## Main

The Green Revolution brought about unprecedented increases in global food supply to meet rapidly rising demand. Yet the promotion of relatively few high-yielding crops and accompanying input-intensive practices has led to serious compromises for nutrition security and the environment4. The development of agriculture in China has followed these same patterns. The country has made marked gains in its agricultural productivity over the past several decades, increasing national crop production by +107% since 1990 alone1. Despite a population of more than 1.4 billion people, the increase in China’s food demand has largely been met by domestic increases in agricultural production, except for soybean1. Yet attaining these high levels of food production has meant mounting environmental challenges across the country. In recent decades, groundwater levels have dropped at alarming rates2, agricultural GHG emissions have increased1, the intensity of fertilizer application has increased substantially1 and pesticide pollution has become more widespread1.

In recognition of these clear tradeoffs, the Chinese government is considering a suite of interventions to improve the sustainability of agriculture without compromising the sector’s high levels of production3. These strategies include developing ‘high-standard farmland’ to improve agriculture productivity while reducing input use (for example, water, fertilizer), implementing ‘water-saving projects’ to improve water-use efficiency and extending technologies for soil testing and nutrient recommendations to reduce fertilizer use, among others. Although all of these solutions promise to reduce the environmental burden of agriculture, they tend to focus on singular outcomes and are based on the assumption that crops are already grown in the locations in which they are most agro-climatically suited and most resource-efficient. Yet recent research has made it increasingly clear that current cropping patterns are suboptimal across several outcomes and that crop switching (that is, changes in crop distribution and/or crop rotations) may offer promise for improving agricultural sustainability. Recent global studies5,6,7,8 have shown that crop redistribution can reduce irrigation (that is, blue) water demand (−12% to −21%) and blue-water scarcity and protect the natural environment and biodiversity while improving or maintaining food production. Several other analyses have recently been performed at the country level, which is necessary to account for policy-relevant factors that can influence the extent to which an agricultural solution is feasible. In India, crop redistribution has been shown to improve dietary nutrient supply, climate resilience and net farmer incomes and reduce natural-resource use and GHG emissions9,10,11. In the United States, studies found that crop switching can reduce blue-water demand12 and climate-related crop losses13. Other research has shown the promise of diversifying crop rotations14,15. In China, field-based experiments in the North China Plain have shown that crop rotations alternative to conventional maize–wheat systems can reduce groundwater depletion and increase economic output14. Long-term evidence from North America has also shown the superior climate resilience of more diversified rotations15. Yet whether and to what extent crop switching would yield similar benefits for agricultural sustainability for the entire country of China remains unquantified.

Crop switching is a promising strategy to complement other sustainable farm-management solutions. The Chinese government has also recognized redistributing crops as a way to enhance the sustainable development of the agriculture sector3,16. For example, in early 2000, a crop-switching research project led by the National Development and Reform Commission (NDRC) put forward regional agriculture development directions based on historical analysis16. More recently, China’s National Sustainable Agriculture Development Plan (2015–2030) also gave general directions by dividing China into three regions: with more emphasis on food production than sustainability (for example, in the Yangtze River region), with equal emphasis on food production and sustainability (for example, in the Northwest) and more emphasis on sustainability than food production (for example, in the Tibetan Plateau)3. To meet these policy priorities, it is therefore essential to quantitatively evaluate where and to what extent crop switching—in an economically feasible way—may contribute to China’s sustainable development targets without compromising food supply. Furthermore, because China alone accounts for large fractions of the global population (19%)1, primary crop production (19%)1, natural-resource use (for example, fertilizers (25%), pesticides (10%), irrigation (13%), cropland (9%))1,17, agrifood-system-related GHGs (12%)1 and farmers (16%)1, efforts undertaken in China to improve its sustainable development goals will have far-reaching implications towards addressing global food security and sustainability challenges.

Here we quantify and assess opportunities for crop switching across China, focusing on 13 crops that collectively account for 94% of China’s primary crop production and 90% of its harvested area18. We combine gridded (5 arcmin) crop-specific data (circa the year 2010) on rainfed and irrigated yields and harvested areas19 with each crop’s water-requirement estimates, GHGs intensity20, fertilizer application rate21, pesticide use21 and farmer net profit21. Using these data, we estimate several sustainability dimensions prioritized in China’s sustainable agriculture plans22, namely, production quantity, water demand, GHG emissions, fertilizer use, pesticide use and economic output of current crop production. We then construct a linear optimization model to simulate the contribution of crop switching to sustainable agricultural development and assess tradeoffs and co-benefits across several dimensions and different regions. Each optimization run assigns priority to one of the following objectives: minimize water demand; minimize GHGs; minimize fertilizer use; minimize pesticides; maximize farmer incomes; or maximize benefits across all dimensions simultaneously—based on three different levels of governmental cooperation (that is, siloed, cross-ministry coordination and central government coordination) (Table 1). Our optimizations reallocate harvested areas between crops and alter cropping rotations with the constraints that: (1) national supply of all crops cannot decrease—a constraint reflecting national self-sufficiency targets; (2) farmer incomes within each grid cell cannot decrease—ensuring that farmer profitability is not adversely affected; (3) only crops grown at present within a grid cell can be planted there; (4) the harvested area within each grid cell is held constant—preventing agricultural expansion; and (5) cropping calendars of rotating crops cannot overlap in time. We also test the uncertainties of relaxing these constraints. Finally, we quantify the outcomes of optimized crop switching and compare the magnitude of benefits to relevant sustainable development targets for China. Such evaluations of several outcomes are essential for identifying interventions capable of improving the multidimensional sustainability of agriculture.

## Sustainability outcomes of potential crop switching

Different sustainability outcomes are administrated by separate government departments in China (for example, the Ministry of Water Resources—irrigation; the Ministry of Ecology and Environment—GHG emissions; the Ministry of Agriculture and Rural Affairs—fertilizers, pesticides and farmer incomes). Consequently, the narrower focus of each department on specific outcomes may work at counter-purposes towards achieving other sustainability goals. With this siloing of ministries in mind, we first explored the extent to which a single dimension of agricultural sustainability could be improved through crop switching (hereinafter referred to as G1 simulations of no coordination; Table 1). We find that there is considerable potential for crop switching to enhance sustainable development. When assigning priority to a single sustainability objective, crop switching can reduce the demand for blue water by as much as −27.8%, green water by −12.6%, GHGs by −17.1%, nitrogen fertilizers by −15.9%, phosphorous fertilizers by −15.5%, potash fertilizers by −20.6% and pesticides by −15.6% relative to current levels—without expanding cropland, reducing the production of any crop or reducing farmer incomes (Fig. 1 and Table S14). However, because a ministry assigns priority to only the sustainability objectives under its mandate, it may not necessarily consider the outcomes of other sustainability objectives for which other ministries are responsible. Accordingly, when our model optimizes an individual dimension of sustainability, we allow other dimensions to potentially degrade. Indeed, we find that, under this scenario (G1), several tradeoffs emerge between different dimensions of agricultural sustainability and between different regions (Fig. 1). We also observe a clear tradeoff with environmental outcomes when attempting to maximize farmer incomes. Under this scenario, crop switching can increase farmer incomes by as much as 90.5%, though at the cost of other environmental outcomes (Figs. S5 and S6). This suggests that efforts to increase farmer profitability under current crop-price structures would probably produce clear environmental tradeoffs.

To address this shortcoming, we examined a set of optimization scenarios in which cross-ministry coordination was enhanced to avoid sustainability tradeoffs. To reflect this, we imposed the constraints that optimizing one sustainability dimension would not degrade outcomes for the other sustainability dimensions (hereinafter referred to as G2 simulations of cross-ministry coordination; Table 1). Under these conditions, we found that crop switching can still achieve sizeable benefits across all dimensions—changes by as much as −18.5% (blue water), −9.5% (green water), −7.9% (GHGs), −12.0% (N fertilizer), −11.4% (P fertilizer), −13.0% (K fertilizer), −10.8% (pesticides) and +20.2% (farmer incomes). Yet, although tradeoffs are avoided between sustainability dimensions and different regions under G2, the optimization of any one objective with cross-ministry coordination would still lead to minimal benefits for other outcomes (Fig. 1 and Table S14).

To this end, we performed a multiobjective optimization to examine to what extent co-benefits can emerge for all sustainability dimensions simultaneously under a scenario in which China’s central government leads the coordination (hereinafter referred to as G3 simulation of central coordination; Table 1). Under these conditions, we optimized for all sustainability dimensions such that the improvement margins in all dimensions are as high as possible while their between-dimension differences are as low as possible. In doing so, we take an agnostic position on the relative importance of each outcome. We also adapt our approach to place different weights on the outcomes to demonstrate different levels of government’s political will (see Extended Data Fig. 1). Under this set of results, we found that crop switching can still achieve considerable benefits: −6.5% (−4.5% to −18.5%) for blue water; −7.5% (−4.4% to −9.5%) for green water; −6.5% (−1.7% to −7.7%) for GHGs; −8.1% (−5.2% to −12.0%) for N fertilizer; −9.8% (−5.1% to −11.4%) for P fertilizer; −8.3% (−4.5% to −13.0%) for K fertilizer; −6.7% (−4.3% to −10.8%) for pesticides; +4.5% (+2.9% to +7.5%) for farmer incomes (Fig. 1 and Table S14).

Comparing across all three levels of coordination highlights cases in which certain sustainability outcomes are similar in magnitude, whereas others can differ substantially at the national level (Table S14). As an example of the former, minimizing P fertilizer use under G1 leads to a modest (6% relative to G3) enhancement in P fertilizer savings while other outcomes are comparable in magnitude (−4% to +5% relative to G3). Conversely, minimizing blue water under G1 leads to 23% greater blue-water savings relative to G3 but produces several losses for other outcomes (−10% to −5% relative to G3). Furthermore, the G1 scenario allows for degradation of certain sustainability criteria in some locations, which does not occur in G2 and G3. These contrasting examples point to an interesting tension between the amount of extra effort accompanying greater levels of coordination, the relative difference in benefits associated with greater coordination and the willingness to accept tradeoffs along some sustainability outcomes and among some regions. Nevertheless, our findings show that crop switching can be used as an effective strategy to address current conditions of resource depletion or unsustainable use (for example, blue-water scarcity) (Fig. 2) and the location of crop switching can be targeted on the basis of a variety of definitions and measures of sustainability (see Fig. S7 for other sustainability dimensions and Table S12 for boundaries of sustainable resource use).

Across the optimization scenarios examined here, we also find certain consistent regional changes in the distributions of specific crops. For instance, regardless of the optimization objective, we observe substantial recommended shifts, for example, wheat decrease in both the North China Plain and the Northwest Region and increase in the Yangtze River Plain; rice decrease in the Yangtze River Plain; maize increase in the Northwest Region; rapeseed decrease in the Yangtze River Plain and cotton decrease in the Northwest Region (see Figs. 3 and S9S11). These findings point to regions in which shifts in certain crops can lead to robust outcomes for several sustainability dimensions without compromising national food production or requiring more cropland. Taken together, all of these regional and national results—accompanied by modest changes in crop rotations (Fig. S8)—demonstrate real opportunities for crop switching to improve environmental sustainability and farmer incomes (Fig. S4). We have also shown the feasibility of the proposed crop switching by comparing it with recent rates of change in crop distributions across China (see Extended Data Figs. 36 and Figs. S12S14). Although this demonstrates that such changes may be feasible in the near future, unprecedented events such as the COVID-19 pandemic could slow the pace of domestic-policy change and implementation. On the other hand, the increasingly consolidated ability of the central government—combined with China’s emphasis on domestic food supply and demonstrated ability to alter cropping patterns in the face of recent past events (for example, SARS and the global financial crisis)—could also mean that change can occur more quickly than has historically occurred if there is political will to do so.

## Meeting China’s agricultural sustainable development targets

#### Current GHG emissions

Current GHG emissions in grid i (TGHGirr/ra,i) were calculated as:

$${{\rm{TGHG}}}_{{\rm{irr/ra}},i}={\sum }_{z}{{\rm{HA}}}_{{\rm{irr/ra}},i,z}\times {{\rm{GHG}}}_{i,z}$$
(12)

in which GHGi,z is the crop-specific GHG intensity (Mg CO2 eq ha−1) in grid i, taken from Carlson et al.20. Because the crop-specific GHG intensities from Carlson et al. are for the year 2000, we used the FAO’s crop emissions data1 to estimate the percent changes in China’s GHG emissions from 2000 to 2010 and update grid-level crop-specific GHG intensities for 2010.

### The crop-switching model

To evaluate different degrees of coordination in government management, we developed three groups of crop-optimization scenarios (Tables 1 and S5) and solved them using the software GAMS (version 22.8). (1) The first group, G1 (no coordination), simulates the potential behaviour of different independent government departments with a narrow focus on their own political responsibility. Specifically, the first group contains eight optimization scenarios that assign priority to a single sustainability objective in each scenario to explore the extent to which a single dimension of agricultural sustainability could be improved through crop switching. (2) The second group, G2 (cross-ministry coordination), aims to enhance cross-ministry coordination by considering other sustainability objectives. Specifically, the second group ensures that assigning priority to one sustainability dimension cannot degrade outcomes for the other sustainability dimensions. There are also eight scenarios in G2 for eight agricultural sustainability dimensions. (3) The third group, G3 (central coordination), examines whether co-benefits can emerge for all sustainability dimensions simultaneously when the central government of China leads the coordination. Specifically, the third group only includes one scenario that optimizes all sustainability dimensions such that the improvement margins in all sustainable dimensions are as high as possible while their between-dimension differences are as low as possible.

1. (1)

G1 (no coordination): siloed approach assigning priority to a single sustainability objective each time.

Min/max SDGDim (minimize national use of blue water or other six sustainable dimensions or maximize national farmer incomes) such that

$${\sum }_{\{{\rm{i}}{\rm{r}}{\rm{r}},{\rm{r}}{\rm{a}}\},i,j}{{\rm{C}}{\rm{A}}}_{{\rm{i}}{\rm{r}}{\rm{r}}/{\rm{r}}{\rm{a}},i}\cdot {x}_{{\rm{i}}{\rm{r}}{\rm{r}}/{\rm{r}}{\rm{a}},i,j}\cdot {R}_{j,z}\cdot {{\rm{Y}}{\rm{L}}{\rm{D}}}_{{\rm{i}}{\rm{r}}{\rm{r}}/{\rm{r}}{\rm{a}},i,z}\ge {\sum }_{\{{\rm{i}}{\rm{r}}{\rm{r}},{\rm{r}}{\rm{a}}\}}{{\rm{P}}{\rm{r}}{\rm{o}}{\rm{d}}{\rm{u}}{\rm{c}}{\rm{t}}{\rm{i}}{\rm{o}}{\rm{n}}}_{{\rm{C}}{\rm{u}}{\rm{r}},{\rm{i}}{\rm{r}}{\rm{r}}/{\rm{r}}{\rm{a}},z}$$
(13)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$
(14)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{UI}}}_{{\rm{Dim}},i,z}\ge {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{CURRENT}}}_{{\rm{Dim,irr/ra}},i}$$
(15)
$$\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{UI}}}_{{\rm{Dim}},i,z}\\ \,\le \,\left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{CURRENT}}}_{{\rm{Dim,irr/ra}},i}| ({{\rm{Ind}}}_{{\rm{Dim}},i}\ge {{\rm{BD}}}_{{\rm{Dim}},i})\\ {{\rm{UPBOUND}}}_{{\rm{Dim}},i}| ({{\rm{Ind}}}_{{\rm{Dim}},i} < {{\rm{BD}}}_{{\rm{Dim}},i})\end{array}\right.\end{array}$$
(16)
$${\sum }_{j}{x}_{{\rm{irr/ra}},i,j}\le 1$$
(17)
$${\sum }_{j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}={\sum }_{z}{{\rm{HA}}}_{{\rm{irr/ra}},i,z}$$
(18)
$${{\rm{SDG}}}_{{\rm{Dim}}}={\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{UI}}}_{{\rm{Dim}},i,z}$$
(19)

in which Dim represents the eight agricultural sustainability dimensions and SDGDim is the total national use of Dim; CAirr/ra,i is the cultivated area of irrigated or rainfed croplands in grid i that was calculated by the harvested area and the growth-stage information of crops in each grid; j is the rotation number (j = s1, s2, …, s153) (Tables S4 and S13); xirr/ra,i,j is the proportion of the irrigated or rainfed cultivated land applying crop rotation j in grid i; Rj,z represents the number that crop z is planted per year in rotation j, which are built using the crop-rotation model (Supplementary Information Section 1.2.2) according to the crop-specific growth-stage information in each region of China (Tables S2 and S3 and Fig. S3); UIDim,i,z is the use (or emissions) intensity of a specific sustainability dimension (Dim) in grid i of crop z; CURRENTDim,irr/ra,i represents the current use (or emissions) of a specific sustainability dimension (Dim) across all crops in grid i; UPBOUNDDim,i represents the upper boundary of the total use (or emissions) across all crops in grid i, which is greater than $${\sum }_{\{{\rm{irr,ra}}\}}{{\rm{CURRENT}}}_{{\rm{Dim,irr/ra}},i}$$ when IndDim,i ≤ BDDim,i. IndDim,i represents an indicator to evaluate the scarcity or stress of a sustainability dimension (Dim) in grid i and BDDim,i is a scientifically defined sustainability boundary. Taking blue water as an example, $${{\rm{U}}{\rm{P}}{\rm{B}}{\rm{O}}{\rm{U}}{\rm{N}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i}={{\rm{B}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i}/{{\rm{I}}{\rm{n}}{\rm{d}}}_{{\rm{B}}{\rm{W}},i}\cdot {{\rm{C}}{\rm{U}}{\rm{R}}{\rm{R}}{\rm{E}}{\rm{N}}{\rm{T}}}_{{\rm{B}}{\rm{W}},{\rm{i}}{\rm{r}}{\rm{r}},i}$$, in which IndBW,i is the blue-water-scarcity indicator, which is equal to blue-water use divided by irrigation water availability, taken from the work of Zhou et al.35 (with boundary equal to 0.2), which is a presumptive standard for environmental flow requirements following Richter et al.41. For nitrogen and phosphorus fertilizer, $${{\rm{UPBOUND}}}_{{\rm{N/P}},i}\,=$$ $${\sum }_{\{{\rm{irr,ra}}\}}{{\rm{CURRENT}}}_{{\rm{N/P,irr/ra}},i}-{{\rm{Ind}}}_{{\rm{N/P}},i}$$, in which IndN/P,i is the nutrient balance indicator representing the excess nitrogen and phosphorus nutrients in the soil (kg)—meant to prevent nutrient loading and eutrophication—taken from West et al.42 and the boundaries BDN/P,i are all 0. For green water and pesticides, we impose the constraint that they cannot degrade at the grid level. For GHGs and potash, considering that the distribution of GHG emissions across grids is inconsequential from a climate change perspective and that the application of potash fertilizer has little adverse impact on the local environment, we impose constraints at the national level on these two dimensions.

Equation (13) represents the constraint on crop production at the national level. Equation (14) is the constraint of farmer incomes at the grid level. Equations (15) and (16) represent the constraints of resource use and environmental footprints on the national and grid levels, respectively. For the grid﻿s experiencing unsustainable resource use at present (IndDim,i ≥ BDDim,i), we do not allow resource use to increase; for the grids in which resource use is not beyond the sustainability boundary (IndDim,i < BDDim,i), we allow resource use to increase but only up to the sustainability boundary. For the scenario that minimizes national total GHG emissions or potash fertilizer use, we omit the estimation of equation (16), as there are no grid-level constraints for these two dimensions. Equations (17) and (18) are constraints of cultivated land and harvested land, respectively. The harvested area is held constant at the grid level. Equation (19) is the overall optimization object.

2. (2)

G2 (cross-ministry coordination): assigns priority to one sustainability dimension while not degrading outcomes for the other sustainability dimensions.

Min/max SDGDim (minimize national use of blue water or other six sustainable dimensions or maximize national farmer incomes) such that

$${\sum }_{\{{\rm{irr,ra}}\},i,j}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{Production}}}_{{\rm{Cur,irr/ra}},z}$$
(20)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$
(21)
$${\sum }_{i,j,z}{{\rm{C}}{\rm{A}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}\cdot {x}_{{\rm{i}}{\rm{r}}{\rm{r}},i,j}\cdot {R}_{j,z}\cdot {{\rm{B}}{\rm{W}}}_{i,z}\le {\sum }_{i}{{\rm{T}}{\rm{B}}{\rm{W}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}$$
(22)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GW}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TGW}}}_{{\rm{irr/ra}},i}$$
(23)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GHG}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TGHG}}}_{{\rm{irr/ra}},i}$$
(24)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FN}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFN}}}_{{\rm{irr/ra}},i}$$
(25)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FP}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFP}}}_{{\rm{irr/ra}},i}$$
(26)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FK}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFK}}}_{{\rm{irr/ra}},i}$$
(27)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{PT}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TPT}}}_{{\rm{irr/ra}},i}$$
(28)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$
(29)
$${\sum }_{j,z}{{\rm{C}}{\rm{A}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}\cdot {x}_{{\rm{i}}{\rm{r}}{\rm{r}},i,j}\cdot {R}_{j,z}\cdot {{\rm{B}}{\rm{W}}}_{i,z}\le \{\begin{array}{c}{{\rm{T}}{\rm{B}}{\rm{W}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}|({{\rm{I}}{\rm{n}}{\rm{d}}}_{{\rm{B}}{\rm{W}},i}\ge {{\rm{B}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i})\\ {{\rm{U}}{\rm{P}}{\rm{B}}{\rm{O}}{\rm{U}}{\rm{N}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i}|({{\rm{I}}{\rm{n}}{\rm{d}}}_{{\rm{B}}{\rm{W}},i} < {{\rm{B}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i})\end{array}$$
(30)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GW}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TGW}}}_{{\rm{irr/ra}},i}$$
(31)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FN}}}_{i,z}\le \left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFN}}}_{{\rm{irr/ra}},i}| ({{\rm{Ind}}}_{{\rm{N}},i}\ge {{\rm{BD}}}_{{\rm{N}},i})\\ {{\rm{UPBOUND}}}_{{\rm{N}},i}| ({{\rm{Ind}}}_{{\rm{N}},i} < {{\rm{BD}}}_{{\rm{N}},i})\end{array}\right.$$
(32)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FP}}}_{i,z}\le \left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFP}}}_{{\rm{irr/ra}},i}| ({{\rm{Ind}}}_{{\rm{P}},i}\ge {{\rm{BD}}}_{{\rm{P}},i})\\ {{\rm{UPBOUND}}}_{{\rm{P}},i}| ({{\rm{Ind}}}_{{\rm{P}},i} < {{\rm{BD}}}_{{\rm{P}},i})\end{array}\right.$$
(33)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{PT}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TPT}}}_{{\rm{irr/ra}},i}$$
(34)
$${\sum }_{j}{x}_{{\rm{irr/ra}},i,j}\le 1$$
(35)
$${\sum }_{j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}={\sum }_{z}{{\rm{HA}}}_{{\rm{irr/ra}},i,z}$$
(36)
$${{\rm{SDG}}}_{{\rm{Dim}}}={\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{UI}}}_{{\rm{Dim}},i,z}$$
(37)

Compared with the G1 scenarios, we set constraints on all sustainable dimensions at the national (equations (21)–(28)) and grid (equations (29)–(34)) levels (except GHG emissions and potash fertilizer at the grid level).

3. (3)

G3 (central coordination): optimizes all sustainability dimensions such that the improvement margins in all dimensions are as high as possible while their between-dimension differences are as low as possible.

Max Aver(GDim)/Var(GDim) such that

$${\sum }_{\{{\rm{irr,ra}}\},i,j}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{Production}}}_{{\rm{Cur,irr/ra}},z}$$
(38)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$
(39)
$${\sum }_{i,j,z}{{\rm{C}}{\rm{A}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}\cdot {x}_{{\rm{i}}{\rm{r}}{\rm{r}},i,j}\cdot {R}_{j,z}\cdot {{\rm{B}}{\rm{W}}}_{i,z}\le {\sum }_{i}{{\rm{T}}{\rm{B}}{\rm{W}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}$$
(40)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GW}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TGW}}}_{{\rm{irr/ra}},i}$$
(41)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GHG}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TGHG}}}_{{\rm{irr/ra}},i}$$
(42)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FN}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFN}}}_{{\rm{irr/ra}},i}$$
(43)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FP}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFP}}}_{{\rm{irr/ra}},i}$$
(44)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FK}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFK}}}_{{\rm{irr/ra}},i}$$
(45)
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{PT}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TPT}}}_{{\rm{irr/ra}},i}$$
(46)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$
(47)
$${\sum }_{j,z}{{\rm{C}}{\rm{A}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}\cdot {x}_{{\rm{i}}{\rm{r}}{\rm{r}},i,j}\cdot {R}_{j,z}\cdot {{\rm{B}}{\rm{W}}}_{i,z}\le \{\begin{array}{c}{{\rm{T}}{\rm{B}}{\rm{W}}}_{{\rm{i}}{\rm{r}}{\rm{r}},i}|({{\rm{I}}{\rm{n}}{\rm{d}}}_{{\rm{B}}{\rm{W}},i}\ge {{\rm{B}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i})\\ {{\rm{U}}{\rm{P}}{\rm{B}}{\rm{O}}{\rm{U}}{\rm{N}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i}|({{\rm{I}}{\rm{n}}{\rm{d}}}_{{\rm{B}}{\rm{W}},i} < {{\rm{B}}{\rm{D}}}_{{\rm{B}}{\rm{W}},i})\end{array}$$
(48)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GW}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TGW}}}_{{\rm{irr/ra}},i}$$
(49)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FN}}}_{i,z}\le \left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFN}}}_{{\rm{irr/ra}},i}| ({{\rm{Ind}}}_{{\rm{N}},i}\ge {{\rm{BD}}}_{{\rm{N}},i})\\ {{\rm{UPBOUND}}}_{{\rm{N}},i}| ({{\rm{Ind}}}_{{\rm{N}},i} < {{\rm{BD}}}_{{\rm{N}},i})\end{array}\right.$$
(50)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FP}}}_{i,z}\le \left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFP}}}_{{\rm{irr/ra}},i}| ({{\rm{Ind}}}_{{\rm{P}},i}\ge {{\rm{BD}}}_{{\rm{P}},i})\\ {{\rm{UPBOUND}}}_{{\rm{P}},i}| ({{\rm{Ind}}}_{{\rm{P}},i} < {{\rm{BD}}}_{{\rm{P}},i})\end{array}\right.$$
(51)
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{PT}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TPT}}}_{{\rm{irr/ra}},i}$$
(52)
$${\sum }_{j}{x}_{{\rm{irr/ra}},i,j}\le 1$$
(53)
$${\sum }_{j,z}{\rm{CA}}{z}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}={\sum }_{z}{{\rm{HA}}}_{{\rm{irr/ra}},i,z}$$
(54)
$${G}_{{\rm{Dim}}}=\left(1-\frac{{\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{UI}}}_{{\rm{Dim}},i,z}}{{\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{CURRENT}}}_{{\rm{Dim,irr/ra}},i}}\right)\times 100 \%$$
(55)

in which Aver(GDim) and Var(GDim) are the average and variance of the improvement of all sustainable dimensions, respectively. Here we perform a limited analysis with weights of 1 or 0 for the seven sustainability indicators to demonstrate the flexibility of our approach (see Extended Data Fig. 1). In the first step, we assign a weight of 0 or 1 to each of the seven indicators so that there are 27 (128) crop-switching solutions, each of which is Pareto optimal. The weights 0 and 1 represent whether the planners consider the corresponding indicator the least or the most important, respectively. We can also simulate the options with more weights, but the solution will not have an ending. In the second step, the planners and decision-makers can choose any solution according to their prioritization of different indicators. In the G3 scenario (blue line in Extended Data Fig. 1), we choose the solution in which improvement margins in all sustainable dimensions are as high as possible while their between-dimension differences are as low as possible. This also provides a way to compare the G3 scenario with the G1 and G2 scenarios.

According to the above explanation, the G3 scenario represents a Pareto-optimal solution when setting a weight of 0 or 1 for each indicator (Extended Data Fig. 1). Of course, if we set other weights between 0 and 1 for each indicator (which can be infinite), other Pareto-optimal solutions may emerge that are closer to the Pareto frontier. As such, our approach provides flexibility by allowing planners and decision-makers to place greater weight on the sustainability outcomes that they deem most important.

### Uncertainties and limitations

We performed uncertainty analyses by relaxing constraints on all sustainability dimensions and farmer incomes at the grid level (Table S6 and Fig. S16), relaxing the constraint of crop production (Tables S6 and S7) and testing the sensitivity of our outcomes to the input data (Table S6 and Fig. S17). The analysis shows that, if these constraints are lifted, there will be increased improvements in environmental sustainability and farmer incomes at the national level (Extended Data Fig. 2). However, there will be some regional tradeoffs. For example, farmer incomes would decrease in some areas (thereby potentially requiring subsidies; Table S8) or blue-water use would increase in some water-scarce areas (Fig. S16). As well as quantifying uncertainties, we note that our findings should be interpreted with several considerations in mind. First, our analysis was limited by the spatial resolution of the available underlying datasets. Specifically, we are not able to capture field-level heterogeneity in suitability for different crops (for example, flood plains versus highlands) and economies of scale that may arise (or degrade) from increases (or decreases) in monoculture cropping, which should be taken into account for the implementation of crop switching. Second, crop production is an interconnected ecological process, in which changing one input would change other inputs, for example, irrigation change would affect fertilizer use and GHG emissions. Although such interconnections are beyond the scope of this study, their potential influence (either positive or negative) on sustainability outcomes is important to take into account when seeking to responsibly implement crop-switching interventions. Moreover, our model has the limitations of not considering the switching costs and assumption of the constant harvested area under crop switching, which are discussed in detail in Supplementary Information Sections 2.6 (Table S8) and 2.7 (Figs. S18 and S19).

### Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.