Impact of Calibration Data on Evaluating Plausibility of Alternative Groundwater Models

校准数据对评估替代地下水模型合理性的影响该奖项是根据2009年美国复苏和再投资法（公法111-5）资助的。水文环境是开放和复杂的，无论现有数据的数量和质量如何，都容易产生多种解释和数学描述。由于认识到这一点，水文学家越来越倾向于为一个地点假设几种不同的水文模型。这里的模型并不局限于控制方程和相关的边界/初始条件，而是指水文系统的概念数学表示（例如，它们的过程和相互作用）。面对可供选择的模型，要回答的科学问题是如何评估模型的合理性，使模型能够正确地使用，以产生最佳的预测。评估模型合理性考虑整个建模过程（包括模型制定、校准和验证），而校准/验证数据在评估过程中起着关键作用。虽然校准单一模型的研究已经进行了几十年，但校准数据对评估多个模型的可信性的影响尚未得到很好的理解。开放的问题如下：什么样的校准数据可以用来最有效地区分模型？需要多少数据才能可靠地评估模型的合理性？数据相关性（空间和时间）如何影响评估？模型可信性的偏倚评价如何影响预测性能？这些基本问题将使用跨学科的方法结合贝叶斯统计和计算方法来解决。模型可信性将使用模型概率来量化，模型概率是在贝叶斯框架中根据模型模拟与校准数据的一致性、模型的复杂性和专家判断来估计的。根据模型概率，可以选择单个模型（即贝叶斯模型选择）或使用多个模型（即贝叶斯模型平均）进行预测。贝叶斯模型选择或平均的预测性能将被研究。假设将使用基于合成和现实世界建模的双管齐下的策略进行测试。对于综合情况，将根据场地异质性和边界条件的不同表示开发替代地下水模型。真实世界的模拟将在科罗拉多州的Naturita进行，那里存在铀可能到达科罗拉多河的风险。根据铀反应输运模型的不同表述方式，如不同官能团数的表面络合模型，将开发替代模型。对于现实世界的建模，将使用交叉验证方法（如leave-one-out和K-fold）评估模型预测性能。合成和真实世界的建模将与美国地质勘探局在博尔德和门洛帕克的科学家一起进行。在这个项目中获得的科学见解将通过具有成本效益的数据收集来改进现有模型和开发环境恢复和保护的新模型，对任何环境建模都是有价值的。

Impact of Calibration Data on Evaluating Plausibility of Alternative Groundwater ModelsThis award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions regardless of the quantity and quality of available data. This recognition has led to a growing tendency among hydrologists to postulate several alternative hydrologic models for a site. Models here are not limited to governing equations and associated boundary/initial conditions, but refer to conceptual-mathematical representations of hydrologic systems (e.g., their processes and interactions). Facing the alternative models, the scientific question to be answered is how to evaluate plausibility of the models so that the models can be properly used to yield optimum predictions. Evaluating model plausibility considers the entire modeling process (including model formulation, calibration, and validation), and calibration/validation data play a key role in the evaluation process. Although calibrating a single model has been studied for decades, impact of calibration data on evaluating plausibility of multiple models has not been well understood. Open questions are as follows: What kinds of calibration data can be used to most effectively discriminate between models? How many data are needed to reliably evaluate model plausibility? How does data correlation (spatial and temporal) affect the evaluation? How does biased evaluation of model plausibility influence predictive performance? These fundamental questions will be addressed using an interdisciplinary approach combining Bayesian statistical and computational methods. Model plausibility will be quantified using model probability, which is estimated, in a Bayesian framework, based on conformity of model simulations to calibration data, complexity of models, and expert judgment. Based on the model probability, one can choose a single model (i.e., Bayesian model selection) or use multiple models (i.e., Bayesian model averaging) to make predictions. Predictive performance of the Bayesian model selection or averaging will be investigated. Hypothesis will be tested using a two-pronged strategy based on both synthetic and real-world modeling. For the synthetic case, alternative groundwater models will be developed based on different representations of site heterogeneity and boundary conditions. The real-world modeling will be conducted at the Naturita site, Colorado, where a risk exists that uranium may reach the Colorado River. Alternative models will be developed based on different ways of formulations of uranium reactive transport models, such as surface complexation models with different numbers of functional groups. For the real-world modeling, model predictive performance will be evaluated using cross-validation methods such as leave-one-out and K-fold. The synthetic and real-world modeling will be conducted together with USGS scientists at Boulder and Menlo Park. Scientific insights gained in this project will be valuable to any environmental modeling through cost-effective data collection for refining existing models and developing new models for environmental restoration and protection.