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Mapping complex biological processes across the landscape: the problem of non-stationarity

绘制整个景观中的复杂生物过程：非平稳性问题

基本信息

批准号：
BB/E001599/1
负责人：
Richard Lark
金额：
$ 55.82万
依托单位：
Rothamsted Research
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=BB%2FE001599%2F1
关键词：
Mapping complex biological processes across

项目摘要

Many important processes happen in the landscape. For example, certain soil bacteria, denitrifiers, use nitrate in their respiration. One product of this is nitrous oxide, a gas with 270 times the impact of carbon dioxide on global warming. Management of farmland affects how much nitrous oxide is released. We must understand and measure these processes, but managed soils and vegetation are extremely variable. They vary at fine spatial scales (e.g. between adjacent clods of an apparently uniform soil) and at coarser scales (e.g. between the bottom of a slope and the top of a hill). But we must make predictions of variables in this complex system from relatively few observations. Scientists do this with methods called geostatistics. We assume that a variable over a region has arisen from a random process. We know that this is not true, of course, but we often make such assumptions: the number on a thrown die depends on Newton's laws of motion, but we can treat it as a random variable, here a number from 1 to 6 that cannot be predicted in advance, and all occur with equal probability. A die will not behave this well if it is not a perfect, uniform cube. We can estimate a better model for a real die if we throw it many times and record the numbers that turn up. In the geostatistical picture of variation, we think of our data, obtained at a set of sites, as numbers obtained by throwing a die. The only complication of the model is that the numbers on two dice thrown at sites near to each other are more likely to be similar than on two dice at sites that are further apart. This is called spatial dependence and geostatistics requires that we can describe it. This is not simple; for any two sites a and b we only have one observation at each, and from this we can make no statements about their joint variation. The solution is to assume that the variation between two observations of a variable separated by some distance (e.g. 10m) in one part of the landscape, and the variation between another two observations 10m apart are, as it were, duplicate information about the variability in space. In this way we build up a model of the spatial dependence, called the variogram, but it depends on this assumption of an underlying process for which the variation between two sites depends only on how far apart they are, not on where they are. This is called stationarity of the variance. This assumption is often unrealistic in the landscape. The variability of a process like denitrification in a wet low-lying area with peaty patches in the soil will be much greater than than in a well-drained, cultivated arable field. The variability of soil pH over short distances may be larger in mixed sediments at the bottom of a slope than on an old eroded land surface. The aim of this project is to develop geostatistical methods to deal with such variation. Our idea is to treat the spatial dependence as a mathematical function of spatial position, adding some extra parameters to the model of spatial dependence. We believe that, while this won't remove assumptions from our analysis, the assumptions will be more plausible than stationarity. As well as developing new models of spatial dependence we shall develop exploratory methods to decide when more complex spatial models are needed, and to help design them for particular problems. We shall also investigate how our scientific knowledge of processes, described mathematically, can be used to help predict them when the variation is complex. We shall test and demonstrate these methods using new data on the rates of nitrous oxide emissions from soils in complex farmed landscapes with many very different land uses. This important variable will vary in a complex way, so that stationarity cannot be assumed with confidence. If successful this project will provide tools to study and predict many different complex variables such as soil biodiversity and pollution.

许多重要的过程发生在景观中。例如，某些土壤细菌，微生物，在呼吸中使用硝酸盐。其中一个产品是一氧化二氮，这种气体对全球变暖的影响是二氧化碳的270倍。农田的管理影响着一氧化二氮的释放量。我们必须了解和测量这些过程，但管理的土壤和植被是非常可变的。它们在精细的空间尺度上（例如，在表面上均匀的土壤的相邻土块之间）和在较粗的尺度上（例如，在斜坡底部和山顶之间）变化。但是，我们必须根据相对较少的观测结果来预测这个复杂系统中的变量。科学家们用一种叫做地质统计学的方法来做这件事。我们假设一个区域上的变量是由随机过程产生的。当然，我们知道这是不正确的，但我们经常做这样的假设：掷出的骰子上的数字取决于牛顿运动定律，但我们可以把它当作一个随机变量，这里是一个从1到6的数字，不能提前预测，并且所有的数字都以相等的概率出现。如果一个骰子不是一个完美的、均匀的立方体，它就不会表现得这么好。如果我们掷多次骰子，并记录下掷出的数字，我们就可以估算出一个更好的真实的骰子模型。在变异的地质统计学图景中，我们认为我们的数据是在一组地点获得的，是掷骰子获得的数字。该模型唯一的复杂之处在于，在两个相距较近的地点掷出的两个骰子上的数字比在两个相距较远的地点掷出的两个骰子上的数字更有可能相似。这就是所谓的空间相关性，地质统计学要求我们能够描述它，但这并不简单;对于任意两个地点a和B，我们在每个地点只有一个观测值，因此我们无法对它们的联合变化做出任何声明。解决办法是假设在景观的一部分中，相隔一定距离（例如10米）的两个变量观测值之间的变化，以及相隔10米的另外两个观测值之间的变化，可以说是关于空间变化的重复信息。通过这种方式，我们建立了一个空间依赖性模型，称为变差函数，但它依赖于一个潜在过程的假设，即两个地点之间的变化只取决于它们相距多远，而不是它们在哪里。这被称为方差的平稳性。这种假设在景观中往往是不现实的。在土壤中有泥炭斑块的潮湿低洼地区，反硝化过程的可变性比排水良好的耕地要大得多。在斜坡底部的混合沉积物中，土壤pH值在短距离内的变异性可能大于老的侵蚀地表。该项目的目的是开发地质统计学方法来处理这种变化。我们的想法是把空间依赖性看作是空间位置的数学函数，在空间依赖性模型中加入一些额外的参数。我们相信，虽然这不会从我们的分析中删除假设，但这些假设将比平稳性更合理。除了开发新的空间依赖模型外，我们还将开发探索性的方法来决定何时需要更复杂的空间模型，并帮助设计它们以解决特定问题。我们还将研究如何利用我们的数学描述的过程的科学知识来帮助预测复杂的变化。我们将测试和证明这些方法使用新的数据在复杂的农业景观与许多非常不同的土地使用的土壤中的一氧化二氮的排放率。这个重要的变量将以复杂的方式变化，因此不能有信心地假设平稳性。如果成功，该项目将提供研究和预测土壤生物多样性和污染等许多不同复杂变量的工具。