Roof Snow Drifts Due to Ground Snow

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For the last 40 years, design provisions in the United States for roof snow drift loads have accounted for snow which originally fell on one portion of the roof and was transported by wind into a snow drift atop another portion of the roof. Specifically, for a leeward drift roof at a step, the upwind fetch l_u references the upper-level roof snow source area. Similarly for a windward drift at a roof step, l_u addresses the lower-level roof where the snow originally fell and eventually ended up in the drift. Finally, for a gable roof with a east-west ridgeline, the across the ridge drift (aka the unbalanced load) atop the northern portion of the roof, l_u is that for the southern portion of the roof. Note in all these cases, snow which originally fell on the ground is not considered as an expected snow source for a roof top snow drift.

However, in certain circumstances, snow which originally fell on the ground can contribute to roof snow drift formation. In one real-world case, the building was a hog containment structure in the Midwest with a roof eave relatively close to the ground surface. The gable roof drift was larger than what one would expect for the roof’s upwind fetch lu.

A second case involved a school building in the Buffalo area which experienced the Blizzard of 1977. According to Wikipedia, the total snow fall was over 8 feet in some places, while peak daily wind speeds were in the 45 to 70 mph range. As sketched in Figure 1, Roofs A and C were one story portions of the school while Roof B (thought to be a gymnasium space) had a higher elevation. A windward drift “snow ramp” was on the ground upwind of Roof A (snow source being snow which originally fell on the ground). Similarly, a windward snow ramp was atop Roof A, immediately upwind of the exterior wall between Roofs A and B (snow source being snow which originally fell on the ground or fell on Roof A). Finally, a large leeward drift was atop Roof C (snow source being snow which originally fell on the ground, Roof A or Roof B).

The mechanism for such ground-to-roof snow transfer is a windward drift which forms at the building upwind wall. When this ground snow drift becomes large enough, it provides a “snow ramp” for windblown ground snow particles to end up atop the building roof.

The drift formation process for windward drift is more complicated than that for leeward drifts. Leeward drifts have a right triangular shape throughout the drift formation process. Initially the slope is about 1:4, thought to be the average angle of repose for drifted snow (i.e. 14°). As the top of the leeward drift approaches the upper-level roof, the slope flattens out until it reaches a rise-to-run of about 1:8. At this point, the drift becomes aerodynamically streamlined (region of aerodynamic shade eliminated) and the growth of the leeward drift stops. The trapping efficiency for leeward drifts during the drift formation process is about 50%, that is, about half of the snow that is blown off the upper-level roof ends up in the leeward drift atop the lower-level roof.

The initial shape of a windward drift is an acute triangle, not a right triangle. So, unlike leeward drifts, the high point of the initial windward drift surcharge is not at the wall. When the windward drift is small with respect to the wall height above the ground snow ho, (see Figure 2) the trapping efficiency towards the center of the wall (i.e., away from the corners) is nominally 100%. That is, during this initial phase, all the windblown snow stops upwind of the building wall and contributes to drift formation, as opposed to flowing up onto the roof.

When the windward drift obtains the shape shown in Figure 2, the snow ramp is large enough that some of the wind-transported ground snow particles reach the building roof and the trapping efficiency at the ground surface windward drift drops below 100%.
Using relations in ASCE 7-22, the expected height of the 50% trapping efficiency leeward drift, h_d, is

where P_g is the design ground snow load (pounds per square foot - psf), l_u is the upwind fetch of the upper-level roof (ft). W₂ is the winter wind parameter (i.e., percent time the wind speed is above 10 mph during October through April) as given in an ASCE 7-22 map and γ is the snow density (pounds per cubic foot-pcf). Equation 1 was based on simulated snow drifts with upwind fetch distances of 1,000 feet or less. Since the width of the leeward is taken to be 4h_d, the corresponding cross-sectional area of the leeward 50% trapping drift A_d is

The cross-sectional area of the windward ground snow drift in Figure 2, A_w, is

However, due to the difference in trapping efficiencies (100% for windward, 50% for leeward), the windward drift A_w cross-sectional area is twice that for the leeward drift or

Hence, the upwind ground snow fetch l_u* corresponding to wind transported ground snow particles beginning to flow up the snow ramp and onto the roof is

Table 1 presents l_u* for ground surface to roof eave distances, h, of 6, 8, and 10 feet for various values of the Winter Wind parameter W₂ and P_g = 10 psf. Using the ASCE 7 relation for snow density, γ = 0.13 P_g + 14, the ground snow depth for P_g = 10 psf is h_g = 0.65 feet and the corresponding ho values in Table 1 are 5.35 (h_o = h – h_g = 6 – 0.65), 7.35 and 9.35 feet respectively. As one would expect, the transition upwind ground snow fetch l_u* is an increasing function of the eave height, h, and a decreasing function of the Winter Wind Parameter W₂.
Note that for Pg = 10 psf, if the eave height is 8 feet or larger, the upwind transition ground snow fetch l_u* would need to be larger than a football field (approx. 360 feet) for wind driven ground snow to reach the building roof.
Tables 2 and 3 present the same l_u* information for Pg = 30 psf, (h_g = 1.68 ft and corresponding h_o values of 4.32, 6.32, 8.32 and 10.32 feet) and for Pg = 50 psf (h_g = 2.43 ft and corresponding h_o values of 3.57, 5.57, 7.57 and 9.57 feet).
For a location with a typical or average Winter Wind Parameter of 0.45, P_g = 30 psf, and a ground snow upwind fetch of a football field (approximately 360 feet), one does not expect ground snow to reach the roof level and contribute to a roof top drift if the eave height is 10 feet (580 feet > 360 feet). For the same W₂ value and ground snow fetch, if P_g = 50 psf, one does not expect ground snow to contribute to a roof top drift if the eave height is 12 feet (610 feet > 360 feet).

Besides the eave height, ground snow load, and the Winter Wind Parameter, the key parameter for ground snow contributing to the roof drift is the ground snow load fetch distance. While determination of the roof fetch is straight forward, the ground snow fetch distance is more complex. Tabler (1994) has written “The upwind end of the fetch is any boundary across which there is no snow transport, such as forest margins, deep gullies or stream channels, row of trees, and shorelines of unfrozen bodies of water.” Tall brush can also be added to this list. For some locations (short eave height buildings close to a frozen lake) the upwind ground snow fetch could be measured in miles as opposed to a building roof fetch which typically is less than a thousand feet. As a matter of fact, as noted above, the largest building roof fetch considered in the determination of Equation 1 is 1,000 feet. For very large ground snow fetch distances, evaporation of ground snow as it is being transported comes into play, which was not considered in the development of Equation 1.

If the expected ground snow fetch from the previous paragraph, lg, is larger than the transition ground snow fetch l_u* in Tables 1 through 3, some of the ground snow transport would add an amount Ad* to the “normal” drift cross-sectional area due to wind induced transport of snow which initially fell atop the roof. The additional amount is given by

Depending on the magnitude of the ground fetch l_g, A_d* could be quite large. In such cases the size of the roof top snow drift would not be larger than the corresponding aerodynamically streamlined “maximum” drift. For either a leeward or windward roof step, the maximum drift would be a right triangle with height h_c and a horizontal extent 8 h_c where h_c is the space available for roof step drift accumulation (roof step elevation distance minus balanced snow depth). For a gable roof geometry, the “maximum” drift is sketched in Figure 3. The top of the drift close to the ridgeline is nominally flat, while close to the eave the drift slope can conservatively be taken as 30˚ which is the assumed maximum angle of repose for drifted snow.

Currently roof snow drift provisions do not envision ground snow blowing up and onto the roof. However, there are certain circumstances, low eave height and strong winds, wherein snow which originally has fallen on the ground contribute to a roof top snow drift. This article has provided procedures for estimating the size of such roof drifts. ■