ADISM v.1.0: an adjoint of a thermomechanical ice-sheet model obtained using an algorithmic differentiation tool
ADISM v.1.0: an adjoint of a thermomechanical ice-sheet model obtained using an algorithmic differentiation tool
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ADISM v.1.0：使用算法微分工具获得的热机械冰盖模型的伴随
DOI：
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发表时间：
2013
期刊：
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通讯作者：
T. Murray
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作者：
J. McGovern;I. Rutt;J. Utke;T. Murray
抽象。伴随模型的应用对当代冰川学中的许多问题都有帮助。在一个简单的水平上，伴随模型可以用来计算相对于空间变化的参数，如基底滑动系数冰盖的敏感性。在更复杂的层次上，伴随模式可用作变分数据同化方案的组成部分，从而解决模式初始化和数据约束演变的问题。基本上，伴随模型计算成本函数对一组控制参数的敏感度。这样的模型灵敏度可替代地通过多次运行模型、依次单独地扰动每个控制参数并计算在每种情况下得到的灵敏度来获得。然而，对于大量的控制参数，例如控制参数对应于模型域中的每个点的情况，计算成本变得过高。伴随模型的使用允许更有效地获得灵敏度-伴随模型灵敏度在单次运行中获得-并且更准确，因为模型的微分是以机器精度完成的。我们提出了一个有限差分浅冰近似（SIA），热力学冰盖模型（正演模型），及其伴随，通过使用OpenAD算法微分工具。我们使用标准SIA基准测试验证冰盖模型，并检查OpenAD计算的导数与某些数值近似导数之间的一致性。典型的伴随计算证明了应用到格陵兰冰盖。
Abstract. A number of problems in contemporary glaciology could benefit from the application of adjoint models. On a simple level, adjoint models can be used to calculate ice-sheet sensitivities with respect to spatially varying parameters such as the basal sliding coefficient. At a more sophisticated level, adjoint models may be used as components of variational data assimilation schemes, allowing problems of model initialization and data-constrained evolution to be tackled. Fundamentally, adjoint models calculate the sensitivity of a cost function to a suite of control parameters. Such model sensitivities can alternatively be obtained by running the model many times, perturbing each control parameter separately in turn, and calculating the resulting sensitivity in each case. For large numbers of control parameters, however, such as the case where a control parameter corresponds to each point in the model domain, the computational cost becomes prohibitive. The use of adjoint models allows sensitivities to be obtained more efficiently – adjoint model sensitivities are obtained in a single run – and more accurately, since the differentiation of the model is done with machine precision. We present a finite-difference shallow ice approximation (SIA), thermomechanical ice-sheet model (the forward model), and its adjoint, as generated by using the OpenAD algorithmic differentiation tool. We verify the ice-sheet model using standard SIA benchmark tests and check the consistency between derivatives computed by OpenAD and certain numerically approximated derivatives. Typical adjoint calculations are demonstrated by application to the Greenland ice sheet.