[论文解读] Tropical precipitation clusters as islands on a rough water-vapor topography

Ziwei Li, Paul A. O’Gorman+1 more|arXiv (Cornell University)|Aug 10, 2021

Climate variability and models参考文献 82被引用 3

一句话总结

本文提出，热带降水簇在粗糙的柱水汽（CWV）地形上，于对流阈值之上表现为‘岛屿’。利用自仿射标度理论，表明降水簇的幂律频率分布与分形维数可自然地从CWV岛屿的统计特性中产生，且面积与体积的幂律指数通过与粗糙度无关的普遍标度关系相互关联。

ABSTRACT

Tropical precipitation clusters exhibit power-law frequency distributions in area and volume (integrated precipitation), implying a lack of characteristic scale in tropical convective organization. However, it remains unknown what gives rise to the power laws and how the power-law exponents for area and volume are related to one another. Here, we explore the perspective that precipitation clusters are islands above a convective threshold on a rough column-water-vapor (CWV) topography. This perspective is supported by the agreement between the precipitation clusters and CWV islands in their frequency distributions as well as fractal dimensions. Power laws exist for CWV islands at different thresholds through the CWV topography, suggesting that the existence of power-laws is not specifically related to local precipitation dynamics, but is rather a general feature of CWV islands. Furthermore, the frequency distributions and fractal dimensions of the clusters can be reproduced when the CWV field is modeled to be self-affine with a roughness exponent of 0.3. Self-affine scaling theory relates the statistics of precipitation clusters to the roughness exponent; it also relates the power-law slopes for area and volume without involving the roughness exponent. Thus, the perspective of precipitation clusters as CWV islands provides a useful framework to consider many statistical properties of the precipitation clusters, particularly given that CWV is well-observed over a wide range of length scales in the tropics. However, the statistics of CWV islands at the convective threshold imply a smaller roughness than is inferred from the power spectrum of the bulk CWV field, and further work is needed to understand the scaling of the CWV field.

研究动机与目标

• 理解热带降水簇中无标度统计的起源。
• 研究为何降水簇在面积和体积上表现出无特征尺度的幂律分布。
• 检验柱水汽（CWV）地形是否能够解释降水簇的观测统计特性。
• 确定面积与体积的幂律指数之间的关系是否由普遍标度定律决定，而非局部动力过程。
• 评估自仿射粗糙度在生成观测到的分形维数与频率分布中的作用。

提出的方法

• 提出一个概念性框架，将降水簇视为在粗糙CWV地形上高于对流阈值的岛屿。
• 通过多个阈值分析CWV岛屿的频率分布与分形维数，以识别普遍标度特性。
• 使用粗糙度指数H = 0.3的自仿射随机场建模，以重现降水簇的观测统计特性。
• 应用自仿射标度理论，推导出簇面积与体积幂律指数之间的普遍关系。
• 将观测到的降水簇统计特性与合成CWV场的统计特性进行比较，以验证模型。
• 采用对数-对数线性回归，从高分辨率CWV与降水数据中量化幂律行为与分形维数。

实验结果

研究问题

• RQ1 为何热带降水簇在面积与体积上表现出幂律频率分布？
• RQ2 幂律行为是否源于柱水汽（CWV）场本身，而非降水动力学的特异性？
• RQ3 簇面积与体积的幂律指数之间存在何种关系？该关系能否由普遍标度原理推导？
• RQ4 在多大程度上可通过将CWV建模为自仿射随机场，重现降水簇的分形维数与统计分布？
• RQ5 粗糙度指数在塑造降水簇观测统计特性方面起何种作用？

主要发现

• 在对流阈值处，降水簇与CWV岛屿的频率分布表现出幂律指数与分形维数的高度一致。
• CWV岛屿的幂律统计在多个阈值下持续存在，表明幂律是粗糙地形的一般特征，而非降水特有。
• 当CWV场被建模为粗糙度指数H = 0.3的自仿射场时，观测到的簇面积幂律指数（τ ≈ 1.84）与体积幂律指数（β ≈ 2.6）得以重现。
• 标度关系α + 2/β ≈ 2.6在所有阈值下均成立，与自仿射标度理论一致，且与粗糙度指数无关。
• 簇周长的分形维数（Dl ≈ 1.35）与体积的分形维数（DV ≈ 1.84）与对流阈值下CWV岛屿的分形维数一致。
• 该模型表明，降水簇的统计特性由底层CWV场的粗糙度决定，而非仅由局部对流过程决定。