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 土壤学报  2021, Vol. 58 Issue (4): 900-910  DOI: 10.11766/trxb202002240069 0

### 引用本文

SHAO Fanfan, WU Junhu, LI Yuchen. Establishment and Validation of the Model for Prediction of Nutrient Loss with Runoff on Bare Slopes in the Loess Plateau. Acta Pedologica Sinica, 2021, 58(4): 900-910.

### 作者简介

Establishment and Validation of the Model for Prediction of Nutrient Loss with Runoff on Bare Slopes in the Loess Plateau
SHAO Fanfan, WU Junhu, LI Yuchen
State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi'an University of Technology, Xi'an 710048, China
Abstract: 【Objective】Under natural rainfall conditions, a large amount of soil nutrients are losing with overland flow or surface runoff on sloping farmlands in the loess area, which exacerbates the decline of soil quality and productivity of the farmlands and causes serious agricultural non-point source pollution to the environment. Therefore, it is particularly important to accurately predict how soil nutrients loing with surface runoff in the loess areas. However, the existing nutrient loss prediction model focuses on estimating the total nutrient loss over a long period of time in an area, but neglects the effect of infiltrating water diluting the nutrients in the exchange layer before runoff starts.Method In this study, according to the characteristics of nutrient migration in different time periods of a rainfall event, the entire process of a rainfall event is divided into three phases: (1) from the beginning of rainfall (t0) to the time when the exchange layer is completely saturated (tsa), (2) from the time when the exchange layer is completely saturated (tsa) to the time when runoff occurs (tp), and (3) from first runoff (tp) to the end of the rainfall. Based on the approximate analytical solution of the motion wave model, an approximate analytical model of nutrient loss was established, which integrated the effects of raindrop splashing, diffusion and infiltration; and then a simulated rainfall experiment was conducted to determine parameters of the model and verify reliability of the model.Result Results show the values of surface runoff and nutrient loss predicted with the model accurately matched the measured values (R2> 0.8, Nash-Sutcliffe efficiency coefficient> 0.347). In this nutrient loss model, the raindrop-induced water transfer rate er was valued in the range of 0.006~0.023 cm·min-1, and the exchange layer depth de in the range of 0.68~1.32 cm. The former significantly affected peak rate of the nitrate nitrogen and ammonium nitrogen loss, whereas the latter did range of the overall variation of the loss rate and boosted total loss of the nutrients. The model was found to be more sensitive to de than to er.【Conclusion】Some field management measures, such as revegetation, deep fertilization, etc. should be adopted to reduce raindrop kinetic energy and lower the content of nutrients in the exchange layer, so as to realize the purpose of reducing nutrient loss. In general, this approximate semi-analytical model has fully considered the influence of water infiltration in unsaturated soil on nutrient transport in the exchange layer, so it can be used to predict nutrient loss processes on bare slopes in arid and semi-arid regions. However, it should be emphasized that accurate calculation of runoff process is the basis of the nutrient loss simulation, so it is advisable to select an appropriate infiltration formula and solute adsorption coefficients in the light of soil texture, nutrient type, and nutrient concentration in rainwater.
Key words: Model of nutrient loss    Depth of exchange layer    Raindrop splashing    Runoff scouring    Diffusion    Infiltration

1 材料与方法 1.1 理论与模型 1.1.1 坡面径流运动过程

 $\frac{{\partial h}}{{\partial t}} + \frac{{\partial q}}{{\partial x}} = p - i$ (1)

 $q(x, t)=(1-c)\left(p-\frac{1}{2} S(t-\Delta t)^{-1 / 2}\right) x$ (2)

 $h(x, t)=\left(\frac{1}{n} S_{0}^{1 / 2}\right)^{-3 / 5}\left\{(1-c)\left(p-\frac{1}{2} S(t-\Delta t)^{-1 / 2}\right) x\right\}^{3 / 5}$ (3)

1.1.2 径流养分流失过程

 图 1 模型物理和化学传输过程的简单示意 Fig. 1 Sketch of physical and chemical transport processes of the model

 $\frac{{d(\alpha {d_e}{C_e})}}{{dt}} = J + {e_r}(\lambda {C_w} - {C_e}) + {i_s}{C_w} - {i_x}{C_e}$ (4)

 $J = - ( - {D_s}\frac{{\partial {C_s}}}{{\partial z}})$ (5)
 ${D_s}\frac{{\partial {C_s}}}{{\partial z}}\left| {_{x = 0} = {C_0}\exp ( - \beta t)(\frac{{\beta \sqrt \alpha }}{{\sqrt {\pi {D_s}} }})} \right.\int_0^t {\frac{\beta }{{\sqrt y }}} dy$ (6)
 $\alpha = \gamma K + {\theta _s}$ (7)

 ${t_{sa}} = \frac{{{d_e}({\theta _s} - {\theta _0})}}{p}$ (8)

 $\begin{array}{l} {C_e}(t) = {C_0}\exp \left( { - A(t - {t_{sa}})} \right) + \frac{{{A^2}}}{{{i_x}}}\sqrt {\frac{{\alpha {D_s}}}{\pi }} \exp \\ \left( { - A(t - {t_{sa}})} \right)\int_{{t_{sa}}}^t {\exp \left( {A(y - {t_{sa}})} \right)\left( {\frac{{t - {t_{sa}}}}{{\sqrt {y - {t_{sa}}} }} - \sqrt {y - {t_{sa}}} } \right)} dy \\ \end{array}$ (9)

 $\begin{array}{l} {C_e}({t_p}) = {C_0}\exp \left( { - A({t_p} - {t_{sa}})} \right) + \frac{{{A^2}}}{{{i_x}}}\sqrt {\frac{{\alpha {D_s}}}{\pi }} \exp \\ \left( { - A({t_p} - {t_{sa}})} \right)\int_{{t_{sa}}}^{{t_p}} {\exp \left( {A(y - {t_{sa}})} \right)\left( {\frac{{{t_p} - {t_{sa}}}}{{\sqrt {y - {t_{sa}}} }} - \sqrt {y - {t_{sa}}} } \right)} dy \\ \end{array}$ (10)

 $\begin{array}{l} {C_e}(t) = {C_e}({t_p})\exp \left( { - B(t - {t_p})} \right) + \frac{{{B^2}}}{{{e_r}}}\sqrt {\frac{{\alpha {D_s}}}{\pi }} \exp \\ \left( { - B(t - {t_p})} \right)\int_{{t_p}}^t {\exp \left( {B(y - {t_p}} \right)\left( {\frac{{t - {t_p}}}{{\sqrt {y - {t_p}} }} - \sqrt {y - {t_p}} } \right)} dy \\ \end{array}$ (11)

 $\frac{{\partial (h{C_w})}}{{\partial t}} + \frac{{\partial q{C_w}}}{{\partial x}} = {e_r}({C_e} - \lambda {C_w}) - {i_s}{C_w}$ (12)

 $h\frac{{\partial {C_w}}}{{\partial t}} + q\frac{{\partial {C_w}}}{{\partial x}} = {e_r}({C_e} - \lambda {C_w}) - p{C_w}$ (13)

 $h\frac{{\partial {C_w}}}{{\partial t}} = {e_r}{C_e} - p{C_w}$ (14)

 $\begin{array}{l} {C_w}(t) = \exp \left( {\int_{{t_p}}^t { - \frac{p}{{h(t)}}dt} } \right) \\ \left( {{C_e}({t_p}) + \int_{{t_p}}^t {\frac{{{e_r}{C_e}(t)}}{{h(t)}}\exp \left( {\int_{{t_p}}^t {\frac{p}{{h(t)}}dt} } \right)} dt} \right) \\ \end{array}$ (15)

 ${M_w}(t) = q(x, t){C_w}(t)x$ (16)

1.2 试验区概况

1.3 试验方法

 图 2 针孔式模拟降雨装置 Fig. 2 Pinhole type artificial rainfall simulation device

1.4 模型基本参数

1.5 数据处理

2 结果与讨论 2.1 产流过程分析及模拟 2.1.1 产流过程分析

 注：p是降雨强度；tp是起始产流时间。Note：p is rainfall intensity；tp is the time of runoff initiation. 图 3 不同降雨强度下的产流时间 Fig. 3 Time of runoff initiation relative to rainfall intensity. Bars are means ± standard deviation.

 图 4 实测单宽流量变化过程 Fig. 4 Variation of measured per unit discharge. Bars are means ± standard deviation.
2.1.2 产流过程模拟

 图 5 降雨强度与入渗率参数c的关系 Fig. 5 Relationship between rainfall intensity and parameter of infiltration rate, c

 图 6 模拟不同降雨强度下的单宽流量变化过程 Fig. 6 Simulated variation of per unit discharge relative to rainfall intensity
2.2 养分流失过程分析及模拟 2.2.1 养分随径流流失过程分析

 图 7 不同降雨强度下硝态氮和铵态氮流失过程 Fig. 7 Processes of nitrate and ammonium nitrogen losses relative to rainfall intensity. Bars are means ± standard deviation
2.2.2 养分流失过程模拟

 图 8 模拟不同降雨强度下的养分流失速率变化过程 Fig. 8 Simulated variation of nutrient loss rate relative to rainfall intensity

3 结论

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