Machine learning calibration of low-cost NO<sub>2</sub> and PM<sub>10</sub> sensors: non-linear algorithms and their impact on site transferability

Abstract

Abstract. Low-cost air pollution sensors often fail to attain sufficient performance compared with state-of-the-art measurement stations, and they typically require expensive laboratory-based calibration procedures. A repeatedly proposed strategy to overcome these limitations is calibration through co-location with public measurement stations. Here we test the idea of using machine learning algorithms for such calibration tasks using hourly-averaged co-location data for nitrogen dioxide (NO2) and particulate matter of particle sizes smaller than 10 µm (PM10) at three different locations in the urban area of London, UK. We compare the performance of ridge regression, a linear statistical learning algorithm, to two non-linear algorithms in the form of random forest regression (RFR) and Gaussian process regression (GPR). We further benchmark the performance of all three machine learning methods relative to the more common multiple linear regression (MLR). We obtain very good out-of-sample R2 scores (coefficient of determination) >0.7, frequently exceeding 0.8, for the machine learning calibrated low-cost sensors. In contrast, the performance of MLR is more dependent on random variations in the sensor hardware and co-located signals, and it is also more sensitive to the length of the co-location period. We find that, subject to certain conditions, GPR is typically the best-performing method in our calibration setting, followed by ridge regression and RFR. We also highlight several key limitations of the machine learning methods, which will be crucial to consider in any co-location calibration. In particular, all methods are fundamentally limited in how well they can reproduce pollution levels that lie outside those encountered at training stage. We find, however, that the linear ridge regression outperforms the non-linear methods in extrapolation settings. GPR can allow for a small degree of extrapolation, whereas RFR can only predict values within the training range. This algorithm-dependent ability to extrapolate is one of the key limiting factors when the calibrated sensors are deployed away from the co-location site itself. Consequently, we find that ridge regression is often performing as good as or even better than GPR after sensor relocation. Our results highlight the potential of co-location approaches paired with machine learning calibration techniques to reduce costs of air pollution measurements, subject to careful consideration of the co-location training conditions, the choice of calibration variables and the features of the calibration algorithm.