The Cycles of Snow Cover in Pyrenees Mountain and Mont Lebanon Analyzed Using the Global Modeling Technique.

Abstract:

The global modeling technique provides a way to obtain ordinary differential equations from single time series¹. This technique, initiated in the 1990s, could be applied successfully to numerous theoretic and experimental systems. More recently it could be applied to environmental systems^2,3.

Here this technique is applied to seasonal snow cover area in the Pyrenees mountain (Europe) and Mont Lebanon (Mediterranean region). The snowpack evolution is complex because it results from combination of processes driven by physiography (elevation, slope, land cover...) and meteorological variables (precipitation, temperature, wind speed...), which are highly heterogeneous in such regions. Satellite observations in visible bands offer a powerful tool to monitor snow cover areas at global scale, with large resolutions range. Although this observable does not directly inform about snow water equivalent, its dynamical behavior strongly relies on it. Therefore, snow cover area is likely to be a good proxy of the global dynamics and global modeling technique a well adapted approach.

The MOD10A2 product (500m) generated from MODIS by the NASA is used after a pretreatment is applied to minimize clouds effect. The global modeling technique is then applied using two packages^4,5. The analysis is performed with two time series for the whole period (2000-2012) and year by year. Low-dimensional chaotic models are obtained in many cases. Such models provide a strong argument for chaos since involving the two necessary conditions in a synthetic way: determinism and strong sensitivity to initial conditions. The models comparison suggests important non-stationnarities at interannual scale which prevent from detecting long term changes.

1: Letellier et al 2009. Frequently asked questions about global modeling, Chaos, 19, 023103.

2: Maquet et al 2007. Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems. J. of Mathematical Biology, 55 (1), 21-39

3: Mangiarotti et al 2014. Two chaotic global models for cereal crops cycles observed from satellite in Northern Morocco. Chaos, 24, 023130.

4 : Mangiarotti et al 2012. Polynomial search and Global modelling: two algorithms for modeling chaos. Physical Review E, 86(4), 046205.

5: http://cran.r-project.org/web/packages/PoMoS/index.html.