Automated adjoints: how much do we really know about the source of the Indian Ocean Tsunami?

海啸是人类面临的最迅速和最具破坏性的地质灾害之一，2004年12月26日的印度洋海啸是近代历史上最强大和最具破坏性的。在此期间的五年中，人们花费了大量的科学努力，试图了解海啸的来源和传播。在许多情况下，从地质、地震和全球定位系统数据中得出的关于海啸震源区域的假设，已经通过运行从该震源开始的数值海洋模型，并将结果与实际海啸事件期间的潮汐计数据和卫星测高数据进行比较来验证。这些研究对我们理解这一毁灭性事件做出了重要贡献，但它们忽略了一个重要的问题：观测结果在多大程度上限制了震源区域，或者震源区域是否存在重要的差异，而这些差异在我们必须进行比较的相对较少的观测中无法检测到？现有研究通常没有解决这个问题的一个原因是，研究模型输出对模型输入的敏感性，这是这里问题的本质，需要使用伴随模型或逆模型。生成海洋正演模型已经是一项重要的研究任务，而生成一个正确匹配的伴随模型是非常困难的，所得到的模型系统通常在处理器运行时间上非常昂贵。该项目将采用令人兴奋的新软件和硬件技术，以极大地简化生成伴随模型的过程，并提供使伴随问题易于处理所需的性能提升。所讨论的软件技术是自动代码生成。在这种方法中，有限元问题的数学公式被自动转换成高效的计算机代码。这极大地减少了开发人员的工作量和代码错误的发生率。这里的新颖之处在于使用这个高级数学公式来自动生成伴随公式，从而避免了建立两个模型的困难，并确保了正演模型和伴随模型之间的一致性。新的硬件技术是图形处理单元（gpu）。帝国理工学院的初步研究表明，gpu自动生成的模型代码比普通处理器的等效代码运行速度快20倍以上。这种硬件和软件的结合将导致开发的便利性和运行附带海啸模型的成本的逐步变化。由此产生的模型将用于对一些已公布的海啸震源情景进行缺失的敏感性分析，从而使我们能够回答这样一个问题：“我们对印度洋海啸的震源究竟了解多少？”

Tsunamis are one of the most rapid and destructive of the geohazards which humanity faces and the Indian Ocean Tsunami of 26 December 2004 was the most powerful and destructive in recent history. In the intervening five years, much scientific effort has been expended attempting to understand the source and propagation of the tsunami. In many cases, hypotheses about the source region of the tsunami, which have been derived from geological, seismic and GPS data, have been tested by running a numerical ocean model starting from that source and comparing the results to tide gauge data and satellite altimetry taken during the actual tsunami event. These studies are an important contribution to our understanding of this devastating event, but they miss one important question: to what extent do the observations constrain the source region or could there be important differences in the source region which are not detectable in the relatively small number of observations we have to compare with? One reason that the existing studies have generally not addressed this problem is that studying the sensitivity of the model outputs to the model inputs, which is the essence of the question here, requires the use of an adjoint, or inverse, model. Producing forward ocean models is already a significant research task and producing a correct and matching adjoint model is very difficult and the resulting model system is typically very expensive in processor time to run. This project will employ exciting new software and hardware technology to vastly simplify the process of producing an adjoint model and deliver the performance increases needed to make adjoint problems tractable. The software technology in question is automatic code generation. In this approach the mathematical formulation of the finite element problem is automatically converted into highly efficient computer code. This dramatically reduces both developer effort and the incidence of code bugs. The novel aspect here will be to use this high level mathematical formulation to automatically generate the adjoint formulation, thereby avoiding the difficulty of building two models and ensuring consistency between forward and adjoint models. The novel hardware technology is graphical processing units (GPUs). Initial studies at Imperial College have indicated that automatically generated model code for GPUs can run more than twenty times faster than the equivalent code for ordinary processors. This combination of hardware and software will result in a step-change in the ease of development and the cost of running adjoint tsunami models. The resulting model will be used to conduct the missing sensitivity analysis of a number of the published tsunami source scenarios and will thereby enable us to answer the question: 'how much do we really know about the source of the Indian Ocean Tsunami?'.