Unit 13 Geoid and Reference Ellipsoid（大地水准面和参考椭球）
The Earth‟s physical surface is a reality upon which the surveying observations are made and points are located.工作【observation观测】在其上进行，点位在其上进行定位。）
However, due to its variable topographic surface and overall shape, it cannot be defined mathematically and so position cannot be computed on its surface.它的起伏不定的【variable可变的、不定的，这里按中文习惯译为起伏不定的】地形表面和总的【overall】形状，它不能被数学的定义，因此点位也不能在其上进行计算。） It is for this reason that in surveys of limited extent, the Earth is treated as flat and plane trigonometry used to define position.（正是因为这个原因，在有限范围内的测量中，地球被当成平的，并用平面三角学【trigonometry三角学】来确定位置。）
If the area under consideration is of limited extent, orthogonal projection of this area onto a plane surface may result in negligible distortion.在考虑中的】区域是有限范围的，该区域在一个平面【plane surface】上的正交投影
【orthogonal projection】导致的【直译为导致，可以意译为：其结果】是可以忽略的
【negligible可以忽略的】变形【distortion】）
Plane surveying techniques could be used to capture field data and plane trigonometry used to compute position.计算位置坐标）
However, if the area extended to a large area beyond limitation and treated as a flat surface the effect of the Earth‟s curvature will produce unacceptable distortion.域延伸【extend】为一个大的区域超过了限度，把它当成一个平面，地球的曲率影响
【effect】将产生不可被接收的【unacceptable】变形）
It can also be clearly seen that the use of a plane surface as a reference datum for the elevations of points is totally unacceptable.作点的高程的参考基准是完全【totally完全地】不可被接受的【不可以的】。）
Therefore, to represent horizontal positions and elevations on maps and charts, we need a mathematical model of the Earth which includes a set of numbers for the size and shape of the Earth.和高程位置，我们需要一个地球的数学模型，它包括一系列地球大小和形状的参数
【number这里译为参数parameter参数】）
We will define a mathematical surface that approximates to the shape of the area under consideration and then fit and orientate it to the Earth‟s surface.面接近【approximates接近v.】于被考虑的【under consideration】区域的形状，然后使之与地球表面相符合【fit and orientate：fit是适合的意思；orientate是定向的意思】） Such a surface is referred in surveying as a „reference ellipsoid‟.被称为【refer提到、涉及】“参考椭球”）
The Geoid （大地水准面）
Since the physical surface of the Earth can‟t be used as a computational surface, a mean sea level surface is instinctively taken into consideration.不能被当作一个计算面来用，平均海平面自然的【instinctively本能地、自然地】被考虑【被考虑作计算面】）
Mean sea level (MSL) is defined as the average level of the ocean surface for all stages of the tide after long periods of observations.观测后得到的整个时期【stage阶段、时期】的海洋表面的平均水平面）
We use MSL as a plane upon which we can reference or describe the heights of features on, above or below the ground.【reference原意为名词，这里词性改变——动词：定位、参考】或描述高于、低于或在地面上特征的高度）
By extending the earth‟s MSL through the land areas, an equipotential surface approximately at MSL would be formed.似【approximately近似地】于平均海平面的等位面【equipotential surface等位面】形成了）
Such a surface is called the „geoid‟. Thus by definition, the geoid is an equipotential surface of the Earth gravity field that most closely approximates the mean sea surface.样一个面被称为“打的水准面”。这样，依照定义，大地水准面是一个地球重力场的等位面【equipotential surface】，非常近似于平均海平面）
The geoid is only a theoretical surface, which is perpendicular at every point to the direction of gravity.【perpendicular垂直的】指向重力方向）
You can‟t see it, touch it or even dig down to find it. The shape of geoid can be actually measured which is based on gravity data collected worldwide.更不能下挖来找到它。大地水准面的形状事实上可以被测出——基于世界范围的重力数据采集）
Although the gravity potential is everywhere the same and the surface is smoother than physical surface of the Earth, it still contains many irregularities which render it unsuitable mathematical location of planimetric position.位、电压、潜能】是处处相等的【指的是大地水准面的】，并且该曲面必地球自然表
面药平滑的多，它依然包含了许多不规则之处【irregularity】，使得【render】它不适于平面位置【planimetric position】的精确定位【mathematical除有‘数学的’意思，也有‘精确的’意思】
These irregularities are thought to be due to mass anomalies throughout the Earth.规则被认为是由于【due to由于 due应当的】遍及地球【throughout介词：遍及】的质量【mass这里是质量的意思】分布不规则【anomaly异常、不规则】）
The geoid remains important to the surveyor, as it is the surface to which all terrestrial measurements are related.译为参考面】，对测量者来说大地水准面依然【remain】重要）
As the direction of the gravity vector (termed the vertical) is everywhere normal to the geoid, it defines the direction of the surveyor‟s plumb-bob line.【term称为】垂线【vertical垂线n.、垂直的adj.】）的方向在各处都垂直【normal垂直的、正交的、垂线、法线】于大地水准面，由测量者的铅垂线【plumb-bob line】方向就可以表示【define明确表示】）
Thus any instrument which is horizontalized by means of a spirit bubble will be referenced to the local equipotential surface.Elevations are related to the equipotential surface passing through MSL.过平均海平面的等位面的数据）【或者翻译为：高程与过平均海平面的等位面有关or高程参考的是过平均海平面的等位面】
Such elevations or heights are called orthometric heights (H) and are the linear distances measured along the gravity vector from a point to the equipotential surface as a reference datum.
准的等位面的直线【linear直线的】距离）
As such, the geoid is the equipotential surface that best fits MSL and heights in question, referred to as heights above or below MSL.面；正被讨论的【in question正在讨论的、正在讨论】高度，指的是【refer to提到；
It can be seen from this that orthormetric heights are datum dependent.正高由其基准面决定【dependent由„„决定的、依靠的】）
The Reference Ellipsoid（参考椭球）
The ellipsoid is a mathematical surface which provides a convenient model of the size and shape of the Earth.参考关于方便的【convenient】模型）
It is represented by an ellipse rotated about its minor axis and is defined by its semi-major axis a or the flattening f.用它的长半轴a和扁率f来定义）
The ellipsoid is chosen to best meet the needs of a particular geodetic datum system design.（这个椭球被选择来最满足特定大地基准系统设计的需要【meet one‟s need满足„„的需要】）【即在设计一套特定的大地基准系统前首先选择一个满足系统设计的椭球】Although the ellipsoid is a concept and not a physical reality, it represents a smooth surface for which formulas can be developed to compute ellipsoidal distance, azimuth and ellipsoidal coordinates.一个光滑的表面，由此公式可以被发展来计算椭球距离，方位和椭球坐标。）
Due to the variable shape of the geoid, it is not possible to have a global ellipsoid of reference for use by all countries.能有一个适用于所有国家的全球【global】参考椭球）
The best-fitting global geocentric ellipsoid is the Geodetic Reference System 1980(GRS80), which has the following dimensions: semi-major axis is 6378137.0 m and semi-minor axis is 6356752.314 m.大地坐标参考系统【80椭球，注意：我国使用的80坐标系使用的是75椭球】，尺寸
【dimension尺寸、元】如下：长半轴为6378137.0 m，短半轴为6356752.314 m） The relationship of all three surfaces which are terrain, geoid and ellipsoid is illustrated in this Figure. （所有三个面：地表、大地水准面和椭球面的关系，由这个图图解说明
【illustrate图例说明】）
We note that the orthometric height H is the height with reference to the MSL, whereas the geodetic height h is the height of anything above the reference ellipsoid.高H是参考MSL的高度，而【whereas】大地高h是参考椭球面的高度）
The relation between the two kinds of heights is shown in the Figure, where the quantity N, the height of the geoid above the reference ellipsoid or the perpendicular distance between the geoid and the reference ellipsoid at a point, is usually called the geoidal height (geoid undulation).水准面高于参考椭球面或者说大地水准面和参考椭球面之间的垂直距离
【perpendicular distance垂直距离】，通常被称为大地水准面高【geoidal height】（大地水准面差距【geoid undulation；undulation波动】）
Thus, the knowledge of the geoid is necessary for transforming the geodetic to orthometric heights and vice versa. （这样，把大地高转换为正高，大地水准面的知识就是必需的，反之亦然【vice versa反之亦然】）
Once we determine the geoid, we can compute the difference between the two surfaces, the ellipsoid and the geoid anywhere in the country.就可以计算这两个面的差距——国家的无论何处的椭球面和大地水准面）
The expression “ellipsoidal height” for (geodetic) height of anything above the reference ellipsoid is also used comparing the acceptance of the standard geodetic term of “geoidal height”.认同】，“椭球高”这个表示高于参考椭球面的高度（大地高）的表达【expression】也被采用。）
Surveyors used to working with spirit levels have referenced orthometric heights (H) to the “average” surface of the earth, as depicted by MSL.地球“平均”表面——用MSL来描述【depicte】，利用水准测量，获得正高（H）） The surface of MSL can be approximated by the geoid.地水准面）
The difference between the two surfaces arises from the fact that seawater is not homogeneous and because of a variety of dynamical effects on the seawater.差别出现在一个事实上——海水不均匀并且有各种不断变化的影响在其上）
The height of the MSL above the geoid is called the sea surface topography (SST).高于大地水准面的高度称为海面地形【sea surface topography】【还有一个SST
It is a very difficult quantity to obtain from any measurements; consequently, it is not yet known very accurately.【consequently】，它尚未【not yet尚未】非常准确的得知）
GPS heights are referenced to the ellipsoid, a mathematical model that does not physically exist.This model, does not agree with mean sea level. That means the height of a point
determined from GPS is not the same as its sea level elevation as determined by leveling. （这个模型，不与平均海平面相吻合。这就意味着一个点由GPS确定的高度与由水准测量确定的海拔高不相同）
The summarizing of the relationships among height systems can be illustrated below:程系统的关系概述举例说明【illustrate】如下【summarize概述n.】：）
⑴MSL elevation is roughly equivalent to orthometric height (H), the technical name for height above the geoid. The geoid is, for all intents and purposes, the same as MSL.高程概略地等同于正高（H）——高于大地水准面的高度的技术名词）
⑵Geoid height (N)is the separation between the geoid and the ellipsoid (sometimes called Geoidal separation). It can be plus or minus. A negative geoidal separation indicates that the geoid is below the ellipsoid.距【separation】（有时也叫大地水准面差距）。它可以是正也可以是负。一个正的大地水准面差距表示【indicate】大地水准面在椭球面下方）
⑶Ellipsoid height (h)is the distance above or below the ellipsoid (plus or minus). Ellipsoid height is also called geodetic height.或负）。椭球高也叫做大地高。）
Unit 13 Geoid and Reference Ellipsoid（大地水准面和参考椭球）
The Earth‟s physical surface is a reality upon which the surveying observations are made and points are located.工作【observation观测】在其上进行，点位在其上进行定位。）
However, due to its variable topographic surface and overall shape, it cannot be defined mathematically and so position cannot be computed on its surface.它的起伏不定的【variable可变的、不定的，这里按中文习惯译为起伏不定的】地形表面和总的【overall】形状，它不能被数学的定义，因此点位也不能在其上进行计算。） It is for this reason that in surveys of limited extent, the Earth is treated as flat and plane trigonometry used to define position.（正是因为这个原因，在有限范围内的测量中，地球被当成平的，并用平面三角学【trigonometry三角学】来确定位置。）
If the area under consideration is of limited extent, orthogonal projection of this area onto a plane surface may result in negligible distortion.在考虑中的】区域是有限范围的，该区域在一个平面【plane surface】上的正交投影
【orthogonal projection】导致的【直译为导致，可以意译为：其结果】是可以忽略的
【negligible可以忽略的】变形【distortion】）
Plane surveying techniques could be used to capture field data and plane trigonometry used to compute position.计算位置坐标）
However, if the area extended to a large area beyond limitation and treated as a flat surface the effect of the Earth‟s curvature will produce unacceptable distortion.域延伸【extend】为一个大的区域超过了限度，把它当成一个平面，地球的曲率影响
【effect】将产生不可被接收的【unacceptable】变形）
It can also be clearly seen that the use of a plane surface as a reference datum for the elevations of points is totally unacceptable.作点的高程的参考基准是完全【totally完全地】不可被接受的【不可以的】。）
Therefore, to represent horizontal positions and elevations on maps and charts, we need a mathematical model of the Earth which includes a set of numbers for the size and shape of the Earth.和高程位置，我们需要一个地球的数学模型，它包括一系列地球大小和形状的参数
【number这里译为参数parameter参数】）
We will define a mathematical surface that approximates to the shape of the area under consideration and then fit and orientate it to the Earth‟s surface.面接近【approximates接近v.】于被考虑的【under consideration】区域的形状，然后使之与地球表面相符合【fit and orientate：fit是适合的意思；orientate是定向的意思】） Such a surface is referred in surveying as a „reference ellipsoid‟.被称为【refer提到、涉及】“参考椭球”）
The Geoid （大地水准面）
Since the physical surface of the Earth can‟t be used as a computational surface, a mean sea level surface is instinctively taken into consideration.不能被当作一个计算面来用，平均海平面自然的【instinctively本能地、自然地】被考虑【被考虑作计算面】）
Mean sea level (MSL) is defined as the average level of the ocean surface for all stages of the tide after long periods of observations.观测后得到的整个时期【stage阶段、时期】的海洋表面的平均水平面）
We use MSL as a plane upon which we can reference or describe the heights of features on, above or below the ground.【reference原意为名词，这里词性改变——动词：定位、参考】或描述高于、低于或在地面上特征的高度）
By extending the earth‟s MSL through the land areas, an equipotential surface approximately at MSL would be formed.似【approximately近似地】于平均海平面的等位面【equipotential surface等位面】形成了）
Such a surface is called the „geoid‟. Thus by definition, the geoid is an equipotential surface of the Earth gravity field that most closely approximates the mean sea surface.样一个面被称为“打的水准面”。这样，依照定义，大地水准面是一个地球重力场的等位面【equipotential surface】，非常近似于平均海平面）
The geoid is only a theoretical surface, which is perpendicular at every point to the direction of gravity.【perpendicular垂直的】指向重力方向）
You can‟t see it, touch it or even dig down to find it. The shape of geoid can be actually measured which is based on gravity data collected worldwide.更不能下挖来找到它。大地水准面的形状事实上可以被测出——基于世界范围的重力数据采集）
Although the gravity potential is everywhere the same and the surface is smoother than physical surface of the Earth, it still contains many irregularities which render it unsuitable mathematical location of planimetric position.位、电压、潜能】是处处相等的【指的是大地水准面的】，并且该曲面必地球自然表
面药平滑的多，它依然包含了许多不规则之处【irregularity】，使得【render】它不适于平面位置【planimetric position】的精确定位【mathematical除有‘数学的’意思，也有‘精确的’意思】
These irregularities are thought to be due to mass anomalies throughout the Earth.规则被认为是由于【due to由于 due应当的】遍及地球【throughout介词：遍及】的质量【mass这里是质量的意思】分布不规则【anomaly异常、不规则】）
The geoid remains important to the surveyor, as it is the surface to which all terrestrial measurements are related.译为参考面】，对测量者来说大地水准面依然【remain】重要）
As the direction of the gravity vector (termed the vertical) is everywhere normal to the geoid, it defines the direction of the surveyor‟s plumb-bob line.【term称为】垂线【vertical垂线n.、垂直的adj.】）的方向在各处都垂直【normal垂直的、正交的、垂线、法线】于大地水准面，由测量者的铅垂线【plumb-bob line】方向就可以表示【define明确表示】）
Thus any instrument which is horizontalized by means of a spirit bubble will be referenced to the local equipotential surface.Elevations are related to the equipotential surface passing through MSL.过平均海平面的等位面的数据）【或者翻译为：高程与过平均海平面的等位面有关or高程参考的是过平均海平面的等位面】
Such elevations or heights are called orthometric heights (H) and are the linear distances measured along the gravity vector from a point to the equipotential surface as a reference datum.
准的等位面的直线【linear直线的】距离）
As such, the geoid is the equipotential surface that best fits MSL and heights in question, referred to as heights above or below MSL.面；正被讨论的【in question正在讨论的、正在讨论】高度，指的是【refer to提到；
It can be seen from this that orthormetric heights are datum dependent.正高由其基准面决定【dependent由„„决定的、依靠的】）
The Reference Ellipsoid（参考椭球）
The ellipsoid is a mathematical surface which provides a convenient model of the size and shape of the Earth.参考关于方便的【convenient】模型）
It is represented by an ellipse rotated about its minor axis and is defined by its semi-major axis a or the flattening f.用它的长半轴a和扁率f来定义）
The ellipsoid is chosen to best meet the needs of a particular geodetic datum system design.（这个椭球被选择来最满足特定大地基准系统设计的需要【meet one‟s need满足„„的需要】）【即在设计一套特定的大地基准系统前首先选择一个满足系统设计的椭球】Although the ellipsoid is a concept and not a physical reality, it represents a smooth surface for which formulas can be developed to compute ellipsoidal distance, azimuth and ellipsoidal coordinates.一个光滑的表面，由此公式可以被发展来计算椭球距离，方位和椭球坐标。）
Due to the variable shape of the geoid, it is not possible to have a global ellipsoid of reference for use by all countries.能有一个适用于所有国家的全球【global】参考椭球）
The best-fitting global geocentric ellipsoid is the Geodetic Reference System 1980(GRS80), which has the following dimensions: semi-major axis is 6378137.0 m and semi-minor axis is 6356752.314 m.大地坐标参考系统【80椭球，注意：我国使用的80坐标系使用的是75椭球】，尺寸
【dimension尺寸、元】如下：长半轴为6378137.0 m，短半轴为6356752.314 m） The relationship of all three surfaces which are terrain, geoid and ellipsoid is illustrated in this Figure. （所有三个面：地表、大地水准面和椭球面的关系，由这个图图解说明
【illustrate图例说明】）
We note that the orthometric height H is the height with reference to the MSL, whereas the geodetic height h is the height of anything above the reference ellipsoid.高H是参考MSL的高度，而【whereas】大地高h是参考椭球面的高度）
The relation between the two kinds of heights is shown in the Figure, where the quantity N, the height of the geoid above the reference ellipsoid or the perpendicular distance between the geoid and the reference ellipsoid at a point, is usually called the geoidal height (geoid undulation).水准面高于参考椭球面或者说大地水准面和参考椭球面之间的垂直距离
【perpendicular distance垂直距离】，通常被称为大地水准面高【geoidal height】（大地水准面差距【geoid undulation；undulation波动】）
Thus, the knowledge of the geoid is necessary for transforming the geodetic to orthometric heights and vice versa. （这样，把大地高转换为正高，大地水准面的知识就是必需的，反之亦然【vice versa反之亦然】）
Once we determine the geoid, we can compute the difference between the two surfaces, the ellipsoid and the geoid anywhere in the country.就可以计算这两个面的差距——国家的无论何处的椭球面和大地水准面）
The expression “ellipsoidal height” for (geodetic) height of anything above the reference ellipsoid is also used comparing the acceptance of the standard geodetic term of “geoidal height”.认同】，“椭球高”这个表示高于参考椭球面的高度（大地高）的表达【expression】也被采用。）
Surveyors used to working with spirit levels have referenced orthometric heights (H) to the “average” surface of the earth, as depicted by MSL.地球“平均”表面——用MSL来描述【depicte】，利用水准测量，获得正高（H）） The surface of MSL can be approximated by the geoid.地水准面）
The difference between the two surfaces arises from the fact that seawater is not homogeneous and because of a variety of dynamical effects on the seawater.差别出现在一个事实上——海水不均匀并且有各种不断变化的影响在其上）
The height of the MSL above the geoid is called the sea surface topography (SST).高于大地水准面的高度称为海面地形【sea surface topography】【还有一个SST
It is a very difficult quantity to obtain from any measurements; consequently, it is not yet known very accurately.【consequently】，它尚未【not yet尚未】非常准确的得知）
GPS heights are referenced to the ellipsoid, a mathematical model that does not physically exist.This model, does not agree with mean sea level. That means the height of a point
determined from GPS is not the same as its sea level elevation as determined by leveling. （这个模型，不与平均海平面相吻合。这就意味着一个点由GPS确定的高度与由水准测量确定的海拔高不相同）
The summarizing of the relationships among height systems can be illustrated below:程系统的关系概述举例说明【illustrate】如下【summarize概述n.】：）
⑴MSL elevation is roughly equivalent to orthometric height (H), the technical name for height above the geoid. The geoid is, for all intents and purposes, the same as MSL.高程概略地等同于正高（H）——高于大地水准面的高度的技术名词）
⑵Geoid height (N)is the separation between the geoid and the ellipsoid (sometimes called Geoidal separation). It can be plus or minus. A negative geoidal separation indicates that the geoid is below the ellipsoid.距【separation】（有时也叫大地水准面差距）。它可以是正也可以是负。一个正的大地水准面差距表示【indicate】大地水准面在椭球面下方）
⑶Ellipsoid height (h)is the distance above or below the ellipsoid (plus or minus). Ellipsoid height is also called geodetic height.或负）。椭球高也叫做大地高。）