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This work presents novel methodology for the simultaneous modelling and forecasting of three-dimensional (3D) wind fields. This is achieved based on a quaternion domain wind model, which naturally accounts for the coupling between the dimensions of the 3D wind field. The proposed quaternion valued processing also facilitates the fusion of external atmospheric parameters, such as air temperature, exhibiting more degrees of freedom and enhanced accuracy. The quaternion least mean square (QLMS) algorithm and its variants are used for short term adaptive forecasting, and a rigorous comparative study with the corresponding algorithms in ℝ4 is performed. Simulations for different wind regimes and over a range of prediction horizons support the approach.