Longwave infrared (LWIR) hyperspectral imaging can be used for many tasks in remote sensing, including detecting and identifying effluent gases by LWIR sensors on airborne platforms. Once a potential plume has been detected, it needs to be identified to determine exactly what gas or gases are present in the plume. During identification, the background underneath the plume needs to be estimated and removed to reveal the spectral characteristics of the gas of interest. Current standard practice is to use ``global" background estimation, where the average of all non-plume pixels is used to estimate the background for each pixel in the plume. However, if this global background estimate does not model the true background under the plume well, then the resulting signal can be difficult to identify correctly. The importance of proper background estimation increases when dealing with weak signals, large libraries of gases of interest, and with uncommon or heterogeneous backgrounds. In this paper, we propose two methods of background estimation, in addition to three existing methods, and compare each against global background estimation to determine which perform best at estimating the true background radiance under a plume, and for increasing identification confidence using a neural network classification model. We compare the different methods using 640 simulated plumes. We find that PCA is best at estimating the true background under a plume, with a median of 18,000 times less MSE compared to global background estimation. Our proposed K-Nearest Segments algorithm improves median neural network identification confidence by 53.2%.