The cryosphere in the Himalaya-Karakoram (H-K) is widespread, and its services significantly affect the SDGs implementation in the region, in particular related to the 'No poverty' (SDG 1), 'zero hunger' (SDG 2), 'good health and well-being' (SDG 3), 'work and economic' (SDG 8) and 'partnership for the goals' (SDG 17). We here established the networks to illustrate the complex relationship of cryosphere services with national SDG priorities in the countries of H-K, including Afghanistan, Pakistan, India, China, Nepal and Bhutan. The cryosphere services contributing to the national SDG priorities and the key targets were elucidated in line with the centralities of the network. It was found that 'freshwater', 'clean energy', 'runoff regulation', 'climate regulation', 'research and education' and 'infrastructure and engineering' are the services that play critical roles in H-K, and they were then applied to assess the impact of cryosphere services on the national SDG priorities. We subsequently identified a set of principal indicators in relation to the key targets of national SDG priorities, which has the explanation up to 85% of six entry points (SEPs) to advance SDGs of each country in H-K. In conjunction with the centrality of the key targets to be contributed by the overall cryosphere services in the network for each country, the dependency of SEPs on the cryosphere services can be established through principal indicators in association with the national SDG priorities in H-K countries.

The cryosphere is able to provide a variety of services for the benefit of human well-being and underpins regional sustainable development. The cryosphere deterioration induced by climate change is impacting the services and will subsequently impede the efforts to meet sustainable development goals (SDGs) in high mountain societies. Here, we detail the context of cryosphere services and establish a dataset for its linkage to SDGs. This allows us to uncover its roles in supporting SDGs, directly by a causal connection and indirectly through either cascading effects or interconnection among SDGs. We find that the SDGs in association with the basic needs of high mountain societies are mostly affected by the cryosphere services. The different types of services pitch in with distinctions to be embraced by various SDGs, whilst some play a prominent role in the contribution to a broad range of SDGs. We further investigate how the services behave in their contributions to SDGs, by taking a view via the lens of a network that deciphers the relationship between the services and SDG targets as well as the interconnections among SDG targets. With an insight into the centrality and modularity of services in the network, we then delineate the inherent criticality of services to SDG targets as a whole, and reveal the specificity of services that co-contribute to a cluster of SDG targets in each network community. We take out the services from the network and maintain their interlinks to the targets of each underlying SDG system represented in six key entry points, so that the services critical to the transformation pathways in the entry points for SDGs in high mountains can be identified. Finally, we discuss the trade-offs that can occur in high mountains, which is unique for the cryosphere services. It creates more complexity in the assessment of overall benefits that the cryosphere services may provide to SDGs, and urges the balance that has to be maintained in attaining those services for the transformation.