Note 573 — Chapter VIII · THE KINGDOM OF SCOTIA.
Reading edition
Post fratris interitum Ealdulfus comes efficitur Northymbrensium, qui, cum superbia extolleretur, Britones satis atrociter devastavit: sed tertio post anno, cum ad Hardecanutum reconciliandus in pace venisset, interfectus est a Siwardo, qui post illum totius provinciæ Northanhymbrorum, id est ab Humbra usque Tuedam Comitatum habuit.—Sim. Dun. Hist. Con.
As the Saxon Chronicle records the death of Eadulf in 1041, this places this invasion in 1038.