修正能量平衡模型並且考慮自然跟人類因素而且使用布迪科模型 來 描述輸出的能量。地球的氣候系統可以分成還海洋跟陸地兩部分， 海洋陸地可以被冰所覆蓋，但是陸地上的植被沒有被冰所覆蓋。此 外，在考慮植被的面積比例的情況下，反照率的變化會影響溫度的平 衡。我們使用冰的覆蓋率跟植被消失的比例來做為模型的參數，並且 跟先前的結過比較，同時我們也計算不同的平衡溫度的穩定性。

In this thesis, we construct a new version of Energy Balance Model (EBM for short) in global climate system which describes the interaction of temperature and vegetation in Earth climate system. The modified climate system is a 2×2 nonlinear system of ordinary differential equations. To construct the Energy Balance Model, we consider the effect from natural and human factors and use the linearization of Stefan-Boltzmann laws from Budyko’s works for outgoing energy. We maps the earth system into the combination of ocean and land. This complex system describes the cases that either ocean can be covered by ice, the land can be covered by ice (with fraction β) and the land covered by the vegetation, or no cover of ice and vegetation on the land. Furthermore, the change of albedo will affect the temperature as well as the equilibria of the system in each region of Earth. We study the stability of the equilibria for this system by using the technique from Dynamical Systems and cases study in term of the variety of parameters β and η (death rate of vegetation). Finally, we compare our results with the previous results of some simple system.

References

[1] Budyko, M.I, The effect of solar radiation variations on the
climate of the earth, Tellus, 1969.
[2] California : NASA: Climate Change and Global Warming. (2017,
March 10). Retrieved 2017, March 10 from
https://climate.nasa.gov/
[3] Colorado : University Corporation for Atmospheric Research
(UCAR). (2017, March 10). Retrieved 2017, March 10 from
https://www.ucar.edu
[4] Ghill, M., Climate stability for a Sellers-type model, Journal of
Atmospheric Science, 33 (1976), 3-20,.
[5] Ghil, M., Hilbert problems for the geosciences in the 21st
century, Nonlinear Processes Geophysics, 8 (2001).
[6] Ghil, M. and Robertson, A. W., Solving problems with GCMs:
general circulation models and their role in the climate
modeling hierarchy, in: General Circulation Model Development:
Past, Present and Future, edited by: Randall, D., Academic Press,
San Diego, (2000), 285-325.
[7] Ghil, M. and Tavantzis, J., Global hopf bifurcation in a simple
climate model, Society for Industrial and Applied Mathematics,
Philadelphia, 43 (1983), 1021.
[8] Jiang et al, Vegetation feedback under future global warming,
Springer-Verlag, (2011).
[9] Kaper, H. and Engler, H., Mathematics and climate, Society for
Industrial and Applied Mathematics, Philadelphia, (2013).
[10] Henderson et al, Global climate models and dynamic
vegetation changes. Global Change Biology 1, (1995).
[11] Herbert et al, Entropy production and multiple equilibria : the
case of the ice-albedo feedback. Earth System Dynamics,
(2011), 13-23.
[12] Nie, Q. and Xu, J., The relationship between vegetation
coverage and climate eements in yellow river basin, china,
PeerJ PrePrints 1:e153v1, (2013).
[13] Rombouts, J. and Ghill,M., Osscilations in a simple
climatevegetation model, Nonlinear Processes Geophysics,
(2015).
[14] Schneider, S.H. and Dickinson, R.E., Climate Modeling, Rev,
Geophysics Space GE, 12 (1974), 447-493.
[15] Scurghers, G., Long term interactions between vegetation and
climate, Max-Planck Institute for Meteorology, 2006.
[16] Sellers, W.D, A global climatic model based on the energy
balance of the earth-atmosphere system, Journal of Applied
Meteorology, 1969.
[17] Trenberth et al, Effects of changing climate on weather and
human activities, University Corporation for Atmospheric
Research , 2000.
[18] Walsh, J. and McGehee, R., Modeling climate dynamically, The
college of Mathematics Journal, 44 (2013).
[19] Watson, A.J. and Lovelock, J.E., Biological homeostatis of the
global environment: the parable of Daisyworld, Tellus B, 35
(1983),284-289.
[20] Widiasih, Esther R., Dynamic of the Budyko energy balance
model, (2003), arXiv:1105.4918v2 [math.DS].
[21] Wood et al, Daisyworld : A Review, American Geophysical
Union, (2008).