Can average depth be used to estimate deco?
Introduction
When we try to estimate how much deco we need to do for a certain profile some people use the average depth of the dive for this.
Some computers and bottomtimers also calculates average depth during the dive for you.
But does using average depth for deco really work?
Example
Let's see how this approach works on different profiles having the same average depth  40 minutes at 30m/100ft.
 Profile 1  Average: 40 min at 30m/100ft
 Profile 2  Deep to shallow: 20 min 40m/130ft + 20 min 20m/70ft
 Profile 3  Shallow to deep: 20 min 20m/70ft + 20 min 40m/130ft
 Profile 4  Cave type: 10 min 40m/130ft + 10 min 20m/70ft and going back 10 min 20m/70ft + 10 min 40m/130ft.
I will run these profile in GAP using RGBM with nominal conservatism and Decoplanner using Buhlmann with gradient factors 30/85 to see how much deco in minutes we have to do for each combination.
Let's use 21/35 as backgas and 50% nitrox for decompression.
Remember, it's the difference in time between the different profiles uing the same deco algorithm we are interrested in.
I just though we could have some variation using both a bubble model as RGBM and a dissolved gas model as Buhlmann
Deco algorithm  1Average  2Deep to shallow  3Shallow to deep  4Cave type

RGBM  19 min  13 min  24 min  17 min

Buhlmann  18 min  17 min  23 min  22 min

Analysis
As you can see doing "Profile 2  Deep to shallow" we will be slightly conservative using the average depth which is fine of course.
However, doing "Profile 3  Shallow to deep" we can't use an regular average is this will NOT give us enough decompression.
Actually the equivalent square profile giving the same amount of deco (24 minutes) is about 34m/111ft for 40 minutes using RGBM.
And on "Profile 4  Cave profile" we have a discrepancy between the different models where RGBM says ok and Buhlmann says you need more deco.
Also using longer deco or different depth differences will yield the same results. You could make the difference larger or smaller if you wanted too.
I just tried to use an example that would be reasonable for a single deco gas dive.
Conclusion
From this we can draw the conclusion that using a straight average is not recommended for profiles going shallow to deep and might be a problem for cave type profiles.
Otherwise it will work fine and even be slightly conservative.
The solution to the problem above is to take the profile into account and using a weighted average where we weight towards the deeper side when we have profile going shallow to deep.
Having experimented with different profiles I found that using 75% of the difference a good rule of thumb. In this case that would be 35m/115ft.
Running average
Of course calculating an average is easier in our example as we used the same time at different depths.
When you spend different times at different depths it is more work for the poor brain.
In real life what I do is keep track of the weighted average during the dive, a running average it could be called. Let's do an example.
Let's say we did "Profile 4  Cave type".
During the dive I would look at my depth and time regularly or when doing major depth changes.
 First we did 10 minutes at 40m/130ft  my average is 10min@40m/130ft.
 Then we spent 10 minutes at 20m  my average is 20min@30m/100ft.
 Then another 10 minutes at 20m  my average is 30min@27m/90ft. (20min@30m/100ft + 10min@20m/70ft).
 Then down to 10 minutes at 40m  my average becomes 40min at 33m/110ft. (30min@27m/90ft + 10min@40m/130ft which mathematically is 40min at 30m/100ft but weighted deeper).
And when in doubt  always err on the deeper side.
Usually we don't dive to exact depths but if you keep running your average in your backhead and guesstimate it to deeper depths you will end up with a good average.
It's also a good idea to practice this using some kind of depth profiler to compare to after the dive.
I have used Reefnet's Sensus Pro device and like that because I can keep it in my pocket and it's easy to download.
Also remember that a lot of dives you actualy spend most of the time at the exact same depth so keeping a running weighted average might be overkill.
And as always we always have the option of using our maximum depth to estimate the deco  the most conservative approach but also the safest.
Have fun!
Peter