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Sampling bias due to weather conditions has been anecdotally reported; however, in this analysis we demonstrate that manual lake sampling is significantly more likely to take place in "fair weather" conditions. We show and quantify how a manual lake monitoring program in Maine, USA, is biased due to wind speed, rainfall intensity, and air temperature. Emulating a manually sampled water quality (WQ) data set, we show that, on average, manual sampling recorded, depending upon depth, higher water temperature (between 0.4 C and 1.2 C), lower dissolved oxygen (DO) (between À0.8 and À0.4 mgL À1 ), and higher chlorophyll values (2.0 μgL À1 ) than average automated monitoring. By analyzing the actual manual monitoring data, we show that manually collected lake water temperatures are on average 1.0 C higher in the epilimnion and 0.5 C (corrected for sensor lag) higher in the hypolimnion compared to those collected using automated methods. We attribute these differences in WQ measurement values to the weather-induced manual sampling bias. We believe that the nature of weather bias on manual monitoring will always record higher water temperatures, higher chlorophyll, and lower DO than automatic monitoring. The methodologies presented in this study will apply to similar manually sampled lake monitoring programs and the manual sampling bias will likely affect other WQ parameters. The weatherinduced water temperature bias reported is of the same order of magnitude as the root mean square errors reported in many lake models and is therefore considered substantial. If generally applicable and not corrected for, these results will have important implications for climate models, and similar applications, where manually collected WQ data are employed.

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We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel MCMC approach of Dodwell et al. (2015) in terms of the Delayed Acceptance (DA) MCMC of Christen & Fox (2005). In particular, DA is extended to use a hierarchy of models of arbitrary depth, and allow subchains of arbitrary length. We show that the algorithm satisfies detailed balance, hence is ergodic for the target distribution. Furthermore, multilevel variance reduction is derived that exploits the multiple levels and subchains, and an adaptive multilevel correction to coarse-level biases is developed. Three numerical examples of Bayesian inverse problems are presented that demonstrate the advantages of these novel methods. The software and examples are available in PyMC3.