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I have a list of single point values that I want to insert into a grid.

point_values = [1, 4, 5, ...]

point_lats = [-12.101, -12.1023, -12.1031, ...]

point_lons = [155.511, 155.520, 155.533, ...]

the grid latitudes and longitudes are currently in 2d arrays of 2030 x 1350

latitudes = array of shape 2030 x 1350 of latitudes

longitudes = array of shape 2030 x 1350 of longitudes

how could I insert the points into the 2D grid if a point falls within the grid boundaries?

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    $\begingroup$ This looks more like a programming question (belonging on Stack Overflow) but is currently very unclear. What do these arrays represent? What grid boundaries are you talking about? $\endgroup$ – Jan Doggen Jul 25 at 11:11
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    $\begingroup$ this is to match up satellite observations from a lidar (calipso) to MODIS data. i would think this is earth science considering i'm doing it to observe earth processes. $\endgroup$ – Alyson Douglas Jul 25 at 13:18
  • $\begingroup$ Although this question is about remote sensing, you likely will get helpful answers from Geographic Information Systems stack exchange. $\endgroup$ – haresfur Jul 26 at 0:50
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Technically, this is a mathematical modelling problem. You just happen to be using earth science data - satellite LIDAR readings.

Ore reserve geologists constantly deal with this, but in three dimensions when they are required to create a block models of a geological deposit from drill hole data.

Scientific fields that use 2D data would include: forestry, meteorology and ground contamination studies looking into pollution effects of smelters.

Methods you need to consider are Inverse Distance Weighting and possibly variography and kriging. Variography and kriging are elements of geostatistics, also known as the Theory of Regionalized Variables.

With inverse distance weighting, the distance variable is usually raised to a power n, i.e. ${1/d^n}$. Choosing the appropriate value of $n$ is the tricky part. When geologists used inverse distance weighting, prior to primary using geostatistics, typically the value of $n$ used was 2, but values between 1 and 3 have been used for different deposits.

Given that you are using two dimension data, you may need to use GIS software or other modelling software that offers grid interpolation methods, such as I have mentioned to achieve what you want.

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