Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and entrainment coefficients results in a large range of plausible values of the source mass flux. Our analysis shows that better constraints on entrainment coefficients for volcanic plumes and more precise observations of plume height are required to obtain tightly constrained estimates of the source mass flux.

中文翻译：

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风吹火山羽流模型的不确定性分析

自然过程的数学模型可用作反演工具，以根据测量量预测未观察到的特性。观测和模型制定的不确定性会影响逆向建模的有效性。我们提出了一种通用方法，即历史匹配，可用于研究观测和模型不确定性对逆建模研究的影响。我们展示了对火山羽流积分模型的历史匹配，该模型用于根据 2010 年冰岛埃亚菲亚德拉冰盖火山喷发和 2011 年冰岛格里姆斯沃特火山喷发期间羽流上升高度的观测来估计源条件。确定了不确定性的来源并量化，并通过整体羽流模型传播。执行初步敏感性分析以识别强烈影响模型预测的不确定模型参数。模型预测是通过不可信性度量根据观察进行评估的，该度量排除了在量化的不确定性的情况下被认为不可信的模型输入。我们证明了火山的源质量通量可以从羽流高度观测中估计出来，但无法准确确定岩浆温度、出口速度和溶出气体质量分数。羽流高度观测值和夹带系数的不确定性导致源质量通量的大范围合理值。