The reconstruction of cool-season (total November-April) precipitation back to AD 1000 was accomplished using stepwise linear regression and artificial neural network techniques. Linear regression relies on the linear relationship between tree-growth and precipitation, while the neural network approach can be used to model both linear and nonlinear relationships between tree-growth and precipitation.
Linear regression is a statistical technique used to quantitatively model the relationship between tree growth and precipitation. Regression models for each climate division are constructed by using a stepwise multiple regression procedure to predict precipitation from one or more of the 19 tree-growth chronologies based upon the linear relationship observed between the data sets. The observed relationship can then be applied to predict precipitation prior to the time period when instrumental records were available. A suite of statistics are used to assess the reliability and strength of the relationship expressed in each regression model.
The neural network technique relies on developing generalized relationships between tree growth and cool-season precipitation after being trained in a self-organizing learning procedure. The neural network technique allows for the definition of complex relationships between input/output data including those that may be nonlinear. Neural network techniques rely on an iterative learning process that functions by repeatedly training the input data used in the model to minimize error. In a sense, a neural network functions like a human's brain in that it learns through repeated trials. The results of these repeated trials are stored as a system of weights that are applied to data used in the final model. The advantage of neural networks lies in their ability to learn and represent complex and often nonlinear relationships directly from the data being modeled.
The 19 tree-ring sites were selected based on several criteria. First, the sites were required to have a strong relationship with cool-season precipitation and extend through at least 1988. Second, all the individual tree-ring samples in a given site needed to be at least 500 years in length to preserve the multi-decadal precipitation signal contained within the tree-rings. The chronologies also had to have sufficient tree-ring sample replication between AD 1000 and the late 20th century in order to maintain the strength of the climate signal during earlier time periods.
Cool-season precipitation for the period 1896-1988 for each of the NOAA climate divisions in Arizona and New Mexico were used to define the relationship between tree growth and precipitation to develop empirical models suitable for the reconstruction. The linear regression reconstructions explain between 11 and 53 percent of the variance in cool-season precipitation between 1896-1930 (with an average of 32 percent). The neural network reconstructions are similar, explaining between 13 to 64 percent of the variance over the same period (31 percent average).
Results indicated that the reconstructions developed using linear regression techniques were better recorders of dry periods while the neural network technique captured wet periods better. To exploit the best qualities of each reconstruction method, the two were combined.