Formulation of the Evolutionary-Based Data Assimilation, and its Implementation in Hydrological Forecasting

Multi-objective evolutionary algorithms (MOEAs) have gained popularity for their capability to handle complex and nonlinear problems. MOEAs are population-based search tools which employ the concept of biological evolution and natural selection. While MOEAs have been applied in numerous hydrological studies for parameter estimation, their formulation for solving data assimilation (DA) problems has not been completely formalized in the literature. This study presents the evolutionary-based data assimilation (EDA) where it formulates the MOEA strategy into an applied DA procedure. The study outlines the stochastic and adaptive capabilities of MOEAs, and shows how MOEA operators including Pareto dominance, crossover, and random variation are naturally suited to handle DA problems. The EDA employs the cost function from variational DA to approximate the least squares estimate between ensemble simulations and perturbed observation. The EDA uses the MOEA strategy to evolve a population of competing members through several cycles of evolution at each assimilation step. The EDA determines several non-dominated members for each assimilation time step, allows these members to evolve, and evaluate updated members for subsequent time steps. Several ensemble members are evaluated for each assimilation time step but the updated ensembles are determined as a subset of the final evolved population which comprise the Pareto-optimal set. The EDA has been illustrated in a practical implementation to assimilate daily streamflow into the Sacramento Soil Moisture Accounting model.