GEOSTATISTICAL DESCRIPTION OF SNOW COVER HETEROGENEITY IN A PHYSICALLY BASED CATCHMENT-SCALE SNOW MODEL

Section
Methods, models and technologies
Keywords: snow melting, river catchment, spatial distribution, physically based model, geostatistics, subgrid variability
(+) Abstract

A method has been developed for geostatistical description of the spatial heterogeneity of snow cover when calculating snow melting using a physically based snow model over the catchment scale (by the example of the catchment area of the Seim River). The average snow depth within the computational grid cell is set according to snow observations at meteorological stations in the region using the ordinary kraging interpolation. An earlier analysis of long-term snow observation data in the Central Black Soil region showed that the empirical variogram of the snow depth can be approximated by a power-law dependence on the distance between the observation points. This made it possible to obtain, based on the method of geostatistical regularization, a simple dependence of the variability of the snow cover depth within each grid cell (subgrid variability) on the ratio of the cell size to the catchment size. Using the model of snow cover formation, the sensitivity of the calculated intensity of snow melting in the catchment area to the detail of the computational grid resolution was estimated. It is shown that the calculated snowmelt both in the entire catchment and within the cells turned out to be almost insensitive to changes in the spatial grid resolution For calculating the hydrograph of snowmelt runoff in the river outlet, the result obtained means the possibility of choosing, when describing snow melting, a coarser grid than the schematization of the catchment area used for calculating overland runoff in physically based distributed models.

(+) About the author(s)

Аlexander N. Gelfan,
Institute for Water Problems, Russian Academy of Sciences, Moscow, Russia; Lomonosov Moscow State University, Moscow, Russia

eLibrary (РИНЦ) SPIN-код: 2193-6327

ORCID ID: 0000-0003-3288-1933

Scopus ID: 6602256614

(+) References

Blöschl G., Grayson R. Spatial observations and interpolation. In Grayson R., Blöschl G. (Eds.) Spatial Pattern in Catchment Hydrology: Observations and Modeling. Cambridge, Cambridge University Press, 2000, pp. 17–50.

Blöschl G., Gutknecht D., Kirnbauer R. Distributed Snowmelt Simulations in an Alpine Catchment: 2. Parameter Study and Model Predictions. Water Resources Research, 1991, vol. 27, iss. 12, pp. 3181–3188. DOI: 10.1029/91WR02251.

Blöschl G., Kirnbauer R. An analysis of snow cover patterns in a small alpine catchment. Hydrological Processes, 1992, vol. 6, iss. 1, pp. 99–109. DOI: 10.1002/hyp.3360060109.

Blöschl G., Sivapalan M. Scale issues in hydrological modelling: a review. Hydrological Processes, 1995, vol. 9, iss. 3–4, pp. 251–290. DOI: 10.1002/hyp.3360090305.

Bruno R., Raspa G. Geostatistical characterization of fractal models of surfaces. In Armstrong M. (Ed.) Proceedings of the Third International Geostatistics Congress (September 5–9, 1988, Avignon, France). Kluwer Academic Publishers, 1989, pp. 77–89. DOI: 10.1007/978-94-015-6844-9_5.

Burrough P.A. Multiscale sources of spatial variation of in soil. I: The application of fractal concept to nested levels of soil variation. Journal of Soil Science, 1983, vol. 34, iss. 3, pp. 577–597. DOI: 10.1111/J.1365-2389.1983.TB01057.X.

Chemerenko E.P. Statisticheskie kharakteristiki polya vysoty snezhnogo pokrova [Statistical characteristics of the snow depth field]. Trudy Gidrometeorologicheskii nauchno-issledovatel'skii tsentr SSSR. Vypusk. 25. Chislennye modeli prognoza stoka [Proceedings of the Hydrometeorological Research Center of the USSR. Issue 25. Numerical models of runoff forecast]. Leningrad, Publ. of Gidrometeoizdat, 1968, pp. 63–74. (In Russian).

Chemerenko E.P. Sravnenie razlichnykh metodov interpolyatsii dlya polya vysoty snezhnogo pokrova [Comparison of various interpolation methods for the field of snow depth] Trudy Gidrometeorologicheskii nauchno-issledovatel'skii tsentr SSSR. Vypusk 72. Raschet i prognoz stoka rek [Proceedings of the Hydrometeorological Research Center of the USSR. Issue 72. Calculation and forecast of river runoff]. Leningrad, Publ. Gidrometeoizdat, 1971, pp. 63–74. (In Russian).

Chemerenko E.P. Ob oshibkakh osredneniya po ploshchadi dannykh o vodosoderzhanii snezhnogo pokrova [On the errors of averaging over the area of data on the water content of the snow cover]. Trudy Gidrometeorologicheskii nauchno-issledovatel'skii tsentr SSSR. Vypusk 113. Raschet i prognoz stoka rek [Proceedings of the Hydrometeorological Research Center of the USSR. Issue 72. Calculation and forecast of river runoff]. Leningrad, Publ. Gidrometeoizdat, 1973, pp. 65–75. (In Russian).

Cline D.W., Bales R.C., Dozier J. Estimating the spatial distribution of snow in mountain basins using remote sensing and energy balance modeling. Water Resources Research, 1998, vol. 34, iss. 5, pp. 1275–1285. DOI: 10.1029/97WR03755.

Gandin L.S., Kagan R.L. O tochnosti opredeleniya srednei vysoty snezhnogo pokrova po diskretnym dannym [On the accuracy of determining the average height of snow cover from discrete data]. In: Metodika meteorologicheskikh nablyudenii (snegomernye nablyudeniya) [Methods of meteorological observations (snow measurements)]. Leningrad, Publ. Gidrometeoizdat, 1962, pp. 3–10. (In Russian).

Gelfan A.N., Moreydo V.M. Opisanie makromasshtabnoi struktury polya snezhnogo pokrova ravninnoi territorii s pomoshch'yu dinamiko-stokhasticheskoi modeli ego formirovaniya [Describing macro-scale structure of the snow cover by a dynamic-stochastic model]. Led i sneg [Ice and snow (Russia)], 2015, vol.55, iss. 4, pp. 61–72. DOI: 10.15356/2076-6734-2015-4-61-72. (In Russian; abstract in English).

Georgakakos A.P., Kitanidis P., Loaiciga H., Rouhani S., Olea R. Yates S. Review of Geostatistics in Geohydrology. I: Basic Concepts. Journal of Hydraulic Engineering, 1990, vol. 116, iss. 5, pp.612–658. DOI: 10.1061/(ASCE)0733-9429(1990)116:5(612).

Gottschalk L., Jutman T. Statistical analysis of snow survey data. SMHI Report SMHI Rapporter «Hydrologi och Oceanografi» No. RHO-20. Norrköping, Sveriges meteorologiska och hydrologiska institut, 1979. 41 p.

Journel A.G., Huijbregts C.J. Mining Geostatistics. London, Publ. Academic Press, 1978. 600 p.

Kagan R.L. Osrednenie meteorologicheskikh polei [Averaging of meteorological fields]. Leningrad, Publ. Gidrometeoizdat, 1979. 213 p. (In Russian; abstract in English).

Killingtveit Å, Sand K. On areal distribution of snowcover in a mountainous area. In: Prowse T.D., Ommanney C.S.L. (eds.) Proceedings of the Northern Hydrology Symposium (10–12 July 1990, Saskatoon, Saskatchewan) «Northern hydrology: selected perspectives». Saskatoon, Publ. National Hydrology Research Centre, 1991, pp. 189–204.

Kuchment L.S., Gelfan A.N. Statistical self-similarity of spatial snow accumulation variations and its application to snowmelt runoff models. Russian Meteorology and Hydrology, 1997, iss. 7, pp. 53–60. (Russ. ed.: Kuchment L.S., Gel'fan A.N. Statisticheskoe samopodobie prostranstvennykh izmenenii snegozapasov i ego primenenie pri modelirovanii talogo stoka. Meteorologiya i gidrologiya, 1997, iss. 6, pp. 80–90).

Kuchment L.S., Gelfan A.N. Statistical self-similarity of spatial variations of snow cover: verification of the hypothesis and application in the snowmelt runoff generation models. Hydrological Processes, 2001, vol. 15, iss. 18, pp. 3343–3355. DOI: 10.1002/HYP.1032.

Kuchment L.S., Gelfan A.N. Estimation of extreme flood characteristics using physically based models of runoff generation and stochastic meteorological inputs. Water International, 2002, vol. 27, iss. 1, pp. 77–86. DOI: 10.1080/02508060208686980.

Kuchment L.S., Gel’fan A.N., Demidov V.N. A model of runoff formation on watersheds in the permafrost zone: case study of the upper Kolyma river. Water Resources, 2020, vol. 27, iss. 4, pp. 392–400. (Russ. ed.: Kuchment L.S., Gel'fan A.N., Demidov V.N. Model' formirovaniya stoka na vodosborakh zony mnogoletnei merzloty (na primere verkhnei Kolymy). Vodnye resursy, 2000, vol. 27, iss. 4, pp. 435–444).

Laikhtman D.L., Kagan R.L. Nekotorye voprosy ratsionalizatsii snegos"emok [Some questions of rationalization of snow surveys]. In: Metodika meteorologicheskikh nablyudenii [Methods of meteorological observations]. Leningrad, Publ. Gidrometeoizdat, 1960, pp. 3–18. (In Russian).

Lovejoy S, Mandelbrot B.B. Fractal properties of rain, and a fractal model. Tellus A: Dynamic Meteorology and Oceanography, 1985, vol. 37, iss. 3, pp. 209–232. DOI: 10.3402/TELLUSA.V37I3.11668.

Mandelbrot B.B. The fractal geometry of nature. San Francisco, Publ. Freeman, 1982. 460 p.

Mark D.M., Aronson P.B. Scale-dependent fractal dimensions of topographic surfaces: an empirical investigation, with applications in geomorphology and computer mapping. Journal of the International Association for Mathematical Geology, 1984, vol. 16, iss. 7, pp. 671–683. DOI: 10.1007/BF01033029.

Matheron G. Traité de géostatistique appliquée. Paris, Éditions Technip, 1962. 650 p. (Russ. ed.: Materon Zh. Osnovy prikladnoi geostatistiki. Moscow, Mir Publ., 1968. 407 p).

Meijerink A.M.J., De Brouwer H.A.M., Mannaerts C.M., Valenzuela C.R. Introduction to the use of geographic information systems for practical hydrology. UNESCO, International Hydrology Programme and ITC publication No. 23. Enschede, Publ. ITC, 1994, 243 pp.

Motovilov Yu.G. Modelirovanie snezhnogo pokrova i snegotayaniya [Simulation of snow cover and snow melting]. In: L.S. Kuchment, E.L. Muzylev (eds.) Modelirovanie gidrologicheskogo tsikla rechnykh vodosborov [Modeling of the hydrological cycle of river catchments]. Moscow, Publ. of NGK RAN, 1993, pp. 9–37. (In Russian).

Pomeroy J.W., Gray D.M. Snowcover accumulation, relocation and management. NHRI. Science Report No. 7. Saskatoon, Publ. National Hydrology Research Centre, 1995. 135 p.

Rozenthal W., Dozier J. Automated mapping of Montane snow cover at subpixel resolution from the Landsat Thematic Mapper. Water Resources Research, 1996, vol. 32, iss. 1, pp. 115–130. DOI: 10.1029/95WR02718.

Shook K., Gray D.M. Small-scale spatial structure of shallow snowcovers. Hydrological Processes, 1996, vol. 10, iss. 10, pp. 1283–1292. DOI: 10.1002/(SICI)1099-1085(199610)10:10<1283::AID-HYP460>3.0.CO;2-M.

Shutov V.A. Raspredelenie zapasov vody v snezhnom pokrove na vodosborakh lesnoi zony [Distribution of water reserves in the snow cover on the catchments of the forest zone]. Meteorologiya i gidrologiya [Russian Meteorology and hydrology], 1994, iss. 9, pp. 85–92. (In Russian).

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Published
2021-11-26
How to Cite
Аlexander N. Gelfan. (2021). GEOSTATISTICAL DESCRIPTION OF SNOW COVER HETEROGENEITY IN A PHYSICALLY BASED CATCHMENT-SCALE SNOW MODEL. Hydrosphere. Hazard Processes and Phenomena, 3(3), 233-249. https://doi.org/10.34753/HS.2021.3.3.233

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