Time Series Analysis to the Rescue

Imagine a State Park that is troubled by low groundwater levels, much lower than a decade or so ago. The State Park thinks that the nearby well field of the local water supply company is the culprit. The water supply company blames the drier weather in the summers since the start of the millennium. You are asked to determine who is right, the State Park, the municipal water supply, or is it a combination of the two? Or maybe even option four, irrigation pumping in the agricultural area on the other side of the State Park? How are you going to find out? You have some budget, so you start gathering information for a groundwater model. You are in luck, as there are three observation wells in the State Park. Wells 1 and 3 are installed in the upper part of the aquifer, while well 2 is installed in the lower part of the aquifer. You get some idea of the subsurface conditions from state geological maps, the bore logs of the well field (including a pumping test), the irrigation wells, and the three observation wells. The data are not really consistent, hinting at some spatial heterogeneity. In addition, you have GIS coverages of topography, streams and land use. There is a weather station 20 km from the State Park, where daily records include rainfall and temperature. Finally, the water supply company records and reports monthly total discharges from the well field, but the discharges of the irrigation wells are not recorded. You fire up your favorite MODFLOW GUI, even though your office mate keeps telling you that you should use FloPy scripts. After a few weeks and turning a bunch of knobs, you have a reasonable five-layer groundwater model running. You can get an ok fit in observation well 1 and in observation well 2, but not with the same set of parameters, while the fit in well 3 is never very good. You are expected to give some estimate of the effect of the well field on the groundwater levels in the State Park. Yet the different parameter sets lead to seriously different answers, and well 3 keeps bugging you. You would like to see if spatial heterogeneity, using PEST calibration with pilot points, gives a better fit, but you have just 2 days left in the budget. Right when you are ready to throw in the towel, your office mate walks in. “What's up with you?” he asks. After hearing your woes, he has an unexpected suggestion: “You ever try time series analysis?” “No,” you have to admit, “that was never taught in my groundwater classes.” “Well,” he explains, “There are several free Python packages available and you only need the input and output series. You want to give it a try?” “The budget is almost shot,” you say. “If you already have the time series, it takes a few hours tops,” he replies. So, you guys start cranking, and by golly, after a little more than an hour, you have a pretty good model fit in all three wells, including an estimate of the drawdown caused by the well field. The model is a bit high in some of the summers, but you expect that may be caused by the irrigation wells. And they lived happily ever after. Is this Editorial indeed a fairy tale? You will find out in this Special Issue on Time Series Analysis. The short answer: this story could really have happened. Time series analysis is a powerful, data-driven approach that can be applied to answer many groundwater questions quickly. Can it solve all problems? No, of course not. Will it always work? Dream on. In this special issue, some real world groundwater questions are answered with a variety of time series analysis approaches, it is discussed how time series analysis can be combined with regular groundwater models, one of the packages is discussed in detail, and some exciting new developments are presented. The take-home message: Give time series analysis a try the next time you have some data. And find a smart office mate.