CN112541275A - Construction method of ice-season river lake and atmosphere heat exchange linearization model - Google Patents

Construction method of ice-season river lake and atmosphere heat exchange linearization model Download PDF

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CN112541275A
CN112541275A CN202011516480.9A CN202011516480A CN112541275A CN 112541275 A CN112541275 A CN 112541275A CN 202011516480 A CN202011516480 A CN 202011516480A CN 112541275 A CN112541275 A CN 112541275A
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杨开林
郭新蕾
王涛
郭永鑫
付辉
李甲振
彭旭明
吴煜楠
潘佳佳
纪平
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China Institute of Water Resources and Hydropower Research
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Abstract

The invention relates to a construction method of a heat exchange linearization model of an ice river lake and atmosphere, which comprises the following steps: calculating the net solar radiation heat flux; calculating the heat flux of long-wave radiation of rivers and lakes; calculating the heat flux of long-wave atmosphere reversely radiated to the river surface; calculating the heat flux of evaporation-cooling; calculating the heat flux of air convection; calculating daily average net heat flux on the surface of the river or lake; constructing a linear river and lake and atmosphere heat exchange model; and constructing a linear heat exchange model of the research area. The invention establishes a nonlinear heat exchange model suitable for iced rivers and lakes and the atmosphere, which comprises solar radiation, long-wave radiation, evaporation-cooling and convection, finds that the surface temperature of the iced rivers and lakes is close to the temperature measured at the height of 1.5m on the river surface, comprises the surface of a snow cover and an exposed ice cover, linearizes the nonlinear heat exchange model of the rivers, lakes and atmosphere, provides a method for adopting linear regression based on historical daily average weather data of a meteorological station, and solves the problem that the values of heat exchange coefficients are greatly different.

Description

Construction method of ice-season river lake and atmosphere heat exchange linearization model
Technical Field
The invention relates to a construction method of a heat exchange linearization model of an ice river lake and atmosphere, which is a hydrological calculation method.
Background
The model for heat exchange between rivers, lakes and the atmosphere is the basis for calculating and analyzing the formation, development and ablation time-space change rules of ice and is an important subject for researching solar energy utilization, climate change, hydrology and water resources. River and lake heat exchange refers to heat exchange among open water, ice and snow covers, solar radiation, long-wave radiation, surface evaporation-cooling and convection, snowfall or rainfall.
Solar radiation refers to the outward transfer of energy from the sun in the form of electromagnetic waves, and refers to the electromagnetic waves and particle flow emitted by the sun into the space. The energy transferred by solar radiation is called solar radiation energy. The solar radiation energy received by the earth is only twenty-billion of the total radiation energy emitted to the space from the sun, but is a main energy source for the earth's atmospheric motion and a main source of the earth's photo-thermal energy.
After the solar radiation reaches the ground, a part of the solar radiation is reflected, and a part of the solar radiation is absorbed by the ground, so that the ground surface temperature changes. The surface temperature is a key parameter for radiation and energy exchange between the surface and the atmosphere. After the solar radiation heat is absorbed by the ground, the ground transfers the heat to the air through long-wave radiation, conduction and convection, which is the main source of the air heat.
When water and air come into contact with each other, some molecules have enough energy to flush out of the water surface and escape into the air as water vapor. Meanwhile, some water molecules in the air penetrate into the water surface, are condensed and become a part of the liquid phase. Evaporation is the net rate of migration of water from the liquid into the air, which is the sum of microscopic evaporation and condensation processes. The heat transport of the two media of water and gas is mainly realized by convection, including turbulent mixing of large-scale flow displacement and vortex diffusion. Convection in the air is basically promoted by pressure, so that the change of the sensible heat flux of the water surface is greatly influenced by wind speed, and river flow can cause turbulent mixing due to friction with the air even in windless weather. In special cases, such as when the water temperature is much higher than the air temperature, buoyancy may be the main cause of convection.
On the earth, water is in continuous circulation, water on the ocean and the ground is heated and evaporated to the sky, and the water vapor moves to other places along with wind, and when the water vapor meets cold air, precipitation is formed and returns to the earth surface again. This precipitation is divided into two categories: one is liquid precipitation, which is raining; the other is solid precipitation, which is snowing or hail, etc. When snow falls into open water, the water temperature is reduced by melting of the snow, and particularly when the water temperature is close to zero in winter and severe cold tide attacks, severe snow falls cause ice flowers in the water to increase rapidly, and serious ice plugs in the downstream can be caused.
The international famous ice engineering specialist Ashton (1986) concluded the heat exchange model between rivers and lakes and the atmosphere at that time in summary, and suggested the adoption of
Figure BDA0002847564820000011
(1924) Calculating solar radiation by using a sunshine percentage model and a Wunderlich (1972) cloud cover percentage model, and describing heat exchange between the ice river lake and the atmosphere by using a linearization model in the process of analyzing the ice condition, namely taking the net heat flux between the river lake and the atmosphere:
Figure BDA0002847564820000021
in the formula: h isasFor coefficient of heat exchange, TsIs the surface temperature of river or lake, TaIs the air temperature. However, he does not give how to get hasThe method of (1).
Edinger et al introduced an assumed equilibrium temperature, i.e., the temperature T of the body of water when the net heat flux at the surface is zeroeObtaining:
Figure BDA0002847564820000022
in the formula:
Figure BDA0002847564820000023
the water surface is used for purifying solar radiation; t isdIs the dew point temperature.
The method of Edinger et al was used to obtain h when there was free icesa＝30.0W/m2DEG C, ice cover hour hsa＝1.7W/m2DEG C. The linearized model form proposed by Ashton (1986) has been widely used in ice engineering. The sinking flood way (2010) of famous specialists of international river ice engineering aims at North America and adopts hsa＝20.0W/m2DEG C. Caelin and Chenzaning (2008),Wing Honglan teaEtc. (2016) for yellow river, when the water surface is open, take hsa＝10.0W/m2DEG C; when the ice is sealed, take hsa＝1.5W/m2DEG C. Obviously, a problem is found from the above, hsaThe values of the two are very different, which is a problem to be solved.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a construction method of a heat exchange linearization model of an ice-season river lake and the atmosphere. The method solves the problem of the heat exchange coefficient calculation method through the selection of the heat exchange model between the river and the lake and the atmosphere and the more reasonable linearization of the nonlinear model.
The purpose of the invention is realized as follows: a construction method of a heat exchange linearization model of an ice river lake and atmosphere is characterized by comprising the following steps:
step 1, calculating the net solar radiation heat flux
Figure BDA0002847564820000024
By calculating the solar heat flux of cloud
Figure BDA0002847564820000025
Indirect calculation of net solar radiation heat flux
Figure BDA0002847564820000026
Figure BDA0002847564820000027
Wherein:
Figure BDA0002847564820000028
is astronomical radiant heat flux; p is the average atmospheric transparency coefficient; m is the optical atmospheric mass; c is cloud amount;
the average calculation is carried out on the data of each observation day to obtain the net heat flux of the solar radiation
Figure BDA0002847564820000029
Step 2, calculating heat flux of long-wave radiation of rivers and lakes
Figure BDA00028475648200000210
Figure BDA00028475648200000211
In the formula: sigma is a Stefan Boltzmann constant; epsilonwIs a correction factor; t issThe surface temperature of the river or lake;
step 3, calculating the heat flux of long-wave atmosphere reversely radiated to the river surface
Figure BDA00028475648200000212
Calculating the saturated vapor pressure e of airs：
Figure BDA00028475648200000213
es0Is TsSaturated water vapour pressure at 0.0 ℃; a and b are constants;
calculating the atmospheric emissivity epsilon in sunny daysa：
εa＝1-0.35exp(-10ez/(273.15+Ta))＝1-0.35exp(-10Rhes/(273.15+Ta))
In the formula: e.g. of the typezThe water vapor pressure in the air at the position of 1.5m away from the river surface; t isaThe temperature measured at a height of 1.5m above the river surface; e.g. of the typesIs the saturated vapor pressure of air; rhIs the relative humidity of the air;
Figure BDA0002847564820000031
γathe reflectivity of the surface of the river or lake to the atmospheric long-wave back radiation is shown; k is a coefficient;
step 4, calculating heat flux of evaporation-cooling
Figure BDA0002847564820000032
Figure BDA0002847564820000033
Wherein: vzThe wind speed is 1.5m away from the surface of the river or lake;
step 5, calculating the heat flux of air convection
Figure BDA0002847564820000034
Figure BDA0002847564820000035
Step 6, calculating daily average net heat flux of the surface of the river and the lake
Figure BDA0002847564820000036
Figure BDA0002847564820000037
Step 7, constructing a linear river lake and atmosphere heat exchange model:
setting Ts＝TaLinearizing a daily average net heat flux model of the surface of the river and the lake:
Figure BDA0002847564820000038
wherein:
Figure BDA0002847564820000039
is Ts＝TaDaily average net heat flux on the surface of the river or lake;
Figure BDA00028475648200000310
is Ts＝TaAtmospheric long wave reverse radiation;
Figure BDA00028475648200000311
is Ts＝TaHeat flux of long-wave radiation of rivers and lakes;
Figure BDA00028475648200000312
is Ts＝TaEvaporative-cooling heat flux in time;
in the formula:
Figure BDA00028475648200000313
Figure BDA00028475648200000314
Figure BDA00028475648200000315
Figure BDA00028475648200000316
Figure BDA00028475648200000317
to pair
Figure BDA00028475648200000318
And
Figure BDA00028475648200000319
at Ts＝TaCalculating partial derivative to obtain:
Figure BDA0002847564820000041
in the formula:
Figure BDA0002847564820000042
Figure BDA0002847564820000043
wherein: h isbaIs the heat exchange coefficient of long wave radiation;
to pair
Figure BDA0002847564820000044
And
Figure BDA0002847564820000045
at Ts＝TaPoint findingPartial derivatives:
Figure BDA0002847564820000046
wherein: h isehEvaporation-cooling and convection heat exchange coefficients;
and 8, constructing a linear heat exchange model of the research area:
carrying out linear regression analysis on the data of the research area to obtain a linear heat exchange model of the research area:
Figure BDA0002847564820000047
due to 0.5Ta＜＜(6.04+2.95Vz)(1-Rh)(c1+c2Ta) Therefore:
Figure BDA0002847564820000048
in the formula: h issa＝10.0(1+0.25Vz)。
The invention has the advantages and beneficial effects that: based on the research results of subjects such as solar energy utilization, climatology, hydrology, water resources and the like, the invention firstly establishes a nonlinear heat exchange model suitable for the icebound rivers and lakes and the atmosphere, including solar radiation, long-wave radiation, evaporation-cooling and convection. On the basis of prototype observation, the method for linearizing the nonlinear heat exchange model of the river lake and the atmosphere at the point that the surface temperature of the iced river lake is close to the air temperature measured at 1.5m height on the river surface comprises the surfaces of a snow cover and a bare ice cover, and the temperature of the surface of the iced river lake is equal to the air temperature measured at 1.5m height on the river surface is found, so that the method for determining the heat exchange coefficient and researching the linear heat exchange model of the region by adopting a linear regression method based on the historical daily average weather data of a meteorological station is provided, and the problem that the values of the heat exchange coefficient of the river lake and the atmosphere are greatly different is solved.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a flow chart of a method according to an embodiment of the invention;
FIG. 2 is the actually measured ice condition of Heilongjiang section of Jicun of the northern desert river;
FIG. 3 shows weather data 2015.12.1-2016.2.29 in Beijing area and hsaLinear regression of (1);
FIG. 4 shows weather data 2016.12.1-2017.2.28 in Beijing area and hsaLinear regression of (1);
FIG. 5 shows the meteorological data of Heilongjiang desert river 2015 at 11 months 1 day to 2016 at 4 months 30 days;
FIG. 6 is a linear regression of 30 long-wave radiation from 11 months 1 days 2015 to 2016 months 4 months 30 in Heilongjiang desert river;
FIG. 7 shows the saturated vapor pressure esIs following TaThe change curve of (2).
Detailed Description
Example (b):
the embodiment is a construction method of a heat exchange linearization model of an ice river lake and the atmosphere. The method is based on research results of subjects such as solar energy utilization, climate, hydrology and water resources, and firstly establishes a nonlinear heat exchange model suitable for the icebound rivers and lakes and the atmosphere, wherein the nonlinear heat exchange model comprises solar radiation, long-wave radiation, evaporation-cooling and convection. On the basis of the above steps:
1) based on prototype observation, the surface temperature T of the icebound river and lake is foundsApproach to TaIncluding snow covers and bare ice cover surfaces, at Ts＝TaA method for linearizing a nonlinear heat exchange model of a river and a lake with the atmosphere.
2) Provides a method for determining a heat exchange coefficient h by adopting linear regression based on historical daily average weather data of a weather stationsaAnd
Figure BDA0002847564820000058
the method of linearizing a model of (1). It should be noted that, there is a certain difference between the historical weather data of the weather station and the actual situation of the river and the lake, but the long-term statistical characteristics are relatively close.
3) A unified linear model formula of heat exchange between the ice river and the lake and the atmosphere in the areas of Beijing, Baoding, Shenyang, Baotou and the like is established.
4) A calculation table of heat exchange linear models of rivers and lakes in the ice period of Heilongjiang and Lhasa and the atmosphere is provided.
The method of this embodiment includes the following steps, and the flow is shown in fig. 1:
step 1, calculating the net solar radiation heat flux
Figure BDA0002847564820000051
Step 2, calculating heat flux of long-wave radiation of rivers and lakes
Figure BDA0002847564820000052
Step 3, calculating the heat flux of long-wave atmosphere reversely radiated to the river surface
Figure BDA0002847564820000053
Step 4, calculating heat flux of evaporation-cooling
Figure BDA0002847564820000054
Step 5, calculating the heat flux of air convection
Figure BDA0002847564820000055
Step 6, calculating daily average net heat flux of the surface of the river and the lake
Figure BDA0002847564820000056
Step 7, constructing a linear river lake and atmosphere heat exchange model;
and 8, constructing a linear heat exchange model of the research area.
The principle of the method described in this embodiment is as follows:
1. nonlinear heat exchange model of river and lake with atmosphere:
the net heat exchange between rivers and lakes and the atmosphere, including solar radiation, long wave radiation, and evaporation-cooling and convection, is:
Figure BDA0002847564820000057
in the formula:
Figure BDA0002847564820000061
the average daily net heat flux of the surface of the river or lake is W/m2；
Figure BDA0002847564820000062
For net heat flux of solar radiation, W/m2；asmIs the daily average albedo of solar radiation;
Figure BDA0002847564820000063
is atmospheric long wave reverse radiation, W/m2；
Figure BDA0002847564820000064
Is the heat flux of long-wave radiation of rivers and lakes, W/m2；
Figure BDA0002847564820000065
Heat flux for evaporation-cooling, W/m2；
Figure BDA0002847564820000066
Heat flux for air convection, W/m2(ii) a When snowing days occur, the snowing heat flux needs to be increased in the formula
Figure BDA0002847564820000067
1.1 solar radiation:
the model for calculating the percentage of solar radiation in cloud sky by climate is composed of
Figure BDA0002847564820000068
(1924) Proposed, mathematical descriptions are:
Figure BDA0002847564820000069
in the formula:
Figure BDA00028475648200000610
is the solar heat flux of the cloud, W/m2；
Figure BDA00028475648200000611
The direct heat flux in a sunny day is realized,
Figure BDA00028475648200000612
W/m2；
Figure BDA00028475648200000613
is astronomical radiant heat flux, W/m2(ii) a P is the average atmospheric transparency coefficient over all wavelength ranges; m is the optical atmospheric mass; s is the percentage of sunshine, and represents the actual sunshine duration TrealAnd theoretical sunshine time TsunI.e. S ═ Treal/TsunS is more than or equal to 0.0 and less than or equal to 1.0.
In the areas where the sunshine observation stations are arranged in China, the fact that the sunshine percentage is replaced by the cloud amount percentage becomes the first-choice factor for calculating the solar radiation in cloud days, and the cloud amount is the conventional forecasting project of the meteorological station.
Based on
Figure BDA00028475648200000614
(1924) Percent insolation model, the cloud cover percent model proposed by Wunderlich (1972) is
Figure BDA00028475648200000615
In the formula: c is cloud amount,%; c is more than or equal to 0.0 and less than or equal to 100 percent.
1.2 Long-wave radiation of rivers and lakes
The heat flux of the long-wave radiation can be calculated from the fourth power law of steve-bletzmann as the river lake acts as a nearly black body:
Figure BDA00028475648200000616
in the formula:
Figure BDA00028475648200000620
is the heat flux of long-wave radiation of rivers and lakes, W/m2；σ＝5.67×10-8W/m2K4Is the Stefan Boltzmann constant; epsilonwFor correction of coefficients, epsilon may be taken for water, ice and snoww＝0.97；TsThe surface temperature of rivers and lakes, DEG C, the surface temperature of the open water, the surface temperature of an ice cover when the ice is sealed, and the surface temperature of snow when the snow cover is covered. At the surface temperature TsWhen the temperature is equal to 0.0 ℃,
Figure BDA00028475648200000617
1.3 atmosphere long wave back radiation
The atmospheric long-wave back radiation can be calculated according to Steven-Boltzmann law:
Figure BDA00028475648200000618
in the formula:
Figure BDA00028475648200000621
the heat flux/(W/m) is the heat flux of long-wave atmosphere reversely radiated to the river surface2)；TaAir temperature/DEG C measured at a height of 1.5m above the river surface; epsilonaAtmospheric emissivity on a sunny day; gamma rayaIs the reflectivity of the surface of the river or lake to the atmospheric long-wave back radiation, gammaaIs approximately equal to 0.03; k is a coefficient. Wunderlich (1972) takes K as 0.17 according to regional observations of Tennessee, USA.
Atmospheric emissivity epsilon for sunny daysaThe Idso-Jackson (1969) formula, epsilon, is often adopted in ChinaaOnly air temperature TaIs recommended by Ashton (1986) using the branch (1932) formula, εaOnly the pressure of water vapour ezAs a function of (c). Huangmiaofen et al (2005) use of measured dataThe material comparison studies 10 commonly used calculations epsilon internationallyaOf empirical formula, including
Figure BDA00028475648200000619
(1918) The formula, the Brant (1932) formula, the Idso-Jackson (1969) formula, the IZiomon (2003) formula and the like, and the results show that: the IZIOmon formula has the minimum mean absolute error and mean square error, and has the maximum consistency index IA and linear correlation coefficient LCC; brant times; the Idso-Jackson formula has the largest mean absolute error and mean square error, and has the smallest consistency index IA and linear correlation coefficient LCC, so that the IZiomon formula is recommended:
εa＝1-0.35exp(-10ez/(273.15+Ta))＝1-0.35exp(-10Rhes/(273.15+Ta)) (1.6)
in the formula: e.g. of the typez＝RhesThe water vapor pressure in the air at the position of the height z between the river surface and 1.5m, hPa; e.g. of the typesIs the saturated water vapor pressure of air, hPa; rhIs the relative humidity of the air. When the air humidity is saturated, Rh1.0. From the formula (1.6), εaNot only with air temperature TaRelated to, and the pressure e of the water vapourzOr relative humidity RhAnd saturated water vapor pressure esIt is related. In the following analysis, the formula IZIOMON (2003) is also used to calculate the emissivity ε in sunny daysa。
Saturated water vapour pressure esIs dependent on the surface temperature TsIs increased with TsThe decrease of the wind energy is reduced, and the world weather organization (WMO) recommends in 1996 to calculate by adopting Magnus-Titos formula:
Figure BDA0002847564820000071
in the formula: t issThe surface temperature of the river or lake is DEG C; e.g. of the types06.11hPa is TsSaturated water vapour pressure at 0.0 ℃; a and b are constants, for water level: t iss> 0, a ═ 17.62, b ═ 35.86; and (3) ice surface treatment: t iss≤0，a＝21.88，b＝7.66。
1.4 evaporative-Cooling and convection model
The water surface evaporation model has been studied for over 200 years. The Dalton (1802) comprehensively considers the influence of wind speed, air temperature and humidity on evaporation capacity according to a water surface evaporation forming principle and a maintenance mechanism, and provides a Dalton model which plays a decisive role in the establishment of a modern evaporation theory. The research on water surface evaporation is also carried out in China from the later 50 s in the 20 th century, and a plurality of empirical formulas for water surface evaporation are proposed at present.
Ashton (1986) concluded that prior studies concluded that only two evaporation-cooling equations could be applied to negative air temperature conditions, one of the russian winter equations proposed by Rimsha and Donchenko (1957), the other by Ryan-Harleman (1974), and that only the russian winter equation was actually applied in north america and iceland for a long time with good results. Russian winter formulas are also adopted in northeast China. Theoretical analysis and experimental verification of Chenhuiquan et al (1995) show that the Ryan-Harleman formula is suitable for the condition of no wind speed and no virtual temperature>5 deg.C (approximately T)s－Ta)>5 ℃ C.), but, for icebound rivers and lakes, (T)s－Ta) Often times, the<5 ℃ is adopted. Later, new or improved surface evaporation formulas were proposed by experts and scholars, such as Adams (1990), Chenhuiquan et al (1995),Li Wan Yi(2000) And the like. However, Adams and Chenhuiquan and the Citizen's formula are primarily directed to power plant cooling water systems,li Wan YiThe formula does not take into account the effect of the temperature difference between the water surface and the atmosphere. Current research indicates a temperature difference (T)s－Ta) The effect on evaporation-cooling is very large and not negligible.
Based on the russian winter equation, the heat flux of evaporation-cooling can be described as:
Figure BDA0002847564820000081
in the formula:
Figure BDA0002847564820000085
heat flux for evaporation-cooling, W/m2；VzThe wind speed is 1.5m away from the surface of the river or lake in m/s.
According to the relationship between Bowen (1926) convection and evaporation-cooling, the heat flux of the convection on the surface of the river or lake is:
Figure BDA0002847564820000082
in the formula:
Figure BDA0002847564820000084
heat flux for air convection, W/m2；paAt local atmospheric pressure, hPa, decreases as elevation of altitude increases.
2. Linearization of river and lake and atmosphere heat exchange model
Although some places in China are establishing ice condition observation stations, such as the north-south water transfer project and the yellow river ice condition observation station, T can be comprehensively observed at regular times、Ta、C、Rh、Vz、paThe time-varying is not available, so how to convert the net heat exchange multi-parameter nonlinear model formula (1.1) of the river and the lake with the atmosphere into only two independent variables TsAnd TaThe linear model has higher precision, not only has important theoretical significance, but also has wide practical value.
In 1 to 4 months of 2016, the ice condition including the water temperature under the ice cover, the vertical distribution of the internal and surface temperatures of the ice cover and the snow cover, and the air temperature were actually measured in the Heilongjiang district, Jicun, the desert Hebei, as shown in FIG. 2, wherein: t iswWater temperature or ice cover, snow cover, air temperature; h isiAnd hsIce thickness and snow thickness respectively; l is the scale of the R-T-O ice and snow condition sensor developed by the university of Taiyuan worker. The R-T-O ice and snow condition sensor is 200cm long, is arranged vertically through the snow cover and the ice cover, the lower end (left chart, vertical distribution of the snow cover, the ice cover and the water temperature at different time) measures the water temperature, the middle section measures the ice temperature and the snow temperature, and the upper end (right chart, change of the ice temperature along with the air temperature)Chemical) measured air temperature TaTemperature T of snow or ices。
From fig. 2, the following conclusions can be drawn:
1. when T isa<At 0.0 ℃, the internal temperatures of the ice cover and the snow cover are approximately linearly distributed; surface temperature T of snow coversWith air temperature TaChange, the former and the latter having a certain time lag, TsIs close to TaA difference of about 1.0 to 3.0 ℃, as shown in region a and region B in fig. 2;
2. when the day is Ta>0.0 ℃ and night Ta<At 0.0 deg.C, the snow cover gradually disappears and the temperature inside the ice cover becomes non-linearly distributed, as shown by curve 2016/4/11 in FIG. 2.
3. When T isa<At 0.0 deg.C, the temperature T of ice surface under the snow coveris(as shown at point C) is much greater than air temperature TaLinearly regressing T according to the data of three observation pointsis≈0.34Ta2.30, which shows that the snow cover has good heat preservation effect, and the surface temperature of the ice cover under the snow cover is far higher than the air temperature.
From 4.11 months to the beginning of 4 months, the ice cover is covered by thick snow, and the water temperature of the ice cover is about equal to 0.0 ℃.
In conclusion, the surface temperature T of the icebound rivers and lakessApproach to TaIncluding the bare ice cover surface, this has led to the idea, at Ts＝TaThe point is linearized with equation (1.1), i.e.:
Figure BDA0002847564820000083
in the formula: the subscript "0" denotes Ts＝Ta；hsaIs the heat exchange coefficient of the river and lake with the atmosphere, W/m2.℃；
Figure BDA0002847564820000091
In the formula:
Figure BDA0002847564820000092
Figure BDA0002847564820000093
Figure BDA0002847564820000094
Figure BDA0002847564820000095
εa0＝1-0.35exp(-10Rhesa/(273.15+Ta))，
Figure RE-GDA0002941956820000096
due to Ts＝TaTime of flight
Figure BDA00028475648200000916
Therefore, formula (2.2) can be rewritten as:
Figure BDA0002847564820000097
because of the solar radiation and the surface temperature T of rivers and lakessIrrelevant, therefore:
Figure BDA0002847564820000098
in the formula:
Figure BDA0002847564820000099
is a long-wave radiation heat exchange coefficient, W/m2.℃；
Figure BDA00028475648200000910
W/m for evaporation-cooling and convection heat exchange coefficient2.℃。
When assuming Ts＝TaIs the equilibrium temperature of the surface of the river or lake, i.e.
Figure BDA00028475648200000915
Then equation (2.1) can be reduced to a linearized model of the form Ashton (1986),
Figure BDA00028475648200000911
it should be noted that, in the following description,
Figure BDA00028475648200000917
this is just one assumption and is not true in some regions.
For long wave radiation, formula (1.4) and formula (1.5) at Ts＝TaCalculating partial derivative to obtain:
Figure BDA00028475648200000912
in the formula:
Figure BDA00028475648200000913
Figure BDA00028475648200000914
for evaporation-cooling and convection formulas (1.8) and (1.9) at Ts＝TaPoint partial derivative calculation:
Figure BDA0002847564820000101
3. linear model for heat exchange between rivers and lakes and atmosphere in typical region
The following will be based on the Chinese dictionaryDetermining the heat exchange coefficient h by linear regression method based on the weather station historical daily average weather data in the type regionsaAnd
Figure BDA0002847564820000102
the linear model of (2). It should be noted that, the weather station historical weather data TaC and RhThe method is different from the actual situation of rivers and lakes, but the long-term statistical properties of the method are relatively close.
3.1 coefficient of heat exchange hsaLinear regression of
FIGS. 3 and 4 show two ice periods T of Beijing areas 2015.12.1-2016.2.29 and 2016.12.1-2017.2.29a、 RhAnd the daily average value of C, the wind speed V in equation (2.7)zWhen 0, first, T is put in order of datea、RhH is calculated by substituting C into the formula (2.6), (2.7) and (2.4)saThen according to TaIs arranged in the order of magnitude of hsaThe value of (b) can be obtained as h shown in FIG. 3 and FIG. 4saWith TaA varying relation curve in which RhThe influence of C and C has been included (the left graphs of FIGS. 3 and 4 show daily average air temperature TaA graph relating to time t; the middle chart is the daily average relative humidity RhAnd a correlation graph of cloud cover C and t; the right side is hsaLinear regression graph of (a).
From FIGS. 3 and 4, h can be derivedsaThe linear regression empirical formula of (a):
2015.12.1—2016.2.29：hsa＝10.11+0.11Ta (3.1a)
2016.12.1—2017.2.28：hsa＝10.11+0.17Ta (3.1b)
formula (3.1a) to formula (3.1b) are
|Δhsa/hsa|＝0.06|Ta|/(10.11+0.11Ta)
As shown in FIGS. 3 and 4, | T is shown in addition to individual extreme cold tidesa|<10.0 deg.C, at which time, | Δ hsa/hsa|<7 percent. Accordingly, an important conclusion can be drawn: heat exchange system obtained by using average weather data of typical annual history days for one regionNumber hsaAnd can be used for predicting heat exchange of other years. The conclusion is also universal for other regions.
By using the method similar to the above, other regions h can be obtainedsaAnd TaThe linear relationship of (c). Typical regions are listed in Table 1, including weather characteristics of desert river, Shenyang, Baotou, Beijing, Baoding, Lassa and different wind speeds VzTime hsaWhere the wind speed is assumed to be the average wind speed on ice days. The Heilongjiang desert river is the region with the largest latitude, the coldest climate, large humidity, large cloud cover and long ice period in China, and hsaHas the smallest average value; the Baotou belongs to an inner Mongolia plateau, and has dry climate, less cloud and longer ice period; small latitude of Tibet Lhasa, air drying, less cloud, long ice period, but lower atmospheric pressure, hsaThe average value of (a) is small; shenyang, Beijing and Baoding belong to plain areas, have high atmospheric pressure throughout the year, are positioned in the middle and north of China, are air-dried and less cloudy, have short ice season time, but have hsaThe average value of (a) is large.
The following conclusions can be drawn from table 1: 1) heat exchange coefficient h between river and lake and atmospheresaProportional to the air temperature Ta; 2) when V is knownzHeat exchange coefficient h of 0.0m/ssa0Then the heat exchange coefficients for different wind speeds can be described as:
hsa＝(1+0.25Vz)hsa0 (3.2)
because of the daily average temperature T of Beijing, baoding, Shenyang and Baotou in the ice periodaAt-17 deg.C to 10 deg.C, 0.20-0.22% of C, Rh＝0.37—0.40，hsaThe values of (A) are not very different, a uniform parameter can be adopted, when V iszWhen h is 0.0, hsa0About 10.0W/m2DEG C. Desert river and Lasa hsaSlightly smaller than that in Beijing and other areas, the former is caused by higher relative humidity in the ice period, and the latter is caused by higher elevation of altitude.
TABLE 1 typical regional meteorological characteristic parameters and linearization results of river, lake and atmosphere heat exchange model
Figure BDA0002847564820000111
3.2 Long-wave radiation
Figure BDA0002847564820000112
And hbaLinear regression of
FIG. 5 shows the black dragon river desert river T from 11 months and 1 day in 2015 to 4 months and 30 days in 2016a、RhAnd C, the dotted line and the solid line represent daytime and nighttime parameters, respectively (the left graph of FIG. 5 represents daily average air temperature TaA graph of time t; the middle chart is the daily average relative humidity RhA graph of the relationship with t; the right graph is a graph of daily average cloud C versus t). The desert river belongs to a high and cold region, the temperature at night from the beginning of 11 months to the late 4 months of the next year is less than zero, the lowest temperature is close to-40 ℃, and the river section of the Heilongjiang river in the region is kept closed; relative humidity is nearly saturated, R, between 11 months and early 4 months of the following yearh→ 1.0; cloudy day with cloud amount C often equal to 100%, for
Figure BDA0002847564820000113
Has a great influence.
Daily average temperature Ta＝(TsunTa1+(24-Tsun)Ta2) Relative humidity R,/24h＝(TsunRh1+(24-Tsun)Rh2) (T) 24 cloud C ═ TsunC1+(24-Tsun)C2) -24, wherein: t issunFor the time of day, subscripts 1 and 2 indicate day and night, respectively. According to the date sequence, Ta、RhAnd C is calculated by formula (13)
Figure BDA0002847564820000128
And hbaThen according to TaAre respectively arranged in sequence
Figure BDA00028475648200001211
And hbaThe value of (D) can be obtained as shown in FIG. 6
Figure BDA0002847564820000129
And hbaWith TaA varying relation curve in which RhThe influence of C and C has been included (left side in FIG. 6 is
Figure BDA00028475648200001210
Linear regression curve of (1); the right side is hbaLinear regression curve of (d).
Linear regression from the right graph of fig. 6 yields:
Figure BDA0002847564820000121
Figure BDA0002847564820000122
namely:
Figure BDA0002847564820000123
the above results are obtained from a typical year analysis of the desert river, and whether it is applicable to other years is an important question. Therefore, the following empirical formula is obtained by linear regression based on the historical weather data of the black dragon river in 2016, 11 months and 1 day to 2017, 4 months and 30 days:
Figure BDA0002847564820000124
from formula (3.3) -formula (3.4):
Figure BDA0002847564820000125
therefore, it is not only easy to use
Figure BDA0002847564820000126
Based on this, an important conclusion can be drawn: to one groundAnd the linear formula of the net long wave radiation obtained by typical annual historical weather data can be used for predicting the net long wave radiation of other years.
From the left graph of fig. 6:
hba≈3.1 (3.4)
similar methods can be used to obtain linearized models of long-wave radiation in other regions, and Table 21.7.2 lists the average ice cloud C and relative humidity R for Heilongjiang desert river, Shenyang, inner Mongolia Baotou, Beijing, Baoding, Tibet LhasahAnd obtained by regression
Figure BDA0002847564820000127
Can be described as TaThe constant term value is increased from 70 to 95.0, the slope value is between 0.4 and 0.9, and h isbaThe value is between 3.0 and 4.0. The Heilongjiang desert river is the region with the largest latitude, the coldest climate, large humidity, large cloud cover and long ice period in China, and hbaThe value is minimum; the Tibetan Lassa has small latitude, but belongs to plateau areas, such as dry air, little cloud and long ice period; the other places are positioned in the middle and the north of China, and the climate is dry, so that the ice period time is short.
TABLE 2 typical regional meteorological parameters and long-wave radiometric results
Figure BDA0002847564820000131
Observing the table 2, the daily average temperature T of Beijing, Baoding, Shenyang, Baotou and Lassa in the ice periodaBetween-20 deg.C and 10 deg.C, 0.20-0.22% of cloudiness C, Rh0.34-0.40, and removing extremely few extreme cold weather T in the regionsa<At times T other than-10 deg.CaBetween-10 ℃ and 10 ℃, so that
Figure BDA0002847564820000132
Middle TaThe front coefficient is changed between 0.5 and 0.90
Figure BDA0002847564820000133
Is not so much affected and can therefore be described in a unified form as:
Figure BDA0002847564820000134
for Ta、C、RhSimilar areas may also be referred to for use.
3.3 Evaporation-Cooling Heat flux
Figure BDA0002847564820000139
Linear model of
Because the daily average temperature T of the ice season in ChinaaGenerally between-40 ℃ and 10 ℃ when Ts＝TaPressure of saturated water vapor esWith TaAs shown in fig. 7, the following is obtained by piecewise linearization:
Figure BDA0002847564820000135
therefore:
Figure BDA0002847564820000136
3.4 Linear Heat exchange model of typical area
In summary, from tables 1 and 2 and formula (3.2), a unified linear model of heat exchange between Beijing, Baoding, Shenyang, Baotou Bingli river lake and atmosphere can be obtained:
Figure BDA0002847564820000137
due to 0.5Ta＜＜(6.04+2.95Vz)(1-Rh)(c1+c2Ta) Therefore:
Figure BDA0002847564820000138
in the formula: h issa＝10.0(1+0.25Vz)。
At wind speed VzWhen equal to 0, hsa＝10.0W/m2The temperature is higher than that of the product shown in Table 2, wherein the long-wave radiant heat exchange coefficient h is Beijing, Baoding, Shenyang and Baotou ice periodba＝3.9W/m2DEG C, i.e. the evaporative-cooling and convective heat exchange coefficient heh＝hsa-hba＝6.1W/m2From this, an important conclusion can be drawn: during the ice season, evaporation-cooling and convection dominate the heat exchange between the river and lake and the atmosphere, and the long-wave radiation is inferior.
Finally, it should be noted that the above is only for illustrating the technical solution of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred arrangement, it should be understood by those skilled in the art that the technical solution of the present invention (such as the way of data application, various formula applications, the sequence of steps, etc.) can be modified or replaced with equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims (1)

1. A construction method of a heat exchange linearization model of an ice river lake and atmosphere is characterized by comprising the following steps:
step 1, calculating the net solar radiation heat flux
Figure FDA0002847564810000018
By calculating the solar heat flux of cloud
Figure FDA0002847564810000019
Indirect calculation of net solar radiation heat flux
Figure FDA00028475648100000110
Figure FDA0002847564810000011
Wherein：
Figure FDA00028475648100000111
Is astronomical radiant heat flux; p is the average atmospheric transparency coefficient; m is the optical atmospheric mass; c is cloud amount;
the average calculation is carried out on the data of each observation day to obtain the net heat flux of the solar radiation
Figure FDA00028475648100000112
Step 2, calculating heat flux of long-wave radiation of rivers and lakes
Figure FDA00028475648100000113
Figure FDA0002847564810000012
In the formula: sigma is a Stefan Boltzmann constant; epsilonwIs a correction factor; t issThe surface temperature of the river or lake;
step 3, calculating the heat flux of long-wave atmosphere reversely radiated to the river surface
Figure FDA00028475648100000114
Calculating the saturated vapor pressure e of airs：
Figure FDA0002847564810000013
es0Is TsSaturated water vapour pressure at 0.0 ℃; a and b are constants;
calculating the atmospheric emissivity epsilon in sunny daysa：
εa＝1-0.35exp(-10ez/(273.15+Ta))＝1-0.35exp(-10Rhes/(273.15+Ta))
In the formula: e.g. of the typezIs empty at a height of 1.5m from the river surfaceVapor pressure in gas; t isaThe temperature measured at a height of 1.5m above the river surface; e.g. of the typesIs the saturated vapor pressure of air; rhIs the relative humidity of the air;
Figure FDA0002847564810000014
γathe reflectivity of the surface of the river or lake to the atmospheric long-wave back radiation is shown; k is a coefficient;
step 4, calculating heat flux of evaporation-cooling
Figure FDA00028475648100000115
Figure FDA0002847564810000015
Wherein: vzThe wind speed is 1.5m away from the surface of the river or lake;
step 5, calculating the heat flux of air convection
Figure FDA00028475648100000116
Figure FDA0002847564810000016
Step 6, calculating daily average net heat flux of the surface of the river and the lake
Figure FDA00028475648100000117
Figure FDA0002847564810000017
Step 7, constructing a linear river lake and atmosphere heat exchange model:
setting Ts＝TaLinearizing daily average net heat of river and lake surfaceFlux model:
Figure FDA0002847564810000021
wherein:
Figure FDA00028475648100000215
is Ts＝TaDaily average net heat flux on the surface of the river or lake;
Figure FDA00028475648100000216
is Ts＝TaAtmospheric long wave reverse radiation;
Figure FDA00028475648100000217
is Ts＝TaHeat flux of long-wave radiation of rivers and lakes;
Figure FDA00028475648100000218
is Ts＝TaEvaporative-cooling heat flux in time;
in the formula:
Figure FDA0002847564810000022
Figure FDA0002847564810000023
Figure FDA0002847564810000024
Figure FDA0002847564810000025
Figure FDA0002847564810000026
to pair
Figure FDA00028475648100000211
And
Figure FDA00028475648100000212
at Ts＝TaCalculating partial derivative to obtain:
Figure FDA0002847564810000027
in the formula:
Figure FDA0002847564810000028
Figure FDA0002847564810000029
wherein: h isbaIs the heat exchange coefficient of long wave radiation;
to pair
Figure FDA00028475648100000213
And
Figure FDA00028475648100000214
at Ts＝TaPoint partial derivative calculation:
Figure FDA00028475648100000210
wherein: h isehEvaporation-cooling and convection heat exchange coefficients;
and 8, constructing a linear heat exchange model of the research area:
carrying out linear regression analysis on the data of the research area to obtain a linear heat exchange model of the research area:
Figure FDA0002847564810000031
due to 0.5Ta＜＜(6.04+2.95Vz)(1-Rh)(c1+c2Ta) Therefore:
Figure FDA0002847564810000032
in the formula: h issa＝10.0(1+0.25Vz)。
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