Data assimilation combines a model forecast with live observations to give a better estimate of a system's current state, such as river flow.
Data assimilation is a set of methods for merging a model's forecast with new observations to get the best estimate of the current state of a system. Neither the model nor the sensors are perfect, so data assimilation weighs each by how uncertain it is. The classic method is the Kalman filter. The model first makes a forecast of the state, x̂⁻. When an observation y arrives, the filter compares it with what the model expected to see, Hx̂⁻, where H maps the model state to the measured quantity. The difference is called the innovation. The state is then corrected by adding a share of the innovation: x̂ = x̂⁻ + K(y - Hx̂⁻). The Kalman gain K is large when the model is uncertain and the sensor is trusted, and small in the opposite case. For nonlinear hydrologic models, the ensemble Kalman filter is widely used: it runs many model copies and estimates the uncertainties from their spread. Particle filters and variational methods are other options. In river flood forecasting, observed water levels or flows at gauges are assimilated into a hydrologic or hydraulic model just before the forecast is issued, so the forecast starts from the river's real state rather than from wherever the model has drifted. In groundwater, head readings from piezometers can update modelled heads and sometimes parameters. Satellite soil moisture and snow data are also assimilated into land surface models. It needs a model, observations with known error, and an estimate of model error. Getting these error estimates right is often the hardest part. Limits: wrong error assumptions can make updates too weak or too strong. Correcting states does not fix a model whose structure is wrong, and the benefit at long lead times can fade as the forecast moves away from the corrected start.