Issues of Uncertainty and Scale in Derived Products

在决定如何利用土地时，规划者需要有关土地状况及其不同用途的相对适宜性的信息。例如，规划人员可能希望比较农业生产（可由土壤性质决定）、资源开采（可由矿物资源资料决定）和住房（将需要有关洪水和生存风险以及土地是否适合建筑的资料）的土地价值。进行这些评估所需的信息通常以空间数据产品的形式提供，其中有关的环境属性（例如土壤pH值或洪水风险等级）是在覆盖有关景观的空间网格的节点上估计出来的。这些空间数据产品来自于所考虑的景观的可用数据和模型。通过对该地区土壤调查中测得的pH值进行插值，可以得到土壤pH空间积。或者，一个综合了气候、地形和排水信息的数学模型可以用来确定洪水的风险。这个项目解决了空间数据产品使用中的两个问题。首先，计划人员不太可能意识到或考虑到与产品相关的不确定性。由于几乎不可能在每个相关地点进行测量，因此几乎不可避免地会出现一些不确定性。其次，空间产品描述了特定空间尺度下环境属性的期望值，而这可能不是需要信息的尺度。例如，在矿物资源产品中，估计的水平比例尺可能对应于测量矿物浓度的钻孔的直径。然而，规划者可能对与采石场大小相等的空间尺度上的矿物浓度感兴趣。如果空间数据产品被用作数学或经验模型的输入，从而导致进一步的数据产品，特别是如果模型被设计为在与数据产品不一致的尺度上联系环境属性，那么这些问题就会进一步传播。在这个项目中，我们将考虑最小化、量化和沟通空间数据产品的不确定性和规模相关问题的策略。我们将把这些问题与关于英国土壤碳含量的两个相关数据集联系起来。我们将确定如何成本有效地设计对这些数据的空间调查，以便在不同的空间尺度上对感兴趣的属性进行准确的估计。我们将开发一种统计算法，该算法可以使用此类调查的数据生成不同空间尺度的数据产品，并探索将该算法提供给数据的最终用户的可行性。最后，我们将考虑使用空间数据产品来推导进一步产品时不确定性的传播。特别是，我们将量化使用土壤辐射特性的空间乘积作为土壤碳浓度模型输入所产生的不确定性。我们将量化这种传播的不确定性，并探索必须提供给辐射产品用户的信息，如果他们也能够确定最终产品中出现的不确定性程度。本项目主要是对空间数据产品的尺度和不确定性问题进行统计研究。但是，除了统计人员外，项目小组还包括产品开发、数据科学和地球科学方面的专家，他们将提供有关项目发现的宝贵信息和建议，以便向空间数据产品的用户传达。

When deciding how land should be utilised, planners require information about the status of that land and its relative suitability for different uses. For instance, planners might wish to compare the value of land for agricultural production (which might be determined from soil properties), for resource extraction (which might be determined from mineral resource information) and for housing (which will require information about flood and subsistence risk and the suitability of the land for building). The information required to make these assessments is often provided as spatial data products in which the relevant environmental property (e.g. soil pH or flood risk rating) is estimated on the nodes of a spatial-grid which covers the relevant landscape. These spatial data products are derived from the data and models which are available for the landscape under consideration. A soil pH spatial product might be produced by interpolation of the pH values that were measured in a soil survey of the region. Alternatively, a mathematical model that integrates information about climate, topography and drainage might be used to determine the flood risk.This project addresses two problems in such use of spatial data products. First, the planners are unlikely to be aware of or account for the uncertainty that is associated with the product. Some uncertainty will almost inevitably arise because it is rarely possible to measure at every relevant location. Second, the spatial product describes the expected value of the environmental property for a specific spatial scale and this might not be the scale at which information is required. For instance, in a mineral resource product, the horizontal scale of the estimates might correspond to the diameter of the boreholes in which the mineral concentrations were measured. However, planners might be interested in the mineral concentrations at a spatial scale equal to the size of a quarry. These issues propagate further if a spatial data product is used as an input to a mathematical or empirical model that leads to a further data product especially if the model has been designed to relate environmental properties at a scale which is inconsistent with the data products.In this project we will consider strategies for minimising, quantifying and communicating the uncertainty and scale related issues of spatial data products. We will relate these issues to two pertinent data sets regarding the carbon content of UK soils. We will determine how a spatial survey of such data might be cost-effectively designed to yield accurate estimates of the property of interest at different spatial scales. We will develop a statistical algorithm that can use the data that result from such a survey to produce data products at different spatial scales and explore the feasibility of making this algorithm available to end users of the data. Finally, we will consider the propagation of uncertainty when spatial data products are used to derive further products. In particular, we will quantify the uncertainty that results from using a spatial product of the radiometric properties of the soil as an input to a model of soil carbon concentrations. We will quantify this propagated uncertainty and explore the information that must be provided to users of the radiometric product if they are too are to be able to determine the degree of uncertainty that will appear in a resultant product.This project is primarily a statistical study of the issues of scale and uncertainty in spatial data products. However, in addition to statisticians the project team includes experts in product development, data science and earth science who will provide valuable information and advice regarding about the project findings can be communicated to users of spatial data products.