Alpine meadows in the arid-humid transition zone of the Qinghai-Tibet Plateau are highly sensitive to climate change, yet long-term assessments that integrate multi-driver interactions and threshold-relevant responses remain limited. Here we investigate semi-arid alpine grasslands in Gannan Prefecture using an optimized Biome-BGC model constrained by eddy-covariance observations. We reconstructed gross primary productivity (GPP) and net ecosystem productivity (NEP) for 1961-2019, conducted a quantitative perturbation experiment (warming, precipitation increase/decrease, CO2 doubling, and their combinations), and projected carbon-sink trajectories and spatial shifts for 2020-2100 under CMIP6 SSP126/SSP245/SSP585. The results showed that: (1) Historically, GPP (600-900 g C m(-2) a(-1)) and NEP (150-300 g C m(-2) a(-1)) increased overall, indicating a persistent carbon sink (NEP >0) with values generally decreasing from southwest to northeast; multi-year means ranked as alpine marshy meadow > subalpine meadow > alpine meadow. (2) In perturbation experiments, warming and precipitation increase enhanced GPP/NEP, whereas precipitation decrease constrained GPP gains, highlighting temperature as the primary driver of GPP potential while moisture regulates realized carbon uptake. The combined forcing TP1C (warming + precipitation increase + CO2 doubling) produced a non-additive (synergistic) enhancement, consistent with a threshold-relevant response under the predefined critical levels. (3) Future projections indicate continued increases in GPP and NEP (approximate to 800-1200 and 200-500 g C m(-2) a(-1)), with a scenario-dependent mid-century slowdown/plateau (similar to 2060-2075) and a northeastward expansion of high carbon-sink areas as emission pathways intensify. These results quantify multi-driver nonlinearities and spatial shifts, providing evidence to support early warning and adaptive management of alpine grassland carbon sinks in semi-arid transition zones.