Abstract
Optimizing water and nitrogen management is essential for improving crop productivity and resource-use efficiency. However, the coordination mechanisms within the soil–root–shoot system under water–nitrogen coupling remain insufficiently understood. A two-year (2024–2025) field experiment under border irrigation was conducted in the Hetao Irrigation District of China, with four irrigation levels (I4: full irrigation; I3, I2, and I1: 85%, 70%, and 55% of I4, respectively) and four nitrogen rates (160, 200, 240, and 280 kg ha −1 ; N1-N4). Soil water–nitrogen distribution, root growth indicators, leaf area index (LAI), photosynthetic characteristics, and yield were systematically analyzed, and a water-nitrogen-regulated LAI model was developed. Irrigation and nitrogen application influenced the spatiotemporal distribution of soil water–nitrogen. Nitrate nitrogen ( NO 3 − -N) was mainly concentrated in the 0–40 cm layer and gradually migrated downward. The active accumulated temperature-based Logistic model effectively described LAI dynamics, while the production function integrating actual evapotranspiration (ET c act ) and nitrogen application rate (N) accurately captured the responses of yield, water productivity ( WP ), and nitrogen partial factor productivity ( NFP ). Crop performance was optimized under I3N3, showing higher root growth, photosynthetic characteristics, biomass, and root–shoot ratio. Yield was positively correlated with biomass, root growth, photosynthesis, and LAI, but negatively correlated with soil water storage and residual nitrogen. Multi-objective optimization identified optimal inputs of ET c act 488–538 mm and N 185–227 kg ha −1 . Overall, irrigation and nitrogen application enhances productivity by regulating soil water–nitrogen transport, root-zone resource availability, and soil–root–shoot coordination.
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Claims 12
Claim · model-written summary
Irrigation and nitrogen application altered the spatial and temporal distribution of soil water and nitrogen.
- Treatment
- Irrigation and nitrogen applicatione0
- Outcome
- spatiotemporal distribution of soil water–nitrogene0
Not reportedComparatorDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Irrigation and nitrogen application influenced the spatiotemporal distribution of soil water–nitrogen.”
t0“maize”
Claim · model-written summary
Nitrate nitrogen was concentrated mainly at 0–40 cm and migrated downward.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Nitrate nitrogen ( NO 3 − -N) was mainly concentrated in the 0–40 cm layer and gradually migrated downward.”
t0“maize”
Claim · model-written summary
The temperature based Logistic model described maize LAI dynamics effectively.
Not reportedComparatorValue
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“The active accumulated temperature-based Logistic model effectively described LAI dynamics”
t0“maize”
Claim · model-written summary
The production function accurately captured maize yield, water productivity and nitrogen partial factor productivity responses.
- Outcome
- responses of yield, water productivity ( WP ), and nitrogen partial factor productivity ( NFP )e0
- Qualifier
- accuratelye0
Not reportedComparatorValue
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“the production function integrating actual evapotranspiration (ET c act ) and nitrogen application rate (N) accurately captured the responses of yield, water productivity ( WP ), and nitrogen partial factor productivity ( NFP )”
t0“maize”
Claim · model-written summary
I3N3 gave higher maize root growth.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Crop performance was optimized under I3N3, showing higher root growth, photosynthetic characteristics, biomass, and root–shoot ratio.”
t0“maize”
Claim · model-written summary
I3N3 gave higher maize photosynthetic characteristics.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Crop performance was optimized under I3N3, showing higher root growth, photosynthetic characteristics, biomass, and root–shoot ratio.”
t0“maize”
Claim · model-written summary
I3N3 gave higher maize biomass and root–shoot ratio.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Crop performance was optimized under I3N3, showing higher root growth, photosynthetic characteristics, biomass, and root–shoot ratio.”
t0“maize”
Claim · model-written summary
Maize yield was positively correlated with biomass, root growth, photosynthesis and LAI.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Yield was positively correlated with biomass, root growth, photosynthesis, and LAI”
t0“maize”
Claim · model-written summary
Maize yield was negatively correlated with soil water storage and residual nitrogen.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Yield was positively correlated with biomass, root growth, photosynthesis, and LAI, but negatively correlated with soil water storage and residual nitrogen.”
t0“maize”
Claim · model-written summary
Multiobjective optimization found optimal evapotranspiration of 488–538 mm.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Multi-objective optimization identified optimal inputs of ET c act 488–538 mm and N 185–227 kg ha −1 .”
t0“maize”
Claim · model-written summary
Multiobjective optimization found optimal nitrogen input of 185–227 kg ha −1.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Multi-objective optimization identified optimal inputs of ET c act 488–538 mm and N 185–227 kg ha −1 .”
t0“maize”
Claim · model-written summary
The authors conclude that irrigation and nitrogen application enhance productivity through soil water and nitrogen transport, resource availability, and soil–root–shoot coordination.
- Treatment
- irrigation and nitrogen applicatione0
- Outcome
- productivitye0
- Qualifier
- regulating soil water–nitrogen transport, root-zone resource availability, and soil–root–shoot coordinatione0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“irrigation and nitrogen application enhances productivity by regulating soil water–nitrogen transport, root-zone resource availability, and soil–root–shoot coordination.”
t0“maize”