基于部分可控性矩阵的模型降阶方法及误差分析

针对单输入单输出系统,利用部分可控性矩阵的M-P广义逆作为集结矩阵,提出了一种新的近似集结法模型降阶方法。首先给出了当系统可控与不可控时的2种降阶模型,然后通过误差最小分析归结为一种降阶模型,并利用向量到子空间的距离给出了不同阶降阶模型误差的一个简单计算方法。以此误差作为标准,可以方便地选择满足需要的降阶阶数及降阶模型。最后以实例表明了该方法的有效性和应用性。     

Climate sensitivity constrained by CO2 concentrations over the past 420 million years

A firm understanding of the relationship between atmospheric carbon dioxide concentration and temperature is critical for interpreting past climate change and for predicting future climate change. A recent synthesis suggests that the increase in global-mean surface temperature in response to a doubling of the atmospheric carbon dioxide concentration, termed 'climate sensitivity', is between 1.5 and 6.2 degrees C (5-95 per cent likelihood range), but some evidence is inconsistent with this range. Moreover, most estimates of climate sensitivity are based on records of climate change over the past few decades to thousands of years, when carbon dioxide concentrations and global temperatures were similar to or lower than today, so such calculations tend to underestimate the magnitude of large climate-change events and may not be applicable to climate change under warmer conditions in the future. Here we estimate long-term equilibrium climate sensitivity by modelling carbon dioxide concentrations over the past 420 million years and comparing our calculations with a proxy record. Our estimates are broadly consistent with estimates based on short-term climate records, and indicate that a weak radiative forcing by carbon dioxide is highly unlikely on multi-million-year timescales. We conclude that a climate sensitivity greater than 1.5 degrees C has probably been a robust feature of the Earth's climate system over the past 420 million years, regardless of temporal scaling.