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Millions of people in Bangladesh drink well water contaminated with arsenic.Despite the severity of this heath crisis, little is known about the extent towhich groundwater arsenic concentrations change over time: Are concentrationsgenerally rising, or is arsenic being flushed out of aquifers? Are spatiallypatterns of high and low concentrations across wells homogenizing over time, orare these spatial gradients becoming more pronounced? To address thesequestions, we analyze a large set of arsenic concentrations that were sampledwithin a 25 km$^2$ area of Bangladesh over time. We compare two blanket surveycollected in 2000/2001 and 2012/2013 from the same villages but relying on alargely different set of wells. The early set consists of 4574 accuratelaboratory measurements, but the later set poses a challenge for analysisbecause it is composed of 8229 less accurate categorical measurements conductedin the field with a kit. We construct a Bayesian model that jointly calibratesthe measurement errors, applies spatial smoothing, and describes thespatiotemporal dynamic with a diffusion-like process model. Our statisticalanalysis reveals that arsenic concentrations change over time and that theirmean dropped from 110 to 96 $\mu$g/L over 12 years, although one quarter ofindividual wells are inferred to see an increase. The largest decreasesoccurred at the wells with locally high concentrations where the estimatedLaplacian indicated that the arsenic surface was strongly concave. However,well with initially low concentrations were unlikely to be contaminated bynearby high concentration wells over a decade. We validate the model using aposterior predictive check on an external subset of laboratory measurementsfrom the same 271 wells in the same study area available for 2000, 2014, and2015.

Making the most of imprecise measurements: Changing patterns of arsenic concentrations in shallow wells of Bangladesh from laboratory and field data