This study examines how artificial intelligence (AI), especially Reinforcement Learning (RL), can be used in farming to boost crop yields, fine-tune nitrogen use and watering, and reduce nitrate runoff and greenhouse gases, focusing on Nitrous Oxide (N$_2$O) emissions from soil. Facing climate change and limited agricultural knowledge, we use Partially Observable Markov Decision Processes (POMDPs) with a crop simulator to model AI agents' interactions with farming environments. We apply deep Q-learning with Recurrent Neural Network (RNN)-based Q networks for training agents on optimal actions. Also, we develop Machine Learning (ML) models to predict N$_2$O emissions, integrating these predictions into the simulator. Our research tackles uncertainties in N$_2$O emission estimates with a probabilistic ML approach and climate variability through a stochastic weather model, offering a range of emission outcomes to improve forecast reliability and decision-making. By incorporating climate change effects, we enhance agents' climate adaptability, aiming for resilient agricultural practices. Results show these agents can align crop productivity with environmental concerns by penalizing N$_2$O emissions, adapting effectively to climate shifts like warmer temperatures and less rain. This strategy improves farm management under climate change, highlighting AI's role in sustainable agriculture.