Errors of Observation and Their Treatment

Topping, J; Worrell, Francis T.

doi:10.1119/1.1934535

Cited by 27 publications

(6 citation statements)

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“…Empirical DOC and discharge relationship was simulated using a best fit parsimonious (3‐parameter) hyperbola equation ( r 2 =0.49) as follows:

{DOC}_{sim} = {DOC}_{o} + \frac{aQ}{b + Q}

where DOC sim corresponds to the simulated concentration, DOC o represents baseflow DOC (2.93 mg/L), a (3.33) and b (0.11) are fitting parameters, and Q is the known stream discharge. Error propagation in MTT, event water contributions, and annual carbon flux was estimated using the root mean square method (Topping, ).…”

Section: Methodsmentioning

confidence: 99%

DOC Transport and Export in a Dynamic Tropical Catchment

et al. 2019

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Dissolved organic carbon (DOC) transport and export from headwater forests into freshwaters in highly dynamic tropical catchments are still understudied. Here we present a DOC analysis (2017) in a pristine and small (~2.6 km2) tropical catchment of Costa Rica. Storm flows governed a rapid surface and lateral allochthonous DOC transport (62.2% of the annual DOC export). Cross‐correlation analysis of rainfall and stream discharge indicated that DOC transport occurred on average ~1.25 hr after the rainfall maxima, with large contributions of event water, ranging from 42.4±0.3% up to 98.2±0.3% of the total discharge. Carbon export flux (annual mean=6.7±0.1 g C · m‐2 · year‐1) was greater than values reported in subtropical and temperate catchments. Specific ultraviolet absorbance indicated a mixture of hydrophobic humic and hydrophilic nonhumic matter during both baseflow and storm events. Our results highlight the rapid storm‐driven DOC transport and export as well as low biogeochemical attenuation during baseflow episodes in a climate sensitive hot spot. By understanding the key factors controlling the amount of organic carbon transported to streams in dynamic tropical landscapes, better global‐ and catchment‐scale model assessments, conservation practices, and water treatment innovations can be identified.

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“…Empirical DOC and discharge relationship was simulated using a best fit parsimonious (3‐parameter) hyperbola equation ( r 2 =0.49) as follows:

{DOC}_{sim} = {DOC}_{o} + \frac{aQ}{b + Q}

Section: Methodsmentioning

confidence: 99%

DOC Transport and Export in a Dynamic Tropical Catchment

et al. 2019

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“…The absolute value of v is simply the amount by which the value of or measured directly is corrected by the least-squares procedure (it is also one quarter of the figure shown in the last column of Table I). The standard error in each of the four measured values is 12 , and by standard methods it can be shown that the standard error in and is , and in is .…”

Section: Reduction Of Resultsmentioning

confidence: 95%

“…The problem is essentially to find the best solution to 4 simultaneous linear equations involving 3 unknowns. The standard method 12 is used, namely, to form the normal equations and to solve them. An exactly analogous problem arises in crystal physics when one wishes to deduce the components of some tensor property of a crystal from a number of measurements made in different crystallographic directions.…”

Section: Reduction Of Resultsmentioning

confidence: 99%

A Method of Determining the Strain-Rate Tensor at the Surface of a Glacier

Nye

1959

J. Glaciol.

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ABSTRACT. The rate of strain tensor at a p oint on the surface of a glacier may be determined by setting up a number of stakes in a pattern and measuring the rate of change of the distances between them. A suitable pattern consists of four stakes at the corners of a square with one stake at the centre. Five such patterns were used on Austerdalsbreen, Norway, in August 1956. The problem is to d educe the best values of the 3 independent components of the strain-rate tensor from the 8 measured quantities, and, for this purpose, a least-squares method, invented by Bond for the analogous problem in crystal physics, is used. The principal strain-rates are found to within about ±o ' 005 yr. -, and their directions relative to the stake system to within about ±0 · 5°. The directions and magnitudes of the principal stresses are then deduced from Glen's flow law and a suitable general theory. The directions of the principal strain-rates are in good agreement with the directions of the crevasses, but the experiment is inconclusive on the question of the magnitude of thl! stress n eeded to form a crevasse.ZUSAMMENFASSUNG. Der Tensor der Deformationsgeschwindigkeit an einem Punkt auf der Gletscheroberflache kann bestimmt werden, indem man St6cke in regelmassiger Anordnung auf dem Gletscher befestigt und die Anderung der Distanzen zwischen ihnen misst. Eine geeignete Anordnung besteht au! 4 Stacken an den Ecken eines Quadrats mit einem Stock in der Mitte. Funf solche Anordnungen wurden im August 1956 auf dem Austerdalsbre in Norwegen aufgestellt. Das Problem besteht nun darin au! 8 Messwerten die besten Werte fUr die 3 unabhangigen Komponenten des DeformationsgeschwindigkeitsTensors abzuleiten. Fur diesen Zweck wurde eine Methode der kleinsten Quadrate verwendet, die von Bond fUr ein analoges Problem in der Kristallphysik erfunden wurde. Die Hauptgeschwindigkeiten wurden innerhalb einer Fehlcrgrenze von ±0,005 Jahre-' bestimmt und ihre Richtungen in Bezug auf das Stocksystem innerhalb ± 0,5 0 . Die Richtungen und Grossen der H a uptspannungen wurden dann aus Glen's Fliessgesetz und einer entsprechenden allgemeinen Theorie abgeleitet. Die Hauptdeformationsrichtungen stimmen mit den Richtungen der GletscherspaIten gut uberei n , aber das Experiment lasst die Frage der zur Spaltenbildung notigen Zugspannung offen.

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“…Correcting for the energy refraction requires precise knowledge of the internal borehole shape, resulting in insignificant improvement of the uncertainties. Realistically, borehole walls undulate as heterogeneous ice properties result in different melting speeds; we consider this equivalent to miscalculating the spatial positioning, and we incorporate it into the borehole separation error d S in the following equation (Topping and Worrell, 1957):…”

Section: Borehole Geometry: Inclinationmentioning

confidence: 99%

Improved accuracy of cross-borehole radar velocity models for ice property analysis

et al. 2016

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Cross-borehole radar (XBHR) is widely used for the quantification of pore-scale liquid water in geologic materials, inferred from bulk velocity variations caused by differences in electromagnetic properties between the water and the surrounding material. The XBHR can accurately and repeatedly measure variation at depth, with sampled material remaining under natural stresses, while maintaining good lateral sampling. However, even small errors in measured radar velocities result in large errors in water content estimates, emphasizing the need to quantify and minimize errors. We have rigorously assessed the sources of uncertainty in XBHR surveys undertaken in a glaciological setting. We have summarized and quantified the three main areas of uncertainty in data collection: (1) instrument time drift, (2) first-break picking, and (3) borehole geometry. Our analysis of field data indicated that contemporary acquisition procedures can produce velocity errors of AE3.0% (AE0.0050 m∕ns), equivalent to AE0.84 vol% water content. We have developed several revisions to produce improved data acquisition. Through enhancement of existing techniques, the velocity uncertainties were improved to AE1.5%. We also found the measurement of borehole diameter during hot-water drilling, which could hypothetically further reduce the velocity uncertainty to AE0.8%, equivalent to AE0.2 vol% water content. The need for such precise measurement is clear because an increase in englacial water content, from 0% to 0.8%, has been proven to triple the strain rate and soften the ice. Liquid water between ice crystals has also been linked to faster velocities in ice streams and surging events.

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Errors of Observation and Their Treatment

Cited by 27 publications

References 0 publications

DOC Transport and Export in a Dynamic Tropical Catchment

DOC Transport and Export in a Dynamic Tropical Catchment

A Method of Determining the Strain-Rate Tensor at the Surface of a Glacier

Improved accuracy of cross-borehole radar velocity models for ice property analysis

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