Sensor networks usually have limited energy and transmission capacity. It is beneficial to reduce the data volume for dissemination in a sensor network that monitors continuous physical processes in order to reduce energy consumption. Data compression schemes in use should be able to adapt to limited bandwidth while preserving high data quality. We propose a wavelet-based, error aware compression algorithm that is targeted to achieving these goals. It is called RACE (rate adaptive compression with error bound). It can adjust its maximum normalized error to current network capacity. Additionally, errors due to multiple passes of compression during multi-hop relaying are additive and thus can be estimated easily upon data reconstruction. Moreover, during data dissemination, error ranges can be narrowed through an opportunistic patching process when excess bit rate is available. Consequently, the performance is less subject to the volatility of physical processes. The algorithm has been evaluated in various aspects and demonstrated to be effective in rate adaptivity, error range narrowing, and preservation of statistical interpretation.