Precipitation interpolation using digital terrain model and multivariate regression in hilly and low mountainous areas of Hungary
Abstract
The relationship between precipitation and elevation is a well-known topic in the field of geography and meteorology. Radar-based precipitation data are often used in hydrologic models, however, they have several inaccuracies, and elevation can be one of the additional parameters that may help to improve them. Thus, our aim in this article is to find a quantitative relationship between precipitation and elevation in order to correct precipitation data input into hydrologic models. It is generally accepted that precipitation increases with elevation, however, the real situation is much more complicated, and besides elevation, the precipitation is dependent on several other topographic factors (e.g., slope, aspect) and many other climatic parameters, and it is not easy to establish statistically reliable correlations between precipitation and elevation. In this paper, we examine precipitation-elevation correlations by using multiple regression analysis based on monthly climatic data. Further on, we present a method, in which these regression equations are combined with kriging or inverse distance weighting (IDW) interpolation to calculate precipitation fields, which take into account topographic elevations based on digital terrain models. Thereafter, the results of the different interpolation methods are statistically compared. Our study areas are in the hilly or low mountainous regions of Hungary (Bakony, Mecsek, Börzsöny, Cserhát, Mátra and Bükk montains) with a total of 52 meteorological stations. Our analysis proved that there is a linear relationship between the monthly sum of precipitation and elevation. For the North Hungarian Mountains, the correlation coefficients were statistically significant for the whole study period with values between 0.3 and 0.5. Multivariate regression analysis pointed out that there are remarkable differences among seasons and even months. The best correlation coefficients are typical of late spring-early summer and October, while the weakest linear relationships are valid for the winter period and August. The vertical gradient of precipitation is between one and four millimetres per 100 metres for each month. The statistical comparison of the precipitation interpolation had the following results: for most months, co-kriging was the best method, and the combined method using topography-derived regression parameters lead to only slightly better results than the standard kriging or IDW.
References
Alpert, P. 1986. Mesoscale indexing of the distribution of orographic precipitation over high mountains. Journal of Climate and Applied Meteorology 25. (4): 532-545. https://doi.org/10.1175/15200450(1986)025<0532:MIOTDO>2.0.CO;2
Azimi-Zonooz, A., Krajewski, W.F., Bowles, D.S. and Seo, D.J. 1989. Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data. Stochastic Hydrology and Hydraulics 3. (1): 51-67. https://doi.org/10.1007/BF01543427
Bartholy, J. and Pongrácz, R. (ed.) 2013. Alkalmazott és városklimatológia (Applied and urban climatology). Budapest, ELTE.
Basist, A., Bell, G.D. and Meentemeyer, V. 1994. Statistical relationships between topography and precipitation patterns. Journal of Climate 7. (9): 1305-1315. https://doi.org/10.1175/15200442(1994)007<1305:SRBTAP>2.0.CO;2
Cambi, C., Valigi, D. and Di Matteo, L. 2010. Hydrogeological study of data-scarce limestone massifs: the case of Gualdo Tadino and Monte Cucco structures (Central Apennines, Italy). Bollettino di Geofisica Teorica ed Applicata 51. (4): 345-360.
Cortesi, N., González-Hidalgo, J.C., Brunetti, M. and Martin-Vide, J. 2012. Daily precipitation concentration across Europe 1971-2010. Natural Hazards and Earth System Sciences 12. (9): 2799-2810. https://doi.org/10.5194/nhess-12-2799-2012
Crochet, P. 2009. Enhancing radar estimates of precipitation over complex terrain using information derived from an orographic precipitation model. Journal of Hydrology 377. (3-4): 417-433. https://doi.org/10.1016/j.jhydrol.2009.08.038
Daly, C., Taylor, G.H. and Gibson, W.P. 1997. The PRISM approach to mapping precipitation and temperature. In Proceedings 10th AMS Conference on Applied Climatology. American Meteorological Society, 20-23 October 1979. Reno, Nevada. Available at https://prism.oregonstate.edu/documents/pubs/1997appclim_PRISMapproach_daly.pdf
Duckstein, L., Fogel, M.M. and Thames, J.L. 1973. Elevation effects on rainfall: A stochastic model. Journal of Hydrology 18. (1): 21-35. https://doi.org/10.1016/0022-1694(73)90023-1
Goodale, C.L., Aber, J.D. and Ollinger, S.V. 1998. Mapping monthly precipitation, temperature, and solar radiation for Ireland with polynomial regression and a digital elevation model. Climate Research 10. (1): 35-49.https://doi.org/10.3354/cr010035
Goodwell, A.E. 2020. "It's raining bits": Patterns in directional precipitation persistence across the United States. Journal of Hydrometeorology 21. (12): 2907-2921. https://doi.org/10.1175/JHM-D-20-0134.1
Goudenhoofdt, E. and Delobbe, L. 2009. Evaluation of radar-gauge merging methods for quantitative precipitation estimates. Hydrology and Earth System Sciences 13. (2): 195-203. https://doi.org/10.5194/hess-13-195-2009
Ha, K.J., Jeon, E.H. and Oh, H.M. 2007. Spatial and temporal characteristics of precipitation using an extensive network of ground gauge in the Korean Peninsula. Atmospheric Research 86. (3-4): 330-339. https://doi.org/10.1016/j.atmosres.2007.07.002
Haiden, T. and Pistotnik, G. 2009. Intensity-dependent parameterization of elevation effects in precipitation analysis. Advances in Geosciences 20. 33-38. https://doi.org/10.5194/adgeo-20-33-2009
Henry, A.J. 1919. Increase of Precipitation with Altitude. Monthly Weather Review 47. 33-41. https://doi.org/10.1175/1520-0493(1919)47<33:IOPWA>2.0.CO;2
Józsa, E. and Fábián, Sz.Á. 2016. Az SRTM-1 felszínmodell korrigálása Magyarországra (Correction of terrain model SRTM-1 for Hungary). Természetföldrajzi Közlemények a Pécsi Tudományegyetem Földrajzi Intézetéből, Pécs, University of Pécs, 1-22. https://doi.org/10.17799/2016.1.13
Lauenroth, W.K., Burke, I.C. and Gutmann, M.P. 1999. The structure and function of ecosystems in the central North American grassland region. Great Plains Research 9. 223-259.
Ly, S., Charles, C. and Degre, A. 2011. Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium. Hydrology and Earth System Sciences 15. (7): 2259-2274. https://doi.org/10.5194/hess-15-2259-2011
Mair, A. and Fares, A. 2010. Comparison of rainfall interpolation methods in a mountainous region of a tropical island. Journal of Hydrologic Engineering 16. (4): 371-383. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000330
Millett, B., Johnson, W.C. and Guntenspergen, G. 2009.Climate trends of the North American prairie pothole region 1906-2000. Climatic Change 93. (1): 243-267. https://doi.org/10.1007/s10584-008-9543-5
Noori, M.J., Hassan, H.H. and Mustafa, Y.T. 2014. Spatial estimation of rainfall distribution and its classification in Duhok governorate using GIS. Journal of Water Resource and Protection 6. (2): 75-75. https://doi.org/10.4236/jwarp.2014.62012
Rabus, B., Eineder, M., Roth, A. and Bamler, R. 2003. The shuttle radar topography mission - A new class of digital elevation models acquired by spaceborne radar. ISPRS Journal of Photogrammetry and Remote Sensing 57. (4): 241-262. https://doi.org/10.1016/S0924-2716(02)00124-7
Rodriguez, E., Morris, C.S. and Belz, J.E. 2006. A global assessment of the SRTM performance. Photogrammetric Engineering & Remote Sensing 72. (3): 249-260. https://doi.org/10.14358/PERS.72.3.249
Roncz, B. 1982. A csapadék magassági rendszere a Mátra hegységben (The altitude system of rainfall in the Mátra mountain range). Acta Academiae Paedagogicae Agriensis. Nova series, Tom. 16. 455-466.
Ruiz Sinoga, J.D., Garcia Marin, R., Martinez Murillo, J.F. and Gabarron Galeote, M.A. 2011. Precipitation dynamics in southern Spain: trends and cycles. International Journal of Climatology 31. (15): 2281-2289. https://doi.org/10.1002/joc.2235
Sasaki, H. and Kurihara, K. 2008. Relationship between precipitation and elevation in the present climate reproduced by the non-hydrostatic regional climate model. Scientific Online Letters on the Atmosphere 4. 109-112. https://doi.org/10.2151/sola.2008-028
Schwarb, M. 2000. The Alpine precipitation climate: Evaluation of a high-resolution analysis scheme using comprehensive rain-gauge data. Doctoral dissertation, Zurich, ETH.
Sinclair, S. and Pegram, G. 2005. Combining radar and rain gauge rainfall estimates using conditional merging. Atmospheric Science Letters 6. (1): 19-22. https://doi.org/10.1002/asl.85
Smith, C.D. 2008. The relationship between monthly precipitation and elevation in the Alberta foothills during the foothills orographic precipitation experiment. In Cold Region Atmospheric and Hydrologic Studies. The Mackenzie GEWEX Experience. Ed.: Woo, M., Berlin-Heidelberg, Springer, 167-185. https://doi.org/10.1007/978-3-540-73936-4_10
Spreen, W.C. 1947. A determination of the effect of topography upon precipitation. Eos, Transactions American Geophysical Union 28. (2): 285-290. https://doi.org/10.1029/TR028i002p00285
Szentimrey, T. and Bihari, Z. 2007. Mathematical background of spatial interpolation, meteorological interpolation based on surface homogenized data bases (MISH). COST Action 719. Budapest, COST Office, 17-27.
van Zyl, J.J. 2001. The shuttle radar topography mission (SRTM): A breakthrough in remote sensing of topography. Acta Astronautica 48. 559-565. https://doi.org/10.1016/S0094-5765(01)00020-0
Velasco-Forero, C.A., Sempere-Torres, D., Cassiraga, E.F. and Gómez-Hernández, J.J. 2009. A non-parametric automatic blending methodology to estimate rainfall fields from rain gauge and radar data. Advances in Water Resources 32. (7): 986-1002. https://doi.org/10.1016/j.advwatres.2008.10.004
Weisse, A.K. and Bois, P. 2001. Topographic effects on statistical characteristics of heavy rainfall and mapping in the French Alps. Journal of Applied Meteorology 40. (4): 720-740. https://doi.org/10.1175/15200450(2001)040<0720:TEOSCO>2.0.CO;2
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