Statistical analysis of hydrological variables related to tree-ring growth

Statistical analysis of hydrological variables related to tree-ring growth Statistical methods that can be used to determine the impact on hydrological indexed tree growth. The ability to determine the effects of different hydrological and climatic variables such as temperature, precipitation, stream flow and groundwater on the growth of Weste Sycamore requires the use of statistical methods and regression require more complex methods such as multiple linear regression analysis factors and the principal component analysis (PCA). A note of basic terms, as the dependent variable, tree-ring growth, measured on a scale, a direct correlation with the hydrological variables is limited to the period of one year. Of course, smaller periods of time are measured and used to determine variables such as precipitation, the groundwater level, temperature and current flow. In order to use the scale to measure finer hydrologic record, the type of aggregation of small scale temporal changes in the season, the trends and indexes used. For example, if the ground water measured quarterly over a month, creating an index of ground-water, which combines the average values in groundwater, with a maximum of recession, or greater change between wet and dry period period three subsets in an effective way of groundwater, which describe the end of the scale variability within the year, record without loss of information on the time dependent variable. Multiple linear regression analysis This type of statistical method combines all the independent variables (precipitation, stream flow, temperature, etc.) in a linear polynomial model that the mean response of the dependent variable (in this case, tree ring growth). A simplified mathematical representation of three independent variables x, X2, X3 model for the mean response m is: where B is a fitting parameter for each independent variable. For the application of tree ring growth, the mean response of the tree population for one year time scale is modeled by n independent variables, such as the hydrological variables described above. The regression model using a least square fit to the data that minimizes the sum of squares of deviations from the vertical data for each model line with a term residual sum of squares of errors. The basic premise of multiple linear regression is that the independent variables and dependent variables are similar differences in the distribution of its values and are normally distributed (eg, non-biased distribution). Analysis of principal components variables useful for hydrological properties of this type of statistical analysis and the application for the tree-ring analysis is that many independent variables collapse in a few main components that capture the maximum variability of the data. For example, rainfall, stream and groundwater may be related to each other, but the multiple linear regression with the tree growth can not be immediately obvious or feasible due to different scales and delays in the time series. However, if you create a variable that is composed of three, the maximum variability of a majority of independent values could be directly related to tree ring data. In practice, the principal component method creates several key components of the independent variables (PC1, PC-2, PC3), which the draft law for the variability of the original documents. The main components are related to variable loads to determine whether a relationship exists. It is important to note that a report on its does not imply a mechanism for the relationship between the dependent and independent variables.