Uncertainty estimates are important when retrieving properties of clouds and aerosols from satellites measurements. These measurements must be interpreted using a form of inverse theory, such as optimal estimation. In atmospheric remote sensing these inverse methods often assume that the forward model is linear in the region of uncertainty. This assumption is not necessarily valid. This paper presents an exact confidence procedure in contrast to the linear approximation using a maximum likelihood estimator. Two simple examples of retrieving the effective radius and optical depth of a volcanic ash cloud and water cloud show a discrepancy between the linear approximation and the exact procedure. The exact procedure is especially useful for inference where the entire parameter space has been forward modelled prior to or during the retrieval, such as using look up tables. When the inference method calculates the likelihood over the whole parameter space, it is less computationally expensive than a linear approximation.

中文翻译：

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在云和气溶胶遥感中评估非线性最大似然最优估计不确定性

从卫星测量中检索云和气溶胶的特性时，不确定性估计很重要。必须使用一种逆理论（例如最佳估计）来解释这些测量。在大气遥感中，这些逆方法通常假设正向模型在不确定性区域内是线性的。此假设不一定有效。与使用最大似然估计器的线性近似相比，本文提出了一种精确的置信度过程。检索火山灰云和水云的有效半径和光学深度的两个简单示例显示了线性逼近与精确过程之间的差异。确切的过程对于在检索之前或检索过程中已对整个参数空间进行正向建模的推断特别有用，例如使用查找表。当推论方法计算整个参数空间上的似然性时，它的计算成本比线性逼近要小。