Mapping the vertical distribution of vegetation
数学专业英语 第2章课后答案
2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadratic equation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs（x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii） maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。
测绘专业英语课文翻译
Geodetic Surveying and Plane SurveyingSurveying has been traditionally defined as the art and science of determining the position of natural and artificial features on, above or below the earth’s surface; and representing this information in analog form as a contoured map, paper plan or chart, or as figures in report tables, or in digital form as a three dimensional mathematical model stored in the computer. As such, the surveyor/geodesist dealt with the physical and mathematical aspect of measurement. The accurate determination and monumentation of points on the surface of the Earth is therefore seen as the major task.Though these surveys are for various purposes, still the basic operations are the same---they involve measurements and computations or, basically, fieldwork and office work. There are many different types of surveys such as land surveys, route surveys, city surveys, construction surveys, hydrographic surveys, etc., but generally speaking, surveying is divided into two major categories: geodetic and plane surveying.Surveys will either take into account the true shape of the Earth（Geodetic surveys）or treat the earth as a flat surface(Plane surveys). Additionally, surveys are conducted for the purpose of positioning features on the ground(Horizontal surveys), determining the elevation or heights of features(Vertical surveys) or a combination of both.Geodetic SurveyingThe type of surveying that takes into account the true shape of the earth is called geodetic surveying.This type of survey is suited for large areas and long lines and is used to find the precise location of basic points needed for establishing control for other surveys. In geodetic surveys, the stations are normally long distances apart, and more precise instruments and surveying methods are required for this type of surveying than for plane surveying.Widely spaced, permanent monuments serve as the basis for computing lengths and distances between relative positions. These basic points with permanent monuments are called geodetic control survey points, which support the production of consistent and compatible data for surveying and mapping projects. In the past, ground-based theodolites, tapes, and electronic devices were the primary geodetic field measurements used. Today, the technological expansion of GPS has made it possible to perform extremely accurate geodetic surveys at a fraction of the cost.A thorough knowledge of the principles of geodesy is an absolute prerequisite for the proper planning and execution of geodetic surveys.In Geodetic Surveys, the shape of the earth is thought of as a spheroid, although in a technical sense, it is not really a spheroid. Therefore, distances measured on or near the surface of the earth are not along straight lines or planes, but on a curved surface. Hence, in the computation of distances in geodetic surveys, allowances are made for the earth’s minor and major diameters from which a spheroid of reference is developed. The position of each geodetic station is related to this spheroid. The positions are expressed as latitudes(angles north or south of the Equator) and longitudes(angles east or west of a prime meridian) or as northings and eastings on a rectangular grid.A geodetic survey establishes the fundamentals for the determination of the surface and gravity field of a country. This is realized by coordinates and gravity values of a sufficiently large number of control points, arranged in geodetic and gravimetric networks. In this fundamental work, curvature and the gravity field of the earth must be considered.The type of surveying in which the mean surface of the earth is considered a plane, or in which the curvature of the earth can be disregarded without significant error, generally is called plane surveying. The term is used to designate survey work in which the distances or areas involved are of limited extent. With regard to horizontal distances and directions, a level line is considered mathematically straight, the direction of the plumb line is considered to be the same at all points within the limits of the survey, and all angles are considered to be plane angles. To make computations in plane surveying, you will use formulas of plane trigonometry, algebra, and analytical geometry. For small areas, precise results may be obtained with plane surveying methods, but the accuracy and precision of such results will decrease as the area surveyed increases in size. For example, the length of an arc 18.5 km long lying in the earth’s surface is only 7mm greater than the subtended chord and, further, the difference between the sum of the angles in a plane triangle and the sum of those in a spherical triangle is only 0.51 second for a triangle at the earth’s surface having an area of 100km2 . It will be appreciated that the curvature of the earth must be taken into consideration only in precise surveys of large areas.A great number of surveys are of the plane surveying type.Surveys for the location and construction of highways, railroads, canals, and in general, the surveys necessary for the works of human beings are plane surveys, as are the surveys made to establish boundaries, except state and national. However, with the increasing size and sophistication of engineering and other scientific projects, surveyors who restrict their practice to plane surveying are severely limited in the types of surveys in which they can be engaged. The operation of determining elevation usually is considered a division of plane surveying. Elevations are referred to the geoid. The geoid is theoretical only.It is the natural extension of the mean sea level surface under the landmass. We could illustrate this idea by digging an imaginary trench across the country linking the Atlantic and Pacific oceans.If we allowed the trench to fill with seawater, the surface of the water in the trench would represent he geoid. So for all intents and purposes, the geoid is the same as mean sea level. Mean sea level is the average level of the ocean surface halfway between the highest and lowest levels recorded. We use mean sea level as a datum or, curiously and incorrectly, a datum plane upon which we can reference or describe the heights of features on, above or below the ground. Imagine a true plane tangent to the surface of mean sea level at a given point. At horizontal distances of 1km from the point of tangency, the vertical distances(or elevations) of the plane above the surface represented by mean sea level are 7.8cm. Obviously, curvature of the earth’s surface is a factor that cannot be neglected in obtaining even rough values of elevations. The ordinary procedure in determining elevations, such as balancing backsight and foresight distance in differential leveling, automatically takes into account the curvature of the earth and compensates for earth curvature and refraction, and elevations referred to the curved surface of reference are secured without extra effort by the surveyor.There is close cooperation between geodetic surveying and plane surveying. The geodetic survey adopts the parameters determined by measurements of the earth, and its own results are available to those who measure the earth. The plane surveys, in turn, are generally tied to the control points of the geodetic surveys and serve particularly in the development of national map series and in the formation of real estate cadastres.Below we are about measure distance, Angle and Direction Measurement and Traversing. Distance MeasurementOne of the fundamentals of surveying is the need to measure distance. Distances are not necessarily linear, especially if they occur on the spherical earth. In this subject we will deal with distances in Euclidean space, which we can consider a straight line from one point or feature to another. Distance between two points can be horizontal, slope, or vertical. Horizontal and slope distances can be measured with lots of techniques of measurement depending on the desired quality of the result. If the points are at different elevations, then the distance is the horizontal length between plumb lines at the points. Here gives a brief summary of relevant techniques and their respective accuracies:Pacing and OdometerPacing is a very useful form of measurement though it is not precise, especially when surveyors are looking for survey marks in the field. Pacing can be performed at an accuracy level of 1/100~1/500 when performed on horizontal land, while the accuracy of pacing can’t be relied upon when pacing up or down steep hills. The odometer is a simple device that can be attached to any vehicle and directly registers the number of revolutions of a wheel. With the circumference of the wheel known, the relation between revolutions and distance is fixed.Ordinary Taping and Precise TapingTaping is a very common technique for measuring horizontal distance between two points. Ordinary taping refers to the very common tapes that we can buy them in stores, such as the plastic tapes or poly tapes. Such tapes have low precision in distance measurements with about 1/3000~1/5000. The precise taping refers to the steel tapes and which are much more expensive than the plastic tape and have higher precision of 1/10000~1/30000. Invar tapes are composed 35% nickel and 65% steel. This alloy has a very low coefficient of thermal expansion, making the tapes useful in precise distance measurement. Many tapes are now graduated with foot units on one side and metric units on the reverse side. Metric units are in meters, centimeter and minimeter with the total length of 20 m, 30 m, 50 m and 100 m.If we want to measure the horizontal distance between the two points A and B, we can do like this: With zero of the tape to the higher point B and tape going along the point A, we can measure the horizontal distance by using the plumb bob with pump line entering to the point A. To judge the exact horizontal line, we should move the tape up and down along the pump line and we will find the changes of reading in the tape. The shortest reading of the tape is the horizontal distance.If the distance is longer than the length of tape, then we can divide the long distance into several segments and get the total distance by plus each segment together. Since different tapes have different starts of zero of the tapes, it is very important to judge where the zero of the tape begins. Tacheometry and StadiaTacheometry is an optical solution to the measurement of distance. The word is derived from the Greek Tacns, meaning “swift”, and metrot, meaning “a measure”. Tacheometry involves the measurement of a related distance parameter either by means of a fixed-angle intercept. Theodolite tacheometry is an example of stadia system.The theodolite is directed at the level staff where the staff is held vertically and the line of sight of the telescope is horizontal.By reading the top and bottom stadia hairs on the telescope view and then the horizontal distance from center of instrument to rod can be obtained by multiplying the stadia interval factor K by the stadia interval and plus the distance C which is from the center of instrument to principal focus, i.e. D=Ks + C. Usually the nominal stadia interval factor K equals 100 which is a constant for a particular instrument as long as conditions remain unchanged, but it may be determined by observation in practice. The value of C is determined by the manufacturer and stated on the inside of the instrument box. For external-focusing telescopes, under ordinary condition, C may be considered as 1 ft without error of consequence. Internal-focusing telescopes are so constructed that C is 0 or nearly so; this is an advantage of internal-focus telescopes for stadia work. Most instruments now used for stadia are equipped with internal-focusing telescopes.Applications of tacheometry include traversing and leveling for the topographic surveys, location of detail surveys, leveling and field completion surveys for the topographic mapping, and hydrographic mapping. The relative precision is 1:1000 to 1:5000.Stadia is a form of tacheometry that uses a telescopic cross-hair configuration to assist in determining distances.A series of rod readings is taken with a theodolite and the resultant intervals are used to determine distances.Electronic Distance Measurement(EDM)The Electronic Distance Measurement(EDM) was first introduced in 1950s by the founders of Geodimeter Inc. The advent of EDM instrument has completely revolutionized all surveyingprocedures, resulting in a change of emphasis and techniques. Distance can now be measured easily, quickly and with great accuracy, regardless of terrain conditions.EDM instruments refer to the distance measurement equipments using light and radio waves. Both light waves and radio waves are electromagnetic. They have identical velocities in a vacuum (or space) to 299,792.458±0.001km/sec.These velocities, which are affected by the air’s density, are reduced and need to be recalculated in the atmosphere. The basic principle of EDM instruments is that distance equals time multiplied by velocity.Thus if the velocity of a radio or light wave and time required for it to go from one point to another are known, the distance between the two points can be calculated.The EDM instruments may be classified according to the type and wavelength of the electromagnetic energy generated or according to their operational range. EDM instruments use three different wavelength bands: (1)Microwave systems with range up to 150km, wave length 3 cm, not limited to line of sight and unaffected by visibility; (2)Light wave systems with range up to 5 km (for small machines), visible light, lasers and distance reduced by visibility; (3)Infrared systems with range up to 3 km, limited to line of sight and limited by rain, fog, other airborne particles. Although there is a wide variety of EDM instruments available with different wavelengths, there are basically only two methods of measurement employed which may divide the instruments into two classification as electro-optical (light waves) and microwaves (radio waves) instruments. These two basic methods are namely the pulse method and more popular phase different method. They function by sending light waves or microwaves along the path to be measured and measuring the time differences between transmitted and received signals, or in measuring the phase differences between transmitted and received signals in returning the reflecting light wave to source. Modern EDM instruments are fully automatic to such an extent that, after the instruments, set up on one station, emits a modulated light beam to a passive reflector set up on the other end of the line to be measured. The operator need only depress a button, and the slope distance is automatically displayed. More complete EDM instruments also have the capability of measuring horizontal and vertical or zenith angles as well as the slope distance. These instruments referred to as total station instruments.Angle and Direction MeasurementHorizontal and vertical angles are fundamental measurements in surveying. It is necessary to be familiar with the meanings of certain basic terms before describing angle and direction measurement. The terms discussed here have reference to the actual figure of the earth.Basic TermsA vertical line at any point on the earth’s surface is the line that follows the direction of gravity at that point.It is the direction that a string will assume if a weight is attached at that point and the string is suspended freely at the point.At a given point there is only one vertical line.A horizontal line at a point is any line that is perpendicular to the vertical line at the point.At any point there are an unlimited number of horizontal lines.A horizontal plane at a point is the plane that is perpendicular to the vertical line at the point. There is only one horizontal plane through a given point.A vertical plane at a point is any plane that contains the vertical line at the point.There are an unlimited number of vertical planes at a given point.Horizontal Angle and Vertical AngleA horizontal angle is the angle formed in a horizontal plane by two intersecting vertical planes, or a horizontal angle between two lines is the angle between the projections of the lines onto a horizontal plane. For example, observations to different elevation pointsB andC from A will give the horizontal angle ∠bac which is the angle between the projections of two lines (AB and AC) onto the horizontal plane. It follows that, although the points observed are at different elevations, it is always the horizontal angle and not the space angle that is measured (Figure 1). The horizontal angle is used primarily to obtain relative direction to a survey control point, or topographic detail points, or to points to be set out.A vertical angle is an angle measured in a vertical plane which is referenced to a horizontal line by plus (up) or minus (down) angles, or to a vertical line from the zenith direction. Plus and minus vertical angles are sometimes referred to as elevation or depression angles, respectively. A vertical angle thus lies between 0°and ±90°. Zenith is the term describing points on a celestial sphere that is a sphere of infinitely large radius with its center at the center of the earth. The zenith is anangle measured in a vertical plane downward from an upward directed vertical line through the instrument. It is thus between 0°and 180°. Obviously the zenith angle is equal to 90°minus the vertical angles. Vertical angles or zeniths are used in the correction of slope distance to the horizontal or in height determined. For the most part, the instrument used in the measurement of angles is called a transit or theodolite, although angles can be measured with clinometers, sextants (hydrographic surveys), or compasses.The theodolite contains a horizontal and vertical circles of either glass or silver.The horizontal and vertical circles of theodolite can be linked to circular protractors graduated from 0°to 360°in a clockwise manner set in horizontal and vertical plane. The horizontal circle is used when measuring or laying off horizontal angles and the vertical circle is used to measure or lay off vertical angles or zenith angles. Usually the units of angular measurement employed in practice are degrees, minutes, and seconds, the sexagesimal system.Angle MeasurementA horizontal angle in surveying has a direction or sense; that is, it is measured or designed to the right or to the left, or it is considered clockwise or counterclockwise. In the above figure, the angle at A fromB toC is clockwise and the angle from C to B is counterclockwise. With the theodolite set up, centered, and leveled over at station A, then a simple horizontal angle measurement between surveying point B, A and C would be taken as follows:⑴Commencing on, say, “face left”, the target set at survey point B is carefully bisected and the reading on horizontal scale is 25°. ⑵The upper plate clamp is released and telescope is turned clockwise to survey point C. The reading on horizontal circle is 75°⑶The horizontal angle is then the difference of the two directions, i.e. (75°-25°) =50°（⑷Change face and observe point C on “face right”, and note the reading=255°⑸Release upper plate and swing counterclockwise to point B and note the reading =205°⑹The reading or the direction must be subtracted in the same order as 255°-205°=50°⑺The mean of two values would be accepted if they are in acceptable agreement. Modern electronic digital theodolites contain circular encoders that sense the rotations of the spindles and the telescope, convert these rotations into horizontal and vertical (or zenith) angles electronically, and display the value of the angles on liquid crystal displays (LCDs) or light-emitting diode displays (LEDs). These readouts can be recorded in a conventional field book or can be stored in a data collector for future printout orcomputation. The instrument contains a pendulum compensator or some other provision for indexing the vertical circle readings to an absolute vertical direction.The circle can be set to zero readings by a simple press of a button or initialized to any value on the instrument.Azimuth is the horizontal angle measured in a clockwise direction from the plane of the meridian, which is a line on the mean surface of the earth joining the north and south poles. Azimuth ranges in magnitude from 0°to 360°, values in excess of 360°, which are sometimes encountered in computations, are simply reduced by 360°before final listing.Bearing is the traditional way of stating the orientation of the line. It is actually the angle measured from the north or south.The bearing, which can be measured clockwise or counterclockwise from the north or south end of the meridian, is always accompanied by letters that locate the quadrant in which the line falls. For example, bearing N32W indicates a line trending 32°west of the north. It is equal to an azimuth of 328°.Bearing S12W indicates a line trending 12°west of the south. It is equal to an azimuth of 192°. It is important to state that the bearing and azimuth are respect to true north..TraversingThe purpose of the surveying is to locate the positions of points on or near the surface of the earth. To determine horizontal positions of arbitrary points on the earth’s surface and elevation of points above or below a reference surface are known as a control survey.The positions and elevations of the points make up a control network.There are different types of control networks depending on where and why they are established.A control network may have very accurate positions but no elevations (called a Horizontal Control Network) or very accurate elevations but no positions (called a Vertical Control Network).Some points in a control network have both accurate positions and elevations.Control networks range from small, simple and inexpensive to large and complex and very expensive to establish.A control network may cover a small area by using a “local” coordinate system that allows you to position the features in relation to the control network but doesn’t tell you where the features areon the surface of the earth, or cover a large area by consisting of a few well-placed and precise-established control points, which is sometimes called the primary control.The horizontal positions of points in a network can be obtained in a number of different ways.（The generally used methods are triangulation, trilateration, traversing, intersection, resection and GPS.The main topic of this text refers to the traversing.TriangulationThe method of surveying called triangulation is based on the trigonometric proposition that if one side and three angles of a triangle are known, the remaining sides can be computed by the law of sines.Furthermore, if the direction of one side is known, the direction of the remaining sides can be determined.And then coordinates of unknown points can be computed by application of trigonometry.TrilaterationSince the advent of long-range EDM instrument, a method of surveying called trilateration was adopted to combine with triangulation.The trilateration is based on the trigonometric proposition that if the three sides of a triangle are known, the three angles can be computed by the law of cosines.Trilateration possesses some advantages over triangulation because the measurement of the distances with EDM instrument is so quick, precise and economical while the measurement of the angles needed for triangulation may be more difficult and expensive. For some precise projects, the combination of triangulation and trilateration which is called triangulateration is applied.TraversingA survey traverse is a sequence of lengths and directions of lines between points on the earth, obtained by or from field angle and distance measurements and used in determining positions of the point. The angles are measured using transits, theodolites, or total stations, whereas the distances can be measured using steel tapes or EDM instruments. A survey traverse may determine the relative positions of the points that if connects in series, and if tied to control stations based on some coordinate system, the positions may be referred to that system. From these computed relative positions, additional data can be measured for layout of new features, such as buildings and roads. Since the advent of EDM equipment, traversing has emerged as the most popular method to establish control networks such as basic area control, mapping, control of hydrographic surveys and construction projects.In engineering surveying, it is ideal way to surveys and dimensional control of route-type projects such as highway, railroad, and pipeline construction. In general, a traverse is always classified as either an open traverse or a closed traverse. An open traverse originates either at a point of known horizontal position with respect to a horizontal datum or at an assumed horizontal position, and terminates at a station whose relative position is not previously known..The open traverse provides no check against mistakes and large errors for its termination at anunknown horizontal position and lack of geometric closure. This lack of geometric closure means that there is no geometric verification possible with respect to the actual positioning of the traverse stations. Thus, the measuring technique must be refined to provide for field verification. At a minimum, distances are measured twice and angles are doubled. Open traverses are often used for preliminary survey for a road or railroad.A closed traverse can be described in any one of the following two ways: ⑴A closed loop traverse, as the name implies, forms a continuous loop, enclosing an area.This type of closed traverse starts at assumed horizontal position or at a known horizontal position with respect to a horizontal datum and ends at the same point. ⑵A connecting traverse starts and ends at separate points, whose relative positions have been determined by a survey of equal or higher order accuracy. A known horizontal position is defined by its geographic latitude and longitude, or by its X and Y coordinates on a grid system.Closed traverses, whether they return to the starting point or not, provide checks on the measured angles and distances.In both cases, the angles can be closed geometrically, and the position closure can be determined mathematically. Therefore they are more desirable and used extensively in control, construction, property, and topographic surveys.As we mentioned above, a closed traverse provides checks on the measured angles and distances. For example, the geometric sum of the interior angles in an n-side closed figure should be (n-2)×180°, but due to systematic and random errors of the measurements, when all the interior angles of a closed traverse are summed, they may or may not total the number of degrees required for geometric closure. The difference between the geometric sum and actual field sum of the interior angles is called angular closure. The total error of angular closure should be distributed evenly to each angle (if all angles were measured with the same precision) before mathematical analysis of the traverse. The important point before doing this is that the overall angular closure can’t be beyond the survey specifications.Closed traverses provide also checks on the measured distances, and the position closure can be determined mathematically, which means that an indication of the consistency of measuring distances as well as angles should be given to a traverse that closes on itself. Theoretically this position closure from the origin back to itself should be zero. But the Errors in the measured distances and angles of the traverses, however, will tend to alter the shape of the traverse, therefore we should compute the algebraic sum of the latitudes and algebraic sum of the departures, and compare them with the fixed latitude and departure of a straight line from the origin to the closing point. By definition, latitude here is the north/south rectangular component of a line and departure is the east/west rectangular component of a line. To differentiate direction, north is considered plus, whereas south is considered minus.Similarly, east is considered plus, whereas west is considered minus.Then the discrepancy should be adjusted by apportioning the closure both in latitudes and in departures on a reasonable basis. The adjusted position of each traverse point is determined with respect to some origin.This position is defined by its Y coordinates and its X coordinates with respect to a plane rectangular coordinate system in which the Y axis is assumed north-south whereas the X axis east-west.。
2025版《师说》高中全程复习构想英语(北师大版)第三讲 名词和数词
4．[2022·新高考Ⅰ卷]The GPNP's main goal is to improve connectivity between separate ________ (population)and homes of giant pandas, and eventually achieve a desired level of population in the wild.
答案与解析：photographer 考查名词。此处表示John Olson之前是一名摄影师。 分析句子结构可知，空格前有冠词“a”和形容词“former”修饰，此处应用可数名词 photographer的单数形式。故填photographer。
7．[2022·全国乙卷]As a main promoter of the International Tea Day, the birthplace of tea and the largest teaproducing country, China has a ________ (responsible) to work with other countries to promote the healthy development of the tea industry.
答案与解析：warning 考查名词。形容词weighty后接名词形式。根据句中不 定冠词a可知，用单数形式。
3．[2023·全国乙卷]But for all its ancient buildings, Beijing is also a place that welcomes the fastpaced development of modern life, with 21stcentury architectural ________ (wonder) standing side by side with historical buildings of the past.
测绘专业英语词汇
测绘专业英语测绘学：geomatics， surveying and mapping， SM；研究与地球有关的基础空间信息的采集、处理、显示、管理、利用的科学与技术。
中华人民共和国测绘法：Surveying and Mapping Law of the People's Republic of China；我国关于测绘的基本法律，是从事测绘活动和进行测绘管理的基本准则和基本依据。
测绘标准：standards of surveying and mapping；由主管部门颁发的关于测绘技术方法、产品质量、品种规格、地图表示等统一规定的技术文件。
测量规范：specifications of surveys；对测量产品的质量、规格以及测量作业中的技术事项所作的统一规定。
地形图图式：topographic map symbols；对地图上地物、地貌符号的样式、规格、颜色、使用以及地图注记和图廓整饰等所作的统一规定。
大地测量学：geodesy；研究和确定地球的形状、大小、重力场、整体与局部运动和地表面点的几何位置以及它们的变化的理论和技术的学科。
地球形状：earth， shape， figure of the earth；地球自然表面的形状或大地水准面的形状。
重力基准：gravity datum；重力的起算值和尺度因子。
重力场：gravity field；地球重力作用的空间。
在该空间中，每一点都有惟一的一个重力矢量与之相对应。
地心坐标系：geocentric coordinate system；以地球质心或几何中心为原点的坐标系。
地球椭球：earth ellipsoid；近似表示地球的形状和大小，并且其表面为等位面的旋转椭球。
大地原点：geodetic origin；大地坐标的起算点。
水准原点：leveling origin；高程起算的基准点。
测量标志：survey mark；标定地面测量控制点位置的标石、觇标以及其他用于测量的标记物的通称。
测量专业常用英语翻译
测量专业常用英语翻译短语或词组中线 midline边线 sideline向左/右移动 left/right前进 forward后退 back路基 subgrade路面 Pavement岔口 fork交叉口 intersection十字路口 crossroads测量 measurement放线Actinomyces中桩 medium pile边桩 edge of pile水平测量Level measurement导线 wire闭合导线 closed traverse附合导线 Connecting traverse 曲线Curve水准仪 Level全站仪Total Station架子 Shelf塔尺 Foot tower线坠Line falling钢尺 Steel band tape量距离 Distance高程 Elevation每米 per meter混凝土Concrete沥青Asphalt石灰Lime水沟Ditch交点Nodal圆缓点 Ease-point circle缓圆点 Ease dots直缓点Direct relief point曲线中点Curve midpoint 边坡Slope渗水Seepage排水沟 Drainage防雨Rainproof防水Waterproof加固Reinforcement 防护Protection安全防护Security 安全帽Helmets水泥Cement 沙石Gravel沙子SandAsphalt 沥青base基层sub base 底基层borrow material 取土土方borrow area取土场地Spoil弃土culvert 涵管fill 土方lot 标段pavement layer结构层路肩shoulder spoiler Carriageway 行车道Site 现场QA quality assurance 质量保证QC quality control 质量监控规范Norms安平精度 setting accuracy比例尺 scale比例误差 proportional error闭合差 closure闭合差 closing error闭合导线 closed traverse闭合水准路线 closed leveling line边长中误差 mean square error of side length边交会法 linear intersection边角测量 triangulateration边角交会法 linear-angular intersection标称精度 nominal accuracy标尺 rod标尺 staff标准差 standard deviation参考数据 reference data参考效应 reference effect参数平差，*间接平差 parameter adjustment侧方交会 side intersection测标 [measuring] mark测杆 measuring bar测高仪 Altimeter测绘标准 standards of surveying and mapping测绘仪器 instrument of surveying and mapping测角中误差 mean square error of angle observation测量标志 survey mark测量规范 specifications of surveys测量控制网 surveying control network测量平差 adjustment of observation测量平差 survey adjustment测量学 surveying测线 survey line测站 station垂线偏差改正 correction for deflection of the vertical 垂线偏差改正 correction for deflection of the vertical 大地方位角 geodetic azimuth导线边 traverse leg导线测量 traverse survey导线点 traverse point导线横向误差 lateral error of traverse导线角度闭合差 angle closing error of traverse导线结点 junction point of traverses导线曲折系数 meandering coefficient of traverse导线全长闭合差 total length closing error of traverse 导线网 traverse network导线相对闭合差relative length closing error of traverse导线折角 traverse angle导线纵向误差 longitudinal error of traverse独立坐标系 independent coordinate system对中杆 centering rod方位角中误差 mean square error of azimuth方向观测法 method by series方向观测法 method of direction observation放样测量 setting-out survey附合导线 connecting traverse附合水准路线 annexed leveling line附加位 additional potential复测法 repetition method高程导线 height traverse高程点 elevation point高程基准 height datum高程控制测量 vertical control survey高程控制点 vertical control point高程控制网 vertical control network高程系统 height system高程中误差 mean square error of height工程控制网 engineering control network工程水准仪 engineer's level公路工程测量 road engineering survey横断面图 cross-section profile后方交会 resection缓和曲线测设 spiral curve location缓和曲线测设 transition curve location基线 base line基线测量 base line measurement基线网 base line network基准台，*差分台 track station基准纬度 latitude of reference极坐标定位，*距离方位定位point coordinate positioning极坐标定位方法,*方位距离定位方法 azimuth distance positioning method极坐标定位方法，*方位距离定位方法 polar positioning method预制涵管precast culvert路缘石kerbstone压实compact填筑fill基底foundation级配碎石gradation crush-stoneCoat 涂层摊铺pavement透层prime双表double seal面层surface骨料aggregate稀浆封层slurry桥bridge梁beam桥面板deck墩柱pier承台cushion cap桩基pile钻孔bore维护maintenance处理treatment附属auxiliary腐蚀corrosion砌石stone-pitching石笼gabion护栏guardrail标杆sign post围栏railing路标1.guide post 2.signpost交通标志traffic sign标线road marking道路专用区road reserved结构structure模版shutter 饰面finishing脚手架falsework结构钢structure steel预压pre pressing预制precast公差tolerance安全岛island额外extra施工工艺construction method 申请statement方案scheme路肩断点shoulder breakpoint 护栏parapet wall人行道foot walk检查井chamber管道pipeline取样sample挖方cut section填方fill section道路专用区road reserve倒角chamfer模版shutter伸缩缝expansion joint独轮车wheelbarrow锤子hammer砖块brick预处理pretreatment预涂premix。
数学专业英语常用词汇
数学专业英语词汇代数部分1. 有关数*算add，plus 加?subtract 减?difference 差??multiply, times 乘?product 积?divide 除?divisible 可被整除的?divided evenly被整除? dividend 被除数，红利?divisor 因子，除数?quotient 商?remainder余数??factorial 阶乘?power 乘方?radical sign, root sign 根号? round to四舍五入?to the nearest 四舍五入2. 有关集合union 并集?proper subset 真子集?solution set 解集??3.有关代数式、方程和不等式algebraic term 代数项?like terms, similar terms同类项?numerical coefficient 数字系数?literal coefficient 字母系数??inequality 不等式?triangle inequality 三角不等式??range 值域??original equation 原方程?equivalent equation 同解方程，等价方程?linear equation 线性方程(e.g.5?x?+6=22)?4.有关分数和小数proper fraction真分数?improper fraction 假分数?mixed number 带分数?vulgar fraction，common fraction 普通分数?simple fraction简分数?complex fraction繁分数??numerator 分子?denominator 分母?(least) common denominator（最小）公分母?quarter 四分之一?decimal fraction 纯小数?infinite decimal 无穷小数recurring decimal循环小数?tenths unit 十分位??5. 基本数学概念arithmetic mean 算术平均值?weighted average 加权平均值?geometric mean 几何平均数?exponent 指数，幂?base 乘幂的底数,底边?cube 立方数，立方体?square root平方根?cube root 立方根??common logarithm 常用对数?digit 数字?constant 常数?variable 变量??inverse function反函数? complementary function 余函数?linear 一次的，线性的?factorization 因式分解?absolute value绝对值，e.g.｜-32｜=32? round off四舍五入 ?6.有关数论natural number 自然数?positive number 正数?negative number 负数?odd integer, odd number 奇数?even integer, even number 偶数? integer, whole number 整数?positive whole number 正整数?negative whole number 负整数?? consecutive number 连续整数?real number, rational number 实数,有理数?irrational（number）无理数??inverse 倒数?composite number 合数 e.g.4,6,8,9,10,12,14,15……?prime number 质数 e.g.2,3,5,7,11,13,15……注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal 倒数??common divisor 公约数?multiple 倍数?(least)common multiple (最小)公倍数??(prime) factor (质)因子?common factor 公因子??ordinary scale, decimal scale 十进制?nonnegative 非负的??tens 十位?units 个位??mode众数?median 中数??common ratio 公比??7.数列arithmetic progression(sequence) 等差数列?geometric progression(sequence) 等比数列??approximate 近似?(anti)clockwise (逆) 顺时针方向? cardinal 基数?ordinal 序数?direct proportion 正比?distinct 不同的?estimation 估计，近似? parentheses 括号?proportion 比例?permutation 排列?combination 组合?table 表格?trigonometric function 三角函数? unit 单位,位?几何部分1. 所有的角alternate angle 内错角? corresponding angle 同位角? vertical angle对顶角?central angle圆心角?interior angle 内角?exterior angle 外角? supplementary angles补角? complementary angle余角? adjacent angle 邻角?acute angle 锐角?obtuse angle 钝角?right angle 直角?round angle周角?straight angle 平角?included angle夹角??2.所有的三角形equilateral triangle 等边三角形? scalene triangle不等边三角形? isosceles triangle等腰三角形? right triangle 直角三角形? oblique 斜三角形?inscribed triangle 内接三角形??3.有关收敛的平面图形，除三角形外semicircle 半圆?concentric circles 同心圆? quadrilateral四边形?pentagon 五边形?hexagon 六边形?heptagon 七边形?octagon 八边形?nonagon 九边形?decagon 十边形?polygon多边形?parallelogram 平行四边形? equilateral 等边形?plane 平面? square 正方形，平方?rectangle 长方形?regular polygon 正多边形?rhombus 菱形?trapezoid梯形??4.其它平面图形arc 弧?line, straight line 直线?line segment 线段?parallel lines 平行线?segment of a circle 弧形??5.有关立体图形cube 立方体，立方数?rectangular solid 长方体?regular solid/regular polyhedron 正多面体?circular cylinder 圆柱体?cone圆锥?sphere 球体?solid 立体的??6.有关图形上的附属物altitude 高?depth 深度?side 边长?circumference, perimeter 周长? radian弧度?surface area 表面积?volume 体积?arm 直角三角形的股?cross section 横截面?center of a circle 圆心?chord 弦?radius 半径?angle bisector 角平分线?diagonal 对角线?diameter 直径?edge 棱?face of a solid 立体的面? hypotenuse 斜边?included side夹边?leg三角形的直角边?median of a triangle 三角形的中线?base 底边，底数（e.g. 2的5次方，2就是底数）?opposite直角三角形中的对边? midpoint 中点? endpoint 端点?vertex (复数形式vertices)顶点? tangent 切线的?transversal截线?intercept 截距??7.有关坐标coordinate system 坐标系? rectangular coordinate 直角坐标系? origin 原点?abscissa横坐标?ordinate纵坐标?number line 数轴?quadrant 象限?slope斜率?complex plane 复平面??8.其它plane geometry 平面几何? trigonometry 三角学?bisect 平分?circumscribe 外切?inscribe 内切?intersect相交?perpendicular 垂直?pythagorean theorem勾股定理? congruent 全等的?multilateral 多边的?1.单位类cent 美分?penny 一美分硬币 ?nickel 5美分硬币?dime 一角硬币?dozen 打（12个）?score 廿(20个)?Centigrade 摄氏?Fahrenheit 华氏?quart 夸脱?gallon 加仑(1 gallon = 4 quart)?yard 码?meter 米?micron 微米?inch 英寸?foot 英尺?minute 分(角度的度量单位，60分=1度)? square measure 平方单位制? cubic meter 立方米?pint 品脱(干量或液量的单位)??2.有关文字叙述题，主要是有关商业intercalary year(leap year) 闰年(366天)?common year 平年(365天)? depreciation 折旧?down payment 直接付款?discount 打折?margin 利润?profit 利润?interest 利息?simple interest 单利?compounded interest 复利?dividend 红利?decrease to 减少到?decrease by 减少了?increase to 增加到?increase by 增加了?denote 表示?list price 标价?markup 涨价?per capita 每人?ratio 比率?retail price 零售价?tie 打Chapter onefunction notation方程符号函数符号quadratic functions 二次函数quadratic equations 二次方程式二次等式chapter twoEquivalent algebraic expressions 等价代数表达式rational expression 有理式有理表达式horizontal and vertical translation of functions 函数的水平和垂直的平移reflections of functions 函数的倒映映射chapter threeExponential functions 指数函数exponential decay 指数式衰减exponent 指数properties of exponential functions 指数函数的特性chapter fourTrigonometry 三角学Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数Discrete functions 离散函数数学 mathematics, maths(BrE), math(AmE) 公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n.)被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.)被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation 四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root集合 aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition值域 range常量 constant变量 variable单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential 导数 derivative极限 limit无穷大 infinite(a.) infinity(n.) 无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral有理数 rational number无理数 irrational number实数 real number虚数 imaginary number复数 complex number矩阵 matrix行列式 determinant几何 geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width菱形 rhomb, rhombus, rhombi(pl.), diamond正方形 square 梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid 五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon 圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference周长 perimeter面积 area轨迹 locus, loca(pl.)相似 similar全等 congruent四面体 tetrahedron五面体 pentahedron六面体 hexahedron平行六面体 parallelepiped 立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron棱锥 pyramid棱柱 prism棱台 frustum of a prism 旋转 rotation轴 axis圆锥 cone圆柱 cylinder圆台 frustum of a cone球 sphere半球 hemisphere 底面 undersurface表面积 surface area体积 volume空间 space坐标系 coordinates坐标轴 x-axis, y-axis, z-axis 横坐标 x-coordinate纵坐标 y-coordinate原点 origin双曲线 hyperbola抛物线 parabola三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE),orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph 柱形统计图 histogram折线统计图 broken line graph 曲线统计图 curve diagram扇形统计图 pie diagram。
识图定向测绘类词汇中英文对照
测绘类词汇中英文对照A阿伯斯投影Albers projection阿贝比长原理Abbe comparator principle阿达马变换Hadamard transformation隘口Cols鞍部Saddle，col安平精度setting accuracy岸台，*固定台base station暗礁reefB靶道工程测量target road engineering survey半导体激光器semiconductor laser半日潮港semidiurnal tidal harbor半色调halftone饱和度saturation北极星任意时角法method by hour angle of Polaris贝塞尔大地主题解算公式Bessel formula for solution of geodetic problem 贝塞尔椭球Bessel ellipsoid贝叶斯分类Bayesian classification被动式遥感passive remote sensing本初子午线prime meridian比较地图学comparative cartography比例尺scale比例量表ratio scaling比例误差proportional error比赛区域competition areas比值变换ratio transformation比值增强ratio enhancement闭合差closing error，closure闭合导线closed traverse闭合水准路线closed leveling line边长中误差mean square error of side length边交会法linear intersection边角测量triangulateration边角交会法linear-angular intersection边角网triangulateration network边缘检测edge detection边缘增强edge enhancement编绘compilation编绘原图compiled original编辑大纲map editorial policy变比例投影varioscale projection变换光束测图affine plotting变线仪variomat变形观测控制网control network for deformation observation变形椭圆indicatrix ellipse标称精度nominal accuracy标尺rod，staff标定地图（“正置地图”）orienting the map标高差改正correction for skew normals标界测量survey for marking of boundary标志灯，*回光灯signal lamp标准差standard deviation标准配置点Gruber point标准纬线standard parallel冰后回弹post glacial rebound波茨坦重力系统Potsdam gravimetric system波带板zone plate波浪补偿compensation of undulation，heave compensation波浪补偿器，*涌浪滤波器heave compensator波罗-科普原理Porro-Koppe principle波谱测定仪spectrometer波谱集群spectrum cluster波谱特征空间spectrum feature space波谱特征曲线spectrum character curve波谱响应曲线spectrum response curve波束角beam angle，wave beam angle泊位Berth补偿器compensator补偿器补偿误差compensating error of compensator布格改正Bouguer correction布格异常Bouguer anomaly布隆斯公式Bruns formula布耶哈马问题Bjerhammar problem捕捉地物catching feature 也叫搜索地物或“撒网”。
Divergenceandvorticity散度、涡度
w
=
∂z ∂t
(1)
in the (x,y,z) coordinate system, or
ω
=
∂p ∂t
=
−
ρgw
(2)
in the (x,y,p) coordinate system is neglected from here on.
Understanding divergence
The divergence of a vector field is relatively easy to understand intuitively. Imagine that the vector field in Figure 1a gives the velocity of some fluid flow. It appears that the fluid is exploding outward from the origin.
Figure 1. Vector field with (a) pure divergence (left) and (b) pure convergence (right).
This expansion of fluid flowing with a velocity field U = (u,v) is captured by the divergence of U, which we denote div U. The divergence of the above vector field is positive since the flow is expanding. In contrast, the vector field in Figure 1b
Mathematically the expressions for the vertical component (ζ) of the vorticity are:
学生专业英文介绍测绘专业介绍
Level (水准仪)
height measurement
The most precise method of determining elevations and most commonly used method is direct leveling or spirit leveling(几何水准测量) which means measuring the vertical distance directly.
share a doggerel（打油诗） about :
测绘人
远看测区像天堂，近看测区像银行， 走进测区像牢房，不如回家放牛羊， 人人都说测量好，傻帽才往测区跑， 测区挣钱测区花，根本没钱寄回家， 漂亮老婆娶不上，娶了老婆用不上， 生了孩子管不上，买了房子住不上， 青春撒在荒山上，CAD画没了我的青春， 全站仪测走了我的梦想，水准仪压碎了我的希望， GPS也不能缝合我的悲伤，控制一声声敲击我的心脏， 等高线一圈圈束缚我的肩膀，RTK曾经让我感觉英姿飒爽， 能不背上它如今变成我的渴望。
A total station integrates the functions of an electronic theodolite（电子经纬仪） for measuring angles,an DEM for measuring distances,digital data and a data recorder.
无人机
轻型低空遥感（无人机） 低空无人机获取数据（汶川）
CCD camera（CCD相机） POS system(动态定位定姿) sensor（传感器）
…………
Geomatics（测绘学）
GPS （ Global Positioning System ） 全球定位系统
利用section描地质图流程
利用section描地质图流程英文回答：To describe the process of using sections to depict a geological map, I will start by explaining the purpose and importance of geological mapping. Geological mapping is a crucial tool used by geologists to understand the distribution and characteristics of different rock units in a specific area. It helps in identifying geological structures, such as faults and folds, and provides valuable information for resource exploration and environmental management.The first step in creating a geological map is to conduct a thorough field survey. This involves visiting the study area and collecting data through observations, measurements, and sampling. Geologists examine the rock outcrops, record their characteristics, and take samplesfor further analysis. They also note the location of geological structures, such as the orientation anddisplacement of rock layers.Once the field survey is complete, the collected data is used to create a base map. This map serves as the foundation for the geological map and includes information about the topography, rivers, roads, and other features of the area. The base map is typically created using geographic information systems (GIS) software, which allows for the integration of various data layers.After the base map is prepared, geologists start creating geological sections. A geological section is a vertical representation of the subsurface geology along a specific line or profile. It provides a cross-sectional view of the rock layers and geological structures beneath the surface. Sections are created by interpreting the field data, including the rock types, their relationships, and the geological structures observed.To create a geological section, geologists first select a line or profile that represents the area of interest. They then plot the elevation along this line and indicatethe location of the different rock units encountered. The rock units are represented by different colors or patterns, allowing for easy identification.In addition to the rock units, geological sections also include symbols and annotations to indicate the presence of geological structures. For example, a fault may be represented by a dashed line with arrows indicating the direction of displacement. Folds can be shown using curved lines or by indicating the orientation of the folded rock layers.Geological sections are an essential component of a geological map as they provide valuable information about the subsurface geology. They help in understanding thethree-dimensional distribution of rock units and structures, which is important for geological modeling and resource assessment. Sections also aid in visualizing the geological history of an area and can help in predicting the presenceof mineral deposits or groundwater resources.中文回答：地质图流程中利用剖面图描绘地质图的过程如下，首先，我会解释地质图绘制的目的和重要性。
垂直摄影测量处理流程
垂直摄影测量处理流程Vertical photogrammetric processing is a crucial step in the field of photogrammetry, which involves the use of aerial photography to measure and map land areas. The process includes the use of specialized software and tools to analyze and interpret the data captured through aerial photography.垂直摄影测量处理是摄影测量领域中一个至关重要的步骤，涉及利用航空摄影测量测绘地区面积。
这一过程包括使用专门的软件和工具来分析和解释通过航空摄影捕捉到的数据。
One of the key aspects of vertical photogrammetric processing is the use of control and tie points to ensure accurate measurements and mapping. Control points are identifiable, fixed positions on the ground that are used as reference points for establishing the scale of the aerial imagery. Tie points are features in the imagery that are identifiable on multiple overlapping photographs and are used to align the images and produce a seamless, accurate map.垂直摄影测量处理的关键方面之一是利用控制点和连接点来确保准确的测量和制图。
设计未来新型农场英语作文
设计未来新型农场英语作文The sun, a fiery orb, dips below the horizon, painting the sky with hues of orange and purple. This familiar sight, a constant in the lives of countless farmers, now holds a new promise - a promise of a future where technology and nature dance in harmony. No longer will the traditional image of a farmer, weathered and calloused, be the norm. Instead, a new breed of farmer will emerge, one equipped with the knowledge and tools to cultivate a future where sustainability and innovation reign supreme.Gone are the days of back-breaking labor, replaced by robotic arms that delicately pluck ripe fruit from branches, their movements precise and efficient. Data, not instinct, guides their every move, analyzing soil conditions, optimizing irrigation, and predicting potential threats with alarming accuracy. Imagine fields buzzing with drones, their high-resolution cameras mapping the land, identifying areas ripe for improvement. This is not science fiction, but a glimpse into the reality of the future.But beyond the technological marvels, there lies a burgeoning appreciation for nature's delicate balance. The wind whispers through fields of genetically modified crops, their resilience defying the harshest conditions. Vertical farms, soaring skyscrapers of vegetation, bloom with life, offering an abundance of food in confined spaces. No longer are we slaves to the whims of the weather, but masters of our own food supply.This vision, an ecosystem of innovation and ecological awareness, is not simply a technological utopia. It is a testament to the enduring spirit of humanity, a yearning to create a world where food security and environmental responsibility walk hand in hand. It is a world where the farmer is not just a producer, but a guardian, a champion of the future. As I gaze up at the stars, a sense of wonder washes over me, for in this world, the future of our food, our planet, and ourselves is within our grasp.。
u v方向英文缩写
u v方向英文缩写UV direction abbreviationThe UV direction abbreviation refers to the English abbreviations of U and V used in a variety of contexts, such as computer graphics, image processing, and textile manufacturing. In these fields, UV coordinates are often used to represent the 2D texture coordinates of a surface or object.In computer graphics, the UV direction abbreviation is commonly used in texture mapping. Texture mapping is the process of applying a 2D image, called a texture, onto a 3D surface. The UV coordinates are used to map each point on the surface to a corresponding point on the texture. The U and V values represent the horizontal and vertical positions on the texture, respectively.The UV direction abbreviation is also used in image processing. In this context, the UV coordinates represent the pixel positions in a 2D image. Each pixel in the image is assigned a unique UV coordinate, with U representing the horizontal position and V representing the vertical position. This allows for precise manipulation and analysis of individual pixels in the image.In textile manufacturing, the UV direction abbreviation is often used in pattern design and printing. Textile patterns are typically created in a 2D software program, using UV coordinates to map the pattern onto the fabric. The U and V values determine the placement and orientation of the pattern on the fabric, ensuring accurate replication during the printing process.It is worth noting that the choice of U and V as the abbreviations for the horizontal and vertical directions is arbitrary and purely conventional. The letters U and V were likely chosen due to their proximity to the letters X and Y, which are commonly used to represent the horizontal and vertical directions in Cartesian coordinate systems.The use of the UV direction abbreviation has become standardized across various industries and software applications. It allows for consistent communication andunderstanding among professionals working with 2D and 3D graphics, images, and textiles. Additionally, the UV direction abbreviation facilitates the development of software tools and algorithms specifically designed for handling UV coordinates.In conclusion, the UV direction abbreviation, represented by the letters U and V, is widely used in computer graphics, image processing, and textile manufacturing. It enables precise mapping and manipulation of 2D texture coordinates, pixel positions, and pattern placement. Despite its arbitrary nature, the UV direction abbreviation has become an industry standard, ensuring effective communication and efficient workflow in various fields.。
vertical造句简单带翻译
vertical造句简单带翻译Vertical。
Vertical is a term used to describe something that is oriented in an upright position, perpendicular to the ground or horizon. In this article, we will explore the various uses and applications of the word "vertical" in different contexts.1. Vertical in Architecture。
In architecture, vertical refers to the height of a building or structure. A skyscraper, for example, is a tall building that is designed to be vertical, rising up into the sky. Verticality is an important aspect ofarchitectural design, as it can create a sense of grandeur and awe in the viewer.2. Vertical in Photography。
In photography, vertical refers to the orientation of a photograph. A vertical photograph is one that is taller than it is wide, while a horizontal photograph is wider than it is tall. Choosing the right orientation for a photograph can have a big impact on its composition and visual impact.3. Vertical in Sports。
基于NDVI_与DEM_的山地植被垂直带定量划分———以太白山南坡为例
第４７卷 第５期２０２３年９月南京林业大学学报（自然科学版）ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ）Ｖｏｌ．４７，Ｎｏ．５Ｓｅｐｔ．，２０２３ 收稿日期Ｒｅｃｅｉｖｅｄ：２０２１ １０ １３ 修回日期Ａｃｃｅｐｔｅｄ：２０２２ ０４ ２０ 基金项目：国家林业公益性行业科研专项（２０１３０４３０９）；陕西省教育厅科研项目（２１ＪＫ０３０５）。
第一作者：赵婷（ｚｈａｏｔｉｎｇｘｐｃ＠１６３．ｃｏｍ），讲师，博士。
引文格式：赵婷，白红英，邓晨晖，等．基于ＮＤＶＩ与ＤＥＭ的山地植被垂直带定量划分———以太白山南坡为例［Ｊ］．南京林业大学学报（自然科学版），２０２３，４７（５）：１６５－１７１．ＺＨＡＯＴ，ＢＡＩＨＹ，ＤＥＮＧＣＨ，ｅｔａｌ．ＡｑｕａｎｔｉｔａｔｉｖｅｄｉｖｉｄｅｄｍｅｔｈｏｄｆｏｒｔｈｅｖｅｇｅｔａｔｉｏｎｖｅｒｔｉｃａｌｂｅｌｔｂａｓｅｄｏｎＮＤＶＩａｎｄＤＥＭ：ａｃａｓｅｓｔｕｄｙｏｆＴａｉｂａｉＭｏｕｎｔａｉｎｏｎｔｈｅｓｏｕｔｈｓｌｏｐｅ［Ｊ］．ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒ ｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ），２０２３，４７（５）：１６５－１７１．ＤＯＩ：１０．１２３０２／ｊ．ｉｓｓｎ．１０００－２００６．２０２１１００２８．基于ＮＤＶＩ与ＤＥＭ的山地植被垂直带定量划分———以太白山南坡为例赵 婷１，２，白红英２，邓晨晖３，他志杰１（１．西安外国语大学旅游学院，陕西 西安 ７１０１２８；２．西北大学城市与环境学院，陕西 西安 ７１０１２７；３．咸阳师范学院地理与环境学院，陕西 咸阳 ７１２０００）摘要：【目的】利用遥感与地理信息技术，剖析不同植被类型植被指数与海拔的关系，实现山地植被垂直带的准确划分，获取山区植被分布空间格局。
【方法】以秦岭主峰太白山南坡为研究区，依据夏秋两季植被垂直带归一化植被指数（ＮＤＶＩ）的差值构建ＤＥＭ ＮＤＶＩ散点图，并利用半峰宽计算法将垂直带边界量化。
数学术语英文
数学术语英⽂代数ALGEBRA1. 数论natural number ⾃然数positive number 正数negative number 负数odd integer, odd number 奇数even integer, even number 偶数integer, whole number 整数positivewhole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrational（number）⽆理数inverse 倒数composite number 合数e.g. 4,6,8,9,10,12,14,15… prime number 质数e.g.2,3,5,7,11,13,15…reciprocal 倒数common divisor 公约数multiple 倍数(minimum) common multiple (最⼩)公倍数(prime) factor (质)因⼦common factor 公因⼦ordinary scale, decimalscale ⼗进制nonnegative ⾮负的tens ⼗位units 个位mode 众数mean平均数median 中值commonratio 公⽐2. 基本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean ⼏何平均数exponent指数,幂base 乘幂的底数,底边cube ⽴⽅数,⽴⽅体square root 平⽅根cube root ⽴⽅根common logarithm常⽤对数digit 数字constant 常数variable 变量inverse function 反函数complementary function 余函数linear ⼀次的,线性的factorization 因式分解absolute value绝对值,e.g.｜-32｜=32 round off 四舍五⼊数学3. 基本运算add,plus 加subtract 减difference 差multiply, times 乘product 积divide除divisible 可被整除的divided evenly 被整除dividend 被除数,红利divisor 因⼦,除数,公约数quotient 商remainder 余数factorial 阶乘power 乘⽅radical sign, root sign 根号round to 四舍五⼊to the nearest 四舍五⼊4. 代数式,⽅程,不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient数字系数literal coefficient 字母系数inequality 不等式triangle inequality 三⾓不等式range 值域original equation 原⽅程equivalent equation 同解⽅程,等价⽅程linear equation 线性⽅程(e.g.5x+6=22)5. 分数,⼩数proper fraction 真分数improper fraction 假分数mixed number 带分数vulgarfraction,common fraction 普通分数simple fraction 简分数complex fraction繁分数numerator 分⼦denominator 分母(least) common denominator （最⼩）公分母quarter四分之⼀decimal fraction 纯⼩数infinite decimal ⽆穷⼩数recurring decimal 循环⼩数tenths unit ⼗分位6. 集合union 并集proper subset 真⼦集solution set 解集7. 数列arithmetic progression(sequence) 等差数列geometric progression(sequence) 等⽐数列8. 其它approximate 近似(anti)clockwise (逆) 顺时针⽅向cardinal 基数ordinal 序数directproportion 正⽐distinct 不同的estimation 估计,近似parentheses 括号proportion ⽐例permutation 排列combination 组合table 表格trigonometric function 三⾓函数unit 单位,位⼏何GEOMETRY1. ⾓alternate angle 内错⾓corresponding angle 同位⾓vertical angle 对顶⾓central angle圆⼼⾓interior angle 内⾓exterior angle 外⾓supplementary angles 补⾓complementary angle 余⾓adjacent angle 邻⾓acute angle 锐⾓obtuse angle 钝⾓right angle 直⾓round angle 周⾓straight angle 平⾓included angle 夹⾓2. 三⾓形equilateral triangle 等边三⾓形scalene triangle 不等边三⾓形isosceles triangle 等腰三⾓形right triangle 直⾓三⾓形oblique 斜三⾓形inscribed triangle 内接三⾓形3. 收敛的平⾯图形,除三⾓形外semicircle 半圆concentric circles 同⼼圆quadrilateral 四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon ⼋边形nonagon 九边形decagon ⼗边形polygon 多边形parallelogram 平⾏四边形equilateral 等边形plane 平⾯square 正⽅形,平⽅rectangle 长⽅形regular polygon 正多边形rhombus 菱形trapezoid 梯形4. 其它平⾯图形arc 弧line, straight line 直线line segment 线段parallel lines 平⾏线segment of acircle 弧形5. ⽴体图形cube ⽴⽅体,⽴⽅数rectangular solid 长⽅体regular solid/regular polyhedron正多⾯体circular cylinder 圆柱体cone 圆锥sphere 球体solid ⽴体的6. 图形的附属概念plane geometry 平⾯⼏何trigonometry 三⾓学bisect 平分circumscribe 外切inscribe内切intersect 相交perpendicular 垂直Pythagorean theorem 勾股定理（毕达哥拉斯定理）congruent全等的multilateral 多边的altitude ⾼depth 深度side 边长circumference, perimeter周长radian 弧度surface area 表⾯积volume 体积arm 直⾓三⾓形的股cross section 横截⾯center of a circle 圆⼼chord 弦diameter 直径radius 半径angle bisector ⾓平分线diagonal 对⾓线化edge 棱face of a solid ⽴体的⾯hypotenuse 斜边included side 夹边leg三⾓形的直⾓边median（三⾓形的）中线base 底边,底数（e.g. 2的5次⽅,2就是底数）opposite 直⾓三⾓形中的对边midpoint 中点endpoint 端点vertex (复数形式vertices)顶点tangent 切线的transversal 截线intercept 截距7. 坐标coordinate system 坐标系rectangular coordinate 直⾓坐标系origin 原点abscissa 横坐标ordinate 纵坐标number line 数轴quadrant 象限slope 斜率complex plane 复平⾯数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem 计算calculation 运算operation 证明prove 假设hypothesis, hypotheses(pl.) 命题proposition 算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand 加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder 乘times(prep.), multiply(v.), multiplication(n.) 被乘数multiplicand, faciend 乘数multiplicator 积product 除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor 商quotient 等于equals, is equal to, is equivalent to ⼤于is greater than ⼩于is lesser than ⼤于等于is equal or greater than ⼩于等于is equal or lesser than 运算符operator 数字digit 数number ⾃然数natural number 整数integer ⼩数decimal ⼩数点decimal point 分数fraction 分⼦numerator 分母denominator ⽐ratio 正positive 负negative 零null, zero, nought, nil ⼗进制decimal system ⼆进制binary system ⼗六进制hexadecimal system 权weight, significance 进位carry 截尾truncation 四舍五⼊round 下舍⼊round down 上舍⼊round up 有效数字significant digit ⽆效数字insignificant digit 代数algebra 公式formula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknown, x-factor, y-factor, z-factor 等式，⽅程式equation ⼀次⽅程simple equation ⼆次⽅程quadratic equation 三次⽅程cubic equation 四次⽅程quartic equation不等式inequation 阶乘factorial 对数logarithm 指数，幂exponent 乘⽅power ⼆次⽅，平⽅square 三次⽅，⽴⽅cube 四次⽅the power of four, the fourth power n次⽅the power of n, the nth power 开⽅evolution, extraction ⼆次⽅根，平⽅根square root 三次⽅根，⽴⽅根cube root 四次⽅根the root of four, the fourth root n 次⽅根the root of n, the nth root 集合aggregate 元素element 空集void ⼦集subset 交集intersection 并集union 补集complement 映射mapping 函数function 定义域domain, field of definition 值域range 常量constant 变量variable 单调性monotonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differential 导数derivative 极限limit ⽆穷⼤infinite(a.) infinity(n.) ⽆穷⼩infinitesimal 积分integral 定积分definite integral 不定积分indefinite integral 有理数rational number ⽆理数irrational number 实数real number 虚数imaginary number 复数complex number 矩阵matrix ⾏列式determinant ⼏何geometry 点point 线line ⾯plane 体solid 线段segment 射线radial 平⾏parallel 相交intersect ⾓angle ⾓度degree 弧度radian 锐⾓acute angle 直⾓right angle 钝⾓obtuse angle 平⾓straight angle 周⾓perigon 底base 边side ⾼height 三⾓形triangle 锐⾓三⾓形acute triangle 直⾓三⾓形right triangle 直⾓边leg斜边hypotenuse 勾股定理Pythagorean theorem 钝⾓三⾓形obtuse triangle 不等边三⾓形scalene triangle 等腰三⾓形isosceles triangle 等边三⾓形equilateral triangle 四边形quadrilateral 平⾏四边形parallelogram 矩形rectangle 长length 宽width 菱形rhomb, rhombus, rhombi(pl.), diamond 正⽅形square 梯形trapezoid 直⾓梯形right trapezoid 等腰梯形isosceles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon ⼋边形octagon 九边形enneagon ⼗边形decagon ⼗⼀边形hendecagon ⼗⼆边形dodecagon 多边形polygon 正多边形equilateral polygon 圆circle 圆⼼centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 周长perimeter ⾯积area 轨迹locus, loca(pl.) 相似similar 全等congruent 四⾯体tetrahedron 五⾯体pentahedron 六⾯体hexahedron 平⾏六⾯体parallelepiped ⽴⽅体cube 七⾯体heptahedron ⼋⾯体octahedron 九⾯体enneahedron ⼗⾯体decahedron ⼗⼀⾯体hendecahedron ⼗⼆⾯体dodecahedron ⼆⼗⾯体icosahedron 多⾯体polyhedron 棱锥pyramid 棱柱prism 棱台frustum of a prism 旋转rotation 轴axis 圆锥cone 圆柱cylinder 圆台frustum of a cone 球sphere 半球hemisphere 底⾯undersurface 表⾯积surface area 体积volume 空间space 坐标系coordinates 坐标轴x-axis, y-axis,z-axis 横坐标x-coordinate 纵坐标y-coordinate 原点origin 双曲线hyperbola 抛物线parabola 三⾓trigonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 相位phase 周期period 振幅amplitude 内⼼incentre(BrE), incenter(AmE) 外⼼excentre(BrE), excenter(AmE) 旁⼼escentre(BrE), escenter(AmE) 垂⼼orthocentre(BrE), orthocenter(AmE) 重⼼barycentre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle 统计statistics 平均数average 加权平均数weighted average ⽅差variance 标准差root-mean-square deviation, standard deviation ⽐例propotion 百分⽐percent 百分点percentage 百分位数percentile 排列permutation 组合combination 概率，或然率probability 分布distribution 正态分布normal distribution ⾮正态分布abnormal distribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram。
中国的地形起伏度及其与人口分布的相关性_英文_
J. Geogr. Sci. (2008) 18: 237-246DOI: 10.1007/s11442-008-0237-8© 2008 Science in China Press Springer-VerlagReceived: 2007-12-02 Accepted: 2008-01-28Foundation: Knowledge Innovation Project of the CAS, No.KZCX2-YW-323Author: Feng Zhiming (1963−), Ph.D. and Professor, specialized in efficient utilization of agricultural resources and re-gional sustainable development. E-mail: fengzm@ Relief degree of land surface and its influence on population distribution in ChinaFENG Zhiming 1, TANG Yan 1,2, YANG Yanzhao 1, ZHANG Dan 1,21. Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China;2. Graduate University of Chinese Academy of Sciences, Beijing 100049, ChinaAbstract: The relief degree of land surface (RDLS) is an important factor for describing the landform at macro-scales. This study defines a concept for RDLS and applies the concept for population distribution study of the entire country. Based on the concept and macro-scale digital elevation model datum and ARC/INFO software, the RDLS at a 10 km×10 km grid size of China is extracted. This paper depicts systemically the spatial distributions of RDLS through analyzing the ratio structure and altitudinal characters of RDLS in China. The con-clusions are drawn as follows: the RDLS in more than 63% of the area is less than one (1) (relative altitude is less than 500 m), reflecting the fact that most of RDLS in China is low. In general, the RDLS in the west is larger than that in the east and so is the south than that of the north in China. The RDLS decreases with the increase of longitude and latitude and the change of RDLS at the latitudes of 28°N, 35°N, 42°N, as well as at the longitudes of 85°E, 102°E, 115°E could reflect the three major ladders of China. In the vertical direction, the RDLS increases with the increase of altitude. Analysis of the correlation between RDLS and population distribution in China and its regional difference shows that the R 2 value between RDLS and population density is 0.91 and RDLS is an important factor influencing the spatial distribution of population. More than 85% of the people in China live in areas where the RDLS is less than one (1), while the population in areas with RDLS greater than 3 accounts only for 0.57% of the total. The regional difference of correlation between RDLS and population within China is significant and such correlation is significant in Central China and South China and weak in Inner Mongolia and Tibet.Keywords: relief degree of land surface (RDLS); population distribution; GIS; China1 IntroductionRelief Degree of Land Surface (RDLS) is a synthetic representation of the altitude and inci-sion depth of a region. The research on RDLS can be traced back to the concept of incision depth brought forward by the Geographical Sciences Institute of Soviet Russia in 1948 (Splitonrof, 1956). RDLS is now accepted as an important criterion for geomorphic classifi-cation in Geomorphic Mapping both at home and abroad and widely used in European in-238Journal of Geographical Sciencesternational geomorphic mapping at a scale of 1:2,500,000 and international uniform legend guideline of geographic mapping at a medium scale. In China, RDLS has been taken as a main indicator of geomorphic classification in Geomorphic Map of China at a scale of 1:4,000,000, geomorphic mapping guidelines at a scale of 1:1,000,000 and geomorphic mapping development of China (Chen, 1993; 1995).In recent years, with the establishment of DEM database and wide use of computer, there has been a rising interest in regional RDLS based on DEM. RDLS has been widely used for sensitivity evaluation of soil erosion (Chen, 2005; Nan, 2003) and freeze-thaw erosion (Pachauri, 1998; Saha, 2005; Li, 2005), water and soil loss evaluation (Ma, 2001, Liu, 2001), geological environment evaluation (Yan, 2000), etc. In eco-environment evaluation, Yang and others took RDLS as one of the evaluation criteria (Yang, 2001; Zhu, 2004; Yao, 2004; Li, 2005; Qi, 2005). In natural environment evaluation of China, Niu gave a definition to RDLS and drew a conclusion that the RDLS of China is larger than the average of the world (Niu, 1996). Besides, RDLS has been taken as an indicator in cost evaluation of city devel-opment and classification of urban land use (SDSRG of CAS, 2005; Liu, 2002). However, the issue remains with RDLS research is how to define the connotation accurately and choose a scientific extraction method according to regional condition of resources and envi-ronment and the specific application so as to improve the validity and maneuverability of RDLS research.In order to evaluate suitability of natural environment for human settlements in China, as an important factor influencing the distribution of population, RDLS is taken as an index for natural environment evaluation of human settlements. Based on the review of RDLS re-search and window-analysis method and the GRID and TABLE module of ARC/INFO soft-ware, this paper aims to develop a new definition and calculation formula for RDLS and extracts RDLS of China with a 10 km×10 km grid size, and depicts the spatial distribution of RDLS by analyzing its ratio structure, spatial distribution and altitudinal characters system-atically and analyzes its correlation with population density at grid size.2 Research methodology2.1 Definition and connotation of RDLSThe definition of RDLS varies for its discrepant application in different fields. In this paper, RDLS is defined as the relative height difference within a certain region. According to pre-vious research (Niu, 1996), the RDLS of China is extracted by the following equation: ()()(){}Max Min 1//500RDLS H H P A A =−×−⎡⎤⎡⎤⎣⎦⎣⎦ (1) where Max(H ) and Min(H ) are the highest and lowest altitudes of a region respectively and P (A ) and A are the flat area and total land area of the region respectively. In this paper, we choose a 10 km×10 km grid size as the basic study unit, so A equals 100 km 2.By using the product of the proportion of regional height difference against national height difference and the proportion of regional non-flat area, Niu et al . (1996) studied the RDLS by provinces in China and found that RDLS ranges from 0 to 0.45 and the regional difference was not significant. In order to depict regional difference of RDLS in China, we choose a height of 500 m in low hilly region as the standard height to evaluate the RDLS,FENG Zhiming et al.:Relief degree of land surface and its influence on population distribution in China 239 which implies that when the RDLS is 2, the RDLS is equivalent to a hill height of 2 stan-dards. As for the extraction of relative height difference, Tu considers the optimum statisticalunit as 21 km2 (Tu, 1990). Based on the 1 km×1 km grid data for the regional assessmentson macroscopic scale, and the compilation methods of China’s geomorphological map and classification of RDLS (Chen, 1995; Li, 1987), this paper defines the criteria for flat areathat the maximum height difference within 25 km2 is less than 30 m.2.2 Data source and its pretreatmentData used in this research include Digital Elevation Model (DEM) of China at a scale of1:1,000,000, national population density raster data of 2000 and latitude and longitude rasterdata of China. DEM is obtained from the Earth Resources Observing Satellite of U.S. Geo-logical Survey with a spatial resolution of 30′. The latitude and longitude raster data of China are extracted from DEM with a spatial resolution of 30′. The 2000 national population density raster data used in this research is supplied by the national scientific data sharing project–Earth System Science Data Sharing Network. Based on county-wide population datain 2000 and simulation model for population density spatial distribution, Liu (2003) simu-lated the population distribution of China in 2000 at a 1 km×1 km grid size by inosculatingthe net primary productivity, digital elevation, city size and density and traffic infrastructure density data sets. By projection transformation and resample, the projection of all data was changed into Krasovsky_1940_Albers and the spatial resolution into 1 km×1 km for main-taining the same projection and resolution system of the output. The projection transforma-tion and resample can be completed by using the project and resample commands of ARC/INFO.2.3 Extraction methodChoosing the window analyzing method and using GRID and TABLE module of ARC/INFO,this paper extracts the RDLS of China with a window of 10 km×10 km.2.3.1Extraction of maximum height difference [Max(H)–Min(H)]Choosing 10 km×10 km window as the extraction unit, this study extracts the maximum height [Max(H)] and the minimum height [Min(H)] within the window and endows them to each window to get two data layers, and subtracts the Min(H) from the Max(H) to get the height difference of each grid. The above calculation can be realized by using the Block range function.2.3.2Extraction of non-flat ratio [1–P(A)/A]The flat area is defined as an area with the maximum height difference within 25 km2 beingless than 30 m. By using the widely adopted window analysis method, the non-flat ratio is extracted through the following steps: (1) to extract the maximum height difference of eachgrid within 25 km2; (2) to choose a grid as the center of the 5 km×5 km window to extractthe maximum and minimum altitudes within the window and get two new data sets, then subtract the minimum altitude from the maximum altitude to get the maximum height dif-ference and endow it to the central grid of the window. By doing so, we get the maximum height difference of each grid. The above process can be realized by using the Focal range240 Journal of Geographical Sciences and Select Tools functions; and (3) to extract the non-flat ratio of each grid. By using the Select Tool, we choose the grid, of which the maximum height difference is less than 30 m, out from the maximum height difference data layer and count the total grid number within a 10 km×10 km window, then divide it by 100 to get the ratio of flat within the window. By subtracting one (1) from the ratio and endowing it to each grid within the window, we get the non-flat ratio of each grid.2.3.3The extraction of RDLSAccording to equation 1, this paper extracts the RDLS of each grid. For avoidance of opera-tion error and emendation, we compile AML program and run it in the ARC/INFO software.3 Spatial distribution of RDLS in China3.1 General spatial distribution of RDLS and its characteristicsThe RDLS in West China is larger than that of the East and so is the South than that of the North (Figure 1). The southeast of Tibetan Plateau, Hengduan Mountain Region and Tian-shan Mountain Region have the largest RDLS and the RDLS of China decreases from those regions gradually except in some huge basins. The lowest value of RDLS is found in North-east China Plain, North China Plain and Tarim Basin. Sichuan Basin, Inner Mongolian Pla-teau, Jiangnan Hilly Region and South China have the second lowest RDLS.Figure 1RDLS with 10 km×10 km grid size in ChinaResults show that where the RDLS is great, the relative height is high and the flat ratio is low, and vice versa (Table 1). Figure 2 is the ratio structure and accumulative area frequencyFENG Zhiming et al .: Relief degree of land surface and its influence on population distribution in China 241of RDLS, which indicates that RDLS is low in most of the areas. When RDLS reaches 0.5 (relative height difference is lower than 250 m), the accumulative area frequency is 42.63% of the total, in which the flat ratio is 16.04%; when RDLS reaches 1 (relative height differ-ence is lower than 500 m), the accumulative area frequency reaches 63.68%; when RDLS reaches 2, it exceeds 85%; while where the RDLS is greater than 3, the accumulative area frequency only accounts for 4.94% of the total.Table 1 The maximum height difference and flatproportion associated with RDLSRDLS [Max(H )–Min(H )]/m P (A )/A0−0.5 0−249 0−10.5−1 250−499 0−11−2 500−999 0−0.622−3 1000−1499 0−0.323−4 1500−1999 0−0.154−5 2000−2498 0−0.095−6 2500−2995 0−0.08 6−7 3012−3485 0−0.037−8 3583−3841 0−0.02 8−9 4077−4150 0 9−10 4529 0 Figure 2 Proportion and accumulative area frequency of RDLS3.2 Spatial distribution of RDLS along the latitudeThe change of RDLS along the latitude is shown in Figure 3. Figure 3a shows the average RDLS along the latitude. From the figure we can see that RDLS of China decreases with the increase of longitude in general and this trend accords with the terrain features of China, i.e.,Figure 3 Change of RDLS along the latitude in China242 Journal of Geographical Sciencesthe west is mountainous and the east is planar. It is obvious that there are a “valley” between 77°−93°E for the existence of the Tarim Basin and Junggar Basin and an “apex” between 93°−103°E for the existence of Hengduan Mountains and Qilian Mountains.Figures 3b−d indicate the changing characteristics of RDLS at latitudes of 28°N, 35°N and 42°N. Figure 3b shows that the RDLS at the latitude of 28°N fluctuates sharply in gen-eral. From west to east, the RDLS fluctuates tempestuously in the Himalayas and Hengduan Mountains and decreases notably in Sichuan Basin and Yangtze River Plain, followed by increases in Jiangnan Hilly Region. The RDLS at 35°N fluctuates meekly at 78°−98°E due to the existence of North Tibetan Plateau and ranges from 0.5 to 3.0 when it reaches the boundaries between Tibetan Plateau, Loess Plateau and North China Plain, then decreases noteably in North China Plain. The RDLS at 42°N presents the shape of a sleeping man with a high head, reflecting the facts that at the cross boundary areas of Tianshan Mountains and Tarim Basin between 80°−86°E, the RDLS is high, while when it reaches Turpan−Hami Ba-sin, Inner Mongolian Plateau and Northeast China Plain, the RDLS is relatively low.3.3 Spatial distribution of RDLS along the longitudeFigure 4 shows the change of RDLS along the longitude in China. It can be seen that in gen-eral the RDLS of China decreases with the increase of latitude, which is in accordance with the geomorphic characteristics, i.e., there are more mountains and hills in the South and more plains and plateaus in the North. In Figure 4a, there is obviously a “valley” located around 21°N because of the existence of Jiangnan Hilly Region, the RDLS in this place is much lower than that of Hengduan Mountains and the Himalayas between 21°−33°N; while in areas north of 33°N, the RDLS decreases gradually, thanks to the existence of Tarim Ba-sin, North China Plain, Loess Plateau, Inner Mongolia Plateau and Northeast China Plain.Figure 4 Change of RDLS along the longitude in ChinaFENG Zhiming et al.:Relief degree of land surface and its influence on population distribution in China 243Figures 4b−d are the changes of RDLS at 85°E, 102°E and 115°E along the latitude. At 85°E, the RDLS fluctuates in the Tibetan Plateau and increases to 4 on its edge, then de-creases notably in the Tarim Basin and increases again in the Tianshan Mountains, and de-creases in the Junggar Basin. It is observed that there are two “hills” for the existence of Hengduan Mountains and Tibetan Plateau and one “valley” for the existence of Inner Mon-golian Plateau (Figure 4c). At 115°E, the RDLS fluctuates in Jiangnan Hilly Region, then decreases notably in the North China Plain between 32°−39°N, and increases when it reaches the edge of the Inner Mongolian Plateau.3.4 Spatial distribution of RDLS along the altitudeThis paper illustrates a tendency that the RDLS in China increases with the increase of lati-tude (Figure 5). There is an abvious “canyon” between altitudes of 2400−3300 m, which are the boundaries between Tibetan Plateau, Tarim Basin, Hexi Corridor, Loess Plateau, Sichuan Basin and Yunnan−Guizhou Plateau. Figure 5a indicates that RDLS increases with the in-crease of altitude, and in regions where the altitude is above 5500 m, the change range of RDLS is 2−3 times larger than the average for the existence of the Himalayas and Kunlun Mountains. Figure 5b shows that in low altitude regions, the RDLS is low, and vice versa.(a) (b)Figure 5 Change of China’s RDLS along with the increase of altitude and its proportions at different altitudes4 Correlation between RDLS and population density4.1 The correlation between RDLS and population densityWith the aid of the Spatial Analysis Model of Arc/Info software, after the registration of RDLS and population raster density, the population density of each RDLS was calculated in this study for the first time by using regional statistical analysis model. Supported by SPSS software, a scatter plot map of RDLS and population density is compiled (Figure 6). This paper gave a correlation analysis between them after removal of outliers. The result shows that R2 value between RDLS and population reaches 0.91.It is found that most of the people in China live in regions with low RDLS (Figure 7). Where the RDLS is 0 (relative height difference is less than 30 m), the accumulative popula-tion is 20.83% of the total in China; where the RDLS is less than 1 (relative height differ-ence is less than 500 m), the accumulative population reaches 85.37% of the total; where the RDLS is less than 2, the accumulative population exceeds 95%; while where the RDLS is244Journal of Geographical SciencesFigure 6 Correlation between RDLS andpopulation density Figure 7 Accumulative frequency of popula- tion at RDLSgreater than 3, the accumulative population accounts for less than 1% of the total. Therefore RDLS is an important factor influencing the population distribution in China and it should be taken as an important factor in human settlements evaluation.4.2 Correlation between RDLS and population density at regional scaleThe study explores the correlation between RDLS and population density at regional scale of the country. According to physical geographical regionalization method developed by Ren and Bao in 1990 (Ren, 1992), the country can be grouped into Northeast China, North China, Central China, South China, Southwest China, Inner Mongolia, Northwest China and Tibet Region (Figure 1).Analysis indicates that the population density decreases with the increase of RDLS in most regions of China and the regional difference is significant (Table 2). Specifically, the average altitude of Northeast China, North China, Central China and South China is less than 800 m and the altitude difference within each region is not significant, while the RDLS of each region is an important factor influencing population distribution due to the fact that the R 2 value of each region is greater than 0.70; as for Northwest China, water resource is the main factor restricting its population distribution and most people are settled on oases, soTable 2 Correlation between RDLS and population at regional scale in ChinaGeographical regionRDLS range Average altitude (m) R 2 Northeast0−2.28 417 0.70 North China0−4.10 663 0.73 Central China0−8.15 525 0.79 South China0−2.89 207 0.78 Southwest0−6.89 1865 0.61 Inner Mongolia0−3.75 1062 0.17 Northwest0−6.28 1877 0.67 Tibet 0−9.05 4536 0.05FENG Zhiming et al.:Relief degree of land surface and its influence on population distribution in China 245 the R2 value is only 0.67; while most areas in Southwest China are featured by mountainsand ravines and there is an unique vertical distribution of population and most of the peopleare settled at altitudes of 800−2000 m, as a result, the R2 value between RDLS and popula-tion distribution is only 0.61. In Inner Mongolia and Tibet Region, the differences of altitudeand RDLS within those regions are not obvious and their population distribution is mainly restricted by climate and land cover conditions, so there is no significant correlation between RDLS and population distribution in those regions.5 Conclusions and discussionBased on grid data of digital elevation model of China at 1:1,000,000 spatial scale, by using window analysis method and GRID and TABLE modules of ARC/INFO software, this paper extracts the RDLS of China at grid size, and depicts systematically spatial distributions of RDLS by analyzing its ratio structure, spatial distribution and vertical character and the cor-relation with population distribution. The conclusions have been drawn as follows:(1) The RDLS for more than 63% of the areas is less than 1 (relative altitude is lower than500 m), showing that the majority of RDLS in China is low; the flat ratio of China is 16%and it decreases with the increase of RDLS.(2) In general, the RDLS of the west is higher than that of the east and so is the south thanthat of the north in the country. The Hengduan Mountains and Tianshan Mountains have the highest RDLS, while the Northeast China Plain, North China Plain and Tarim Basin have the lowest one. The RDLS of China decreases with the increase of longitude and latitude and the change of RDLS at latitudes of 28°N, 35°N, 42°N, as well as at longitudes of 85°E, 102°E, 115°E is related to the terrain features of China.(3) With the increase of altitude, the RDLS and its changing range increase simultane-ously and the ratio of high RDLS increases as well.(4) More than 85% of the people in China live in areas where the RDLS is lower than 1and the R2 value of logarithmic curve between RDLS and population density is 0.91, which shows that RDLS is an important factor influencing population distribution.(5) The correlation between RDLS and population distribution at regional scale is sig-nificant, especially in Northeast China, North China, Central China and South China. In In-ner Mongolia and Tibet Region, such correlation is not observed.In summary, the study defines a new concept and formula for RDLS and it can reflect the features and spatial distribution of landform in China very well. Empirical analysis showsthat RDLS is an important factor influencing the population distribution of China and it should be taken as a crucial index in natural environment evaluation of human settlements. ReferencesChen Jianjun, Zhang Shuwen, Li Hongxing et al., 2005. Assessment on sensitivity of soil erosion in Jilin Province.Bulletin of Soil and Water Conservation, 25(3): 49–53. (in Chinese)Chen Zhiming, 1993. On the principle, contents and methods used to compile the Chinese geomorphological maps: Taking the 1:4000000 geomorphological map as an example. Acta Geographica Sinica, 48(2): 105–113.(in Chinese)Chen Zhiming, Liu Zhendong, Yu Xiubo, 1995. The compilation of China geomorphological map. Cartography246 Journal of Geographical SciencesSpecial, 36-38. (in Chinese)Dong Chun, Liu Jiping, Zhao Rong et al., 2002. A discussion on correlation of geographical parameter with spa-tial population distribution. Remote Sensing Information, (4): 61–64. (in Chinese)Kodagali V, 1988. Influence of regional and local topography on the distribution of polymetallic nodules in cen-tral Indian Ocean Basin. Geo-Marine Letters, 8(3): 173–178.Li Zhixiang, Tian Mingzhong, Wu Fadong et al., 2005. Ecological environment evaluation on Bashang District in Hebei Province. Geography and Geo-Information Science, 21(2): 91–93. (in Chinese)Liu Jiyuan, Yue Tianxiang, Wang Yingan et al., 2003. Digital simulation of population density in China. Acta Geographica Sinica, 58(1): 17–24. (in Chinese)Liu Xinhua, Yang Qinke, Tang Guoan, 2001. Extraction and application of relief of China based on DEM and GIS Method. Bulletin of Soil and Water Conservation, 21(1): 57–62. (in Chinese)Ma Xiaowei, Yang Qinke, 2001. A study on indexes choice and extraction of China potential soil and water loss based on GIS. Bulletin of Soil and Water Conservation, 21(2): 42–44. (in Chinese)Nan Qiuju, Hua Luo, 2003. Recent progress of the soil erosion in the world. Journal of Capital Normal University (Natural Science Edition), 24(2): 86–95. (in Chinese)Niu Wenyuan, Harris W M, 1996. China: The forecast of its environmental situation in the 21st century. Journal of Environmental Management, 47: 101–114.Pachauri A K, Gupta P V, Chander R, 1998. Landslide zoning in a part of the Garhwal Himalayas. Environmental Geology, 36(3/4): 325–334.Qi Qingwen, He Daming, Zou Xiuping et al., 2005. Theory, method and technology on 3S based ecosystem monitoring, evaluation and adjustment along Yunnan border area. Progress in Geography, 24(2): 2–12. (in Chinese)Ren Mei’e, Bao Haosheng, 1992. Geographical Regionalization of China and Its Development and Rectification.Beijing: Science Press. (in Chinese)Research Group on the Sustainable Development Strategy of the Chinese Academy of Science, 2005. 2005 Stra-tegic Reports: China’s Sustainable Development. Beijing: Science Press, 273. (in Chinese)Saha A K, Gupta R P, Sarkar I et al., 2005. An approach for GIS-based statistical landslide susceptibility zonation: With a case study in the Himalayas. Landslides, 2(1): 61–69.Spilitonnorf A N, 1956. Geomorphological Mapping. Beijing: Geology Press, 81–84. (in Chinese)Tu Hanming, Liu Zhendong, 1990. Demonstration on optimum statistic unit of relief amplitude in China. Journal of Hubei University (Natural Science), 12(3): 266–271. (in Chinese)Wang Hong, Wang Jun, 2004. Preliminary study on specification of basic terrain-unit dataset. Science of Survey-ing and Mapping, 29(3): 22–25. (in Chinese)Xu Yan, Zhou Ronghua, 2003. A preliminary study on advances in assessment of eco-environment quality in China. Arid Land Geography, 26(2): 166–172. (in Chinese)Yan Mancun, Li Huamei, Wang Guangqian, 2000. Quantitative assessment of geological-environmental quality of the land along Guangdong coast. Journal of Engineering Geology, 8(2): 416–425. (in Chinese)Yang Duogui, Chen Duogui, Wang Haiyan et al., 2001. Evaluation and analysis of the sustainability of Yunnan Province. Geography and Territorial Research, 17(3): 1–6. (in Chinese)Yao Jian, Ding Jing, Ai Nanshan, 2004. Assessment of ecological vulnerability in upper reaches of Minjiang River.Resources and Environment in the Yangtze Basin, 13(4): 380–383. (in Chinese)Zhang Shanyu, 1996. Study on Vertical Distribution of the Population and Reasonable Redistribution in the Chi-nese Mountain Areas. Shanghai: East China Normal University Press, 162–167. (in Chinese)Zhu Hui, 2004. The actuality and assessment of eco-environment quality of Qinghai Province. Journal of Qinghai Environment, 14(1): 12–14. (in Chinese)。
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基于分形理论的水流混掺长度垂线分布公式修正
基于分形理论的水流混掺长度垂线分布公式修正吴立春;倪志辉【摘要】已有的混掺长度公式形式多样,对于不同形式的水流需采用不同的经验常数.基于分形理论,结合挟沙水流的混掺长度的运动机理理论,推导了一种混掺长度垂线分布公式的修正模式;分析了修正模式的混掺长度分维数的大小,指出了含沙量与混掺长度分维数的关系.实验数据验证表明:修正模式精度较好;与线性分布式、抛物分布式相比,修正分布模式最优.【期刊名称】《重庆交通大学学报（自然科学版）》【年(卷),期】2014(033)003【总页数】5页(P67-71)【关键词】水利工程;分形理论;线性分布式;抛物分布式【作者】吴立春;倪志辉【作者单位】重庆第二师范学院,重庆400067;重庆交通大学国家内河航道整治工程技术研究中心水利水运工程教育部重点实验室,重庆400074;重庆交通大学西南水运工程科学研究所,重庆400016【正文语种】中文【中图分类】P3330 引言混掺长度是水流紊动的重要特性，其垂线分布规律与水流阻力、泥沙运动及环境工程均密切相关，直接影响着底床冲刷和淤积的演变过程。
因此，研究挟沙水流混掺长度的垂线分布规律既有重要的理论意义，又有助于解决实际工程问题。
为此，国内外许多学者进行了大量测量和分析工作[1-5]，这些研究大都通过明渠、圆管、平板边界层等的水流试验展开。
L.Prandtl[1]参照分子碰撞中自由行程的概念引入混掺长度概念，表示当流体质点从速度的层因脉动而跳至另一层时，流体质点的原有动量刚好转换并等于新的一层处的动量。
该两层之间的距离称为混掺长度 l。
根据L.Prandtl混掺长度理论，在近壁紊流中，假定 l 与从固体壁面算起的法向距离y 成比例，即：l=κy(1)式中：l为混掺长度，它与流动情况有关，可由试验确定；κ为卡门常数，对于清水水流情况，κ≈ 0.4。
对于充分发展的管流和明渠，J.Nikuradse[2]提出的混掺长度分布公式：(2)式中：R为管的半径或明渠的水深。
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Mapping the vertical distribution of vegetation and typical plant community of Wuyi Mountain Reserve with remote sensing images Zhou, Xiaocheng1, Chen, Chongcheng1, Grégory, Lucas2, Bela, Markus2, Géza, Király31 Key Laboratory of Spatial Data Mining & Information Sharing, Ministry of Education, Institute of Mathematics andComputer Science, Fuzhou University, 2 Xue Yuan Road350002, Fuzhou, Chinazhouxc@, chencc@2 Land and GeoInformation Knowledge Center, Faculty of Geoinformatics, University of West Hungary,Budai út 43,8000, Székesfehérvár, Hungaryg.lucas@.hu, mb@.hu3 Faculty of Forestry, University of West Hungary,Ady Endre u. 5, 9400, Sopron, Hungarykiraly.geza@emk.nyme.huAbstract. Wuyi Mountain Reserve is the only reserve area for world biosphere, cultural and naturalheritage of China. Mapping vegetation type by general remote sensing technology in mountainousarea is known to be a very difficult work. Studying bio-diversity by remote sensing technology inWuyi mountain has not been done before. This paper addresses methods for mapping verticaldistribution of vegetation and typical plant community of Wuyi Mountain Reserve Area with remotesensing images. Wuyi mountain digital elevation model (DEM) with vertical vegetation zonation wasmapped with SPOT 5 remote sensing image and DEM data, which made multidimensionalvisualization of vertical zonation on the base of mapping vegetation types. Knowledge rules forextracting rarely typical plant community was established according to published paper and fieldsample. Typical plant communities such as Tsuga chinensis and Pinus taiwanensis are mappedusing merged SPOT 5 satelites image and DEM data. The result provides basic information forfurther studying forest scene diversity. However, in order to get more reliable result, there still has ademand for higher resolution remote sensing images (e.g. QuickBird), large scale DEM data andmore detailed field data.Keywords: Wuyi mountain nature reserve area; SPOT 5; remote sensing; plant community, verticalzonation1 IntroductionIn 1999, WuYiShan city became one of the world nature and culture Heritage site. It has such honorable names as follows: the world natural and culture heritage site; the State key scenic area and State key nature Reserve; the National Tourist Resort Area; the State First Rate Air Harbour, the world’ Human & Biosphere Preserve.Located in the western part of the WuYiShan the Wuyi Mountain natural reserve has largest and most representative semitropical original forest ecosystem in China. It was praised by the bio-scientists both at home and abroard as “the world of insects”, “the world biological bank”, “the paradise of the birds”, “the kingdom of snakes”.Investigation on bio-diversity in Wuyi Mountain was mainly going by the means of field investigation. In the past decades, plenty of information and observation data has been collected. Lan (2003) analyzed plant community diversity in Wuyi mountain reserve area with community samples. Feng(2004) has studied species diversity and Spatial patterns about Pinus taiwanensis. Qian(2007) has studied bio-diversity of Tsuga chinensis.As for the other parts of the world, mapping vegetation types by general remote sensing technology in mountainous area is a difficult task and bio-diversity studies by remote sensing technology in the Wuyi mountain were not tried yet. This paper addresses method for mapping vertical distribution of vegetation and typical plant community in Wuyi Mountain Reserve Area with remote sensing images. The vertical vegetation zonation was realized using SPOT 5 remote sensing images and DEM data.. Knowledge rules for extracting rarely typical plant community was established according to published papers and field samples. Typical plant communities such as Tsuga chinensis and Pinus taiwanensis are mapped using merged SPOT 5 satelite images and DEM data. The result provides basis information for further studying forest scene diversity.2 Study area and database2.1 Study areaFig.1. Location of the Study areaWuyi Mountain is the only reserve area for world biosphere, cultural and natural heritage of China. It is located between latitude 27°33′ -27°54′ N and longitude 117°27′-117°51′E, in the Southeast of China (See figure 1). Total area cover approximately 56500 hectares. It has the largest and most completely preserved sub-tropical forest ecosystems in southeast of China. The climate is characterized as semi-tropic monsoon type. The relative high peaks in the northeast part form a natural barrier and produce a kind of micro-climate, characterized by low temperatures, large precipitations, high humidity, long fog days and significant changes in vertical distribution of species.The Reserve preserves primitive forests with an area of over 20,000 hectares. Its vegetation types mainly include evergreen broadleaved forest, mixed coniferous and broad-leaved forest, evergreen and deciduous broadleaved mixed forest, coniferous forest, shrubs and bamboo forest. There are nearly 4,000 plant species in the reserve, 19 of which such as ginkgo, Chinese hemlock, Chinese tulip, China cypress and ornament plants are under the first-grade state protection. In addition, there are dozens of rare or local special plant species.2.2 DatabaseData source in this investigation are the following:- SPOT 5 cloud-free images, acquired on October 16, 2004 (cover up part of the study area) and on February 1, 2005 (cover down part of the study area),- digital elevation model (DEM) with scale 1:50000,- forest maps- field data about typical plant community obtained by the Global Positioning System (GPS).3 MethodologyWe can establish the flow for mapping vertical distribution of vegetation and typical plant community with remote sensing images, see figure 2. Softwares used in this study are ERDAS9.0 and ARCGIS9.0.3.1 Extract vertical distribution knowledge of vegetationWuyi Mountain Nature Reserve lies in the main part of Wuyi mountain range, with an average elevation of over 1,200 meters. The main peak, Huanggangshan peak, reaches 2,158 meters above sea level. It is the highest peak of the all not only in Wuyi mountain range, but also in the entire southeastern area of the Chinese mainland. Wuyi mountain range has great disparity of altitude. For instance, in an area of 556.7 square kilometers, the highest point tops 2,158 meters while the lowest is only 300 meters above sea level.Because of the great difference between altitude (1700 meters), vegetation differs with altitude and shows a vertical zonation. There are subtropical evergreen broadleaved forest, mixed coniferous and broad-leaved forest, coniferous forest, middle mountain dwarf forest, Middle mountain top meadow, in turn from down to top in Wuyi mountain reserve.Subtropical evergreen broadleaved forestSubtropical evergreen broadleaved forest is a kind of vegetation type in the center subtropical monsoon zone in China. It is also basic vegetation type at the bottom of vertical zonation in Wuyi mountain. There is a large area subtropical evergreen broadleaved forest from elevation 350 meters to 1100 meters.Fig. 2. Flow for Mapping Vertical distribution of vegetationand typical plant community with remote sensing imagesMixed coniferous and broadleaved forestMixed coniferous and broadleaved forest stand from 1100 to 1500 meters elevation. It is a transitional forest type.Coniferous forestConiferous forest stand from 1500 to 1800 meters. The biocoenoses is mainly composed of Pinus taiwanensis, Tsuga chinensis and Cryptomeria.Middle mountain dwarf forestMiddle mountain dwarf forest cover areas with elevation from 1700 to 1970 meters. Middle mountain dwarf forest is a kind of special community derived from subtropical evergreen broad-leaved forest which degraded under the special eco-environment like high altitude. The forest exists in high elevation zone. There is the thinner soil, steeper slope and stronger wind, perennial humidity with low temperature.Middle mountain top meadowMiddle mountain top meadow lies from 1900 to 2158 meters. The forest zone is mainly composed of gramineousness and sedge with some short Pinus taiwanensis and shrub.3.2 Mapping digital elevation model with vertical vegetation zonationThe following information gather knowledge rules based on literature review. The information primary comes from observation and field study work. The knowledge rules were implemented in the model as follow:IF elevation>350m AND elevation <1100m THEN Subtropical evergreen broadleaved forestIF elevation >1100m AND elevation<1500 THEN Mixed coniferous and broadleaved forestIF elevation>1500 AND elevation < 1800 THEN coniferous forestIF elevation>1700 AND elevation<1970 THEN Middle mountain dwarf forestIF elevation>1900 THEN Middle mountain top meadowDigital elevation model with vertical vegetation zonation can be made according to the following steps: - elevation data at the scale of 1:50000 (DEM) is segmented separately according to the knowledge rule above with ArcGIS desktop or ERDAS software; the result was transformed into vector format.- SPOT 5 image of study area created by merging 2.5×2.5m panchromatic with 10×10m multi-spectral data using so-called pansharp method.- Merged SPOT 5 image was draped over 25×25m digital elevation model (DEM) with virtual GIS module in ERDAS9.0 .The result will be used for the background of vegetation zonation- Add vegetation zonation data with vector format and set color semi-transparent- Add title and legend. Then map for digital elevation model with vertical vegetation zonation was created (see Figure 3).3.3 Mapping typical plant community based on remote sensing imagePlant community structure is complicated because it is composed of many species. The object community to be extracted is sparse in space and the scale of individual plant is lesser than the spatial resolution of remote sensing image. Consequently it is very difficult to extract rare plant community from the high resolution remote sensing images like SPOT 5.Typical plant community mapping such as Tsuga chinensis and Pinus taiwanensis was tried using merged SPOT 5 remote sensing image and DEM data.Knowledge rules of typical plant communityA preliminary work is necessary before processing remote sensing image and DEM data. NDVI was created from Merged SPOT 5 image. NDVI was calculated using the SPOT scaled band near infrared and red reflectance data: NDVI = (near infrared-red) / (near infrared+red). Topographic data was calculated from 50,000 DEM data of Bureau of Surveying and Mapping of Fujian province using ArcGIS software. Slope and aspect were derived from DEM. NDVI, elevation, slope and aspect are main factors to extract rarely typical plant community. Knowledge rules about rarely typical plant communities were acquired from former paper.Interpretation features for Tsuga chinensis and Pinus taiwanensis should be established based on merged SPOT 5 remote sensing image, DEM, GPS survey points and forest map (see Table 1).Table 1. Interpretation features for Tsuga chinensis and Pinus taiwanensis communitycommunity InterpretationFeatures Field photos Spot color image Tsuga chinensis Light green Smooth hueforming larger patchcoarse texturePinus taiwanensis bottle green Smaller patchHigher elevationExtract Tsuga chinensis communityTsuga chinensis is a key protected species in Fujian province, which exists in the mountain forest in the south of Changjiang river (Qiu,1994).There is an important area of Tsuga chinensis in the Wuyi mountain nature reserve area. According to published paper, their distribution can be wide (from 700 to 2000 meters), but most of the individuals are located in place with elevation from 1650 to 1900m which lies in the southeast and northwest slope of Huanggang peak (Zheng, 2003). Additionally, most of Tsuga chinensis are located under slope of 25 to 35 degrees.According to field GPS samples and characteristics of vegetation in the reserve area,,the NDVI of vegetation coverage is generally more than 0.6, which NDVI has been normalized to the range [-1 ,1 ]. Slope knowledge for Tsuga chinensis is ascertained as 15°-38°because of its higher elevation. So knowledge rules for mapping Tsuga chinensis was built based on analysis above as follows: IF NDVI > 0.6 and 15 < slope < 38 and 1650 < elevation < 1900 Then Tsuga chinensisTsuga chinensis was extracted automatically based on the knowledge rules above with expert classifier module in software ERDAS 9.0.Extract Pinus taiwanensis communityPinus taiwanensis is a particularly interesting community, which most exists the southeast of China (Hong, 1997, Bi, 2001). It is know that Pinus taiwanensis grows at the higher elevation. There is a significant dominance when elevation is above 1550 meters with shade and semi-shade slope. Moreover, Pinus taiwanensis grows in a wide range of slopes (Song, 2005). So, slope knowledge for Pinus taiwanensis we ascertained is about 20°-38°.We can establish knowledge rules according to published paper and analysis above as follows:IF NDVI > 0.6 and 20 < slope < 38 and Aspect < 90 or aspect > 270 and 1500 < elevation < 2100 and Tsuga chinensis false THEN Pinus taiwanensisPinus taiwanensis community was extracted automatically based on the knowledge rules above with expert classifier module in software ERDAS 9.0.Accuracy assessmentBecause of the few field samples, the result from expert classification can only be validated withvegetation map provided by the Wuyishan Nature Reserve bureau. The classification identified eightspots with Tsuga chinensis communities out of the sixteen figured on the vegetation map. Pinus taiwanensis community area covers 157 hectares on the vegetation map but only 89 hectares were classified with our method (about 57 percent). A manual modification is necessary for improving the accuracy from the automatic classification.Manual modification of the result from expert classificationThe result from knowledge rules was modified using a manual method according to the information from the vegetation map.The final thematic map was draped over DEM in ArcGIS 9.0 and became spatial distribution map of Tsuga chinensis and Pinus taiwanensis community in Wuyi mountain reserve (see figure 4).4 ResultFig. 3. Wuyi mountain digital elevation model with vertical vegetation zonation- With three-dimensional map for vegetation it is possible to appreciate terrain information and distribution of vegetation vertically and horizontally. The map has a better visual value and is better readable than general two dimensional’ ones. This method, is more appropriated to show the vertical distribution of vegetation.- Because of rigid thresholds and uncertain knowledge rules, the result from expert classification shows that most of Tsuga chinensis was extracted. On the one hand, There are still some communities that we know from forest map and field data that are missing. On the other hand, some false information were also extracted. These mistakes were corrected through manual method.- The area of Tsuga chinensis that resulted from interpretation is about 730 hectares. It shows Tsuga chinensis mainly exists in two sites in space: one is near Huanggang peak, the other one is near Zhumu hillock. Further, Tsuga chinensis distributes like a strip from northeast to southwest in a narrow elevation range.- The area of Pinus taiwanensis that resulted from interpretation is about 89 hectares. Pinus taiwanensis mainly exists in the southeast slope of Huanggang peak and northwest of Xingcun village, scattered in other zones.Fig. 4.Spatial distribution of Tsuga chinensis and Pinus taiwanensis community in Wuyi mountain reserve5 Discussion and Conclusion- Three-dimensional map for vegetation with terrain information has a better visual impact and are better readable than classic maps. Vertical distribution of vegetation can be exhibited better with this method.- The area of Tsuga chinensis resulting from interpretation is about 730 hectares. It shows Tsuga chinensis mainly exists in two sites in space: one is near Huanggang peak and the other is near Zhumu hillock. Further, Tsuga chinensis distributes like a strip from northeast to southwest in a narrow elevation range. The area of Pinus taiwanensis derived from interpretation is about 89 hectares. Pinus taiwanensis mainly exists the southeast slope of Huanggang peak and northwest of Xingcun village. It is scattered in other zones.- Community are composed of many species and their structure is complicated. Object community to be identified is sparse in space and the scale of individual plant is lesser than the spatial resolution of remote sensing image like SPOT 5. It is very difficult to extract rare plant community from high resolution remote sensing images. Consequently, the result only shows primary information of community.- Because this study is limited by the resolution of remote sensing image, of DEM and few field GPS survey, the result only shows coarse distribution information for Tsuga chinensis and Pinus taiwanensis. Main distribution characteristic of Tsuga chinensis and Pinus taiwanensis can be embodied. In order to get more reliable result, higher resolution remote sensing images, large scale DEM data and more detailed field data would be preferable. Fox example, QuickBird remote sensing image with 0.61 meter spatial resolution may be used for extracting tree crown of typical plant, which is significant to get more exact result.AcknowledgementThis research takes place in the framework of the inter-government science and technology program me between Hungary and China (2009-2011). It is partially supported by the National Science Foundation of China (Grant No.60602052, 30671680, 30972299), National High Technology R&D Program of China (Grant No. 2007AA10Z227), the Program of New Century Excellent Talents in University of Fujian (Grant No.KJ2006-35) and science & technology project of Education Department of Fujian Province (Grant No. JB07025)ReferenceBI X.l ; HONG W; WU C.z.(2001). 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