CN108491362B - Statistical method for average deviation characteristic rule of regional solar altitude angles - Google Patents
Statistical method for average deviation characteristic rule of regional solar altitude angles Download PDFInfo
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Abstract
The invention relates to a statistical method of regional solar altitude angle average deviation characteristic rules, which comprises 3 steps of sample data preparation, average deviation calculation and calculation result induction, wherein a calculation method of regional solar altitude angle average deviation is required to be used, and the calculation method comprises 4 steps of formulating calculation planning, calculating solar altitude angle, introducing weight rules and calculating regional solar altitude angle average deviation. The characteristic rule of the average deviation of the regional solar altitude angles is summarized, the mathematical relation between the average deviation of the regional solar altitude angles and the regional diameter is a nearly linear relation, and the linear coefficient is 0.0019084-0.0019030 degrees km‑1The area diameter is a substantive relevant factor of the average deviation of the area solar altitude, which is beneficial to realizing the value of the area solar altitude related to solar radiation, solving the representative problem of the area solar altitude and providing scientific basis for determining the data density of the solar radiation parameters of the earth system application model.
Description
Technical Field
The invention belongs to the technical field of geography and remote sensing, and relates to a statistical method of regional solar altitude angle average deviation characteristic rules related to a solar altitude angle scale effect in solar radiation, which needs to use a calculation method of regional solar altitude angle average deviation.
Technical Field
Solar radiation is the main energy transmission source on the earth, is the basis for the growth of everything on the earth, and is the driving source spring of each earth system. Solar radiation mainly determines a surface atmospheric temperature field, a pressure field, an electric field, a magnetic field, photosynthesis and photochemical reaction to change the material structure of the surface atmosphere, and natural phenomena such as water circulation, carbon circulation, atmospheric circulation, ocean current, ozone holes and the like on the earth are directly related to solar radiation, so that the solar radiation is a hotspot for the research of an earth system. Many scholars have conducted extensive research on the earth system and solar radiation, and have achieved a series of fruitful results. The solar altitude is the most important parameter for the radiation energy of the sun to the earth surface, and the unbalance of the region and season for obtaining the solar radiation on the ground exists. Due to the ground curvature factor, the solar elevation angle scale effect is generated, the representative problem of the solar elevation angle area exists, and the data density of the solar radiation parameters of the earth system model needs to be implemented. Under the condition of ensuring certain data accuracy, the complex models are used for solving large data processing, the data volume and the calculated amount must be reduced as much as possible, and reasonable data density needs to be considered. Different solar altitude angle data densities can influence the application model to generate different degrees of result differences, if the solar altitude angle data densities are too low, the data representativeness is poor, the simulation capability of the application model is reduced, and the due benefits of the application system cannot be fully exerted; if the solar altitude angle data density is too high, information redundancy is generated, the occupation of resources such as storage, operation and transmission is increased, the investment cost is increased, and the time benefit of an application system is reduced. The characteristic rule of regional solar altitude angle deviation is a mathematical relation which needs to be constructed for reasonably determining the data density of the solar altitude angle, so that the study on the characteristic rule of regional solar altitude angle deviation is of particular significance. The inventor researches the maximum deviation characteristic rule of the regional solar altitude in a space-based remote sensing block interpolation solar altitude calculation method, and discusses the representative problem of the solar altitude region from another angle by the average deviation characteristic rule of the regional solar altitude.
Disclosure of Invention
The invention designs a statistical method of the average deviation characteristic rule of the regional solar altitude angle in order to solve the representative problem of the solar altitude angle region and aim at the influence relation generated by the solar altitude angle data density on the calculation result of the earth system application model.
The invention is realized by the following steps:
a statistical method for the average deviation characteristic rule of the regional solar altitude angles is characterized by firstly designing a calculation method for the average deviation of the regional solar altitude angles and then customizing the statistical method for the average deviation characteristic rule of the regional solar altitude angles on the basis. The statistical method of the characteristic rule of the average deviation of the regional solar altitude angle needs to use a calculation method of the average deviation of the regional solar altitude angle.
The method for calculating the average deviation of the regional solar altitude angle comprises 4 steps of making a calculation plan, calculating the solar altitude angle, introducing a weight rule and calculating the average deviation of the regional solar altitude angle. The method comprises the following steps that (1) calculation planning is formulated, namely, a circular area is adopted from the perspective of the average deviation of the sun altitude of an investigation area, a two-dimensional array is required from the perspective of programming calculation, a square area is adopted, the circular area is contained in the square area, a weight rule is introduced to distinguish an effective calculation area from an ineffective calculation area, and the number of rows and columns of the two-dimensional array is determined. And (2) calculating the solar altitude angle, namely determining a solar altitude angle calculation method of each grid point in the area according to a solar altitude angle formula and the two-dimensional array row number, performing calculation of declination, latitude and time angle parameter calculation methods related to the solar altitude angle, and substituting each parameter value to calculate the solar altitude angle of each grid point in the area. And (3) introducing a weight rule, namely considering the inconsistency of the statistical average deviation area and the calculation array representative area, and solving the inconsistency by using the weight rule, wherein the weight rule comprises a point state judgment rule and a point weight value payment rule. And (4) calculating the average deviation of the regional solar altitude angles, namely calculating the solar altitude angle of each grid point of the region minus the solar altitude angle of the middle point to obtain the solar altitude angle deviation of each grid point of the region, paying a value to a weight parameter of each grid point of the region according to a weight rule, and calculating the average value of the absolute value of the solar altitude angle deviation of the effective circular region by using the weight value of each grid point of the region.
The statistical method of the average deviation characteristic rule of the solar altitude angle of the region comprises 3 steps of sample data preparation, average deviation calculation and calculation result induction. The sample data preparation in the step (1) comprises investigation factor relation and representative data arrangement, in order to summarize the characteristic rule of the average deviation of the regional solar altitude, the investigation factors comprise regional diameters, regional points, years, seasons and time point representative parameters, and sample data of different regional diameters, different regional points, different years, different seasons and different time points which are reasonably distributed are arranged. And (2) calculating the average deviation, namely forming a data set, designing a calculation method, implementing a processing process, compiling calculation software and a data calculation result, forming 1 or more data sets according to sample data of the investigation factor, designing a calculation method of the average deviation of the solar altitude angles of the region, implementing a data processing process of the average deviation of the solar altitude angles of the region, compiling the calculation software according to the calculation method and the data processing process of the average deviation of the solar altitude angles of the region, and operating the calculation software to obtain the calculation result. And (3) summarizing calculation results including grouping investigation and grouping summarization, and summarizing the characteristic rule of the average deviation of the solar altitude of the region according to the average deviation of the solar altitude of the grouping investigation region and each group of summarization results of region diameter, region point, year, season and time point factors:
in the formula DRThe diameter of the circular area is the diameter of the circular area,
for monitoring the central point latitude, λ0Comprehensively inspecting theta for monitoring longitude of a central point, y for monitoring year, m for monitoring month, d for monitoring day and h for monitoring time pointSEVPAnd the conditions of the mean value, the maximum value, the minimum value and the dispersion degree reflect the correlation between the characteristic rule of the average deviation of the regional solar altitude and the regional diameter, the region, the year, the season and the time point.
The invention has the advantages and positive effects that: the invention designs a calculation method of the average deviation of the regional solar altitude angle, which provides core technical support for a statistical method for formulating the characteristic rule of the average deviation of the regional solar altitude angle, and the statistical method of the characteristic rule of the average deviation of the regional solar altitude angle provides a technical method for searching the characteristic rule of the average deviation of the regional solar altitude angle; the characteristic rule of the average deviation of the regional solar altitude angles is summarized, the mathematical relation between the average deviation of the regional solar altitude angles and the regional diameter is a nearly linear relation, and the linear coefficient is 0.0019084-0.0019030 degrees km-1The linear coefficient is slightly reduced along with the increase of the area diameter, and the area diameter is a substantial correlation factor of the average deviation of the solar altitude of the area; the influence relation of the solar altitude angle scale effect on the average deviation of the regional solar altitude angles is discussed, the regional solar altitude angle value related to solar radiation is favorably realized, the representative problem of the solar altitude angle region is solved, and a scientific basis is provided for determining the data density of the solar radiation parameters of the earth system application model.
Drawings
FIG. 1 is a schematic diagram illustrating a calculation process of average deviation of solar altitude in a region;
fig. 2 is a schematic diagram of a statistical process of the average deviation characteristic law of the regional solar altitude.
Detailed Description
The specific embodiments of the present invention will be described with reference to the accompanying drawings. The procedures specifically illustrated for these example data are not to be construed as limiting the invention in view of understanding and operation. The statistical method of the characteristic rule of the average deviation of the regional solar altitude angle needs to use a calculation method of the average deviation of the regional solar altitude angle.
1. Method for calculating average deviation of regional solar altitude angles
The calculation method of the average deviation of the regional solar altitude angle comprises 4 steps of making a calculation plan, calculating the solar altitude angle, introducing a weight rule and calculating the average deviation of the regional solar altitude angle, and is shown in figure 1.
1.1 formulating a calculation plan
From the perspective of the average deviation of the sun altitude angles of the investigation region, a circular region is adopted, from the perspective of programming calculation, a two-dimensional array is required to be used, a square region is adopted, the circular region is contained in the square region, and a weighting rule is introduced to distinguish an effective calculation region from a non-effective calculation region.
(1) The solar deflection is considered, the average deviation of the solar altitude of the area is favorably measured, and a circular area is selected as a surveying object;
(2) let the diameter of the circular area be DR(km), the resolution of the two-dimensional array statistic data (i.e. the data grid point width) is DS(km), determining the two-dimensional array row and column numbers m, n:
①INT(DR/DS)＝DR/DS(note: INT () is a rounding function), two-dimensional array of rows and columns m-n-INT (D)R/DS)+1；
②INT(DR/DS)＜DR/DSTwo-dimensional array row and column numbers m-n-INT (D)R/DS)+3。
1.2 solar altitude calculation
According to the solar elevation angle formula and the number of rows and columns of the two-dimensional array, the calculation method of the solar elevation angle of each lattice point in the area is determined, according to the astronomical parameter formula improved by scholars such as Wangzhou loyalty and the like, the calculation method of declination, latitude and time angle parameters related to the solar elevation angle is actually calculated, and the declination, latitude and time angle parameters are substituted into each parameter value to calculate the solar elevation angle of each lattice point in the area.
(1) Formula of solar altitude angle
In the formula [ theta ]SETo observe the elevation angle of the earth's sun, delta is the declination of the sun's declination of the observation day,
to observe the latitude of the earth, τ is the observation chronohorizon. The latitude of the equator is 0 degree, the north latitude is 0 to +90 degrees, and the south latitude is 0 to-90 degrees; the longitude of the Greenwich astronomical clock is 0 degree, the west longitude is 0 to minus 180 degrees, and the east longitude is 0 to plus 180 degrees. Grid points of area
Wherein i, j is 0, 1, 2, …, n-1.
(2) Calculation of each parameter of solar altitude
Calculating declination parameter
Solar declination delta is the latitude of the earth directly irradiated by the sun in the observation day, and the solar declination calculation formula
δ＝0.3723+23.2567sinθ+0.1149sin2θ－0.1712sin3θ－0.758cosθ+0.3656cos2θ+0.0201cos3θ，
θ＝2π{Jd－79.6764－0.2422(Jy－1985)+INT[(Jy－1985)/4]+ΔJ}/365.2422(2)
Wherein θ is the solar angle (rad), JdFor accumulated days, calculated from the monitoring date, JyFor the year of monitoring, Δ J is a correction value (d), Δ J ═ Δ J1+ΔJ2In the formula, Δ J1For correction of longitude, Δ J1＝-0.00278λ0In the formula of0To monitor the ground longitude (°), Δ J2For time correction, Δ J2And T/24, wherein T is the international time (h) of the monitoring place.
② latitude of each lattice point
Parameter calculation
According to the latitude of the central point of the region
By 111.193km (assuming a circular shape), etcCalculating the latitude of each grid point in the region according to the width of the latitude difference of 1 degree, and calculating the latitude of each grid point in the region
③ time angle of each lattice point Ti,jParameter calculation
Time angle τ 15 (t)0-12), in which t0To observe the true solar time (h) of the ground, the time angle of each lattice point in the region
τi,j＝15(ta+Δt/60)+λi,j－300，
Δt＝0.0028－1.9857sinθ+9.9059sin2θ－9.0924cosθ－0.6882cos2θ (3)
In the formula taIs an observation point of Beijing time (h), lambdai,jThe longitude (°) of the observation point is shown, Δ t is the true mean solar time difference in minutes (min), and each grid point t of the region is setaAnd Δ t are the same, and θ is calculated by equation (1).
Calculate the longitude λ of each lattice pointi,jThe parameter can be based on the longitude λ of the region center point0The center longitude is used as a reference. If the longitude and latitude span of the whole calculation area is small, the distances among grid points are equal and the longitude difference is equal,
the latitude of the center point of the region.
If the longitude and latitude span of the whole calculation area is large, the longitude of each grid point is calculated accurately, and the longitude of each grid point is calculated according to the equal distance between the grid points:
in the formula REThe radius of the earth is taken as 6371.004km, Di,j(km) is the distance of each grid point from the center point, Di,j＝DS{[i－INT(n/2)]2+[j－INT(m/2)]2}1/2. In the formula, the angular value is in degrees (degree), and if radian (rad) is taken as a unit, the trigonometric function angle and the inverse trigonometric function angle need to be converted.
(3) Calculating the solar altitude theta of each lattice pointSEi,j
Substituting the declination, latitude and time angle parameters into the formula to calculate the solar altitude angle of each lattice point in the region
Wherein i, j is 0, 1, 2, …, n-1.
1.3 introducing weight rules
And (4) considering that the statistical average deviation area is inconsistent with the calculation array representative area, and solving the inconsistency by using a weight rule, wherein the weight rule comprises a point state judgment rule and a point weight value-giving rule.
(1) Point State judgment rule
The interior point condition in the circular region is DR≥2DS{[(i－INT(n/2))2+(j－INT(m/2))2]1/2+1/2} with an outlier condition of DR≤2DS{[(i－INT(n/2))2+(j－INT(m/2))2]1/2-1/2 } and the boundary point condition is 2DS{[(i－INT(n/2))2+(j－INT(m/2))2]1/2－1/2}＜DR＜2DS{[(i－INT(n/2))2+(j－INT(m/2))2]1/2+1/2}；
(2) Point weight value-of-weight rule
The weight of the inner point in the circular area is 1, the weight of the outer point is 0, the boundary point is subjected to simplification processing, the center of the boundary point is weighted to be 1 in the circular area, and the center of the boundary point is weighted to be 1 in the circular areaWeight outside the region is 0; i.e. each lattice weight is represented as Wi,jIf D isR≥2DS{[i－INT(n/2)]2+[j－INT(m/2)]2}1/2Let Wi,j1 is ═ 1; if D isR＜2DS{[i－INT(n/2)]2+[j－INT(m/2)]2}1/2Let Wi,j＝0。
1.4 regional solar altitude average deviation calculation
Calculating the sun altitude of each lattice point of the area minus the sun altitude of the midpoint to obtain the sun altitude deviation of each lattice point of the area, giving a value to the weighting parameter of each lattice point of the area according to the weighting rule, and calculating the average value of the absolute values of the sun altitude deviation of the effective circular area by using the weighting value of each lattice point of the area.
(1) Calculating the solar altitude deviation theta of each lattice pointSEVi,j
According to the formula of the solar altitude angle, calculating the solar altitude angle deviation theta of each lattice pointSEVi,j＝θSEi,j－θSE0，θSEi,jWith reference to the foregoing calculation, θSE0The solar altitude is the central point of the area;
(2) traversing and calculating two-dimensional array region point weight Wi,j
According to the point weight value-adding rule, if the lattice point is in the set circular area or on the area line, the value is added to be 1, if the lattice point is out of the area, the value is added to be 0, and the determined i and j value fields are traversed and calculated to obtain the two-dimensional array area Wi,j；
(3) Calculating the average deviation of the solar altitude angles of the circular areas
According to the above-mentioned thetaSEVi,jAnd Wi,jCalculating the mean value of the absolute value of the deviation of the solar altitude angle of each grid point in the circular area by considering the weight
2. Statistical method for average deviation characteristic rule of regional solar altitude angles
The statistical method of the average deviation characteristic rule of the regional solar altitude angle comprises 3 steps of sample data preparation, average deviation calculation and calculation result induction, and is shown in figure 2.
2.1 sample data preparation
Sample data preparation includes examining factor relationships and representative data arrangements.
(1) Investigating factor relationships
From the mathematical relationship of the calculation process of the average deviation of the regional solar altitude, the regional diameter, the regional point, the year, the season and the time point are relevant factors, from the general deviation characteristic rule of the regional solar altitude, the average deviation of the regional solar altitude and the regional diameter have positive correlation, more regional diameter data with different scales are arranged, and proper data investigation should be performed on different regional points, different years, different seasons and different time points;
(2) representing data arrangements
The characteristic rule of the average deviation of the solar altitude angle in the statistical region is representative, sample data distributed reasonably is used as much as possible, the region diameter is selected from the small size to the large size of more than 10 sizes, high, medium and low latitude multi-type representative points are selected in different regions, a plurality of years with certain intervals are selected in different years, representative days in different seasons or a plurality of days with certain intervals from the far and near days are selected, and the whole daytime points in the morning and afternoon of the international time, the local time or the real solar time are selected at different time points.
2.2 mean deviation calculation
The average deviation calculation comprises the steps of forming a data set, designing a calculation method, implementing a processing process, compiling calculation software and calculating a data result.
(1) Forming a data set
Combining the factor data according to the area diameter, the longitude and latitude of the area point, the year, the season and the time point to form a certain amount of set data, dividing the set data into 1 or more data sets according to the program calling requirement, and inputting the sample data set of the program callout to form a data file;
(2) design calculation method
The method for calculating the average deviation of the elevation angle of the regional sun comprises the following steps: firstly, planning calculation planning, namely taking a circular area from the angle of the average deviation of the sun altitude of an investigation area, taking a square area from the angle of programming calculation by using a two-dimensional array, introducing a weight rule to distinguish an effective calculation area from a non-effective calculation area, and determining the number of rows and columns of the two-dimensional array; calculating the solar altitude angle, namely determining a solar altitude angle calculation method of each grid point in the area according to a solar altitude angle formula and the row number of two-dimensional array, performing calculation of declination, latitude and time angle parameters related to the solar altitude angle, and substituting each parameter value to calculate the solar altitude angle of each grid point in the area; introducing a weight rule, namely considering the inconsistency of the statistical average deviation area and the calculation array representative area, and solving the inconsistency by the weight rule, wherein the weight rule comprises a point state judgment rule and a point weight value rule; calculating the average deviation of the sun altitude angles of the regions, namely calculating the sun altitude angle of each lattice point of the regions minus the sun altitude angle of the middle point to obtain the sun altitude angle deviation of each lattice point of the regions, paying a value to a weight parameter of each lattice point of the regions according to a weight rule, and calculating the average value of the absolute values of the sun altitude angle deviations of the effective circular regions by using the weight values of each lattice point of the regions;
(3) implementation process
Considering the influence on the statistical result, determining the row and column number of the two-dimensional array by adopting a denser grid point mode, grading the sample data according to different area diameters, calculating the solar altitude of each grid point in the area of each group of sample data of the level group according to a calculation method of the average deviation of the solar altitude of the area, calculating the average deviation of the solar altitude of the effective area according to a weight rule, recording the result in the corresponding level array, and finishing the calculation of all the sample data of the level group.
(4) Compiling computing software
Designing calculation software according to a calculation method of the average deviation of the solar altitude angles of the regions and a data processing process, arranging and calling sample data set data, calculating the solar altitude angles of all lattice points of the regions according to the row and column numbers of two-dimensional groups, designing a basic unit for calculation according to the calculation method of the average deviation of the solar altitude angles of the regions, circularly calculating according to the number of samples of the same group, and circularly calculating according to the number of samples of different region diameters. Writing corresponding program codes by adopting a proper computer language, and debugging computing software;
(5) data calculation results
And operating calculation software, automatically calling sample data of each level group, calculating the average deviation of the solar altitude of each lattice point of the area and the solar altitude of the effective area, and respectively recording the calculation results in the corresponding level groups for induction and analysis.
2.3 summary of the calculation results
The summary of the calculation results includes grouping investigation and grouping summary.
(1) Group inspection
Considering that the area diameter size and the average deviation of the area solar altitude angle have obvious positive correlation, researching the actual correlation of the area diameter and the average deviation of the area solar altitude angle according to the area diameter grading groups, counting the average deviation obtained by calculating each grade group to obtain the mean value, the maximum value, the minimum value and the dispersion, and researching the correlation of the area point, year, season and time point factors in each grade group with different area diameters and the average deviation of the area solar altitude angle;
(2) group summary
Summarizing the characteristic rule of the average deviation of the regional solar altitude according to the average deviation of the regional solar altitude and the group induction results of the regional diameter, the regional point, the year, the season and the time point factors:
in the formula, y is a monitoring year, m is a monitoring month, d is a monitoring day, h is a monitoring time point, and theta is comprehensively consideredSEVPAnd the conditions of the mean value, the maximum value, the minimum value and the dispersion degree reflect the correlation between the characteristic rule of the average deviation of the regional solar altitude and the regional diameter, the region, the year, the season and the time point.
The invention is further illustrated by two examples of stated features:
example 1: example of method for calculating average deviation of regional solar altitude angles
The sample data of this example is: regional points are Guangzhou latitude
At 23.13N and a longitude of (lambda)0)113.28 DEG E; date 2015, 6 months and 22 days, Guangzhou true solar time (t)01) When 15 is true; (iii) diameter of area (D)R) The grid point density of statistical data is 5m multiplied by 5m, which is 10 km; the calculation method of the average deviation of the solar elevation angle of the region by using the specific data is explained as follows:
the calculation method of the average deviation of the regional solar altitude angle comprises 4 steps of making a calculation plan, calculating the solar altitude angle, introducing a weight rule and calculating the average deviation of the regional solar altitude angle, and is shown in figure 1.
1.1 formulating a calculation plan
From the perspective of the average deviation of the sun altitude angles of the investigation region, a circular region is adopted, from the perspective of programming calculation, a two-dimensional array is required to be used, a square region is adopted, the circular region is contained in the square region, and a weighting rule is introduced to distinguish an effective calculation region from a non-effective calculation region.
(1) The solar deflection is considered, the average deviation of the solar altitude of the area is favorably measured, and a circular area is selected as a surveying object;
(2) according to the sample data, the diameter D of the circular regionR10km, two-dimensional array data grid point width DS0.005 km; determining the number of rows and columns of the two-dimensional array, m-n-INT (D)R/DS)+1＝2001；
1.2 solar altitude calculation
According to the solar elevation angle formula and the number of rows and columns of the two-dimensional array, the calculation method of the solar elevation angle of each lattice point in the area is determined, according to the astronomical parameter formula improved by scholars such as Wangzhou loyalty and the like, the calculation method of declination, latitude and time angle parameters related to the solar elevation angle is actually calculated, and the declination, latitude and time angle parameters are substituted into each parameter value to calculate the solar elevation angle of each lattice point in the area.
(1) Formula of solar altitude angle
In the formula [ theta ]SETo observe the altitude angle of the earth's sun, delta is the viewThe declination of the sun is measured,
to observe the latitude of the earth, τ is the observation chronohorizon. The latitude of the equator is 0 degree, the north latitude is 0 to +90 degrees, and the south latitude is 0 to-90 degrees; the longitude of the Greenwich astronomical clock is 0 degree, the west longitude is 0 to minus 180 degrees, and the east longitude is 0 to plus 180 degrees. Grid points of area
Where i, j is 0, 1, 2, …, 2000.
(2) Calculation of each parameter of solar altitude
Calculating declination parameter
Solar declination delta is the latitude of the earth directly irradiated by the sun in the observation day, and the solar declination calculation formula
δ＝0.3723+23.2567sinθ+0.1149sin2θ－0.1712sin3θ－0.758cosθ+0.3656cos2θ+0.0201cos3θ，
θ＝2π{Jd－79.6764－0.2422(Jy－1985)+INT[(Jy－1985)/4]+ΔJ}/365.2422(2)
Wherein the product day J is determined according to the sample datadYear J, 173y2015, and the correction value Δ J is Δ J1+ΔJ2＝-0.00278λ0+(t01－λ0The daily angle θ is 1.60077rad, and the declination δ is 23.44176 °.
② latitude of each lattice point
Parameter calculation according to regional center point latitude
Width of 1 degree difference in latitude at 111.193km, and m 2001, DSCalculating the latitude of each lattice point in the area as 0.005km,
③ time angle of each lattice point Ti,jParameter calculation
Reference time angle calculation formula τ 15 (t)0-12), in which t0To observe the true solar time (h) of the ground, the time angle of each lattice point in the region
τi,j＝15(t01－12)+Δλi,j(3)
In the formula t01Is the true solar time (h), delta lambda, of the central point of the regioni,jIs the difference (degrees) in longitude between the observation point and the center point.
If the distances between the grid points of the area are equal and the longitude differences are equal,
substitution into t01When the number is 15,
to obtain taui,j＝45+5(i－1000)/[111193cos(23.13)]。
(3) Calculating the solar altitude theta of each lattice pointSEi,j
The foregoing has determined particular
Delta and taui,jThe calculation method comprises substituting the obtained parameter values according to the solar altitude angle formula, and calculating the solar altitude angle theta of each lattice point in the regionSEi,j。
1.3 introducing weight rules
And (4) considering that the statistical average deviation area is inconsistent with the calculation array representative area, and solving the inconsistency by using a weight rule, wherein the weight rule comprises a point state judgment rule and a point weight value-giving rule.
(1) Point State judgment rule
Consider specific sample data DR10km and DS0.005km, the interior point condition in the circular area is 1000 ≧ [ (i-1000)2+(j－1000)2]1/2+1/2, the exterior point condition is more than or equal to 1000 [ (i-1000)2+(j－1000)2]1/2-1/2, the boundary point condition being { [ (i-1000)2+(j－1000)2]1/2－1/2}＜1000＜{[(i－1000)2+(j－1000)2]1/2+1/2}；
(2) Point weight value-of-weight rule
The weight of an inner point in the circular area is 1, the weight of an outer point is 0, the boundary point is subjected to simplification processing, the weight of the center of the boundary point in the circular area is 1, and the weight of the center of the boundary point outside the circular area is 0; i.e. each lattice weight is represented as Wi,jConsider a specific sample data DR10km and DS0.005km, 1000 ≧ i (i-1000)2+(j－1000)2]1/2Let Wi,j1 is ═ 1; if 1000 < [ (i-1000)2+(j－1000)2]1/2Let Wi,j＝0。
1.4 regional solar altitude average deviation calculation
Calculating the sun altitude of each lattice point of the area minus the sun altitude of the midpoint to obtain the sun altitude deviation of each lattice point of the area, giving a value to the weighting parameter of each lattice point of the area according to the weighting rule, and calculating the average value of the absolute values of the sun altitude deviation of the effective circular area by using the weighting value of each lattice point of the area.
(1) Calculating the solar altitude deviation theta of each lattice pointSEVi,j
According to the formula of the solar altitude angle, calculating the solar altitude angle deviation theta of each lattice pointSEVi,j＝θSEi,j－θSE0，θSEi,jWith reference to the foregoing calculation, θSE0Calculating theta for the sun altitude of the central point of the region according to specific sample dataSE0＝48.83931°；
(2) Traversing and calculating two-dimensional array region point weight Wi,j
According to the point weight value-adding rule, if the lattice point is in the set circular area or on the area line, the value is added to be 1, if the lattice point is out of the area, the value is added to be 0, and the determined i and j value fields are traversed and calculated to obtain the two-dimensional array area Wi,j；
(3) Calculating the average deviation of the solar altitude angles of the circular areas
According to the above-mentioned thetaSEVi,jAnd Wi,jCalculating the absolute value of the deviation of the solar altitude angle of each grid point in the circular area by considering the weightMean value of
Example 2: statistical method example of regional solar altitude angle average deviation characteristic rule
The statistical method of the characteristic rule of the average deviation of the regional solar altitude angles comprises 3 steps of sample data preparation, average deviation calculation and calculation result induction, the average deviation of the regional solar altitude angles of each group is calculated by using the prepared data, and the characteristic rule of the average deviation is induced.
(1) Sample data preparation
Sample data preparation includes examining factor relationships and representative data arrangements. The statistical region sun altitude angle average deviation characteristic rule needs to prepare sample data, and the region diameter, region, year, season and time point factor are mainly considered. Adopting 13 different areas with diameters of 1, 10, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 and 2000km respectively; selecting 4 representative points of high, medium and low latitudes in different regions, taking Jia Musi, Beijing, Chengdu and Guangzhou as examples; selecting 4 years with certain intervals in different ages, taking 1925, 1975, 2005 and 2015 as examples; selecting 4-day representative seasons for different seasons, such as spring divided days (3 months and 21 days), summer solstice days (6 months and 22 days), autumn divided days (9 months and 23 days), and winter solstice days (12 months and 22 days); the real sun hours are selected at different times for 8 daylight hours, for example 08, 09, 10, 11, 13, 14, 15, 16. The representative longitude and latitude of Jia Musi, Beijing, Chengdu and Guangzhou are shown in Table 1. The various factors combine to yield 6656 sets of sample data.
TABLE 1 geographical points and their latitude and longitude
| Region point | latitude/DEG N | longitude/DEG E |
| Jia mu Si | 46.82 | 130.37 |
| Beijing | 39.91 | 116.39 |
| Chengdu | 30.67 | 104.07 |
| Guangzhou province | 23.13 | 113.28 |
(2) Mean deviation calculation
The average deviation calculation comprises the steps of forming a data set, designing a calculation method, implementing a processing process, compiling calculation software and calculating a data result.
(1) Forming a data set
Forming 1 data set by 13 area diameter parameters, forming 512 other 1 data sets by area point latitude longitude, year, month, day and time point, and recording the data sets to form an original data file.
(2) Design calculation method
The method for calculating the average deviation of the elevation angle of the regional sun comprises the following steps: firstly, planning calculation planning, namely taking a circular area from the angle of the average deviation of the sun altitude of an investigation area, taking a square area from the angle of programming calculation by using a two-dimensional array, introducing a weight rule to distinguish an effective calculation area from a non-effective calculation area, and determining the number of rows and columns of the two-dimensional array; calculating the solar altitude angle, namely calculating declination, latitude and time angle parameters related to the solar altitude angle of the region according to a solar altitude angle formula, and substituting the declination, the latitude and the time angle parameters into parameter values to calculate the solar altitude angle of each lattice point of the region; introducing a weight rule, namely considering the inconsistency of the statistical average deviation area and the calculation array representative area, and solving the inconsistency by the weight rule, wherein the weight rule comprises a point state judgment rule and a point weight value rule; calculating the average deviation of the sun altitude angles of the regions, namely calculating the sun altitude angle of each lattice point of the regions minus the sun altitude angle of the middle point to obtain the sun altitude angle deviation of each lattice point of the regions, paying a value to a weight parameter of each lattice point of the regions according to a weight rule, and calculating the average value of the absolute values of the sun altitude angle deviations of the effective circular regions by using the weight values of each lattice point of the regions;
(3) implementation process
Considering the influence on the statistical result, determining the row and column number of the two-dimensional array by adopting a denser grid point mode, grading the sample data according to different area diameters, calculating the solar altitude of each grid point in the area of each group of sample data of the level group according to a calculation method of the average deviation of the solar altitude of the area, calculating the average deviation of the solar altitude of the effective area according to a weight rule, recording the result in the corresponding level array, and finishing the calculation of all the sample data of the level group.
(4) Compiling computing software
Designing calculation software according to a calculation method of the average deviation of the solar altitude angles of the regions and a data processing process, arranging and calling sample data set data, calculating the solar altitude angles of all lattice points of the regions according to the row and column numbers of two-dimensional groups, designing a basic unit for calculation according to the calculation method of the average deviation of the solar altitude angles of the regions, circularly calculating according to the number of samples of the same group, and circularly calculating according to the number of samples of different region diameters. The IDL language is adopted in the embodiment, corresponding program codes are compiled, and the calculation software is well debugged;
(5) data calculation results
And operating calculation software, automatically calling sample data of each level group, calculating the average deviation of the solar altitude of each lattice point of the area and the solar altitude of the effective area, and respectively recording the calculation results in the corresponding level groups for induction and analysis.
2.3 summary of the calculation results
The summary of the calculation results includes grouping investigation and grouping summary.
(1) Group inspection
Considering that the area diameter size and the average deviation of the area solar altitude angle have obvious positive correlation, researching the actual correlation of the area diameter and the average deviation of the area solar altitude angle according to the area diameter grading groups, counting the average deviation obtained by calculating each grade group to obtain the mean value, the maximum value, the minimum value and the dispersion, and researching the correlation of the area point, year, season and time point factors in each grade group with different area diameters and the average deviation of the area solar altitude angle;
(2) group summary
And (3) checking and calculating 6656 groups of sample data in 13 diameter regions to obtain the relation between the mean value, the maximum value, the minimum value and the standard deviation of the solar altitude angle average deviation and the region diameter in the region shown in the table 2, and summarizing the relation into a characteristic rule of the solar altitude angle average deviation: the mean value of the mean deviation of the solar altitude angles of the regions and the diameter of the regions are in a positive correlation and have a nearly linear relationship, and the diameter of the regions is a substantial correlation factor of the mean deviation of the solar altitude angles of the regions.
TABLE 2 relation of mean, maximum, minimum and standard deviation of mean angle of solar elevation of area to area diameter
Mean value theta of mean deviation of regional solar altitudeSEVPAnd area diameter DAIn relation to (2)
θSEVP＝C1·DA (4)
In the formula C1(°·km-1) Linear coefficient of mean angular deviation of regional solar altitude to regional diameter, see table 3, C as regional diameter increases1Slightly reduced.
TABLE 3 area diameter and Linear coefficient
Although the solar altitude is directly related to the monitored ground warp latitude, the monitoring date and the monitoring time factor, the average deviation of the regional solar altitude is reflected to be weakly related to the monitored ground warp latitude, the monitoring date and the monitoring time factor.
The degree of dispersion reflecting the mean deviation of the angular height of the area sun is primarily related to the area diameter factor, with the standard deviation increasing with increasing area diameter. When different regions (or seasons and time points) are examined, the average deviation of the solar altitude angle of the regions in different regions (or seasons and time points) changes slightly and regularly as the diameter of the region increases.
If the calculation method for the average deviation of the solar altitude angles of the regions adopts a flexible mode, such as changing the statistical circular region into the square or 5-edge or 6-edge region, or changing the solar altitude angle calculation formula and the astronomical parameter calculation formula into other forms, or omitting or changing the weight rule, etc., all the steps are completed under the guidance of the invention.
If the statistical method for the average deviation characteristic law of the sun altitude angle of the region adopts an alternative mode, such as adopting other sample data to calculate the sun altitude angle, adopting different metadata densities of the region to change the array size, or adopting no data file form for the sample data, hiding the sample data in a program code, or adopting no software mode in the whole calculation process, or adopting a similar mode of changing some link sequences in the calculation process, and the like, the statistical method is finished under the guidance of the invention.
Claims (2)
1. A method for calculating the average deviation of the regional solar altitude angles is characterized in that a calculation plan is formulated and a weight rule is introduced according to a solar altitude angle calculation formula to realize the calculation of the average deviation of the regional solar altitude angles, and comprises the following 4 steps:
(1) making a calculation plan;
(2) calculating the solar altitude angle;
(3) introducing a weight rule;
(4) calculating the average deviation of the regional solar altitude;
the method comprises the following steps that (1) calculation planning is formulated, namely a circular area is adopted from the angle of the average deviation of the sun altitude of an investigation area, a two-dimensional array is required from the programming calculation angle, a square area is adopted, the circular area is contained in the square area, a weight rule is introduced to distinguish an effective calculation area from an ineffective calculation area, and the number of rows and columns of the two-dimensional array is determined;
the solar altitude angle calculation in the step (2) is to determine a solar altitude angle calculation method of each grid point in the area according to a solar altitude angle formula and the two-dimensional array row number, to realize calculation of declination, latitude and time angle parameter calculation methods related to the solar altitude angle, and to substitute each parameter value to calculate the solar altitude angle of each grid point in the area;
the formula of the solar altitude angle is
In the formula [ theta ]SETo observe the elevation angle of the earth's sun, delta is the declination of the sun's declination of the observation day,
in order to observe the latitude of the earth, tau is the observation time angle of the earth;
the solar altitude angle calculation method of each grid point of the area is
the declination, latitude and time angle parameter calculation method is
Calculating declination parameter
Formula for calculating declination delta of sun
δ＝0.3723+23.2567sinθ+0.1149sin2θ－0.1712sin3θ－0.758cosθ+0.3656cos2θ+0.0201cos3θ，
θ＝2π{Jd－79.6764－0.2422(Jy－1985)+INT[(Jy－1985)/4]+ΔJ}/365.2422 (2)
Wherein θ is the solar angle (rad), JdFor accumulated days, calculated from the monitoring date, JyFor the year of monitoring, Δ J is a correction value (d), Δ J ═ Δ J1+ΔJ2In the formula, Δ J1For correction of longitude, Δ J1＝-0.00278λ0In the formula of0For monitoring the earth longitude, Δ J2For time correction, Δ J2T/24, where T is the international time (h) of monitoring;
② latitude of each lattice point
Parameter calculation
According to the latitude of the central point of the region
Calculating the latitude of each grid point of the region according to the width of 111.193km equal to 1 degree latitude difference
Wherein DS(km) is the grid point width;
③ time angle of each lattice point Ti,jParameter calculation
Time angle τ 15 (t)0-12), in which t0To observe the true solar time (h) of the ground, the time angle of each lattice point in the region
τi,j＝15(ta+Δt/60)+λi,j－300，
Δt＝0.0028－1.9857sinθ+9.9059sin2θ－9.0924cosθ－0.6882cos2θ (3)
In the formula taTo watchMeasuring the Beijing hour time (h), lambdai,jThe longitude (°) of the observation point is shown, Δ t is the true mean solar time difference in minutes (min), and each grid point t of the region is setaAnd Δ t are the same;
the step (3) introduces a weight rule, namely, the inconsistency between the statistical average deviation area and the calculation array representative area is considered and solved by the weight rule, wherein the weight rule comprises a point state judgment rule and a point weight assignment rule;
and (4) calculating the average deviation of the regional solar altitude, namely calculating the solar altitude of each grid point of the region minus the solar altitude of the midpoint to obtain the solar altitude deviation of each grid point of the region, assigning a weight parameter to each grid point of the region according to a weight rule, and calculating the average value of the absolute value of the solar altitude deviation of the effective circular region by using the weight value of each grid point of the region.
2. A statistical method of regional solar altitude angle average deviation characteristic rules is characterized in that a calculation method is designed, the regional solar altitude angle average deviation is calculated by reasonably distributed sample data, and the characteristic rules are summarized, and the statistical method comprises the following 3 steps:
(1) sample data preparation;
(2) calculating the average deviation;
(3) summarizing a calculation result;
the sample data preparation in the step (1) comprises investigation factor relation and representative data arrangement, in order to summarize the characteristic rule of the average deviation of the solar altitude of the region, the investigation factors comprise region diameters, region points, years, seasons and time point representative parameters, and sample data of different reasonably distributed region diameters, different region points, different years, different seasons and different time points are arranged;
the average deviation calculation in the step (2) comprises forming a data set, designing a calculation method, implementing a processing process, compiling calculation software and a data calculation result, forming 1 or more data sets according to sample data of the investigation factor, designing a calculation method of the average deviation of the solar altitude angles of the region, implementing a data processing process of the average deviation of the solar altitude angles of the region, compiling calculation software according to the calculation method and the data processing process of the average deviation of the solar altitude angles of the region, and operating the calculation software to obtain the calculation result;
the calculation result induction in the step (3) comprises grouping investigation and grouping summarization, and the characteristic rule of the average deviation of the regional solar altitude is summarized according to the average deviation of the regional solar altitude and each group induction result of regional diameter, regional point, year, season and time point factors:
in the formula [ theta ]SEVPIs the mean value of the absolute value of the deviation of the solar altitude angle of each grid point in the area, DRThe diameter of the circular area is the diameter of the circular area,
for monitoring the central point latitude, λ0Comprehensively inspecting theta for monitoring longitude of a central point, y for monitoring year, m for monitoring month, d for monitoring day and h for monitoring time pointSEVPAnd the conditions of the mean value, the maximum value, the minimum value and the dispersion degree reflect the correlation between the characteristic rule of the average deviation of the regional solar altitude and the regional diameter, the region, the year, the season and the time point.
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