冰川冻土 ›› 2021, Vol. 43 ›› Issue (2): 437-452.doi: 10.7522/j.issn.1000-0240.2020.0090
付子腾1,2(), 吴青柏2, DYCK Miles3, 何海龙1(
)
收稿日期:
2019-08-02
修回日期:
2020-06-22
出版日期:
2021-04-30
发布日期:
2021-05-18
通讯作者:
何海龙
E-mail:fuziteng@lzb.ac.cn;hailong.he@hotmail.com
作者简介:
付子腾,博士研究生,主要从事寒区陆面过程研究. E-mail: fuziteng@lzb.ac.cn
基金资助:
Ziteng FU1,2(), Qingbai WU2, Miles DYCK3, Hailong HE1(
)
Received:
2019-08-02
Revised:
2020-06-22
Online:
2021-04-30
Published:
2021-05-18
Contact:
Hailong HE
E-mail:fuziteng@lzb.ac.cn;hailong.he@hotmail.com
摘要:
土壤冻融特征曲线(SFTC)可以描述冻融过程中未冻水含量随负温的变化关系。准确刻画土壤冻融特征曲线对土壤的冻融过程及相关的水热耦合运移研究至关重要。以往研究中土壤冻融特征曲线适用范围较窄,无法满足实际需要。通过类比水分特征曲线,考虑初始含水量和溶质浓度对未冻水含量的影响,提出了一种新的冻融特征曲线模型,经广泛的文献数据验证表明,新模型能准确拟合观测数据,平均纳什效率系数高于0.95。与另外五种土壤冻融特征曲线模型相比,新模型在不同质地、初始含水量、溶质含量的土壤中表现良好。此外,敏感性分析显示,影响模型性能的主要因素为土壤自身物理特性、土壤溶质浓度以及残余水含量。新模型及研究结果有助于更好地理解土壤冻融过程中的水热传输过程,可为气候变化条件下冻融区生产建设和环境研究奠定坚实的理论基础,并为寒区工程相关数值模拟提供参考。
中图分类号:
付子腾, 吴青柏, DYCK Miles, 何海龙. 一种新的土壤冻融特征曲线模型[J]. 冰川冻土, 2021, 43(2): 437-452.
Ziteng FU, Qingbai WU, Miles DYCK, Hailong HE. A new model to describe soil freezing-thawing characteristic curve[J]. Journal of Glaciology and Geocryology, 2021, 43(2): 437-452.
表3
五个初始含水量下分别得到的参数α、β值及其在不同初始含水量情况下的统计指标(加黑数值表示该含水量下对应的指标值)"
不同初始含水量下的参数值 | 初始含水量/(cm³·cm-³) | RMSE/(cm3·cm-3) | AD/(cm3·cm-3) | NSE | 综合指标 |
---|---|---|---|---|---|
θinit=0.254, α=1.336, β=2.071 | 0.459 | 0.029 | -0.022 | 0.922 | RMSE=0.017 AD=-0.011 NSE=0.964 |
0.398 | 0.014 | -0.009 | 0.982 | ||
0.357 | 0.014 | -0.011 | 0.975 | ||
0.313 | 0.013 | -0.008 | 0.975 | ||
0.254 | 0.009 | -0.009 | 0.980 | ||
θinit=0.313, α=1.351, β=2.062 | 0.459 | 0.028 | -0.022 | 0.923 | RMSE=0.017 AD=-0.011 NSE=0.964 |
0.398 | 0.013 | -0.009 | 0.982 | ||
0.357 | 0.014 | -0.011 | 0.975 | ||
0.313 | 0.013 | -0.008 | 0.975 | ||
0.254 | 0.090 | -0.060 | 0.981 | ||
θinit=0.357, α=1.385, β=2.062 | 0.459 | 0.028 | -0.021 | 0.928 | RMSE=0.016 AD=-0.011 NSE=0.967 |
0.398 | 0.013 | -0.009 | 0.984 | ||
0.357 | 0.013 | -0.01 | 0.978 | ||
0.313 | 0.012 | -0.008 | 0.977 | ||
0.254 | 0.008 | -0.006 | 0.983 | ||
θinit=0.398, α=1.318, β=2.082 | 0.459 | 0.029 | -0.022 | 0.921 | RMSE=0.017 AD=-0.011 NSE=0.964 |
0.398 | 0.014 | -0.009 | 0.982 | ||
0.357 | 0.014 | -0.011 | 0.975 | ||
0.313 | 0.013 | -0.008 | 0.975 | ||
0.254 | 0.009 | -0.006 | 0.980 | ||
θinit=0.459, α=1.761, β=1.972 | 0.459 | 0.025 | -0.023 | 0.942 | RMSE=0.016 AD=-0.011 NSE=0.969 |
0.398 | 0.014 | -0.010 | 0.982 | ||
0.357 | 0.013 | -0.011 | 0.978 | ||
0.313 | 0.013 | -0.009 | 0.972 | ||
0.254 | 0.008 | -0.007 | 0.981 |
表4
四种经验公式计算的Tf值在不同土壤溶质浓度下的表现,其中参数α、β通过公式(19)拟合得到"
经验公式 | 浓度/(g·L-1 NaCl) | α | β | Tf /℃ | RMSE/(cm3·cm-3) | AD/(cm3·cm-3) | NSE | 综合指标 |
---|---|---|---|---|---|---|---|---|
0 | 35.4 | 1.38 | 1.26 | 0.018 | -0.0008 | 0.932 | RMSE=0.014 AD=-0.0002 NSE=0.960 | |
10 | 3.92 | 1.61 | 1.26 | 0.008 | -0.0003 | 0.977 | ||
20 | 1.60 | 1.82 | 1.26 | 0.009 | 0.0010 | 0.985 | ||
35 | 0.83 | 1.93 | 1.26 | 0.017 | -0.0002 | 0.864 | ||
0 | 18.41 | 1.46 | 0 | 0.015 | -0.0050 | 0.951 | RMSE=0.013 AD=-0.0002 NSE=0.965 | |
10 | 2.89 | 1.70 | 0.61 | 0.006 | -0.0003 | 0.984 | ||
20 | 1.58 | 1.81 | 1.22 | 0.010 | 0.0007 | 0.985 | ||
35 | 1.15 | 1.76 | 2.09 | 0.017 | 0.0002 | 0.856 | ||
0 | 92.27 | 1.29 | 5.52 | 0.022 | -0.0010 | 0.895 | RMSE=0.010 AD=-0.0003 NSE=0.962 | |
10 | 10.76 | 1.42 | 5.92 | 0.012 | -0.0004 | 0.944 | ||
20 | 5.20 | 1.46 | 5.92 | 0.03 | -0.0001 | 0.999 | ||
35 | 2.60 | 1.5 | 5.92 | 0.019 | -0.0002 | 0.829 | ||
0 | 18.41 | 1.46 | 0 | 0.015 | -0.0005 | 0.951 | RMSE=0.016 AD=-0.0004 NSE=0.946 | |
10 | 11.74 | 1.41 | 6.61 | 0.012 | -0.0004 | 0.941 | ||
20 | 13.55 | 1.32 | 16.71 | 0.012 | -0.00001 | 0.976 | ||
35 | 14.44 | 1.27 | 38.69 | 0.023 | 0.00002 | 0.753 |
表5
式(18)和式(19)在不同溶质浓度土壤中的拟合指标,式(19)中Tf的值分别用经验公式(20)计算和参数拟合"
条件 | 溶质浓度/(g·L-1 NaCl) | α | β | Tf /℃ | RMSE/(cm3·cm-3) | AD/(cm3·cm-3) | NSE | 综合指标 |
---|---|---|---|---|---|---|---|---|
不考虑Tf ,用 | 0 | 18.41 | 1.46 | 0.015 | -0.0005 | 0.951 | RMSE=0.014 AD=0.00007 NSE=0.960 | |
10 | 1.87 | 1.86 | 0.005 | -0.0002 | 0.992 | |||
20 | 0.65 | 2.42 | 0.017 | 0.0020 | 0.952 | |||
35 | 0.33 | 2.81 | 0.016 | -0.0001 | 0.877 | |||
考虑Tf,用 | 0 | 18.41 | 1.46 | 0 | 0.015 | -0.0050 | 0.951 | RMSE=0.013 AD=-0.0002 NSE=0.965 |
10 | 2.89 | 1.70 | 0.61 | 0.006 | -0.0003 | 0.984 | ||
20 | 1.58 | 1.81 | 1.22 | 0.010 | 0.0007 | 0.985 | ||
35 | 1.15 | 1.76 | 2.09 | 0.017 | 0.0002 | 0.856 | ||
考虑Tf,用 | 0 | 18.41 | 1.46 | 0 | 0.015 | -0.005 | 0.951 | RMSE=0.013 AD=-0.0002 NSE=0.965 |
10 | 1.87 | 1.86 | 0 | 0.005 | -0.002 | 0.992 | ||
20 | 3.98 | 1.52 | 4.33 | 0.003 | -0.001 | 1 | ||
35 | 0.57 | 2.18 | 0.60 | 0.017 | -0.002 | 0.897 |
附表1
38种土壤样品的参数α和β值及模型拟合指标"
土壤样品 | 测定方法 | α | β | RMSE/(cm3·cm-3) | AD/(cm3·cm-3) | NSE |
---|---|---|---|---|---|---|
Harbin clay | Ult | 0.99 | 2.13 | 0.004 | -0.0007 | 0.999 |
LZ loess | Ult | 16.77 | 1.47 | 0.015 | -0.0020 | 0.833 |
Christ-sand | TDR | 2.18 | 2.66 | 0.014 | 0.0060 | 0.988 |
Christ-silt sand | TDR | 1.07 | 1.88 | 0.010 | -0.0006 | 0.989 |
Christ-silt | TDR | 1.76 | 1.63 | 0.017 | -0.0001 | 0.955 |
QT Plateau-silt clay | NMR | 1.76 | 1.93 | 0.007 | -0.0020 | 0.995 |
ST-Manchester silt | TDR | 49.40 | 1.76 | 0.003 | 0.0004 | 0.981 |
ST-West Lebanon gravel | NMR | 78.50 | 1.72 | 0.002 | -0.0004 | 0.997 |
ST-Kaolinite | TDR | 7.47 | 2.04 | 0.004 | -0.0010 | 0.981 |
ST-Chena Hot Springs silt | NMR | 22.96 | 1.85 | 0.002 | -0.0005 | 0.999 |
ST-Leda silt | TDR | 3.76 | 2.03 | 0.013 | -0.0050 | 0.981 |
ST-Morin clay | NMR | 19.30 | 1.57 | 0.010 | -0.0020 | 0.977 |
ST-Goodrich clay | TDR | 10.56 | 1.83 | 0.008 | -0.0030 | 0.976 |
ST-OB clay | NMR | 16.96 | 1.58 | 0.017 | -0.0050 | 0.968 |
ST-Tuto clay | TDR | 7.98 | 2.03 | 0.010 | 0.0010 | 0.986 |
ST-Sweden VFB 478 clay | MNR | 1.71 | 2.08 | 0.025 | 0.0010 | 0.968 |
ST-Suffield silt clay | TDR | 16.24 | 1.85 | 0.003 | -0.0009 | 0.998 |
ST-Ferderick clay | NMR | 15.89 | 1.61 | 0.011 | -0.0020 | 0.980 |
ST-Ellsworth clay | TDR | 15.19 | 1.68 | 0.007 | -0.0010 | 0.970 |
ST-Regina clay | NMR | 28.07 | 1.54 | 0.015 | -0.0030 | 0.961 |
ST-Umiat bentonite | TDR | 5.67 | 2.05 | 0.010 | -0.0010 | 0.994 |
ST-Lanzhou silt | NMR | 0.47 | 2.85 | 0.008 | -0.0030 | 0.991 |
ST-Niagara silt | TDR | 13.76 | 1.60 | 0.009 | -0.0010 | 0.967 |
ST-Norway LE-1 clay | NMR | 9.61 | 1.62 | 0.011 | -0.0030 | 0.989 |
ST-Athena silt loam | TDR | 31.56 | 1.71 | 0.004 | -0.0004 | 0.958 |
ST-Sweden CTH 201 clay | NMR | 4.83 | 1.75 | 0.025 | -0.0100 | 0.967 |
ST-Hectorite | NMR | 5.31 | 1.96 | 0.010 | -0.0010 | 0.993 |
Tice-Morin Clay | NMR | 1.24 | 2.02 | 0.008 | -0.0020 | 0.988 |
Patterson-silty clay (0 g | TDR | 18.41 | 1.46 | 0.015 | -0.0005 | 0.951 |
Patterson-silty clay (10 g | TDR | 1.87 | 1.86 | 0.005 | -0.0002 | 0.992 |
Patterson-silty clay (20 g | TDR | 0.65 | 2.42 | 0.017 | 0.0020 | 0.952 |
Patterson-silty clay (35 g | TDR | 0.33 | 2.81 | 0.016 | -0.0001 | 0.877 |
Wet Waukegan silt loam | TDR | 14.26 | 1.75 | 0.007 | -0.0020 | 0.990 |
Dry Waukegan silt loam | TDR | 1.72 | 2.56 | 0.009 | 0.0020 | 0.956 |
W-Sand1 | NMR | 64.38 | 1.67 | 0.008 | -0.0040 | 0.991 |
W-silt loam | NMR | 2.24 | 1.86 | 0.007 | -0.0020 | 0.992 |
M tiantian-silt | NMR | 114.74 | 1.85 | 0.008 | 0.0040 | 0.994 |
M tiantian-clay | NMR | 42.28 | 1.63 | 0.010 | 0.0006 | 0.995 |
附表2
土样数据的来源、测定方法和基本性质"
作者(年份) | 土壤样本 | 测定方法 | 比表面积/(m2·g-1) | 干密度/(g·cm-3) | 溶质浓度/% | 初始含水量/(cm3·cm-3) |
---|---|---|---|---|---|---|
Smith and Tice[ | Manchester黏土 | TDR | 18 | 1.425 | - | 0.471 |
West Lebanon砾石 | NMR | 15 | 1.563 | - | 0.375 | |
高岭土 | TDR | 23 | 1.262 | - | 0.503 | |
Chena Hot Springs粉土 | NMR | 40 | 1.456 | - | 0.414 | |
Leda粉土 | TDR | 58 | 1.412 | - | 0.471 | |
Morin黏土 | NMR | 60 | 1.305 | - | 0.472 | |
Goodrich黏 | TDR | 68 | 1.289 | - | 0.467 | |
OB黏土 | NMR | 61 | 1.352 | - | 0.515 | |
Tuto黏土 | TDR | 78 | 0.920 | - | 0.674 | |
Sweden VFB 478黏土 | MNR | 113 | 1.116 | - | 0.548 | |
Suffield粉质黏土 | TDR | 148 | 1.339 | - | 0.494 | |
Ferderick黏土 | NMR | 159 | 1.209 | - | 0.492 | |
Ellsworth黏土 | TDR | 184 | 1.210 | - | 0.450 | |
Regina黏土 | NMR | 291 | 0.961 | - | 0.572 | |
Umiat膨润土 | TDR | 714 | 0.365 | - | 0.821 | |
Lanzhou粉土 | NMR | 34 | 1.655 | - | 0.364 | |
Niagara粉土 | TDR | 37 | 1.645 | - | 0.365 | |
Norway LE-1黏土 | NMR | 52 | 1.415 | - | 0.477 | |
Athena黏土 | TDR | 83 | 1.296 | - | 0.456 | |
ST-Sweden CTH 201黏土 | NMR | 106 | 1.128 | - | 0.573 | |
锂辉石 | NMR | 419 | 0.706 | - | 0.722 | |
Morin黏土 | NMR | 60 | 1.433 | - | 0.287 | |
Patterson and Smith[ | 粉质黏土 | TDR | 148 | 1.19 | 0 | 0.523 |
TDR | 148 | 1.19 | 10 | 0.523 | ||
TDR | 148 | 1.19 | 20 | 0.523 | ||
TDR | 148 | 1.19 | 35 | 0.523 | ||
Spaans and Baker[ | 湿Waukegan粉质黏土 | TDR | 83 | 1.287 | - | 0.355 |
干Waukegan粉质黏土 | TDR | 83 | 1.319 | - | 0.241 | |
Suzuki[ | Brown Lowland soil | TDR | 110.8 | 0.7560 | - | 0.30 |
TDR | 110.8 | 0.5616 | - | 0.48 | ||
王大雁等[ | Harbin黏土 | 超声波 | 29.9 | 1.34 | - | 0.456 |
Lanzhou黄土 | 超声波 | 10.28 | 1.54 | - | 0.291 | |
Christ and Park[ | 砂土 | TDR | 15.32 | 1.90 | - | 0.372 |
粉砂土 | TDR | 29.36 | 1.82 | - | 0.417 | |
粉土 | TDR | 37.10 | 1.53 | - | 0.473 | |
Watanabe and Wake[ | 砂土 | NMR | 1.6 | 1.43 | - | 0.26 |
粉质黏土 | NMR | 29.9 | 1.13 | - | 0.370 | |
NMR | 29.9 | 1.13 | - | 0.211 | ||
温智等[ | 青藏高原粉质黏土 | NMR | 8.12 | 1.56 | - | 0.45900 |
NMR | 8.12 | 1.56 | - | 0.39780 | ||
NMR | 8.12 | 1.56 | - | 0.35646 | ||
NMR | 8.12 | 1.56 | - | 0.25428 | ||
NMR | 8.12 | 1.56 | - | 0.31278 | ||
马田田等[ | 粉土 | NMR | 6.22 | 1.6 | - | 0.45 |
黏土 | NMR | 22.63 | 1.4 | - | 0.49 |
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