This study focuses on 36 prefecture-level cities in Northeast China for the year 2017, covering Liaoning, Jilin, and Heilongjiang provinces. Input-output data were obtained from the 2017 City-LevelMulti-RegionalInput-OutputTableforChina published by the China Carbon Emission Accounts and Datasets (CEADs). Built upon 42 unmerged sectors, this dataset provides an MRIO framework encompassing 1512 “city-sector” units, including intermediate input matrices, final demand matrices, value-added matrices, and total output vectors, establishing the foundational data support for city-scale virtual water accounting.

To balance water data availability with analytical interpretability, and in accordance with the IndustrialClassificationforNationalEconomicActivities (GB/T 4754-2011), the 42 sectors were aggregated into 7 major categories: Agriculture, Mining, Manufacturing, Electricity and Water Supply, Construction, Transportation, and Services (Table 1). The MRIO table was consolidated accordingly.

Regarding water use data, agricultural water use was obtained directly from the water resources bulletins of each region. For each city, water use data were preferentially taken from the 2017 Water Resources Bulletin of the corresponding city. For cities without a separately published prefecture-level water resources bulletin, data were derived from the 2017 Water Resources Bulletins of Liaoning, Jilin, and Heilongjiang provinces and statistical yearbooks, and disaggregated in proportion to agricultural value added, gross industrial output, or water use. The water use variable in this study follows the “water use” definition in the Water Resources Bulletin, i.e., water withdrawal, including surface water, groundwater, other water sources, and self-supplied water, without deducting return flow. Therefore, the virtual water accounting in this study reflects virtual water flows under a water withdrawal perspective rather than a consumptive water use perspective; if comparison with consumptive water use is required, return flow should be further deducted.

For mining, manufacturing, electricity and water supply, construction, transportation, and services, water use was indirectly allocated using industrial water use and urban public water use, with reference to existing studies [21]. Specifically, industrial water use was allocated to mining, manufacturing, and electricity and water supply, while urban public water use was allocated to construction, transportation, and services. The allocation coefficients were determined by the proportion of intermediate inputs from the “production and supply of water” sector to the corresponding sectors in each city, and the specific formula is provided in reference [22]. If the intermediate input of a sector is zero or missing, allocation is based on the proportion of that sector’s total output or value added in the total output or value added of sectors in the same group; if allocation remains infeasible, the water use of that sector is set to zero. Agricultural water use was obtained directly from the water resources bulletins and was not involved in the above allocation. If the intermediate input of a sector is zero or missing, the allocation is based on the proportion of that sector’s total output or value added in the total output or value added of sectors in the same group; if allocation remains infeasible, the water use of that sector is set to zero.

Table 1. Sector aggregation mapping for 36 cities in Northeast China (7 merged sectors).

Multi-Regional Input-Output Model

The multi-regional input-output (MRIO) model captures economic interdependencies across sectors in different regions, serving as a key tool for accounting inter-regional virtual water flows.

Assuming an input-output system containing m cities and n sectors, the total number of sectoral units in the system is N = m × n . The basic MRIO formulation is expressed as:

where x i K represents total output of sector i in region K ; x i j K S denotes intermediate flow from sector i in region K to sector j in region S ; Y i K S is final demand in region S for goods/services from sector i in region K ; and E i K is exports from sector i in region K outside the economic system.

The direct input coefficient a i j K S measures direct input required from sector i in region K per unit of total output in sector j in region S :

where x j S represents total input (output) of sector j in region S .

Substituting Equation (2) into Equation (1) yields:

In matrix form:

where X , A , Y , and E represent total output matrix, direct input coefficient matrix, final demand matrix, and export coefficient matrix, respectively.

Transforming Equation (4) into demand-driven form:

where L = ( I − A ) − 1 is the Leontief inverse matrix. The element l i j K S represents output generated in sector i of region K to satisfy one unit of final demand in sector j of region S .

Incorporating water consumption into the IO framework, direct water intensity q j K is defined as:

where q j K is direct water intensity of sector j in region K ; W j K is direct water consumption of sector j in region K ; and X j K is total output of sector j in region K .

Total water consumption coefficient d i K S represents total (direct + indirect) water consumption induced in region K to satisfy one unit of final demand in sector i of region S :

Virtual water outflow from sector i in region K to final demand in region S is calculated as:

where t i K s is virtual water flow from origin K to sector i in destination S ; d i K S is total water consumption coefficient; and Y i K S is final demand satisfied by region K for region S .

Similarly, virtual water flow from origin S to sector i in destination K (virtual water inflow to city K ) is:

Net virtual water flow for city K ( N V W K ) is:

where S ≠ K . N V W K < 0 denotes net virtual water outflow, while N V W K > 0 represents net virtual water inflow.

This study further distinguishes “inter-city virtual water flows within Northeast China” from “virtual water exports outside Northeast China”. The total scale of bilateral inter-city virtual water flows within Northeast China is defined as：

where the summation excludes S ≠ K , and both K and S refer to the 36 prefecture-level cities in Northeast China. This indicator only accounts for virtual water embodied in inter-city trade within Northeast China and excludes exports outside the system. Virtual water exports outside Northeast China are defined as：

where t i K , o u t , out denotes the virtual water embodied in final demand exports from sector i in city K to regions outside Northeast China. This part is not included in T o t a l V W i n t e r n a l

Total actual regional water use is

In this study, T o t a l V W i n t e r n a l / W t o t a l = 230 / 559.6 ≈ 41.1 % .

The total positive net inflow is defined as the sum of net inflows of all cities with N V W K K > 0 :

If only inter-city trade within Northeast China is considered, the sum of net flows across all cities is zero, i.e.,

The total positive net inflow equals the total negative net outflow in absolute value. If exports and imports outside Northeast China are included, the regional net output should be calculated separately.

Direct water consumption (DWC) coefficients and total water consumption (TWC) coefficients across the 7 aggregated sectors exhibit substantial polarization (Table 2). Agriculture has the highest direct water coefficient (0.051338 × 10⁸ m³/10⁸ yuan, i.e., 513.38 m³/10⁴ yuan), approximately 24.5 and 76.8 times higher than Mining (0.002095 × 10⁸ m³/10⁸ yuan) and Manufacturing (0.000669 × 10⁸ m³/10⁸ yuan), respectively. reflecting agriculture’s extreme direct dependence on water resources.

Table 2. Sectoral direct water consumption coefficients and total water consumption coefficients.

Note: Coefficients are intensity indicators in 10⁸ m³ per 10⁸ yuan, i.e., water use per unit of monetary output; monetary output is in 2017 current prices; 1 unit = 10⁴ m³ per 10⁴ yuan.

However, evaluated by total water consumption coefficients, ratios of TWC to DWC for Manufacturing (0.01996 × 10⁸ m³/10⁸ yuan) and Construction (0.006597 × 10⁸ m³/10⁸ yuan) reach 29.77 and 17.59, respectively. This highlights secondary industry’s implicit water consumption profile: “low direct consumption, high upstream inducement”. Through complex intermediate supply chain networks, manufacturing and construction indirectly consume vast amounts of water embedded in upstream agricultural products (e.g., raw materials for food processing) and utility inputs. Although Transportation exhibits a high ratio (51.91), its small base value primarily reflects marginal inducement driven by indirect demand for energy and agricultural goods. These results demonstrate that evaluating sectoral water consumption solely based on direct water use overlooks hidden transfer risks along middle-stream supply chains.

Total volume and spatial distribution of inter-city virtual water flows characterize internal coupling between economic links and resource consumption across Northeast China (Figure 1). In 2017, total virtual water flows among the 36 cities reached 230 × 10⁸ m³, accounting for 41.1% of total actual regional water use. This scale demonstrates that nearly 40% of water consumption undergoes transboundary implicit transfer via inter-city trade in goods and services, making virtual water allocation a crucial mechanism regulating regional water cycles. This total excludes virtual water exports outside Northeast China; such exports require separate accounting. The strategic role of Northeast China as a net supplier of primary industrial and agricultural resources nationwide remains notable.

At the urban scale, net virtual water flows exhibit a distinct “core-periphery” spatial polarization. Only 10 cities act as net virtual water importers, while 26 cities are net exporters. Net inflow regions are concentrated in top-tier central cities: Changchun, Harbin, and Dalian record net inflows of 10.14 × 10⁸ m³, 9.56 × 10⁸ m³, and 8.33 × 10⁸ m³, respectively. Combined net inflows of these three hubs total 27.99 × 10⁸ m³, accounting for 79.2% of the total positive net inflow (35.34 × 10⁸ m³) in the region. The remaining seven net-importing cities, such as Shenyang and Jilin, exhibit relatively modest net inflow volumes. If only intra-Northeast China trade is considered, the sum of net flows across all cities is zero, and the total positive net inflow equals the total negative net outflow in absolute value. This concentration pattern indicates that high-tier urban centers serve as primary destination sinks for virtual water transfers, driven by large population scales, strong consumer demand, and clusters of high-value-added industries.

Conversely, the 26 net-exporting cities are widely dispersed geographically. Jiamusi ranks first in net outflow volume, reaching 10.38 × 10⁸ m³; net outflows from Jixi, Qiqihaer, and Songyuan follow at 2.54 × 10⁸ m³, 2.29 × 10⁸ m³, and 1.86 × 10⁸ m³, respectively. These cities are predominantly agricultural resource-based or resource-exhausted regions. Their substantial net virtual water exports reflect their socio-economic roles as key suppliers of primary agricultural commodities and raw materials within regional division of labor. Spatially, net virtual water inflow hubs cluster as distinct patches along key transit corridors (e.g., Harbin-Changchun and Harbin-Dalian railways), whereas net outflow regions spread across the Sanjiang Plain, Songnen Plain, and Western Liaoning, painting a spatial landscape of “core consumption driving peripheral resource support”.

If only intra-Northeast China trade is considered, the sum of net flows across all cities is zero, and the total positive net inflow equals the total negative net outflow in absolute value.

Figure 1. Net virtual water flows across Northeast China. Note: The base map is derived from the Fundamental Geographic Information Database; no alterations have been made to national administrative boundaries.

Differences in virtual water inflow and outflow dynamics across cities are fundamentally shaped by sectoral trade structures. As illustrated in Figure 2 and Figure 3, trade in agricultural products serves as the primary driver of virtual water outflows due to agriculture’s significantly higher direct water intensity relative to other sectors. For example, Jiamusi’s massive net outflow (10.38 × 10⁸ m³) stems mainly from agricultural exports. As a key commercial grain hub in Heilongjiang Province, Jiamusi exports water-intensive agricultural products to consumption hubs like Harbin and Changchun. Conversely, although Harbin possesses well-developed manufacturing and service sectors, agricultural virtual water continues to comprise the largest share of its net virtual water inflows. This underscores how large resident populations and high consumption levels in provincial capitals generate strong indirect resource dependence on agricultural water.

Figure 2. Inter-sectoral net virtual water outflows in Northeast China.

Figure 3. Sectoral composition of total virtual water inflows in Northeast China. Note: Figure 3 shows total virtual water inflows (from all source cities), whereas the net inflows reported in Section 3.2 refer to total inflows minus total outflows. Therefore, values in Figure 3 are larger than the net inflow values reported in Section 3.2.

Implicit water pull effects generated by manufacturing and construction are more pronounced in central cities. In Dalian, a coastal industrial center, local manufacturing water consumption primarily serves municipal output; however, through upstream supply-chain linkages, Dalian indirectly absorbs substantial virtual water embodied in mining and raw materials from surrounding cities. This demonstrates how secondary processing industries pull water resources from foundational sectors. Furthermore, manufacturing products with strong cross-regional marketability lead to dispersed virtual water destinations, primarily transferring to regions outside Northeast China and developed coastal areas. Virtual water flows associated with construction correlate strongly with fixed-asset investment and infrastructure scale, resulting in significantly higher net construction-related virtual water inflows in central cities compared to small- and medium-sized cities.

To isolate core backbone pathways within complex trade networks while filtering out noise from low-volume connections, the top 120 virtual water flow paths were selected to generate a chord diagram network. These 120 primary pathways account for over 85% of total inter-city virtual water flows, accurately representing the network’s key topology.

Network analysis indicates (Figure 4) that inter-city virtual water flows in Northeast China exhibit strong intra-provincial agglomeration and are constrained by administrative boundaries. Intra-provincial flows in Heilongjiang exhibit the highest intensity, forming a unipolar network anchored by Harbin and radiating outward. Cities such as Jiamusi, Qiqihaer, Daqing, and Suihua funnel virtual water to Harbin through thick flow chords. After absorbing regional agricultural and resource-based virtual water, Harbin utilizes a portion to meet municipal consumption and exports the remainder outside the province. Jilin Province exhibits a similar unipolar clustering pattern centered on Changchun, with substantial industrial and agricultural virtual water flowing in from neighboring cities like Jilin City and Siping. Liaoning Province exhibits a dual-core driving structure led by Shenyang and Dalian: Shenyang exerts strong radiative pull over the Central-South Liaoning urban agglomeration, while Dalian absorbs diversified inter-city inputs via its coastal location. Nevertheless, intra-provincial transfers remain dominant across Liaoning.

In contrast, inter-provincial virtual water flows remain small in scale and weak in connectivity, appearing sparsely as agricultural virtual water transfers from Heilongjiang to Liaoning and intermediate manufacturing flows from Jilin to Liaoning. Total intra-provincial flows within Heilongjiang reach 36.13 × 10⁸ m³, vastly outstripping cross-provincial flows. This network topology reveals underlying mechanisms governing water constraints and industrial coordination in Northeast China: bound by existing administrative divisions and localized industrial chain architectures, individual provinces prioritize completing production-consumption cycles of water-intensive products internally. Consequently, spatial market-based allocation of water elements remains constrained by provincial administrative barriers.

Figure 4. Chord diagram of inter-city virtual water flows in Northeast China.