CN102668899B - Crop planting mode recognition method - Google Patents

Crop planting mode recognition method Download PDF

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CN102668899B
CN102668899B CN201210085386.1A CN201210085386A CN102668899B CN 102668899 B CN102668899 B CN 102668899B CN 201210085386 A CN201210085386 A CN 201210085386A CN 102668899 B CN102668899 B CN 102668899B
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vegetation
growing season
crops
cropping
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CN102668899A (en
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朱文泉
刘建红
姜楠
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Beijing Normal University
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Abstract

The invention discloses a crop planting mode recognition method which comprises the following steps: inputting remote-sensing vegetation index time series data, and determining the vegetation growth threshold; optimizing parameters by selecting training samples to obtain the shortest length of the growing season of the crops, the longest length of the growing season of the crops and the smallest growth magnitude of the crops; extracting the vegetation growth information which is the number of the growing season of the crops in one year, the length of each growing season of the crops and the growth magnitude of the crops, and eliminating the non-crops; calculating the number of the growing season of the crops to obtain the multiple cropping index in one year; and finally determining the crop planting mode comprehensively according to the multiple cropping indexes of the crops in the last year, current year and next year. Due to the adoption of the technical scheme, the crop planting mode can be recognized directly according to the remote-sensing vegetation index time series data, and the problems the experience of calculating parameters is deficient, and the peak numbers do not correspond to the crop planting modes are solved. The crop planting mode recognition method has the advantages of strong noise resisting capability, less required parameters and strong versatility.

Description

A kind of crop growing mode recognition methods
Technical field
The present invention relates to agricultural remote sensing technical field, particularly relate to a kind of crop growing mode recognition methods.
Background technology
Cropping pattern (Cropping pattern, CP) is the space expression of shift of crops, is the summary to stubble order before and after crops.Crop planting model is related to making full use of of the resources such as water, heat, light, soil fertility, is to improve field per unit area yield and total important technical links of producing, and has very important significance for efficient, controlled agricultural management.Along with the redistributing of the agricultural natural resources such as world wide light, heat, water, the continuing to increase and minimizing trend that arable land storage is potential of world population, cropping pattern also occurs to change.In time, accurate measurements agricultural planting pattern and change in time and space thereof, be conducive to prediction grain yield and change thereof and formulation agricultural development policy.Rational cropping pattern should be conducive to the most effectively utilizing of the various resources such as soil, sunlight, heat and water, obtains the best society of production estimation under prevailing condition, economy and environment benefit, and can develop sustainably.Crop growing mode monitoring can Timeliness coverage correct unsuitable planting patterns, keeps the sustainable development potentiality of ploughing, and then Ensuring Food Safety.
Chinese scholars attempts adopting meteorological data or statistical data, be minimum research unit reflecting regional and grown worldwide pattern with administrative area, from the spatial variations of macroscopically showing cropping pattern.But natural conditions of agriculture has the feature of Partial little climate, and internal diversity be can not ignore.Be such as that the Cultivate administration pattern of unit makes ecological region planting pattern complexity various with peasant household, this method can not describe the space characteristics of cropping pattern exactly.In addition, also there is certain hysteresis quality in the acquisition of meteorological data and statistical data, statistical data itself exists certain error, brings uncertainty to result of study.Large for spatial dimension, ageingly require the research of high cropping pattern, this method is difficult to reach requirement.
Satellite remote sensing is the most effective means of detection Land_use change/coverings general layout and change, and remotely-sensed data is the ideal data source of acquisition crop growing mode.Crop growing mode remote sensing recognition method has two kinds: a kind of is recognition methods based on multidate Moderate-High Spatial Resolution Remote Sensing Image, and a kind of is recognition methods based on time series remotely-sensed data.
Cropping pattern recognition methods based on multidate middle high-resolution image utilizes multidate, the middle high-resolution multi-spectral Satellite Images identification crop growing mode of different crops Growing season.Concrete grammar each crop growth season obtained many scapes middle high-resolution multispectral image in 1 year, carries out decipher and classification respectively, extract the crops of each Growing season to the image of different Growing season; The situation of different Growing season Planting Crops is being analyzed, thus is determining the cropping pattern of crops.Due to the impact by satellite revisiting period and weather conditions, obtain in Growing Season of Crops sufficient, quality good middle high-resolution data are very difficult, limit the application of the method in the identification of large scale cropping pattern.
The development of satellite remote sensing technology, for we providing long-term repeated measures data, makes us can study the long-time change of things, to find characteristic sum rule wherein.Recent two decades has carried out extensive and deep research by remote sensing time series data to natural vegetation phenology both at home and abroad, has the algorithm and model identification vegetation phenology feature of many maturations.And the crops of upper plantation of ploughing also embody obvious phenology feature in the influence process to factors such as weather, the hydrology, humanities, this makes to utilize remote sensing time series data to carry out identification to cropping pattern becomes possibility.
The vegetation index of remotely-sensed data inverting can reflected well vegetation growth status, and seasonal effect in time series vegetation index is then the mark of vegetation dynamic changes monitoring, and namely the timing variations of vegetation index corresponds to the growth of vegetation and the season activity process such as weak.For arable land, the dynamic change of temporal series of vegetation index embodies the process of growth of crops, namely from sowing, emerge, jointing, heading is to periodicity situation that is ripe, harvesting.The arable land vegetation index curve in 1 year ripe region completed the dynamic process of a circulation in 1 year, and the arable land in two crops a year region completes two circulations, and the arable land in three crops per annual region will complete three growth cycles.Therefore, the cyclically-varying of time series vegetation index is utilized can to complete the monitoring of arable land cropping pattern.
Cropping pattern research at present based on time series data is all based on remote sensing time series vegetation index data, first adopts various filtering and noise reduction algorithm to obtain comparatively level and smooth crop growth curve, then carries out the extraction of cropping pattern.The method of discrimination of remote sensing cropping pattern mainly comprises classification, spectrum (sequential spectrum) matching method and Peak Intensity Method.Classification directly adopts Classification in Remote Sensing Image technical limit spacing different land use patterns classification to the time series vegetation index curve after filtering and noise reduction.Spectral matching is first to time series vegetation index filtering and noise reduction, cropping pattern Standard Curve Database is set up again according to representative point, then adopt the matching degree of the time series vegetation index curve after Spectral Matching Technique calculating denoising and cropping pattern calibration curve, thus determine various cropping pattern classification.
The basic assumption of Peak Intensity Method is: within upper one year of ploughing, the peak value of the number of times of long-term cropping and the vegetation index change curve in arable land was more identical, namely the vegetation index curve of 1 year ripe cropping pattern is formed significantly unimodal within the year, and the vegetation index curve that two crops a year cropping pattern is ploughed is formed bimodal.Therefore, the cropping pattern of ploughing can be determined by the peak value number of monitoring vegetation index curve.Peak Intensity Method is divided into again direct comparison method and two-order-difference method.At present, Peak Intensity Method is applied the most widely owing to being simple and easy to be used in the cropping pattern monitoring of arable land obtain.
Overview is got up, and the cropping pattern extracting method at present based on remote sensing time series data mainly comprises following three kinds of technical schemes:
Technical scheme one: classification.Classification in Remote Sensing Image technology is adopted to classify to the time series vegetation index data after denoising, according to the time-serial position determination cropping pattern of each class crops.Sorting technique can be supervised classification method, also can be not supervised classification.
Classification requires that operating personnel are very familiar to the crop growing mode of study area, selects sample to carry out Classification and Identification cropping pattern (supervised classification) thus, or carries out cropping pattern differentiation (unsupervised classification) to cluster result.Nicety of grading depends on the selection of sorting technique on the one hand, depends on the experience of researcher on the other hand.Therefore, the repeatability of classification identification cropping pattern is poor, region adaptedness is lower.
Technical scheme two: spectral matching.First set up cropping pattern Standard Curve Database according to the vegetation index timing curve of representative point, then calculate the vegetation index timing curve of every pixel and the matching degree of standard species implant model curve.Matching degree refers to considers the reason such as phenology, sowing time difference, relative translation is carried out to the time shaft of vegetation index timing curve, calculates the vegetation index timing curve of each pixel and the matching degree of vegetation index timing curve on different time position in standard species implant model storehouse.Identify cropping pattern using matching degree as similarity indices, choose matching degree maximum time cropping pattern as the cropping pattern of pixel to be identified.
A complete cropping pattern Standard Curve Database is set up in spectral matching requirement in advance, because the variation of remote sensing vegetation index sequential is larger, cropping pattern Standard Curve Database is difficult to all possible cropping pattern calibration curve of limit, and requires that researcher is very familiar to the crop growing mode of study area equally.
Technical scheme three: Peak Intensity Method.First adopt direct comparison method or two-order-difference method to extract peak value to vegetation index time series data, through certain differentiation, determine peak value number.Then according to the cropping pattern of the number determination pixel of peak value.Direct comparison method judges the vegetation index value of adjacent with front and back for the vegetation index value of each time point several time point to be compared in interval at one, obtains the time point that in this interval, vegetation exponential quantity is maximum, be the peak in this interval; So repeatedly, quantity and the Annual distribution point thereof of all peak values in the Growing season of whole arable land can be obtained.N number of vegetation index of time series vegetation index in 1 year is formed array by two-order-difference method in chronological order, first deducts the vegetation index value before it by vegetation index value below, forms the new value of N-1; Again assignment is carried out, if negative is then decided to be-1, if positive number is then decided to be 1 to the new value of this N-1; Then carry out first difference to N-1 value of new assignment again by method above, obtain the array that N-2 forms by-2,0,2, wherein element is-2 and the point that front and back element is all 0 is exactly peak point.
Peak Intensity Method has three deficiencies: the first, and Peak Intensity Method is to noise-sensitive, high to the requirement of time series data filtering and noise reduction sound algorithm.Although current filtering method can eliminate some obvious noises preferably, filtered curve is not perfectly smooth curve, still there are some trickle noises, and each peak value all can be detected by Peak Intensity Method.The second, the method depends on researcher's experience and region characteristic, and the universality of method is not strong.3rd, peak number and cropping pattern are not relations one to one, are inaccurate with peak number representative species implant model.Peak number reflection be the number of times (cropping index) of long-term cropping in a year of ploughing, but a complete cropping pattern can not complete sometimes in 1 year, the time to need 2 years or more.Such as in two Nian Sanshu districts, cropping pattern is stable, but the peak number of First Year and Second Year is generally different.Therefore the peak value number change between 2 years is a kind of " pseudo-change ", infers that the change of cropping pattern is unreasonable especially thus.
In a word, the existing method Regional suitability based on remote sensing vegetation index time series data identification crop growing mode is low, versatility is more weak.
Summary of the invention
The object of the invention is to propose a kind of crop growing mode recognition methods, input remote sensing vegetation index time series data and a small amount of training sample just can realize the extraction of crop growing mode, and desired parameters is few, highly versatile.
For reaching this object, the present invention by the following technical solutions:
A kind of crop growing mode recognition methods, comprises the following steps:
A, input remote sensing vegetation index time series data;
B, determine vegetation growth threshold value, by areal bare area and vegetation-covered area, the vegetation index value when difference appears in spring and summer is the earliest defined as vegetation growth threshold value;
C, selection crops training sample;
D, parameter optimization, according to training sample, random combine is carried out to the shortest Length of growing season of study area crops, the longest Length of growing season and these 3 parameters of minimum growth amplitude, select the parameter value the highest to training sample cropping pattern accuracy of identification to combine as optimized parameter;
E, extraction vegetation growth information;
F, get rid of non-crop area, the vegetation growing season length judging pixel to be identified successively whether between the shortest Length of growing season of crops and the longest Length of growing season of crops, whether vegetation growth amplitude be greater than the minimum growth amplitude of crops, as long as have 1 not meet in these 2 conditions, then this pixel to be identified is judged to be non-crop area;
G, the crops cropping index determined according to crop growth season number in a year;
H, according to the previous year, comprehensively determine crop growing mode with the crops cropping index of latter a year then.
In step e, the vegetation growth information extracted comprises the vegetation growing season number in a year, the length of each Growing season and growth amplitude 3 indexs, concrete extraction step comprises: the value of all for vegetation index time series data time points and vegetation growth threshold value are made comparisons by (1), be 1 by the time point assignment being more than or equal to 0, the time point assignment being less than 0 is 0, thus obtains a time series be made up of 0 and 1 value; (2) value in new time series being 1 is continuously added up, if run into 0, then restarts to add up, obtain one cumulative after time series; (3) for the time series after cumulative, promising 1 the time point at value place be defined as the from date of vegetation growing season, allly be greater than 0 and first Close Date being the time point at the value place of 0 and being defined as vegetation growing season following closely, the vegetation growing season from date extracted and vegetation growing season Close Date are alternately, if last is vegetation growing season from date, then deleted; (4) number of times occurred according to vegetation growing season from date in a year determines vegetation growing season number, determine vegetation growing season length according to the initial of each Growing season and Close Date, the difference according to the vegetation index value of vegetation growing season from date and the vegetation index maximum between the Close Date and vegetation growing season from date determines Growing season amplitude.
In step H, according to the previous year, comprehensively determine crop growing mode with the cropping index of latter a year then, the cropping index combination of 3 years has 4 3the situation of kind, concrete step comprises: (1) is contained in the combination of 0 all, uncultivated area is defined as when within 3 years, cropping index is 0 entirely, then cropping index be 0 and have in the previous year or latter 1 year be not 0 situation time be defined as leisure cultivated land, other are contained to the combination of 0, by cropping index then, cropping pattern then determines that (cropping index is the ripe cropping pattern of 1 expression 1 year, cropping index is the double-cropped cropping pattern of 2 expression, and cropping index is the cropping pattern of 3 expression three crops per annual); (2) remaining all contain 3 combination, cropping pattern is then determined by cropping index then; (3) to the remaining combination be made up of 1 and 2, two kinds of principles are adopted to determine, one is homogeny principle, as long as cropping index is then identical with the cropping index of any a year in the previous year or latter a year, then by the cropping pattern that identical cropping index is determined then; Two is symmetry principles, and to (1,2,1) and (2,1,2) combination, they are all complete three proportion of crop plantings in two years, therefore cropping pattern be 2 years three ripe.
Have employed technical scheme of the present invention, directly can extract crop growing mode to remote sensing vegetation index time series data, there is following advantage:
(1) principle is simple, and operation efficiency is high, easily realizes with program language.
(2) do not need other auxiliary datas, noise resisting ability is strong, and results contrast is reliable, stable, is specially adapted to as agricultural sector or government department provide space distribution information about crop growing mode in time.
(3) desired parameters is few, reduces the applicability requirement in region, improves the versatility of method.
(4) human intervention is few, and the degree of automatic operating is high.
Accompanying drawing explanation
Fig. 1 is vegetation growing season from date, Length of growing season, growth amplitude schematic diagram.
Fig. 2 is the flow chart of crop growing mode identification in the specific embodiment of the invention.
Embodiment
Technical scheme of the present invention is further illustrated by embodiment below in conjunction with accompanying drawing.
The main thought of technical solution of the present invention is to propose a kind of method and rational crop growing mode recognition methods of one comparatively automatically can determining optimized parameter.Vegetation growth parameter of the present invention comprises vegetation growing season length and growth amplitude.Vegetation growing season from date characterizes the time point that vegetation starts growth, the namely time point (Fig. 1) of vegetation index when spring and summer reaches vegetation growth threshold value the earliest.Length of growing season refers to that vegetation completes the time span in a complete growth cycle.Growth amplitude refers to the amplitude of variation of the vegetation index value of the vegetation index maximum distance vegetation growth threshold value in vegetation growth process.Because all green vegetations all have such feature, in order to effectively identify crop growth season, need to determine the shortest Length of growing season of study area crops, the longest Length of growing season and minimum growth amplitude.The shortest Length of growing season of crops refers to that crops in region complete complete shortest time needed for growth cycle, the longest Length of growing season of crops refers to that crops in region complete a complete maximum duration needed for growth cycle, and crops minimum growth amplitude refers to crops minimum vegetation index amplitude of variation that should reach in process of growth in region.
Fig. 2 is the flow chart of crop growing mode identification in the specific embodiment of the invention.Crop growing mode identification process of the present invention comprises the following steps:
Step 101, input remote sensing vegetation index time series data.
Step 102, determine vegetation growth threshold value, by areal bare area and vegetation-covered area, the vegetation index value when difference appears in spring and summer is the earliest defined as vegetation growth threshold value.
Step 103, selection training sample, the selection of training sample with reference to crops shortening zoning map, if study area is in same shortening district, then directly can select a set of sample; If study area is across different shortening districts, then in each shortening district, choose sample respectively; The cropping pattern of training sample can be determined according to the vegetation index curve of sample and the interpretation of multidate intermediate-resolution image visualization, also can determine according to ground observation data.
Step 104, parameter optimization, according to training sample, random combine is carried out to the shortest Length of growing season of study area crops, the longest Length of growing season and these 3 parameters of minimum growth amplitude, select the parameter value the highest to training sample cropping pattern accuracy of identification to combine as optimized parameter.
Step 105, extract vegetation growth information, vegetation growth information comprises the vegetation growing season number in a year, the length of each Growing season and growth amplitude 3 indexs, and concrete extraction step is as follows:
(1) value of all for vegetation index time series data time points and vegetation growth threshold value are made comparisons, be 1 by the time point assignment being more than or equal to 0, the time point assignment being less than 0 is 0, thus obtains a time series be made up of 0 and 1 value;
(2) value in new time series being 1 is continuously added up, if run into 0, then restarts to add up, obtain one cumulative after time series;
(3) for the time series after cumulative, promising 1 the time point at value place be defined as the from date of vegetation growing season, be allly greater than 0 and first Close Date being the time point at the value place of 0 and being defined as vegetation growing season following closely; The vegetation growing season from date extracted and vegetation growing season Close Date alternately, if last is vegetation growing season from date, are then deleted;
(4) number of times occurred according to vegetation growing season from date in a year determines vegetation growing season number, determine vegetation growing season length according to the initial of each Growing season and Close Date, the difference according to vegetation growing season from date and the vegetation index maximum between the Close Date and vegetation growth threshold value determines Growing season amplitude.
Step 106, judge whether the vegetation growing season length extracted is less than the shortest Length of growing season of crops that step 104 obtains, and if so, then goes to step 107, if not, then go to step 108.
Step 107, crop growth season must reach certain length, and the independent growths phase of such as China staple crops is all more than 90 days.Because the independent growths cycle comprises sowing time, and the growth cycle that remote sensing vegetation index monitors is from crops turn green, and therefore the crop growth season length that arrives of remote sensing monitoring is slightly short, but still will be longer than the Length of growing season of non-crops.The grass that very short Growing season may be the vegetables of short-term, turn green before the winter leading peak of winter wheat or crop seeding and shrubbery are formed.If the vegetation growing season length extracted is less than the shortest Length of growing season of crops, so deletes this Growing season, and go to step 108.
Step 108, judge the minimum growth amplitude of crops whether the growth amplitude of vegetation growing season extracted is less than step 104 and obtains if so, then to go to step 109, if not, then go to 110.
Step 109, remote sensing monitoring to crop growth amplitude must reach certain height, such as, for MODIS enhancement mode meta file (EVI), the growth amplitude of winter wheat field of North China Plain is generally between 0.3 ~ 0.4, and the growth amplitude of corn is generally between 0.35 ~ 0.45.If the growth amplitude of a vegetation growing season is less than the minimum growth amplitude of crops, then deletes this Growing season, and go to step 110.
Step 110, judge whether the Length of growing season extracted is greater than the longest Length of growing season of crops that step 104 obtains, and if so, then goes to step 111; If not, then go to 112.
If the length of step 111 Growing season is greater than the longest Length of growing season of crops, then deletes this Growing season, and go to step 112.
Step 112, the crops cropping index determined according to Growing season number in a year.
Step 112, according to the previous year, comprehensively determine crop growing mode with the crops cropping index of latter a year then, for a pixel to be identified, the cropping index combination of 3 years has 4 3plant plantation situation, namely have the cropping pattern (table 1) that 64 kinds are possible, operating procedure is as follows:
(1) contain in the combination of 0 all, when within 3 years, cropping index is 0 entirely, be defined as uncultivated area; Then cropping index be 0 and have in the previous year or latter 1 year be not 0 situation time be defined as leisure cultivated land; Other are contained to the combination of 0, by cropping index then, cropping pattern then determines that (cropping index is the ripe cropping pattern of 1 expression 1 year, cropping index is the double-cropped cropping pattern of 2 expression, and cropping index is the cropping pattern of 3 expression three crops per annual).
(2) to remaining all contain 3 combination, expression is potential three crops per annual growing area, so cropping pattern take 1 year one ripe, to yield two crops a year or three crops per annual is all fine, therefore cropping pattern is then determined by cropping index then.
(3) to the remaining combination be made up of 1 and 2, two kinds of principles are adopted to determine.Principle one: homogeny principle.As long as cropping index then with in the previous year or latter 1 year any 1 year with identical, then by the cropping pattern that identical cropping index is determined then.Principle two: symmetry principle.(1,2,1) and (2,1,2) combination is all complete three proportion of crop plantings in two years, therefore cropping pattern be 2 years three ripe.Thus, the cropping pattern of all combinations can be determined, as shown in table 1.
The table 1 cropping pattern table of comparisons
The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, any people being familiar with this technology is in the technical scope disclosed by the present invention; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (1)

1. a crop growing mode recognition methods, is characterized in that, comprises the following steps:
A, input remote sensing vegetation index time series data;
B, determine vegetation growth threshold value, by areal bare area and vegetation-covered area, the vegetation index value when difference appears in spring and summer is the earliest defined as vegetation growth threshold value;
C, selection crops training sample;
D, parameter optimization, according to training sample, random combine is carried out to the shortest Length of growing season of study area crops, the longest Length of growing season and these 3 parameters of minimum growth amplitude, select the parameter value the highest to training sample cropping pattern accuracy of identification to combine as optimized parameter;
E, extraction vegetation growth information, concrete steps comprise: (1) deducts vegetation growth threshold value by the vegetation index value of all time points of vegetation index time series, be 1 by the data point assignment being more than or equal to 0 in result, be 0 by the data point assignment being less than 0, thus obtain the sequence of differences that is made up of 0 and 1 value; (2) value in sequence of differences being 1 is continuously added up, if run into 0, then restart to add up, obtain the sequence after adding up; (3) in cumulative sequence promising 1 the time point at value place be defined as the from date of vegetation growing season; (4) allly in cumulative sequence be greater than 0 and the time point that value is following closely the value place of 0 is defined as Close Date of vegetation growing season, if cumulative last value of sequence is greater than 0, then corresponding time point is considered as end of growing season; (5) number of vegetation growing season equals the number of times that vegetation growing season from date occurs; (6) vegetation growing season length was determined by the initial of each Growing season and Close Date; (7) the growth amplitude of vegetation growing season is determined by vegetation index maximum in the season of growth and vegetation growth threshold value, the vegetation index maximum-vegetation growth threshold value in i-th vegetation growing season growth amplitude=the i-th vegetation growing season;
F, judge whether the vegetation growing season length extracted is less than the shortest Length of growing season of crops that step D obtains, and if so, then deletes this Growing season, then goes to step G, if not, then directly go to step G;
G, judge the minimum growth amplitude of crops whether the growth amplitude of vegetation growing season extracted is less than step D and obtains, if so, then delete this Growing season, then go to step H, if not, then directly go to step H;
H, judge whether the vegetation growing season length extracted is greater than the longest Length of growing season of crops that step D obtains, and if so, then deletes this Growing season, then goes to step I, if not, then directly go to step I;
I, meet step F, the vegetation growing season of G, H Rule of judgment is crop growth season, can determine the crops cropping index in a year according to crop growth season number;
J, according to the previous year, comprehensively determine crop growing mode with the crops cropping index of latter a year then, because the cropping index combination of 3 years has 4 3the situation of kind, concrete decision method is: first, for all contain 0 combination, uncultivated area is defined as when within 3 years, cropping index is 0 entirely, then cropping index be 0 and have in the previous year or latter 1 year be not 0 situation time be defined as leisure cultivated land, other are contained to the combination of 0, cropping pattern is then determined by cropping index then, namely cropping index is the ripe cropping pattern of 1 expression 1 year, cropping index is the double-cropped cropping pattern of 2 expression, and cropping index is the cropping pattern of 3 expression three crops per annual; Secondly, to remaining all contain 3 combination, cropping pattern is then determined by cropping index then; Again, to the remaining combination be made up of 1 and 2, adopt two kinds of principles to determine, one is homogeny principle, as long as cropping index is then identical with the cropping index of any a year in the previous year or latter a year, then by the cropping pattern that identical cropping index is determined then; Two is symmetry principles, and to (1,2,1) and (2,1,2) combination, they are all complete three proportion of crop plantings in two years, therefore cropping pattern be 2 years three ripe.
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