Abstract
In the arid sandy region of northern Shaanxi, China, precise water–potassium (K) coupling is crucial for improving potato ( Solanum tuberosum L.) productivity and resource-use efficiency, but the optimal management thresholds and underlying physiological mechanisms under different hydrological years remain unclear. In this study, a two-year field experiment was conducted during 2022–2023 in the wind-blown sandy grassland area of northern Shaanxi, China. Three irrigation levels (W1: 60% ET c , W2: 80% ET c , W3: 100% ET c ) and seven K application rates (K0–K6: 0–420 kg K ha −1 ) were imposed, and key indicators including canopy structure (leaf area index and Chlorophyll content), photosynthetic gas-exchange parameters ( P n , T r ), plant K nutritional status, dry matter accumulation, and yield components were systematically measured. Bivariate quadratic regression models and a Partial Least Squares Path Model (PLS-PM) were then used to analyze the quantitative thresholds and driving pathways of water–K coupling. The results showed that water–K interactions significantly regulated canopy structure, photosynthetic traits, and yield formation. In the wet year (2022), moderate irrigation combined with a high K rate (W2K5) achieved the highest tuber yield (53.37 t ha −1 ) and water productivity ( WP c , 12.43 kg ha −1 mm −1 ), whereas in the dry year (2023), full irrigation combined with a moderate K rate (W3K4) performed best, with a yield of 45.88 t ha −1 and a WP c of 9.44 kg ha −1 mm −1 . The bivariate quadratic regression models quantified the threshold-shift phenomenon of optimal management: to simultaneously maximize yield and WP c (>95% of their theoretical potential), the recommended irrigation range increased from 132.5 to 183.0 mm in the wet year to 259.9–282.3 mm in the dry year, while the optimal K application range narrowed from 222.9 to 420.0 kg ha −1 to 240.0–342.9 kg ha −1 . The PLS-PM revealed that water and K inputs independently drove evapotranspiration ( ET , β = 0.91) and plant K concentration ( PKC , β = 0.95), respectively. These factors jointly enhanced canopy function (Leaf parameters), which in turn drove dry matter accumulation ( β = 1.00) and yield formation ( β = 0.97). Crucially, the positive effect of yield increase on WP c ( β = 1.19) was stronger than the negative effect associated with increased ET ( β = −0.85), confirming that a high-yield strategy can simultaneously achieve high efficiency. These findings provide a theoretical basis and quantitative operational window for adaptive water–K management in potato cultivation on sandy soils under climate variability. • Optimal water–K strategies shifted significantly between hydrological years. • Regression models quantified precise windows for dual-objective optimization. • Yield gain was the dominant driver of water productivity, offsetting high ET costs. • PLS-PM revealed water and K as independent hydraulic and nutritional drivers. • Full irrigation with moderate K (W3K4) is optimal for dry years in sandy regions.
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Claims 13
Claim · model-written summary
Water-K interactions significantly regulated canopy structure, photosynthetic traits and yield formation of potato.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- water–K interactionse0
- Outcome
- canopy structure, photosynthetic traits, and yield formatione0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“water–K interactions significantly regulated canopy structure, photosynthetic traits, and yield formation”
Claim · model-written summary
In the wet year (2022), moderate irrigation with a high K rate (W2K5) gave the highest potato tuber yield, 53.37 t/ha.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- moderate irrigation combined with a high K rate (W2K5)e0
- Outcome
- tuber yielde0
- Direction
- higheste0
- Value
- 53.37 t ha −1e0
- Setting
- wet year (2022)e0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“wet year (2022), moderate irrigation combined with a high K rate (W2K5) achieved the highest tuber yield (53.37 t ha −1 )”
Claim · model-written summary
In the wet year (2022), W2K5 also gave the highest water productivity, 12.43 kg/ha/mm.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- moderate irrigation combined with a high K rate (W2K5)e0
- Outcome
- water productivitye0
- Direction
- higheste0
- Value
- 12.43 kg ha −1 mm −1e0
- Setting
- wet year (2022)e0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“wet year (2022), moderate irrigation combined with a high K rate (W2K5) achieved the highest tuber yield (53.37 t ha −1 ) and water productivity ( WP c , 12.43 kg ha −1 mm −1 )”
Claim · model-written summary
In the dry year (2023), full irrigation with a moderate K rate (W3K4) performed best, with a yield of 45.88 t/ha.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- full irrigation combined with a moderate K rate (W3K4)e0
- Outcome
- yielde0
- Direction
- beste0
- Value
- 45.88 t ha −1e0
- Setting
- dry year (2023)e0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“dry year (2023), full irrigation combined with a moderate K rate (W3K4) performed best, with a yield of 45.88 t ha −1”
Claim · model-written summary
In the dry year (2023), W3K4 gave a water productivity of 9.44 kg/ha/mm.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- full irrigation combined with a moderate K rate (W3K4)e0
- Outcome
- WP ce0
- Direction
- beste0
- Value
- 9.44 kg ha −1 mm −1e0
- Setting
- dry year (2023)e0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“dry year (2023), full irrigation combined with a moderate K rate (W3K4) performed best, with a yield of 45.88 t ha −1 and a WP c of 9.44 kg ha −1 mm −1”
Claim · model-written summary
Regression models indicate the recommended irrigation range increased from 132.5-183.0 mm in the wet year to 259.9-282.3 mm in the dry year.
- Taxon
- potato
Solanum tuberosumt0 - Outcome
- recommended irrigation rangee0
- Direction
- increasede0
- Value
- 132.5 to 183.0 mm in the wet year to 259.9–282.3 mm in the dry yeare0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“the recommended irrigation range increased from 132.5 to 183.0 mm in the wet year to 259.9–282.3 mm in the dry year”
Claim · model-written summary
Regression models indicate the optimal K application range narrowed from 222.9-420.0 to 240.0-342.9 kg K/ha.
- Taxon
- potato
Solanum tuberosumt0 - Outcome
- optimal K application rangee0
- Direction
- narrowede0
- Value
- 222.9 to 420.0 kg ha −1 to 240.0–342.9 kg ha −1e0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“the optimal K application range narrowed from 222.9 to 420.0 kg ha −1 to 240.0–342.9 kg ha −1”
Claim · model-written summary
PLS-PM showed water input drove evapotranspiration (beta = 0.91).
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- watere0
- Outcome
- evapotranspiratione0
- Value
- β = 0.91e0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“water and K inputs independently drove evapotranspiration ( ET , β = 0.91)”
Claim · model-written summary
PLS-PM showed K input drove plant K concentration (beta = 0.95).
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- K inputse0
- Outcome
- plant K concentratione0
- Value
- β = 0.95e0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“water and K inputs independently drove evapotranspiration ( ET , β = 0.91) and plant K concentration ( PKC , β = 0.95)”
Claim · model-written summary
Canopy function drove dry matter accumulation (beta = 1.00).
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- canopy functione0
- Outcome
- dry matter accumulatione0
- Value
- β = 1.00e0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“canopy function (Leaf parameters), which in turn drove dry matter accumulation ( β = 1.00)”
Claim · model-written summary
Canopy function drove yield formation (beta = 0.97).
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- canopy functione0
- Outcome
- yield formatione0
- Value
- β = 0.97e0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“These factors jointly enhanced canopy function (Leaf parameters), which in turn drove dry matter accumulation ( β = 1.00) and yield formation ( β = 0.97)”
Claim · model-written summary
Yield increase had a positive effect on water productivity (beta = 1.19), stronger than the negative effect of increased ET.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- yield increasee0
- Outcome
- WP ce0
- Direction
- positivee0
- Value
- β = 1.19e0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“the positive effect of yield increase on WP c ( β = 1.19) was stronger than the negative effect associated with increased ET ( β = −0.85)”
Claim · model-written summary
Increased evapotranspiration had a negative effect on water productivity (beta = -0.85), weaker than the positive effect of yield increase.
- Taxon
- potato
Solanum tuberosumt0 - Treatment
- increased ETe0
- Outcome
- WP ce0
- Direction
- negativee0
- Value
- β = −0.85e0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
t0“potato”
e0“the positive effect of yield increase on WP c ( β = 1.19) was stronger than the negative effect associated with increased ET ( β = −0.85)”
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