A hybrid LS-HE and LS-SVM model to predict time series of precipitable water vapor derived from GPS measurements

Precipitable water vapor (PWV) is one of the key parameters for the analysis of global climate systems, formation of clouds, and short-term forecasts of precipitation. Since water vapor is highly variable both spatially and temporally, it can be problematic, requiring modeling and efficient techniques in order to measure its quantity. Global Positioning System (GPS) stations provide total water column at high quality under all weather conditions with high temporal resolution. The technique used in this work is Precise Point Positioning (PPP) for single dual-frequency GPS receiver aided by precise orbit and clock product. Zenith wet delay (ZWD) is estimated through a stochastic process called random walk at 5-min intervals. The seasonal and diurnal variations of PWV for four GPS stations located in Europe are investigated. Latitude and station height are the most influential factors for the amount of water vapor when we compare their amplitudes and offsets to NASA Water Vapor Dataset-M (NVAP-M) and station heights. The area-averaged accumulated rain time series retrieved from Tropical Rainfall Measuring Mission (TRMM) product also shows that high PWV levels do not necessarily lead to rainfall. The amplitudes of diurnal and semi-diurnal variations are found to be of much lower amount than those of seasonal variations. In order to validate the capability of GPS-sensed PWV measurements, two episodes in wintertime and summertime are simulated using Weather Research Forecast (WRF) model. Both simulated PWV and observational PWV are consistent with each other. The main objective of this paper is to model and forecast the PWV time series which would be useful information on climatology and meteorology. Due to the distinct harmonic characteristics of PWV time series, the least squares harmonic estimation (LS-HE) is applied to time series of PWV derived from 4-year GPS station observations. Subsequently, least squares support vector machine (LS-SVM) optimized by cross-validation strategy is used to model non-harmonic components of the signal. The underlying motivation for using LS-SVM is the proficiency of this methodology to precisely model time series data when the underlying model is usually non-stationary, not defined a priori, and non-linear which are major characteristics of PWV data. The modeled time series shows that the hybrid approach (LS-HE and LS-SVM) can efficiently filter white noise in the observations and then perform forecasting. The bias (similar to 0.37 mm) and standard deviation (similar to 3 mm) of observed and predicted values presents the sound capability of the proposed model.