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Critical climate applications like cyclone tracking and earthquake modeling require high-performance simulations and online visualization simultaneously performed with the simulations for timely analysis. Remote visualization of critical climate events enables joint analysis by geographically distributed climate science community. However, resource constraints including limited storage and slow networks can limit the effectiveness of such online visualization. In this work, we have developed an adaptive framework that simultaneously performs numerical simulations and online remote visualization of critical climate applications in resource-constrained environments. Our framework considers both application and resource dynamics to adapt various application and resource parameters including simulation resolutions, resource configurations and amount of data for visualization. We have developed two algorithms for processor allocation for simulations and the frequency of data for visualization. We show that our optimization method is able to provide about 30% higher simulation rate and consumes about 25-50% lesser storage space than the greedy approach.