High Mountain Asia (HMA) glaciers are critical water reserves for montane regions, which are readily influenced by climate change. The glacier mass balance during 2000–2021 over HMA was estimated by comparing the elevations from ICESat-2 and the NASADEM. Radar penetration depth could be one of the intrinsic error sources in estimating glacier mass balance by using NASADEM. Therefore, we doubled elevation differences between the X-band Shuttle Radar Topography Missions (SRTMs) and NASADEM to estimate the potential error. The spatial characteristics of the altitude-dependent penetration depth can be detected in most sub-regions of HMA. Relatively deep penetrations in the Himalaya (2.3–3.7 m) and Hissar Alay (4.3 m) regions and small penetrations in the south-eastern HMA (1.0 m) were observed. The HMA region experienced a significant mass loss at a rate of −0.18 ± 0.12 m w.e. a−1, in which the Hengduan Shan exhibited the highest mass loss of −0.62 ± 0.10 m w.e. a−1, the West Kun Lun experienced a substantial mass gain of 0.23 ± 0.13 m w.e. a−1, and the Karakoram showed a more or less balance. Our results are in agreement with previous studies that assessed the mass balance of HMA glaciers from different methods.

Integrable couplings of the Boiti-Pempinelli-Tu hierarchy are constructed by a class of non-semisimple block matrix loop algebras. Further, through using the variational identity theory, the Hamiltonian structures of those integrable couplings are obtained. The method can be applied to obtain other integrable hierarchies.