Análise da influência da densidade amostral na interpolação batimétrica por Krigagem: estudo de caso no Açude Pacatuba

Abstract

Efficient water resource management is a constant challenge, particularly in regions with high rainfall variability, where water availability heavily depends on surface reservoir storage. Effective management requires precise knowledge of a reservoir's actual capacity and submerged topography. Bathymetric surveys provide this essential data, yet their execution is time-consuming, infrastructure-intensive, and costly, raising a critical question: what is the necessary sample density to achieve reliable volumetric calculations while avoiding both under-sampling and excessive effort? This study analyzes the influence of sample density on the accuracy of reservoir volume estimates. Data were acquired using a single-beam echo sounder and interpolated via ordinary kriging in a Python environment to identify the optimal balance between operational cost and estimation accuracy. The Pacatuba Reservoir (Sapé-PB, Brazil) was used as a case study, with 12,034 depth points collected on October 30-31, 2024. Depth data were interpolated using different variogram models (spherical, exponential, Gaussian, and linear) and spatial resolutions (20 m and 10 m), with each configuration's performance evaluated through cross-validation. The exponential variogram proved most suitable, demonstrating the lowest error and best fit (RMSE = 0.069 m; MAE = 0.037 m; R² ≈ 0.999). A 10 m resolution was established as standard, as further reductions did not yield significant changes in estimated volume. To assess the impact of sample density, 100 independent interpolations were performed for each percentage of data points used (2.5% to 80%), enabling the calculation of means, standard deviations, and coefficients of variation. Results indicated that densities ≤ 5% produce inconsistent volumes with high dispersion. From 12.5% of the points, reliable estimates were achieved (RMSE = 0.31 m; CV = 3.8%). Using 25% of the points, variability became negligible (RMSE = 0.01 m; CV = 0.3%), and volumes matched the reference value. Thus, the range of 12.5% to 25% represents the optimal trade-off between sampling cost and volumetric precision, confirming the robustness of the methodology.