The opportunity to model the local context of rainfall in Bayombong is presented by the Weather Monitoring System (WMS) of NVSU. The study looked into modeling the periodic component of the monthly precipitation time series of Bayombong from the WMS rainfall data from 2012 to 2015.

Fourier series harmonic analysis was employed through backward elimination stepwise Multiple Linear Regression (MLR) with the method of least squares in mathematical modeling. The four models obtained explained 90 percent variation in the observed data. The model with the first and second harmonics and the cosine term of the fifth harmonics is the best fit model and is parsimonious accounting for the 12, 6 and 2.4 months periods in the observed data. The best fit model has the highest adjusted coefficient of determination (R2) of 0.9043, the least root mean square error (RMSE) or magnitude of error of 55.99 mm and the least Akaike information (AIC) of 530.23. The model captured the long term periodic monthly rainfall of Bayombong described as Type III in Corona's climate classification which is relatively dry from November to April and wet the rest of the year. The model revealed that periodic rainfall peaks in July and August and is least in January. Periodic rainfall considerably increases in May and considerably decreases in November. Hence, the model can aid the WMS in providinglocal farmers practical knowledge about climatic rainfall conditions conducive to farming and can also be used in modeling the rainfall of Bayombong at different time scales.

Keywords: Best Fit Model, Fourier Series Harmonic Analysis, Least Squares, Mathematical Modeling, Multiple Linear Regression, Rainfall, Weather Monitoring System.

Thesis (Master of Science in Teaching s- Mathematics)

Includes appendices and bibliographical references.