传递函数模型的发展和农田尺度下硝态氮淋失的数值预报
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摘要
氮素淋失对农业水土环境质量的影响是重要的生态农业研究课题，该研究中颇具挑战性的科学难题之一是对农田土壤中同时受到物理、化学和生物作用影响的硝态氮淋失动态的精确模拟和预报。为了对氮素运移和转化行为在生态环境演变过程中的作用有更明晰的认识，本文采用不同的数学模型分别从点尺度和农田尺度对此进行了研究。
本文研究的第一部分通过引入概率密度函数的修正因子，发展了一个可区分表施氮素和土壤残留氮对硝态氮淋失贡献的传递函数模型。假设累积排水量的概率密度函数的形状不随水流状态而改变，概率密度函数于不同水流条件下的差异体现在贮水量差的变化，将Jury等(1990)提出的非稳定流条件下保守溶质运移的传递函数模型推广到田间土壤硝态氮淋失的模拟中。在模型中考虑了氮素的矿化、固持、氨挥发和作物吸氮作用，把源汇项对硝态氮淋失的影响视为对溶质运移体中初始驻留浓度的输入，将各转化量与土壤贮水量或蒸散量建立了较简单的函数形式得到净矿化、氨挥发和吸氮浓度。以考虑源汇项作用时的硝态氮淋失浓度的均方根差为目标函数，采用二分法对概率密度函数的修正因子进行优化。使用1999年冬小麦—夏玉米生长条件下土壤剖面2米埋深处硝态氮淋失动态的试验观测数据，检验了所发展的模型的有效性。接着，分析了模型中各参量对模拟精度的影响，计算了模拟时段内淋失的硝态氮占肥料氮的比例。表明：作者所发展的能够估计表施氮素和残留氮对硝态氮淋失贡献的传递函数模型的计算结果是合理的；同时考虑流场变化、残留氮影响和氮素转化作用的传递函数模型具有更高的模拟精度，模拟的累积硝态氮淋失量的相对误差仅为0.99％；而既不考虑流场变化又不考虑氮素转化作用影响的模拟结果的相对误差达19.62％；仅考虑源汇项作用的硝态氮淋失量的模拟结果与发展的传递函数模型的模拟结果相差不大，相对误差为3.03％，说明在北方旱田深排水条件下长作物生育期内硝态氮淋失的模拟中，考虑氮素的转化作用对模拟结果的影响更大；表施氮的淋失量只占总淋失量的0.42％，占总施氮量的0.10％，所淋失的硝态氮大部分是土壤的残留氮，占总淋失量的99.58％。表施氮素迁移时间的概率密度函数的修正因子的取值对模拟精度的影响较大，取零时，模拟淋失量的相对误差为9.68％，取1时，相对误差为21.61％，取值在0.28到0.32之间时，对于与本文试验条件类似的农田土壤，应用我们所发展的数学模型可以获得满意的模拟结果。根据本文所发展的能区分表施氮和残留氮的传递函数模型，可为田间的~(15)N示踪试验提供一种定量的参考工具。
本文研究的第二部分在开展大规模田间试验的基础上，获得大量具有空间变异特征的模型参数，对农田尺度下硝态氮的淋失风险进行了数值预报。北京通州区永乐店试验站的小区面积为27×27m~2(网格间距3m)，采集30—50cm土层的样品；山东德州地区禹城试验站的小区面积为40×40m~2(网格间距5m)，采集0—20和20—40 cm土层的样品。根据土壤传递函数方法，生成了各个采样点的土壤水力学参数和弥散度。假设土壤有机氮的矿化速率常数(零级动力学)与有机质含量成正比得到矿化速率在空间上的分布。基于柱模型假设，即，土壤由一系列不发生相互作用的一维土柱组成，运用HYDRUS-1D软件，对永乐店2000—2001年和禹城2001—2003冬小麦—夏玉米生长条件下农田尺度下土壤氮素的转化和硝态氮的淋失风险进行了数值模拟。为评价矿化作用产生的无机氮对感兴趣深度的硝态氮淋失的影响，本文设计了两种数值模拟方案，即，不考虑和考虑土壤有机氮矿化速率的空间变异性(分别简记为方案1和方案2)。
模拟结果表明：(1)永乐店冬小麦生育期内剖面250cm埋深处平均的土壤水渗透量、累积硝
态氮淋失量分别为2.25mm、0.0098m沙m，，夏玉米生育期内的值分别为l.35mm、o.oo65m沙m，，
变异系数均在1.46以上，具有很强的空间变异性;(2)禹城冬小麦生育期内剖面ZO0cm埋深处
平均的土壤水渗透量、累积硝态氮淋失量分别为1930mm、0.0790m沙mZ，夏玉米生育期内的值
分别为24.48mm、0.0948m沙m，，变异系数均在0.50以上，表现为中等变异强度;(3)与总输入
量相比，空间上平均的土壤水渗透量和硝态氮淋失量不高，而某些采样点处土壤水渗透量和硝态
氮淋失量大大高于均值，是农田管理和环境监测的脆弱带;(4)两种数值模拟方案对模拟的下边
界处(永乐店:250cm;禹城:ZO0cm)硝态氮淋失的影响很小，其差异主要在于方案2对土壤
氮素各转化量的影响更大，由于考虑了氮素矿化作用的空间变异性，方案2中各氮素转化量的空
间变异性大大高于方案1的模拟结果;(5)蒸发量、蒸腾量和蒸散量具有较低的空间变异性
(CV<0 .06)，而剖面不同埋深处的水通量(250、200、150、IO0cm)呈现较强的空间变异性。
运用地统计学软件GEOPACK对实测土壤性状、模型参数和模拟结果进行地统计学分析，表
明:(l)永乐店采样小区的大部分参数(参量)的半方差可用球状模型表示，其中，容重、饱和
导水率(K:)、有机质含量(oM)的变程分别为26.26m、18.57m、4.77m;禹城采样小区大部
分参数的半方差函数用线性无基台值模型或纯块金模型描?
Nitrogen (N) leaching has caused an increasing potential concern over N fertilizer impact on environmental diversity. It is very promising to estimate the leaching of N in soils attributable to the complicated physical, chemical, and biological processes of the chemical not only at point scale but also at field scale. Different theories and models have been applied to describe N transformation and transport at every scale.
In the first part of this study, a transfer function model was developed to simulate the outflow concentration of nitrate-nitrogen (NO3-N) at the depth of 2m in the agricultural field, considering the influence of transient water flow, the applied N as input, the initial residual N in the soil, and main N transformations on the NO3-N leaching process. The probability density function (pdf) was assumed to be invariant under transient drainage except for differences in the water storage volume. And then the drainage pdf was corrected for storage volume differences between transient water flow and steady state and can be extended to represent transient outflow flux concentration. On N transformations the study model included immobilization, mineralization, volatilization, plant uptake, and their effects on NO3-N leaching were treated as an input to the initial concentration. Through the simple relationship between N transformations and water storage or evapotranspiration, concentration of source-sink te
rms was obtained. A weighting factor was introduced to quantify the contributions from the applied and residual N to the leaching process. The root mean square error of leaching concentration with considering source-sink terms was taken as target function to optimize weighting factor, and according to the bi-sectional method the optimized weighting factor was determined. The developed transfer function model was tested based on data of the field experiment conducted for 196 d during the growing periods for winter wheat (Triticum aestivum L.) and summer maize (Zea mays, L.) at Quzhou experiment station of China Agricultural University, Hebei province. Soil water potential and NO3-N concentrations were measured along two 2-m deep soil profiles during the investigation period. After calibrated at steady state, the developed transfer function model was used to simulate NO3-N concentration and leaching amount at the interest depth under transient flow. Four different methods were introduced to compar
e the effects of water flow and source-sink terms on the estimation accuracy, i.e., 1) considering both the transient water flow condition and the source-sink terms (Method 1), 2) considering the transient water flow condition only (Method 2), 3) considering neither the transient water flow condition nor the source-sink terms (Method 3), 4) considering the source-sink terms only (Method 4). Comparisons between the experimental data and simulated results with the transfer function showed that Method 1 provided the most reasonable prediction of the N leaching process as well as its total amount leached. Results also indicated that considering the transient water condition and N transformations in the transfer function significantly increased the estimation accuracy. Compared with the measured data, relative error of the estimated total amount leached N were 0.99 and 19.62%, respectively, with and without considering the transient water condition and the N transformations. The estimated results using Me
thods 1 and 4 were similar, which showed that
practically it may be necessary to consider the source-sink terms only and treat the water flow domain as a steady state when we simulate long-time chemical processes in dry croplands. The leached N resulting from the applied N accounted for 0.42% of the total leached N and 0.10% of the applied N, and the leached N was mainly from the residual N, which accounted for 99.58% of the total leached N. Calculations showed that the N leaching portions during the winter wheat and summer maize seasons, were 0.03 and 0.14% of the applie
本文研究的第一部分通过引入概率密度函数的修正因子，发展了一个可区分表施氮素和土壤残留氮对硝态氮淋失贡献的传递函数模型。假设累积排水量的概率密度函数的形状不随水流状态而改变，概率密度函数于不同水流条件下的差异体现在贮水量差的变化，将Jury等(1990)提出的非稳定流条件下保守溶质运移的传递函数模型推广到田间土壤硝态氮淋失的模拟中。在模型中考虑了氮素的矿化、固持、氨挥发和作物吸氮作用，把源汇项对硝态氮淋失的影响视为对溶质运移体中初始驻留浓度的输入，将各转化量与土壤贮水量或蒸散量建立了较简单的函数形式得到净矿化、氨挥发和吸氮浓度。以考虑源汇项作用时的硝态氮淋失浓度的均方根差为目标函数，采用二分法对概率密度函数的修正因子进行优化。使用1999年冬小麦—夏玉米生长条件下土壤剖面2米埋深处硝态氮淋失动态的试验观测数据，检验了所发展的模型的有效性。接着，分析了模型中各参量对模拟精度的影响，计算了模拟时段内淋失的硝态氮占肥料氮的比例。表明：作者所发展的能够估计表施氮素和残留氮对硝态氮淋失贡献的传递函数模型的计算结果是合理的；同时考虑流场变化、残留氮影响和氮素转化作用的传递函数模型具有更高的模拟精度，模拟的累积硝态氮淋失量的相对误差仅为0.99％；而既不考虑流场变化又不考虑氮素转化作用影响的模拟结果的相对误差达19.62％；仅考虑源汇项作用的硝态氮淋失量的模拟结果与发展的传递函数模型的模拟结果相差不大，相对误差为3.03％，说明在北方旱田深排水条件下长作物生育期内硝态氮淋失的模拟中，考虑氮素的转化作用对模拟结果的影响更大；表施氮的淋失量只占总淋失量的0.42％，占总施氮量的0.10％，所淋失的硝态氮大部分是土壤的残留氮，占总淋失量的99.58％。表施氮素迁移时间的概率密度函数的修正因子的取值对模拟精度的影响较大，取零时，模拟淋失量的相对误差为9.68％，取1时，相对误差为21.61％，取值在0.28到0.32之间时，对于与本文试验条件类似的农田土壤，应用我们所发展的数学模型可以获得满意的模拟结果。根据本文所发展的能区分表施氮和残留氮的传递函数模型，可为田间的~(15)N示踪试验提供一种定量的参考工具。
本文研究的第二部分在开展大规模田间试验的基础上，获得大量具有空间变异特征的模型参数，对农田尺度下硝态氮的淋失风险进行了数值预报。北京通州区永乐店试验站的小区面积为27×27m~2(网格间距3m)，采集30—50cm土层的样品；山东德州地区禹城试验站的小区面积为40×40m~2(网格间距5m)，采集0—20和20—40 cm土层的样品。根据土壤传递函数方法，生成了各个采样点的土壤水力学参数和弥散度。假设土壤有机氮的矿化速率常数(零级动力学)与有机质含量成正比得到矿化速率在空间上的分布。基于柱模型假设，即，土壤由一系列不发生相互作用的一维土柱组成，运用HYDRUS-1D软件，对永乐店2000—2001年和禹城2001—2003冬小麦—夏玉米生长条件下农田尺度下土壤氮素的转化和硝态氮的淋失风险进行了数值模拟。为评价矿化作用产生的无机氮对感兴趣深度的硝态氮淋失的影响，本文设计了两种数值模拟方案，即，不考虑和考虑土壤有机氮矿化速率的空间变异性(分别简记为方案1和方案2)。
模拟结果表明：(1)永乐店冬小麦生育期内剖面250cm埋深处平均的土壤水渗透量、累积硝
态氮淋失量分别为2.25mm、0.0098m沙m，，夏玉米生育期内的值分别为l.35mm、o.oo65m沙m，，
变异系数均在1.46以上，具有很强的空间变异性;(2)禹城冬小麦生育期内剖面ZO0cm埋深处
平均的土壤水渗透量、累积硝态氮淋失量分别为1930mm、0.0790m沙mZ，夏玉米生育期内的值
分别为24.48mm、0.0948m沙m，，变异系数均在0.50以上，表现为中等变异强度;(3)与总输入
量相比，空间上平均的土壤水渗透量和硝态氮淋失量不高，而某些采样点处土壤水渗透量和硝态
氮淋失量大大高于均值，是农田管理和环境监测的脆弱带;(4)两种数值模拟方案对模拟的下边
界处(永乐店:250cm;禹城:ZO0cm)硝态氮淋失的影响很小，其差异主要在于方案2对土壤
氮素各转化量的影响更大，由于考虑了氮素矿化作用的空间变异性，方案2中各氮素转化量的空
间变异性大大高于方案1的模拟结果;(5)蒸发量、蒸腾量和蒸散量具有较低的空间变异性
(CV<0 .06)，而剖面不同埋深处的水通量(250、200、150、IO0cm)呈现较强的空间变异性。
运用地统计学软件GEOPACK对实测土壤性状、模型参数和模拟结果进行地统计学分析，表
明:(l)永乐店采样小区的大部分参数(参量)的半方差可用球状模型表示，其中，容重、饱和
导水率(K:)、有机质含量(oM)的变程分别为26.26m、18.57m、4.77m;禹城采样小区大部
分参数的半方差函数用线性无基台值模型或纯块金模型描?
Nitrogen (N) leaching has caused an increasing potential concern over N fertilizer impact on environmental diversity. It is very promising to estimate the leaching of N in soils attributable to the complicated physical, chemical, and biological processes of the chemical not only at point scale but also at field scale. Different theories and models have been applied to describe N transformation and transport at every scale.
In the first part of this study, a transfer function model was developed to simulate the outflow concentration of nitrate-nitrogen (NO3-N) at the depth of 2m in the agricultural field, considering the influence of transient water flow, the applied N as input, the initial residual N in the soil, and main N transformations on the NO3-N leaching process. The probability density function (pdf) was assumed to be invariant under transient drainage except for differences in the water storage volume. And then the drainage pdf was corrected for storage volume differences between transient water flow and steady state and can be extended to represent transient outflow flux concentration. On N transformations the study model included immobilization, mineralization, volatilization, plant uptake, and their effects on NO3-N leaching were treated as an input to the initial concentration. Through the simple relationship between N transformations and water storage or evapotranspiration, concentration of source-sink te
rms was obtained. A weighting factor was introduced to quantify the contributions from the applied and residual N to the leaching process. The root mean square error of leaching concentration with considering source-sink terms was taken as target function to optimize weighting factor, and according to the bi-sectional method the optimized weighting factor was determined. The developed transfer function model was tested based on data of the field experiment conducted for 196 d during the growing periods for winter wheat (Triticum aestivum L.) and summer maize (Zea mays, L.) at Quzhou experiment station of China Agricultural University, Hebei province. Soil water potential and NO3-N concentrations were measured along two 2-m deep soil profiles during the investigation period. After calibrated at steady state, the developed transfer function model was used to simulate NO3-N concentration and leaching amount at the interest depth under transient flow. Four different methods were introduced to compar
e the effects of water flow and source-sink terms on the estimation accuracy, i.e., 1) considering both the transient water flow condition and the source-sink terms (Method 1), 2) considering the transient water flow condition only (Method 2), 3) considering neither the transient water flow condition nor the source-sink terms (Method 3), 4) considering the source-sink terms only (Method 4). Comparisons between the experimental data and simulated results with the transfer function showed that Method 1 provided the most reasonable prediction of the N leaching process as well as its total amount leached. Results also indicated that considering the transient water condition and N transformations in the transfer function significantly increased the estimation accuracy. Compared with the measured data, relative error of the estimated total amount leached N were 0.99 and 19.62%, respectively, with and without considering the transient water condition and the N transformations. The estimated results using Me
thods 1 and 4 were similar, which showed that
practically it may be necessary to consider the source-sink terms only and treat the water flow domain as a steady state when we simulate long-time chemical processes in dry croplands. The leached N resulting from the applied N accounted for 0.42% of the total leached N and 0.10% of the applied N, and the leached N was mainly from the residual N, which accounted for 99.58% of the total leached N. Calculations showed that the N leaching portions during the winter wheat and summer maize seasons, were 0.03 and 0.14% of the applie
引文
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