eXplainable Artificial Intelligence (XAI) has emerged as an essential requirement when dealing with mission-critical applications, ensuring transparency and interpretability of the employed black box AI models. The significance of XAI spans various domains, from healthcare to finance, where understanding the decision-making process of deep learning algorithms is essential. Most AI-based computer vision models are often black boxes; hence, providing explainability of deep neural networks in image processing is crucial for their wide adoption and deployment in medical image analysis, autonomous driving, and remote sensing applications. Recently, several XAI methods for image classification tasks have been introduced. On the contrary, image segmentation has received comparatively less attention in the context of explainability, although it is a fundamental task in computer vision applications, especially in remote sensing. Only some research proposes gradient-based XAI algorithms for image segmentation. This paper adapts the recent gradient-free Sobol XAI method for semantic segmentation. To measure the performance of the Sobol method for segmentation, we propose a quantitative XAI evaluation method based on a learnable noise model. The main objective of this model is to induce noise on the explanation maps, where higher induced noise signifies low accuracy and vice versa. A benchmark analysis is conducted to evaluate and compare performance of three XAI methods, including Seg-Grad-CAM, Seg-Grad-CAM++ and Seg-Sobol using the proposed noise-based evaluation technique. This constitutes the first attempt to run and evaluate XAI methods using high-resolution satellite images.