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Simulation of roof snow loads based on a multi-layer snowmelt model: Impact of building heat transfer

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Abstract

To investigate the impact of building heat transfer on roof snow loads, roof snow loads and snow load thermal coefficients from 61 Chinese sites over a period of 50 years are simulated based on basic meteorological data such as temperature, humidity, wind speed, and precipitation, and a multi-layer snowmelt model considering the building heat transfer. Firstly, the accuracy of the multi-layer snowmelt model is validated using the data of observed ground snow load and roof snow melting tests. The relationship between meteorological conditions, snow cover characteristics, and thermal coefficients of snow loads in three representative sites is then studied. Furthermore, the characteristics of thermal coefficients in each zone are analyzed by combining them with the statistical results of meteorological data from 1960 to 2010, and the equations of thermal coefficients in different zones on indoor temperatures and roof heat transfer coefficients are fitted separately. Finally, the equations in this paper are compared with the thermal coefficients in the main snow load codes. The results indicate that the snowmelt model using basic meteorological data can effectively provide samples of roof snow loads. In the cold zone where the snow cover lasts for a long time and does not melt easily, the thermal coefficients of the snow loads on the heating buildings are lower than those in the warm zone due to the long-term influence of the heat from inside the buildings. Thermal coefficients are negatively correlated with indoor temperatures and roof heat transfer coefficients. When the indoor temperature is too low or the roof insulation is good, the roof snow load may exceed the ground snow load. The thermal coefficients for heated buildings in the main snow load codes are more conservative than those calculated in this paper, and the thermal coefficients for buildings with lower indoor temperatures tend to be smaller.

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Abbreviations

A :

snow surface albedo

A n :

dimensionless coefficient, subscripts n = h, g, u, Ah = SHI,R/ Sh,R, Ag = SHI,R/ Sg,R, Au = SHI,R/Su,R

c ha :

adjust bulk transfer coefficient

c va :

adjust bulk transfer coefficient, cva = cha

c n :

specific heat of n (kJ·kg−1·K−1), n = s, i, w, a, which denote snow, ice, water, and air, respectively

C r :

water retention capacity of snow

C t,a :

annual thermal coefficient of snow load

C t,R :

thermal coefficient of snow load at a certain recurrence interval

C t,Rn :

thermal coefficient normalized by snow load on the n at a certain recurrence interval, subscripts n = g, h, u, which denote ground, heated roof, and unheated roof, respectively

C 1t,R :

thermal coefficient Ct,R when the roof heat transfer coefficient is below 1.0 W·m−2·K−1

C 1t,Rg :

thermal coefficient Ct,Rg when the roof heat transfer coefficient is below 1.0 W·m−2·K−1

D 0 :

number of days per year with a daily average temperature less than 0 °C

D 5 :

number of days per year with a daily average temperature less than s °C

e(T a):

air vapor pressure (kPa)

e(T s):

vapor pressure at the snow surface (kPa)

E 1 :

latent heat flux (kJ·m−2·h−1)

g :

gravitational acceleration, 9.8 m·s−2

h 0 :

windless convection coefficient (kJ·m−2·h−1·°C−1)

h v :

latent heat of evaporation, 2470 kJ·kg−1

h s :

latent heat of sublimation, 2834 kJ·kg−1

h f :

latent heat of fusion, 335 kJ·kg−1

H :

sensible heat flux (kJ·m−2·h−1)

H is :

the ith snow layer thickness (m)

k e :

effective heat conductivity (W·m−2·K−1)

K :

heat transfer coefficients of the building roof (W·m−2·K−1)

L a :

incoming longwave radiation (kJ·m−2·h−1)

L t :

outgoing longwave radiation (kJ·m−2·h−1)

M iout :

rate of outflow of the ith snow layer (m·h−1)

MRI:

mean recurrence period (kPa)

p n :

fitting parameters, subscripts n =1, 2, 3, 4

p 1n :

fitting parameter when the roof heat transfer coefficient is below 1.0 W·m−2·K−1, subscripts n = 1, 2, 3, 4

P :

precipitation (m·h−1)

P rain :

rainfall (m·h−1)

P snow :

snowfall (m·h−1)

P s :

pressure of snow above the snow layer (N·m−2)

Q c :

heat conduction through the snowpack (kJ·m−2·h−1)

Q p :

heat advected by precipitation (kJ·m−2·h−1)

Q g :

ground heat flux (kJ·m−2·h−1)

Q r :

heat flux from inside the building (kJ·m−2·h−1)

R d :

dry gas constant, 0.287 kJ·kg−1·K−1

R 2 :

coefficient of determination

R i :

thermal resistance of the building roof (m2·K·W−1)

RMSE:

root mean square error

S 0 :

potential solar radiation (kJ·m−2·h−1)

S n :

shortwave radiation (kJ·m−2·h−1)

S r :

annual maximum of roof snow load (kPa)

S r,HI :

annual maximum of roof snow load under heat insulation (kPa)

S r,R :

annual maximum of roof snow load at a certain recurrence interval (kPa)

S HI,R :

annual maximum of roof snow load under heat insulation at a certain recurrence interval (kPa)

S n,R :

annual maximum of snow load on the n at a certain recurrence interval (kPa), subscripts n = g, h, u, which denote ground, heated roof, and unheated roof, respectively

t :

physical time (h)

T :

snowpack temperature (°C)

T a :

air temperature (°C)

T in :

indoor temperature (°C)

T s :

snow surface temperature (°C)

T is :

temperature of the ith snow layer (°C)

T sb :

temperature of the bottom snow layer (°C)

v a :

wind speed at the measured height (m·s−1)

v(z):

wind speed at z height above the ground (m·s−1)

v b :

wind speed at the measured height (m·s−1)

W i :

snow water equivalent of the ith snow layer (m)

W e :

sublimation or evaporation from snowpack (m·h−1)

W iliq :

liquid water content of ith snow layer

z :

height above the ground (m)

z b :

reference height (m)

Δz :

thickness of the layer (m)

Z :

coordinates along the depth of the snow (m)

α :

terrain roughness, α = 0.16 when the terrain is Category B

γ n :

mass of n per unit volume of snow (kg·m−3), subscripts n = i, w, a, which denote ice, water, and air, respectively

ε ac :

cloudy sky emissivity

ε s :

snow surface emissivity

θ n :

volume fraction of n to snow, subscripts n = i, w, a, which denote ice, water, and air, respectively

μ t :

atmospheric transmittance

ρ n :

bulk density of n (kg·m−3), subscripts n = s, i, w, a, which denote snow, ice, water, and air, respectively

σ SB :

Stefan-Boltzmann constant, 2.07·10−7 kJ·m−2·K−4·h−1

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Acknowledgements

This project is supported by the National Natural Science Foundation of China (52078380), which is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China

    Xuanyi Zhou, Heng Chen, Yue Wu & Tiange Zhang

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  1. Xuanyi Zhou
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  2. Heng Chen
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  3. Yue Wu
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  4. Tiange Zhang
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Xuanyi Zhou, Heng Chen, Yue Wu, Tiange Zhang. The first draft of the manuscript was written by Yue Wu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yue Wu.

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Zhou, X., Chen, H., Wu, Y. et al. Simulation of roof snow loads based on a multi-layer snowmelt model: Impact of building heat transfer. Build. Simul. (2024). https://doi.org/10.1007/s12273-024-1119-4

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  • DOI: https://doi.org/10.1007/s12273-024-1119-4

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