2:30 PM - 2:45 PM
[SGD01-04] Level Measurement Error Theory Revisited
—Systematic Errors in the Digital Level Era—
Keywords:leveling, systematic error, digital level, premature observation, gravity geoid model
Introduction
The weak point of level surveying is that it is not possible to advance even 100 m in a single observation, and as the distance increases, the number of observations increases and errors accumulate. If it is a systematic error, an error of 0.1 mm at 100 m may become 1 cm when the distance is 10 km.
According to the statistics of first-order level surveys conducted by the GSI, the standard deviation calculated from round-trip differences, which is an index of error for short distances, is less than 0.5 mm/km, while the standard deviation calculated from ring-closure differences, which is an index of error for long distances (several hundred km), is 1.0 to 1.5 mm/km. This indicates that the errors in current level surveys still include a large amount of systematic errors that accumulate over long distances.
In this presentation, we reconsider the systematic errors in recent level surveys and consider the optimal method of determining elevations in the future together with the gravity geoid model.
Round-Trip Difference Plus by “Flying Observation”
Digital levels have greatly improved the efficiency of leveling operations. However, since it is so easy to make observations, “flying observations,” in which observations are made before the tripod and stuffs are stabilized, have resulted not only in unstable measurements but also in new errors due to asymmetric measurements, causing round-trip differences that should normally vary around zero to be biased toward the positive.
Fig. 1 shows the GSI’s level survey results from Kakegawa to Omaezaki, and the round-trip difference (blue line) tends to be positive after the introduction of the digital levels. Even if the round-trip difference is accumulated, it should not be offset of the relative height. However, since the tripod and stuffs need only be set up the same way on the return trip, there is a concern that “flying observations” will further accelerate on the return trip, and it is essential to “aim for slow and uniform observations” with the digital levels.
Error Depends on Season and Route Direction
In the repeated level survey from Kakegawa to Omaezaki, the annual variation was very large with tilting levels used until around 2000, and then it became smaller after the introduction of auto-levels, which was further improved by the digital levels. However, as shown in Fig. 2, there is still a systematic difference of about 5 mm between summer and winter, and the variation is also larger in the winter season.
Such seasonal and route direction-dependent errors have been observed throughout Japan, and Sawada (2015) states that the tripod loading the level is stretched by solar radiation from one side, causing the level to continuously tilt, and the error is caused by the time lag of the level's horizontal compensation function. This effect is thought to be greater on clear winter days when the sun tends to shine from a fixed direction at a low angle on north-south routes.
Geoid Model Reveals Nationwide Systematic Errors
By comparing the precise gravity geoid model being developed by the GSI with the difference between the height of the ellipsoid and the level elevation obtained by GNSS observations on the benchmarks, it is now possible to estimate the systematic errors in the level elevation across Japan.
The present level elevation is already 10 cm higher than the elevation based on the precise gravity geoid model in the northern part of Kanto, and reaches +20 cm at the northern end of Honshu. In western Japan, the present level elevation and the geoid model are relatively consistent, but the present level elevation deviates by –10 cm at the southern tip of Kyushu. It should be noted that systematic errors in leveling surveys include crustal deformations and other factors that occur between the observation periods of adjacent lines, and that systematic errors can be longer-range than expected.
The weak point of level surveying is that it is not possible to advance even 100 m in a single observation, and as the distance increases, the number of observations increases and errors accumulate. If it is a systematic error, an error of 0.1 mm at 100 m may become 1 cm when the distance is 10 km.
According to the statistics of first-order level surveys conducted by the GSI, the standard deviation calculated from round-trip differences, which is an index of error for short distances, is less than 0.5 mm/km, while the standard deviation calculated from ring-closure differences, which is an index of error for long distances (several hundred km), is 1.0 to 1.5 mm/km. This indicates that the errors in current level surveys still include a large amount of systematic errors that accumulate over long distances.
In this presentation, we reconsider the systematic errors in recent level surveys and consider the optimal method of determining elevations in the future together with the gravity geoid model.
Round-Trip Difference Plus by “Flying Observation”
Digital levels have greatly improved the efficiency of leveling operations. However, since it is so easy to make observations, “flying observations,” in which observations are made before the tripod and stuffs are stabilized, have resulted not only in unstable measurements but also in new errors due to asymmetric measurements, causing round-trip differences that should normally vary around zero to be biased toward the positive.
Fig. 1 shows the GSI’s level survey results from Kakegawa to Omaezaki, and the round-trip difference (blue line) tends to be positive after the introduction of the digital levels. Even if the round-trip difference is accumulated, it should not be offset of the relative height. However, since the tripod and stuffs need only be set up the same way on the return trip, there is a concern that “flying observations” will further accelerate on the return trip, and it is essential to “aim for slow and uniform observations” with the digital levels.
Error Depends on Season and Route Direction
In the repeated level survey from Kakegawa to Omaezaki, the annual variation was very large with tilting levels used until around 2000, and then it became smaller after the introduction of auto-levels, which was further improved by the digital levels. However, as shown in Fig. 2, there is still a systematic difference of about 5 mm between summer and winter, and the variation is also larger in the winter season.
Such seasonal and route direction-dependent errors have been observed throughout Japan, and Sawada (2015) states that the tripod loading the level is stretched by solar radiation from one side, causing the level to continuously tilt, and the error is caused by the time lag of the level's horizontal compensation function. This effect is thought to be greater on clear winter days when the sun tends to shine from a fixed direction at a low angle on north-south routes.
Geoid Model Reveals Nationwide Systematic Errors
By comparing the precise gravity geoid model being developed by the GSI with the difference between the height of the ellipsoid and the level elevation obtained by GNSS observations on the benchmarks, it is now possible to estimate the systematic errors in the level elevation across Japan.
The present level elevation is already 10 cm higher than the elevation based on the precise gravity geoid model in the northern part of Kanto, and reaches +20 cm at the northern end of Honshu. In western Japan, the present level elevation and the geoid model are relatively consistent, but the present level elevation deviates by –10 cm at the southern tip of Kyushu. It should be noted that systematic errors in leveling surveys include crustal deformations and other factors that occur between the observation periods of adjacent lines, and that systematic errors can be longer-range than expected.