Projection in Hilbert Space for flood forecasting of the Pomahaka River, New Zealand

Abstract

A proper flood forecast of river flows can provide communities and/or governmental agencies with a quite effective tool for flood warning and in turn reducing/mitigating the negative impacts of incoming flood events. This research presents a new approach for flood forecasting of the Pomahaka River in Otago, New Zealand. This methodology is based on the projection in Hilbert Space of hourly flows of the Pomahaka River at Burkes Ford on the span of hourly rainfall data and/or previous flows of the same flow site or other flow sites. The projection theorem in Hilbert Space guarantees that the estimated parameters will produce a model with the least mean squared error. The Pomahaka catchment has rural aspects and its land use is mainly agricultural activities. The Pomahaka catchment is about 1871 km2, and has several flow and rainfall sites. Only 3 rainfall sites and 3 flow sites have been used in this research due to data availability. Hourly flows and rainfall data for this catchment have been investigated and 26 high flow events of the Pomahaka River at Burkes Ford, have been identified for the modelling process. A new model for simulating hydrologic abstractions have been developed and compared to the commonly used NRCS method. Results of the flood forecast modeling process, based on projection in Hilbert Space, for producing a 10 hr forecast model for the Pomahaka River, achieved an overall value of 0.76 for R squared and 0.87 for Filliben correlation coefficient.