Implications and impacts of transforming lognormal variables into normal variables in VAR
Implications and impacts of transforming lognormal variables into normal variables in VAR
复制标题
将 VAR 中的对数正态变量转换为正态变量的含义和影响
DOI：
10.1127/0941-2948/2007/0243
复制
发表时间：
2007
影响因子：
1.2
通讯作者：
S. Fletcher
中科院分区：
文献类型：
--
作者：
S. Fletcher
在本文中，我们比较了在 3 维变分数据同化框架中处理对数正态变量/观测值及其误差的两种不同方法。第一种方法使用变换将对数正态随机变量变成正态随机变量，因此我们可以使用当前的数据同化技术。第二种方法通过混合分布对正态和对数正态随机变量的集合使用正确的分布，该混合分布给出了不同的成本函数以最小化。这两种不同方法的特性是，第一种方法找到分析中值，而第二种方法找到分析模式。通过使用具有不同观测误差方差和不同观测之间时间长度的 Lorenz 1963 模型对两者进行比较。事实证明，第二种方法优于第一种方法；然而，第一种方法通常在运营中心中使用，并具有某种形式的偏差校正，因此我们在本文末尾讨论了这一含义。
In this paper we compare two different approaches to deal with lognormal variables/observations, and hence their errors, in a 3-dimensional variational data assimilation framework. The first approach uses a transform to make the lognormal random variable into a normal random variable and hence we can use the current data assimilation techniques. The second approach uses the correct distribution for a collection of normal and lognormal random variables through a hybrid distribution which gives a different cost function to minimise. The properties of these two different approaches is that the first finds an analysis median whilst the second find the analysis mode. The two are compared through using the Lorenz 1963 model with different observational error variances and different lengths of time between the observations. It is demonstrated that the second approach out-performs the first here; however, the first is often used in operational centres with a form of bias correction and so we discuss this implication at the end of the paper.