4.3 Trigonometric Leveling
4.3.1 Trigonometric leveling route should be arranged as leveling network or leveling traverse on the basis of horizontal control network.
4.3.2 The main technical requirements for trigonometric leveling shall be as specified in Table 4.3.2.
Table 4.3.2 Main technical requirements for trigonometric leveling
Note:1 D is the leg length measured with EDM instrument，km.
2 Fourth-order trigonometric leveling should start and end with elevation points of third or higher order.Fifth-order trigonometric leveling should start and end with elevation points of fourth or higher order.
3 Trigonometric leveling route shall not be longer than the required total length of leveling route of the equivalent accuracy.
4 The elevation of complementary point may be obtained by intersecting two or more individual directions，and the discrepancy between elevation differences shall meet the requirements for reciprocal observation.
4.3.3 The technical requirements for trigonometric leveling shall be as specified in Table 4.3.3.
Table 4.3.3 Technical requirements for trigonometric leveling
Note:For DJ2 instruments，the index errors of vertical angles shall not exceed 1'.
4.3.4 Observation methods of vertical angles shall be as follows:
1 The procedure of observing each vertical angle in a group for one observation set is as follows:（1）Set the vertical circle in a position，and sight the middle wire of the telescope with each target in the observation group，or successively sight the upper，middle and lower wire of the telescope with each target；（2）Rotate the telescope in vertical plane to set the circle in another position，and sight the middle wire of the telescope with each target in the observation group，or successively sight the lower，middle and upper wire of the telescope with each target.
2 The two images of the same target sighted in left face and right face positions shall be symmetrical about the vertical wire.The positions sighted in the same direction shall be identical.Where three-wire observation method is applied，the horizontal wires shall in any case be sighted in the sequence of upper，middle and lower wire.
3 The spirit level of alidade shall be leveled prior to observation of vertical angles.The bubble in vertical circle shall be precisely centered whenever the vertical circle is to be read.For electronic theodolites and total stations，the level tube of alidade shall be precisely leveled prior to observation，with the deviation from center not more than one bar.
4 The formulas for calculating vertical angle and index error may vary with the form of graduations on vertical circle.For DJ2（T2 and 010）instruments，the following formulas shall apply:
Where:
L——face left reading；
R——face right reading；
α——vertical angle；
i——index error.
5 Zenith angle should be directly used to calculate elevation difference.For total stations，the elevation difference can be read directly on display screen after corrections are entered.
4.3.5 Trigonometric leveling observation shall comply with the following requirements:
1 For distance measurement instruments with centering bars，read the height of instrument directly.For those without centering bars，the heights of instrument and target shall be measured using special tools such as caliper and steel square before and after observation and read to the nearest millimeter.Record the average height.
2 The trigonometric leveling shall be performed under favorable weather conditions when targets can be stably imaged，rather than in rainy，foggy，or windy weather or in direct sunlight.
3 In foresight observation，measure the distance first，and then the vertical angle；in backsight observation，observe in the reverse sequence.Where conditions permit，complete the reciprocal observation of vertical angles in one observation period.
4 The targets shall be clearly visible，and the line of sight shall be at least 1.5m apart from any obstacle during observation.
5 During distance measurement，barometers shall be leveled and shall avoid excessive exposure to sunlight，and thermometers shall be suspended at least 1.5m above the ground.Use of dry and wet bulb thermometers shall follow the user manuals.
6 For the purpose of observing vertical angles，the observation targets should be specially fabricated.
7 Generally，vertical angles should be observed with middle wire for three observation sets.One observation set is a process in which the upper and lower edges of target are sighted with middle wire respectively in face left and face right positions.The observations of upper and lower edges shall be averaged for recording.The height of target shall be measured up to the target center.
4.3.6 Trigonometric leveling data processing shall comply with the following requirements:
1 The elevation difference obtained from bidirectional observation shall be corrected for earth curvature and refraction error using the following formula:
Where:
r——correction for earth curvature and refraction error（m）；
R——mean radius of earth curvature，which equals to 6369km for latitude of 35o；
S——horizontal distance of the measured leg（m）；
K——refraction coefficient，taken as 0.13.
2 The original field records and the starting calculation data shall be checked strictly.Where records are kept in electronic version，the original observation data shall be printed out for checking and correction.The elevation differences resulting from reciprocal observation and the misclosure of connecting or loop route shall be calculated，and they shall meet the requirements defined in Table 4.3.2.
3 The total RMSE of elevation difference per kilometer shall be calculated using formula（4.2.12-2）prior to adjustment.
4 For elevation networks of any accuracy order，least square adjustment and calculation of total RMSE of elevation difference per kilometer shall both be required.
5 The observed elevations shall be recorded to the nearest 1mm.
4.3.7 In trigonometric leveling，the accidental RMSE and total RMSE of elevation difference per kilometer shall be calculated as follows:
1 Calculate the accidental RMSE of elevation difference per kilometer using the discrepancy of elevation differences obtained by reciprocal observation:
Where:
MΔ——accidental RMSE of elevation difference per kilometer（mm）；
d——discrepancy between elevation differences obtained by reciprocal observation（mm）；
S——horizontal distance of the measured leg（km）；
N——number of d.
2 Calculate the total RMSE of elevation difference per kilometer using the misclosure of connecting or loop route:
Where:
Mw——total RMSE of elevation difference per kilometer（mm）；
fh——misclosure of connecting or loop route（mm）；
S——length of connecting or loop route（km）；
N——number of individual connecting or loop routes.
4.3.8 Computer programs should be used for adjustment of elevation networks.For independent leveling routes，adjustment in proportion to leg length is allowed.The software used for adjustment computations shall comply with 1.0.4，and the original data entered into computer shall be checked.
4.3.9 The calculations in office work shall be accurate to the nearest 1mm.