Chin J Plant Ecol ›› 2016, Vol. 40 ›› Issue (3): 221-235.DOI: 10.17521/cjpe.2015.0243
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Hai-Qing HU1, Xin LU1, Long SUN1,*(
), Zhi-Lin QU2, Yu LIANG1, Hai-Yang LI1
Received:2015-06-26
Revised:2015-11-27
Online:2016-03-10
Published:2016-03-25
Contact:
Long SUN
Hai-Qing HU, Xin LU, Long SUN, Zhi-Lin QU, Yu LIANG, Hai-Yang LI. Effects of air temperature and relative humidity on equilibrium moisture content and time-lag of forest land surface dead fine fuels[J]. Chin J Plant Ecol, 2016, 40(3): 221-235.
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| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 平衡含水率随气温变化方程 Equations of EMC versus air temperature | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 | 20 | y = (0.3933e - 5)x3 - (0.2141e + 3)x2 + 0.7909x + 0.0781 | 0.966 6 |
| Larix gmelinii leaves | 40 | y = -(0.2787e + 4)x3 + 0.0014x2 - 0.0253x + 0.2305 | 0.994 7 |
| 60 | y = (0.3800e - 4)x3 + 00159x2 - 0.0018x + 0.1707 | 0.990 1 | |
| 80 | y = (0.1347e - 4)x3 - (0.7339e + 3)x2 + 0.0026x + 0.3091 | 0.999 9 | |
| 白桦叶片 | 20 | y = - (0.6667e + 6)x3 + (0.8943e - 4)x2 - 0.0055x + 0.1337 | 0.988 9 |
| Betula platyphylla leaves | 40 | y = - (0.5733e + 5)x3 + (0.4414e - 4)x2 - 0.0145x + 0.2243 | 0.993 9 |
| 60 | y = (0.8633e - 4)x3 - 0.0037x2 + 0.0357x + 0.1594 | 0.987 5 | |
| 80 | y = (0.2026e - 4)x3 - 0.0012x2 + 0.0087x + 0.3316 | 0.996 8 | |
| 落叶松-白桦叶片混合物 | 20 | y = (0.7733e - 5)x3 - (0.2829e + 3)x2 - (0.1876e + 3)x + 0.1024 | 0.999 8 |
| Mixture of L. gmelinii | 40 | y = (0.6733e - 5)x3 - (0.1881e + 3)x2 - 0.0046x + 0.1736 | 0.980 7 |
| and B. platyphylla leaves | 60 | y = (0.3513e - 4)x3 - 0.0012x2 + (0.7709e - 3)x + 0.2628 | 0.988 9 |
| 80 | y = (0.1679e - 4)x3 - (0.5594e + 3)x2 - 0.0065x + 0.3746 | 0.999 8 |
Table 1 Equations of equilibrium moisture content (EMC) versus air temperature and coefficient of determination under different relative humidity
| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 平衡含水率随气温变化方程 Equations of EMC versus air temperature | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 | 20 | y = (0.3933e - 5)x3 - (0.2141e + 3)x2 + 0.7909x + 0.0781 | 0.966 6 |
| Larix gmelinii leaves | 40 | y = -(0.2787e + 4)x3 + 0.0014x2 - 0.0253x + 0.2305 | 0.994 7 |
| 60 | y = (0.3800e - 4)x3 + 00159x2 - 0.0018x + 0.1707 | 0.990 1 | |
| 80 | y = (0.1347e - 4)x3 - (0.7339e + 3)x2 + 0.0026x + 0.3091 | 0.999 9 | |
| 白桦叶片 | 20 | y = - (0.6667e + 6)x3 + (0.8943e - 4)x2 - 0.0055x + 0.1337 | 0.988 9 |
| Betula platyphylla leaves | 40 | y = - (0.5733e + 5)x3 + (0.4414e - 4)x2 - 0.0145x + 0.2243 | 0.993 9 |
| 60 | y = (0.8633e - 4)x3 - 0.0037x2 + 0.0357x + 0.1594 | 0.987 5 | |
| 80 | y = (0.2026e - 4)x3 - 0.0012x2 + 0.0087x + 0.3316 | 0.996 8 | |
| 落叶松-白桦叶片混合物 | 20 | y = (0.7733e - 5)x3 - (0.2829e + 3)x2 - (0.1876e + 3)x + 0.1024 | 0.999 8 |
| Mixture of L. gmelinii | 40 | y = (0.6733e - 5)x3 - (0.1881e + 3)x2 - 0.0046x + 0.1736 | 0.980 7 |
| and B. platyphylla leaves | 60 | y = (0.3513e - 4)x3 - 0.0012x2 + (0.7709e - 3)x + 0.2628 | 0.988 9 |
| 80 | y = (0.1679e - 4)x3 - (0.5594e + 3)x2 - 0.0065x + 0.3746 | 0.999 8 |
| 气温 Air tempe- rature (℃) | 相对湿度 Relative humi- dity (%) | 落叶松叶片 Larix gmelinii leaves | 决定 系数 Coefficient of determination (R2) | 白桦叶片 Betula platyphylla leaves | 决定 系数 Coefficient of determi- nation (R2) | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 决定 系数 Coefficient of determination (R2) |
|---|---|---|---|---|---|---|---|
| 5 | 20 | y = 0.0763 + 0.7502exp(-0.0959t) | 0.994 1 | y = 0.1090 + 0.6817exp(-0.0793t) | 0.994 3 | y = 0.0954 + 0.7567exp(-0.0872t) | 0.997 2 |
| 40 | y = 0.1346 + 0.7134exp(-0.0811t) | 0.994 9 | y = 0.1612 + 0.6449exp(-0.0653t) | 0.990 6 | y = 0.1453 + 0.6858exp(-0.0678t) | 0.988 7 | |
| 60 | y = 0.2127 + 0.6171exp(-0.0656t) | 0.996 7 | y = 0.2537 + 0.5559exp(-0.0474t) | 0.989 9 | y = 0.2388 + 0.5515exp(-0.0524t) | 0.984 7 | |
| 80 | y = 0.3056 + 0.5030exp(-0.0454t) | 0.983 6 | y = 0.3493 + 0.4769exp(-0.0357t) | 0.991 8 | y = 0.3304 + 0.5058exp(-0.0416t) | 0.995 3 | |
| 10 | 20 | y = 0.0723 + 0.7777exp(-0.1144t) | 0.996 3 | y = 0.0843 + 0.7230exp(-0.0974t) | 0.997 2 | y = 0.0796 + 0.7726exp(-0.1043t) | 0.995 5 |
| 40 | y = 0.0916 + 0.7293exp(-0.0859t) | 0.990 4 | y = 0.1210 + 0.6995exp(-0.0821t) | 0.998 3 | y = 0.1209 + 0.7302exp(-0.0942t) | 0.997 3 | |
| 60 | y = 0.1854 + 0.6218exp(-0.0673t) | 0.985 9 | y = 0.2403 + 0.5778exp(-0.0631t) | 0.987 4 | y = 0.1916 + 0.6068exp(-0.0645t) | 0.976 2 | |
| 80 | y = 0.2766 + 0.5367exp(-0.0539t) | 0.992 9 | y = 0.3163 + 0.4952exp(-0.0438t) | 0.977 1 | y = 0.2693 + 0.5429exp(-0.0498t) | 0.993 4 | |
| 15 | 20 | y = 0.0495 + 0.7928exp(-0.1567t) | 0.992 2 | y = 0.0731 + 0.7392exp(-0.1262t) | 0.996 9 | y = 0.0625 + 0.7660exp(-0.1227t) | 0.994 2 |
| 40 | y = 0.0667 + 0.7667exp(-0.1246t) | 0.997 1 | y = 0.0815 + 0.7332exp(-0.1139t) | 0.998 1 | y = 0.0766 + 0.7684exp(-0.1098t) | 0.994 6 | |
| 60 | y = 0.1501 + 0.6801exp(-0.1036t) | 0.995 9 | y = 0.1366 + 0.6214exp(-0.0846t) | 0.994 6 | y = 0.1086 + 0.6858exp(-0.0851t) | 0.994 7 | |
| 80 | y = 0.2284 + 0.6192exp(-0.0648t) | 0.996 8 | y = 0.2731 + 0.4999exp(-0.0510t) | 0.990 1 | y = 0.2092 + 0.6259exp(-0.0547t) | 0.994 3 | |
| 20 | 20 | y = 0.0435 + 0.7602exp(-0.2031t) | 0.985 5 | y = 0.0515 + 0.7774exp(-0.1917t) | 0.978 3 | y = 0.0470 + 0.7741exp(-0.1928t) | 0.979 3 |
| 40 | y = 0.0621 + 0.7208exp(-0.1818t) | 0.992 9 | y = 0.0682 + 0.7349exp(-0.1711t) | 0.992 2 | y = 0.0655 + 0.7504exp(-0.1567t) | 0.989 5 | |
| 60 | y = 0.0806 + 0.7157exp(-0.1236t) | 0.994 1 | y = 0.0863 + 0.6989exp(-0.0991t) | 0.996 2 | y = 0.0810 + 0.7189exp(-0.1174t) | 0.998 3 | |
| 80 | y = 0.1774 + 0.6130exp(-0.0760t) | 0.991 2 | y = 0.1927 + 0.6004exp(-0.0691t) | 0.986 3 | y = 0.1539 + 0.6745exp(-0.0695t) | 0.995 8 | |
| 25 | 20 | y = 0.0246 + 0.7845exp(-0.2366t) | 0.981 4 | y = 0.0424 + 0.7462exp(-0.2749t) | 0.976 2 | y = 0.0418 + 0.7459exp(-0.2298t) | 0.997 1 |
| 40 | y = 0.0338 + 0.7880exp(-0.2139t) | 0.993 7 | y = 0.0470 + 0.7328exp(-0.1925t) | 0.993 8 | y = 0.0446 + 0.7779exp(-0.2039t) | 0.982 9 | |
| 60 | y = 0.0601 + 0.7739exp(-0.1612t) | 0.987 5 | y = 0.0752 + 0.7267exp(-0.1389t) | 0.996 9 | y = 0.0703 + 0.7309exp(-0.1257t) | 0.994 8 | |
| 80 | y = 0.1274 + 0.6767exp(-0.1064t) | 0.997 1 | y = 0.1325 + 0.6731exp(-0.1085t) | 0.996 2 | y = 0.1248 + 0.6735exp(-0.0977t) | 0.997 0 |
Appendix table 1 Equations of moisture content dynamics of fuels under different air temperature and relative humidity
| 气温 Air tempe- rature (℃) | 相对湿度 Relative humi- dity (%) | 落叶松叶片 Larix gmelinii leaves | 决定 系数 Coefficient of determination (R2) | 白桦叶片 Betula platyphylla leaves | 决定 系数 Coefficient of determi- nation (R2) | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 决定 系数 Coefficient of determination (R2) |
|---|---|---|---|---|---|---|---|
| 5 | 20 | y = 0.0763 + 0.7502exp(-0.0959t) | 0.994 1 | y = 0.1090 + 0.6817exp(-0.0793t) | 0.994 3 | y = 0.0954 + 0.7567exp(-0.0872t) | 0.997 2 |
| 40 | y = 0.1346 + 0.7134exp(-0.0811t) | 0.994 9 | y = 0.1612 + 0.6449exp(-0.0653t) | 0.990 6 | y = 0.1453 + 0.6858exp(-0.0678t) | 0.988 7 | |
| 60 | y = 0.2127 + 0.6171exp(-0.0656t) | 0.996 7 | y = 0.2537 + 0.5559exp(-0.0474t) | 0.989 9 | y = 0.2388 + 0.5515exp(-0.0524t) | 0.984 7 | |
| 80 | y = 0.3056 + 0.5030exp(-0.0454t) | 0.983 6 | y = 0.3493 + 0.4769exp(-0.0357t) | 0.991 8 | y = 0.3304 + 0.5058exp(-0.0416t) | 0.995 3 | |
| 10 | 20 | y = 0.0723 + 0.7777exp(-0.1144t) | 0.996 3 | y = 0.0843 + 0.7230exp(-0.0974t) | 0.997 2 | y = 0.0796 + 0.7726exp(-0.1043t) | 0.995 5 |
| 40 | y = 0.0916 + 0.7293exp(-0.0859t) | 0.990 4 | y = 0.1210 + 0.6995exp(-0.0821t) | 0.998 3 | y = 0.1209 + 0.7302exp(-0.0942t) | 0.997 3 | |
| 60 | y = 0.1854 + 0.6218exp(-0.0673t) | 0.985 9 | y = 0.2403 + 0.5778exp(-0.0631t) | 0.987 4 | y = 0.1916 + 0.6068exp(-0.0645t) | 0.976 2 | |
| 80 | y = 0.2766 + 0.5367exp(-0.0539t) | 0.992 9 | y = 0.3163 + 0.4952exp(-0.0438t) | 0.977 1 | y = 0.2693 + 0.5429exp(-0.0498t) | 0.993 4 | |
| 15 | 20 | y = 0.0495 + 0.7928exp(-0.1567t) | 0.992 2 | y = 0.0731 + 0.7392exp(-0.1262t) | 0.996 9 | y = 0.0625 + 0.7660exp(-0.1227t) | 0.994 2 |
| 40 | y = 0.0667 + 0.7667exp(-0.1246t) | 0.997 1 | y = 0.0815 + 0.7332exp(-0.1139t) | 0.998 1 | y = 0.0766 + 0.7684exp(-0.1098t) | 0.994 6 | |
| 60 | y = 0.1501 + 0.6801exp(-0.1036t) | 0.995 9 | y = 0.1366 + 0.6214exp(-0.0846t) | 0.994 6 | y = 0.1086 + 0.6858exp(-0.0851t) | 0.994 7 | |
| 80 | y = 0.2284 + 0.6192exp(-0.0648t) | 0.996 8 | y = 0.2731 + 0.4999exp(-0.0510t) | 0.990 1 | y = 0.2092 + 0.6259exp(-0.0547t) | 0.994 3 | |
| 20 | 20 | y = 0.0435 + 0.7602exp(-0.2031t) | 0.985 5 | y = 0.0515 + 0.7774exp(-0.1917t) | 0.978 3 | y = 0.0470 + 0.7741exp(-0.1928t) | 0.979 3 |
| 40 | y = 0.0621 + 0.7208exp(-0.1818t) | 0.992 9 | y = 0.0682 + 0.7349exp(-0.1711t) | 0.992 2 | y = 0.0655 + 0.7504exp(-0.1567t) | 0.989 5 | |
| 60 | y = 0.0806 + 0.7157exp(-0.1236t) | 0.994 1 | y = 0.0863 + 0.6989exp(-0.0991t) | 0.996 2 | y = 0.0810 + 0.7189exp(-0.1174t) | 0.998 3 | |
| 80 | y = 0.1774 + 0.6130exp(-0.0760t) | 0.991 2 | y = 0.1927 + 0.6004exp(-0.0691t) | 0.986 3 | y = 0.1539 + 0.6745exp(-0.0695t) | 0.995 8 | |
| 25 | 20 | y = 0.0246 + 0.7845exp(-0.2366t) | 0.981 4 | y = 0.0424 + 0.7462exp(-0.2749t) | 0.976 2 | y = 0.0418 + 0.7459exp(-0.2298t) | 0.997 1 |
| 40 | y = 0.0338 + 0.7880exp(-0.2139t) | 0.993 7 | y = 0.0470 + 0.7328exp(-0.1925t) | 0.993 8 | y = 0.0446 + 0.7779exp(-0.2039t) | 0.982 9 | |
| 60 | y = 0.0601 + 0.7739exp(-0.1612t) | 0.987 5 | y = 0.0752 + 0.7267exp(-0.1389t) | 0.996 9 | y = 0.0703 + 0.7309exp(-0.1257t) | 0.994 8 | |
| 80 | y = 0.1274 + 0.6767exp(-0.1064t) | 0.997 1 | y = 0.1325 + 0.6731exp(-0.1085t) | 0.996 2 | y = 0.1248 + 0.6735exp(-0.0977t) | 0.997 0 |
Fig. 1 Curves of dynamics of moisture content in different fuels under different air temperature and relative humidity. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves. a, b, c, and d show relative humidity of 20%, 40%, 60%, 80%, respectively.
| 气温 Air temperature | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | |
| 5 ℃ | 1.00 | 0.719 | 0.399 | 0.166 | 0.070 | 1.00 | 0.724 | 0.314 | 0.103 | 0.044* | 1.00 | 0.597 | 0.202 | 0.089 | 0.055 |
| 10 ℃ | - | 1.00 | 0.619 | 0.284 | 0.120 | - | 1.00 | 0.511 | 0.089 | 0.120 | - | 1.00 | 0.374 | 0.152 | 0.084 |
| 15 ℃ | - | - | 1.00 | 0.543 | 0.237 | - | - | 1.00 | 0.488 | 0.235 | - | - | 1.00 | 0.525 | 0.296 |
| 20 ℃ | - | - | - | 1.00 | 0.466 | - | - | - | 1.00 | 0.528 | - | - | - | 1.00 | 0.606 |
| 25 ℃ | - | - | - | - | 1.00 | - | - | - | - | 1.00 | - | - | - | - | 1.00 |
Appendix table 2 Significance level of equilibrium moisture content (EMC) under different air temperature
| 气温 Air temperature | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | |
| 5 ℃ | 1.00 | 0.719 | 0.399 | 0.166 | 0.070 | 1.00 | 0.724 | 0.314 | 0.103 | 0.044* | 1.00 | 0.597 | 0.202 | 0.089 | 0.055 |
| 10 ℃ | - | 1.00 | 0.619 | 0.284 | 0.120 | - | 1.00 | 0.511 | 0.089 | 0.120 | - | 1.00 | 0.374 | 0.152 | 0.084 |
| 15 ℃ | - | - | 1.00 | 0.543 | 0.237 | - | - | 1.00 | 0.488 | 0.235 | - | - | 1.00 | 0.525 | 0.296 |
| 20 ℃ | - | - | - | 1.00 | 0.466 | - | - | - | 1.00 | 0.528 | - | - | - | 1.00 | 0.606 |
| 25 ℃ | - | - | - | - | 1.00 | - | - | - | - | 1.00 | - | - | - | - | 1.00 |
Fig. 2 Comparison between equilibrium moisture content (EMC) predicted by EMC-air temperature model and that of measurements. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves.
| 相对湿度 Relative humidity | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | |
| 20% | 1.00 | 0.269 | 0.026* | 0.001** | 1.00 | 0.343 | 0.060 | 0.002** | 1.00 | 0.263 | 0.068 | 0.004** |
| 40% | - | 1.00 | 0.105 | 0.004** | - | 1.00 | 0.182 | 0.008** | - | 1.00 | 0.245 | 0.016* |
| 60% | - | - | 1.00 | 0.087 | - | - | 1.00 | 0.124 | - | - | 1.00 | 0.150 |
| 80% | - | - | 1.00 | - | - | 1.00 | - | - | 1.00 | |||
Appendix table 3 Significance level of equilibrium moisture content (EMC) under different relative humidity
| 相对湿度 Relative humidity | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | |
| 20% | 1.00 | 0.269 | 0.026* | 0.001** | 1.00 | 0.343 | 0.060 | 0.002** | 1.00 | 0.263 | 0.068 | 0.004** |
| 40% | - | 1.00 | 0.105 | 0.004** | - | 1.00 | 0.182 | 0.008** | - | 1.00 | 0.245 | 0.016* |
| 60% | - | - | 1.00 | 0.087 | - | - | 1.00 | 0.124 | - | - | 1.00 | 0.150 |
| 80% | - | - | 1.00 | - | - | 1.00 | - | - | 1.00 | |||
| 气温 Air temperature (℃) | 落叶松叶片 Larix gmelinii leaves | 决定系数 Coefficient of determination (R2) | 白桦叶片 Betula platyphylla leaves | 决定系数 Coefficient of determination (R2) | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|---|---|---|
| 5 | y = 0.3670x1.5427 + 0.0456 | 0.999 9 | y = 0.3918x1.6392 + 0.0791 | 0.998 3 | y = 0.3843x1.6237 + 0.0649 | 0.997 2 |
| 10 | y = 0.3652x2.2000 + 0.0561 | 0.987 7 | y = 0.3914x1.5672 + 0.0464 | 0.978 2 | y = 0.3092x1.6848 + 0.0579 | 0.999 0 |
| 15 | y = 0.3182x2.1564 + 0.3458 | 0.986 6 | y = 0.4901x3.9617 + 0.0708 | 0.999 7 | y = 0.3526x3.9870 + 0.0641 | 0.998 6 |
| 20 | y = 0.3536x4.5456 + 0.0487 | 0.990 6 | y = 0.4191x5.0574 + 0.0568 | 0.992 8 | y = 0.2442x3.9114 + 0.5126 | 0.986 4 |
| 25 | y = 0.2315x3.6433 + 0.0245 | 0.999 7 | y = 0.2010x3.5001 + 0.0406 | 0.999 0 | y = 0.1941x3.7051 + 0.0401 | 0.998 6 |
Table 2 Equations of equilibrium moisture content (EMC) versus relative humidity and coefficient of determination under different air temperature
| 气温 Air temperature (℃) | 落叶松叶片 Larix gmelinii leaves | 决定系数 Coefficient of determination (R2) | 白桦叶片 Betula platyphylla leaves | 决定系数 Coefficient of determination (R2) | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|---|---|---|
| 5 | y = 0.3670x1.5427 + 0.0456 | 0.999 9 | y = 0.3918x1.6392 + 0.0791 | 0.998 3 | y = 0.3843x1.6237 + 0.0649 | 0.997 2 |
| 10 | y = 0.3652x2.2000 + 0.0561 | 0.987 7 | y = 0.3914x1.5672 + 0.0464 | 0.978 2 | y = 0.3092x1.6848 + 0.0579 | 0.999 0 |
| 15 | y = 0.3182x2.1564 + 0.3458 | 0.986 6 | y = 0.4901x3.9617 + 0.0708 | 0.999 7 | y = 0.3526x3.9870 + 0.0641 | 0.998 6 |
| 20 | y = 0.3536x4.5456 + 0.0487 | 0.990 6 | y = 0.4191x5.0574 + 0.0568 | 0.992 8 | y = 0.2442x3.9114 + 0.5126 | 0.986 4 |
| 25 | y = 0.2315x3.6433 + 0.0245 | 0.999 7 | y = 0.2010x3.5001 + 0.0406 | 0.999 0 | y = 0.1941x3.7051 + 0.0401 | 0.998 6 |
Fig. 3 Comparison between equilibrium moisture content (EMC) predicted by EMC-relative humidity model and that of measurements. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves.
| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 平衡含水率随气温、相对湿度变化的方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 10 < H < 50 | E = 1.075569 + 0.1226H - 0.003633T | 0.895 3 |
| H ≥ 50 | E = 0.76452 - 1.37034H + 1.838824H2 - 0.01221HT | 0.982 1 | |
| 白桦叶片 Betula platyphylla leaves | 10 < H < 50 | E = 1.336947 + 0.1186H - 0.004472T | 0.913 6 |
| H ≥ 50 | E = 0.940213 - 1.70177H + 2.218485H2 - 0.015047HT | 0.956 1 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 10 < H < 50 | E = 1.182743 + 0.1266H - 0.003966T | 0.906 1 |
| H ≥ 5 | E = 0.871213 - 1.53921H + 2.024026H2 - 0.013797HT | 0.965 3 |
Table 3 Simard equilibrium moisture content (EMC) model
| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 平衡含水率随气温、相对湿度变化的方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 10 < H < 50 | E = 1.075569 + 0.1226H - 0.003633T | 0.895 3 |
| H ≥ 50 | E = 0.76452 - 1.37034H + 1.838824H2 - 0.01221HT | 0.982 1 | |
| 白桦叶片 Betula platyphylla leaves | 10 < H < 50 | E = 1.336947 + 0.1186H - 0.004472T | 0.913 6 |
| H ≥ 50 | E = 0.940213 - 1.70177H + 2.218485H2 - 0.015047HT | 0.956 1 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 10 < H < 50 | E = 1.182743 + 0.1266H - 0.003966T | 0.906 1 |
| H ≥ 5 | E = 0.871213 - 1.53921H + 2.024026H2 - 0.013797HT | 0.965 3 |
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | Ed = -44.9323H0.001095 + 44.86805e0.073957H + 0.147607(33.97835 - T)(1 - e-0.08471H) | 0.988 8 |
| 白桦叶片 Betula platyphylla leaves | Ed = -26.3152H-0.00478 + 26.71372e0.137453H + 0.062646(12.75931 + T)(1 - e-0.258312H) | 0.975 1 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | Ed = -18.9629H-0.00775 + 19.39976e0.171261H + 0.065635(5.407862 + T)(1 - e-0.223153H) | 0.978 8 |
>Table 4 Van Wanger equilibrium moisture content (EMC) model
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | Ed = -44.9323H0.001095 + 44.86805e0.073957H + 0.147607(33.97835 - T)(1 - e-0.08471H) | 0.988 8 |
| 白桦叶片 Betula platyphylla leaves | Ed = -26.3152H-0.00478 + 26.71372e0.137453H + 0.062646(12.75931 + T)(1 - e-0.258312H) | 0.975 1 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | Ed = -18.9629H-0.00775 + 19.39976e0.171261H + 0.065635(5.407862 + T)(1 - e-0.223153H) | 0.978 8 |
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | Ed = 1.31779H-0.051049 + 0.329983e0.866517H + 0.006145(0.117326 - T) | 0.938 7 |
| 白桦叶片 Betula platyphylla leaves | Ed = 0.757326H1.462077 + 2.306681e-0.23901H - 0.007577(2.06381 + T) | 0.917 8 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | Ed = 1.971964H-0.00503 + 0.33744e2.343505H - 0.006854(0.244327 + T) | 0.906 8 |
Table 5 Anderson equilibrium moisture content (EMC) model
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | Ed = 1.31779H-0.051049 + 0.329983e0.866517H + 0.006145(0.117326 - T) | 0.938 7 |
| 白桦叶片 Betula platyphylla leaves | Ed = 0.757326H1.462077 + 2.306681e-0.23901H - 0.007577(2.06381 + T) | 0.917 8 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | Ed = 1.971964H-0.00503 + 0.33744e2.343505H - 0.006854(0.244327 + T) | 0.906 8 |
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | E = 0.217687 - 0.000873(-8.314T/18LogH) | 0.557 9 |
| 白桦叶片 Betula platyphylla leaves | E = 0.245242 - 0.000926(-8.314T/18LogH) | 0.488 7 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | E = 0.197390 - 0.012316(-8.314T/18LogH) | 0.553 5 |
Table 6 Nelson equilibrium moisture content (EMC) model
| 可燃物类型 Fuel type | 平衡含水率随气温、相对湿度变化方程 Equations of EMC versus air temperature and relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | E = 0.217687 - 0.000873(-8.314T/18LogH) | 0.557 9 |
| 白桦叶片 Betula platyphylla leaves | E = 0.245242 - 0.000926(-8.314T/18LogH) | 0.488 7 |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | E = 0.197390 - 0.012316(-8.314T/18LogH) | 0.553 5 |
Fig. 4 Distributions of errors in modeled equilibrium moisture content (EMC) of fine fuels. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves. MAE, mean absolute error; MRE, mean relative error; RMSE, root mean square error.
| 气温 Air temperature | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | |
| 5 ℃ | 1.00 | 0.653 | 0.161 | 0.066 | 0.019* | 1.00 | 0.401 | 0.146 | 0.042* | 0.012* | 1.00 | 0.439 | 0.172 | 0.043* | 0.014* |
| 10 ℃ | - | 1.00 | 0.262 | 0.098 | 0.023* | - | 1.00 | 0.429 | 0.119 | 0.025* | - | 1.00 | 0.498 | 0.131 | 0.041* |
| 15 ℃ | - | - | 1.00 | 0.500 | 0.153 | - | - | 1.00 | 0.396 | 0.098 | - | - | 1.00 | 0.336 | 0.112 |
| 20 ℃ | - | - | - | 1.00 | 0.449 | - | - | - | 1.00 | 0.334 | - | - | - | 1.00 | 0.502 |
| 25 ℃ | - | - | - | - | 1.00 | - | - | - | - | 1.00 | - | - | - | - | 1.00 |
Appendix table 4 Significance level of time-lag under different air temperature
| 气温 Air temperature | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | 5 ℃ | 10 ℃ | 15 ℃ | 20 ℃ | 25 ℃ | |
| 5 ℃ | 1.00 | 0.653 | 0.161 | 0.066 | 0.019* | 1.00 | 0.401 | 0.146 | 0.042* | 0.012* | 1.00 | 0.439 | 0.172 | 0.043* | 0.014* |
| 10 ℃ | - | 1.00 | 0.262 | 0.098 | 0.023* | - | 1.00 | 0.429 | 0.119 | 0.025* | - | 1.00 | 0.498 | 0.131 | 0.041* |
| 15 ℃ | - | - | 1.00 | 0.500 | 0.153 | - | - | 1.00 | 0.396 | 0.098 | - | - | 1.00 | 0.336 | 0.112 |
| 20 ℃ | - | - | - | 1.00 | 0.449 | - | - | - | 1.00 | 0.334 | - | - | - | 1.00 | 0.502 |
| 25 ℃ | - | - | - | - | 1.00 | - | - | - | - | 1.00 | - | - | - | - | 1.00 |
| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 气温 Air temperature (℃) | ||||
|---|---|---|---|---|---|---|
| 5 | 10 | 15 | 20 | 25 | ||
| 落叶松叶片 Larix gmelinii leaves | 20 | 10.43 | 8.74 | 6.38 | 4.92 | 4.23 |
| 40 | 12.33 | 11.64 | 8.03 | 5.50 | 4.68 | |
| 60 | 15.24 | 14.86 | 9.65 | 8.09 | 6.20 | |
| 80 | 22.03 | 18.55 | 15.43 | 13.16 | 9.40 | |
| 白桦叶片 Betula platyphylla leaves | 20 | 12.61 | 10.27 | 7.92 | 5.22 | 3.64 |
| 40 | 15.31 | 12.18 | 8.78 | 5.84 | 5.19 | |
| 60 | 21.10 | 15.85 | 11.82 | 10.09 | 7.20 | |
| 80 | 28.01 | 22.83 | 19.59 | 14.47 | 9.22 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 20 | 11.47 | 9.59 | 8.15 | 5.19 | 4.35 |
| 40 | 14.75 | 10.62 | 9.11 | 6.38 | 4.90 | |
| 60 | 19.08 | 15.50 | 11.75 | 8.52 | 7.96 | |
| 80 | 24.04 | 20.08 | 18.28 | 14.39 | 10.24 | |
Table 7 Time-lag of fuels under different air temperature and relative humidity (h)
| 可燃物类型 Fuel type | 相对湿度 Relative humidity (%) | 气温 Air temperature (℃) | ||||
|---|---|---|---|---|---|---|
| 5 | 10 | 15 | 20 | 25 | ||
| 落叶松叶片 Larix gmelinii leaves | 20 | 10.43 | 8.74 | 6.38 | 4.92 | 4.23 |
| 40 | 12.33 | 11.64 | 8.03 | 5.50 | 4.68 | |
| 60 | 15.24 | 14.86 | 9.65 | 8.09 | 6.20 | |
| 80 | 22.03 | 18.55 | 15.43 | 13.16 | 9.40 | |
| 白桦叶片 Betula platyphylla leaves | 20 | 12.61 | 10.27 | 7.92 | 5.22 | 3.64 |
| 40 | 15.31 | 12.18 | 8.78 | 5.84 | 5.19 | |
| 60 | 21.10 | 15.85 | 11.82 | 10.09 | 7.20 | |
| 80 | 28.01 | 22.83 | 19.59 | 14.47 | 9.22 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 20 | 11.47 | 9.59 | 8.15 | 5.19 | 4.35 |
| 40 | 14.75 | 10.62 | 9.11 | 6.38 | 4.90 | |
| 60 | 19.08 | 15.50 | 11.75 | 8.52 | 7.96 | |
| 80 | 24.04 | 20.08 | 18.28 | 14.39 | 10.24 | |
| 相对湿度 Relative humidity | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | |
| 20% | 1.00 | 0.463 | 0.111 | 0.007** | 1.00 | 0.560 | 0.108 | 0.017* | 1.00 | 0.538 | 0.086 | 0.007** |
| 40% | - | 1.00 | 0.350 | 0.121 | - | 1.00 | 0.259 | 0.204 | - | 1.00 | 0.228 | 0.195 |
| 60% | - | - | 1.00 | 0.026* | - | - | 1.00 | 0.038* | - | - | 1.00 | 0.023* |
| 80% | - | - | - | 1.00 | - | - | - | 1.00 | - | - | - | 1.00 |
Appendix table 5 Significance level of time-lag under different relative humidity
| 相对湿度 Relative humidity | 落叶松叶片 Larix gmelinii leaves | 白桦叶片 Betula platyphylla leaves | 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | |
| 20% | 1.00 | 0.463 | 0.111 | 0.007** | 1.00 | 0.560 | 0.108 | 0.017* | 1.00 | 0.538 | 0.086 | 0.007** |
| 40% | - | 1.00 | 0.350 | 0.121 | - | 1.00 | 0.259 | 0.204 | - | 1.00 | 0.228 | 0.195 |
| 60% | - | - | 1.00 | 0.026* | - | - | 1.00 | 0.038* | - | - | 1.00 | 0.023* |
| 80% | - | - | - | 1.00 | - | - | - | 1.00 | - | - | - | 1.00 |
| 可燃物类型 Fuel type | 空气相对湿度 Relative humidity (%) | 时滞随气温变化方程 Equations of time-lag versus air temperature | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 20 | y = (0.9600e - 3)x3 - 0.0349x2 - 0.0066x + 11.2399 | 0.998 5 |
| 40 | y = 0.0031x3 - 0.1365x2 + 1.3218x + 8.7975 | 0.996 6 | |
| 60 | y = 0.0029x3 - 0.1332x2 + 1.2189x + 12.2780 | 0.966 4 | |
| 80 | y = -0.0012x3 + 0.0561x2 - 1.3631x + 27.6359 | 0.995 6 | |
| 白桦叶片 Betula platyphylla leaves | 20 | y = (0.7533e - 3)x3 - 0.0306x2 - 0.1156x + 13.8320 | 0.999 1 |
| 40 | y = 0.0017x3 - 0.0613x2 + 0.0108x + 16.5599 | 0.999 8 | |
| 60 | y = -0.0016x3 + 0.0915x2 - 2.2090x + 30.1219 | 0.997 5 | |
| 80 | y = -0.0014x3 + 0.5634x2 - 1.5598x + 34.4934 | 0.997 9 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 20 | y = 0.0011x3 - 0.0488x2 + 0.2400x + 11.2699 | 0.987 4 |
| 40 | y = -(0.9133e + 3)x3 + 0.0528x2 - 1.3674x + 20.2920 | 0.990 4 | |
| 60 | y = 0.0036x3 - 0.1468x2 + 1.0602x + 17.0516 | 0.998 0 | |
| 80 | y = -0.0016x3 + 0.0656x2 - 1.4069x + 329.5488 | 0.995 3 |
Table 8 Equations of time-lag versus temperature and coefficient of determination under different relative humidity
| 可燃物类型 Fuel type | 空气相对湿度 Relative humidity (%) | 时滞随气温变化方程 Equations of time-lag versus air temperature | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 20 | y = (0.9600e - 3)x3 - 0.0349x2 - 0.0066x + 11.2399 | 0.998 5 |
| 40 | y = 0.0031x3 - 0.1365x2 + 1.3218x + 8.7975 | 0.996 6 | |
| 60 | y = 0.0029x3 - 0.1332x2 + 1.2189x + 12.2780 | 0.966 4 | |
| 80 | y = -0.0012x3 + 0.0561x2 - 1.3631x + 27.6359 | 0.995 6 | |
| 白桦叶片 Betula platyphylla leaves | 20 | y = (0.7533e - 3)x3 - 0.0306x2 - 0.1156x + 13.8320 | 0.999 1 |
| 40 | y = 0.0017x3 - 0.0613x2 + 0.0108x + 16.5599 | 0.999 8 | |
| 60 | y = -0.0016x3 + 0.0915x2 - 2.2090x + 30.1219 | 0.997 5 | |
| 80 | y = -0.0014x3 + 0.5634x2 - 1.5598x + 34.4934 | 0.997 9 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 20 | y = 0.0011x3 - 0.0488x2 + 0.2400x + 11.2699 | 0.987 4 |
| 40 | y = -(0.9133e + 3)x3 + 0.0528x2 - 1.3674x + 20.2920 | 0.990 4 | |
| 60 | y = 0.0036x3 - 0.1468x2 + 1.0602x + 17.0516 | 0.998 0 | |
| 80 | y = -0.0016x3 + 0.0656x2 - 1.4069x + 329.5488 | 0.995 3 |
| 可燃物类型 Fuel type | 气温 Air temperature (℃) | 时滞随相对湿度变化方程 Equations of time-lag versus relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 5 | y = 7.5029lnx + 21.1219 | 0.787 6 |
| 10 | y = 6.8015lnx + 18.9909 | 0.937 7 | |
| 15 | y = 5.7026lnx + 14.5197 | 0.757 8 | |
| 20 | y = 5.3324lnx + 12.2630 | 0.728 1 | |
| 25 | y = 3.3324lnx + 8.84310 | 0.733 7 | |
| 白桦叶片 Betula platyphylla leaves | 5 | y = 10.5346lnx + 27.423 | 0.860 8 |
| 10 | y = 8.2426lnx + 21.9998 | 0.800 2 | |
| 15 | y = 7.3834lnx + 18.0445 | 0.698 1 | |
| 20 | y = 6.3568lnx + 14.0853 | 0.791 6 | |
| 25 | y = 3.8974lnx + 9.48770 | 0.934 5 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 5 | y = 8.6887lnx + 24.4157 | 0.918 8 |
| 10 | y = 7.6462lnx + 20.4986 | 0.841 9 | |
| 15 | y = 6.4491lnx + 12.0780 | 0.720 9 | |
| 20 | y = 5.8443lnx + 13.3826 | 0.739 4 | |
| 25 | y = 4.1722lnx + 10.2602 | 0.830 1 |
Table 9 Equations of time-lag versus relative humidity and coefficient of determination under different temperature
| 可燃物类型 Fuel type | 气温 Air temperature (℃) | 时滞随相对湿度变化方程 Equations of time-lag versus relative humidity | 决定系数 Coefficient of determination (R2) |
|---|---|---|---|
| 落叶松叶片 Larix gmelinii leaves | 5 | y = 7.5029lnx + 21.1219 | 0.787 6 |
| 10 | y = 6.8015lnx + 18.9909 | 0.937 7 | |
| 15 | y = 5.7026lnx + 14.5197 | 0.757 8 | |
| 20 | y = 5.3324lnx + 12.2630 | 0.728 1 | |
| 25 | y = 3.3324lnx + 8.84310 | 0.733 7 | |
| 白桦叶片 Betula platyphylla leaves | 5 | y = 10.5346lnx + 27.423 | 0.860 8 |
| 10 | y = 8.2426lnx + 21.9998 | 0.800 2 | |
| 15 | y = 7.3834lnx + 18.0445 | 0.698 1 | |
| 20 | y = 6.3568lnx + 14.0853 | 0.791 6 | |
| 25 | y = 3.8974lnx + 9.48770 | 0.934 5 | |
| 落叶松-白桦叶片混合物 Mixture of L. gmelinii and B. platyphylla leaves | 5 | y = 8.6887lnx + 24.4157 | 0.918 8 |
| 10 | y = 7.6462lnx + 20.4986 | 0.841 9 | |
| 15 | y = 6.4491lnx + 12.0780 | 0.720 9 | |
| 20 | y = 5.8443lnx + 13.3826 | 0.739 4 | |
| 25 | y = 4.1722lnx + 10.2602 | 0.830 1 |
Fig. 5 Comparison between fuel time-lag predicted by time-lag-air-temperature model and that of measurements. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves.
Fig. 6 Comparison between fuel time-lag predicted by time-lag-relative humidity model and that of measurements. A, Larix gmelinii leaves. B, Betula platyphylla leaves. C, Mixture of L. gmelinii and B. platyphylla leaves.
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