Recording and analysing environmental audio recordings has become a common approach for monitoring the environment. A current problem with performing analyses of environmental recordings is interference from noise that can mask sounds of interest. This makes detecting these sounds more difficult and can require additional resources. While some work has been done to remove stationary noise from environmental recordings, there has been little effort to remove noise from non-stationary sources, such as rain, wind, engines, and animal vocalisations that are not of interest. In this paper, we address the challenge of filtering noise from rain and cicada choruses from recordings containing bird sound. We improve upon previously established classification approaches using acoustic indices and Mel Frequency Cepstral Coefficients (MFCCs) as acoustic features to detect these noise sources, approaching the problem with the motivation of removing these sounds. We investigate the use of acoustic indices, and machine learning classifiers to find the most effective filters. The approach we use enables users to set thresholds to increase or decrease the sensitivity of classification, based on the prediction probability outputted by classifiers. We also propose a novel approach to remove cicada choruses using band-pass filters Our threshold-based approach (Random Forest with Acoustic Indices and Mel Frequency Cepstral Coefficients (MFCCs)) for rain detection achieves an AUC of 0.9881 and is more accurate than existing approaches when set to the same sensitivities. We also detect cicada choruses in our training set with 100% accuracy using 10-folds cross validation. Our cicada filtering approach greatly increased the median signal to noise ratios of affected recordings from 0.53 for unfiltered audio to 1.86 to audio filtered by both the cicada filter and a stationary noise filter.