Numerical weather prediction revisions using the locally trained differential polynomial network

• Differential polynomial neural network (D-PNN) extends the GMDH network structure.
• D-PNN constructs and solves the general partial differential equation with sum series.
• D-PNN is trained with historical time-series for actual local weather data relations.
• The correction model can apply NWP outputs to revise one target 24-hour forecast.
• NWP model revisions of the temperature, relative humidity and dew point were done.

Meso-scale forecasts result from global numerical weather prediction models, which are based upon the differential equations for atmospheric dynamics that do not perfectly determine weather conditions near the ground. Statistical corrections can combine complex numerical models, based on the physics of the atmosphere to forecast the large-scale weather patterns, and regression in post-processing to clarify surface weather details according to local observations and climatological conditions. Neural networks trained with local relevant weather observations of fluctuant data relations in current conditions, entered by numerical model outcomes of the same data types, may revise its one target short-term prognosis (e.g. relative humidity or temperature) to stand for these methods. Polynomial neural networks can compose general partial differential equations, which allow model more complicated real system functions from discrete time-series observations than using standard soft-computing methods. This new neural network technique generates convergent series of substitution relative derivative terms, which combination sum can define and solve an unknown general partial differential equation, able to describe dynamic processes of the weather system in a local area, analogous to the differential equation systems of numerical models. The trained network model revises hourly-series of numerical prognosis of one target variable in sequence, applying the general differential equation solution of the correction multi-variable function to corresponding output variables of the 24-hour numerical forecast. The experimental results proved this polynomial network type can successfully revise some numerical weather prognoses after this manner.