On the other side of the watershed , the rivers Tyne , Tees , Swale , Calder , Aire , Don , and Trent flow east to the North Sea . On the other side of the watershed , the rivers Tyne , Tees , Wear , Swale , Ure , Nidd , Calder , Wharfe , Aire , Don and Trent also rise in the region but flow eastwards to the North Sea .