catchment-scale analysis despite being parsimonious insofar that can be expeditiously evaluated, e.g., by remote sensing, measurements or available databases
such as channel slope, discharge, width, or bed grain size, with higher influence on
the first two. An important detail is that these models are not dependent on particle
size distribution as much as with topographic data of discharge.
Empirical formulations are, however, biased by uncertainties related to the
multitude of variables and interactions involved, which justify the development of
alternative theoretical approaches for deepening the knowledge of processes
involved as for the betterment of empirical models.
For example, Eq. (6.159) relative to the transport of bed sediments was shown as
more accurate to fine-grained sizes with coarse-grained streams likely to be
near-threshold conditions where the possible incertitude in critical stream power
may deliver greater variability in transport rates. Another example, presented by
Parker et al. (2011), of the source of complexity is the interpretation of the positive
relationship between slope and critical mean bed shear stress. According to these
authors, the possible location in steep headwater streams of prominent stabilizing
bed structures, hiding effects, or form roughness or of flow aeration at high slopes
are reflected in an increase of flow resistance with slope and in a decrease of local
flow velocity around bed particles. All these factors add sources of uncertainty in
the complex problem of flow analysis that must be subjected to continuous analysis.
References
Arya, S. P. (1988). Introduction to micrometeorology (Vol. 42, 307 pp.). International geophysics
series. Academic Press.
Bagnold, R. A. (1936). The movement of desert sand. Proceedings of the Royal Society of London.
Series A, 157, 594–620.
Bagnold, R. A. (1941). The physics of blown sand and desert dunes (p. 265). London: Methuen.
Bagnold, R. A. (1980). An empirical correlation of bedload transport rates in flumes in natural
rivers. Proceedings of Royal Society of London A, 372(1751), 453–473.
Bennet, I. (1965). Monthly maps of mean daily insolation for the United States. Solar Energy, 9,
145–152.
Brown, G. W. (1969). Prediction temperatures of small streams. Water Resources Research, 5,
67–75.
Camenen, B. (2012). Discussion of understanding the influence of slope on the threshold of coarse
grain motion: Revising critical stream power by C. Parker, N. J. Clifford and C.R. Throne.
Geomorphology, 126, 51–65.
Campbell, G. S., & Norman, J. M. (1998). An introduction to environmental biophysics (293 pp.).
Springer.
Cheng, X. L., Zeng, Q. C., & Hu, F. (2012). Stochastics modeling the effect of wind gust on dust
entrainment during sand-storm. Chinese Science Bulletin, 57, 3595–3602.
Eaton, B. C., & Church, M. (2011). A rational sediment transport scaling relation based on
dimensionless stream power. Earth Surface Processes and Landforms, 36, 901–910.
Ferguson, R. I. (2005). Estimating critical stream power for bedload transport calculations in
Gravel-Bed rivers. Geomorphology, 70, 33–41.
Ferguson, R. I. (2012). River chanel slope, flow resistance, and gravel entrainment thresholds.
Water Resources Research, 48, 1–13.
Foken, T. (2017). Micrometeorolog (2nd ed., 362 pp.). Berlin: Springer.
234
6 Heat and Mass Transfer Processes
such as channel slope, discharge, width, or bed grain size, with higher influence on
the first two. An important detail is that these models are not dependent on particle
size distribution as much as with topographic data of discharge.
Empirical formulations are, however, biased by uncertainties related to the
multitude of variables and interactions involved, which justify the development of
alternative theoretical approaches for deepening the knowledge of processes
involved as for the betterment of empirical models.
For example, Eq. (6.159) relative to the transport of bed sediments was shown as
more accurate to fine-grained sizes with coarse-grained streams likely to be
near-threshold conditions where the possible incertitude in critical stream power
may deliver greater variability in transport rates. Another example, presented by
Parker et al. (2011), of the source of complexity is the interpretation of the positive
relationship between slope and critical mean bed shear stress. According to these
authors, the possible location in steep headwater streams of prominent stabilizing
bed structures, hiding effects, or form roughness or of flow aeration at high slopes
are reflected in an increase of flow resistance with slope and in a decrease of local
flow velocity around bed particles. All these factors add sources of uncertainty in
the complex problem of flow analysis that must be subjected to continuous analysis.
References
Arya, S. P. (1988). Introduction to micrometeorology (Vol. 42, 307 pp.). International geophysics
series. Academic Press.
Bagnold, R. A. (1936). The movement of desert sand. Proceedings of the Royal Society of London.
Series A, 157, 594–620.
Bagnold, R. A. (1941). The physics of blown sand and desert dunes (p. 265). London: Methuen.
Bagnold, R. A. (1980). An empirical correlation of bedload transport rates in flumes in natural
rivers. Proceedings of Royal Society of London A, 372(1751), 453–473.
Bennet, I. (1965). Monthly maps of mean daily insolation for the United States. Solar Energy, 9,
145–152.
Brown, G. W. (1969). Prediction temperatures of small streams. Water Resources Research, 5,
67–75.
Camenen, B. (2012). Discussion of understanding the influence of slope on the threshold of coarse
grain motion: Revising critical stream power by C. Parker, N. J. Clifford and C.R. Throne.
Geomorphology, 126, 51–65.
Campbell, G. S., & Norman, J. M. (1998). An introduction to environmental biophysics (293 pp.).
Springer.
Cheng, X. L., Zeng, Q. C., & Hu, F. (2012). Stochastics modeling the effect of wind gust on dust
entrainment during sand-storm. Chinese Science Bulletin, 57, 3595–3602.
Eaton, B. C., & Church, M. (2011). A rational sediment transport scaling relation based on
dimensionless stream power. Earth Surface Processes and Landforms, 36, 901–910.
Ferguson, R. I. (2005). Estimating critical stream power for bedload transport calculations in
Gravel-Bed rivers. Geomorphology, 70, 33–41.
Ferguson, R. I. (2012). River chanel slope, flow resistance, and gravel entrainment thresholds.
Water Resources Research, 48, 1–13.
Foken, T. (2017). Micrometeorolog (2nd ed., 362 pp.). Berlin: Springer.
234
6 Heat and Mass Transfer Processes