# Advice on imputation of multiple time series

Background
In the first year of the study 60 streams had temperature data loggers installed (temperature measured every 30 seconds). The second year only 30 of these same streams had data loggers. During the second year animals were surveyed on a single day. During the survey, the temperature was measured once with a handheld thermometer.

The 30 stream subset with loggers in year 2 were picked because they were known to have the target species.

My data look something like this:

ID  Survey_date     Survey_Temp  24_degree_hrs
01   07June2015       11.5          285
02   11June2015       13.1          310
03   15June2015       16.7          N/A (no logger)
04   15June2015       14.4          315
...
60   ...


Goal
I am interested in characterizing the thermal regime in the 24 hours preceding the animal survey by calculating the total degree-hours the stream experienced (e.g. constant 10 degree stream would be 240 degree-hours). Since only 30/60 of the streams have data loggers I will have to impute this value for half of the data set. This will then be used as a co-variate to model animal detections.

Possible solutions

• I could just use the Survey_Temp as a proxy for the thermal regime but the streams were sampled at different times of the day, which adds additional noise. Does this survey-time-noise exceed that introduced by imputation?

• I could run the 24_degree_hrs~Survey_Temp regression and use the results of the regression to predict the missing 30 values. I would feel best about this except the 30 stream subset with loggers in year 2 was not picked randomly and I suspect would be colder with lower daily amplitude than the total set.

• I could link the year one logger data to the year two logger data. Using the example above, I don't have a logger for stream 03 in year 2 but I did in year 1. Furthermore I had 30 loggers running on 15June2015 so I have a fairly good idea of what weather the watershed was experiencing on that day. So I would find the most similar 24 hour period in 2014 and use those values to calculate 24_degree_hrs for stream 03. Obviously this description is a bit wishy-washy because I don't know how to go about running this search. Perhaps I locate the day in year 1 that has the most similar temperature at noon and midnight to my target window?

Any advice you can give me on the methods I described above or other methods that I haven't considered would be great. This is a minor component of the study so I was hoping to avoid tackling entirely new methods (i.e. Amelia) unless they seem absolutely necessary.