Human-related activities are primarily accountable for climate change resulting in natural disasters. Therefore, it has become essential to analyze and evaluate public awareness of climate change globally. With the prevalence of social networks like Twitter, sentiment classification has been recognized as a powerful tool to determine public opinion and concern on such ecological issues. Therefore, this study proposes a framework to classify the tweets containing public opinion towards climate change using Bi-directional Long Short-Term Memory (Bi-LSTM) Networks. The proposed framework quantified the intensity of the public opinion classified by the Bi-LSTM model to measure the strength of the public concern towards climate change and validated it using three case studies: Earth Day, Delhi Air Pollution, and Australian Bushfires. The intensity values of the public sentiments concerning these events were obtained as 98.50%, 96.57%, and 98.33%, respectively. The proposed work was further augmented with a lexicon-based emotion analyzer to categorize the emotions associated with the tweets into positive, negative, neutral, and mixed to substantiate the results. This framework can be utilized before enforcing the policy decisions on the general public in any domain.