Statistical analysis of hydrological variables on the three

Statistical analysis of hydrological variables on the three Statistical methods that can be used to determine hydrologic impacts capacity growth.The tree indexes to evaluate the impact of different hydrological and climatic variables such as temperature, precipitation, stream flow and groundwater on the growth of Weste Sycamore requires use of statistical techniques regression and may require more complex methods such as multiple linear regression, factor analysis and principal component analysis (PCA). A note at the time, the base scalesSince dependent variable, tree-ring growth, measured on an annual scale, any direct correlation with hydrological variables is limited to the period of one year. Of course, small time scales may be used and the variables measured to determine how the rainfall, the groundwater level, temperature and current flow. By the end of the scale of measurement for hydrological data, the type of aggregation of small scale temporal seasonal changes, trends and indexes used. For example, if the ground water measured quarterly over a month, the creation of a land-water Aggregate Index, the average values in groundwater, with a maximum of recession, or period, among the biggest change and wet period Dry, effective on three subsets of groundwater that may the end of the scale variability within the year, record without loss of information on the time dependent variable. Multiple linear RegressionThis 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 average response of the structure of the population for one year time scale is modeled by n independent variables, such as the hydrological variables. 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 in line due to a residual sum of squares error.The basic premise of multiple linear regression is that the independent variables and the dependent variables have similar variance of the distribution of their values and are normally distributed (eg, not a skewed distribution). Analysis of principal components variables useful for hydrological properties of this type of statistical analysis and the application for tree ring analysis can compress that there are many independent variables in a few main components that capture the maximum variability in data. For example, precipitation, groundwater flow and can cover all together, but the multiple linear regression with each tree growth can not be immediately obvious or feasible due to various levels and delays in the time series. However, if a variable could be created by three, the maximum variability of most of the independent values can then be connected to the tree ring data directly.In practice, the principal component method creates several key components of the independent variables (PC1 PC 2 PC3?) that the draft law for the variability of the original data. The main components are then combined with the dependent variables to determine whether a relationship exists. It is important to note that the existence of a relationship does not mean that the mechanism for the relationship between the dependent and independent variables. The author hydraulics and environmental fluid mechanics engineer