A calculation method for glacier meltwater discharge in arid regions considering dynamic glacier melting

Abstract

The present invention discloses a method for calculating the glacier meltwater discharge of rivers in arid regions considering dynamic glacier melting, which relates to the field of hydrology. The method includes the following steps: obtaining the glacier areas of all glaciers in the basin; calculating the glacier volumes according to the glacier volume-area ratio relationship; allocating the glacier areas and glacier volumes to each sub-basin of the basin to calculate the total glacier coverage area and glacier volume of each sub-basin; obtaining the solar radiation amount in the basin based on the basin's longitude, latitude and sunshine hours; obtaining the meteorological data within and around the basin, and interpolating the meteorological data to the sub-basins according to the Thiessen polygon method to obtain the meteorological conditions on each sub-basin; calculating the glacier surface temperature on the day of ice melting; calculating the glacier melting amount on each sub-basin based on the ice surface temperature and solar radiation amount, so as to realize the calculation of the glacier meltwater discharge in arid regions.

Description

Technical Field

[0001] The present invention relates to the field of hydrology, and more specifically, to a method for calculating the glacier meltwater flow in arid areas considering the dynamic melting of glaciers. Background Art

[0002] Glaciers are an important part of water resources and one of the most critical hydrological elements in arid areas. Alpine glaciers are known as "solid reservoirs", storing solid precipitation and releasing glacier meltwater, which plays an important role in replenishing and regulating rivers, making the annual runoff variation of rivers relatively stable. During droughts, due to reduced precipitation and increased glacier melting, the proportion of glacier meltwater in glacier runoff can be as high as 40%. Alpine glaciers play an extremely important role in protecting the downstream population from the impact of drought. The summer meltwater of alpine glaciers in Central Asia is sufficient to meet the basic needs of 136 million people (Pritchard, 2017). Therefore, accurately calculating the melting of mountain glaciers is of great significance for local water resources and the water cycle, and has become a hot issue in the current research on the water cycle.

[0003] Hydrological models are important tools for analyzing the changes in hydrological processes and planning the sustainable utilization of water resources, with characteristics such as high accuracy and strong reliability. However, traditional hydrological models only consider rainfall runoff and snowmelt runoff, and generally do not include the processes of glacier ablation and accumulation. This will inevitably lead to deviations in mountain hydrological simulations, with obvious complementary effects among different hydrological components and significant effects of different parameters with the same effect.

[0004] There are many algorithms for calculating glacier meltwater, which can be divided into two categories. One is the method based on energy balance, and the other is the degree-day factor method based on empirical statistical relationships. The method based on energy balance is a physical method that considers glacier flow and energy balance and is achieved by solving partial differential equations. However, this type of method requires a large amount of observational data, including the thickness, ice surface temperature, ice surface wind speed, etc. of each glacier, and has a high calculation cost and is not applicable in hydrological simulations at the basin scale. The model based on empirical statistical relationships is based on the relationship between glacier mass balance and temperature, and calculates glacier ablation based on the temperature index, generally mainly using the degree-day factor method, that is, only using the daily air temperature and glacier area to calculate the daily glacier melting amount. This type of method is easy to implement and has been widely used in practice. However, for alpine glaciers in arid areas, solar radiation directly affects the glacier ablation rate. If solar radiation is not considered, the glacier melting amount at noon under cloudless weather conditions will be underestimated, resulting in deviations in the estimated glacier meltwater. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the glacier meltwater flow in arid areas considering the dynamic melting of glaciers to solve the problems in the background art.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for calculating the glacier meltwater discharge in arid regions considering glacier dynamics, comprising the following steps:

[0008] Obtain the glacier areas of all glaciers in the basin;

[0009] Calculate the glacier volume according to the glacier volume-area ratio relationship;

[0010] Allocate the glacier area and glacier volume to each sub-basin of the basin, and calculate the total glacier coverage area and glacier volume of each sub-basin;

[0011] Obtain the solar radiation in the basin based on latitude and sunshine duration;

[0012] Obtain the meteorological data within and around the basin, and interpolate the meteorological data into the sub-basins according to the Thiessen polygon method;

[0013] Calculate the glacier surface temperature on the day of ice melting;

[0014] Calculate the glacier melt of each sub-basin based on the ice surface temperature and solar radiation, and obtain the glacier meltwater discharge in arid regions.

[0015] Optionally, the formula for calculating the glacier volume is as follows:

[0016]

[0017] Where V is the glacier volume of a single glacier; A is the area of a single glacier.

[0018] Optionally, the calculation formula for solar radiation is as follows:

[0019]

[0020] Where, R s is the solar radiation, R a is the extraterrestrial radiation, N is the maximum possible sunshine duration, a s represents the transmission coefficient of extraterrestrial radiation reaching the Earth's surface on cloudy days; b s represents the transmission coefficient of extraterrestrial radiation reaching the Earth's surface on sunny days, and n is a constant.

[0021] Optionally, the calculation formula for extraterrestrial radiation is as follows:

[0022]

[0023] G sc is the solar constant, d r is the inverse mean Earth-Sun distance, ω sis the angle at sunset, is the latitude, and δ is the solar declination.

[0024] Optionally, the calculation formula for the glacier surface temperature on the day of ice melting is as follows:

[0025]

[0026] The glacier temperature on the d n th day is expressed as a function of the glacier temperature of the previous day and the air temperature of the current day .

[0027] Optionally, it further includes constructing a temperature radiation factor:

[0028]

[0029] Gmfmx and Gmfmn are the glacier melting factors on August 1st and February 1st respectively; dn is the Julian day of the year.

[0030] Optionally, calculate the glacier melting amount based on the ice surface temperature and solar radiation amount on each sub-basin, and the calculation formula is as follows;

[0031]

[0032] where gla cov is the proportion of the glacier coverage area within the sub-basin; T max is the daily maximum air temperature, Gmtmp is the glacier melting base temperature, and R s is the solar radiation of the sub-basin on the current day.

[0033] Optionally, it further includes updating the corresponding relative changes of the glacier volume δV and the glacier area δA according to the glacier volume-area ratio relationship, specifically as follows:

[0034]

[0035]

[0036] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a method for calculating the glacier meltwater flow in arid areas considering dynamic glacier melting, which can effectively simulate the recharge effect of glacier meltwater on runoff. At the same time, considering the strong driving effect of solar radiation on glacier melting on the sunny slope, it reduces the model's equivalent parameter effect, making the simulated runoff formation process or flood formation process closer to the actual situation and conforming to the existing physical runoff generation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on the provided drawings.

[0038] Figure 1 It is a flow diagram of the present invention. Detailed implementation manners

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0040] An embodiment of the present invention discloses a method for calculating the glacier meltwater flow in arid areas considering the dynamic melting of glaciers, which is as follows:

[0041] (1) Obtain the glacier areas of all glaciers in the basin. According to the glacier volume - area ratio relationship, use the glacier area to estimate the glacier volume, expressed as:

[0042]

[0043] where V (m 3 ) is the glacier volume of a single glacier. A (m 2) ) is the area of a single glacier. In this embodiment, a glacier density coefficient of 0.92 kg / m 3 is used to convert the glacier volume into glacier water volume.

[0044] (2) Allocate the glacier area and glacier volume to each sub - basin in the basin, and calculate the total glacier coverage area and glacier volume of each sub - basin.

[0045] (3) Obtain the longitude, latitude and daily - scale actual sunshine hours n of all meteorological stations in and around the basin. According to the relationship between solar radiation, extraterrestrial radiation and relative sunshine, obtain the solar radiation Rs (MJ m -2 day -1 ) of the corresponding meteorological station:

[0046]

[0047] where: R a is the extraterrestrial radiation (unit: MJm -2 day -1 ), which is obtained by the following formula:

[0048]

[0049] N is the maximum possible sunshine duration (unit: hour), which is obtained by the following formula:

[0050]

[0051] The corresponding parameters in Formula 3 and Formula 4 are as follows:

[0052] G sc —— Solar constant, with a value of 0.0820 megajoules per square meter per minute (MJm -2 min -1 );

[0053] d r —— Inverse mean sun-earth distance, J is the day sequence number, with a value range of 1 to 365 or 366, and the day sequence number is 1 on January 1;

[0054] ω s —— Sunset hour angle, in radians (rad),

[0055] —— Latitude, in radians (rad);

[0056] δ —— Solar magnetic declination, in radians (rad),

[0057] a s —— Transmittance coefficient of extraterrestrial radiation reaching the earth's surface on cloudy days (n = 0);

[0058] a s +b s —— Transmittance of extraterrestrial radiation reaching the earth's surface on sunny days (n = N).

[0059] a s and b s vary with atmospheric conditions (humidity, dust) and solar magnetic declination (latitude and month). In the Xinjiang region, the values of a s and b s are shown in Table 1.

[0060] Table 1 Values of a s and b s in each month

[0061] Month a b 1 0.2814 0.4862 2 0.2596 0.5124 3 0.2525 0.4992 4 0.3046 0.4037 5 0.3151 0.3868 6 0.3514 0.3355 7 0.3138 0.3731 8 0.3281 0.3461 9 0.3247 0.364 10 0.2963 0.4193 11 0.2398 0.4989 12 0.2499 0.5050

[0062] (4) Obtain the daily-scale temperature, precipitation, wind speed, and relative humidity data of all meteorological stations within and around the basin. According to the Thiessen polygon method, interpolate the meteorological stations to the sub-basins to calculate the evapotranspiration of the conventional sub-basins.

[0063] (5) Calculate the glacier surface temperature on the day of ice melting. The glacier temperature on the d n th day can be expressed as a function of the glacier temperature of the previous day and the air temperature of the current day :

[0064]

[0065] where Gla_timp is the introduced temperature lag factor. When Gla_timp is closer to 1, it indicates that the influence of the average air temperature of the current day on the glacier temperature is increasing.

[0066] (6) Construct the temperature radiation factor:

[0067]

[0068] where Gmfmx and Gmfmn (mm H 2 O / (day℃)) are the glacier melting factors on August 1st and February 1st respectively; d n is the Julian day of the year.

[0069] (7) Calculate the glacier melt amount considering the ice surface temperature and solar radiation on each sub-basin.

[0070]

[0071] where gla cov is the proportion of the glacier-covered area within the sub-basin; T max is the daily maximum air temperature, Gmtmp is the glacier melting base temperature (℃), and Rs is the solar radiation of the sub-basin on the current day.

[0072] (8) Based on the area-volume relationship, update the corresponding relative changes of the glacier volume (δV) and glacier area (δA) daily. These changes can be expressed respectively as:

[0073]

[0074]

[0075] (9) According to the updated glacier area and glacier volume, start the simulation of glacier meltwater for the next day.

[0076] In this embodiment, the simulation results of the Kaidu River on the southern slope of the Tianshan Mountains, the Kumalake River, and the Yarkand River on the northern slope of the Kunlun Mountains show that the glacier meltwater ratios of the three simulated rivers are 15.0%, 37.3%, and 43.2% respectively. In addition, this flood forecasting technology in arid regions that takes into account the dynamic melting of glaciers can greatly improve the simulation accuracy of floods. The test results in the Kaidu River Basin on the southern slope of the Tianshan Mountains in China show that because the proportion of glacier meltwater in the Kaidu River Basin is relatively low, the improved flow prediction technology has only a slight improvement, with the NSE increasing from 0.73 to 0.75, and R 2 increasing from 0.78 to 0.79; there is a significant improvement in the experimental results of the Kumalake River in the western section of the southern slope of the Tianshan Mountains in China, with the NSE increasing from 0.18 to 0.64, and R 2 increasing from 0.51 to 0.66; there is also a significant improvement in the simulation accuracy in the Yarkand River Basin on the northern slope of the Kunlun Mountains, with the NSE increasing from 0.31 to 0.89, and R 2 increasing from 0.68 to 0.89 (as shown in Table 2).

[0077] Table 2 Comparison of flow prediction effects before and after improvement

[0078]

[0079] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same and similar parts among the embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and reference can be made to the method part for the relevant parts.

[0080] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting, characterized in that, it includes the following steps: Obtain the glacier areas of all glaciers within the basin; Calculate the glacier volume according to the glacier volume - area ratio relationship; Allocate the glacier area and glacier volume to each sub - basin within the basin, and calculate the total glacier coverage area and glacier volume of each sub - basin; Obtain the solar radiation amount within the basin based on latitude and sunshine hours; Obtain the meteorological data within and around the basin, and interpolate the meteorological data into the sub - basins according to the Thiessen polygon method; Calculate the glacier surface temperature on the day of ice melting; Calculate the glacier melt amount on each sub - basin based on the ice surface temperature and solar radiation amount, so as to obtain the glacier meltwater flow in arid regions.

2. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, the formula for calculating the glacier volume is as follows: where V is the glacier volume of a single glacier; A is the area of a single glacier.

3. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, the formula for calculating the solar radiation amount is as follows: Among them, R s is the solar radiation amount, R a is the extraterrestrial radiation, N is the maximum possible sunshine hours, a s represents the transmission coefficient of extraterrestrial radiation reaching the earth's surface on cloudy days; b s represents the transmission coefficient of extraterrestrial radiation reaching the earth's surface on sunny days, and n is a constant.

4. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 3, characterized in that, the formula for calculating the extraterrestrial radiation is as follows: G sc is the solar constant, d r is the inverse mean sun-earth distance, ω s is the hour angle at sunset, is the latitude, and δ is the solar declination.

5. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, the formula for calculating the glacier surface temperature on the day of ice melting is as follows: Day d n The glacier temperature on day is expressed as a function of the previous day's glacier temperature and the air temperature on that day .

6. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, it also includes constructing a temperature - radiation factor: Gmfmx and Gmfmn are the glacier melting factors on August 1st and February 1st respectively, that is, the times when the maximum and minimum ice melting rates occur in a year; dn is the Julian day in a year.

7. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, calculate the glacier melt amount on each sub - basin based on the ice surface temperature and solar radiation amount, and the calculation formula is as follows; Among them, GLA mlt is the glacier meltwater volume on the main river basin of the day; gla cov is the proportion of glacier-covered area within the sub-basin; T max is the highest temperature of the day, Gmtmp is the basic temperature for glacier melting, and R s is the solar radiation of the sub-basin for the day.

8. The method for calculating the glacier meltwater flow in arid regions considering dynamic glacier melting according to claim 1, characterized in that, it also includes updating the corresponding relative changes of the glacier volume δV and glacier area δA according to the glacier volume - area ratio relationship, specifically as follows: Among them, GLA mlt is the glacier meltwater volume on the main river basin of the day.

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