Liaoning Province (38˚43'N-43˚26'N, 118˚53'E-125˚46'E) is located in the southern part of Northeast China. It has a total area of 14.86 × 10⁴ km². As the northernmost coastal province of China, Liaoning Province borders the Yellow Sea and the Bohai Sea to the south, and thus possesses a highly advantageous geographical location. The topography and landforms are mainly composed of three major regions: the mountainous and hilly area in the east, the Lower Liaohe Plain in the central part, and the low mountain and hilly area in the west. Liaoning Province is characterized by a temperate continental monsoon climate with distinct seasonal variation, featuring cold winters and hot summers. The mean annual temperature is approximately 7˚C - 11˚C, and the region receives relatively abundant precipitation. There are numerous rivers within the province, with more than 300 rivers of varying sizes in total, the major ones including the Liao River and the Hun River.

2.2.1. The InVEST Water Yield Model

This study employed the Annual Water Yield module of the InVEST model to simulate annual water yield in Liaoning Province by inputting data such as precipitation and evapotranspiration, thereby providing an in-depth understanding of the temporal dynamics and spatial distribution patterns of water resources in Liaoning Province. The formula [9][10] is as follows:

where Y ( x j ) represents the annual water yield of grid cell x; P x denotes the annual precipitation of grid cell x; and A E T ( x j ) denotes the annual actual evapotranspiration of grid cell x.

The calculation formula is based on the Budyko hydrothermal coupling equilibrium hypothesis proposed by Zhang et al. [11]:

where A E T ( x j ) P x represents the ratio of actual evapotranspiration to precipitation; R x j denotes the Budyko dryness index for grid cell x in land-use type j; and ω x represents the ratio of annual vegetation water demand to annual precipitation.

where Z is a constant; and AWC_x denotes the plant available water content of grid cell x(mm). The dimensionless parameter Z represents the seasonal precipitation pattern and local hydrogeological characteristics. Following previous studies in Liaoning Province [12], we set Z = 3. The chosen Z = 3 produced water yield estimates that matched well with the multi-year average runoff coefficients reported for major river basins in Liaoning Province, confirming its plausibility.

Plant available water content. Soil data were obtained from the Harmonized World Soil Database (HWSD), from which the required soil parameters were extracted. The calculation was performed using the “Zhou Wenzuo formula”, as follows [13]:

where PAWC represents plant available water content; SAND% denotes the percentage of sand content in the soil; SILT% denotes the percentage of silt content in the soil; CLAY% denotes the percentage of clay content in the soil; and OM% denotes the percentage of soil organic matter content [9].

2.2.2. The InVEST Carbon Storage Model

This chapter uses the Carbon Storage module of the InVEST model to simulate different land cover types, aiming to provide a scientific and quantitative basis for reducing carbon emissions and promoting ecological conservation. The carbon stocks of four carbon pools for each land use type were calculated separately, and then aggregated to obtain the total carbon storage of Liaoning Province. The formula is as follows [14][15]:

where C t o t a l , C a b o v e , C b e l o w , C s o i l , C d e a d represent total carbon storage, aboveground biomass carbon storage, belowground biomass carbon storage, soil organic carbon storage, and dead organic matter carbon storage, respectively.

The data required for the water yield and carbon storage modules mainly include annual precipitation, land use, mean annual potential evapotranspiration, maximum soil rooting depth, study area boundary, a biophysical coefficient table containing land use/land cover types and corresponding coefficients, the Zhang coefficient, and a carbon pool data table. The sources of the basic data are listed in Table 1. All data were projected using the Krasovsky_1940_Albers coordinate system and preprocessed in ArcGIS. All spatial datasets were resampled to a uniform grid resolution of 100 m × 100 m to ensure consistency. Land use data for 2000, 2010, and 2020 were derived from Landsat TM/OLI images with a spatial resolution of 30 m, which were then aggregated to 100 m using the majority rule. Precipitation and potential evapotranspiration data were interpolated to 100 m grids using the ANUSPLIN method based on meteorological station observations. Soil data (1 km resolution) were also resampled to 100 m using bilinear interpolation. The biophysical coefficients for each land use/land cover (LULC) category used in the model are presented in Table 2. The matching between LULC classes and biophysical parameters (root depth, Kc, LULC_veg) followed the InVEST user guide and local literature [12]. Six LULC types (cultivated land, forest, grassland, water, construction land, unused land) were classified from the original data using the same scheme for all three years to maintain temporal consistency. The carbon pool data are provided in Table 3.

Table 1. Acquisition of the parameters.

Table 2. Biophysical table.

Biophysical table used for the InVEST water yield mode. The required data were obtained from relevant reference [12], mainly including Lucode (land use/land cover type), vegetation (LULC_veg), root depth for each LULC class, and plant evapo-transpiration coefficient (Kc). The specific values are shown in Table 2.

The carbon pool parameters were primarily derived from the relevant [17], and the carbon pool data table was obtained as Table 3:

Table 3. Carbon density of each land use type.

3.1.1. Temporal Variation Characteristics of Water Yield Function

Annual water yield for Liaoning Province in 2000, 2010, and 2020 was simulated using the InVEST model’s Annual Water Yield module. The results indicate that the water yield in Liaoning Province exhibited a trend of initial increase followed by a subsequent decrease. The mean water yield in Liaoning Province in 2000, 2010, and 2020 was 489.60 mm, 908.65 mm, and 773.94 mm, respectively; the total water yield was 162.27 × 10⁸ m³, 646.87 × 10⁸ m³, 448.79 × 10⁸ m³, respectively; and the actual evapotranspiration was 377.31 mm, 465.51 mm, and 466.18 mm, respectively. From 2000 to 2010, the water yield increased by 85.59%, showing a significant upward trend, whereas from 2010 to 2020, the water yield decreased by 14.82%, indicating a slight decline. Over the 20-year period, although the water yield in Liaoning Province exhibited certain fluctuations, it showed an overall increasing trend. This pattern was mainly driven by changes in precipitation: annual precipitation annual precipitation first increased and then decreased. While afforestation programs may have influenced evapotranspiration, the dominant factor controlling water yield variability in this period appears to be precipitation.

3.1.2. Spatial Variation Characteristics of the Water Yield Function

The spatial distribution characteristics of water yield in Liaoning Province in 2000, 2010, and 2020 indicate that the spatial variation of water yield in Liaoning Province is significant, exhibiting a clear decreasing trend from the eastern mountainous areas toward the western hilly regions. A further analysis shows that high water yield values are mainly concentrated in the eastern mountainous areas and central plains of the study region, with a maximum annual mean value reaching 876.43 mm, primarily distributed in the southeastern part of Dandong City and the eastern coastal areas of Dalian City. In contrast, the lowest water yield values are concentrated in the western low mountainous and hilly regions of Liaoning Province, with a minimum annual mean value of 0 mm. The dominant land use type in the eastern mountainous and hilly regions is forest land, with exceptionally rich forest resources, which confer strong soil and water conservation capacity; therefore, water yield in this region is relatively high. The central region is characterized by relatively low terrain and predominantly plain landscapes, with cropland as the main land use type; The relatively high water yield in this area may be associated with regional precipitation recharge from the main streams of the Liao River and Hun River systems; The western low mountain and hilly region borders the desert areas of Inner Mongolia and mainly includes Chaoyang City, Huludao City, and Jinzhou City. This region belongs to the central-western hilly zone, characterized by low vegetation cover, frequent sunny days, and low precipitation. These conditions result in relatively high evapotranspiration, and consequently, a low water yield.

3.2.1. Temporal Variation Characteristics of Carbon Storage

From a temporal perspective, the carbon storage in Liaoning Province shows an overall increasing trend. The total carbon storage in Liaoning Province in 2000, 2010, and 2020 was 1.81 × 10⁹ t, 1.85 × 10⁹ t, 1.86 × 10⁹ t, respectively, which directly reflects the growth in total carbon storage in the province. From 2000 to 2010, carbon storage increased by 4.38 × 10⁷ t, with a growth rate of 2.42%, indicating that carbon storage in Liaoning Province increased during this period, but the rate of increase was relatively slow. From 2010 to 2020, carbon storage increased by 0.73 × 10⁷ t, and compared with the previous decade, the growth rate decreased to 0.40%, indicating a gradual slowdown in the rate of increase in carbon storage. This may be associated with land use changes, policy adjustments, and other factors. Overall, the total carbon storage in the study area shows the pattern: 2020 > 2010 > 2000, exhibiting a slow and stable upward trend over time. To validate these results, we compared the 2020 carbon storage estimate (1.86 × 10⁹ t) with a previous study for Liaoning Province using a different method [17], showing a difference of only 2.2%.

3.2.2. The InVEST Water Yield Model

From a spatial perspective, the carbon storage in Liaoning Province from 2000 to 2020 shows a gradual decreasing trend from both the eastern and western sides of the study area toward the central region. The highest values are distributed in the eastern mountainous areas of Liaoning Province, which is closely related to the extensive vegetation coverage in this region. The abundant vegetation not only effectively absorbs and stores large amounts of CO₂ but also provides strong protection for the soil, thereby enhancing soil conservation capacity. From the perspective of administrative divisions, relatively high carbon storage values are mainly distributed in Tieling City, Fushun City, Benxi City, and Dandong City, which are located in the eastern mountainous region. Although the carbon storage capacity of the western low mountainous and hilly region is lower than that of the eastern mountainous area, it still exhibits a relatively strong carbon sequestration capacity. In the central region of Liaoning Province, dense human settlements and accelerated urbanization have led to extensive vegetation loss, resulting in relatively low carbon storage in the ecosystem.