1. Resampling to estimate significance level
- Resampling is a robust method for estimating the significance level of a test statistic. It is particularly useful when the test assumptions are violated.
- In resampling, the orginal time series data are resampled to provide many replicates of time series data of equal length as the original data. The time series data for each replicate are obtained by randomly selecting data value from any year in the orginal time series continously until a time series of equal length as the orginal data is construced. In TREND, the data are resampled with replacement (bootstrap method), i.e., the replicate series may contain more than one of some values in the original series and none of the other values.
- The test statistic value of the original time series data is then compared with the rest statistic values of the generated data (replicates) to estimate the significance level. For example, if the test statistic value of the orginal data is the same as the 950th highest from 1000 replicates, Ho is rejected at a=0.05 (i.e., a trend/change is detected, with a 5% probability that this trend/Change is incorrectly detected.
2. Parametric and non-parametric tests
- Most statistical tests assume that the time series data are independent and identically distributed.
- The parametric test also assumes that the time series data and the errors (deviations from the trend) follow a particular distribution. most parametric tests assume that the data are normally distributed. Parametric tests are useful as they also quantify the change in the data. Parametric tests are generally more powerful than non-parametric tests.
- Non-parametric tests are generally distributed free. They detect trend/change but do not quantify the size of the trend/change. They are very useful because most hydrologic time series data are not normally distributed.
非参数检验只能给出趋势是否显著,但无法给出具体的趋势值
3. We compare the model fit parameters with the fit parameters obtained from observational data. We only use the model if the fit parameters of the model are within the 95% CI (Confidence Interval) of those from observations. 如何选模式,选择模式模拟得到的分布参数,落在观测参数估计的95%范围以内。
4. 1.5℃和2℃下的PR变化计算方法,极端多ensemble平均下的全球地表温度达到1.5℃和2℃的时间
5. historical, natural world: 1901-2005; Current world: 2006-2015;
6. CMIP5得到1.5℃和2℃的方法,计算每个模式10年平均温度落在1.3℃-1.7℃代表1.5℃;平均温度落在1.8℃-2.2℃代表2℃。所有模式所有情境下10年的数据集合在一起
7. 用KS评估模式与观测的分布一致性,样本要用与气候态的差异(温度)以及百分比(降水)。如果有三分之二的模式得到的模式变量与观测相似(p>0.05),则通过检验(pass the test)
8. 首先对每个站点的极端温度指数计算相对于1961-1990年的距平,之后对5°×5°的经纬度网格点的所有站点的指数求平均,得到中国区域1961-2017年5°×5°极端气候指数网格化距平序列,再通过面积加权平均得到中国极端气候指数变化序列。
9. 1950 DJF=Dec 1949-Feb 1950