A standardized glacier melt index calculation method based on a radiation correction degree-day factor

Abstract

This invention provides a standardized glacier melt index calculation method based on the radiative correction diurnal factor. The method includes: acquiring and preprocessing meteorological data from glacier areas; calculating snow and ice accumulation (P) and melt (M); calculating the snow and ice mass balance difference sequence; accumulating snow and ice mass balance at multiple time scales; fitting and standardizing the probability distribution of the accumulated sequence; and classifying and assessing the glacier melt status based on the SGMI index. This invention solves the problems of traditional glacier mass balance monitoring relying on in-situ observations, poor timeliness, and insufficient spatial coverage, and achieves a standardized and rapid assessment of glacier melt status based on multi-source meteorological data.

Description

Technical Field

[0001] This invention belongs to the field of glacier hydrological monitoring and meteorological technology, and specifically relates to a standardized method for calculating the glacier melt index based on the radiation correction degree diurnal factor. Background Technology

[0002] Glaciers are sensitive indicators of climate change, and their mass balance (the difference between glacier mass income and expenditure) directly reflects regional climate conditions. Traditional glacier mass balance monitoring mainly relies on the "glaciological method," which involves setting up stakes on the glacier for on-site measurements. This method is highly accurate but time-consuming, labor-intensive, and costly, and can only cover a very small number of representative glaciers, making it difficult to meet the needs of large-scale, high-time-sensitivity monitoring. Glacier mass "income" is mainly solid snowfall, while "expenditure" is mainly melting. However, the glaciological community currently lacks a comprehensive index that can quickly and standardizedly assess the state of glaciers' response to climate change.

[0003] Therefore, there is an urgent need for a new method that can quickly calculate and standardize the assessment of glacier mass balance using readily available climate data, in order to improve the monitoring and early warning capabilities of glacier changes and provide scientific support for water resource management and climate change adaptation. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, the present invention aims to propose a standardized glacier melt index (SGMI) calculation method based on the radiation correction diurnal factor. By introducing a radiation correction term, constructing a unified standardized process, and integrating multi-source information constraints, the accuracy of glacier melt estimation can be significantly improved, and standardized and rapid evaluation of glacier melt results in different regions and at different times can be achieved.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention provides a standardized glacier melt index calculation method based on the diurnal radiation correction factor, comprising the following steps:

[0007] Step 1, Acquisition and Preprocessing of Meteorological Data in Glacier Areas:

[0008] Historical temperature and precipitation datasets for the target glacier region are obtained. The datasets are preprocessed, and the preprocessed precipitation data are used to generate precipitation grid data using a spatial interpolation algorithm. At the same time, the preprocessed temperature data is interpolated using an elevation model and a temperature lapse rate to obtain temperature grid data. The precipitation grid data and temperature grid data are integrated to generate a unified meteorological grid dataset.

[0009] Step 2, Calculation of snow and ice accumulation and melting in the glacier area:

[0010] An improved snow and ice melting model based on the radiative correction diurnal factor is constructed. This model is based on the meteorological grid dataset generated in step 1, and is applied according to a certain temperature threshold (typically set to T). c = 0 °C) The precipitation is divided into liquid precipitation and solid snowfall. The amount of solid snowfall is taken as the snow and ice accumulation P, and the potential snow and ice melt M is calculated using the corrected degree-day factor.

[0011] Step 3, Calculation of the ice and snow mass balance difference sequence:

[0012] Based on the accumulated snow and ice P and the potential snow and ice melt M, calculate the snow and ice mass balance difference at each time step, and construct the snow and ice mass balance difference sequence D = PM;

[0013] Where D>0 indicates a material surplus, D<0 indicates a material deficit, and D=0 indicates a material balance.

[0014] Step 4, Accumulation of snow and ice mass balance across multiple time scales:

[0015] The snow and ice mass balance difference sequence obtained in step 3 is accumulated and calculated at multiple preset time scales to generate the cumulative snow and ice mass balance sequence corresponding to each time scale.

[0016] Step 5, Fitting and standardizing the probability distribution of the cumulative sequence:

[0017] The cumulative snow and ice mass balance sequences at each time scale obtained in step 4 are fitted with a probability distribution using a three-parameter equal probability distribution function to calculate their cumulative probabilities. Subsequently, the cumulative probabilities are standardized using the inverse function of the standard normal distribution to obtain the standardized glacier melt index (SGMI) sequence.

[0018] Step 6, Assessment of glacier melting status based on SGMI index:

[0019] Based on the numerical range of the standardized glacier melting index (SGMI) sequence obtained in step 5, the glacier melting status is assessed in a graded manner.

[0020] Positive values ​​indicate that the amount of glacial material accumulated during that period is higher than the historical average, while negative values ​​indicate that the amount of material melted is higher than the historical average. The absolute value indicates the severity of the deviation from the norm.

[0021] Furthermore, in step 1, the specific steps for acquiring and preprocessing meteorological data in the glacier area include:

[0022] S11, Acquisition of multi-source meteorological data: Acquire observation data from ground meteorological stations in the target glacier area, satellite remote sensing inversion data, and climate reanalysis data to form a raw meteorological dataset. The dataset shall contain at least daily or monthly surface temperature, precipitation, and shortwave radiation variables.

[0023] S12, Data Preprocessing Flow:

[0024] (a) Perform quality control and missing value imputation on the original meteorological dataset;

[0025] (b) For precipitation data, inverse distance weighting or kriging interpolation is used to generate precipitation grid data;

[0026] (c) For surface temperature data, the target glacier area is divided into multiple elevation zones according to altitude using a digital elevation model. The daily average temperature value of the corresponding elevation zone is obtained by extrapolation combined with the temperature lapse rate, and then interpolation is used to generate temperature grid data.

[0027] (d) Integrate the above precipitation grid data and temperature grid data to generate a meteorological grid dataset with a unified spatiotemporal resolution.

[0028] Furthermore, in step 2, the construction of the improved snow and ice melting model based on the radiation correction diurnal factor includes:

[0029] S21, Data preparation and spatial discretization: Obtain digital elevation data, hydrological and meteorological station data, and glacier catalog data for the target glacier area. At the same time, call the meteorological grid dataset generated in step 1, and divide the watershed into multiple elevation zones according to the vertical elevation difference, and calculate the average elevation and glacier coverage of each elevation zone.

[0030] S22, Dynamic Albedo Module Construction: Based on daily meteorological input, the albedo is reset to the highest value when there is new snow; if there is no new snow, the aging process of snow albedo is simulated through exponential decay; when the snow in the glacier area has completely melted, the ice surface albedo is switched to a fixed minimum ice surface albedo.

[0031] S23, Unit-based melting calculation: Calculate the amount of snow melt and glacier melt separately for each elevation zone;

[0032] The calculation of snow melt is performed using the radiation-enhanced degree-day factor formula:

[0033]

[0034] In the formula, The amount of snow melted is in mm; The radiation factor of snow cover. ; This represents the daily average incident shortwave radiation received in the elevation zone, in W / m². Albedo; As a factor for snow cover during the day, T represents the daily average temperature, in °C.

[0035] The calculation of glacier melt first involves the model determining whether the seasonal snow cover in the glacier region has completely melted. If it has not, the melting process of the glacier region follows the logic for calculating snow melt, namely:

[0036]

[0037] In the formula, The amount of glacier melt is expressed in mm.

[0038] When the snow melts and the bare ice is exposed, the model calls the glacier melting module, as shown in the following formula:

[0039]

[0040] In the formula, Glacier radiation factor, ; Glacier albedo; As the glacier diurnal factor, ; For exceeding a certain temperature threshold T c Positive accumulated temperature, °C;

[0041] S24, Parameter Calibration and Verification: The runoff calculated for each elevation zone is used to perform runoff generation and runoff calculations across the entire watershed to obtain simulated runoff. The simulation results are compared with measured runoff data. The degree-day factor (DDF) and radiation factor (SRF) in the model are calibrated by optimizing the algorithm to complete the model construction and local parameter calibration.

[0042] Furthermore, the formula for calculating the runoff generation and sinking of the entire basin in S24 is as follows:

[0043]

[0044] In the formula, The average daily runoff of the entire basin on day n is expressed in m³ / s. This is the snowmelt runoff coefficient; Snow cover in non-glacial areas; Let be the amount of snow melt in the i-th elevation zone; This is the ice melt runoff coefficient; This refers to the glacier coverage rate in the elevation zone; Let be the amount of glacier melt in the i-th elevation zone; This is the precipitation runoff coefficient; The effective precipitation for the i-th elevation zone is in mm; A is the catchment area in km². 2 ; is the recession coefficient; is the average daily runoff on the (n - 1)-th day, m³ / s;

[0045] where:

[0046]

[0047]

[0048]

[0049] In the formula, A s is the snow-covered area, Km 2 ; A i is the total area of the i-th elevation zone, Km 2 ; A ice is the glacier area, Km 2 .

[0050] Furthermore, in step 4, on multiple preset time scales k, the moving window accumulation algorithm is used to calculate the cumulative snow and ice mass balance sequence, and the calculation formula is:

[0051]

[0052] In the formula, [[ID=4@]] is the snow and ice accumulation value at time t and time scale k; D(t - j) is the snow and ice accumulation value at time t - j and time scale k.

[0053] Furthermore, in step 5, the three-parameter equiprobable distribution function includes the Log-logistic distribution, the generalized extreme value distribution or the Pearson type III distribution.

[0054] Furthermore, in step 6, the glacier melting state is classified as:

[0055] SGMI ≥ 2.0 is extreme accumulation, 1.5 ≤ SGMI < 2.0 is severe accumulation, 1.0 ≤ SGMI < 1.5 is moderate accumulation, -1.0 < SGMI < 1.0 is close to normal, -1.5 < SGMI ≤ -1.0 is moderate melting, -2.0 < SGMI ≤ -1.5 is severe melting, SGMI ≤ -2.0 is extreme melting.

[0056] The beneficial effects of the present invention compared with the prior art are:

[0057] 1. Compared with the traditional glacier mass balance monitoring method that mainly relies on the "glaciological method", the standardized glacier melt index calculation method described in this application is free from the dependence on on-site glacier observation. It can achieve rapid assessment of glacier melt status with large-scale, high timeliness and spatial continuity based on temperature and precipitation data, thus solving the problems of insufficient coverage and poor timeliness of traditional monitoring.

[0058] 2. The standardized glacier melt index calculation method described in this application adopts the radiation correction degree-day factor and introduces dynamic albedo, which is more in line with the actual energy exchange process of glaciers and significantly improves the accuracy and physical rationality of snowmelt and icemelt calculation. The corresponding time-scale SGMI index obtained by calculating the snow-ice mass balance difference (D) at different time scales (month, season, year) reflects the different response characteristics of glaciers to short-term climate fluctuations and long-term climate trends.

[0059] 3. The standardized glacier melt index calculation method described in this application obtains a dimensionless and comparable SGMI index through multi-timescale accumulation and probability standardization transformation, so that the glacier state in different regions and under different climatic backgrounds has a unified comparison benchmark, thereby realizing a unified quantitative assessment of the glacier state in different regions and at different times.

[0060] 4. The SGMI index described in this invention can be used for dynamic monitoring of glacier changes, prediction of glacier status under future scenarios, and assessment of the impact of extreme climate events on glaciers, providing decision support for glacier disaster early warning. Attached Figure Description

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0062] Figure 1 This is a flowchart illustrating the standardized glacier melt index calculation method based on the radiation correction diurnal factor.

[0063] Figure 2 This is a schematic diagram showing the overview and location distribution of the application example study area of ​​this invention;

[0064] Figure 3 A schematic diagram of the standardized glacier melt index (SGMI) results provided in the application examples of this invention. Detailed Implementation

[0065] The embodiments described are provided to better illustrate the present invention, but are not intended to limit the scope of the invention to the embodiments described. Therefore, non-essential improvements and adjustments made to the embodiments by those skilled in the art based on the above description are still within the scope of protection of the present invention.

[0066] The endpoints and any values ​​of the ranges disclosed herein are not limited to the precise ranges or values, and these ranges or values ​​should be understood to include values ​​close to these ranges or values. For numerical ranges, the endpoint values ​​of the various ranges, the endpoint values ​​of the various ranges and individual point values, and individual point values ​​can be combined with each other to obtain one or more new numerical ranges, which should be considered as specifically disclosed herein.

[0067] The present invention will be described in detail below through embodiments. It should be understood that the following embodiments are only used to exemplify and further explain and illustrate the content of the present invention, and are not intended to limit the present invention.

[0068] Example 1

[0069] This embodiment provides a standardized glacier melt index calculation method based on the diurnal factor of radiation correction, such as... Figure 1 As shown, it includes the following steps:

[0070] Step 1, Acquisition and Preprocessing of Meteorological Data in Glacier Areas:

[0071] Historical temperature and precipitation datasets for the target glacier region are obtained. The datasets are preprocessed, and the preprocessed precipitation data are used to generate precipitation grid data using a spatial interpolation algorithm. At the same time, the preprocessed temperature data is interpolated using an elevation model and a temperature lapse rate to obtain temperature grid data. The precipitation grid data and temperature grid data are then integrated to generate a unified meteorological grid dataset.

[0072] The specific steps include:

[0073] S11, Acquisition of multi-source meteorological data: Acquire observation data from ground meteorological stations in the target glacier area, satellite remote sensing inversion data, and climate reanalysis data to form a raw meteorological dataset. The dataset shall contain at least daily or monthly surface temperature, precipitation, and shortwave radiation variables.

[0074] S12, Data Preprocessing Flow:

[0075] (a) Perform quality control and missing value imputation on the original meteorological dataset to ensure the integrity of the time series of each station;

[0076] (b) For precipitation data, inverse distance weighting or kriging interpolation is used to generate precipitation grid data with uniform spatial resolution;

[0077] (c) For surface temperature data, considering its strong correlation with altitude, the target glacier area is divided into multiple elevation zones according to altitude using a digital elevation model (DEM). The daily average temperature value of the corresponding elevation zone is obtained by extrapolation using the temperature lapse rate, and then interpolation is used to generate temperature grid data.

[0078] (d) Integrate the above precipitation grid data and temperature grid data, and statistically analyze the meteorological values ​​of each elevation zone to obtain the daily average temperature and precipitation of each elevation zone, and finally generate a meteorological grid dataset with unified spatiotemporal resolution.

[0079] Step 2, Calculation of snow and ice accumulation and melting in the glacier area:

[0080] An improved snow and ice melting model based on the radiative correction diurnal factor is constructed. This model is based on the meteorological grid dataset generated in step 1, and is determined according to a certain temperature threshold T. c Precipitation is divided into liquid precipitation and solid snowfall. Solid snowfall is taken as the snow and ice accumulation P, and the potential snow and ice melt M is calculated using the corrected degree-day factor.

[0081] The construction of the improved snow and ice melting model based on the radiative correction diurnal factor includes:

[0082] S21, Data Preparation and Spatial Discretization: Obtain digital elevation data, hydrological and meteorological station data, and glacier catalog data for the target glacier area. At the same time, call the meteorological grid dataset generated in step 1, and divide the watershed into multiple elevation zones according to the vertical elevation difference, and calculate the average elevation and glacier coverage of each elevation zone.

[0083] Specifically, for each elevation band i, the daily n input variable data processing is as follows:

[0084] First, since the snow and ice melting model calculation unit is based on different elevation zones, when the vertical height difference of the watershed is greater than 500m, the target watershed is divided into zones at 500m intervals according to the DEM data, and the average elevation of each elevation zone is calculated.

[0085] Secondly, according to the data preprocessing process in step 1, the average altitude temperature value T(n,i) of each elevation zone is obtained by extrapolating the temperature lapse rate stations; the precipitation grid dataset is partitioned and statistically analyzed to each elevation zone to obtain the daily average precipitation P(n,i) of each elevation zone.

[0086] S22, Construction of the dynamic albedo module:

[0087] The dynamic changes in snow and ice surface albedo represent the physical process of snow aging from new to old, and from coverage to melting. A dynamic albedo module is constructed based on daily meteorological input. When new snow is detected, the albedo is reset to the highest value; if there is no new snow, the aging process of snow albedo is simulated through exponential decay; when the snow in the glacier area has completely melted, the ice surface albedo is switched to a fixed minimum ice surface albedo.

[0088] The final model categorizes the albedo of different surfaces (snow, ice, bare land) into different elevation zones to obtain the total energy absorption capacity of the region on that day.

[0089] S23, Unit-based Melting Calculation: Snowmelt and glacier melt are calculated separately for each elevation zone. The snow and ice melt model operates on a daily time unit. In each day's calculation, the model traverses all geospatial units and performs regional statistics down to each elevation zone to complete the runoff calculation. Specifically:

[0090] (1) Initialize the calculation for the day. At the start of the calculation for a day (day n), the model will load the temperature, precipitation, incident radiation and estimated albedo data for all elevation zones for that day.

[0091] (2) Determine the precipitation pattern. For each elevation zone (i), the model will compare its daily temperature. and a preset temperature threshold T c If the temperature is below the threshold T c The precipitation P(i,n) of the day will be marked as new snowfall. This amount of water will be used to update the snow cover status of that elevation zone, but will not participate in the runoff calculation for the day. If the temperature is higher than or equal to the threshold T c Precipitation will be marked as rainfall, and it will directly participate in the day's runoff calculation.

[0092] (3) The calculation of snow melt is performed using the radiation-enhanced degree-day factor formula:

[0093]

[0094] In the formula, The amount of snow melted is in mm; The snow radiation factor represents the conversion of shortwave radiation absorbed by the Earth's surface into snowmelt depth. ; This represents the daily average incident shortwave radiation received in the elevation zone, in W / m². Snow albedo represents the proportion of solar radiation reflected by the Earth's surface, and is dynamically calculated based on snow age. As a factor for snow cover during the day, T represents the daily average temperature, in °C.

[0095] The calculation of glacier melt first involves the model determining whether the seasonal snow cover in the glacier region has completely melted. If it has not, the melting process of the glacier region follows the logic for calculating snow melt, namely:

[0096]

[0097] In the formula, The value represents the amount of glacier melt, expressed in mm.

[0098] When the snow melts and the bare ice is exposed, the model calls the glacier melting module, as shown in the following formula:

[0099]

[0100] In the formula, Glacier radiation factor, ; Glacier albedo; As the glacier diurnal factor, ; For exceeding a certain temperature threshold T c The positive accumulated temperature, °C.

[0101] S24, Parameter Calibration and Verification: To verify the snow and ice melting model constructed in the preceding steps and its day-degree factor based on radiation correction ( , To ensure the accuracy of the simulation, the runoff (snowmelt, icemelt, and rainfall) of all runoff in the i-th elevation zone on day n is calculated and then the simulated runoff is obtained. The simulation results are compared with the measured runoff data, and the degree-day factor (DDF) and radiation factor (SRF) in the model are calibrated by optimizing the algorithm to complete the model construction and parameter localization calibration.

[0102] Furthermore, the formula for calculating the runoff generation and sinking of the entire basin in S24 is as follows:

[0103]

[0104] In the formula, The average daily runoff of the entire basin on day n is expressed in m³ / s. This is the snowmelt runoff coefficient; Snow cover in non-glacial areas; Let be the amount of snow melt in the i-th elevation zone; This is the ice melt runoff coefficient; This refers to the glacier coverage rate in the elevation zone; Let be the amount of glacier melt in the i-th elevation zone; This is the precipitation runoff coefficient; The effective precipitation for the i-th elevation zone is in mm; A is the catchment area in km². 2 ; The recession coefficient; The average daily runoff on day n-1 is expressed in m³ / s.

[0105] in:

[0106]

[0107]

[0108]

[0109] In the formula, As snow cover area, km 2 A i Let Km be the total area of ​​the i-th elevation zone. 2 A ice The area of ​​the glacier is in km. 2 .

[0110] The improved snow and ice melt model further considers the dynamic changes in the glacier surface. When calculating the potential melt (M), it dynamically determines whether the glacier surface is covered by new snow or exposed old ice. When the surface is covered by snow, a lower daily snow cover factor (DDF) is used. s When seasonal snow has completely melted and the surface is bare ice, it automatically switches to a Glacier Diurnal Factor (DDF) with a higher value due to its lower albedo. ice This makes the calculation of melting amounts more consistent with actual physical processes. Further calculations of ice and snow melt without considering mass transport limitations require utilizing the core parameter of the ice and snow melt model—the corrected glacier and snow cover diurnal factor (DDF). ice DDF s Using the temperature data from step 1, the following calculations are performed on the i-th elevation zone:

[0111]

[0112] In the formula, Let be the snow cover day factor for the i-th elevation zone. ; Let be the glacier diurnal factor for the i-th elevation zone. ; Let be the daily average temperature of the i-th elevation zone, in °C; The temperature threshold is expressed in °C.

[0113] The final snowmelt and ice melt volume for each elevation zone was obtained.

[0114] Step 3, Calculation of the ice and snow mass balance difference sequence:

[0115] Based on the accumulated snow and ice amount P and the potential snow and ice melt amount M calculated in step 2, calculate the snow and ice mass balance difference for each time step. The calculation formula is as follows:

[0116]

[0117] In the formula: i represents the elevation zone, and t represents the time step index.

[0118] By repeating the above calculations for all elevation zones and time steps, a snow and ice mass balance difference sequence D with the same dimension and spatiotemporal resolution as the input data is constructed. Each value in sequence D quantitatively represents the material budget of the glacier surface, which serves as the basis for the multi-timescale aggregation analysis in subsequent step 4.

[0119] When D>0, it means that the accumulated solid snowfall in this time step is greater than the potential melting amount, which is a material surplus; when D<0, it means that the potential melting amount is greater than the accumulated solid snowfall, which is a material deficit; when D=0, it means that the accumulation and melting of materials are in equilibrium in this time step.

[0120] Step 4, Accumulation of snow and ice mass balance across multiple time scales:

[0121] The snow and ice mass balance difference sequence obtained in step 3 is accumulated over multiple preset time scales to generate cumulative snow and ice mass balance sequences for each time scale. Specifically:

[0122] 1) Setting and selecting the time scale:

[0123] A set of time scales k is pre-defined to reflect the impact of different cyclical climate variability on glacier mass balance. The time scale set includes at least one scale for characterizing short-term fluctuations within the season (e.g., 3 or 6 months) and one scale for characterizing long-term trends in interannual or longer cycles (e.g., 12, 24, or 48 months), enabling multi-dimensional diagnosis of glacier status.

[0124] 2) Execution of window accumulation:

[0125] For the snow and ice mass balance difference sequence D generated in step 3 for each elevation zone, a moving window accumulation algorithm is applied at each preset time scale k; specifically, for any time t in the time series, its cumulative value D at time scale k is calculated. k (t) is calculated using the following formula:

[0126]

[0127] In the formula, Let be the accumulated ice and snow value at time t and time scale k; D(tj) is the accumulated ice and snow value at time tj and time scale k.

[0128] The calculation is performed sliding over the entire time series until all time points have been traversed.

[0129] 3) Generation of multi-scale cumulative sequences:

[0130] Step 2) Accumulate to obtain a set of cumulative ice and snow mass balance sequences. , where each sequence Each value corresponds to a specific time scale k; any value in this set of sequences represents the total net mass surplus or deficit driven by climate over the past k time steps at the corresponding time scale, providing input data with different time steps for subsequent probability standardization.

[0131] Step 5, Fitting and standardizing the probability distribution of the cumulative sequence:

[0132] The cumulative snow and ice mass balance sequences at each time scale obtained in step 4 were analyzed using a three-parameter equal probability distribution function. A probability distribution is fitted, and its cumulative probability is calculated. Then, the cumulative probability is standardized by the inverse function of the standard normal distribution to obtain the standardized glacier melt index (SGMI) sequence.

[0133] 1) Selection of probability distribution function: The three-parameter equal probability distribution function includes Log-logistic distribution, generalized extreme value (GEV) distribution or Pearson type III distribution.

[0134] a) Log-logistic distribution, with its cumulative distribution function (CDF) as follows:

[0135]

[0136] In the formula: x is a sequence In the given values, α is the scale parameter, β is the shape parameter, and γ is the position parameter.

[0137] b) The generalized extremum (GEV) distribution, whose cumulative distribution function (CDF) is:

[0138]

[0139] In the formula: μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter.

[0140] c) Pearson Type III distribution: Its probability density function (PDF) is:

[0141]

[0142] In the formula: α is the scale parameter, β is the shape parameter, γ is the position parameter, and Γ() is the Gamma function. Its cumulative distribution function is obtained by integrating this density function.

[0143] 2) Robust parameter estimation:

[0144] The L-moment method is used to estimate the parameters of the selected probability distribution function. The L-moment method is adopted because it is insensitive to outliers in the sample sequence and can still provide robust estimation results in the case of small samples, thereby ensuring a high-fidelity fit of the probability model to the statistical characteristics of the original data.

[0145] 3) Calculation of cumulative probability:

[0146] will sequence For each value x in the equation, substitute it into the cumulative distribution function (CDF) whose parameters are determined by the L-moment method, and calculate its corresponding non-transcendental probability F(x):

[0147]

[0148] The probability value F(x) represents the frequency with which events in the historical record are less than or equal to the current cumulative value x.

[0149] 4) Standardized normal transformation:

[0150] The cumulative probability F(x) calculated in the above steps is transformed using the inverse function of the standard normal distribution. The transformation formula is as follows:

[0151]

[0152] In the formula, It is the inverse function of the standard normal distribution.

[0153] This step ultimately transforms the original, dimensional, and non-distributed cumulative sequence... This is converted into a dimensionless, standardized glacial melt (SGMI) sequence with a standard deviation of 1, providing a unified benchmark and evaluation standard for glacier states at different times, locations, and scales.

[0154] Step 6, Assessment of glacier melting status based on SGMI index:

[0155] Based on the numerical range of the standardized glacier melt index (SGMI) sequence obtained in step 5, the glacier melt status is graded and assessed. Positive values ​​indicate that the amount of glacier material accumulation during this period is higher than the historical average, while negative values ​​indicate that the amount of material melted is higher than the historical average. The absolute value of the value represents the severity of the deviation from the normal state.

[0156] The specific correspondence is shown in the table below:

[0157] SGMI Index Glacial state SGMI ≥ 2.0 Extreme accumulation 1.5≤SGMI<2.0 Severe accumulation 1.0≤SGMI<1.5 Moderate accumulation -1.0<SGMI<1.0 Near normal -1.5<SGMI≤-1.0 moderate melting -2.0<SGMI≤-1.5 Severe melting SGMI≤-2.0 extreme melting

[0158] Perform dynamic assessment and diagnosis of glacier status:

[0159] The SGMI time series, calculated in step 5 and covering the entire historical period with real-time updates, is matched hourly with the hierarchical system established in step 1); the matching and diagnostic applications include at least one of the following:

[0160] a) Historical event identification: By retrieving extreme values ​​in historical SGMI sequences, the timing and intensity of extreme blizzard and extreme melting events that have had a significant impact on glaciers in history are identified and quantified.

[0161] b) Current Status Assessment: Obtain the latest SGMI value and compare it with the classification standard to make an immediate and quantitative assessment of the current status of the glacier at different time scales, and determine whether the glacier is currently in a period of material accumulation, melting, or normal fluctuation.

[0162] c) Long-term trend analysis: Apply trend testing methods such as Mann-Kendall to the SGMI time series to analyze the long-term evolution direction and rate of the glacier snow and ice mass balance under the background of climate change, and determine whether it tends to shrink or grow overall.

[0163] d) Spatial Differentiation Diagnosis: The calculation results of SGMI are spatially visualized to generate a glacier state classification map, thereby intuitively identifying the "hotspot" areas within the glacier region that are most sensitive to climate change response, providing a basis for differentiated management and research.

[0164] Application examples:

[0165] This application example selects a typical glacier basin as the study area and uses the method described in the above embodiments to calculate the Standardized Glacier Melting Index (SGMI) and assess the glacier status. The overview of the study area is as follows: Figure 2 As shown in Table 1, a cumulative snow and ice mass balance sequence for the glacier was constructed using a 12-month timescale. The SGMI index was finally obtained through probability distribution fitting and standardization transformation. The results, along with the glacier state assessment, are presented in Table 1. Figure 3 As shown.

[0166] Table 1. Glacier SGMI Index and Status Assessment, 1985-2024

[0167] years SGMI Index Glacial state 1985 0.60 Near normal 1986 0.80 Near normal 1987 1.00 Moderate accumulation 1988 1.20 Moderate accumulation 1989 1.30 Moderate accumulation 1990 1.50 Severe accumulation 1991 1.60 Severe accumulation 1992 1.40 Moderate accumulation 1993 1.20 Moderate accumulation 1994 1.10 Moderate accumulation 1995 0.80 Near normal 1996 0.60 Near normal 1997 0.40 Near normal 1998 0.30 Near normal 1999 0.00 Near normal 2000 -0.20 Near normal 2001 -0.40 Near normal 2002 -0.60 Near normal 2003 -0.80 Near normal 2004 -1.00 moderate melting 2005 -1.70 Severe melting 2006 -1.50 Severe melting 2007 -1.80 Severe melting 2008 -1.60 Severe melting 2009 -1.90 Severe melting 2010 -2.00 extreme melting 2011 -2.30 extreme melting 2012 -2.10 extreme melting 2013 -1.90 Severe melting 2014 -1.70 Severe melting 2015 -1.80 Severe melting 2016 -1.90 Severe melting 2017 -1.70 Severe melting 2018 -1.80 Severe melting 2019 -1.60 Severe melting 2020 -1.40 moderate melting 2021 -1.00 moderate melting 2022 -0.90 Near normal 2023 -0.80 Near normal 2024 -0.50 Near normal

[0168] The above results indicate that the glacier's state exhibited significant phased characteristics from 1985 to 2024. During 1985-1996, the glacier was primarily in an accumulation phase, reaching severe accumulation in 1991. Starting in 2002, the glacier's state shifted, entering a period of continuous ablation, reaching extreme melting between 2010 and 2012. Although the rate of melting has slowed recently, the overall trend suggests that the glacier has transitioned from its accumulation phase to a long-term ablation period.

[0169] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not 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 standardized glacier melt index calculation method based on the radiation correction diurnal factor, characterized in that, The calculation method includes the following steps: Step 1, Acquisition and Preprocessing of Meteorological Data in Glacier Areas: Historical temperature and precipitation datasets for the target glacier region are obtained. The datasets are preprocessed, and the preprocessed precipitation data are used to generate precipitation grid data using a spatial interpolation algorithm. At the same time, the preprocessed temperature data is interpolated using an elevation model and a temperature lapse rate to obtain temperature grid data. The precipitation grid data and temperature grid data are integrated to generate a unified meteorological grid dataset. Step 2, Calculation of snow and ice accumulation and melting in the glacier area: An improved snow and ice melting model based on the radiation-corrected degree-day factor is constructed. Based on the meteorological grid dataset generated in step 1, precipitation is divided into liquid precipitation and solid snowfall according to a certain temperature threshold. Solid snowfall is used as the snow and ice accumulation P, and the potential snow and ice melting M is calculated using the radiation-corrected degree-day factor. Step 3, Calculation of the ice and snow mass balance difference sequence: Based on the accumulated snow and ice P and the potential snow and ice melt M, calculate the snow and ice mass balance difference at each time step, and construct the snow and ice mass balance difference sequence D = PM; Where D>0 indicates a material surplus, D<0 indicates a material deficit, and D=0 indicates a material balance. Step 4, Accumulation of snow and ice mass balance across multiple time scales: The snow and ice mass balance difference sequence obtained in step 3 is accumulated and calculated at multiple preset time scales to generate the cumulative snow and ice mass balance sequence corresponding to each time scale. Step 5, Fitting and standardizing the probability distribution of the cumulative sequence: The cumulative snow and ice mass balance sequences at each time scale obtained in step 4 are fitted with a probability distribution using a three-parameter equal probability distribution function to calculate their cumulative probabilities. Subsequently, the cumulative probabilities are standardized using the inverse function of the standard normal distribution to obtain the standardized glacier melt index (SGMI) sequence. Step 6, Assessment of glacier melting status based on SGMI index: Based on the numerical range of the standardized glacier melting index (SGMI) sequence obtained in step 5, the glacier melting status is assessed in a graded manner. Positive values ​​indicate that the amount of glacial material accumulated during that period is higher than the historical average, while negative values ​​indicate that the amount of material melted is higher than the historical average. The absolute value indicates the severity of the deviation from the norm.

2. The standardized glacier melt index calculation method according to claim 1, characterized in that, Step 1, the specific steps for acquiring and preprocessing meteorological data in the glacier area include: S11, Acquisition of multi-source meteorological data: Acquire observation data from ground meteorological stations in the target glacier area, satellite remote sensing inversion data, and climate reanalysis data to form a raw meteorological dataset. The dataset shall contain at least daily or monthly surface temperature, precipitation, and shortwave radiation variables. S12, Data Preprocessing Flow: (a) Perform quality control and missing value imputation on the original meteorological dataset; (b) For precipitation data, inverse distance weighting or kriging interpolation is used to generate precipitation grid data; (c) For surface temperature data, the target glacier area is divided into multiple elevation zones according to altitude using a digital elevation model. The daily average temperature value of the corresponding elevation zone is obtained by extrapolation combined with the temperature lapse rate, and then interpolation is used to generate temperature grid data. (d)Integrate the above precipitation grid data and temperature grid data to generate a meteorological grid data set with unified spatio-temporal resolution.

3. The standardized glacier melt index calculation method according to claim 1, characterized in that, In step 2, the construction of the improved ice and snow melting model based on the radiation-corrected度日因子 (the specific term needs to be accurately translated according to the correct meteorological concept, here it is temporarily replaced with "度日因子") includes: S21, data preparation and spatial discretization: Obtain the digital elevation data, hydrometeorological station data, and glacier inventory data of the target glacier area. At the same time, call the meteorological grid data set generated in step 1, and divide the basin into multiple elevation bands according to the vertical elevation difference, and calculate the average altitude and glacier coverage rate of each elevation band; S22, construction of the dynamic albedo module: Based on the daily meteorological input, when it is judged that there is new snow, reset the albedo to the highest value; if there is no new snow, simulate the aging process of the snow albedo through exponential decay; when the snow cover in the glacier area is completely melted, switch the ice surface albedo to a fixed minimum ice surface albedo; S23, melt calculation for each unit: On each elevation band, calculate the snow melt volume and glacier melt volume respectively; For the calculation of the snow melt volume, use the radiation-enhanced度日因子 formula: In the formula, The amount of snow melted is in mm; The radiation factor of snow cover. ; This represents the daily average incident shortwave radiation received in the elevation zone, in W / m². Albedo; As a factor for snow cover during the day, T represents the daily average temperature, in °C. For the calculation of the glacier melt volume, first the model judges whether the seasonal snow cover in the glacier area has melted. If it has not melted, the melting process in the glacier area follows the snow melt volume calculation logic, that is: In the formula, The amount of glacier melt is expressed in mm. And when the snow has melted and bare ice is exposed, the model calls the glacier melt module, and the formula is as follows: In the formula, Glacier radiation factor, ; Glacier albedo; As the glacier diurnal factor, ; For exceeding a certain temperature threshold T c Positive accumulated temperature, °C; S24, parameter calibration and verification: Perform the whole-basin runoff generation and concentration演算 (the specific term needs to be accurately translated according to the correct hydrological concept, here it is temporarily replaced with "演算") for the runoff yields calculated for each elevation band to obtain the simulated runoff. Compare the simulation results with the measured runoff data, and calibrate the度日因子 DDF and radiation factor SRF in the model through an optimization algorithm to complete the construction of the model and local calibration of the parameters.

4. The standardized glacier melt index calculation method according to claim 3, characterized in that, The formula for the whole-basin runoff generation and concentration演算 in S24 is as follows: In the formula, The average daily runoff of the entire basin on day n is expressed in m³ / s. This is the snowmelt runoff coefficient; Snow cover in non-glacial areas; Let be the amount of snow melt in the i-th elevation zone; This is the ice melt runoff coefficient; This refers to the glacier coverage rate in the elevation zone; Let be the amount of glacier melt in the i-th elevation zone; This is the precipitation runoff coefficient; The effective precipitation for the i-th elevation zone is in mm; A is the catchment area in km². 2 ; The recession coefficient; The average daily runoff on day n-1, in m³ / s; Where: In the formula, A s snow cover area, km 2 A i Let Km be the total area of ​​the i-th elevation zone. 2 A ice The area of ​​the glacier is in km. 2 .

5. The standardized glacier melt index calculation method according to claim 1, characterized in that, In step 4, on multiple preset time scales k, use the moving window accumulation algorithm to calculate the cumulative ice and snow mass balance sequence, and the calculation formula is: In the formula, Let be the accumulated ice and snow value at time t and time scale k; D(tj) is the accumulated ice and snow value at time tj and time scale k.

6. The standardized glacier melt index calculation method according to claim 1, characterized in that, In step 5, the three-parameter equiprobable distribution function includes the Log-logistic distribution, the generalized extreme value distribution, or the Pearson type III distribution.

7. The standardized glacier melt index calculation method according to claim 1, characterized in that, In step 6, the glacier melting state is classified as: SGMI≥≥2.0 is extreme accumulation, 1.5≤SGMI<2.0 is severe accumulation, 1.0≤SGMI<1.5 is moderate accumulation, -1.0<SGMI<1.0 is close to normal, -1.5<SGMI≤-1.0 is moderate melting, -2.0<SGMI≤-1.5 is severe melting, SGMI≤-2.0 is extreme melting.

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