# What's the minimum number of days needed for reporting a "monthly average" of daily satellite retrievals?

NASA's Earth Observing System produces many maps of air quality and land-surface variables, from instruments like MODIS, AIRS, OMI, VIIRS, etc. Both NASA and the scientific community produce maps of the retrieved data on a daily basis, but there are often gaps (e.g. no data) for many locations because of clouds, satellite coverage, or other limitations. Daily retrievals are often averaged by month or season so that a complete global map (or sub-region) can be made and then presented to the public and put into publications.

Some locations have very few retrievals available for a monthly average (e.g. if there is a predominant cloud mass that sticks around for a long time). So, researchers must choose some threshold where no data is reported. As a graduate student, I would report the average if I had at least 4 days in the month, which seemed reasonable to me at the time for some reason. However, the number of available data points for a monthly average fluctuates so much, that the minimum number of members in the monthly average that I chose affected my temporal trendlines.

What's the minimum number of days needed for satellite-derived maps of monthly averages? I can't call 3 days of data a "monthly average" in good faith, but is 4 days enough? For the purposes of this question, assume there is only one possible data retrieval per day per geo-location.

• I asked a similar question on GIS - gis.stackexchange.com/questions/150865/… Jan 31 '16 at 3:03
• I would say you need 30 or 40. Jan 31 '16 at 3:06
• there's only 31 days max in a month... sooooo
– f.thorpe
Jan 31 '16 at 3:11
• don't some satellites provide more than one pass in a day? Jan 31 '16 at 3:12
• OK . Good luck with your question then. Jan 31 '16 at 3:17

Provide a monthly average in every grid cell, and describe how many measurements were used for each cell.

There is no fixed rule for the minimum number of days for reporting a monthly average. A reasonable threshold will depend on the geophysical quantity of interest y, in particular on how much y varies on short and long timescales.

If y varies from month to month, but does not vary a lot from day to day (example: sea surface temperature), you can probably get away with reporting a monthly average even when only one or two days have cloud-free measurements. On the other hand, if you're measuring precipitation, your signal will be relatively noisy even if you choose a threshold of 20 days. And any threshold is going to introduce a bias, because a lack of observation is typically due to clouds. Although you will get a bias in any case. In other words, if you only have one day per month you see a gap and in the clouds to observe whatever you want to know, it is a pity to throw it away. Therefore, personally I choose a minimum of 1 observation.

Critically important though: when releasing the product, add a field that tells the user how many days worth of measurements make up the monthly average in any given cell! Like that, the user can decide which ones to use and which ones not to use. More broadly speaking: producers should document everything they do.

For your specific examples: search for the ATBD and/or scientific papers describing the product. Hopefully, there is a field in the level-3 product that describes the number of measurements per cell. If the answer is not in there, write to the producers and tell them to redo the product... You will need this information to accurately calculate a yearly average!

• When mapping geospatial data across large regions (e.g. thousands of grid-cells), it is unconventional to then map data contribution by location. I've used whisker-bar charts to show the change in contribution by month, which is effective. However, data regularly gets published as maps and no such companion chart is available. I think map-makers should adopt a minimum to go into the map, and exclude those as "no data". Unfortunately, I see a lot of NASA data reported that doesn't get scrutinized to that level.
– f.thorpe
Feb 2 '16 at 3:14
• On a single map you can't show such information, but in the actual level-3 data files one should have multiple fields, one for mean, one for count, and probably others showing other statistics.
– gerrit
Feb 2 '16 at 10:27