Optimization of Precipitation Monitoring Network via Robust Empirical Orthogonal Function Analysis with QR Column Pivoting

The design of optimal precipitation station configuration (network) is pivotal for obtaining accurate spatiotemporal data in a cost-efficient manner in terms of high operation, management and maintenance costs of stations, and missing data completion. In the present study, historical spatiotemporal precipitation data of 18 stations located in the Upper Euphrates watershed basin are initially exposed to empirical orthogonal function (EOF) analysis to exploit the general intrinsic low dimensionality of the precipitation phenomenon. Along with the basic EOF analysis, robust and mean-centered versions are also developed to improve the prediction accuracy of spatiotemporal precipitation data and optimize the number of stations in the watershed basin. Importantly, for the first time, robust EOF (R-EOF) analysis has been carried out in a hydrological predictive study. The matrix that contains the obtained modes (EOFs) is fed into the QR factorization with a column pivoting algorithm and sparse precipitation gauge locations are identified. The assessment of the model using the Nash-Sutcliffe coefficient of efficiency (CE), root mean square error (RMSE), and mean absolute error (MAE) metrics reveals that the complete dimensional state space can be reconstructed effectively, and its future evolution can be predicted accurately even with a small number of observation stations. Remarkably, the spatiotemporal precipitation data for the entire field can be reconstructed using only four, five, 10, or 12 stations, utilizing robust mean-centered (R-MC-EOF), robust (R-EOF), mean-centered (MC-EOF), and standalone EOF models. These models demonstrate high performance with CE values of 0.96, 0.94, 0.84, and 0.81 and RMSE values of 2.2, 3.8, 5.7, and 6.8 mm, respectively. Notably, both the R-EOF and MC-EOF models outperformed their standalone counterparts in terms of model performance. When a sufficient amount of spatiotemporal data is available, the optimal number and locations of precipitation gauges can be easily determined using the QR with a column pivoting algorithm. This algorithm is user friendly and can be implemented in popular programming environments such as Python, MATLAB, and R. Due to the limited budgets and/or low accessibility conditions, challenging basin topography, and bad weather conditions, not many areas are extensively equipped with instruments to measure the precipitation; thus, high-resolution data is not always available. Acquiring reliable and accurate data is critical for water resources management, flood and drought warning, irrigation networks, hydrological (e.g., watershed, rain-runoff) modeling, and urban and environmental planning. This renders the proposed methodology very crucial in obtaining high-fidelity spatiotemporal data.