Varying Snow Density

Introduction

In earlier articles I show how to measure the in-place snow load on a roof (or ground) and on-site snow density. The background of the first article is that of determining snow loads on structures for evaluations of building safety. The background of the second article is the idea of being able to estimate snow load from measurement of snow depth (only), say if actually measuring the snow weight is too dangerous, or inconvenient. Or, as in the example below, simply being curious of the weight of a big pile of snow. And in that second article it turned out (at least on a particular day in my neighborhood) that Mommy's rule of thumb: "ten inches of snow equals one inch of water" was surprisingly accurate.

Background

The literature supports two notions: 1) that the density of snow increases with snow depth; and, 2) density increases with snow age. And, it goes without saying, that human activity can change the density of snow. The first notion stated perhaps most simply: as snow keeps falling it packs the snow below. The second notion became most apparent to me over a season of hydrology work high in the Wallowa Mountains of Oregon. During that study we measured stream flow once a month in a high mountain stream. Once winter hit the flow in the stream was quite minimal. As winter progressed, snow depth increased, and the flow in the stream stayed minimal. Past the new year and into the warmer months, where at lower elevations snow was giving way to rain, the snow depth in the mountains increased and the stream flow stayed minimal. The peak snow depth in the area of our study was about 9 feet. Then, as warmer temperatures crept into the mountains, the snow depth decreased but the stream flow STAYED minimal. In fact, the snow depth decreased to a depth of about five feet, with no increase in flow in the stream. Where did it go? It didn't go anywhere. The snow was consolidating, or `ripening'. Finally, in late spring / early summer, the snow was truly melting and the stream swelled.

University of Idaho Study

Can we put some numbers to what is described above? The answer is yes. And, in fact, others already have. Researchers at the University of Idaho in Ground and Roof Snow Loads for Idaho (1986), reported some cool stuff. Having studied the data from some 300 snow info stations, they provide equations for ground snow load, or weight (P_g) versus snow depth; I repeat them below.

P_g = 0.90 h ... for depths of snow up to 22 in., and

P_g = 2.36 h - 31.9 ... for depths of 22 in. and greater,

where,

P_g = ground snow load (weight) in pounds per square foot (psf), and

h = snow depth in inches.

So, for a snow depth of 13 inches,

Pg = 0.90 (13) = 11.7 psf (about 12 psf).

Recall that for our `neighborhood measured' 13 inches we had about 8 psf (here).

But our snow was relatively fresh (on order of a week old), and the University of Idaho equations are for snow `smeared' over a whole season.

We can take the U of I equations and cast them in terms of `density' (specific weight) as follows.

P_g / h = 0.90 h / h = 0.90.

But we need to get the units straight, since h was in inches; we can do so as follows.

The 0.90 in the equation above has units of psf per inch. So, we need it in psf / ft.

... 0.90 psf / in. x 12 in./ft = 10.8 psf / ft (or pcf).

So,

P_g / h = γ = 10.8 pcf ... (depths up to 22 in.)

Actually, what this says is that for the first 22 inches the density is constant. (This, of course, is a straight-line simplification.)

Now let's bring in the term `specific gravity'. Specific gravity (call it SG) is the weight of something as a fraction (or multiple) of the weight of water. Water weighs 62.4 pcf, so ...

SG = γ / 62.4 pcf = 10.8 pcf / 62.4 pcf = ...

SG = 0.17 ... or about 1/6 ... (depths up to 22 in.)

So, actually, `Mommy was wrong' (according to the University of Idaho study) if we consider snow sitting there all season long (however long or short the season is). On the average (for depths up to 22 inches), only about six inches of snow is equivalent to one inch water.

The second `University of Idaho' equation is a bit more cumbersome.

P_g / h = 2.36 - 31.9 / h ... all divided by 12 to get it into specific gravity units ...

P_g / h = γ = 2.36 (12) - 31.9 (12) / h =

P_g / h = γ = 28.3 pcf - 31.9 psf / h ... where, now, h is in ft ... (depths of 22 in. and greater).

In terms of Specific Gravity ... (divide by 63.4 pcf for water)

SG = 0.45 pcf - 0.51 psf ft / h ... (depths of 22 in. or more).

So, if we take a depth of 5 ft ...

SG = 0.45 - 0.51 ft /5 ft = 0.35 ... (about 1/3).

Mommy was really wrong with deep snows, where only 3 inches of snow equals one inch of water.

The equations above are `season averages'. The University of Idaho study reported another methodology that considers specific gravities from 0.19 to 0.39 in the non-melt period of the year and from 0.24 to 0.43 during the spring melt period. And so, yeah, I wasn't just dreaming in the Wallowas; as the season progressed the snow consolidated to nearly half its depth, and thus became twice as dense.

Real Life Example

Finally, now, let's take all this and estimate the weight of snow piled 6 ft high on the deck of the cabin in the photograph. Let's assume `average' density. Using the original University of Idaho equation for a depth of 72inches (6ft), we get,

P_g = (2.36 psf / in.)(72 in.) - 31.9 psf = ...

Pg = 138 psf for the `in-place' snow load.

In terms of specific weight (density), we get,

... γ = P_g / h = 138 psf / 6 ft = ...

... γ = 23 pcf.

In terms of specific gravity,

SG = 23 pcf / 62.4 pcf for water = ...

SG = 0.37 ... (37 percent that of water).

My guess (from what I know of the particular cabin, the area, etc., as I was there) is that these values are a bit heavy. The snow on the deck is actually from snow falling on the deck directly and from snow drifting and sliding off the roof. If we use the specific gravity corresponding to, say, 3 ft of snow, then,

SG = 0.45 - 0.51/3 = 0.28.

Then γ = 0.28 (62.4 pcf) = 17.5 pcf.

Then P_g = 17.5 pcf x 6 ft = 105 psf.

Conclusion

So, the density of snow varies. As snow gets deeper, and older, it consolidates, ripens, and becomes denser. Deep snows later in the season have been measured to have specific gravities of one third to nearly one half that of water. The pile of snow on the deck in the example is probably loading the deck in place with 100 to 150 psf. As I point out in an article on Snow load design (here), the loads on decks may be two or three times the design Snow load on the roof. And that is why I design decks in snow country for very heavy loads!

Update

The snow depth at the location of the measurement cited at the beginning of the article is now 20 in. I measured the weight, depth, size of hole, etc. to compute new values of load and density (here). Interestingly the density is almost identical as that for the original depth of 13 in. (a tiny bit more). The Ground Snow load, and density, for both depths are less than the `average' values from the University of Idaho equations. Indeed, for the University of Idaho equation, for the 20 in. depth, the predicted Ground Snow load, P<sub>g</sub> = 0.90 (20) = 18 psf. I measured 12 psf. Interesting, however, though the density is different than the average from the U of I study, it is still constant up to 20 in., which is like the U of I `average' information.

Further Update

Since the updated information above we have had off and on wind, rain and above-freezing temperatures. The snow depth is now 16 in. (down from 20 in.); the density is 12.5 pcf (50% greater); the ground snow load is 16 psf (increased!); and the standing water equivalent is 3.0 in. So, even though the snow depth is less, there is actually more total water in the snow profile. Also, now the U of I study `average' equations give P_g = 0.9 (16) = 14 psf, ... less than the in-place density.

References

Measuring Snow Loads on Roofs , Jeff Filler, Associated Content.

Measuring Snow Density, Jeff Filler, Associated Content.

Ground and Roof Snow Loads for Idaho, R.L. Sack, A. Sheikh-Taheri, University of Idaho, Department of Civil Engineering, Moscow, Idaho 83844.

Snow Loads on Roofs and Decks, Jeff Filler, Associated Content.

More Snow in Idaho, Jeff Filler, Associated Content.