Proper specification of measurement and prior error covariance matrices play an important role in Bayesian inverse problems. No canned strategies can be adopted to construct these error covariance matrices as their specification depends on the quantity that we want to infer from the data. For e.g. an exponential covariance model cannot be used to model the prior error covariance associated with carbon dioxide emissions from power plants, as they are point sources and their emissions are not smoothly varying quantity. Contrarily, prior error covariance for on road carbon dioxide emissions can be specified by measuring number of vehicles passing on a highway within a given timeframe. With this premise about error covariance matrices, we test their influence on inverse estimates of carbon dioxide (CO2) fluxes in Los Angeles basin. The error covariance matrices that we prescribe mimic the processes that influence CO2 emissions and include night-lights, taxicab rides and twitter feeds among others. We use reduced chi-square and Bayesian information criterion in a simulated and real data framework to rank the influence of these covariance matrices.