Thursday, January 26, 2012

Precise levelling in Canada

The precise levelling method is a well-known approach that has been used for more than 200 years (Gareau, 1986) and still provides the most accurate method for determining height differences over short distances. It involves making differential height measurements between two vertical graduated rods, approximately 100 metres apart, using a tripod mounted telescope whose horizontal line of sight is controlled to better than one second of arc by a spirit level vial or a suspended prism. This process is repeated in a leap-frog fashion to produce elevation differences between established benchmarks that constitute the vertical control network (Véronneau et al., 2006). Despite its precision, precise levelling is costly, time consuming, laborious and remains restricted to almost flat areas, when the network is established. After the measurement is done, however, other difficulties will arise in terms of stability and maintenance of the network. The first problem is especially important for the areas subject to uplift or subsidence, e.g., due to GIA or mineral exploration. The second problem is mostly faced in urban areas, where the construction has a higher rate, and therefore, levelling benchmarks are subject to demolition.

The currently publishing Canadian heights are a construct that results from annual survey observations dating back to 1904. Despite the great efforts to minimize potential error sources, the network was established in a piece-meal fashion by combining observations made over consecutive years and adjusted locally. This led to significant regional distortions in the current published heights. Further degradation of the accuracy of the published height is originated from GIA over time. Comparisons of the heights currently published against more recent scientific network re-adjustments and the most recent geoid models indicate regional distortions of up to one metre. Although, the consistency of relative heights is probably still at the sub-centimetre precision level locally, the regional distortion impede on the application of new technology such as GPS to obtain accurate point heights consistent with the current datum (Véronneau et al., 2006).

As an extension of the latter difficulty, the current published heights were based on the assumption that the Pacific and Atlantic oceans were at the same height. In fact, according to oceanographic evidence, the water level at Vancouver could be higher than the water level at Halifax by 40 to 70 cm (Véronneau et al., 2006). This discrepancy causes a national-scale tilt in the published heights that has significant impact on a number of applications. Along with this problem, the GIA-related uplift and subsidence across the Canadian landmass was not known at time of developing the CGVD28, and naturally, this phenomenon was not accounted for in the network adjustment.

In recent years, limitations of the current height reference system such as instability, distortion, limited spatial coverage, high maintenance costs, along with opportunities and pressures of new technology, forced GSD to begin a modernization program to fully support and realize the substantial benefits of GPS and related modern technologies (e.g., gravimetry) for accurate height measurement to provide an up-to-date height reference in Canada (Véronneau et al., 2006). This led to re-observation of a large portion of the primary vertical network. From 1972 to 2000, the Canadian vertical network was almost entirely re-surveyed with about 124,000 km of levelling lines observed.

Despite the existing problems in the levelling network, the re-surveyed data makes it possible to compute the benchmarks height differences. The data quality, however, should be checked due to the problems in the network, and the data should be corrected for the systematic and localized errors. For example, Koohzare (2007) has made a criterion to reject the levelling data based on the height difference differences per distance in time. Based on this criterion, the author has rejected the data with height difference differences greater than 0.1 mm km-1 yr-1. The author has also removed the short levelling lines that have just included a few segments. After the data screening, the rest of the levelling data can participate in the data processing.

Assuming the velocity to be constant in time, the vertical velocity at each levelling benchmark can be computed by:

V = Δ H Δ t = H ( t 2 ) H ( t 1 ) t 2 t 1 V = {%DELTA H} over {%DELTA t} = {H(t_2) - H(t_1)} over {t_2 - t_1}

where H is the orthometric height of the benchmark and t denotes the measuring time. The difference of vertical velocities of the two re-levelled adjacent benchmarks can be computed by:

V AB = V B V A = [ H B ( t 2 ) H B ( t 1 ) ] [ H A ( t 2 ) H A ( t 1 ) ] t 2 t 1 = Δ H Δ t ∆V_{AB} = V_B − V_A = {[H_B(t_2) − H_B(t_1)] − [H_A(t_2) − H_A(t_1)]} over {t_2 - t_1} = {nabla %DELTA H} over {%DELTA t}

where VA and VB are the vertical velocities at benchmarks A and B, respectively and HA(t1), HB(t1), HA(t2), HB(t2) are the heights of the same benchmarks measured at time t1 and t2.

Gareau, R. M. (1986). History of precise levelling in Canada and the North American vertical datum readjustment (M.Sc. Thesis). University of Calgary, Calgary, Alberta.

Koohzare, A. (2007). A physically meaningful model of vertical crustal movements in Canada using smooth piecewise algebraic approximation: Constraints for glacial isostatic adjustment models (Ph.D. Thesis). University of New Brunswick.

Véronneau, M., Duval, R., and Huang, J. (2006). A Gravimetric Geoid Model as a vertical datum in Canada. Geomatica, 60(2), 165-172.

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