# Problems when interpolating time series data (average problem)

Hi I want to create two isotope data (1970-1980) and (2010-2020). As you can mention, the interpolation for the two maps is based on the average value measured at different stations in each time period.

However, I now have the problem that I do not have the data from the particular years for all stations.

For example, station B has data from 1970-1974 and 1979-1980. So the data from 1975-1978 are missing!

But if I now calculate the average at this station and interpolate it with the data that includes a data set (A) for all 10 years, I will distort my model! Is there a simple mathematical solution for weighting the data?

Is it a solution to multiply the B Average Value with 0.7, so the weighted average value will be 3.5?

• You state "As you can see" but there is no table, image, or link included for us to look at. Jun 2, 2022 at 15:06
• @GrapefruitIsAwesome so I fixed it :) Jun 3, 2022 at 7:53
• Thank you, the question is clearer now. Jun 3, 2022 at 10:11

Is it a solution to multiply the B Average Value with 0.7, so the weighted average value will be 3.5?

No, this is not a solution. Doing this effectively assigns a value of zero to the stations that do not have data, which is the wrong thing to do.

If you want to fill in the missing data you have to apply data interpolation techniques. Such techniques are only valid if there is correlation between the sampling points.

To fill in those missing gaps you will have to do additional calculations. Which technique you use depends on the result you want or what is now considered state of the art for the field the data is applicable to.

Until the mid 1990s to early 2000s, when estimating values of grade for ore reserves, using block modelling methods, inverse distance weighting methods were used. Initially, $$\frac{1}{d}$$ was used as this was a relatively quick calculation to perform. It was later discovered that inverse distance squared $$(\frac{1}{d^2})$$ gave better results. In some instances, inverse distance to the power $$n$$, $$(\frac{1}{d^n})$$, where $$n$$ generally ranged between 2 and 2.5 was also used. Generally, however, inverse distance squared became industry "standard" for a period of time.

The benefit of inverse distance squared weighting compared to simple inverse distance weighting was it gave less weighting to more distance samples. This is based on the logic that samples that are close to one another are more likely to have been deposited under more similar conditions and thus would more likely be related to one another.

Since the early 2000s inverse distance weighting methods have been replaced by kriging. One of the main differences between kriging and all forms of inverse distance weighting is with kriging, the sum of the weights equals 1. With the other methods, there is no limit, or specification to what the sum of the weight should be.

• Thanks a lot :) Jun 3, 2022 at 13:56

With year long data-gaps, any type of interpolation which does not account for environmental forcing (i.e. models) would be an inadequate comparison. For example, extreme years that are included in A but not in B would affect your comparison greatly. I would rather mask the A dataset to match the years available in B or fill the missing years using a process based model with environmental forcing data outputting the isotope data you need.