Characterizing Cumulus Cloud Cover with Transilient Matrices

低层大气中浅积云的模式模拟表明，对未来状态的预测对这些云在大气初始状态下的表现具有敏感性。在天气和气候模式中处理这些云的数值方案已经存在多年，但新技术仍在继续建立和改进这些方案。这项研究将使用一种叫做“瞬变矩阵”的数学工具，在模型的低层大气表征中更好地表征这些云，进而改进基于这些云的未来天气和气候状态的预测。通过提高对天气和气候模式对低层大气中浅积云特征的敏感性的理解，这些改进将反过来造福社会。拟议的研究旨在测试与浅积云有关的云量的假设。其中一种假设将云量与云沉降率联系起来，时间尺度取决于云的大小和涡流扩散率；这个尺度与气候模式中使用的典型尺度相差两个数量级。时间标度的表达式将使用一个完善的数学工具进行测试和改进，该数学工具被称为瞬变矩阵（TM），以输出大涡模拟（LES）和云雷达的观测结果。由于各种全球气候模式（GCMs）之间的浅积云覆盖差异已被确定为造成气候预估不确定性的主要因素，因此本研究具有改进未来气候预测的潜力。

Model simulations of shallow cumulus clouds in the lower atmosphere demonstrate the sensitivity of predictions of future states to the representation of these clouds in the initial state of the atmosphere. Numerical schemes to handle these clouds in weather and climate models have been in existence for many years, yet new techniques continue to build upon and improve these schemes. This research will use a mathematical tool, called Transilient Matrices, to better characterize these clouds in the model's representation of the lower atmosphere and in turn improve forecasts of future weather and climate states based on these clouds. These improvements will in turn benefit society through an improved understanding of the sensitivity of weather and climate models to the characterization of shallow cumulus clouds in the lower atmosphere. The proposed research seeks to test hypotheses for the amount of cloud cover associated with shallow cumulus. One such hypothesis relates the amount of cloud cover to the rate of cloud detrainment by a timescale that depends on cloud size and eddy diffusivity; this scale differs from the typical scale used in climate models by two orders of magnitude. The expression for timescale will be tested and refined using a well established mathematical tool known as the Transilient Matrix (TM) to output from large-eddy simulation (LES) and observations from cloud radar. Since differences in shallow cumulus cloud cover among various Global Climate Models (GCMs) have been identified as major contributions to uncertainty in climate projections, this research has the potential of improving forecasts of future climate.