CN110502722A - The measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load - Google Patents
The measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load Download PDFInfo
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Abstract
The present invention provides the measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load, the component that will affect Alpine Grasslands Second productivity is decomposed into snow disaster load force, the maintenance energy of Grassland ecosystems function, avenge disaster prevention and control force, four functional modules of livestock products productivity, interaction between the component and state of four modules, it influences each other and restricts the size and level of the secondary production capacity of Alpine Grasslands, the Alpine Grasslands ecosystem is under the stress and load action of snow disaster evil, meadow Second productivity support system will occur to be displaced accordingly, snow disaster load force is bigger, phylogenetic displacement is also bigger, and meadow Second productivity is smaller.The present invention portrays the logical relation of snow disaster load-displacement response, and the size of meadow Second productivity is portrayed according to system displacement inverse, improves science, objectivity and the accuracy of quantitative expression meadow Second productivity.
Description
Technical field
The present invention relates to Alpine Grasslands Second productivity dynamics under eco-environment technology field, especially snow disaster load to ring
The measuring method answered.
Background technique
The primary productivity on meadow occurs in the form of resource, is the base that meadow economic benefit and mankind's happiness are promoted
Plinth.Meadow Second productivity is the ability of unit area grassland resources production livestock products in the regular period, and it is raw to embody meadow
The final purpose of service mankind's happiness is produced, the livestock products index only produced with meadow just can truly reflect the production on meadow
Ability.It is made by a variety of natures, social factor in view of meadow Second productivity to the dependence of grassland resources and natural environment
About, and these restricting relations show sufficiently complex nonlinear characteristic mostly.Therefore, how more objectively to portray
This nonlinear characteristic establishes the quantitative determination model for being applied to theoretical research and Instructing manufacture, is always both at home and abroad on meadow
Weaker link in Second productivity research, the measurement of the secondary production capacity in meadow is even more Practaculture Science, geography
One of key problem.
The research on standard of livestock products measurement Productivity.It is raw with animality that meadow production contains vegetalitas production in itself
The overall process of production, due to this production routine, the complexity of production process, for a long time, in the measurement mark of Productivity
There is misunderstanding and confusion in quasi- aspect, main problem is the product some intermediaries as final products, and evaluation grass accordingly
Ground production capacity.Meadow actual production capacity is accurately measured, is needed by final products, the meaning of livestock products unit is it
According to the truth of the last one transformation stage in the theoretical reflection production process of Grassland ecosystems, in grassland science and grass
In the energy and material conversion process of the ground ecosystem, new a concept and scale are provided.This scale not only can be direct
Productivity itself is measured, can also reflect the interdisciplinary science technical level (appoint after week etc., 1979) of meadow production indirectly.It is real
On border, measured with livestock products research origin the sixth of the twelve Earthly Branches of Productivity long (Wiegert and Evans, 1967；
Petrusewicz and Macfadyen,1970；Heal and MacLean, 1975), early in the thirties in last century, Li Chasen
(1938,1939) are just it is proposed that the concept of meadow production unit (GPU), attempts the measuring and calculating mark of one Productivity of building
Standard, but finally growth of animal amount and available livestock products ultimate output are not separated, thus cannot define from animal increment to
The inversion quantity of the output of live-stock product can be used.In this regard, Ren Jizhou et al. (1979) endeavours Animal resources and animal product on attribute
It is distinguished, has specially worked out the livestock products unit commutation table of all kinds of livestock products, specifically to measure the secondary production in China meadow
Ability.According to the commutation table, the scholars such as the peak Lan Yun (1999) using Wulanchabu League meadow as case, to meadow Second productivity into
It has gone detailed evaluation, has reflected the secondary production capacity of dry steppe, two class difference grassland types of desert steppe.
The analog study of meadow Second productivity.No matter natural system or Economical service life, all exist simultaneously
Positive feedback and negative feedback structure.Positive feedback structure is the internal motivation that forward direction or reversal evolvement occur for system, and negative feedback structure
It is then the inherent tied mechanism that system reaches certain homeostasis, grassland agriculture is exactly that both simultaneous were both mutually interconnected
System, the again opposition of conflicting internal motivation and uniformly, are also exactly the alternation sum coupling of these positive-negative feedbacks, constitute grass
The feedback system of ground animal husbandry complexity.According to the grass poultry equilibrium of supply and demand and meadow cattle-breeding system positive and negative feedback principle, Chinese scholar
Lv Shengli and Song Bingfang (1991,1992) establishes the secondary production kinetic model in meadow from micro and macro two angles.
While the exploitation of the model is intended to protect grassland resources, the ability of the secondary production in meadow is improved, model structure fully considers
Domestic animal increases positive feedback loop, herbage total output positive feedback loop, forage yield and livestock number negative feedback loop, livestock and goes out
Column negative feedback loop, by system dynamics method, the meadow the Lai Shixian primary, the coordination of secondary production and uniformly are shown
The change procedure that forage yield and domestic animal energy i (in vivo) are consumed and accumulated, has reproduced pasture stock periodic cycle, is meadow-
Cattle-breeding system theoretical research and production management provide a kind of tool of " experiment " property.
In addition, China's some scholars have also carried out the Study on influencing factors of meadow Second productivity.As Chen You is fervent and old
Space (1994) experimental study influences of 6 kinds of grazing intensities to Yak Growth and meadow Second productivity, the results showed that, it herds
Intensity has a significant effect to yak daily gain, increase of the discovery with grazing intensity, the rule that yak daily gain is substantially reduced.Dong
For the whole people etc. (2005) using Qinghai-Tibet Platean as object, emphasis is directed to Alpine meadow type, analyzes Grazing Intensities for Yaks and Kobresia pygmaea
The relationship of Meadow Pasture Second productivity.
Although domestic and foreign scholars have carried out the research of more range to meadow Second productivity, it is secondary to achieve meadow
The costing standard of productivity, grazing impact, system simulate the achievement and progress of three main aspects, but for Alpine Grasslands ecology
For the explorations of intensions such as the Second productivity driving factors of system, dynamic change, structure law, still there are many Cognition Gaps
And theory and practice short slab.Currently, the modeling research method of meadow Second productivity is still in exploratory stage, system
Dynamics is quantization means common in the past, and this method considers the positive and negative feedback circuit between resource, product, highlights careless poultry
The principle of balance, embodies being closely connected between grassland resources and livestock products output, but the height restricted as particular surroundings
Cold Grassland ecosystems, the frozen soil environment for influencing Alpine Grasslands ecosystem Heat And Water Balance are changing, and meadow primary is raw
Force of labor is again extremely sensitive to climate change, and the natural calamity event increases, harm based on snow disaster evil are reinforced, and is measuring and is simulating
During the Second productivity of meadow, if not paying attention to these elements, these phenomenons, these processes, meadow is secondary
Measurement, the assessment of productivity will undoubtedly lose objectivity, actually occur deviation with the service function of cold area's Grassland ecosystems, and
The micro and macro kinetic model of meadow Second productivity established based on system dynamics, it is difficult to clearly characterize meadow
Dynamic response relationship, the structure interactive relationship of Second productivity structural element.The shadow of existing Alpine Grasslands Second productivity
Elements research is rung, does not also fully consider cold area's frozen soil, snow disaster, the mankind to the key player of the intervention of disaster.Meadow is secondary
The classification of productivity is calculated, although improving the accuracy of the final livestock products output form in meadow, is difficult to answer grassland ecology
Cause-consequence connection between exterior load pressure-Productivity response can not parse in Grassland ecosystems closely
Associated weather-resource-yield difference component, different link, the role between different role power and correlation.It is further
Science, normalization, directiveness and the application for the research of Alpine Grasslands Second productivity are improved, Alpine Grasslands must be reinforced
The Hazard Loads and response simulation of Second productivity are studied, and a kind of can reflect its reality, inherent, dynamic, knot is established
The speciality method of structure, realize to Alpine Grasslands load-Productivity response quantitative measure, dynamic monitoring, Structure Identification target, from
And service the sustainable development of Alpine Grasslands, grassland agriculture, local herdsman, plateau pastoral area.
Summary of the invention
In view of the above technical problems, the present invention using snow disaster load force, ecosystem function maintenance energy, snow disaster prevention and control power,
Livestock products Structure of Productive Forces module parses Alpine Grasslands Second productivity to the responsive state under snow disaster load action, carries out
Snow disaster load-ecological functions-snow disaster prevention and control-product output internal relation and Study on mechanism, portray snow disaster load-displacement
The logical relation of response portrays the size of meadow Second productivity according to system displacement inverse, improves quantitative expression meadow the
Science, objectivity and the accuracy of two property productivity.
Specific technical solution are as follows:
The measuring method of Alpine Grasslands Second productivity dynamic response under a kind of snow disaster load, comprising the following steps:
(1) the measurement frame that Alpine Grasslands Second productivity responds under snow disaster load
Load-response and analytic dynamics principle, using snow disaster load force, Grassland ecosystems function maintenance energy, plateau
Snow disaster prevention influences each other, interacts quantitatively to sentence knowledge with four control force, Alpine Grasslands livestock products productivity power plant modules
The responsive state of Alpine Grasslands Second productivity under snow disaster load；Snow disaster load intensity is bigger, deviates the secondary production in meadow
The displacement of power normal level is also bigger, on the contrary, then smaller, therefore, it is secondary that the inverse of system displacement can objectively respond meadow
Responsiveness of the productivity to snow disaster load；
(2) rating model that Alpine Grasslands Second productivity responds under snow disaster load
According to the measurement frame that Alpine Grasslands Second productivity under snow disaster load responds, meadow Second productivity is to snow
The response of calamity load is load force (P (t)), inertia forceDamping force4 important changes of elastic force (Ku (t))
Measure synthesis nonlinear function, load force corresponds to snow disaster load intensity, elastic force correspond to Grassland ecosystems function maintenance energy,
Damping force corresponds to plateau snow disaster prevention Alpine Grasslands livestock products productivity corresponding with control force, inertia force, utilizes analytic dynamics
Load-is responded the static problems that this kinematics problem is converted into any moment, makes system by equation of motion direct balanced method
It in dynamic equilibrium state, and then obtains under different snow disaster load intensities, the measurement letter of Alpine Grasslands Second productivity response
Number:
In formula, M, C, K are respectively the mass matrix, damping matrix and stiffness matrix of system；u(t),Respectively
It is displacement, the velocity and acceleration vector of system unit node；P (t) is external load vector；Above-mentioned power balance equation is actually
It is exactly inertia force related with accelerationDamping force related with speedAnd the related bullet with displacement
Standing balance of the property power (Ku (t)) in moment t and load；
(3) four torque battle array key vectors and dimension
According to model, meadow Second productivity, that is, livestock products productivity to the response of snow disaster load depend on load force,
Interactive synthesis result between 4 torque battle array different dimensions of inertia force, damping force and elastic force, different vectors, each torque
Battle array is corresponding with 4 dimensional vectors；The crucial vector of each torque battle array of the equation of motion is indicated with the following table 1:
1 equation of motion torque battle array of table and corresponding vector
(4) measurement of meadow Second productivity response
In order to eliminate the influence of different dimensions, different variables are handled using very poor standard law.Wherein, positive variable
Using formula (2), negative sense variable uses formula (3).In portraying 4 dimensional vector of torque battle array, ever-frozen ground active layer thickness variable is removed
It is negative outward, remaining variables are forward direction.
X in formulaiFor variable actual value；xmin、xmaxRespectively to the maximum and minimum value of dependent variable；Table respectively
Show the standard value of positively and negatively variable.
The two sides for the measurement functional expression (1) that Alpine Grasslands Second productivity is responded are the same as multiplied by mass of system inverse of a matrix
Matrix M-1:
It is displaced for the response of solving system load, introduces transposed matrixKinetics equation (4) is converted into shape
State space equation:
In formula, I, O, D, G are respectively unit matrix, null matrix, sytem matrix and control matrix.
The solution of equation (5) are as follows:
In formula, eDtQ (0) indicates system free vibration caused by unit initial displacement and speed；eD(t-τ)It is rung for unit pulse
Function is answered,When indicating pulse change τ, variable quantity is responded with the system that functional integration indicates；It utilizes
Matlab software solves equation (7), obtains displacement components u (t) solution, the inverse of displacement is considered as meadow Second productivity pair
The response of snow disaster load.
Compared with existing method, meadow Second productivity response measuring method tool under snow disaster load provided by the invention
Have it is following 3 aspect comparative advantages and the utility model has the advantages that
(1) meadow Second productivity responds measuring method under snow disaster load of the present invention, by the secondary life in meadow
Force of labor to the response of snow disaster load be decomposed into snow disaster load force, livestock products productivity, snow disaster prevention and control power, resources support capacity four it is close
The key variables of association, interaction are cut, pressure outside disaster that is both comprehensive, being comprehensively reflected influence meadow Second productivity
Power, the mankind support the internal and external environment feature of livestock products production status to the intervention of disaster and grassland resources itself, and sufficiently,
The natural quality (weather and hydrothermal condition) and human intervention difference for influencing Alpine Grasslands Second productivity is systematically contemplated,
The internal association and interactive process from snow disaster load cause to meadow Second productivity response results are highlighted.
(2) meadow Second productivity responds measuring method under snow disaster load of the present invention, snow disaster load is strong, poultry
Production power, snow disaster prevention and control power, resources support capacity and the load force in analytic dynamics, inertia force, damping force, elastic force are tight
It thickly connects, and utilizes load-response action and reaction principle, pass through the function of game mutual between four torque battle arrays
Relationship, variable restricting relation of the characterization meadow Second productivity to snow disaster load response, index system of both avoiding over conjunction
At entitled subjectivity, and four torque battle arrays and key dimension can be parsed to the classification effect of Second productivity and goniochromatism
It is different, it fully demonstrated meadow Second productivity response factor identification under snow disaster load, enhanced flexibility, the correspondence for applying plan.
(3) meadow Second productivity responds measuring method under snow disaster load of the present invention, is applied to climate change
The quantitative analysis that responds with meadow Second productivity to snow disaster, process study and judge, plan is applied in dynamic monitoring, Scenarios, synergy, together
When this method frame, mentality of designing can both deduce and be applied to different natural hazards risks, different livestock grazing intensities, difference
Mankind's activity presses the response measurement of lower meadow (or land resource) productivity, also can be applied to different spaces scale resource,
To the quantitative measure of load response, this method is with a wide range of applications and obviously for environment and social economic system support force
Realistic meaning.
Detailed description of the invention
Fig. 1 is the measurement frame that Alpine Grasslands Second productivity responds under snow disaster load of the present invention；
Fig. 2 is the rating model that Alpine Grasslands Second productivity responds under snow disaster load of the present invention；
Fig. 3 is the variation of embodiment snow disaster load and the response of Alpine Grasslands Second productivity.
Specific embodiment
It is described in conjunction with the embodiments the specific technical solution of the present invention.
The measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load of the invention, including following step
It is rapid:
1, the measurement frame that Alpine Grasslands Second productivity responds under snow disaster load
According to the overall process of Animal husbandry production, can reflect Productivity with three kinds of modes: primary productivity is one
The ability of unit area production plant product (Grassland Biomass, forage grass and feed) in the timing phase, measurement index are " unit plane
Long-pending grass yield ".Second productivity is the ability of unit area production animal product in the regular period, and measurement index is
" the unit area output of live-stock product ".Third is that not influenced under livestock nutritional condition, unit area meadow can hold in certain grazing season
The livestock number received, measurement index are " animal number ".
For Alpine Grasslands often due to height above sea level, temperature are low, the frequency that snow disaster evil occurs is high, to Grassland ecosystems function,
There is significant, direct influence, i.e. snow disaster load intensity and Alpine Grasslands second in the output of grassland resources and livestock products
Property productivity between there are close response relation, and the measurement of this load-response is often complex, more difficult, mistake
It goes to commonly use several index weighted sums, form composite index quantization load-response degree, but this weight several indexs is asked
And method can not objective expression snow disaster pressure between Alpine Grasslands ecosystem function and livestock products output capacity
In association, structure interactive state, load-response dynamic process cannot be especially expressed.To avoid this defect, the present invention according to
It is pre- using snow disaster load force, Grassland ecosystems function maintenance energy, plateau snow disaster according to load-response and analytic dynamics principle
It is anti-to influence each other, interacted quantitatively to sentence and know snow disaster lotus with four control force, Alpine Grasslands livestock products productivity power plant modules
Carry the responsive state of lower Alpine Grasslands Second productivity, such as Fig. 1.Snow disaster load intensity is bigger, deviates the secondary production in meadow
The displacement of power normal level is also bigger, on the contrary, it is then smaller, therefore the inverse of system displacement can objectively respond the secondary production in meadow
Responsiveness of the power to snow disaster load.
2, the rating model that Alpine Grasslands Second productivity responds under snow disaster load
According to the measurement frame that Alpine Grasslands Second productivity under snow disaster load responds, meadow Second productivity is to snow
The response of calamity load is load force (P (t)), inertia forceDamping forceElastic force (Ku (t)) 4 is important
Variable synthesis nonlinear function, load force correspond to snow disaster load intensity, elastic force correspond to Grassland ecosystems function maintenance
Power, damping force correspond to plateau snow disaster prevention Alpine Grasslands livestock products productivity corresponding with control force, inertia force, such as Fig. 2, using dividing
Dynamical motion equation direct balanced method is analysed, load-is responded into the static(al) knowledge that this kinematics problem is converted into any moment
Topic makes system be in dynamic equilibrium state, and then obtains under different snow disaster load intensities, the response of Alpine Grasslands Second productivity
Measurement function:
In formula, M, C, K are respectively the mass matrix, damping matrix and stiffness matrix of system；u(t),Respectively
It is displacement, the velocity and acceleration vector of system unit node；P (t) is external load vector；Above-mentioned power balance equation is actually
It is exactly inertia force related with accelerationDamping force related with speedAnd the related elasticity with displacement
Standing balance of the power (Ku (t)) in moment t and load；
3, four torque battle array key vectors and dimension
According to model, meadow Second productivity, that is, livestock products productivity to the response of snow disaster load depend on load force,
Interactive synthesis result between 4 torque battle array different dimensions of inertia force, damping force and elastic force, different vectors, for high and cold
The special water in meadow (meadow season of growth precipitation) heat (meadow season of growth temperature) environment and Alpine Grasslands ecosystem function
The crucial vector of the features such as regulation of ever-frozen ground element can be limited by, each torque battle array of the equation of motion can be indicated with the following table 1.
1 equation of motion torque battle array of table and corresponding vector
4, the measurement of meadow Second productivity response
To eliminate dimension impact, data are comparable, original variable is handled using very poor standard law.Its
In, positive variable uses formula (2), and negative sense variable uses formula (3).In portraying 4 dimensional vector of torque battle array, except ever-frozen ground activity
Layer gauge variation is negative outward, and remaining variables are forward direction.
In formula, xi·For variable actual value；xmin、xmaxRespectively to the maximum and minimum value of dependent variable；Respectively
Indicate the standard value of positively and negatively variable.
The two sides for the measurement functional expression (1) that Alpine Grasslands Second productivity is responded are the same as multiplied by mass of system inverse of a matrix
Matrix M-1:
It is displaced for the response of solving system load, introduces transposed matrixKinetics equation (4) is converted into
State space equation:
In formula, I, O, D, G are respectively unit matrix, null matrix, sytem matrix and control matrix.
The solution of equation (5) are as follows:
In formula, eDtQ (0) indicates system free vibration caused by unit initial displacement and speed；eD(t-τ)Unit impulse response
Function,When indicating pulse change τ, variable quantity is responded with the system that functional integration indicates；By
Matlab software solves equation (7), obtains displacement components u (t) solution, the inverse of displacement is considered as meadow Second productivity pair
The response of snow disaster load.
The present embodiment is by taking the Changjiang river, Yellow River source (Lantsang) as an example, 7.46 × l0 of drainage area4km2.Source region is located at blueness
Plateau innerland is hidden, 4 000m or more of mean sea level has typical land plateau climate characteristic.River gathers in area, lake, natural pond
Pool is numerous, and snow mountain glacier blazons, and is that height above sea level highest, area be maximum in the world, the most abundant area of Wetland Type, is known as " rivers
Source ", " Asia water tower " title.Administrative division is covered the Maqin of Yellow River source, Gande, Banma County and is controlled long, Dagri, Madoi County
Most of and Qumalai County fraction；And Source Region of The Yangtze River Zhiduo County, claim more, Qumarleb, Zaduo County and Yushu County and Tang's Gu
Most of region in the town La Shan.Source region climate change is sensitive, is one of main Alpine-arctic Pastoral in China, based on agriculture and animal husbandry population, herds
The people are strong to the dependence of grassland agriculture, and meadow livestock products are the main supports of local herdsman's livelihood, due to snow disaster occurrence frequency
High, harm causes great threat greatly, to source region herdsman production, life.
It is obvious that snow disaster load intensity rises, system displacement increases, meadow Second productivity reduces；On the contrary, snow disaster lotus
Carry strength reduction, system displacement is reduced, meadow Second productivity is promoted；Snow disaster load intensity is directly proportional to system displacement, with
Meadow Second productivity is inversely proportional.During from 1984 to 2014 year, source region snow disaster load intensity coefficient reduces 75.2%, and
Corresponding meadow Second productivity response coefficient then increases 75.2%.
In addition, Lantsang meadow Second productivity trend is continuously increased, on the one hand have benefited from snow disaster load intensity
Weaken, even more important is that the inertia force increase for influencing meadow Second productivity and the mankind damp snow disaster prevention and control ability
The significant reinforcing of power, load force, inertia force, damping force, four power of elastic force are mutually contended, the especially increasing of inertia force, damping force
Add the negative role and function that largely reduced snow disaster load to meadow Second productivity, to effectively promote meadow
Two property productivity continue, are firm soaring.
Claims (2)
1. the measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load, which is characterized in that including following step
It is rapid:
(1) the measurement frame that Alpine Grasslands Second productivity responds under snow disaster load
Load-response and analytic dynamics principle, using snow disaster load force, Grassland ecosystems function maintenance energy, plateau snow disaster
Prevention influences each other, interacts quantitatively to sentence knowledge snow disaster with four control force, Alpine Grasslands livestock products productivity power plant modules
The responsive state of Alpine Grasslands Second productivity under load；Snow disaster load intensity is bigger, is deviateing meadow Second productivity just
The flat displacement of ordinary water is also bigger, on the contrary, then smaller, therefore, the inverse of system displacement can objectively respond the secondary production in meadow
Responsiveness of the power to snow disaster load；
(2) rating model that Alpine Grasslands Second productivity responds under snow disaster load
According to the measurement frame that Alpine Grasslands Second productivity under snow disaster load responds, meadow Second productivity is to snow disaster lotus
The response of load is load force (P (t)), inertia forceDamping force4 significant variables of elastic force (Ku (t)) close
At nonlinear function, load force corresponds to snow disaster load intensity, elastic force correspond to Grassland ecosystems function maintenance energy, damping
Power corresponds to plateau snow disaster prevention Alpine Grasslands livestock products productivity corresponding with control force, inertia force, is moved using analytic dynamics
Load-is responded the static problems that this kinematics problem is converted into any moment, is in system by equation direct balanced method
Dynamic equilibrium state, and then obtain under different snow disaster load intensities, the measurement function of Alpine Grasslands Second productivity response:
In formula, M, C, K are respectively the mass matrix, damping matrix and stiffness matrix of system；u(t),It is respectively
The displacement of system cell node, velocity and acceleration vector；P (t) is external load vector；Above-mentioned power balance equation is actually
Inertia force related with accelerationDamping force related with speedAnd the related elastic force with displacement
The standing balance of (Ku (t)) in moment t and load；
(3) four torque battle array key vectors and dimension
According to model, meadow Second productivity, that is, livestock products productivity depends on load force, inertia to the response of snow disaster load
Interactive synthesis result between 4 torque battle array different dimensions of power, damping force and elastic force, different vectors, each torque battle array are right
There should be 4 dimensional vectors；
(4) measurement of meadow Second productivity response
Firstly, being handled using very poor standard law different variables；Wherein, positive variable uses formula (2), and negative sense variable uses
Formula (3)；In portraying 4 dimensional vector of torque battle array, except ever-frozen ground active layer thickness variable is negative outward, remaining variables are positive
To；
In formula, xiFor variable actual value；xmin、xmaxRespectively to the maximum and minimum value of dependent variable；It respectively indicates just
To the standard value with negative sense variable；
Secondly, measuring and calculating meadow Second productivity response；The measurement functional expression (1) that Alpine Grasslands Second productivity is responded
Two sides with multiplied by mass of system inverse of a matrix matrix M-1Will, obtain following formula:
It is displaced for the response of solving system load, introduces transposed matrixKinetics equation (4) is converted into state sky
Between equation:
In formula, I, O, D, G are respectively unit matrix, null matrix, sytem matrix and control matrix；
The solution of equation (5) are as follows:
In formula, eDtQ (0) indicates system free vibration caused by unit initial displacement and speed；eD(t-τ)For unit impulse response letter
Number,When indicating pulse change τ, variable quantity is responded with the system that functional integration indicates；It is soft using Matlab
Part solves equation (7), obtains displacement components u (t) solution, the inverse of displacement is considered as meadow Second productivity to snow disaster load
Response.
2. the measuring method of Alpine Grasslands Second productivity dynamic response under snow disaster load according to claim 1,
It is characterized in that, 4 dimensional vectors are respectively as follows:
Load force: average annual snowfall, mm；Average annual snowfall number of days, d；Average snow depth, cm；Snow disaster frequency, %；
Inertia force: cattle and sheep meat production, ton；Cattle and sheep milk yield, ton；Rate of domestic animals for sale, %；At the poultry death rate, %；
Damping force: unit livestock brooder area, m2/sheep unit；Unit livestock artificial pasture area, hm2/10000sheep
unit；The sensible density of road, m/km2；Information level of coverage, %；
Elastic force: NPP, gC/m2yr；Meadow season of growth mean temperature, DEG C；The meadow season of growth adds up precipitation, mm；Freeze for many years
Native active layer thickness, m.
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| CN111401727A (en) * | 2020-03-12 | 2020-07-10 | 中国科学院、水利部成都山地灾害与环境研究所 | Visual expression method for economic conduction effect of snow disaster on grassland livestock |
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| CN113642877A (en) * | 2021-08-05 | 2021-11-12 | 中国农业科学院草原研究所 | Snow disaster situation assessment method and system based on actual disaster damage of herdsmen |
| CN114707344A (en) * | 2022-04-15 | 2022-07-05 | 西南交通大学 | Method for calculating thickness of permafrost movable layer based on system dynamics |
| CN114707344B (en) * | 2022-04-15 | 2023-09-19 | 西南交通大学 | Permafrost active layer thickness calculation method based on system dynamics |
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