Di Xu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Di Xu has a total of 63 co-authors. Here are the top co-authors by number of shared publications:
- Shaohui Zhang
State Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, China
13 shared publications - Yinong Li
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
11 shared publications - Meijian Bai
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
9 shared publications Meijian Bai
China Institute of Water Resource and Hydropower Research
4 shared publications- Baozhong Zhang
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
2 shared publications - Jiandong Wang
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
2 shared publications
Latest Publications
- Open Access
- 13 February 2023
- Published by MDPI AG in Remote Sensing
- Vol. 15 (4) , 1025
Early Yield Forecasting of Maize by Combining Remote Sensing Images and Field Data with Logistic Models
Early forecasting of crop yield from field to region is important for stabilizing markets and safeguarding food security. Producing a precise forecasting result with fewer inputs is an ongoing goal for the large-area yield evaluation. We present one approach of yield prediction for maize that was explored by incorporating remote-sensing-derived land surface temperature (LST) and field in-season data into a series of logistic models with only a few parameters. Continuous observation data of maize were utilized to calibrate and validate the corresponding logistic models for regional biomass estimating based on field temperatures (including crop canopy temperature (Tc)) and relative dry/fresh biomass accumulation. The LST maps from MOD11A1 products, which are considered to be matched as Tc in large irrigation districts, were assimilated into the validated models to estimate the biomass accumulation. It was found that the temporal-scale difference between the instantaneous LST and the daily average value of field-measured Tc was eliminated by data normalization method, indicating that the normalized LST could be input directly into the model as an approximation of the normalized Tc. Making one observed biomass in-season as the driving force, the maximum of dry/fresh biomass accumulation (DBA/FBA) at harvest could be estimated. Then, grain yield forecasting could be achieved according to the local harvest index of maize. Silage and grain yields were evaluated reasonably well compared with field observations based on the regional map of LST values obtained in 2017 in Changchun, Jilin Province, China. Here, satisfactory grain and silage yield forecasting was provided by assimilating once measured value of DBA/FBA at the middle growth period (early August) into the model in advance of harvest. Meanwhile, good results were obtained in the application of this approach using field data in 2016 to predict grain yield ahead of harvest in the Jiefangzha sub-irrigation district, Inner Mongolia, China. This study demonstrated that maize yield can be forecasted accurately prior to harvest by assimilating remote-sensing-derived LST and field data into the logistic models at a regional scale considering the spatio-temporal scale extension of ground information and crop dynamic growth in real time.
- 13 February 2023
- Published by MDPI AG in Remote Sensing
- Vol. 15 (4) , 1025
Open AccessEarly Yield Forecasting of Maize by Combining Remote Sensing Images and Field Data with Logistic Models
Early forecasting of crop yield from field to region is important for stabilizing markets and safeguarding food security. Producing a precise forecasting result with fewer inputs is an ongoing goal for the large-area yield evaluation. We present one approach of yield prediction for maize that was explored by incorporating remote-sensing-derived land surface temperature (LST) and field in-season data into a series of logistic models with only a few parameters. Continuous observation data of maize were utilized to calibrate and validate the corresponding logistic models for regional biomass estimating based on field temperatures (including crop canopy temperature (Tc)) and relative dry/fresh biomass accumulation. The LST maps from MOD11A1 products, which are considered to be matched as Tc in large irrigation districts, were assimilated into the validated models to estimate the biomass accumulation. It was found that the temporal-scale difference between the instantaneous LST and the daily average value of field-measured Tc was eliminated by data normalization method, indicating that the normalized LST could be input directly into the model as an approximation of the normalized Tc. Making one observed biomass in-season as the driving force, the maximum of dry/fresh biomass accumulation (DBA/FBA) at harvest could be estimated. Then, grain yield forecasting could be achieved according to the local harvest index of maize. Silage and grain yields were evaluated reasonably well compared with field observations based on the regional map of LST values obtained in 2017 in Changchun, Jilin Province, China. Here, satisfactory grain and silage yield forecasting was provided by assimilating once measured value of DBA/FBA at the middle growth period (early August) into the model in advance of harvest. Meanwhile, good results were obtained in the application of this approach using field data in 2016 to predict grain yield ahead of harvest in the Jiefangzha sub-irrigation district, Inner Mongolia, China. This study demonstrated that maize yield can be forecasted accurately prior to harvest by assimilating remote-sensing-derived LST and field data into the logistic models at a regional scale considering the spatio-temporal scale extension of ground information and crop dynamic growth in real time.
- 1 March 2021
- Published by Elsevier in Journal of Hazardous Materials
- Vol. 406, 124773
Occurrence, uptake, and health risk assessment of nonylphenol in soil-celery system simulating long-term reclaimed water irrigation
- 1 March 2021
- Published by Elsevier in Journal of Hazardous Materials
- Vol. 406, 124773
Occurrence, uptake, and health risk assessment of nonylphenol in soil-celery system simulating long-term reclaimed water irrigation
- 24 January 2020
- Published by Taylor & Francis in Archives of Agronomy and Soil Science
- Vol. 67 (2) , 191-204
Plastic film mulching with drip irrigation promotes maize (Zea mays L.) yield and water-use efficiency by improving photosynthetic characteristics
It is important to reveal the physiological mechanism of water saving and yield increasing of mulched drip irrigation. Three treatments were applied at a spring maize field in Northeast China: mulched drip irrigation (MD), non-mulched drip irrigation (ND), and rain-fed practice (CK). Grain yield (GY), photosynthetic capacity (Amax), the maximum carboxylation rate (Vcmax), leaf nitrogen content (Nmass), and leakiness of the bundle-sheath cells to CO2 (L) were determined. MD treatment increased 5-year (2014-2018) average GY by 18.6% compared with the CK. The GY showed significant linear positive correlations with Amax and Vcmax. The mean Amax and Vcmax for two years (2017-2018) of MD were significantly increased by 21.1% (P < 0.05) and 10.7% (P < 0.05), respectively, compared with CK. The increase of Amax and Vcmax was partially contributed by the descending L. And L of MD was decreased by 6.5-12.4% (P < 0.05) during the jointing and tasseling–milk stages. The relationships between Amax and Nmass, and between Vcmax and Nmass, were affected by mulching treatments, which indicates that the higher leaf N use efficiency of the MD and ND treatments. This study provides a theoretical basis for implementation of film-mulching and drip-irrigation technology in Northeast China.
- 24 January 2020
- Published by Taylor & Francis in Archives of Agronomy and Soil Science
- Vol. 67 (2) , 191-204
Plastic film mulching with drip irrigation promotes maize (Zea mays L.) yield and water-use efficiency by improving photosynthetic characteristics
It is important to reveal the physiological mechanism of water saving and yield increasing of mulched drip irrigation. Three treatments were applied at a spring maize field in Northeast China: mulched drip irrigation (MD), non-mulched drip irrigation (ND), and rain-fed practice (CK). Grain yield (GY), photosynthetic capacity (Amax), the maximum carboxylation rate (Vcmax), leaf nitrogen content (Nmass), and leakiness of the bundle-sheath cells to CO2 (L) were determined. MD treatment increased 5-year (2014-2018) average GY by 18.6% compared with the CK. The GY showed significant linear positive correlations with Amax and Vcmax. The mean Amax and Vcmax for two years (2017-2018) of MD were significantly increased by 21.1% (P < 0.05) and 10.7% (P < 0.05), respectively, compared with CK. The increase of Amax and Vcmax was partially contributed by the descending L. And L of MD was decreased by 6.5-12.4% (P < 0.05) during the jointing and tasseling–milk stages. The relationships between Amax and Nmass, and between Vcmax and Nmass, were affected by mulching treatments, which indicates that the higher leaf N use efficiency of the MD and ND treatments. This study provides a theoretical basis for implementation of film-mulching and drip-irrigation technology in Northeast China.
- Open Access
A Non-Uniform Broadcast Fertilization Method and Its Performance Analysis under Basin Irrigation
The broadcast fertilization method is widely used under basin irrigation in China. A reasonable broadcast fertilization method can effectively improve application performance of fertilization and reduce pollution from non-point agricultural sources. In this study, firstly, a non-uniform broadcast fertilization method and a non-uniform application coefficient were proposed. The value of non-uniform application coefficient is defined in this paper. It represents the ratio of the difference between the maximum and the average fertilization amount of fertilizer applied on the basin surface to the average fertilization amount of fertilizer applied on the basin surface. Secondly, field experiments were conducted to study the movement characteristics of fertilizer under non-uniform broadcast fertilization for basin irrigation. Field experiment results showed that under the condition of basin irrigation, the non-uniform broadcast fertilization method could weaken the non-uniform distribution of fertilizer due to erosion and transport capacity of solid fertilizer by irrigation water flow, which could significantly improve the uniformity of soil solute content. Thirdly, the solute transport model for broadcast fertilization was corroborated by the field experiment results. The variation rule of fertilization performance with non-uniform application coefficient under different basin length and inflow rate was achieved by simulation. The simulation results showed that fertilization uniformity and fertilization storage efficiency increased first and then decreased with the increase of non-uniform application coefficient. In order to be practically applicable, suitable irrigation programs of non-uniform application coefficient under different basin length and inflow rate conditions were proposed by numerical simulation.
Open AccessA Non-Uniform Broadcast Fertilization Method and Its Performance Analysis under Basin Irrigation
The broadcast fertilization method is widely used under basin irrigation in China. A reasonable broadcast fertilization method can effectively improve application performance of fertilization and reduce pollution from non-point agricultural sources. In this study, firstly, a non-uniform broadcast fertilization method and a non-uniform application coefficient were proposed. The value of non-uniform application coefficient is defined in this paper. It represents the ratio of the difference between the maximum and the average fertilization amount of fertilizer applied on the basin surface to the average fertilization amount of fertilizer applied on the basin surface. Secondly, field experiments were conducted to study the movement characteristics of fertilizer under non-uniform broadcast fertilization for basin irrigation. Field experiment results showed that under the condition of basin irrigation, the non-uniform broadcast fertilization method could weaken the non-uniform distribution of fertilizer due to erosion and transport capacity of solid fertilizer by irrigation water flow, which could significantly improve the uniformity of soil solute content. Thirdly, the solute transport model for broadcast fertilization was corroborated by the field experiment results. The variation rule of fertilization performance with non-uniform application coefficient under different basin length and inflow rate was achieved by simulation. The simulation results showed that fertilization uniformity and fertilization storage efficiency increased first and then decreased with the increase of non-uniform application coefficient. In order to be practically applicable, suitable irrigation programs of non-uniform application coefficient under different basin length and inflow rate conditions were proposed by numerical simulation.
- Open Access
Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition
This paper investigates the physical processes involved in the water filling and air expelling process of a pipe with multiple air valves under water slow filling condition, and develops a fully coupledwater–air two-phase stratified numerical model for simulating the process. In this model, the Saint-Venant equations and the Vertical Average Navier–Stokes equations (VANS) are respectively applied to describe the water and air in pipe, and the air valve model is introduced into the VANS equations of air as the source term. The finite-volume method and implicit dual time-stepping method (IDTS) with two-order accuracy are simultaneously used to solve this numerical model to realize the full coupling between water and air movement. Then, the model is validated by using the experimental data of the pressure evolution in pipe and the air velocity evolution of air valves, which respectively characterize the water filling and air expelling process. The results show that the model performs well in capturing the physical processes, and a reasonable agreement is obtained between numerical and experimental results. This agreement demonstrates that the proposed model in this paper offers a practical method for simulating water filling and air expelling process in a pipe with multiple air valves under water slow filling condition.
Open AccessExperimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition
This paper investigates the physical processes involved in the water filling and air expelling process of a pipe with multiple air valves under water slow filling condition, and develops a fully coupledwater–air two-phase stratified numerical model for simulating the process. In this model, the Saint-Venant equations and the Vertical Average Navier–Stokes equations (VANS) are respectively applied to describe the water and air in pipe, and the air valve model is introduced into the VANS equations of air as the source term. The finite-volume method and implicit dual time-stepping method (IDTS) with two-order accuracy are simultaneously used to solve this numerical model to realize the full coupling between water and air movement. Then, the model is validated by using the experimental data of the pressure evolution in pipe and the air velocity evolution of air valves, which respectively characterize the water filling and air expelling process. The results show that the model performs well in capturing the physical processes, and a reasonable agreement is obtained between numerical and experimental results. This agreement demonstrates that the proposed model in this paper offers a practical method for simulating water filling and air expelling process in a pipe with multiple air valves under water slow filling condition.
- Open Access
Study on Characteristics of Nitrogen and Phosphorus Loss under an Improved Subsurface Drainage
Agricultural drainage plays an effective role in preventing waterlogging and salinity disasters and also is the main transport pathway for agricultural non-point source pollutants into rivers and lakes. Hence, the water quality of agricultural drainage should be a point of focus. In this paper, nitrogen and phosphorus loss under improved subsurface drainage with different filter materials (gravel, layered sand-gravel, mixed sand-gravel, straw) were studied by a three-year field experiment (2016–2018) compared with the conventional subsurface drainage. The pH values, total nitrogen, ammonia nitrogen, nitrate nitrogen, total phosphorus and soluble reactive phosphate were considered. The results showed that the nitrogen and phosphorus concentrations of drain outflow under improved subsurface drainage with gravel filter were larger than that with layered sand-gravel filter and mixed sand-gravel filter. The improved subsurface drainages with layered sand-gravel filter and mixed sand-gravel filter had an effect on reducing the ammonia nitrogen, total phosphorus and soluble reactive phosphate concentrations of the outflow. Meanwhile, the characteristics of nitrogen and phosphorus loss under the improved subsurface drainage with straw filter were different from that with layered sand-gravel filter and mixed sand-gravel filter. For the improved subsurface drainage with layered sand-gravel filter outflow, the ammonia nitrogen, total phosphorus, and soluble reactive phosphate concentrations were about 13%–78%, 38%–63%, 40%–68% less, and total nitrogen, nitrate nitrogen concentrations were 24%–80%,18%–96% more than that under conventional subsurface drainage. Meanwhile, for the improved subsurface drainage with straw filter outflow, compared with conventional subsurface drainage outflow, the percentage changes of the total nitrogen, nitrate nitrogen, ammonia nitrogen, total phosphorus and the soluble reactive phosphate concentrations were about −76%–62%, −77%–78%, −152%–−274%, −103%–−400% and −221%–−291%, respectively. Additionally, in the outflow of all subsurface drainage patterns, there were much higher total nitrogen and nitrate nitrogen concentrations which should be focused on and the agricultural water management should be adopted.
Open AccessStudy on Characteristics of Nitrogen and Phosphorus Loss under an Improved Subsurface Drainage
Agricultural drainage plays an effective role in preventing waterlogging and salinity disasters and also is the main transport pathway for agricultural non-point source pollutants into rivers and lakes. Hence, the water quality of agricultural drainage should be a point of focus. In this paper, nitrogen and phosphorus loss under improved subsurface drainage with different filter materials (gravel, layered sand-gravel, mixed sand-gravel, straw) were studied by a three-year field experiment (2016–2018) compared with the conventional subsurface drainage. The pH values, total nitrogen, ammonia nitrogen, nitrate nitrogen, total phosphorus and soluble reactive phosphate were considered. The results showed that the nitrogen and phosphorus concentrations of drain outflow under improved subsurface drainage with gravel filter were larger than that with layered sand-gravel filter and mixed sand-gravel filter. The improved subsurface drainages with layered sand-gravel filter and mixed sand-gravel filter had an effect on reducing the ammonia nitrogen, total phosphorus and soluble reactive phosphate concentrations of the outflow. Meanwhile, the characteristics of nitrogen and phosphorus loss under the improved subsurface drainage with straw filter were different from that with layered sand-gravel filter and mixed sand-gravel filter. For the improved subsurface drainage with layered sand-gravel filter outflow, the ammonia nitrogen, total phosphorus, and soluble reactive phosphate concentrations were about 13%–78%, 38%–63%, 40%–68% less, and total nitrogen, nitrate nitrogen concentrations were 24%–80%,18%–96% more than that under conventional subsurface drainage. Meanwhile, for the improved subsurface drainage with straw filter outflow, compared with conventional subsurface drainage outflow, the percentage changes of the total nitrogen, nitrate nitrogen, ammonia nitrogen, total phosphorus and the soluble reactive phosphate concentrations were about −76%–62%, −77%–78%, −152%–−274%, −103%–−400% and −221%–−291%, respectively. Additionally, in the outflow of all subsurface drainage patterns, there were much higher total nitrogen and nitrate nitrogen concentrations which should be focused on and the agricultural water management should be adopted.
- Open Access
Modeling the Effects of Spatial Variability of Irrigation Parameters on Border Irrigation Performance at a Field Scale
The interaction between surface and subsurface water flows plays an important role in surface irrigation systems. This interaction can effectively be simulated by the physical-based models, which have been developed on the basis of the numerical solutions to the Saint-Venant and Richards’ equations. Meanwhile, the spatial variability of field physical properties (such as soil properties, surface micro-topography, and unit discharge) affects the interaction between surface and subsurface water flows and decreases the accuracy of simulating surface irrigation events at large scales. In this study, a new numerical methodology is developed based on the physical-based model of surface irrigation and the Monte Carlo simulation method to improve the modeling accuracy of surface irrigation performance at a field scale. In the proposed numerical methodology, soil properties, unit discharge, surface micro-topography, roughness, border length, and the cutoff time for the unit discharge are used as the stochastic parameters of the physical-based model, while field slope is assumed as the constant value because of the same field tillage and management conditions at a field scale. Monte Carlo simulation is used to obtain the stochastic parameter sample combinations of the physical-based model to represent the spatial variability of field physical properties. The updated stochastic simulation model of surface micro-topography, which is developed to model the spatial distribution of surface elevation differences (SED), is used to obtain the surface micro-topography samples at a field scale. Compared with the distributed-parameter modelling methodology and the field experimental data, the proposed numerical methodology presents the better simulation performance.
Open AccessModeling the Effects of Spatial Variability of Irrigation Parameters on Border Irrigation Performance at a Field Scale
The interaction between surface and subsurface water flows plays an important role in surface irrigation systems. This interaction can effectively be simulated by the physical-based models, which have been developed on the basis of the numerical solutions to the Saint-Venant and Richards’ equations. Meanwhile, the spatial variability of field physical properties (such as soil properties, surface micro-topography, and unit discharge) affects the interaction between surface and subsurface water flows and decreases the accuracy of simulating surface irrigation events at large scales. In this study, a new numerical methodology is developed based on the physical-based model of surface irrigation and the Monte Carlo simulation method to improve the modeling accuracy of surface irrigation performance at a field scale. In the proposed numerical methodology, soil properties, unit discharge, surface micro-topography, roughness, border length, and the cutoff time for the unit discharge are used as the stochastic parameters of the physical-based model, while field slope is assumed as the constant value because of the same field tillage and management conditions at a field scale. Monte Carlo simulation is used to obtain the stochastic parameter sample combinations of the physical-based model to represent the spatial variability of field physical properties. The updated stochastic simulation model of surface micro-topography, which is developed to model the spatial distribution of surface elevation differences (SED), is used to obtain the surface micro-topography samples at a field scale. Compared with the distributed-parameter modelling methodology and the field experimental data, the proposed numerical methodology presents the better simulation performance.
- Open Access
Impact of Long-Term Reclaimed Water Irrigation on Trace Elements Contents in Agricultural Soils in Beijing, China
The rapid increase of reclaimed water irrigation on agricultural soils requires investigation of its impact on soil health. In this study, a simulation experiment for various lengths of long-term reclaimed water irrigation time (98, 196 and 236 years, respectively) was conducted in the southeast suburb of Beijing, China. Unirrigated soil served as the control. The environmental behavior of seven trace elements (As, Cd, Cr, Cu, Hg, Pb and Zn) at different soil depths in 0–600 cm profiles was analyzed. Results showed that the 0–30 and 200–300 cm soil layers were more likely to accumulate trace elements under long-term reclaimed water irrigation, although the accumulation in the 0–600 cm profiles was not particularly obvious. Correlation analysis showed that the trace element concentrations and distribution were significantly related to clay fraction and organic matters (OM), whereas they were not related to redox potential (Eh). The potential ecological risk assessment showed that the long-term reclaimed water irrigation did not result in a significantly increased ecological risk. However, Cd and Hg were identified as the metals with the highest potential ecological risk in the study area and the trace element contents in the top 0–30 cm soil layer should be carefully monitored. Future studies are required to clarify the environmental risks of trace elements under long-term reclaimed water irrigation as they might slowly accumulate in soil with time.
Open AccessImpact of Long-Term Reclaimed Water Irrigation on Trace Elements Contents in Agricultural Soils in Beijing, China
The rapid increase of reclaimed water irrigation on agricultural soils requires investigation of its impact on soil health. In this study, a simulation experiment for various lengths of long-term reclaimed water irrigation time (98, 196 and 236 years, respectively) was conducted in the southeast suburb of Beijing, China. Unirrigated soil served as the control. The environmental behavior of seven trace elements (As, Cd, Cr, Cu, Hg, Pb and Zn) at different soil depths in 0–600 cm profiles was analyzed. Results showed that the 0–30 and 200–300 cm soil layers were more likely to accumulate trace elements under long-term reclaimed water irrigation, although the accumulation in the 0–600 cm profiles was not particularly obvious. Correlation analysis showed that the trace element concentrations and distribution were significantly related to clay fraction and organic matters (OM), whereas they were not related to redox potential (Eh). The potential ecological risk assessment showed that the long-term reclaimed water irrigation did not result in a significantly increased ecological risk. However, Cd and Hg were identified as the metals with the highest potential ecological risk in the study area and the trace element contents in the top 0–30 cm soil layer should be carefully monitored. Future studies are required to clarify the environmental risks of trace elements under long-term reclaimed water irrigation as they might slowly accumulate in soil with time.
- Open Access
The Application of a Modified Version of the SWAT Model at the Daily Temporal Scale and the Hydrological Response unit Spatial Scale: A Case Study Covering an Irrigation District in the Hei River Basin
As a well-built, distributed hydrological model, the Soil and Water Assessment Tool (SWAT) has rarely been evaluated at small spatial and short temporal scales. This study evaluated crop growth (specifically, the leaf area index and shoot dry matter) and daily evapotranspiration at the hydrological response unit (HRU) scale, and SWAT2009 was modified to accurately simulate crop growth processes and major hydrological processes. The parameters of the modified SWAT2009 model were calibrated using data on maize for seed from 5 HRUs and validated using data from 7 HRUs. The results show that daily evapotranspiration, shoot dry matter and leaf area index estimates from the modified SWAT2009 model were satisfactory at the HRU level, and the RMSE values associated with daily evapotranspiration, shoot dry matter, and leaf area index were reduced by 17.0%, 1.6%, and 71.2%, compared with SWAT2009. Thus, the influences of various optimal management practices on the hydrology of agricultural watersheds can be effectively assessed using the modified model.
Open AccessThe Application of a Modified Version of the SWAT Model at the Daily Temporal Scale and the Hydrological Response unit Spatial Scale: A Case Study Covering an Irrigation District in the Hei River Basin
As a well-built, distributed hydrological model, the Soil and Water Assessment Tool (SWAT) has rarely been evaluated at small spatial and short temporal scales. This study evaluated crop growth (specifically, the leaf area index and shoot dry matter) and daily evapotranspiration at the hydrological response unit (HRU) scale, and SWAT2009 was modified to accurately simulate crop growth processes and major hydrological processes. The parameters of the modified SWAT2009 model were calibrated using data on maize for seed from 5 HRUs and validated using data from 7 HRUs. The results show that daily evapotranspiration, shoot dry matter and leaf area index estimates from the modified SWAT2009 model were satisfactory at the HRU level, and the RMSE values associated with daily evapotranspiration, shoot dry matter, and leaf area index were reduced by 17.0%, 1.6%, and 71.2%, compared with SWAT2009. Thus, the influences of various optimal management practices on the hydrology of agricultural watersheds can be effectively assessed using the modified model.