CN109598082B - Calculation method of lake evaporation capacity and key hydrological information based on hydrogen and oxygen isotopes - Google Patents
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- 238000004364 calculation method Methods 0.000 title claims abstract description 24
- 239000001301 oxygen Substances 0.000 title claims abstract description 23
- 229910052760 oxygen Inorganic materials 0.000 title claims abstract description 23
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 title claims abstract description 20
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 title claims abstract description 19
- 239000001257 hydrogen Substances 0.000 title claims abstract description 19
- 229910052739 hydrogen Inorganic materials 0.000 title claims abstract description 19
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 59
- 238000000034 method Methods 0.000 claims abstract description 29
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Abstract
The invention provides a method for calculating lake evaporation capacity and key hydrological information based on hydrogen and oxygen isotopes, which comprises the following steps: (1) acquiring the annual average precipitation and annual average evaporation capacity of an area where a lake is located, taking the lake as a sub-basin outlet, dividing the corresponding sub-basins of the lake by using digital elevations, and estimating the areas of the lake and the sub-basins; (2) collecting and measuring the abundance of hydrogen and oxygen isotopes in lake water and rainfall as well as the temperature and relative humidity on the surface of the lake during the sampling period according to a certain frequency; (3) providing a water quantity balance equation and an isotope mass conservation equation of the lake, and establishing a calculation model; (4) simulating and calculating evaporation items of the lake and the isotope abundance of water vapor above the lake; (5) and combining the isotope abundance information and a model equation, and calculating the evaporation ratio and key hydrological information of the lake. The invention provides a new method for acquiring hydrological ecological information and monitoring the field in remote areas without data; the reliability of the analysis result is high, and the method is suitable for various lakes.
Description
Technical Field
The invention belongs to the field of hydrological water resources, and particularly relates to a technical method for calculating lake evaporation capacity and key hydrological information by constructing a mass conservation model based on hydrogen and oxygen isotopes.
Background
In recent years, the close integration of hydrological information and water isotope mass conservation models in individual aquifer systems has been a focus of research. In particular, the isotope mass conservation model is ideally suitable for quantitatively outputting lake hydrological information and hydraulic communication signals. By using hydrogen and oxygen isotopes (18O，2H) The method has the advantages that a simple quality model can be constructed to effectively identify a plurality of parameters of the lake balance process, hydrological basic data are quite deficient for remote mountainous areas and river source areas, however, the lake hydrological conditions of the areas are very critical, the current situation of the water resource environment of the areas is controlled, and the future hydrological change situation is influenced, so that it is very urgent to find a reasonable and effective observation means to understand the regional lake hydrological factors.
At present, some researches believe that if an isotope mass conservation model can be applied to the research of lakes, an effective method for isotope sampling of lakes with a certain frequency is provided, and a method for constructing a lake water balance model to obtain the current situation of lake hydrological factors can solve the problems of short-term continuous observation, single observation means, high uncertainty of observation results, insufficient precision and the like. In addition, it is a great innovation and challenge to find a technical method for performing short-term rapid isotope monitoring on lakes and even performing representative isotope sampling and analysis to highly represent the current state features of lake hydrology.
The research on isotope information diagnosis of a plurality of specific lakes is quite lacking, the existing isotope models of lakes are monotonous at present, interaction between the lakes and the surrounding water vapor environment is too simplified for input and output changes of the lakes, most of the existing isotope models of lakes stay in the aspect of estimating the evaporation capacity of the lakes qualitatively or semi-quantitatively, and the role and the quantitative role played by the lakes in hydrological circulation are difficult to show objectively and comprehensively.
Disclosure of Invention
In order to solve the defects in the prior art, the calculation method of the lake evaporation capacity and key hydrological information based on the hydrogen-oxygen isotope is based on a simple and efficient lake isotope conservation model, utilizes the hydrogen-oxygen isotope characteristics of the lake in combination with a water balance equation of the lake to invert and explain the hydrological situation of the lake, quantitatively calculates each element function of the lake participating in hydrological circulation, including key hydrological information such as input and output items of the lake, evaporation capacity estimation and water yield of the lake, and provides a new technical method for researching the lake hydrological effect of a basin.
In order to solve the problems, the invention specifically adopts the following technical scheme:
the method for calculating the lake evaporation capacity and the key hydrological information based on the hydrogen and oxygen isotopes is characterized by comprising the following steps of:
step 1, acquiring the average precipitation p and the average evaporation e of a lake in a region, taking the lake as a sub-basin outlet, dividing the corresponding sub-basins of the lake by using a digital elevation model, and estimating the area of the lake and the area of the sub-basins;
step 2, collecting the precipitation of lake water and nearby lakes according to a certain frequency and measuringHydrogen and oxygen isotopes (in lake water and precipitation)2H，18O) abundance, and temperature T and relative humidity h on the surface of the lake during sampling period;
step 3, providing a water quantity balance equation and an isotope mass conservation equation of the lake, and establishing a calculation model;
step 4, simulating and calculating the isotope abundance of water vapor above the lake and lake evaporation items;
and 5, combining the isotope abundance information and the calculation model in the steps 2, 3 and 4 to calculate the key hydrological information of the lake.
The calculation method of the lake evaporation capacity and the key hydrological information based on the hydrogen and oxygen isotopes is characterized in that in the step 2, the hydrogen and oxygen isotope abundances in the lake water and the rainfall are collected and measured according to a certain frequency, and the frequency can be once or several times; when the samples are sampled for several times, the isotope abundance of the lake water adopts the maximum value of the isotope abundance of the lake water samples for several times, and the isotope abundance of the precipitation adopts the weighted isotope abundance average value of the precipitation weight. Preferably, in general practical studies, it is recommended to use the lake water isotopic abundance at 9-10 months of the year.
The method for calculating the lake evaporation capacity and the key hydrological information based on the hydrogen and oxygen isotopes is characterized in that in the step 3,
the water balance equation of the lake is as follows:
I＝Q+E (1)
i, Q, E are respectively the input item, excretion item and evaporation item of the lake;
I＝P+R (2)
wherein P is the precipitation falling on the surface of the lake, and R is the unobserved inflow;
the isotope conservation of mass equation for lakes is as follows:
IδI＝QδQ+EδE(3)
in the formula, deltaI、δQ、δERespectively corresponding isotope abundances of an input item I, an excretion item Q and an evaporation item E of the lake;
integrating (1), (2) and (3) to obtain:
E/I＝(δI-δQ)/(δE-δQ) (4)
wherein E/I is the ratio of the evaporation term to the input term of the lake;
delta of the discharge term Q of the lake under the assumption that the lake water is fully mixedQUsually with isotopic abundance delta of lake waterLReplacing; generally, the isotopic abundance of the unperceived flux R is difficult to determine, assuming δI≈δp，δpIs the isotopic abundance of precipitation.
The method for calculating the lake evaporation capacity and the key hydrological information based on the hydrogen and oxygen isotopes is characterized in that in the step 4, the isotope abundance delta of the lake evaporation itemEThe calculation method of (2) is as follows:
δE＝((δL-ε+)/α+-hδA-εK)/(1-h+10-3εK) (5)
wherein h is the relative humidity on the surface of the lake during the sampling period, epsilon+is the equilibrium separation value of the isotope, α+Is the equilibrium fraction coefficient of the isotope, ε+＝α+-1，εKIs the isotopic kinetic separation value, deltaAThe isotopic abundance of water vapor above the lake;
wherein alpha is+Depending on the temperature, it is possible to determine,
α+(18O)＝exp[-7.685/10-3+6.7123/(273.15+T)-1666.4/(273.15+T)2+350410/(273.15+T)3]) (17)
α+(2H)＝exp[1158.8(273.15+T)3/1012)-1620.1×((273.15+T)2/109)+794.84((273.15+T)/106)-161.04/103+2999200/(273.15+T)3](18)
accordingly, equation (4) is rewritten as: E/I ═ deltaL-δI)/(m(δ*-δL)) (6)
In the formula,
m＝(h-10-3×(εK+ε+/α+))/(1-h+10-3εK) (7)
δ*＝(hδA+εK+ε+/α+)/(h-10-3×(εK+ε+/α+)) (8)。
the method for calculating the evaporation capacity of the lake and the key hydrological information based on the hydrogen and oxygen isotopes is characterized in that in the step 4, the isotopic abundance delta of water vapor above the lakeAThe calculation method of (2) is as follows:
(1) when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is less than 1000mm for many years,
δA＝(δP-ε+)/(1+10-3ε+) (9)
(2) when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is more than or equal to 1000mm for many years,
δA＝(δP-kε+)/(1+10-3·kε+) (10)
wherein k is 0.5+ (e-1000)/2 e;
(3) when the lake area is more than 1km2Considering that the evaporation of the lake itself has an influence on the water vapor, the isotopic abundance of the water vapor above the lake is recorded as delta'A，
δ′A＝(1-f)·δA+f·δE(11)
Wherein, f is (1-h),
isotopic abundance of such lake evaporation terms is δ'EThus, therefore, it is
δ′E＝((δL-ε+)/α+-hδ′A-εK)/(1-h+10-3εK) (12)。
the method for calculating the lake evaporation capacity and the key hydrological information based on the hydrogen-oxygen isotope is characterized in that the key hydrological information of the lake in the step 5 comprises the proportion E/I of the evaporation item of the lake and the input item, the unobserved inflow R of the evaporation lake, the production flow WY of the lake basin, the runoff coefficient Z of the lake and the retention time г of the lake;
the ratio E/I of the lake evaporation item to the input item is calculated by the formula (6);
the calculation method of the unobserved inflow R of the lake comprises the following steps:
R＝e·LA/(E/I)-p·LA (13)
wherein e and p are the annual average evaporation and annual average precipitation over many years, respectively, and LA is the lake area;
the method for calculating the production flow WY of the lake basin comprises the following steps:
WY＝R/WA (14)
wherein WA is the basin area;
the runoff coefficient Z of the lake is calculated as follows:
Z＝R/(p·LA) (15)
the retention time r of a lake is calculated as follows:
г＝(E/I·V)/e (16)
wherein V is the volume of the lake.
The invention has the beneficial effects that:
1. according to the invention, the evaporation capacity and various key hydrological information of the lake can be obtained only by once collecting lake water and precipitation isotope samples and testing the isotope abundance thereof and constructing the lake water balance and isotope mass conservation equation, the lake does not need to be monitored complexly and continuously, time and labor are saved, and a new method is provided for hydrological ecological information acquisition and field monitoring in remote non-data areas;
2. the method has high reliability of an analysis result, is based on effective coupling of water isotope phase state change and a hydrological model, has a physical basis, can obtain hydrological information of various key lakes, can be suitable for various lakes such as large/small lakes, seasonal/non-seasonal lakes and the like, and provides a new thought and important scientific reference for interactive development of multiple subjects such as hydrological weather and chemistry.
Drawings
FIG. 1 is a technical flow chart of the inventive method.
Detailed Description
The invention is further described below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, in the embodiment, the evaporation capacity and the key lake hydrological information are obtained by applying the method of the present invention to a plurality of hot melt lakes in the northeast of the Qinghai-Tibet plateau, and 1 hot melt lake is selected for the representative calculation. The area is a cross area of a monsoon and a non-monsoon area, the ecological environment of a dry area in a cold area is obvious, the cause and the change trend of a lake are complex, the degradation of frozen soil around the hot-melt lake is accelerated due to the existence and the development of the hot-melt lake, and the allocation of surface water resources is deeply influenced. In the background of dry and warm climate, the thermal melting lake pond which is widely expanded at present is likely to be obviously and rapidly reduced or even disappear in the future. Relevant research in China currently focuses on the change and feedback of frozen soil degradation of the Qinghai-Tibet plateau on the hot-melt lake, and few targeted researches on the effect of the hot-melt lake in the hydrologic cycle process under the control of frozen soil for many years are carried out.
1. The method for calculating the lake water yield based on the hydrogen and oxygen isotopes comprises the following preparation steps in the early stage, namely step 1 and step 2:
looking up hydrological yearbook data of the area, and knowing the annual average precipitation p (322.3mm) and annual average evaporation e (1354.1mm) of the area where the lake is located;
taking the lake as an outlet of the sub-watershed, dividing the corresponding sub-watershed of the lake by using a digital elevation model, and estimating the areas of the lake and the sub-watershed, wherein the area of the lake is simplified to be less than 1km2The area of the drainage basin is 6km2；
Determination of hydrogen and oxygen isotopes of lake water and precipitation (2H，18O) abundance, water surface temperature T and relative humidity h at the sampling period, field sampling was performed 4 months in 2014, and a liquid water isotope analyzer (model: picaro L-2130i),18o ensures the precision to be 0.025 per mill,2h ensures the precision to be 0.1 per mill, and the determination result is as follows: lake water deltaL:δ18O＝-0.88‰，δ2H-26.87 ‰, and d as precipitationP:δ18O＝-12.20‰，δ2H＝-86.40‰，T＝272.9K，h＝0.588。
And step 3: providing a water quantity balance equation and an isotope mass conservation equation of the lake, and establishing a calculation model;
wherein, the water balance equation of the lake is as follows:
I＝Q+E (1)
i, Q, E are respectively the input item, excretion item and evaporation item of the lake;
I＝P+R (2)
wherein P is the precipitation falling on the surface of the lake, and R is the unobserved inflow;
the isotope conservation of mass equation for lakes is as follows:
IδI＝QδQ+EδE(3)
in the formula, deltaI、δQ、δERespectively corresponding isotope abundances of an input item I, an excretion item Q and an evaporation item E of the lake;
integrating (1), (2) and (3) to obtain:
E/I＝(δI-δQ)/(δE-δQ) (4)
wherein E/I is the ratio of the evaporation term to the output term;
assuming that the lake water is fully mixed, the delta of the lake discharge term QQUsually with isotopic abundance delta of lake waterLReplacing; generally, the isotopic abundance of the unperceived flux R is difficult to determine, assuming δI≈δp，δpIs the isotopic abundance of precipitation.
Step 4, simulating and calculating evaporation items of the lake and the isotopic abundance of water vapor above the lake;
isotopic abundance delta of lake evaporationEThe calculation method of (2) is as follows:
δE＝((δL-ε+)/α+-hδA-εK)/(1-h+10-3εK) (5)
wherein h is the relative humidity on the surface of the lake during the sampling period, epsilon+is the equilibrium separation value of the isotope, α+Is the equilibrium fraction coefficient of the isotope, ε+＝α+-1，εKIs the isotopic kinetic separation value, deltaAOn a lakeIsotopic abundance of the square vapor;
wherein,
α+(18O)＝exp[-7.685/10-3+6.7123/(273.15+T)-1666.4/(273.15+T)2+350410/(273.15+T)3]) (17)
α+(2H)＝exp[1158.8(273.15+T)3/1012)-1620.1×((273.15+T)2/109)+794.84((273.15+T)/106)-161.04/103+2999200/(273.15+T)3](18)
equation (4) is rewritten as:
E/I＝(δL-δI)/(m(δ*-δL)) (6)
in the formula,
m＝(h-10-3×(εK+ε+/α+))/(1-h+10-3εK) (7)
δ*＝(hδA+εK+ε+/α+)/(h-10-3×(εK+ε+/α+)) (8)；
isotopic abundance delta of water vapor above lakeAThe calculation method of (2) is as follows:
(1) when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is less than 1000mm for many years,
δA＝(δP-ε+)/(1+10-3ε+) (9)
(2) when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is more than or equal to 1000mm for many years,
δA＝(δP-kε+)/(1+10-3·kε+) (10)
wherein k is 0.5+ (e-1000)/2 e;
(3) when the lake area is more than 1km2Considering that the evaporation of the lake itself has an influence on the water vapor, the isotopic abundance of the water vapor above the lake is recorded as delta'A，
δ′A＝(1-f)·δA+f·δE(11)
Wherein, f is (1-h),
isotopic abundance of such lake evaporation terms is δ'EThus, therefore, it is
δ′E＝((δL-ε+)/α+-hδ′A-εK)/(1-h+10-3εK) (12)，
In the embodiment, the lake area is less than 1km2And the average evaporation amount over years is 1000mm or more, therefore, the formula (10) δ is adoptedA＝(δP-kε+)/(1+10-3·kε+) Calculating deltaAWherein k is 0.5+ (e-1000)/2e is 0.631.
And 5, combining the isotope abundance information and the calculation model in the steps 2, 3 and 4, and calculating the evaporation capacity and the key hydrological information of the lake:
the key hydrological information of the lake comprises the proportion E/I of evaporation items and input items of the lake, the unobserved inflow R of the evaporation lake, the production flow WY of a lake basin, the runoff coefficient Z of the lake and the retention time г of the lake;
the ratio E/I of the lake evaporation item to the input item is calculated by a formula (6);
the calculation method of the unobserved inflow R of the lake comprises the following steps:
R＝e·LA/(E/I)-p·LA (13)
wherein e and p are the annual average evaporation and annual average precipitation over the years, respectively, and LA is the lake area;
the method for calculating the production flow WY of the lake basin comprises the following steps:
WY＝R/WA (14)
wherein WA is the basin area;
the runoff coefficient Z of the lake is calculated as follows:
Z＝R/(p·LA) (15)
the retention time r of a lake is calculated as follows:
г＝(E/I·V)/e (16)。
shown in table 1 are the results of key hydrological information (E/I ratio of evaporation item to input item in lake, R inflow rate not observed in lake, WY flow rate of lake basin, Z runoff coefficient of lake, R retention time of lake):
TABLE 1 calculation of key hydrological information of lakes
| E/I | R(mm) | WY(mm) | Z | г(d) | |
| 18Result of O calculation | 1.06 | 1113.87 | 168.86 | 0.346 | 61.8 |
| 2H calculated result | 0.81 | 776.50 | 87.09 | 0.241 | 76.3 |
| Average result | 0.94 | 945.185 | 127.975 | 0.2935 | 69.05 |
As can be seen from the table:
the ratio of evaporation to replenishment of the lake is close to 1, which shows that the water balance of the lake is stable, more than half of the amount of replenishment received by the lake is a non-precipitation source, and the average residence time of the lake water reaches 70 days. The early-stage field geological survey report of the lake shows that the output of the lake basin is 125mm, the supply amount and the discharge amount of the lake are almost balanced, and the result is very close to the calculation result (E/I is 0.94, and WY is 127 mm).
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. The method for calculating the lake evaporation capacity and the key hydrological information based on the hydrogen and oxygen isotopes is characterized by comprising the following steps of:
step 1, acquiring the average precipitation p and the average evaporation e of a lake in a region, taking the lake as a sub-basin outlet, dividing the corresponding sub-basins of the lake by using a digital elevation model, and estimating the area of the lake and the area of the sub-basins;
step 2, collecting lake water and precipitation according to a certain frequency, and measuring the hydrogen and oxygen isotope abundances in the lake water and the precipitation as well as the temperature T and the relative humidity h on the surface of the lake during the sampling period;
collecting and measuring the hydrogen and oxygen isotope abundances in lake water and precipitation according to a certain frequency in the step 2, wherein the frequency is one or a plurality of times of sampling; when the samples are sampled for several times, the isotope abundance of the lake water adopts the maximum value of the isotope abundance of the lake water samples for several times, and the isotope abundance of the precipitation adopts the weighted isotope abundance mean value of the precipitation weight;
step 3, providing a water quantity balance equation and an isotope mass conservation equation of the lake, and establishing a calculation model;
in the step 3, the step of the method is that,
the water balance equation of the lake is as follows:
I＝Q+E (1)
i, Q, E are respectively the input item, excretion item and evaporation item of the lake;
I＝P+R (2)
wherein P is the precipitation falling on the surface of the lake, and R is the unobserved inflow;
the isotope conservation of mass equation for lakes is as follows:
IδI＝QδQ+EδE(3)
in the formula, deltaI、δQ、δERespectively corresponding isotope abundances of an input item I, an excretion item Q and an evaporation item E of the lake;
integrating the formula (1), the formula (2) and the formula (3) to obtain:
E/I＝(δI-δQ)/(δE-δQ) (4)
wherein E/I is the ratio of the evaporation term to the output term;
delta of the excretion term Q of the lake under the condition that the water bodies of the lake are fully mixedQBy isotopic abundance delta of lake waterLReplacing; and deltaI≈δp，δpIs the isotopic abundance of precipitation;
step 4, simulating and calculating evaporation items of the lake and the isotopic abundance of water vapor above the lake;
in step 4, the isotopic abundance delta of the evaporation item of the lakeEThe calculation method of (2) is as follows:
δE＝((δL-ε+)/α+-hδA-εK)/(1-h+10-3εK) (5)
wherein h is the relative humidity on the surface of the lake during the sampling period, epsilon+is the equilibrium separation value of the isotope, α+Is the equilibrium fraction coefficient of the isotope, ε+＝α+-1，εKIs the isotopic kinetic separation value, deltaAThe isotopic abundance of water vapor above the lake;
wherein formula (4) is rewritten as
E/I＝(δL-δI)/(m(δ*-δL)) (6)
In the formula,
m＝(h-10-3×(εK+ε+/α+))/(1-h+10-3εK) (7)
δ*＝(hδA+εK+ε+/α+)/(h-10-3×(εK+ε+/α+)) (8)；
in step 4, the isotopic abundance delta of the water vapor above the lakeAThe calculation method of (2) is as follows:
when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is less than 1000mm for many years,
δA＝(δP-δ+)/(1+10-3ε+) (9)
when the lake area is less than 1km2And when the average evaporation capacity of the evaporator is more than or equal to 1000mm for many years,
δA＝(δP-kε+)/(1+10-3·kε+) (10)
wherein k is 0.5+ (e-1000)/2 e;
when the lake area is more than 1km2Considering that the evaporation of the lake itself has an influence on the water vapor, the isotopic abundance of the water vapor above the lake is recorded as delta'A，
δ′A＝(1-f)·δA+f·δE(11)
Wherein f is (1-h);
the isotopic abundance of such lake evaporation terms is recorded as δ'EAs follows
δ′E＝((δL-ε+)/α+-hδ′A-εK)/(1-h+10-3εK) (12)；
And 5, combining the isotope abundance information and the calculation model in the steps 2, 3 and 4, and calculating the evaporation capacity and the key hydrological information of the lake.
2. the method of claim 1, wherein the key hydrological information of the lake in step 5 includes E/I ratio of evaporation item to input item, unobserved inflow R of the evaporation lake, WY flow of the lake basin, Z runoff coefficient of the lake and the detention time г of the lake;
the ratio E/I of the lake evaporation item to the input item is calculated by a formula (6);
the calculation method of the unobserved inflow R of the lake comprises the following steps:
R＝e·LA/(E/I)-p·LA (13)
wherein e and p are the annual average evaporation and annual average precipitation over many years, respectively, and LA is the lake area;
the method for calculating the production flow WY of the lake basin comprises the following steps:
WY＝R/WA (14)
wherein WA is the basin area;
the runoff coefficient Z of the lake is calculated as follows:
Z＝R/(p·LA) (15)
the retention time r of a lake is calculated as follows:
г＝(E/I·V)/e (16)
wherein V is the volume of the lake.
3. The method for calculating lake evaporation capacity and key hydrological information based on hydrogen and oxygen isotopes according to claim 1, wherein the lake water isotopic abundance is the lake water isotopic abundance at 9-10 months in a year.
4. the method for calculating lake evaporation capacity and key hydrological information based on hydrogen and oxygen isotopes as claimed in claim 1, wherein α is+Depending on the temperature, it is possible to determine,
α+(18O)＝exp[-7.685/10-3+6.7123/(273.15+T)-1666.4/(273.15+T)2+350410/(273.15+T)3]) (17)
α+(2H)＝exp[1158.8(273.15+T)3/1012)-1620.1×((273.15+T)2/109)+794.84((273.15+T)/106)-161.04/103+2999200/(273.15+T)3](18)
wherein T is the temperature of the surface of the lake in the sampling period.
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