Erosion agents and patterns profoundly affect hillslope soil loss characteristics. However, few attempts have been made to analyze the effects of rainfall and inflow on soil erosion for hillslopes dominated by sheet e...Erosion agents and patterns profoundly affect hillslope soil loss characteristics. However, few attempts have been made to analyze the effects of rainfall and inflow on soil erosion for hillslopes dominated by sheet erosion or rill erosion in the Chinese Mollisol region. The objective of this study was to discuss the erosive agent(rainfall or inflow), hillslope erosion pattern(sheet erosion or rill erosion) and slope gradient effects on runoff and soil losses. Two soil pans(2.0 m long, 0.5 m wide and 0.5 m deep) with 5° and 10° slopes were subjected to rainfall(0 and 70 mm h–1) and inflow(0 and 70 mm h–1) experiments. Three experimental combinations of rainfall intensity(RI) and inflow rate(IR) were tested using the same water supply of 70 mm by controllingthe run time. A flat soil surface and a soil bed with a straight initial rill were prepared manually, and represented hillslopes dominated by sheet erosion and rill erosion, respectively. The results showed that soil losses had greater differences among treatments than total runoff. Soil losses decreased in the order of RI70+IR70 > RI70+IR0 > RI0+IR70. Additionally, soil losses for hillslopes dominated by rill erosion were 1.7-2.2 times greater at 5° and 2.5-6.9 times greater at 10° than those for hillslopes dominated by sheet erosion. The loss of <0.25 mm soil particles and aggregates varying from 47.72%-99.60% of the total soil loss played a dominant role in the sediment. Compared with sheet erosion hillslopes, rill erosion hillslopes selectively transported more microaggregates under a relatively stable rill development stage, but rills transported increasinglymore macroaggregates under an active rill development stage. In conclusion, eliminating raindrop impact on relatively gentle hillslopes and preventing rill development on relatively steep hillslopes would be useful measures to decrease soil erosion and soil degradation in the Mollisol region of northeastern China.展开更多
Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed modul...Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.展开更多
基金funded by the National Natural Science Foundation of China(Grant Nos.41601281,41701313)the National Key R&D Program of China(Grant No.2016YFE0202900)
文摘Erosion agents and patterns profoundly affect hillslope soil loss characteristics. However, few attempts have been made to analyze the effects of rainfall and inflow on soil erosion for hillslopes dominated by sheet erosion or rill erosion in the Chinese Mollisol region. The objective of this study was to discuss the erosive agent(rainfall or inflow), hillslope erosion pattern(sheet erosion or rill erosion) and slope gradient effects on runoff and soil losses. Two soil pans(2.0 m long, 0.5 m wide and 0.5 m deep) with 5° and 10° slopes were subjected to rainfall(0 and 70 mm h–1) and inflow(0 and 70 mm h–1) experiments. Three experimental combinations of rainfall intensity(RI) and inflow rate(IR) were tested using the same water supply of 70 mm by controllingthe run time. A flat soil surface and a soil bed with a straight initial rill were prepared manually, and represented hillslopes dominated by sheet erosion and rill erosion, respectively. The results showed that soil losses had greater differences among treatments than total runoff. Soil losses decreased in the order of RI70+IR70 > RI70+IR0 > RI0+IR70. Additionally, soil losses for hillslopes dominated by rill erosion were 1.7-2.2 times greater at 5° and 2.5-6.9 times greater at 10° than those for hillslopes dominated by sheet erosion. The loss of <0.25 mm soil particles and aggregates varying from 47.72%-99.60% of the total soil loss played a dominant role in the sediment. Compared with sheet erosion hillslopes, rill erosion hillslopes selectively transported more microaggregates under a relatively stable rill development stage, but rills transported increasinglymore macroaggregates under an active rill development stage. In conclusion, eliminating raindrop impact on relatively gentle hillslopes and preventing rill development on relatively steep hillslopes would be useful measures to decrease soil erosion and soil degradation in the Mollisol region of northeastern China.
基金supported by National Natural Science Foundation of China(Grant Nos.11171015 and 11301568)
文摘Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.
