An improved empirical framework for long-term reconstruction of terrestrial water storage and runoff in Pan-Arctic basins

Abstract. Long-term and continuous observations of terrestrial water storage (TWS) and runoff remain limited in the Pan-Arctic region, constraining our understanding of freshwater variability before the satellite era. Here, we developed two empirical models within a common framework for long-term TWS and runoff reconstruction. Monthly TWS is reconstructed from precipitation, air temperature, and snow information using an improved state-update empirical model, and runoff is subsequently estimated from TWS using a refined runoff–TWS relationship. The TWS model is constrained by observations from the Gravity Recovery and Climate Experiment (GRACE) mission, whereas the runoff model is calibrated against gauge observations. Using this framework, we reconstructed monthly TWS and runoff for 12 major Pan-Arctic basins from 1952 to 2025. The improved TWS model closely reproduces the mean seasonal cycle observed by GRACE and GRACE Follow-On (GRACE-FO), with a median Nash–Sutcliffe efficiency of 0.97. It also captures the major non-seasonal variations in most basins, with a median correlation coefficient of 0.74. Evaluation using GRACE (-FO) TWS shows that the refined runoff–TWS relationship improves monthly runoff reconstruction relative to the previous formulation, increasing the median Kling–Gupta efficiency (KGE) from 0.82 to 0.90 and reducing systematic seasonal biases. When applied to reconstructed TWS, the relationship maintains similar performance beyond the parameter-estimation periods, with median monthly KGE values of 0.92 during the 8-year parameter-estimation periods and 0.93 over the remaining available observations. Reconstructed annual runoff also captures the major interannual variations in observed runoff, with a median annual KGE of 0.65 across the 12 stations. This agreement with long-term gauge observations provides a complementary indirect assessment of the historical TWS reconstruction. Comparisons with existing GRACE-like TWS products and a gridded runoff reconstruction further support the long-term consistency of the framework, while sensitivity experiments show limited dependence on the parameter-estimation period. The proposed approach provides a simple means of extending Pan-Arctic TWS records into the pre-GRACE era and producing continuous runoff reconstructions over the full study period, thereby supporting investigations of long-term Pan-Arctic freshwater variability.