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I am curious if R or any other open source code can deal with forecasting changes in water elevation based on a predicted/forecasted value of rain.

I have a ton of data that shows water elevations (height ft) measured every hour for almost 30 years. I would like to quantify the relationship between the volume of rainfall received (inches) and change in water elevation (river/lake). In the end, creating a distribution curve that shows the relationship and expected outcome of change in water elevation based on rainfall volumes.

I am only interested in a statistical approach based on data trends over time at this point. I understand when dealing with changes to water body elevations, there are numerous other factors to consider.

Any suggestions on available open source code or references to similar would be appreciated.

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    $\begingroup$ I am keenly interested in this topic and would value answers that describe readily implementable, informed, and effective (that is, not speculative) modeling approaches. This is an archetype of a time series modeling problem in which one (extensive) time series is driven by another at multiple lags, with the added complications of (annual) seasonality and underlying trends (due to changes in weather, climate, and human use). To those answers that contribute something of substance and authority--even if they only partially address the problem--I will add a bounty between 50 and 500 points. $\endgroup$
    – whuber ♦
    Commented Jun 17, 2015 at 15:33
  • $\begingroup$ This also relates to geology and landscape. If the forest is rich then it holds more water. If there was a pest then it can harm the forest and the ability to restrain water from going to the river. This is an incomplete information problem. $\endgroup$
    – EngrStudent
    Commented Jun 17, 2015 at 18:13
  • $\begingroup$ Do you have data on rainfall over the watershed, given that the level of a river or lake can depend on rain that fell far away? Or are you attempting to include watershed characteristics implicitly in a model based solely on local rainfall and river/lake levels? $\endgroup$
    – EdM
    Commented Jun 17, 2015 at 18:17
  • $\begingroup$ The first level approach is to generate the stats and trends of weather impact on water at a location. I have both gridded and interpolated weather data, plus point - time series water data. The attempt here is to develop stats that can identify trends based on known data collection points. I am not interested in roughness coefficients at this time or volumetric spatial and temporal distribution of rainfall data. The exercise is first to develop the stats, then layer in the physical data constraints. Adding physical constraints may in fact not show any statistically significant gain. $\endgroup$
    – Martin
    Commented Jun 17, 2015 at 18:58
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    $\begingroup$ Ian Mcleod wrote a book on this. It's available here: fisher.stats.uwo.ca/faculty/aim/1994Book/default.htm $\endgroup$
    – user242509
    Commented Nov 19, 2019 at 18:31

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You might want to work at a higher level of aggregation (time bucket) say weekly/monthly in order to develop the relationship that you are after. You should investigate Transfer Function Models also known as Dynamic Regression Models. I have seen papers on this written by the USGS. At this time I can't find the references, but I will continue to look. One name that comes to mind is "Dick March, Senior Researcher, South Florida Water Management District" as he has written on this subject. You might pursue that thread.

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    $\begingroup$ Because the response of rivers to rainfall has a lag between minutes and a week or two, it is likely that weekly or monthly aggregation will lose much of the information of interest. $\endgroup$
    – whuber ♦
    Commented Jun 17, 2015 at 17:06
  • $\begingroup$ Thanks for the comments and suggestions. The hourly resolution is really important for the forecasted results. As suggested by whuber, there is a lag time. In addition, some bodies of water respond to rainfall very quickly some respond very slowly. I am hoping to identify these lag/response trends as well. Both scenarios are important for my research. I am curious, will R software be able to graphical display these trends? $\endgroup$
    – Martin
    Commented Jun 17, 2015 at 17:26
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    $\begingroup$ OK ... Transfer Function Models can also be used at the hourly level. $\endgroup$
    – IrishStat
    Commented Jun 17, 2015 at 19:34

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