Wheels adapted to roll on and across surfaces of fields, for example, as part of irrigation systems of types used in agricultural applications. Such a wheel has an axis of rotation, a center portion comprising a central hub concentrically disposed on the axis of the wheel and multiple spokes radiating from the central hub, and a tread portion circumscribing the center portion. A radially outermost extent of each spoke terminates at a spade that is oriented parallel to the axis of the wheel. The tread portion includes tread plates, each located between and attached to adjacent pairs of the spokes. The spades protrude radially outward between and beyond adjacent pairs of the tread plates.