A method for calculating contribution decomposition of lake expansion

Abstract

The application discloses a lake expansion contribution decomposition calculation method, extracts lake area and reverses water quantity change through remote sensing image and digital elevation model, discriminates precipitation phase state by using a temperature threshold method, estimates ice and snow ablation amount by combining a degree-day factor method, and calculates total glacier runoff; a single-layer evaporation model is constructed, net radiation, sensible heat, latent heat and water body heat storage and other fluxes are calculated based on a lake surface energy balance equation, and daily lake surface evaporation is obtained; quantile mapping and Bayesian fusion are combined to correct lake surface precipitation; non-glacier runoff is calculated according to a lake water balance equation; the stable period and the expansion period are divided according to the lake area trend, the stable period hydrological mean value is taken as a benchmark to calculate the expansion period abnormal value, and finally, the expansion contribution of each hydrological factor is determined according to the proportion of the abnormal value in the total water quantity increment. Through the method, the contribution intensity of different driving factors is clear, scientific support is provided for simulating lake change and predicting evolution, and ecological protection and management strategies are more targeted.

Description

Technical Field

[0001] This invention relates to the field of hydrological analysis technology, and in particular to a method for calculating the contribution decomposition of lake expansion. Background Technology

[0002] Lakes serve as a link between multiple spheres, playing various functions such as regulating regional climate and maintaining ecosystem balance. They are core carriers of regional hydrological cycles and responses to climate change. Lakes profoundly influence regional ecological and hydrological processes by regulating near-surface air temperature, altering heat fluxes, and regional circulation. In recent years, driven by factors such as global warming, plateau lakes have shown a significant and continuous expansion trend. Taking the Qinghai-Tibet Plateau as an example, the lake area has expanded by more than 10,000 square kilometers in the past 30 years. This rapid expansion of lakes not only reduces surrounding grasslands and pastures, threatening the production and livelihoods of local herders, but may also submerge major engineering facilities, endangering regional ecological security and sustainable development.

[0003] Remote sensing technology provides strong support for lake monitoring. Multispectral satellites such as Landsat and MODIS, as well as altimeter satellites such as CryoSat-2, have enabled long-term observation of changes in lake area, water level, and water volume. Combined with methods such as digital elevation models, key data such as lake water volume growth can be obtained. However, due to the complex terrain and sparse hydrological and meteorological stations in plateau regions, existing remote sensing monitoring data mostly remain at the level of phenomenon recording, without in-depth analysis of regional hydrological characteristics. Quantitative research on the precipitation-evaporation-runoff-lake water storage and water balance processes is even more limited, making it impossible to clearly define the contribution of each hydrological component to changes in lake water volume. In addition, climate warming-induced glacier retreat, accelerated snowmelt, and permafrost degradation further exacerbate the complexity of regional hydrological processes. Currently, there is still a lack of unified understanding of the driving mechanisms of lake expansion, and the relative contributions of factors such as precipitation, glacier melting, evaporation, and permafrost degradation urgently need quantitative assessment.

[0004] Therefore, conducting research on the decomposition of lake expansion contributions and clarifying the contribution intensity of different driving factors can provide scientific support for simulating future lake changes and predicting evolution trends, and can also make ecological protection and management strategies more targeted. In the ecological dimension, it can guide the protection of plateau biological habitats, the maintenance of ecological functions, and the prevention and control of grassland and wetland degradation. In the dimension of people's livelihood, it can provide early warning of the risk of lakes flooding transportation routes and settlements, thereby ensuring the drinking water safety of billions of people downstream and the stability of local herders' production and life. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method for calculating the contribution decomposition of lake expansion, applicable to hydrological analysis of plateau inland lakes lacking monitoring data. This method can quantify and identify different driving factors of lake expansion and their contribution intensity, providing a scientific basis for simulating future lake changes and predicting evolution trends, and enabling more targeted subsequent response strategies, thereby improving lake management efficiency.

[0006] This invention is implemented as follows:

[0007] A method for decomposing and calculating the contribution of lake expansion includes the following steps:

[0008] Step 1: Extract lake area and invert lake water volume changes based on remote sensing imagery and digital elevation model:

[0009] Remote sensing image data covering the study area was acquired. Normalized water index was calculated for each valid lake boundary image. An adaptive threshold segmentation algorithm was used to determine the optimal threshold to separate water bodies from non-water bodies and extract the corresponding lake areas. Lake areas were extracted based on daily images, and the maximum lake area for each month was calculated to form a monthly lake area sequence. A high-resolution digital elevation model was acquired to construct the lake area-reservoir capacity relationship, and the corresponding water volume changes were calculated based on the lake area.

[0010] Step 2: Construct a single-layer evaporation model to obtain the daily evaporation rate of the lake surface:

[0011] Collect the required daily-scale meteorological data, including air temperature T. a Relative humidity (RH), wind speed (U), and air pressure (P) a Downward shortwave radiation K↓, downward longwave radiation L↓; and lake parameters, including lake surface albedo α, lake surface emissivity ε, and lake mean depth Z;

[0012] A single-layer evaporation model is constructed, assuming an initial lake surface temperature T. s Based on this temperature, the net radiation R is calculated sequentially. n The components of sensible heat flux H, latent heat flux λE, and water heat storage G are used, with the lake surface energy balance equation as the boundary condition. An iterative algorithm is employed to determine the lake surface temperature T. s Iterative optimization is performed until the energy balance equation meets the convergence requirement. Finally, the daily lake evaporation E is calculated from the converged latent heat flux λE. lake ;

[0013] Step 3: Calculate the glacier runoff sequence based on daily precipitation and average temperature data:

[0014] The glacier-covered area within the study region was divided into several computational units; using the daily precipitation P and average temperature T of each unit, the precipitation phase was determined to obtain the liquid precipitation P. liqAnd by performing snow and ice melt calculations, the diurnal glacier runoff sequence R was obtained. g ;

[0015] Step 4: Correct for lake surface precipitation and estimate non-glacial runoff:

[0016] The lake surface precipitation sequence P was obtained by correcting the lake surface precipitation using a method combining quantile mapping and Bayesian fusion. lake Based on the water balance equation of inland closed lakes, combined with the extracted lake area sequence, the area-storage capacity relationship was constructed, and the calculated glacial runoff, lake surface precipitation, and evaporation data were used to estimate the non-glacial runoff R. p ;

[0017] Step 5, Decomposition of Lake Expansion Contributions and Quantitative Attribution of Driving Factors:

[0018] The lake area change trend is divided into a stable period and an expansion period. Multi-year average values ​​of each hydrological component during the stable period are calculated and used as a reference benchmark for calculating anomalies during the expansion period, including lake surface precipitation. Lake surface evaporation glacial runoff Non-glacial runoff and the average lake surface area over many years corresponding to the stable period. The difference between the mean values ​​of each hydrological component during the expansion and stabilization periods was calculated, and the cumulative outlier value ΔI was obtained. i Combined with the total increase in lake water volume ΔV during the expansion period total The proportions and quantitative decomposition yield the relative contributions of each factor to lake expansion.

[0019] Furthermore, in step 1, the normalized water index is calculated using the following formula:

[0020]

[0021] Where: ρ Green For green light band reflectivity, ρ NIR This refers to the reflectivity in the near-infrared band.

[0022] Furthermore, in step 1, the construction of the lake area-storage capacity relationship involves first converting the digital elevation model (DEM) projection into an equal-area projection, then extracting the lake surface area indicated by the data, and taking the lake surface corresponding to the lowest point of the lake basin in the DEM as the benchmark, assuming its water storage capacity is zero.

[0023] Starting from this reference lake surface, calculate the area A of the lake surface at each elevation at fixed elevation intervals Δh. i (i=1,2,3,…), and the difference in water storage volume between adjacent levels is calculated using the lake surface area corresponding to different elevations, thus obtaining the change in lake water volume. The calculation formula is as follows:

[0024]

[0025] In the formula: , These correspond to the lake surface area A. i and A i-1 The lake's water storage capacity, and = 0;

[0026] Through multiple groups (A) i V i Establish a regression relationship between lake surface area and lake storage capacity:

[0027]

[0028] In the formula: c1, c2, c3, and c4 are the corresponding regression coefficients.

[0029] Furthermore, in step 2, the net radiation R n The calculation formula is as follows:

[0030]

[0031] In the formula, α is the lake surface albedo, and K↓ is the downward shortwave radiation from the lake surface (W / m²). 2 ), Let T be the lake surface emissivity, σ be the Stefan-Boltzmann constant, and T be the lake surface emissivity. s Lake surface temperature (K), L↓ represents downward atmospheric longwave radiation (W / m²). 2 )

[0032] The formula for calculating lake thermal storage (G) is as follows:

[0033]

[0034] In the formula, c w is the specific heat capacity of water (J / (kg·K)). Let Z be the density of water, and Z be the average depth of the lake (m). The rate of change of water temperature over time;

[0035] Lake surface sensible heat flux (H) and latent heat flux (H) The calculation formula is as follows:

[0036]

[0037]

[0038] In the formula, c is the specific heat capacity of air (J / (kg·K)); ρ is the air density (kg / m³). 3 ); T aλ is the air temperature (K); λ is the latent heat of vaporization; U is the wind speed (m / s); C H and C E These are the overall transport coefficients of sensible heat and latent heat, respectively; q s The water surface temperature is T s The water surface saturation specific humidity at that time, q a The air is more humid than normal.

[0039] The energy balance constraints on the lake surface are as follows:

[0040]

[0041] In the formula, R n Where H is the net radiation and H is the sensible heat flux. Where is latent heat flux and G is the heat storage of the lake water, both in W / m³. 2 ;

[0042] Lake surface evaporation is determined by latent heat flux ( The conversion is as follows:

[0043] .

[0044] Furthermore, in step 3, the glacier-covered area is divided into several computational units based on the spatial resolution of glacier distribution data and meteorological data.

[0045] Furthermore, in step 3, the glacier runoff sequence R g The calculation method involves using a temperature threshold method to determine the phase state of precipitation, and separating liquid precipitation P from the total precipitation P. liq The calculation formula is as follows:

[0046]

[0047] In the formula, T is the average temperature (°C) within the calculation unit; P liq P represents the liquid precipitation (mm) within the calculation unit; P represents the total precipitation (mm) within the calculation unit; T represents the total precipitation (mm) within the calculation unit. liq and T soild These are the critical temperatures (°C) for liquid and solid precipitation, respectively.

[0048] The formula for calculating snow and ice melt (M) is as follows:

[0049]

[0050] In the formula, DDF snow / ice The day-dwelling factor for snow and ice, mm / (d·℃); T m It is the baseline temperature (°C) for snow and ice melting.

[0051] Calculate glacier runoff (R)g The calculation formula is as follows:

[0052]

[0053] In the formula, S(i) is the area of ​​the calculation unit (km²). 2 f is the meltwater infiltration-freezing rate, dimensionless; P liq (i) represents the amount of liquid precipitation (mm) within the calculation unit; k is the unit conversion factor.

[0054] Furthermore, in step 4, the formula for calculating the quantile mapping is as follows:

[0055]

[0056] Among them, P qm F represents the precipitation value after quantile correction. obs (p) and F raw (p) represents the measured precipitation data P. obs Compared with P obtained through meteorological reanalysis or satellite precipitation data raw The empirical distribution function is constructed.

[0057] Furthermore, in step 4, the Bayesian fusion calculation formula is as follows:

[0058]

[0059] Among them, P k w represents the corrected precipitation value from the k-th data source. k The Bayesian weights, derived from the error distribution and reliability of each data source, satisfy ∑w k = 1.

[0060] Furthermore, in step 4, the non-glacial runoff R p The calculation formula is as follows:

[0061]

[0062] Among them, A lake ΔV represents the lake surface area during this period, ΔV represents the change in lake water volume during a certain period, and k is the unit conversion factor.

[0063] Furthermore, in step 5, the stability period analysis uses an annual time scale, with the maximum value of the lake area in each year as representative. The Pettitt test is used to identify abrupt change points in the lake area sequence to determine the starting year of the expansion phase. In the time period before the abrupt change point, consecutive years with an annual area variation of less than 5% and a corresponding water volume change close to zero are further screened as candidate intervals for the stability period. Finally, a time period with good continuity, minimal fluctuations, and a duration of no less than N years (N ≥ 5) is selected as the baseline period for the decomposition of lake expansion contribution.

[0064] The beneficial effects of this invention are: This invention provides a method for calculating the contribution decomposition of lake expansion, which is used for hydrological analysis of inland lakes in plateau regions lacking monitoring data. The data acquisition is efficient and comprehensive. Relying on remote sensing technology and a high-resolution digital elevation model (DEM), it can achieve synchronous monitoring of lakes throughout the plateau region. The data acquisition cycle can be shortened to the daily level, which greatly improves monitoring efficiency and coverage.

[0065] With higher analysis precision, combined with high-resolution DEM, it can accurately invert lake water volume changes. Through a dedicated model, it quantitatively decomposes the contribution ratio of various driving factors such as glacial runoff, precipitation, and evaporation, making the results more accurate and convincing.

[0066] The analysis dimensions are more systematic, fully covering the entire chain of lake water inflow (glacial runoff, precipitation, non-glacial runoff) and outflow (lake surface evaporation), while also considering the correlation between various hydrological elements, avoiding the limitations of single-factor analysis;

[0067] With broader application value, it can accumulate continuous monitoring data to support research on long-term trends, and predict potential risks of lake expansion based on quantitative attribution results. It can also provide a scientific basis for plateau ecological protection, disaster prevention and mitigation, and water conservancy planning, making subsequent response strategies more targeted, thereby improving the efficiency of lake management, guiding the protection of plateau biological habitats, maintenance of ecological functions, and prevention of grassland and wetland degradation; and providing early warning of the risk of lakes flooding transportation routes and settlements, as well as the stability of local herders' production and life.

[0068] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0069] Figure 1 This is a flowchart of a method for calculating the contribution decomposition of lake expansion according to the present invention. Detailed Implementation

[0070] A method for decomposing and calculating the contribution of lake expansion, such as... Figure 1 As shown, it includes the following steps:

[0071] Step 1: Extract lake area and invert lake water volume changes based on remote sensing imagery and high-resolution digital elevation models:

[0072] 1. Acquire remote sensing imagery data covering the study area, such as Landsat series (TM / ETM+ / OLI) and Sentinel-2, etc., and select images with clear lake boundaries, no cloud cover, and no snow cover. Perform geometric, atmospheric, and radiometric corrections to ensure image accuracy. Calculate the Normalized Difference Water Index (NDWI) for each valid image using the following formula:

[0073] (1-1)

[0074] Where: ρ Green For green light band reflectivity, ρ NIR The reflectance is measured in the near-infrared band. For each image, an adaptive threshold segmentation algorithm (such as Otsu's method) is used to automatically determine the optimal threshold, thereby separating water bodies from non-water bodies and extracting the corresponding lake areas. On a temporal scale, lake areas are extracted based on daily imagery, and finally, the maximum lake area for each month is calculated to form a monthly lake area sequence.

[0075] 2. Obtain a high-resolution digital elevation model, such as SRTM (Space Shuttle Radar Topography Mission) or ASTERGDEM (Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model), and construct the lake area-reservoir capacity relationship. Convert the SRTM DEM projection to an equal-area projection, then extract the lake surface area indicated by the SRTM data. Using the lake surface corresponding to the lowest point of the lake basin in the DEM as the baseline, set its water storage capacity. It is zero.

[0076] Starting from this reference lake surface, calculate the area A of the lake surface at each elevation at fixed elevation intervals Δh. i (i=1,2,3,…), and the difference in water storage volume between adjacent levels is calculated using the lake surface area corresponding to different elevations, thus obtaining the change in lake water volume. The calculation formula is as follows:

[0077] (1-2)

[0078] In the formula: , These correspond to the lake surface area A. i and A i-1 The lake's water storage capacity, and = 0.

[0079] Through multiple groups (A) i V i A regression relationship can be established between lake surface area and lake capacity. The regression formula is as follows:

[0080] (1-3)

[0081] In the formula: c1, c2, c3, and c4 are the corresponding regression coefficients.

[0082] 3. Calculate the corresponding water volume change based on the lake's area. The calculation formula is as follows:

[0083] (1-4)

[0084] Step 2: Construct a single-layer evaporation model to obtain the daily evaporation rate of the lake surface:

[0085] Collect the required daily-scale meteorological data, including air temperature Ta, relative humidity RH, wind speed U, and air pressure P. a Downward shortwave radiation K↓, downward longwave radiation L↓; and lake parameters, including lake surface albedo α, lake surface emissivity ε, and lake mean depth Z.

[0086] A single-layer evaporation model is constructed, assuming an initial lake surface temperature T. s Based on this temperature, the net radiation R is calculated sequentially. n The system uses equal components of sensible heat flux H, latent heat flux λE, and water heat storage G, with the lake surface energy balance equation as the boundary condition, and employs an iterative algorithm to determine the lake surface temperature T. s Iterative optimization is performed until the energy balance equation meets the convergence requirement. Finally, the daily lake evaporation E is calculated from the converged latent heat flux λE. lake ;

[0087] The constraints on the lake surface energy balance equation are as follows:

[0088] (2-1)

[0089] In the formula, R n Where H is the net radiation and H is the sensible heat flux. Where is latent heat flux and G is the heat storage of the lake water, both in W / m³. 2 .

[0090] Net radiation R n Represented as:

[0091] (2-2)

[0092] In the formula, α is the lake surface albedo, and K↓ is the downward shortwave radiation from the lake surface (W / m²). 2 ), Let T be the lake surface emissivity, σ be the Stefan-Boltzmann constant, and T be the lake surface emissivity. s Lake surface temperature (K), L↓ represents downward atmospheric longwave radiation (W / m²). 2 ).

[0093] Lake thermal storage (G) is represented as:

[0094] (2-3)

[0095] In the formula, c w is the specific heat capacity of water (J / (kg·K)). Let Z be the density of water, and Z be the average depth of the lake (m). This represents the rate of change of water temperature over time.

[0096] Lake surface sensible heat flux (H) and latent heat flux (H) ), respectively represented as:

[0097] (2-4)

[0098] (2-5)

[0099] In the formula, c is the specific heat capacity of air (J / (kg·K)); ρ is the air density (kg / m³). 3 ); T a λ is the air temperature (K); λ is the latent heat of vaporization; U is the wind speed (m / s); C H and C E These are the overall transport coefficients of sensible heat and latent heat, respectively; q s The water surface temperature is T s The water surface saturation specific humidity at that time, q a The air is more humid than the surrounding air.

[0100] In response to the situation of lake surface freezing in winter, formula (2-4) introduces a correction for ice surface sublimation in the evaporation term. When the lake surface temperature is below 0℃, the evaporation process takes the form of sublimation.

[0101] The humidity involved in formula (2-5) is calculated using the following formula:

[0102] (2-6)

[0103] (2-7)

[0104] (2-8)

[0105] (2-9)

[0106] In the formula, e is the air vapor pressure (hPa), e s P is the saturated vapor pressure (hPa) of the lake surface. a RH represents air pressure (hPa) and relative humidity (%).

[0107] Lake surface evaporation is determined by latent heat flux ( The conversion yields the following expression:

[0108] (2-10).

[0109] Step 3: Calculate the glacier runoff sequence based on daily precipitation and average temperature data:

[0110] Based on glacier distribution data (such as the results of the Second National Glacier Inventory of China or remote sensing interpretation), and combined with the spatial resolution of meteorological data, the glacier-covered area within the study region was divided into several computational units. The daily precipitation P and average temperature T of each unit were used to determine the precipitation phase and obtain the liquid precipitation P. liq Based on snow and ice melt calculations, the daily-scale glacier runoff sequence R is obtained. g .

[0111] The phase state of precipitation is determined using the temperature threshold method, and the total precipitation P is divided into liquid precipitation P0. liq Solid precipitation, liquid precipitation P liq The calculation formula is as follows:

[0112] (3-1)

[0113] In the formula, T is the average temperature (°C) within the calculation unit; P liq P represents the liquid precipitation (mm) within the calculation unit; P represents the total precipitation (mm) within the calculation unit; T represents the total precipitation (mm) within the calculation unit. liq and T soild These are the critical temperatures (°C) for liquid and solid precipitation, respectively.

[0114] The formula for calculating snow and ice melt (M) is as follows:

[0115] (3-2)

[0116] In the formula, DDF snow / ice The day-dwelling factor for snow and ice, mm / (d·℃); T m It is the baseline temperature (°C) for snow and ice melting.

[0117] Glacier runoff (R) g The calculation formula is as follows:

[0118] (3-3)

[0119] In the formula, S(i) is the area of ​​the calculation unit (km²). 2 f is the meltwater infiltration-freezing rate, dimensionless; P liq (i) represents the amount of liquid precipitation (mm) within the calculation unit; k is the unit conversion factor.

[0120] Step 4: Correct for lake surface precipitation and estimate non-glacial runoff:

[0121] Lake surface precipitation correction employs a combination of quantile mapping (QM) and Bayesian fusion to improve the accuracy and representativeness of precipitation data.

[0122] First, based on the precipitation data P from the measured stations obs Compared with meteorological reanalysis or satellite precipitation data P raw Construct its empirical distribution function F obs (p) and F raw (p). For each daily value P in the original precipitation sequence raw Correction is performed using quantile mapping relationships, the formula for which is as follows:

[0123] (4-1)

[0124] Among them, P qm This represents the precipitation value after quantile correction.

[0125] After quantile correction, a weighted combination of multi-source precipitation data (such as station, satellite, and reanalysis products) is employed using a Bayesian fusion method. Bayesian fusion determines the weights of each data source based on posterior probabilities, calculated using the following formula:

[0126] (4-2)

[0127] Among them, P k w represents the corrected precipitation value from the k-th data source. k The Bayesian weights, derived from the error distribution and reliability of each data source, satisfy ∑w k = 1.

[0128] Finally, the lake surface precipitation sequence P was obtained. lake :

[0129] (4-3)

[0130] Lake area is affected by changes in its water balance. In inland enclosed lakes, the inflow of water over a given period is mainly due to precipitation and runoff, while the outflow is primarily due to evaporation. Considering glacial meltwater, the lake's water balance equation is expressed as:

[0131] (4-4)

[0132] In the formula, ΔV is the change in lake water volume over a certain period of time; P lakeIt is the amount of precipitation that falls directly onto the lake surface during that period; E lake This refers to the amount of water lost through evaporation from the lake during that period; A lake R represents the lake's surface area during that period. g This refers to the runoff generated by glacial meltwater in the upstream basin of the lake; k is the unit conversion factor.

[0133] Non-glacial runoff R p The calculation formula is obtained by rearranging terms from the water balance equation (4-4), and is as follows:

[0134] (4-5)

[0135] Step 5, Decomposition of Lake Expansion Contributions and Quantitative Attribution of Driving Factors:

[0136] To accurately identify the main controlling factors of lake expansion, the lake expansion period is divided into a stable period and an expansion period. The stable period refers to the stage when the lake experiences relatively small climate fluctuations and its water budget is basically balanced, serving as a baseline reference; the expansion period corresponds to the stage where the lake area and water storage increase significantly. By comparing the differences in water budget characteristics between the two stages, the relative contributions of each hydrological component to lake expansion can be quantified.

[0137] Using an annual timescale, the maximum lake area within each year is taken as representative. To determine the stable period, the Pettitt test is first used to identify abrupt change points in the lake area sequence, thus determining the starting year of the expansion phase. Then, within the time period before the abrupt change points, consecutive years with small annual area variations (|ΔA| ≤ 5%) and corresponding water volume changes close to zero are further screened as candidate intervals for the stable period. Finally, a time period with good continuity, minimal volatility, and a duration of at least N years (N ≥ 5) is selected as the baseline period for the decomposition of lake expansion contributions.

[0138] Based on this, the multi-year average values ​​of each hydrological component during the stable period were calculated as a reference benchmark for calculating anomalies during the expansion period. This includes lake surface precipitation. Lake surface evaporation glacial runoff Non-glacial runoff and the average lake surface area over many years corresponding to the stable period.

[0139] For the expansion period, the difference between each input and the mean of the stable period is calculated year by year, and the cumulative outlier ΔI is obtained. i ， The expression is as follows:

[0140] (5-2)

[0141] Where t represents the year during the expansion period, and i represents different hydrological inputs (lake surface precipitation, lake surface evaporation, glacial runoff, non-glacial runoff), and so on.

[0142] The total increase in lake water volume during the expansion period is defined as:

[0143] (5-3)

[0144] Among them, V t Let t be the maximum annual water storage capacity of the lake in year t.

[0145] The relative contribution rates of each hydrological factor (lake surface precipitation, lake surface evaporation, glacial runoff, and non-glacial runoff) can be calculated using the following formula:

[0146] (5-4)

[0147] This invention provides a method for calculating the contribution decomposition of lake expansion. It extracts lake area and inverts water volume changes through remote sensing images and digital elevation models, uses the temperature threshold method to determine the precipitation phase, and combines the degree-day factor method to estimate snow and ice melt, and calculates the total glacier runoff including solid precipitation, liquid precipitation and snow and ice melt.

[0148] Based on the lake surface energy balance equation, the fluxes of net radiation, sensible heat, latent heat and water body heat storage are calculated, a single-layer evaporation model is constructed, and the daily lake surface evaporation is obtained.

[0149] A combination of quantile mapping and Bayesian fusion was used to correct lake surface precipitation; based on the lake water balance equation, combined with the extracted lake area sequence, the constructed area-storage capacity relationship, and the calculated glacial runoff, lake surface precipitation and evaporation data, non-glacial runoff was inferred.

[0150] Based on the trend of lake area, a stable period and an expansion period are defined. The average hydrological value during the stable period is used as a benchmark to calculate the outliers during the expansion period. Finally, the relative contributions of each hydrological factor (lake surface precipitation, lake surface evaporation, glacial runoff, and non-glacial runoff) to lake expansion are determined according to the proportion of outliers to the total water volume increase. This method clarifies the contribution intensity of different driving factors, providing scientific support for simulating lake changes and predicting evolution, and making ecological protection and management strategies more targeted.

[0151] The above description is only used to illustrate the technical solutions of the present invention and is not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for decomposing and calculating the contribution of lake expansion, characterized in that, Includes the following steps: Step 1: Extract lake area and invert lake water volume changes based on remote sensing imagery and digital elevation model: Remote sensing image data covering the study area was acquired. Normalized water index was calculated for each valid lake boundary image. An adaptive threshold segmentation algorithm was used to determine the optimal threshold to separate water bodies from non-water bodies and extract the corresponding lake areas. Lake areas were extracted based on daily images, and the maximum lake area for each month was calculated to form a monthly lake area sequence. A high-resolution digital elevation model was acquired to construct the lake area-reservoir capacity relationship, and the corresponding water volume changes were calculated based on the lake area. Step 2: Construct a single-layer evaporation model to obtain the daily evaporation rate of the lake surface: Collect the required daily-scale meteorological data, including air temperature T. a Relative humidity (RH), wind speed (U), and air pressure (P) a Downward shortwave radiation K↓, downward longwave radiation L↓; and lake parameters, including lake surface albedo α, lake surface emissivity ε, and lake mean depth Z; A single-layer evaporation model is constructed, assuming an initial lake surface temperature T. s Based on this temperature, the net radiation R is calculated sequentially. n The sensible heat flux H, latent heat flux λE, and water heat storage G components are used as boundary conditions constrained by the lake surface energy balance equation. An iterative algorithm is employed to determine the lake surface temperature T. s Iterative optimization is performed until the energy balance equation meets the convergence requirement. Finally, the daily lake evaporation E is calculated from the converged latent heat flux λE. lake ; Step 3: Calculate the glacier runoff sequence based on daily precipitation and average temperature data: The glacier-covered area within the study region was divided into several computational units; using the daily precipitation P and average temperature T of each unit, the precipitation phase was determined to obtain the liquid precipitation P. liq And by performing snow and ice melt calculations, the diurnal glacier runoff sequence R was obtained. g ; Step 4: Correct for lake surface precipitation and estimate non-glacial runoff: The lake surface precipitation sequence P was obtained by correcting the lake surface precipitation using a method combining quantile mapping and Bayesian fusion. lake Based on the water balance equation of inland closed lakes, combined with the extracted lake area sequence, the area-storage capacity relationship was constructed, and the calculated glacial runoff, lake surface precipitation, and evaporation data were used to estimate the non-glacial runoff R. p ; Step 5, Decomposition of Lake Expansion Contributions and Quantitative Attribution of Driving Factors: The lake area change trend is divided into a stable period and an expansion period. Multi-year average values ​​of each hydrological component during the stable period are calculated and used as a reference benchmark for calculating anomalies during the expansion period, including lake surface precipitation. Lake surface evaporation glacial runoff Non-glacial runoff and the average lake surface area over many years corresponding to the stable period. The difference between the mean values ​​of each hydrological component during the expansion and stabilization periods was calculated, and the cumulative outlier value ΔI was obtained. i Combined with the total increase in lake water volume ΔV during the expansion period total The proportions and quantitative decomposition yield the relative contributions of each factor to lake expansion.

2. The method for decomposing and calculating the contribution of lake expansion according to claim 1, characterized in that, In step 1, the normalized water index is calculated using the following formula: Where: ρ Green For green light band reflectivity, ρ NIR This refers to the reflectivity in the near-infrared band.

3. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 1, the construction of the lake area-storage capacity relationship involves first converting the digital elevation model (DEM) projection into an equal-area projection, then extracting the lake surface area indicated by the data, and taking the lake surface corresponding to the lowest point of the lake basin in the DEM as the benchmark, assuming its water storage capacity is zero. Starting from this reference lake surface, calculate the area A of the lake surface at each elevation at fixed elevation intervals Δh. i (i=1,2,3,…), and the difference in water storage volume between adjacent levels is calculated using the lake surface area corresponding to different elevations, thus obtaining the change in lake water volume. The calculation formula is as follows: In the formula: , These correspond to the lake surface area A. i and A i-1 The lake's water storage capacity, and = 0; Through multiple groups (A) i V i Establish the regression relationship between lake surface area and lake capacity. The regression formula is as follows: In the formula: c1, c2, c3, and c4 are the corresponding regression coefficients.

4. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 2, the net radiation R n The calculation formula is as follows: In the formula, α is the lake surface albedo, and K↓ is the downward shortwave radiation from the lake surface (W / m²). 2 ), Let T be the lake surface emissivity, σ be the Stefan-Boltzmann constant, and T be the lake surface emissivity. s Lake surface temperature (K), L↓ represents downward atmospheric longwave radiation (W / m²). 2 ) The formula for calculating lake thermal storage (G) is as follows: In the formula, c w is the specific heat capacity of water (J / (kg·K)). Let Z be the density of water, and Z be the average depth of the lake (m). The rate of change of water temperature over time; Lake surface sensible heat flux (H) and latent heat flux (H) The calculation formula is as follows: In the formula, c is the specific heat capacity of air (J / (kg·K)); ρ is the air density (kg / m³). 3 ); T a λ is the air temperature (K); λ is the latent heat of vaporization; U is the wind speed (m / s); C H and C E These are the overall transport coefficients of sensible heat and latent heat, respectively; q s The water surface temperature is T s The water surface saturation specific humidity at that time, q a The air is more humid than normal. The energy balance constraints on the lake surface are as follows: In the formula, R n Where H is the net radiation and H is the sensible heat flux. Where is latent heat flux and G is the heat storage of the lake water, both in W / m³. 2 ; Lake surface evaporation is determined by latent heat flux ( The conversion is as follows: 。 5. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 3, the glacier-covered area is divided into several calculation units based on the spatial resolution of glacier distribution data and meteorological data.

6. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 3, the glacier runoff sequence R g The calculation method involves using a temperature threshold method to determine the phase state of precipitation, and separating liquid precipitation P from the total precipitation P. liq The calculation formula is as follows: In the formula, T is the average temperature (°C) within the calculation unit; P liq P represents the liquid precipitation (mm) within the calculation unit; P represents the total precipitation (mm) within the calculation unit; T represents the total precipitation (mm) within the calculation unit. liq and T soild These are the critical temperatures (°C) for liquid and solid precipitation, respectively. The formula for calculating snow and ice melt (M) is as follows: In the formula, DDF snow / ice The day-dwelling factor for snow and ice, mm / (d·℃); T m It is the baseline temperature (°C) for snow and ice melting. Calculate glacier runoff (R) g The calculation formula is as follows: In the formula, S(i) is the area of ​​the calculation unit (km²). 2 f is the meltwater infiltration-freezing rate, dimensionless; P liq (i) represents the amount of liquid precipitation (mm) within the calculation unit; k is the unit conversion factor.

7. The method for decomposing and calculating the contribution of lake expansion according to claim 1, characterized in that, In step 4, the formula for calculating the quantile mapping is as follows: Among them, P qm F represents the precipitation value after quantile correction. obs (p) and F raw (p) represents the measured precipitation data P. obs Compared with P obtained through meteorological reanalysis or satellite precipitation data raw The empirical distribution function is constructed.

8. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 4, the Bayesian fusion calculation formula is as follows: Among them, P k w represents the corrected precipitation value from the k-th data source. k The Bayesian weights, derived from the error distribution and reliability of each data source, satisfy ∑w k = 1.

9. The method for calculating the contribution decomposition of lake expansion according to claim 1, characterized in that, In step 4, the non-glacial runoff R p The calculation formula is as follows: Among them, A lake To estimate the lake surface area during the same calculation period for non-glacial runoff, ΔV is the change in lake water volume during the same calculation period for non-glacial runoff, and k is the unit conversion factor.

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