GMDD Geoscientific Model Development Discussions GMDD 1991-962X Copernicus GmbH Göttingen, Germany 10.5194/gmdd-5-1041-2012 TopoSUB: a tool for efficient large area numerical modelling in complex topography at sub-grid scales Fiddes J. 1 Gruber S. 1 Glaciology, Geomorphodynamics & Geochronology, Department of Geography, University of Zurich, Switzerland 02 05 2012 5 2 1041 1076 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.geosci-model-dev-discuss.net/5/1041/2012/gmdd-5-1041-2012.html The full text article is available as a PDF file from http://www.geosci-model-dev-discuss.net/5/1041/2012/gmdd-5-1041-2012.pdf

Mountain regions are highly sensitive to global climate change. However, large scale assessments of mountain environments remain problematic due to the high resolution required of model grids to capture strong lateral variability. To alleviate this, tools are required to bridge the scale gap between gridded climate datasets (climate models and re-analyses) and unresolved (by coarse grids) sub-grid mountain topography. We address this problem with a sub-grid method. It relies on sampling the most important aspects of land surface heterogeneity through a lumped scheme, allowing for the application of numerical land surface models (LSM) over large areas in mountain regions. This is achieved by including the effect of mountain topography on these processes at the sub-grid scale using a multidimensional informed sampling procedure together with a 1-D lumped model that can be driven by gridded climate datasets. This paper provides a description of this sub-grid scheme, TopoSUB, as well as assessing its performance against a distributed model. We demonstrate the ability of TopoSUB to approximate results simulated by a distributed numerical LSM at around 10<sup>4</sup> less computations. These significant gains in computing resources allow for: (1) numerical modelling of processes at fine grid resolutions over large areas; (2) extremely efficient statistical descriptions of sub-grid behaviour; (3) a "sub-grid aware" aggregation of simulated variables to course grids; and (4) freeing of resources for treatment of uncertainty in the modelling process.

 References Avissar, R.: A statistical-dynamical approach to parameterize subgrid-scale land-surface heterogeneity in climate models, Surveys in Geophysics, 12, 155–178, 1991. Avissar, R. and Pielke, R A.: A parameterization of heterogenous land surfaces or atmospheric numerical models and its impact on regional meteorology), Mon. Weather Rev., 117, 2113–2136, 1989. Barnett, T P., Adam, J C., and Lettenmaier, D P.: Potential impacts of a warming climate on water availability in snow-dominated regions, Nature, 438, 303–309, 2005. Barry, R G.: The status of research on glaciers and global glacier recession: a review, Progress in Physical Geography, 30, 285, 2006. Bartelt, P. and Lehning, M.: A physical SNOWPACK model for the Swiss avalanche warning:: Part I: numerical model, Cold Reg. Sci. Technol., 35, 123–145, 2002. Beven, K.: How far can we go in distributed hydrological modelling?, Hydrol. Earth Syst. Sci., 5, 1–12, http://dx.doi.org/10.5194/hess-5-1-2001doi:10.5194/hess-5-1-2001, 2001. Boeckli, L., Brenning, A., Gruber, S., and Noetzli, J.: A statistical approach to modelling permafrost distribution in the European Alps or similar mountain ranges, The Cryosphere, 6, 125–140, http://dx.doi.org/10.5194/tc-6-125-2012doi:10.5194/tc-6-125-2012, 2012. Burrough, P A., van Gaans, P. F M., and MacMillan, R A.: High-resolution landform classification using fuzzy k-means, Fuzzy Sets and Systems, 113, 37–52, 2000. Burrough, P A., Wilson, J P., Gaans, P. F. M V., and Hansen, A J.: Fuzzy k-means classification of topo-climatic data as an aid to forest mapping in the Greater Yellowstone Area , USA, Landscape Ecology, 523–546, 2001. Dall'Amico, M., Endrizzi, S., Gruber, S., and Rigon, R.: A robust and energy-conserving model of freezing variably-saturated soil, The Cryosphere, 5, 469–484, http://dx.doi.org/10.5194/tc-5-469-2011doi:10.5194/tc-5-469-2011, 2011. Dimri, A P.: Impact of subgrid scale scheme on topography and landuse for better regional scale simulation of meteorological variables over the western Himalayas, Clim. Dynam., 32, 565–574, 2009. Endrizzi, S. and Marsh, P.: Observations and modeling of turbulent fluxes during melt at the shrub-tundra transition zone 1: point scale variations, Hydrol. Res., 41, 471–491, http://dx.doi.org/10.2166/nh.2010.149doi:10.2166/nh.2010.149, 2010. Famiglietti, J S. and Wood, E F.: Multiscale modeling of spatially variable water and energy balance processes, Water Resour. Res., 30, 3061–3078, 1994. Genizi, A.: Decomposition of r2 in multiple regression with correlated regressors, Statistica Sinica, 3, 407–420, 1993. Giorgi, F. and Avissar, R.: Representation of heterogeneity effects in earth system modeling - Experience from land surface modeling, Rev. Geophys., 35, 413–438, 1997. Gruber, S.: Derivation and analysis of a high-resolution estimate of global permafrost zonation, The Cryosphere, 6, 221–233, http://dx.doi.org/10.5194/tc-6-221-2012doi:10.5194/tc-6-221-2012, 2012. Gruber, S., Hoelzle, M., and Haeberli, W.: Rock-wall temperatures in the Alps: modelling their topographic distribution and regional differences, Permafrost and Periglacial Processes, 15, 299–307, 2004. Gubler, S., Fiddes, J., Keller, M., and Gruber, S.: Scale-dependent measurement and analysis of ground surface temperature variability in alpine terrain, The Cryosphere, 5, 431–443, http://dx.doi.org/10.5194/tc-5-431-2011doi:10.5194/tc-5-431-2011, 2011. Harris, C., Vonder Muhll, D., Isaksen, K., Haeberli, W., Sollid, J L., King, L., Holmlund, P., Dramis, F., Guglielmin, M., and Palacios, D.: Warming permafrost in European mountains, Global Planet. Change, 39, 215–225, 2003. Hartigan, J A. and Wong, M A.: A k-means clustering algorithm, Journal of the Royal Statistical Society, Series C, Applied statistics, 28, 100–108, 1979. Hebeler, F. and Purves, R S.: The influence of resolution and topographic uncertainty on melt modelling using hypsometric sub-grid parameterization, Hydrol. Process., 22, 3965–3979, 2008. Immerzeel, W W., Van Beek, L. P H., and Bierkens, M. F P.: Climate change will affect the Asian water towers, Science, 328, 1382, http://dx.doi.org/10.1126/science.1183188doi:10.1126/science.1183188, 2010. Isaksen, K., Holmlund, P., Sollid, J L., and Harris, C.: Three deep Alpine-permafrost boreholes in Svalbard and Scandinavia, Permafrost and Periglacial Processes, 12, 13–25, 2001. Kanungo, T., Mount, D M., Netanyahu, N S., Piatko, C D., Silverman, R., and Wu, A Y.: An efficient-means clustering algorithm: Analysis and implementation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 881–892, 2002. Klok, E J. and Oerlemans, J.: Model study of the spatial distribution of the energy and mass balance of Morteratschgletscher, Switzerland, J. Glaciol., 48, 505–518, 2002. Koster, R. and Suarez, M.: Modeling the land surface boundary in climate models as a composite of independent vegetation stands, J. Geophys. Res., 97, 2697–2715, 1992. Kotlarski, S.: A Subgrid Glacier Parameterisation for Use in Regional Climate Modelling, Ph.D. thesis, Max Planck Institute for Meteorology, 2007. Laternser, M. and Schneebeli, M.: Long-term snow climate trends of the Swiss Alps (1931–99), Int. J. Climatol., 23, 733–750, 2003. Leung, L R. and Ghan, S J.: A subgrid parameterization of orographic precipitation, Theor. Appl. Climatol., 52, 95–118, 1995. Liang, X Z., Xu, M., Choi, H. I L., Kunkel, K E., Rontu, L., Geleyn, J F., Müller, M D., Joseph, E., and Wang, J. X L.: Development of the regional climate-weather research and forecasting model (CWRF): Treatment of subgrid topography effects, in: Proceedings of the 7th Annual WRF User's Workshop, Boulder, CO, 2006. Mote, P W., Hamlet, A F., Clark, M P., and Lettenmaier, D P.: Declining mountain snowpack in western North America, B. Am. Meteorol. Soc., 86, 39–44, 2005. Okeke, F. and Karnieli, A.: Linear mixture model approach for selecting fuzzy exponent value in fuzzy c-means algorithm, Ecological Informatics, 1, 117–124, 2006. Paul, F. and Kotlarski, S.: Forcing a distributed glacier mass balance model with the regional climate model REMO. Part II: downscaling strategy and results for two swiss glaciers, J. Climate, 23, 1607–1620, http://dx.doi.org/10.1175/2009JCLI3345.1doi:10.1175/2009JCLI3345.1, 2010. Paul, F., Kaab, A., and Haeberli, W.: Recent glacier changes in the Alps observed by satellite: consequences for future monitoring strategies, Global Planet. Change, 56, 111–122, 2007. Rigon, R., Bertoldi, G., and Over, T M.: GEOtop: A distributed hydrological model with coupled water and energy budgets, J. Hydrometeorol., 7, 371–388, 2006. Riseborough, D., Shiklomanov, N., Etzelmüller, B., Gruber, S., and Marchenko, S.: Recent Advances in Permafrost Modelling, Permafrost and Periglacial Processes, 156, 137–156, http://dx.doi.org/10.1002/ppp.615doi:10.1002/ppp.615, 2008. Seth, A., Giorgi, F., and Dickinson, R E.: Simulating fluxes from heterogeneous land surfaces: explicit subgrid method employing the biosphere-atmosphere transfer scheme (BATS), J. Geophys. Res., 99, 18651–18667, http://dx.doi.org/10.1029/94JD01330doi:10.1029/94JD01330, 1994. Sokal, R R. and Sneath, P. H A.: Principles of taxonomy, Science, 156, 1356, http://dx.doi.org/10.1126/science.156.3780.1356doi:10.1126/science.156.3780.1356, 1967. Walland, D J. and Simmonds, I.: Sub-grid scale topography and the simulation of Northern Hemisphere snow cover, Int. J. Climatol., 16, 961–982, 1996. Wood, E F., Sivapalan, M., Beven, K., and Band, L.: Effects of spatial variability and scale with implications to hydrologic modeling, J. Hydrol., 102, 29–47, http://dx.doi.org/10.1016/0022-1694(88)90090-Xdoi:10.1016/0022-1694(88)90090-X, 1988. Zadeh, L A.: Fuzzy sets*, Information and control, 8, 338–353, 1965. Zemp, M., Haeberli, W., Hoelzle, M., and Paul, F.: Alpine glaciers to disappear within decades, Geophys. Res. Lett., 33, L13504, http://dx.doi.org/10.1029/2006GL026319doi:10.1029/2006GL026319, 2006.