Machine learning ARIMA for modelling and forecasting variations inearth’s surface phenomenon using sparse time series satellite data—acase study of sea surface salinity in the Nigerian coastal zone

Abstract

<title>Abstract</title> The tropical coasts, particularly the Nigerian coastal zone, have been traditionally undersampled using appropriate in situ methods and understudied using appropriate remote sensing techniques despite the proliferation of satellite missions for earth observation. The contemporary all-weather satellite observations of phenomena of interest are characterized by relatively sparse time series data that discourage their utilization as input in building efficient machine learning (ML) models for both exploratory and predictive purposes. Additionally, data-poor areas usually have difficulties meeting the multiple predictor variable requirement of building appropriate multivariate ML regression models. We utilized a relatively sparse sea surface salinity (SSS) dataset from the Soil Moisture Active Passive Mission (SMAP) satellite products (Jan., 2016-Dec., 2021) for this study. We determined the accuracy and variability of the relatively sparse SSS data for the study area to be approximately 6.5° × 4.5°. We built ML autoregressive integrated moving average (ARIMA) models and determined and validated the best model for modelling (Jan., 2016-Dec., 2020) and forecasting (Jan.-Dec., 2021) Earth’s surface phenomenon (ESP) using relatively sparse SSS data as a case study. We show root mean squared differences (RMSDs) of 0.1279 psu and 0.1162 psu for modelling and forecasting data accuracy, respectively. We show a standard deviation (SD) of 0.2528 for the interannual SSS variability (iSSSv). We show the modelling accuracy with an R-squared (R²) of 0.8345281 and its validation with a mean absolute percentage error (MAPE) of 0.7779% and the forecasting accuracy with a root mean squared error (RMSE) of 0.9850 psu and its validation with a MAPE of 2.7670% for the best ML ARIMA model. The relatively low SD value suggests a relatively stable iSSSv along the Nigerian coastal zone. The R²and MAPE results suggest relatively high modelling and prediction accuracy. The results imply that relatively sparse satellite time series data of at least 60 epochs (hourly, daily, weekly, monthly or yearly observations) can be utilized for building a relatively accurate ML ARIMA model for modelling and forecasting variations in any ESP in any geographical area.