thaw (

**orange**) and summer rains (

**green**) periods.

**Figure 9.**Whisker-box plot (

**left column**) and 95th percentile (

**right column**) of total daily precipitation for seven stations (

**red**) and the nearest grid points of ERA5 reanalysis (

**blue**) for cold (

**a**,

**b**), snow thaw (

**c**,

**d**) and summer rains (

**e**,

**f**) periods. Boxes indicate the lower and upper quartile. Horizontal line in each box represents the median t2m air temperature. Vertical lines extending from each box represent the minimum and maximum temperature recorded for that station.

**Figure 10.**Error statistics (ERA5 versus observational data) for total daily precipitation: root mean square error (RMSE) (

**a**), correlation coefficient (

**b**), the ratio of the standard deviations (STD) of the ERA5 reanalysis and observed values (

**c**) for seven stations and the nearest grid points of ERA5 reanalysis for cold (

**blue**), snow thaw (

**orange**) and summer rains (

**green**) periods.

**Figure 11.**Whisker-box plot of maximum snow height at the end of cold season for seven stations (

**red**) and the nearest grid points of ERA5 reanalysis (

**blue**) (

**a**) and RMSE for maximum snow height for seven stations and the nearest grid points of ERA5 reanalysis (

**b**). Boxes in (

**a**) indicate the lower and upper quartile. Horizontal line in each box represents the median t2m air temperature. Vertical lines extending from each box represent the minimum and maximum temperature recorded for that station.

**Figure 12.**Mean date of maximum snow height at the end of cold season (

**a**) and RMSE (

**b**) for seven stations and the nearest grid points of ERA5 reanalysis.

**Figure 13.**Effect of variability of total surface runoff X

_{sa}during snow thaw period on the variability of the maximum daily runoff X

_{s_max.}

**Figure 14.**Effect of variability of maximum daily surface runoff X

_{s_max}on the parameter A (

**a**) and B (

**b**) of the exponential changes in duration of daily runoff X

_{s}(Equation (20)).

**Figure 15.**Changes in shape of hydrograph of daily runoff during the snow thaw period with variations of daily air temperatures, an example for 1992 year.

**Figure 16.**Changes in mean daily runoff maximum (

**triangles**) and duration of the snow thaw period (

**circles**) with variations of daily air temperatures.

**Figure 17.**The differences in air temperature regimen during the snow thaw period and associated types of respond of timing of maximum X

_{s_max}to an increase of k

_{sm}. For details, see the text.

**Figure 18.**Changes in the duration of the warm period (

**triangles**) and in the mean daily runoff maximum (

**circles**) with variations of daily air temperatures.

**Figure 19.**ERA5 grid and corresponding MSK-1964 coordinates (in km from datum) for the Yamal peninsula.

**Figure 20.**Spatial distributions of mean annual H

_{s}, its temporal variability C

_{v}and skewness C

_{s.}on the Yamal peninsula.

**Figure 21.**Temporal changes of maximum snow pack depth at the end of the winter at the Novy Port station for two periods–1940–2016 and 1985–2016, and the same for the second mentioned interval from ERA5 reanalysis at the nearest grid node.

**Figure 22.**Spatial distributions of mean annual X

_{sa}and its temporal variability C

_{v}and skewness C

_{s}on the Yamal peninsula.

**Figure 23.**Spatial distributions of mean annual maximum of daily surface runoff X

_{s_max}for the period of snow thaw, its temporal variability C

_{v}and skewness C

_{s}on the Yamal peninsula.

**Figure 24.**The relationship between parameter A and duration of snow show period (

**left**) and spatial distributions of parameters A and B in Equation (20).

**Figure 25.**Spatial distributions of mean surface runoff X

_{r}, its temporal variability C

_{v}and skewness C

_{s}for the period of summer rains on the Yamal peninsula.

**Figure 26.**Spatial distributions of daily maximum of surface runoff X

_{r_max}, its temporal variability C

_{v}and skewness C

_{s}for the period of summer rains on the Yamal peninsula

_{.}

**Figure 27.**The relationship between parameter A and duration of summer rains period (left) and spatial distributions of parameters A and B in Equation (20) on the Yamal peninsula.

**Figure 28.**Characteristics of de-trended sequences of snow pack depth at the Novy Port station. See the text for the details.

**Figure 29.**Spatial distribution of C

_{s}/C

_{v}ratios for sequences of annual maximum snow pack depth H

_{s}during the years 1985–2013 with linear trend excluded.

**Figure 30.**Probability density functions (PDF) for typical combinations of C

_{s}and C

_{v}of normalized annual maximum H

_{s}: black line–PDF on measured data; red–PDF calculated with Equation (21). The upper figure shows the position (

**stars**) of these combinations of C

_{s}(

**blue dots**) and C

_{v}(

**red dots**) along the south-north direction (from 66 to 73.5° N). The scatter shows change of the statistics in west-east direction.

**Table 1.**Range of temporal variation of model characteristics used in sensitivity analysis. The number of numerical experiments n = 1 + (Max − Min)/Step.

Model Characteristics, Varied in Sensitivity Analysis | Min | Max | Step | |
---|---|---|---|---|

Input values | Snow depth at the beginning of snow thaw, mm | 10 | 350 | 10 |

Variation of air temperature from reanalysis data, °C | −2 | +2 | 0.5 | |

Model coefficients | melt coefficient k_{sm} mm/°C | 2.5 × 10^{−5} | 2.35 × 10^{−4} | 1 × 10^{−5} |

Coefficient of water freezing k_{f} mm/(°C)^{0}.^{5} | 1.85 × 10^{−6} | 3.7 × 10^{−5} | 1.85 × 10^{−6} | |

Coefficient of water content in snow k_{wc} | 0.0163 | 0.326 | 0.0163 | |

Standard deviation in Equation (18) | 0.1 | 0.9 | 0.1 |

Meteorological Characteristic, Daily Mean | Error in ERA5 | Hydrological Model Sensitivity | |||||
---|---|---|---|---|---|---|---|

Xd_max, | A | B | |||||

Aer (mm) | Rer, % | Aer, Days | Rer (%) | Aer (mm) | Rer (%) | ||

Air temperature during snow thaw period, °C | 0.8/−0.6 | −2/+7 | −4/+14 | 1/−2 | 4/−11 | −0.005/0.008 | −9/14 |

Air temperature during the summer, °C | 1.3/−0.9 | +0.3/−9 | +2/−6 | 11/−9 | 13/−11 | 0/−0.003 | 0/−0.8 |

Maximum depth of snow pack (water equivalent), mm | 30/−60 | +4.4/8.8 | +10/−20 | 2/−5 | 9/−26 | 0.013/−0.035 | 13/−36 |

Rainfall during the summer, mm | 2.6/−1.6 | 0.12/−0.1 | 0.6/−0.4 | <±1 | 0.7/−0.5 | 0.002/−0.001 | 0.6/−0.4 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Matveeva, T.; Sidorchuk, A.
Modelling of Surface Runoff on the Yamal Peninsula, Russia, Using ERA5 Reanalysis. *Water* **2020**, *12*, 2099.
https://doi.org/10.3390/w12082099

**AMA Style**

Matveeva T, Sidorchuk A.
Modelling of Surface Runoff on the Yamal Peninsula, Russia, Using ERA5 Reanalysis. *Water*. 2020; 12(8):2099.
https://doi.org/10.3390/w12082099

**Chicago/Turabian Style**

Matveeva, Tatiana, and Aleksey Sidorchuk.
2020. "Modelling of Surface Runoff on the Yamal Peninsula, Russia, Using ERA5 Reanalysis" *Water* 12, no. 8: 2099.
https://doi.org/10.3390/w12082099