# Simulation of Flow and Agricultural Non-Point Source Pollutant Transport in a Tibetan Plateau Irrigation District

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{4}

^{+}-N) and nitrate nitrogen (NO

_{3}

^{−}-N) transport processes. Sobol’s method was used to evaluate the sensitivity of simulated flow and transport processes to the model inputs. The results showed that with a 21.2% increase of rainfall and irrigation in the highland barley growing period, the average NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in the soil layer decreased by 10.8% and 14.3%, respectively, due to increased deep seepage. Deep seepage of rainfall water accounted for 0–52.4% of total rainfall, whereas deep seepage of irrigation water accounted for 36.6–45.3% of total irrigation. NH

_{4}

^{+}-N and NO

_{3}

^{−}-N discharged into the drainage canal represented 19.9–30.4% and 19.4–26.7% of the deep seepage, respectively. The mean Nash–Sutcliffe coefficient value, which was close to 0.8, and the lowest values of root mean square errors, the fraction bias, and the fractional gross error indicated that the simulated flow rates and nitrogen concentrations using the proposed method were very accurate. The Sobol’s sensitivity analysis results demonstrated that subsurface lateral flow had the most important first-order and total-order effect on the simulated flow and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the surface drainage outlet.

## 1. Introduction

_{4}

^{+}-N) and nitrate nitrogen (NO

_{3}

^{−}-N).

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, respectively. Spring highland barley was the main crop planted in this district. From 1953 to 2014, the average annual temperature was 8.7 °C and the extreme maximum and minimum temperatures were 32.4 °C and −15.3 °C, respectively. The annual average relative humidity was 64.2%. The average annual precipitation was 664.5 mm, which was predominantly concentrated during the period from May to September (81.4% of the annual precipitation). The average annual pan evaporation was 1734.1 mm. The annual average wind speed was 1.68 m/s, and the annual average hours of sunshine were 2064.6 h.

^{2}for the first and second irrigation, respectively.

#### 2.2. Monitoring Hydrological and ANPS Pollution Transport and Transformation Processes in the Soil and Rock

_{4}

^{+}-N and NO

_{3}

^{−}-N). All soil samples were collected using a cutting ring with a volume of 100 cm

^{3}. Fourteen and fifteen sampling events were conducted during the growing period of highland barley in 2014 and 2015, respectively. The soil water content and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in these samples were measured at the Farmland Water Conservancy Laboratory of the Tibet Agriculture and Animal Husbandry College.

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations. The area between sections A and B was covered with a rainproof film to prevent water infiltration into the soil. The amount of irrigation in the experimental site was identical to that in the field during the growing period of highland barley.

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations were measured on the sampling day and 7 days later. The mass difference was taken as the amount of pollutant transformation. Samples were taken at three positions in the soil layer (10–40 cm depth) and loose rock layer (70–90 cm depth). The measurements were made twice, three times, and once, respectively, during the sowing–tilling, jointing–heading, and flowering–filling stages of the highland barley.

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in the surface drainage.

#### 2.3. Simulation of Hydrological and ANPS Pollution Transport Processes in the Plateau Irrigation District

_{i}that enters the rock from the soil can be expressed as

_{i}seeps into the rock from the soil and moves laterally toward to the surface drainage canal as well as vertically into the groundwater. The lateral inflow flux from soil seepage L

_{i}

_{ − 1}at section i is denoted as S

_{i}(Figure 3b). In the interval from section i to section i + 1, only a partial flux of S

_{i}continuously moves to the surface drainage canal due to high arbitrariness of flow in the loose fractured rock.

_{i}decreases to S

_{i,i+1.}The flux at section i + 1 also includes lateral flow from soil seepage L

_{i}, denoted as flux S

_{i + 1}. At section i, the lateral flux to the surface drainage canal is the superposition of all fluxes and can be expressed as

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in the soil profile were used as inputs in the subsurface lateral flow and transport simulation.

_{gwi,i + 1}is the groundwater flow into the surface drainage canal, $\mu $ is the specific yield of the shallow aquifer (cm

^{3}/cm

^{3}), and L

_{g}is the distance from the ridge of the groundwater to the surface drainage canal. Water flow and pollutant transport processes in the drainage canal can be characterized by the following Equations:

_{0}are the hydraulic radius and longitudinal slope of the drainage channel, respectively; and i

_{f}is the friction slope. Due to the prevention of field ridges and the high soil permeability in the irrigation zone, irrigation and rainfall did not typically produce runoff.

_{t}and c

_{t+}

_{1}are the concentrations of pollutants (NH

_{4}

^{+}-N or NO

_{3}

^{−}-N) at times t and t + 1 (mg/L). The k is a lump factor to quantify pollutant transformation caused by various physical, chemical, and biological processes in the rock or in the drainage water (day

^{−1}).

#### 2.4. Calibration of Model Parameters

_{4}

^{+}-N and NO

_{3}

^{−}-N concentration at sections A and B in the rock and at the outlet of the drainage canal during the highland barley growing period in 2014 were used to calibrate model parameters. The objective function was defined as

_{q}is the number of monitoring variables (flow rate, NH

_{4}

^{+}-N concentration, and NO

_{3}

^{−}-N concentration), n

_{qj}is the monitoring number of variable j, ${{g}_{j}}^{*}(x,{t}_{i})$ is the monitored value of variable j at time t

_{i}in the monitoring position, and ${g}_{j}(x,{t}_{i},[b])$ is the result of using optimized parameter [b]. Additionally, v

_{j}is the weight of variable j, which is used to reduce the magnitude effect of different variables and different monitoring events on the calculated results.

_{4}

^{+}-N and NO

_{3}

^{-}-N concentrations were evaluated using four indicators: the Nash–Sutcliffe coefficient (NSE) [30], the relative root mean square error (rRMSE), the fraction bias (F

_{B}), and the fractional gross error (F

_{E}) [31]; NSE, F

_{B}, and F

_{E}are calculated as follows:

_{t}and P

_{t}are the monitored and calculated values at time t, respectively, $\overline{O}$ is the mean of the monitored value, and n is the number of observation points. The ideal value of NSE was 1. F

_{B}and F

_{E}were used to describe the systematic error and total deviation between the observed and simulated values, respectively.

#### 2.5. Sobol’s Sensitivity Analysis

_{1}, x

_{2},…x

_{n}) is the parameter and physical variable set. For all of parameters and physical variables used in the model, two low-discrepancy random sequences are generated using the random sampling method [32].

_{i}) with the ith column data in matrix A.

_{i}, and the total-order sensitivity index, S

_{Ti}, were calculated as follows:

_{i}, is a measure of the variance contribution of the individual parameter x

_{i}to the total model variance. The difference between the first-order sensitivity index and the total-order sensitivity index can be regarded as a measure of the interaction between parameter x

_{i}and the other parameters.

## 3. Results

#### 3.1. Characterization of Flow and NH_{4}^{+}-N and NO_{3}^{−}-N Transport

_{4}

^{+}-N and NO

_{3}

^{−}-N, respectively, at different depths and during the highland barley growing period of 2014. Figure 4c,d shows the same distributions for 2015. Compared with the mean NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at different depths in 2014, the mean NH

_{4}

^{+}-N concentration decreased by 14.22, 11.47, and 6.78%, respectively, and the mean NO

_{3}

^{−}-N concentration decreased by 3.18, 22.4, and 17.3%, respectively, during the sowing–tilling, jointing–heading, and flowering–filling stages of 2015. Due to a 21.2% increase in rainfall and irrigation during the highland barley growing period of 2015, the mean concentrations of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N decreased by 10.8 and 14.3%, respectively. In the bottom soil layer (40–50 cm), the peak concentrations of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N during the highland barley growing period of 2014 were 0.86 and 4.08 mg/L, respectively, whereas for 2015, these concentrations were 0.65 and 3.76 mg/L, representing a decrease of 24.4 and 7.8%, respectively.

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in the subsurface lateral flow, monitored at the lateral flow experimental site during the experimental periods of 2014 and 2015. Table 2 compares the deep seepage fluxes of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N measured during each growth stage. For the three irrigation events in 2014 (Figure 5a), the amount of seepage water entering the rock through the soil accounted for 37.4, 36.6, and 41.2% of the irrigation, respectively. For 2015, seepage accounted for 40.2, 45.3, and 39.4% of the irrigation, respectively. Seepage due to rainfall accounted for 0 to 52.4% of total rainfall in two years.

_{4}

^{+}-N in subsurface lateral flow appeared after fertilization in both 2014 and 2015. Compared with the flow rate and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at Section A in 2014, the mean value of the flow rate and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at Section B decreased by 34.2, 54.8, and 44.6%, respectively, and the peak values decreased by 82.4, 44.2, and 38.7%, respectively. With increased rainfall and irrigation in 2015, the difference in flow rate and pollution concentrations between Section A and B decreased; the mean value of the flow rate and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at position B decreased by 24.2, 34.5, and 28.7%, respectively, and the peak values decreased by 74.4, 24.2, and 14.7%, respectively.

#### 3.2. Simulation of ANPS Pollutant Transport and Transformation Processes

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the outlet (Section O) of the surface drainage canal.

_{E}, and F

_{B}listed in Table 4. The NSE value exceeded 0.6. The F

_{B}remained less than 15% throughout the growing period of highland barley, demonstrating no systematic error between the simulated and measured results. F

_{B}and F

_{E}indexes of the simulated values were within the range of ±0.15/0.3 (F

_{B}/F

_{E}), indicating high accuracy of the simulation [31]. All the results of the Nash–Sutcliffe coefficient, rRMSE, and F

_{E}demonstrate that the model can effectively describe the transport and transformation processes of pollutants in the rock and estimate the pollution load accurately in this plateau irrigation area.

_{4}

^{+}-N, and NO

_{3}

^{−}-N from the soil during various stages of the highland barley growing period in 2015, which included the mass of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N in deep seepage from the soil into the rock, the mass of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N pollutants transformed in the rock, and the mass of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N discharged into the surface drainage canal. Overall, 29.4% of deep seepage water was due to irrigation and rainfall discharged into the drainage channel. The transformation of NH

_{4}

^{+}-N accounted for 13.0–22.4% of total NH

_{4}

^{+}-N in the deep seepage, whereas NH

_{4}

^{+}-N discharge into the drainage channel accounted for 19.9–30.4% of total NH

_{4}

^{+}-N in the deep seepage. The transformation of NO

_{3}

^{−}-N accounted for 11.2–14.1% of total NO

_{3}

^{−}-N in the deep seepage, whereas NO

_{3}

^{−}-N discharge into the drainage channel accounted for 19.4–26.7% of total NO

_{3}

^{−}-N in the deep seepage.

#### 3.3. Sensitivity Evaluation of Model Parameters

_{4}

^{+}-N, and NO

_{3}

^{−}-N from groundwater than from subsurface lateral flow.

_{i}for soil NH

_{4}

^{+}-N concentration was higher than the rates of deep seepage from the soil into the rock. The difference in S

_{i}and S

_{Ti}values for the NH

_{4}

^{+}-N transformation coefficient in lateral transport and surface drainage transport was significantly higher than the differences between other parameters. The results also showed that 65.2% of the variations in the simulated NH

_{4}

^{+}-N concentrations at the surface drainage outlet were caused by variations of α and β in Equation (3) and 18.4% of the variations were attributed to the transformation of NH

_{4}

^{+}-N. Although the values of α and β in Equation (3) were the most sensitive parameters in the NO

_{3}

^{−}-N transport simulation, the values decreased by 45.2 and 27.2% compared to the values of α and β in the flow and NH

_{4}

^{+}-N simulations, respectively. The sensitivity of NO

_{3}

^{−}-N concentrations in the soil was also lower than that of NH

_{4}

^{+}-N concentrations in the soil.

## 4. Discussion

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations are directly affected by the subsurface lateral flow process. The NH

_{4}

^{+}-N and NO

_{3}

^{−}-N leaching per unit rainfall and irrigation were 4.25 and 18.45 kg km

^{−2}mm

^{−1}, and the ratio of the total N leaching to the fertilizer N application was 0.34. These results were substantially different with those of Ju and Zhang [33], who reported that the N leaching in hilly barley crop land was in the range of 1.05 × 10

^{−2}to 1.18 kg km

^{−2}mm

^{−1}, and the ratio of the N leaching to the fertilizer N application was in the range of 0.044 to 0.249. The thin soil layer, irregularities in rainfall distribution, and heavy irrigation attributed to the higher N leaching in the Danniang irrigation district, especially the NH

_{4}

^{+}-N leaching, was mainly attributed to heavy irrigation because fertilizer N was applied during the first and second irrigation and soil NH

_{4}

^{+}-N concentrations were maintained at high levels after fertilization. In total, 45.8 kg km

^{−2}of NH

_{4}

^{+}-N, or 84.7% of total NH

_{4}

^{+}-N leaching, was caused by the irrigation. Given that the soil thickness is sufficient, the spatial and temporal distribution of NO

_{3}

^{−}-N in the soil profile may be significantly changed by fertilization, irrigation, and precipitation events [34,35]. NH

_{4}

^{+}-N can be converted to NO

_{3}

^{−}-N rapidly under favorable water and heat conditions. As a result, less NH

_{4}

^{+}-N leaching occurs [36]. In the studied irrigation district, 28.7 and 72.3% of the total NO

_{3}

^{−}-N leaching was caused by irrigation and rainfall, respectively, due to the thin and highly permeable soil.

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the outlet of the drainage canal were accurately simulated, the coefficient of variation (the ratio of standard deviation to mean) of flow rates and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations were overestimated. Due to a 21.2% increase in total rainfall and irrigation in 2015, the monitored coefficients of variation of the flow rate and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the outlet of the drainage canal increased by 15.7, 18.9, and 8.2%, respectively, while the simulated increase of the coefficients of variation were 24.2, 28.4, and 10.8%, respectively. The deviations between the measured and the simulated flow rates and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations might be attributed to using the lumping factor to characterize the various flow and transformation processes. The storage effect and the nonlinear flow processes in the rock also affected the accuracy of the calculated concentrations. As shown in Figure 6, the flow rates simulated with the calibrated parameters were lower than the values measured in July 2015. The mean values of the measured and simulated flow rates were 0.0338 and 0.0402 m

^{3}/s, respectively, at the outlet of the drainage canal. Soil seepage into the rock was significantly reduced because rainfall was only 14.5 mm in June 2015 (Figure 4), and part of the seepage was stored in fractures and pores in the rock instead of being discharged into the surface drainage canal. As a result, the model underestimated flow rates and overestimated NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations by 4.71 and 5.64%, respectively, for this period.

_{4}

^{+}-N and NO

_{3}

^{−}-N) transport and transformation processes. The Sobol’s sensitivity indices of α were significantly greater than the indices of β for the flow process, whereas the indices of α decreased and the indices of β increased for the nitrogen transport and transformation processes. The result showed that the peak flow rate after rainfall or irrigation has more influence on the estimation of flow process, and the description of the nonlinear subsurface flow process was more influential on the simulated output of the NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations.

## 5. Conclusions

_{4}

^{+}-N and NO

_{3}

^{−}-N) transport and transformation from the soil to the outlet of the surface drainage canal. Water flow and transport processes were simulated in irrigation subdistricts with different parameters related to the irrigation events and the size of the irrigation subdistricts. A stepwise method was used to describe subsurface lateral flow in the rock. The flow and pollution fluxes at the outlet of the drainage canal represented the confluence and superposition processes of flow discharged from the rock, including subsurface lateral flow and groundwater.

_{4}

^{+}-N concentration, and NO

_{3}

^{−}-N concentration exhibited systematic deviations of less than 15%. Across the growing period of highland barley, the mean values of the Nash–Sutcliffe coefficient, rRMSE, the fraction bias, and the fractional gross error between the simulated and observed flow rates and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the outlet of the surface drainage canal were 0.712, 7.01%, 0.04, and 0.255, respectively. These indicate that the proposed method can effectively simulate the hydrological and ANPS pollutant migration processes in this plateau irrigation district. As a result of the 21.2% increase in the rainfall and irrigation amount during the highland barley growing period in 2015, the average NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations in the soil layer decreased by 10.8 and 14.3%, respectively, due to increased deep seepage. Deep seepage due to rainfall accounted for 0–52.4% of all rainfall, whereas deep seepage due to irrigation accounted for 36.6–45.3% of all irrigation. NH

_{4}

^{+}-N and NO

_{3}

^{−}-N discharge into the drainage channel represented 19.9–30.4% and 19.4–26.7% of the deep seepage, respectively. Parameters in the subsurface lateral flow simulation were shown to have the most important first-order and total-order effects on the simulated flow and NH

_{4}

^{+}-N and NO

_{3}

^{−}-N concentrations at the outlet of the surface drainage canal.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Irrigation and drainage system, sampling positions, and experimental site in the Danniang irrigation district.

**Figure 2.**Schematic diagram of the system for monitoring subsurface lateral flow and nitrogen transport processes in the rock.

**Figure 3.**Illustration of (

**a**) subsurface flow in the rock and (

**b**) the procedure of the stepwise method used to calculate the subsurface lateral flow process.

**Figure 4.**Concentrations of (

**a**) NH

_{4}

^{+}-N and (

**b**) NO

_{3}

^{−}-N measured in the vertical soil profile during the experimental periods in 2014 and concentrations of (

**c**) NH

_{4}

^{+}-N and (

**d**) NO

_{3}

^{−}-N measured at various depths during the experimental periods in 2015.

**Figure 5.**(a) Rainfall and irrigation events (i.e., R

_{1}, R

_{2}and R

_{3}), flow rates per unit width, and (b) NH

_{4}

^{+}-N and (c) NO

_{3}

^{−}-N concentrations of the subsurface lateral flow in the rock at Sections A and B.

**Figure 6.**Comparison of (

**a**) the simulated and measured flow rates, (

**b**) NH

_{4}

^{+}-N concentrations, and (

**c**) NO

_{3}

^{−}-N concentrations at the outlet of the drainage channel of the irrigation district.

**Figure 7.**Comparison of the first- and total-orders of Sobol’s sensitivity indices (S

_{i}and S

_{Ti}) of the parameters in the simulation of (

**a**) flow rates, (

**b**) NH

_{4}

^{+}-N concentration, and (

**c**) NO

_{3}

^{−}-N concentration.

Depth (cm) | Clay (%) | Sand (%) | Silt (%) | Bulk Density (g/cm^{3}) | |||
---|---|---|---|---|---|---|---|

Mean ± STD ^{a} | Max/Min ^{b} | Mean ± STD | Max/Min | Mean ± STD | Max/Min | Max/Min | |

0–10 | 12.4 ± 4.3 | 17.3/10.6 | 53.6 ± 2.3 | 55.4/47.0 | 24.7 ± 4.6 | 28.6/16.4 | 0.98/1.32 |

20–30 | 12.9 ± 9.6 | 20.4/10.1 | 55.0 ± 8.7 | 57.9/47.4 | 27.1 ± 0.9 | 30.0/22.0 | 1.20/1.42 |

30–40 | 10.4 ± 7.7 | 14.8/9.4 | 52.3 ± 4.1 | 61.3/48.2 | 27.3 ± 3.9 | 31.0/23.0 | 1.24/1.48 |

40–50 | 11.8 ± 6.3 | 19.4/7.3 | 52.4 ± 3.6 | 54.9/45.6 | 27.8 ± 5.6 | 33.8/21.5 | 1.22/1.38 |

50+ | 0 | 0 | 100.0 ± 0.0 | 100/100 | 0 | 0 | 1.36/1.40 |

^{a}Value of mean and standard deviation;

^{b}Maximum and minimum values.

**Table 2.**Comparison of NH

_{4}

^{+}-N and NO

_{3}

^{−}-N mass seepage flux per area (kg/s/km

^{2}) during the highland barley growing periods.

Chemical | Sowing and Tilling Stages | Jointing and Heading Stages | Flowering and Filling Stages | |||
---|---|---|---|---|---|---|

Mean | Max/Min ^{a} | Mean | Max/Min | Mean | Max/Min | |

2014 | ||||||

NH_{4}^{+}-N | 6.14 × 10^{−6} | 9.78 × 10^{−5}/3.30 × 10^{−6} | 4.24 × 10^{−6} | 1.01 × 10^{−4}/1.77 × 10^{−6} | 2.11 × 10^{−6} | 8.94 × 10^{−6}/1.57 × 10^{−6} |

NO_{3}^{−}-N | 3.25 × 10^{−6} | 5.14 × 10^{−5}/1.07 × 10^{−6} | 3.44 × 10^{−5} | 5.78 × 10^{−4}/1.21 × 10^{−5} | 8.60 × 10^{−6} | 1.84 × 10^{−5}/3.39 × 10^{−6} |

2015 | ||||||

NH_{4}^{+}-N | 7.44 × 10^{−6} | 1.26 × 10^{−4}/0.54 × 10^{−6} | 3.99 × 10^{−6} | 7.93 × 10^{−5}/1.15 × 10^{−6} | 2.02 × 10^{−6} | 4.64 × 10^{−6}/1.33 × 10^{−6} |

NO_{3}^{−}-N | 3.18 × 10^{−6} | 8.74 × 10^{−5}/2.21 × 10^{−6} | 4.04 × 10^{−5} | 6.48 × 10^{−4}/2.04 × 10^{−5} | 7.54 × 10^{−5} | 1.02 × 10^{−4}/5.48 × 10^{−5} |

^{a}Maximum and minimum values.

No. | Brief Description (Unit) | Calibrated | Minimum | Maximum |
---|---|---|---|---|

1 | Seepage from soil into rock (mm day^{−1}), LE | -^{a} | 1.4 | 12.6 |

2 | NH_{4}^{+}-N concentration in the soil water(mg L^{−1}) | - | 0.4 | 6.2 |

3 | NO_{3}^{−}-N concentration in the soil water(mg L^{−1}) | - | 1.8 | 8.4 |

4 | α, parameter in Equation (3) | 1.554 | 1.00 | 2.05 |

5 | β, parameter in Equation (3) | 0.0182 | 0.0020 | 0.110 |

6 | NH_{4}^{+}-N transformation rate in the lateral flow in the rock (day^{−1}) | 0.142 | 0.102 | 0.20 |

7 | NO_{3}^{−}-N transformation rate in the lateral flow in the rock (day^{−1}) | 0.171 | 0.144 | 0.224 |

8 | K_{sat}, parameter in Equation (6) (m s^{−1}) | 3.42 × 10^{−5} | 3.08 × 10^{−5} | 3.94 × 10^{−5} |

9 | µ, parameter in Equation (6) | 0.15 | 0.12 | 0.18 |

10 | L, parameter in Equation (6) (m) | 240 | 200 | 280 |

11 | NH_{4}^{+}-N transformation rate in the surface drainage (day^{−1}) | 0.11 | 0.09 | 0.14 |

12 | NO_{3}^{−}-N transformation rate in the surface drainage (day^{−1}) | 0.09 | 0.06 | 0.13 |

^{a}Measured data were used.

Flow rate and Chemical Concentrations | NSE | rRMSE (%) | F_{E} | F_{B} |
---|---|---|---|---|

Flow rate | 0.791 | 5.132 | 0.2014 | 0.031 |

NH_{4}^{+}-N concentration | 0.701 | 8.364 | 0.2466 | 0.048 |

NO_{3}^{−}-N concentration | 0.644 | 7.532 | 0.3172 | −0.051 |

^{a}NSE, rRMSE, F

_{E}, and F

_{B}denote the Nash–Sutcliffe efficiency, relative root mean square error, fraction bias, and fractional gross error, respectively.

**Table 5.**Mass balance of non-point source pollution types during the highland barley growing periods.

Growing Stages | Water (10^{4} m^{3} km^{−1}) | NH_{4}^{+}-N Mass (kg km^{−1} ) | NO_{3}^{−}-N Mass (kg km^{−1}) | ||||
---|---|---|---|---|---|---|---|

Seepage | Transformation | Discharge | Seepage | Transformation | Discharge | ||

Sowing and tilling stages | 2.16 | 2.550 | 5.71 | 7.74 | 43.8 | 4.91 | 9.77 |

Jointing and heading stages | 3.64 | 2.386 | 3.29 | 6.42 | 84.2 | 11.90 | 22.45 |

Flowering and filling stages | 3.87 | 0.492 | 0. 64 | 0.98 | 74.5 | 9.77 | 14.42 |

Total | 9.67 | 5.428 | 9.64 | 15.14 | 202.5 | 26.58 | 46.64 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, Y.; Zhou, Z.; Wang, K.; Xu, C. Simulation of Flow and Agricultural Non-Point Source Pollutant Transport in a Tibetan Plateau Irrigation District. *Water* **2019**, *11*, 132.
https://doi.org/10.3390/w11010132

**AMA Style**

Li Y, Zhou Z, Wang K, Xu C. Simulation of Flow and Agricultural Non-Point Source Pollutant Transport in a Tibetan Plateau Irrigation District. *Water*. 2019; 11(1):132.
https://doi.org/10.3390/w11010132

**Chicago/Turabian Style**

Li, Yuqing, Zuhao Zhou, Kang Wang, and Chongyu Xu. 2019. "Simulation of Flow and Agricultural Non-Point Source Pollutant Transport in a Tibetan Plateau Irrigation District" *Water* 11, no. 1: 132.
https://doi.org/10.3390/w11010132