Mathematical model of Marmota bobak burrow temperature dynamics during the year. Godovaïa dinamika tempertouri v norakh stepnogo sourka (Marmota bobak): matematitcheskoe modelirovanie. [Model mathématique de la dynamique de la température des terriers de marmota bobak au cours de l’année].

Résumé

Mammals’ burrow temperature is mainly controlled by the temperature of surrounding soil layers whereas air heat transfer plays minor role (Nikol’skii & Khutorskoy, 2001). That is why mathematical model can be used to calculate marmot burrows’ temperature (Nikol’skii, 2002). The model is based on numerical solution of usual thermal conduction equation (two-dimensional case). Mean month temperature of soil surface and temperature of underlying layers are the boundary conditions. Thermal properties of soil were considered to be homogeneous for every soil type. Calculating was carried out with program « Termgraf » (Khutorskoy, 1996). Calculated data were compared with straightly observed temperature in M. bobak burrow in Kharkov region, Ukraine. Differences are statistically uncertain. Basing the model yearly temperature changes was calculated for four populations of M. bobak: Ukraine, Kharkov region; Russia, Saratov and Orenburg regions; Central Kazakhstan. Research depth is from 1.5 to 4.5 m. This depth is most usual for nest chambers of M. bobak. According to the model hibernation period of M. bobak contemporizes with soil cooling at the depth of hibernacula. At the depth of 1.5-2 meters temperature can lower to 0° C and more. End of marmots’ hibernation coincides with the temperature minimum of hibernacula. Annual temperature amplitude is lower at the deeper layers so at the depth of 4.5 meters temperatures don’t reach 0°C. Date of hibernation beginning distinctly differs between eastern (Orenburg and Kazakhstan) and western (Saratov and Ukraine) populations. However burrow temperature changes synchronous for all four cases. Temperature is not the only hibernation-regulating factor.