Penerapan Metode Kuadratur Gauss-Legendre dalam Estimasi Akumulasi Curah Hujan Harian DAS Bengawan Solo

Abstract

This study applies the Gauss-Legendre Quadrature method with order variations n = 2 to n = 6 to calculate discrete daily rainfall accumulation at the Jurug 2 Station of BBWS Bengawan Solo during the period of March 17 - April 15, 2026, which is directly relevant to the major flooding event in Solo Raya on April 14 - 15, 2026. The method adaptation was carried out through interval transformation using the formula xᵢ = 15tᵢ + 16 and linear interpolation to obtain function values at non-integer evaluation points, with all computations implemented using Microsoft Excel. The actual rainfall accumulation value of 353.5 mm was used as the error reference. The calculation results show that the estimates for each order are 293.222 mm (n = 2; error 17.05%), 78.114 mm (n =  3; error 77.90%), 289.299 mm (n = 4; error 18.16%), 252.338 mm (n = 5; error 28.62%), and 414.449 mm (n = 6; error 17.24%). The error convergence pattern is non-monotonic and deviates from theoretical expectations due to the non-smooth characteristics of daily rainfall data with 13 zero-value days. Order n = 2 produces the smallest error, although this advantage is situational. The study concludes that simultaneous cross-order validation is more reliable than applying a single order to support flood early warning systems.