Modeling data relationships with a local variance reducing technique: Applications in hydrology

The assessment of an appropriate function describing the relationship between hydrological variables is a frequent problem. The usual way of estimating an overall function is a difficult task if the relationship between the variables is highly nonlinear. Nearest neighbor methods provide an alternative. In this paper different generalizations of the nearest neighbor method are suggested. Besides using different estimators the problem of finding an appropriate distance measure is discussed. Linear embedding of the observation space into an appropriate Euclidean space can improve the distance‐based methods substantially. The suggested transformations and the corresponding local linear estimators are applied to two different examples: the prediction of local discharge characteristics from catchment properties and a simple 1 day flood forecasting problem.