A method for estimating glacial meltwater runoff

Abstract

A method for estimating glacial meltwater runoff is disclosed, comprising the following steps: S1, obtaining glacier geographical distribution information and calculating driving data; S2, simulating glacier ablation; S3, calculating glacial meltwater runoff. A relatively accurate glacial meltwater runoff estimation model is established, solving the problem of significant uncertainty in existing meltwater runoff estimation methods, and is able to simulate the changing characteristics of each glacier.

Description

Technical Field

[0001] This invention relates to the field of glacial meltwater runoff calculation technology, specifically to a method for estimating glacial meltwater runoff. Background Technology

[0002] Methods for calculating glacial meltwater runoff include regression analysis and coupled simulation of glacial ablation. Regression analysis determines the functional relationship between meltwater runoff depth and its influencing factors, which are generally meteorological. Coupled simulation of glacial ablation requires coupling the equilibrium relationships of the glacier's solid and liquid states and the heat affecting ice melting to calculate glacial meltwater runoff. Both methods heavily rely on glacial flow monitoring data; however, due to the difficulty in monitoring glacial meltwater runoff in high-altitude mountainous areas, the accuracy of these estimates cannot be guaranteed.

[0003] Because the high-altitude mountainous areas where glaciers are located present challenges in monitoring glacial meltwater runoff, there is considerable uncertainty in establishing a relatively accurate method for estimating glacial meltwater runoff. Summary of the Invention

[0004] The technical problem solved by this invention is that, due to the complex terrain and difficulty in monitoring runoff in the high-altitude and cold mountainous areas where glaciers are located, it is very difficult to establish a relatively accurate method for estimating glacial meltwater runoff.

[0005] To solve the above problems, the technical solution of the present invention is as follows:

[0006] This invention provides a method for estimating glacial meltwater runoff, comprising:

[0007] S1. Obtain glacier geographical distribution information and calculate driving data.

[0008] The geographical distribution information of the glaciers includes glacier area and glacier vector boundary data.

[0009] The driving data is calculated as follows: after interpolating the meteorological data, separating precipitation and snowfall, and calculating the positive accumulated temperature, the driving data is obtained.

[0010] The meteorological data includes: air temperature at the glacier surface and precipitation at the glacier surface, wherein the precipitation includes snowfall and rainfall.

[0011] The driving data includes monthly precipitation on the glacier surface, monthly snowfall on the glacier surface, positive accumulated temperature on the glacier surface, and digital elevation model;

[0012] S2. Simulated glacier ablation: The positive accumulated temperature on the glacier surface is compared with the positive accumulated temperature of potential snowmelt to determine the monthly snowmelt and monthly icemelt of the glacier. Then, the mass balance of the glacier surface, i.e. the change in glacier volume, is calculated using the ablation principle formula of the day-day factor model. Finally, the change in glacier area is calculated by substituting the change in glacier volume into the area-volume conversion formula.

[0013] S3. Calculate glacial meltwater runoff: Calculate glacial meltwater runoff by combining the change in glacial area with the mass balance of the glacial surface.

[0014] As one aspect of the present invention, interpolation processing of meteorological data includes the following:

[0015] S1011. Using the longitude, latitude, and altitude of the meteorological station, as well as the meteorological data observed by the meteorological station, establish an interpolation formula between monthly meteorological data and the longitude, latitude, and altitude of the meteorological station.

[0016] S1012. Using a digital elevation model, each glacier is divided into equally spaced glacier elevation zones. The longitude, latitude, and altitude of each glacier elevation zone are obtained. The longitude, latitude, and altitude of the center of each glacier elevation zone are substituted into the interpolation formula obtained in step S1011 month by month to obtain the monthly meteorological data of each glacier elevation zone. The monthly meteorological data of each glacier elevation zone includes the monthly precipitation and the monthly average temperature of each glacier elevation zone.

[0017] As one aspect of the present invention, the precipitation-snow separation process includes the following:

[0018] S1021. After interpolating the meteorological data, the monthly precipitation for each glacier elevation zone is obtained. The monthly precipitation for each glacier elevation zone is then processed using a double critical temperature method to separate rain and snowfall. The calculation formula for this rain-snow separation process is as follows:

[0019]

[0020] In the above formula, S j,m P represents the snowfall at the j-th glacier elevation zone in the m-th month, in mm. j,m The monthly precipitation (in mm) for the j-th glacier elevation zone in the m-th month is given in T. j,m The average monthly temperature is expressed in °C (°C) or T. s The critical temperature for snowfall, in °C (T). r The critical temperature for precipitation is given in °C, j represents the number of altitudinal zones, and m represents the number of monthly temperatures within a single ablation cycle.

[0021] S1022, Error Correction:

[0022] Considering the potential errors in precipitation observations from meteorological stations, error correction is performed on rainfall and snowfall. The calculation formula for this error correction is as follows:

[0023] R j,Br =B r ×(P j,m —S j,m )

[0024] S j,m =B s × m,m

[0025] In the above formula, S j,m P represents the snowfall at the j-th glacier elevation zone in the m-th month, in mm. j,m R represents the monthly precipitation (in mm) of the j-th glacier elevation zone in the m-th month. j,m B represents the monthly rainfall in mm for the j-th glacier elevation zone in the m-th month. r B is the correction factor for rainfall. s is the correction factor for snowfall, j is the number of altitudinal zones, and m is the number of months within a melting cycle.

[0026] As one aspect of the present invention, the positive accumulated temperature calculation includes the following:

[0027] After interpolating the meteorological data, the monthly average temperature for each glacier elevation zone is obtained. The positive accumulated temperature of the glacier surface is then obtained by integrating the monthly average temperature of each glacier elevation zone. The formula for calculating the positive accumulated temperature of the glacier surface is as follows:

[0028]

[0029] In the above formula, PDD j,m Let T be the positive accumulated temperature of the glacier surface at the j-th glacier elevation zone in the m-th month, and let T be the average temperature during the calculation period in °C. j,m σ represents the temperature at various points in time within the m-th month, in °C. m Let be the standard deviation of the temperature distribution, j be the number of altitudinal zones, and m be the number of months within an ablation cycle.

[0030] As one aspect of the present invention, the positive accumulated temperature on the glacier surface is compared with the potential positive accumulated temperature of snowmelt to determine the monthly snowmelt and monthly ice melt of the glacier, including the following:

[0031] Potential positive snowmelt temperature is the positive temperature required for the complete melting of snow on the glacier surface. Snow on the glacier surface includes both new snow and old snow. This month's snowfall is defined as new snow, and last month's snow that has not completely melted is defined as old snow. The formula for calculating potential positive snowmelt temperature is:

[0032] PDDnsj,m =NS j,m / DDFns j,m

[0033] PDDos j,m =OS j,m / DDFos j,m

[0034] NS j,m This is the amount of new snow this month, in mm and OS. j,m Snowfall amount for this month, in mm, PDDns j,m PDDos is the positive accumulated temperature required for all new snow to melt. j,m The positive accumulated temperature required for the complete melting of Chen Xue, DDFns j,m The day-to-day factor for fresh snow is generally a fixed constant, with a value of 2.5 mm / d. -1 ℃ -1 ,DDFos j,m Let j represent Chen Xue's daily living factor, j be the number of segmented elevation zones, and m be the number of months within a single ablation cycle.

[0035] Chen Xue's daily life factor DDFos j,m The calculation formula is as follows:

[0036] DDFos j,m =64.533―0.837Lat+0.047Lon―2.85×10―3H―1.092T+2.822×10 ―3 P

[0037] In the above formula, Lat is the latitude of the glacier in °, Lon is the longitude of the glacier in °, H is the elevation of the glacier terminus in m, T is the average annual temperature in °C, and P is the annual precipitation in mm.

[0038] By comparing the positive accumulated temperature at the glacier surface with the positive accumulated temperature required for potential snowmelt, the monthly snowmelt and ice melt volume of the glacier are determined. The formulas for calculating the monthly snowmelt and ice melt volume of the glacier are as follows:

[0039]

[0040]

[0041]

[0042] MS j,m =MNS j,m +MOS j,m

[0043] In the above formula, MI j,mThis represents the monthly ice ablation, expressed in mm (PDD). j,m This is the total positive accumulated temperature for this month, PDDns j,m PDDos is the positive accumulated temperature required for all new snow to melt. j,m MNS is the positive accumulated temperature required for the complete melting of Chen Xue. j,m The monthly snow melt volume, in mm (s). j,m Total snowfall for this month, in mm, DDFns j,m The day-to-day factor for fresh snow is generally a fixed constant, MOS. j,m This represents Chen Xue's monthly ablation amount, in mm and MS. j,m denoted as , where is the monthly snow ablation, DDF is the diurnal factor for glacier ablation, j is the number of altitudinal zones, and m is the number of monthly ablation cycles.

[0044] When the snow on the glacier surface has not completely melted this month, all the snow accumulation on the glacier surface becomes the snow cover for the following month. The formula for calculating the snow cover for the following month is:

[0045]

[0046] In the above formula, OS j,m+1 Snowfall amount for next month, in mm, OS j,m Snowfall amount for this month, in mm, MOS j,m This represents Chen Xue's monthly ablation amount, in mm (neutral). j,m This is the amount of new snow this month, in mm (MNS). j,m The monthly snowmelt is expressed in mm, j represents the number of elevation zones, and m represents the monthly snowmelt within a snowmelt cycle.

[0047] As one aspect of the present invention, the mass balance of the glacier surface is calculated using the ablation principle formula of the day-degree factor model, including the following:

[0048] The mass balance of a glacier during an ablation cycle can be calculated using the ablation principle formula, which is:

[0049]

[0050] In the above formula, MB i,y Let be the mass balance of a single glacier, m be the monthly quantity within one ablation cycle, n be the number of glacier elevation zones of a single glacier, γ be the refreezing coefficient of snowmelt and ice melt, and ΔOS be the mass balance of a single glacier. j,y S represents the change in snow cover on the glacier surface. j,m This represents the total snowfall for the month, in mm. (R) j,m This represents the total rainfall for this month, in mm (MI). j,m, represents the monthly ice ablation amount in mm, j represents the number of elevation zones, and m represents the monthly number within a single ablation cycle;

[0051] By substituting the change in glacier volume into the area-volume conversion formula, the change in glacier area is calculated, including the following:

[0052] The initial area of ​​the glacier in the next ablation cycle is calculated using the area-volume conversion formula, which is:

[0053]

[0054] In the above formula, A y+1 MB represents the initial area of ​​the glacier for the next melting cycle. y V represents the mass balance of a single glacier. y Let α be the initial volume of the glacier during the current ablation cycle, α be the first fixed parameter calibrated, and β be the second fixed parameter calibrated.

[0055] After obtaining the initial glacier area for the next ablation cycle, the amount of glacier shrinkage during the current ablation cycle is calculated. The formula for calculating the amount of glacier shrinkage during the current ablation cycle is as follows:

[0056] ΔA y =A y+1 —A y

[0057] In the above formula, A y+1 A represents the initial area of ​​the glacier in the next melting cycle. y Let ΔA be the initial area of ​​the glacier during the current ablation cycle. y This represents the amount of glacier shrinkage over two melting cycles, i.e., the change in glacier area.

[0058] When ΔA y When the area is less than 0, the glacier terminus shrinks, and the amount of terminus shrinkage equals the total change in glacier area, including the following two cases:

[0059] When ΔA y <0 and ΔA y When the absolute value is less than the area of ​​the lowest glacier elevation zone, the area of ​​the lowest glacier elevation zone decreases accordingly.

[0060] When ΔA y <0 and ΔA y When the absolute value is greater than the area of ​​the lowest-altitude glacier elevation zone, the area of ​​the lowest-altitude glacier elevation zone completely disappears, and the area of ​​the second-highest-altitude glacier elevation zone decreases accordingly.

[0061] When ΔA yWhen the area is greater than 0, the glacier area increases, and its increase follows the opposite pattern to the shrinkage pattern. Only when the area of ​​the terminal elevation zone fills the initial distribution area does the glacier extend to lower elevation zones.

[0062] When ΔA y When the value is 0, the glacier area remains unchanged.

[0063] As one aspect of the present invention, the formula for calculating glacial meltwater runoff is as follows:

[0064]

[0065] In the above formula, Runoff is the glacial meltwater runoff, γ is the refreezing coefficient of snowmelt and ice melt, and MI j,m The monthly ablation of ice at the j-th glacier elevation zone in the m-th month is expressed in mm (ms). j,m R represents the monthly snow ablation at the j-th glacier elevation zone in the m-th month, expressed in mm. j,m Rainfall in the glacier area, in mm, A j,y The area of ​​the glacier in the j-th glacier elevation zone during the y-th ablation cycle is expressed in km². 2 A j,y The glacier surface accumulation in the previous ablation cycle plus the glacier area change ΔA in step S2. y The mass balance of the glacier surface is obtained as MI. j,m MS j,m The summation is as follows: j represents the number of elevation zones, y represents the ablation cycle, n represents the number of elevation zones of a single glacier, and m represents the number of months within a single ablation cycle.

[0066] As one aspect of the present invention, the ablation cycle of the estimation model is 1 year, the ablation cycle starts in October and ends in September of the following year, the calculation cycle of steps S1 and S2 is monthly, and step S3 obtains the glacier meltwater runoff for each ablation cycle by accumulating the glacier meltwater runoff each month.

[0067] The beneficial effects of this invention are:

[0068] This invention addresses the parameter uncertainties in the calculation of positive accumulated temperature, precipitation-snow separation, and daily temperature factor calibration in glacier meltwater runoff models. Building upon existing research, it improves the time scale of positive accumulated temperature calculation to an hourly scale and the precipitation-snow separation temperature to a spatially heterogeneous parameter. Furthermore, it establishes a calibration scheme for obtaining glacier daily temperature factors one by one from glacier catalog data. The advantage of this improved parameterization scheme is that it can obtain independent parameter combinations for each glacier using only ground meteorological station data and glacier catalog data, and the daily temperature factor model based on the new parameterization scheme is capable of simulating the variation characteristics of each glacier. Attached Figure Description

[0069] Figure 1 This is a structural diagram of a method for estimating glacial meltwater runoff according to the present invention;

[0070] Figure 2 This is a flowchart illustrating the calculation method for estimating glacial meltwater runoff according to the present invention.

[0071] The process includes: 1- Obtaining information on the geographical distribution of glaciers and preparing driving data; 2- Simulating glacier ablation; and 3- Calculating glacier meltwater runoff. Detailed Implementation

[0072] First, some technical terms involved in this invention will be explained:

[0073] Positive accumulated temperature is the sum of the daily average temperatures above 0°C during a certain period or growing season.

[0074] A Digital Elevation Model (DEM) is a digital simulation of ground topography (i.e., a digital representation of the surface morphology of terrain) achieved through limited terrain elevation data. It is a physical ground model that represents ground elevation using an ordered array of numerical values. It is a branch of Digital Terrain Models (DTMs), from which various other terrain features can be derived. Generally, a DTM is considered to describe the spatial distribution of linear and nonlinear combinations of various geomorphic factors, including elevation, slope, aspect, and rate of change of slope. A DEM is a zero-order, simple, single-factor digital geomorphic model; other geomorphic characteristics such as slope, aspect, and rate of change of slope can be derived from the DEM.

[0075] Day-of-day factor model: The day-of-day factor model is a statistical model based on the relationship between glacier ablation and temperature. Day-of-day factor (mm / d) -1 ℃ -1The day-degree factor is a simplified description of the energy transfer and transformation process on the surface of ice and snow, and its spatial variation characteristics have a significant impact on the accuracy of glacier ablation simulations. The day-degree factor generally uses the average temperature or positive accumulated temperature over a period of time as the temperature index to characterize energy input. When the input data is average temperature, considering that the average temperature over a period of time is equal to or less than zero, there may be moments with temperatures above 0°C within this period; therefore, the critical temperature for ice and snow ablation needs to be set to sub-zero temperatures. The magnitude of the day-degree factor characterizes the sensitivity of glaciers to climate change; the larger the day-degree factor, the higher the sensitivity of the glacier to climate change. At the glacier scale, the day-degree factor can be obtained through glacier ablation and temperature observations; at the regional / global scale, the day-degree factor exhibits significant spatiotemporal variability. In studies applying the day-degree model to regional / global glacier simulations, the day-degree factors of glacier ice and snow are calibrated based on typical glacier mass balance observation data, and then extended to each glacier.

[0076] The dual-critical temperature method: By statistically setting critical temperatures for precipitation and snowfall, when the temperature is higher than the critical temperature for precipitation, precipitation is considered to be 100% precipitation; when the temperature is lower than the critical temperature for snowfall, precipitation is considered to be 100% snowfall; when the temperature is between the two critical temperatures, the ratio of precipitation to snowfall is calculated separately using the linear relationship between temperature and precipitation-snowfall ratio.

[0077] Example

[0078] This embodiment presents a method for estimating glacial meltwater runoff, belonging to the glacial ablation diurnal factor model. Due to the high correlation between air temperature and energy balance factors, and the ease of obtaining air temperature, air temperature becomes the sole parameter characterizing energy input in glacial ablation models (Braithwaite and Olesen 1989; Hock, 2003). Braithwaite and Olesen (1989) found that glacial ablation is more closely correlated with positive accumulated temperature; therefore, the ablation principle of the diurnal factor is often expressed as:

[0079] M = DDF·PDD

[0080] In the above formula, M represents the total glacier ablation over a period of time; PDD represents the positive accumulated temperature over a period of time; and DDF represents the degree-day factor of glacier ablation, in mm℃. -1 d -1 Since the principle of snow and ice melting is the same, the above formula is used to calculate snow ablation. When calculating the amount of snow ablation, DDF is the day-of-snow factor.

[0081] The ablation cycle of the estimation model in this embodiment is 1 year, starting in October and ending in September of the following year. The estimation method in this embodiment involves acquiring glacier geographic distribution information, preparing driving data, and simulating glacier ablation on a monthly timescale. The steps include:

[0082] S1. Obtain glacier geographical distribution information and calculate driving data.

[0083] The driving data is calculated as follows: after interpolating the meteorological data, separating precipitation and snowfall, and calculating the positive accumulated temperature, the driving data is obtained. The driving data includes monthly precipitation on the glacier surface, monthly snowfall on the glacier surface, and positive accumulated temperature on the glacier surface.

[0084] In the above steps, meteorological data includes: glacier surface temperature, glacier surface precipitation (including snowfall and rainfall), glacier geographic distribution information (including glacier area and glacier vector boundary data), and driving data (including digital elevation model).

[0085] In the above-mentioned acquisition of glacier geographic distribution information and preparation of driving data, meteorological data includes: glacier surface temperature and glacier surface precipitation, including snowfall and rainfall; glacier geographic distribution information includes glacier area and glacier vector boundary data; and driving data also includes digital elevation models.

[0086] The above steps involve interpolating meteorological data, including the following:

[0087] S1011. Using the longitude, latitude, and altitude of the meteorological station, as well as the meteorological data observed by the meteorological station, establish an interpolation formula between monthly meteorological data and the longitude, latitude, and altitude of the meteorological station.

[0088] The above interpolation formulas include temperature interpolation formulas and precipitation interpolation formulas.

[0089] The temperature interpolation formula is:

[0090]

[0091] In the above formula, T 1m The temperature observed at the first weather station in the m-th month, in °C (°C) and T (°C). 2m The temperature observed at the second weather station in the m-th month, in °C (°C) and T (°C). km f is the temperature observed at the k-th meteorological station in the m-th month, in °C. m (la1) is the fitting function of longitude and temperature in the m-th month observed by the first meteorological station, f m (la2) is the fitting function of longitude and temperature in the m-th month observed at the second meteorological station, f m (la kLet g be the fitting function of longitude and temperature in the m-th month observed at the k-th meteorological station. m (lo1) is the fitting function of latitude and temperature in the m-th month observed by the first meteorological station, g m (lo2) is the fitting function of latitude and temperature in the m-th month observed at the second meteorological station, g m (lo k Let h be the fitting function of latitude and temperature observed at the k-th meteorological station in the m-th month. m (alt1) is the fitting function for the altitude and temperature in the m-th month observed at the first weather station, h m (alt2) is the fitting function for the altitude and temperature in the m-th month observed at the second weather station, h m (alt k Let be the fitting function of altitude and temperature observed at the k-th meteorological station in the m-th month, and c be the altitude. m1 This is the first constant term.

[0092] The precipitation interpolation formula is:

[0093]

[0094] In the above formula, W 1m The precipitation observed at the first weather station in the m-th month is expressed in mm (W). 2m The precipitation observed at the second weather station in the m-th month is expressed in mm (W). km The precipitation in the m-th month observed at the k-th meteorological station is expressed in mm. m (la1) is the fitting function of longitude and precipitation in the m-th month observed by the first meteorological station, j m (la2) is the fitting function of longitude and precipitation in the m-th month observed by the second meteorological station, j m (la k Let be the fitting function of longitude and precipitation in the m-th month observed at the k-th meteorological station, where k is the longitude. m (lo1) is the fitting function of latitude and precipitation in the m-th month observed by the first meteorological station, k m (lo2) is the fitting function of latitude and precipitation in the m-th month observed by the second meteorological station, k m (lo k Let be the fitting function of latitude and precipitation in the m-th month observed at the k-th meteorological station, l m (alt1) is the fitting function for the relationship between altitude and precipitation observed at the first meteorological station in the m-th month. m (alt2) is the fitting function for the relationship between altitude and precipitation observed at the second meteorological station in the m-th month.m (alt k Let be the fitting function of altitude and precipitation observed at the k-th meteorological station in the m-th month, and c be the altitude. m2 This is the second constant term.

[0095] S1012. Using a digital elevation model, each glacier is divided into equally spaced glacier elevation zones. The longitude, latitude, and altitude of each glacier elevation zone are obtained. The longitude, latitude, and altitude of the center of each glacier elevation zone are substituted into the interpolation formula obtained in step S1011 month by month to obtain the monthly meteorological data of each glacier elevation zone. The monthly meteorological data of each glacier elevation zone includes the monthly precipitation and the monthly average temperature of each glacier elevation zone.

[0096] In this embodiment, when positive accumulated temperature acts on the glacier surface, it is generally assumed that melting will only begin after the snow has completely melted. Therefore, before conducting the melting simulation, it is necessary to obtain the air temperature and precipitation at the glacier surface. Since the altitude range of a single glacier is wide, and both air temperature and precipitation have altitude gradients, this embodiment uses a digital elevation model (30m×30m) to divide each glacier into glacier elevation zones with intervals of 30m.

[0097] In the above steps, the precipitation-snow separation process includes the following:

[0098] S1021. After interpolating the meteorological data, the monthly precipitation for each glacier elevation zone is obtained, and then analyzed using the double critical temperature method. (1992) Monthly precipitation for each glacier elevation zone was processed using a rain-snow separation method. The calculation formula for this rain-snow separation method is as follows:

[0099]

[0100] In the above formula, S j,m P represents the snowfall at the j-th glacier elevation zone in the m-th month, in mm. j,m The monthly precipitation (in mm) for the j-th glacier elevation zone in the m-th month is given in T. j,m The average monthly temperature is expressed in °C (°C) or T. s The critical temperature for snowfall, in °C (T). r The critical temperature for precipitation is given in °C, j represents the number of altitudinal zones, and m represents the number of monthly temperatures within a single ablation cycle.

[0101] S1022, Error Correction:

[0102] Considering the inherent errors in precipitation observations from meteorological stations, error correction is performed on rainfall and snowfall. The calculation formula for error correction is as follows:

[0103] R j,m =Br ×(P j,m —S j,m )

[0104] S j,m =B s ×S j,m

[0105] In the above formula, S j,m P represents the snowfall at the j-th glacier elevation zone in the m-th month, in mm. j,m R represents the monthly precipitation (in mm) of the j-th glacier elevation zone in the m-th month. j,m B represents the monthly rainfall in mm for the j-th glacier elevation zone in the m-th month. r B is the correction factor for rainfall. s is the correction factor for snowfall, j is the number of altitudinal zones, and m is the number of months within a melting cycle.

[0106] The positive accumulated temperature calculation in the above steps includes the following:

[0107] After interpolating the meteorological data, the monthly average temperature of each glacier elevation zone is obtained. The positive accumulated temperature (PDD) of the glacier surface is obtained by integrating the monthly average temperature of each glacier elevation zone. In traditional models, the monthly positive accumulated temperature (PDD) can be obtained by accumulating the monthly positive daily average temperature (Braithwaite et al., 1993), but the calculation result has low accuracy. Reeh (1991) believes that the annual temperature follows a normal distribution. Therefore, the formula for calculating the positive accumulated temperature of the glacier surface in this embodiment is:

[0108]

[0109] In the above formula, PDD j,m Let T be the positive accumulated temperature of the glacier surface at the j-th glacier elevation zone in the m-th month, and let T be the average temperature during the calculation period in °C. j,m σ represents the temperature at various points in time within the m-th month, in °C. m Let be the standard deviation of the temperature distribution, j be the number of altitudinal zones, and m be the number of months within an ablation cycle.

[0110] S2. Simulated Glacier Melting: The positive accumulated temperature on the glacier surface is compared with the positive accumulated temperature of potential snowmelt to determine the monthly snowmelt and icemelt volume of the glacier. Then, the mass balance of the glacier surface, i.e. the change in glacier volume, is calculated using the melting principle formula of the degree-day factor model. Finally, the change in glacier area is calculated by substituting the change in glacier volume into the area-volume conversion formula.

[0111] In the above steps, the positive accumulated temperature at the glacier surface is compared with the positive accumulated temperature of potential snowmelt to determine the monthly snowmelt and monthly ice melt of the glacier, including the following:

[0112] PDDns j,m =NS j,m / DDFns j,m

[0113] PDDos j,m =OS j,m / DDFos j,m

[0114] NS j,m This is the amount of new snow this month, in mm and OS. j,m Snowfall amount for this month, in mm, PDDns j,m PDDos is the positive accumulated temperature required for all new snow to melt. j,m The positive accumulated temperature required for the complete melting of Chen Xue, DDFns j,m The day-to-day factor for fresh snow is generally a fixed constant, with a value of 2.5 mm / d. -1 ℃ -1 ,DDFos j,m Let j represent Chen Xue's daily living factor, j be the number of segmented elevation zones, and m be the number of months within a single ablation cycle.

[0115] Chen Xue's daily life factor DDFos j,m The calculation formula is as follows:

[0116] DDFos j,m =64.533-0.837Lat+0.047Lon-2.85×10 ―3 H―1.092T+2.822×10 ―3 P

[0117] In the above formula, Lat is the latitude of the glacier in °, Lon is the longitude of the glacier in °, H is the elevation of the glacier terminus in m, T is the average annual temperature in °C, and P is the annual precipitation in mm.

[0118] The positive accumulated temperature at the glacier surface is compared with the positive accumulated temperature required for potential snowmelt. If the positive accumulated temperature at the glacier surface is less than or equal to the positive accumulated temperature for potential snowmelt, then only snowmelt occurs in that month. If the positive accumulated temperature at the glacier surface is greater than the positive accumulated temperature for potential snowmelt, then both snowmelt and ice melt occur in that month. This allows us to determine the monthly snowmelt and ice melt volume of the glacier.

[0119] In actual melting processes, the sublimation / evaporation of ice and snow occurs simultaneously with the melting process. However, due to the lack of large-scale research data and the fact that the amount of sublimation / evaporation is partially offset by the amount of deposition / condensation, the estimation model ignores the impact of ice and snow evaporation / sublimation on melting.

[0120] The formulas for calculating the monthly snowmelt and ice melt of glaciers are as follows:

[0121]

[0122]

[0123]

[0124] MS j,m =MNS j,m +MOS j,m

[0125] In the above formula, MI j,m This represents the monthly ice ablation, expressed in mm (PDD). j,m This is the total positive accumulated temperature for this month, PDDns j,m PDDos is the positive accumulated temperature required for all new snow to melt. j,m MNS is the positive accumulated temperature required for the complete melting of Chen Xue. j,m The monthly snow melt volume, in mm (s). j,m Total snowfall for this month, in mm, DDFns j,m The day-to-day factor for fresh snow is generally a fixed constant. The day-to-day factor for fresh snow typically varies less than that for old snow. Previous research indicates that the day-to-day factor for fresh snow ranges from 1.8 to 2.7 mm / day. -1 ℃ -1 The value is typically assigned as 2.5mm d. -1 ℃ -1 MOS j,m This represents Chen Xue's monthly ablation amount, in mm and MS. j,m denoted as , where is the monthly snow ablation, DDF is the diurnal factor for glacier ablation, j is the number of altitudinal zones, and m is the number of monthly ablation cycles.

[0126] When the snow on the glacier surface has not completely melted this month, all the snow accumulation on the glacier surface becomes the snow cover for the following month. The formula for calculating the snow cover for the following month is:

[0127]

[0128] In the above formula, OS j,m+1 Snowfall amount for next month, in mm, OS j,m Snowfall amount for this month, in mm, MOS j,mThis represents Chen Xue's monthly ablation amount, in mm (neutral). j,m This is the amount of new snow this month, in mm (MNS). j,m The monthly snowmelt is expressed in mm, j represents the number of elevation zones, and m represents the monthly snowmelt within a snowmelt cycle.

[0129] The above steps involve calculating the mass balance of the glacier surface using the ablation principle formula of the day-degree factor model, including the following:

[0130] Glaciers undergo complex motion from high to low altitudes, their speed influenced by glacier topography, glacier properties, and the surrounding climate (Cuffey and Paterson, 2010). While glacier movement can be simulated using numerical models based on glacier dynamics, simulating the motion of each individual glacier across a region is challenging, and verifying the accuracy of these simulations is difficult. Glacier retreat is generally considered to occur primarily at the glacier terminus tongue. Therefore, in models, glacier area changes are specified to occur only at the lowest elevation of each glacier (the area at which the glacier's surface area changes). (and Schneider, 2010), and the area change only occurs after one ablation cycle.

[0131] Based on the amount of snow and ice melt, the mass balance of the glacier during one melting cycle is calculated using the ablation principle formula, which is:

[0132]

[0133] In the above formula, MB i,y Let be the mass balance of a single glacier, m be the monthly quantity within one ablation cycle, n be the number of glacier elevation zones of a single glacier, γ be the refreezing coefficient of snowmelt and ice melt, and ΔOS be the mass balance of a single glacier. j,y S represents the change in snow cover on the glacier surface. j,m This represents the total snowfall for the month, in mm. (R) j,m This represents the total rainfall for this month, in mm (MI). j,m denoted as the monthly ice melt volume in mm, j represents the number of elevation zones divided, and m represents the monthly number of ice melts within a melt cycle.

[0134] In the previous step, the change in glacier volume was substituted into the area-volume conversion formula to calculate the change in glacier area, including the following:

[0135] Bahr et al. (1997) discovered a fixed correlation between the area and volume of mountain glaciers through statistical analysis, and based on this, established a glacier area-volume conversion method:

[0136] V=αA β

[0137] In the above formula, V represents the glacier volume; A represents the glacier area; and α and β are fixed parameters that have been calibrated. Based on the glacier area-volume conversion method, the following can be derived:

[0138] The initial area of ​​the glacier in the next ablation cycle is calculated using the area-volume conversion formula, which is:

[0139]

[0140] In the above formula, A y+1 MB represents the initial area of ​​the glacier for the next melting cycle. y V represents the mass balance of a single glacier. y Let α be the initial volume of the glacier during the current ablation cycle, α be the first fixed parameter calibrated, and β be the second fixed parameter calibrated.

[0141] After obtaining the initial glacier area for the next ablation cycle, the amount of glacier shrinkage during the current ablation cycle is calculated. The formula for calculating the amount of glacier shrinkage during the current ablation cycle is as follows:

[0142] ΔA y =A y+1 —A y

[0143] In the above formula, A y+1 A represents the initial area of ​​the glacier in the next melting cycle. y Let ΔA be the initial area of ​​the glacier during the current ablation cycle. y This represents the amount of glacier shrinkage over two melting cycles, i.e., the change in glacier area.

[0144] When ΔA y When the area is less than 0, the glacier terminus shrinks, and the amount of terminus shrinkage equals the total change in glacier area, including the following two cases:

[0145] When ΔA y <0 and ΔA y When the absolute value is less than the area of ​​the lowest glacier elevation zone, the area of ​​the lowest glacier elevation zone decreases accordingly.

[0146] When ΔA y <0 and ΔA y When the absolute value is greater than the area of ​​the lowest-altitude glacier elevation zone, the area of ​​the lowest-altitude glacier elevation zone completely disappears, and the area of ​​the second-highest-altitude glacier elevation zone decreases accordingly.

[0147] When ΔA y When the area is greater than 0, the glacier area increases, and its increase follows the opposite pattern to the shrinkage pattern. Only when the area of ​​the terminal elevation zone fills the initial distribution area does the glacier extend to lower elevation zones.

[0148] When ΔA y When the value is 0, the glacier area remains unchanged.

[0149] S3. Calculate glacial meltwater runoff: Calculate glacial meltwater runoff by combining the change in glacial area with the mass balance of the glacial surface.

[0150] The formula for calculating glacial meltwater runoff in the above steps is:

[0151]

[0152] In the above formula, Runoff is the glacial meltwater runoff, γ is the refreezing coefficient of snowmelt and ice melt, and MI j,m The monthly ablation of ice at the j-th glacier elevation zone in the m-th month is expressed in mm (ms). j,m R represents the monthly snow ablation at the j-th glacier elevation zone in the m-th month, expressed in mm. j,m Rainfall in the glacier area, in mm, A j,y The area of ​​the glacier in the j-th glacier elevation zone during the y-th ablation cycle is expressed in km². 2 A j,y The glacier surface accumulation in the previous ablation cycle plus the glacier area change ΔA in step S2. y The mass balance of the glacier surface is obtained as MI. j,m MS j,m The summation is as follows: j represents the number of elevation zones, y represents the ablation cycle, n represents the number of elevation zones of a single glacier, and m represents the number of months within a single ablation cycle.

[0153] Due to different research objectives, there are different definitions of glacial runoff. However, the more commonly used definitions include three categories:

[0154] (1) Melt runoff, also known as net glacier runoff: refers to the runoff generated by melting ice during the process of glacier ablation. Its runoff depth is the amount of ice melted, and the runoff area is the real-time glacier area.

[0155] (2) Glacier runoff: This is the sum of meltwater runoff, snowmelt runoff, and precipitation runoff. Its runoff depth is the mass balance of the glacier surface, and the runoff area is also the real-time glacier area;

[0156] (3) Glacier runoff, including runoff from the ice surface and runoff from exposed areas after glacier melt, is often used to measure the impact of glacier melt on regional runoff. The runoff area of ​​glacier runoff is the initial area of ​​the glacier, where the runoff depth of glacier runoff is the same as that of glacier runoff, and the runoff depth of exposed areas is the amount of snowmelt and rainfall.

[0157] The estimation model in this embodiment calculates glacier runoff according to the second definition. The formula for calculating glacier runoff is as follows:

[0158]

[0159] In the above formula, Runoff is the glacial meltwater runoff, γ is the refreezing coefficient of snowmelt and ice melt, and MI j,m The monthly ablation of ice at the j-th glacier elevation zone in the m-th month is expressed in mm (ms). j,m R represents the monthly snow ablation at the j-th glacier elevation zone in the m-th month, expressed in mm. j,m Rainfall in the glacier area, in mm, A j,y The area of ​​the glacier in the j-th glacier elevation zone during the y-th ablation cycle is expressed in km². 2 A j,y The glacier surface accumulation in the previous ablation cycle plus the glacier area change ΔA in step S2. y The mass balance of the glacier surface is obtained as MI. j,m MS j,m The summation is as follows: j represents the number of elevation zones, y represents the ablation cycle, n represents the number of elevation zones of a single glacier, and m represents the number of months within a single ablation cycle.

[0160] This embodiment estimates the model calibration and validation.

[0161] As the most important parameter in the glacier day-temperature factor model, the glacier day-temperature factor is often difficult to obtain directly due to the difficulty of observation. Furthermore, its strong spatial heterogeneity and sensitivity to the environment result in irregularities in the altitudinal gradient across regions and even individual glaciers (Zhang et al., 2016). Therefore, it is also difficult to obtain the day-temperature factor for all simulation units through interpolation. Thus, distributed glacier day-temperature factor models generally obtain the day-temperature factor for regions, grids, or individual glaciers through calibration. In addition, some large-scale day-temperature factor models also adjust for temperature and precipitation through calibration. The typical steps for model calibration include:

[0162] (1) Set initial parameter values ​​by comparing limited observation data within or near the region. Directly set the parameter range based on existing research.

[0163] (2) Use iterative calculations to obtain simulation results corresponding to different input parameters.

[0164] (3) Compare the corresponding observed values ​​and simulated values ​​to select the optimal parameters.

[0165] After determining all model parameters, the glaciers in the target area are simulated, and the accuracy of the simulation results is obtained through model validation. Similarly limited by the amount of observational data, early model validation could only be performed on a few glaciers with available observational data. Validation data typically included glacier area, mass balance, or calculated mass balance line height for a specific period. Huss and Hock (2015) argued that using a single glacier to validate regional model results could potentially lead to serious simulation errors.

[0166] With the development of glacier research and the expansion of glacier observation data, glacier models are now more inclined to be validated line by line. Validation data includes not only glacier area but also mass balance. Meanwhile, regional glacier meltwater runoff obtained through methods such as isotope separation can also be used as a reference to verify the accuracy of glacier models. In this method, the accuracy of model calibration and validation is measured using the improved Nash coefficient NSE (Nash-Sutcliffe coefficient) (Nash and Sutcliffe, 1970; Chen et al., 2003) and the coefficient of determination R0. 2 Evaluation of (coefficient of determination):

[0167]

[0168]

[0169] In the above formula, A i,obs These are the observed values; A is the average of the observed values; i,sim These are simulated values. Whether it's NSE or R... 2 The closer the value is to 1, the higher the accuracy of the simulation value.

Claims

1. A method for estimating glacial meltwater runoff, characterized in that, include: S1. Obtain glacier geographical distribution information and calculate driving data. The geographical distribution information of the glaciers includes glacier area and glacier vector boundary data. The driving data is calculated as follows: after interpolating the meteorological data, separating precipitation and snowfall, and calculating the positive accumulated temperature, the driving data is obtained. The meteorological data includes: air temperature at the glacier surface and precipitation at the glacier surface, wherein the precipitation includes snowfall and rainfall. The driving data includes monthly precipitation on the glacier surface, monthly snowfall on the glacier surface, positive accumulated temperature on the glacier surface, and digital elevation model; S2. Simulated glacier ablation: The positive accumulated temperature on the glacier surface is compared with the positive accumulated temperature of potential snowmelt to determine the monthly snowmelt and monthly icemelt of the glacier. Then, the mass balance of the glacier surface, i.e. the change in glacier volume, is calculated using the ablation principle formula of the day-day factor model. Finally, the change in glacier area is calculated by substituting the change in glacier volume into the area-volume conversion formula. S3. Calculate glacial meltwater runoff: Calculate glacial meltwater runoff by combining the change in glacial area with the mass balance of the glacial surface; the formula for calculating glacial meltwater runoff is: In the above formula, This refers to the runoff of glacial meltwater. The refreezing coefficient for snow and ice melt. For the first The first glacier elevation zone The monthly ice melt during the month, in mm. For the first The first glacier elevation zone The monthly snow melt volume during the month, measured in mm. Rainfall in the glacier area, in mm. For the first The first glacier elevation zone Glacier area per melting cycle, in km² 2 , The glacier surface accumulation in the previous ablation cycle plus the glacier area change in step S2. The mass balance at the glacier surface is obtained as follows: , The sum of all additions For the ablation cycle, n This refers to the number of glacier elevation zones for a single glacier. m The monthly quantity within a single ablation cycle.

2. The method as described in claim 1, characterized in that, The interpolation processing of meteorological data includes the following: S1011. Using the longitude, latitude, and altitude of the meteorological station, as well as the meteorological data observed by the meteorological station, establish an interpolation formula between monthly meteorological data and the longitude, latitude, and altitude of the meteorological station. S1012. Using a digital elevation model, each glacier is divided into equally spaced glacier elevation zones. The longitude, latitude, and altitude of each glacier elevation zone are obtained. The longitude, latitude, and altitude of the center of each glacier elevation zone are substituted into the interpolation formula obtained in step S1011 month by month to obtain the monthly meteorological data of each glacier elevation zone. The monthly meteorological data of each glacier elevation zone includes the monthly precipitation and the monthly average temperature of each glacier elevation zone.

3. The method as described in claim 2, characterized in that, The precipitation-snow separation process includes the following: S1021. After interpolating the meteorological data, the monthly precipitation for each glacier elevation zone is obtained. The monthly precipitation for each glacier elevation zone is then processed using a double critical temperature method to separate rain and snowfall. The calculation formula for this rain-snow separation process is as follows: In the above formula, For the first j The glacier elevation zone is at the [number]th [location]. m Monthly snowfall, in mm. For the first j The glacier elevation zone is at the [number]th [location]. m Monthly precipitation, in mm. The average monthly temperature is expressed in degrees Celsius (°C). This is the critical temperature for snowfall, expressed in °C. The critical temperature for rainfall is expressed in °C.

4. The method as described in claim 2, characterized in that, The positive accumulated temperature calculation includes the following: After interpolating the meteorological data, the monthly average temperature for each glacier elevation zone is obtained. The positive accumulated temperature of the glacier surface is then obtained by integrating the monthly average temperature of each glacier elevation zone. The formula for calculating the positive accumulated temperature of the glacier surface is as follows: In the above formula, For the first j The glacier elevation zone is at the [number]th [location]. m The glacier surface has been accumulating heat for months. T The average temperature over the calculation period is expressed in °C. For the first m Temperatures at various points in time within a month, in degrees Celsius. denoted as the standard deviation of the temperature distribution.

5. The method as described in claim 4, characterized in that, By comparing the positive surface temperature of the glacier with the potential positive snowmelt temperature, the monthly snowmelt and monthly ice melt of the glacier are determined, including the following: Potential positive snowmelt temperature is the positive temperature required for the complete melting of snow on the glacier surface. Snow on the glacier surface includes both new snow and old snow. This month's snowfall is defined as new snow, and last month's snow that has not completely melted is defined as old snow. The formula for calculating potential positive snowmelt temperature is: This is the amount of new snow this month, in mm. This is the snowfall amount for this month, in mm. The positive accumulated temperature required for all new snow to melt. The positive accumulated temperature required for the complete melting of Chen Xue As a factor for passing the days with fresh snow, For Chen Xue's daily living expenses, By comparing the positive accumulated temperature at the glacier surface with the positive accumulated temperature required for potential snowmelt, the monthly snowmelt and ice melt volume of the glacier are determined. The formulas for calculating the monthly snowmelt and ice melt volume of the glacier are as follows: = + In the above formula, This represents the monthly ice ablation, expressed in mm. This is the total positive accumulated temperature for this month. The positive accumulated temperature required for all new snow to melt. The positive accumulated temperature required for the complete melting of Chen Xue This represents the monthly snowmelt, expressed in mm. This represents the total snowfall for the month, in mm. As a factor for passing the days with fresh snow, This represents Chen Xue's monthly ablation amount, in mm. The amount of snow melted each month. As a factor contributing to glacial melting, When the snow on the glacier surface has not completely melted this month, all the snow accumulation on the glacier surface becomes the snow cover for the following month. The formula for calculating the snow cover for the following month is: In the above formula, The snowfall amount for next month, in mm. This is the snowfall amount for this month, in mm. This represents Chen Xue's monthly ablation amount, in mm. This is the amount of new snow this month, in mm. This represents the monthly snow melt, expressed in mm.

6. The method as described in claim 5, characterized in that, The mass balance of the glacier surface is calculated using the ablation principle formula of the day-death factor model, including the following: The mass balance of a glacier during an ablation cycle can be calculated using the ablation principle formula, which is: In the above formula, This represents the mass balance of a single glacier. The refreezing coefficient for snow and ice melt. This represents the change in snow cover on the glacier surface. This represents the total snowfall for the month, in mm. This represents the total rainfall for this month, in mm. This represents the monthly ice melt, expressed in mm.

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