Articles | Volume 23, issue 4
https://doi.org/10.5194/npg-23-269-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/npg-23-269-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
15 Aug 2016
Research article |
| 15 Aug 2016
Fractal behavior of soil water storage at multiple depths
Wenjun Ji
Department of Natural Resource Sciences, McGill University, 21111 Lakeshore Road, Ste-Anne-de-Bellevue, Québec, H9X3V9, Canada
Mi Lin
Department of Natural Resource Sciences, McGill University, 21111 Lakeshore Road, Ste-Anne-de-Bellevue, Québec, H9X3V9, Canada
Department of Natural Resource Sciences, McGill University, 21111 Lakeshore Road, Ste-Anne-de-Bellevue, Québec, H9X3V9, Canada
Bing C. Si
Department of Soil Science, University of Saskatchewan, Saskatoon, Saskatchewan, S7N5A8, Canada
Henry W. Chau
Department of Soil and Physical Sciences, Lincoln University, P.O. Box 85084, Lincoln, 7647 Christchurch, New Zealand
Hamish P. Cresswell
CSIRO Land and Water, 2601 Canberra, ACT, Australia
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M. K. Firozjaei, S. Fathololuomi, S. K. Alavipanah, M. Kiavarz, A. Vaezi, A. Biswas, and A. Ghorbani
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLII-4-W18, 395–399, https://doi.org/10.5194/isprs-archives-XLII-4-W18-395-2019, https://doi.org/10.5194/isprs-archives-XLII-4-W18-395-2019, 2019
Mark J. P. Sigouin and Bing C. Si
The Cryosphere, 10, 1181–1190, https://doi.org/10.5194/tc-10-1181-2016, https://doi.org/10.5194/tc-10-1181-2016, 2016
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The cosmic-ray soil moisture probe (CRP) uses the natural above ground neutron intensity to measure soil water content at a landscape scale. The goal of our research was to use the CRP to monitor how much water is in snowpacks, since snow and soil water affect neutron intensity similarly. We developed a relationship between neutron intensity and snow water. We used the relationship to estimate snow water non-invasively in an area of ~ 300 m radius using neutron intensity readings from the CRP.
W. Hu and B. C. Si
Hydrol. Earth Syst. Sci., 20, 571–587, https://doi.org/10.5194/hess-20-571-2016, https://doi.org/10.5194/hess-20-571-2016, 2016
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Spatiotemporal SWC was decomposed into into three terms (spatial forcing, temporal forcing, and interactions between spatial and temporal forcing) for near surface and root zone; Empirical orthogonal function indicated that underlying patterns exist in the interaction term at small watershed scales; Estimation of spatially distributed SWC benefits from decomposition of the interaction term; The suggested decomposition of SWC with time stability analysis has potential in SWC downscaling.
W. Hu and B. C. Si
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-10-12829-2013, https://doi.org/10.5194/hessd-10-12829-2013, 2013
Revised manuscript not accepted
Related subject area
Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Brief communication: Climate science as a social process – history, climatic determinism, Mertonian norms and post-normality
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Comparing estimation techniques for temporal scaling in palaeoclimate time series
The impact of entrained air on ocean waves
Ordering of trajectories reveals hierarchical finite-time coherent sets in Lagrangian particle data: detecting Agulhas rings in the South Atlantic Ocean
Approximate multifractal correlation and products of universal multifractal fields, with application to rainfall data
Stratified Kelvin–Helmholtz turbulence of compressible shear flows
Quantifying the changes of soil surface microroughness due to rainfall impact on a smooth surface
Influence of atmospheric stratification on the integral scale and fractal dimension of turbulent flows
Multifractal behaviour of the soil water content of a vineyard in northwest Spain during two growing seasons
Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks
Kenneth M. Golden, N. Benjamin Murphy, Daniel Hallman, and Elena Cherkaev
Nonlin. Processes Geophys., 30, 527–552, https://doi.org/10.5194/npg-30-527-2023, https://doi.org/10.5194/npg-30-527-2023, 2023
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Our paper tours powerful methods of finding the effective behavior of complex systems, which can be applied well beyond the initial setting of sea ice. Applications include transport properties of porous and polycrystalline media, such as rocks and glacial ice, and advection diffusion processes that arise throughout geophysics. Connections to random matrix theory establish unexpected parallels of these geophysical problems with semiconductor physics and Anderson localization phenomena.
Shaun Lovejoy
Nonlin. Processes Geophys., 30, 311–374, https://doi.org/10.5194/npg-30-311-2023, https://doi.org/10.5194/npg-30-311-2023, 2023
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How big is a cloud?and
How long does the weather last?require scaling to answer. We review the advances in scaling that have occurred over the last 4 decades: (a) intermittency (multifractality) and (b) stratified and rotating scaling notions (generalized scale invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.
Hans von Storch
Nonlin. Processes Geophys., 30, 31–36, https://doi.org/10.5194/npg-30-31-2023, https://doi.org/10.5194/npg-30-31-2023, 2023
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Climate science is, as all sciences, a social process and as such conditioned by the zeitgeist of the time. It has an old history and has attained different political significances. Today, it is the challenge of anthropogenic climate change – and societies want answers about how to deal with it. In earlier times, it was mostly the ideology of climate determinism which led people to construct superiority and eventually colonialism.
Lei Liu, Yu Shi, and Fei Hu
Nonlin. Processes Geophys., 29, 123–131, https://doi.org/10.5194/npg-29-123-2022, https://doi.org/10.5194/npg-29-123-2022, 2022
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We find a new kind of non-stationarity. This new kind of non-stationarity is caused by the intrinsic randomness. Results show that the new kind of non-stationarity is widespread in small-scale variations of CO2 turbulent fluxes. This finding reminds us that we need to handle the short-term averaged turbulent fluxes carefully, and we also need to re-screen the existing non-stationarity diagnosis methods because they could make a wrong diagnosis due to this new kind of non-stationarity.
Shaun Lovejoy
Nonlin. Processes Geophys., 29, 93–121, https://doi.org/10.5194/npg-29-93-2022, https://doi.org/10.5194/npg-29-93-2022, 2022
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The difference between the energy that the Earth receives from the Sun and the energy it emits as black-body radiation is stored in a scaling hierarchy of structures in the ocean, soil and hydrosphere. The simplest scaling storage model leads to the fractional energy balance equation (FEBE). We examine the statistical properties of FEBE when it is driven by random fluctuations. In this paper, we explore the statistical properties of this mathematically simple yet neglected equation.
Bérengère Dubrulle, François Daviaud, Davide Faranda, Louis Marié, and Brice Saint-Michel
Nonlin. Processes Geophys., 29, 17–35, https://doi.org/10.5194/npg-29-17-2022, https://doi.org/10.5194/npg-29-17-2022, 2022
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Present climate models discuss climate change but show no sign of bifurcation in the future. Is this because there is none or because they are in essence too simplified to be able to capture them? To get elements of an answer, we ran a laboratory experiment and discovered that the answer is not so simple.
Allen Hunt, Boris Faybishenko, and Behzad Ghanbarian
Nonlin. Processes Geophys., 28, 599–614, https://doi.org/10.5194/npg-28-599-2021, https://doi.org/10.5194/npg-28-599-2021, 2021
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The same power law we previously used to quantify growth of tree roots in time describes equally the assemblage of river networks in time. Even the basic length scale of both networks is the same. The one difference is that the basic time scale is ca. 10 times shorter for drainage networks than for tree roots, since the relevant flow rate is 10 times faster. This result overturns the understanding of drainage networks and forms a basis to organize thoughts about surface and subsurface hydrology.
Raphaël Hébert, Kira Rehfeld, and Thomas Laepple
Nonlin. Processes Geophys., 28, 311–328, https://doi.org/10.5194/npg-28-311-2021, https://doi.org/10.5194/npg-28-311-2021, 2021
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Paleoclimate proxy data are essential for broadening our understanding of climate variability. There remain, however, challenges for traditional methods of variability analysis to be applied to such data, which are usually irregular. We perform a comparative analysis of different methods of scaling analysis, which provide variability estimates as a function of timescales, applied to irregular paleoclimate proxy data.
Juan M. Restrepo, Alex Ayet, and Luigi Cavaleri
Nonlin. Processes Geophys., 28, 285–293, https://doi.org/10.5194/npg-28-285-2021, https://doi.org/10.5194/npg-28-285-2021, 2021
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A homogenization of Navier–Stokes to wave scales allows us to determine that air bubbles suspended near the ocean surface modify the momentum equation, specifically enhancing the vorticity in the flow. A model was derived that relates the rain rate to the production of air bubbles near the ocean surface. At wave scales, the air bubbles enhance the wave dissipation for small gravity or capillary waves.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 28, 43–59, https://doi.org/10.5194/npg-28-43-2021, https://doi.org/10.5194/npg-28-43-2021, 2021
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Fluid parcels transported in complicated flows often contain subsets of particles that stay close over finite time intervals. We propose a new method for detecting finite-time coherent sets based on the density-based clustering technique of ordering points to identify the clustering structure (OPTICS). Unlike previous methods, our method has an intrinsic notion of coherent sets at different spatial scales. OPTICS is readily implemented in the SciPy sklearn package, making it easy to use.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys., 27, 133–145, https://doi.org/10.5194/npg-27-133-2020, https://doi.org/10.5194/npg-27-133-2020, 2020
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This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.
Omer San and Romit Maulik
Nonlin. Processes Geophys., 25, 457–476, https://doi.org/10.5194/npg-25-457-2018, https://doi.org/10.5194/npg-25-457-2018, 2018
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We study the scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability.
Benjamin K. B. Abban, A. N. (Thanos) Papanicolaou, Christos P. Giannopoulos, Dimitrios C. Dermisis, Kenneth M. Wacha, Christopher G. Wilson, and Mohamed Elhakeem
Nonlin. Processes Geophys., 24, 569–579, https://doi.org/10.5194/npg-24-569-2017, https://doi.org/10.5194/npg-24-569-2017, 2017
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We examine rainfall-induced change in soil microroughness of bare soil surfaces in agricultural landscapes with initial microroughness length scales on the order of 2 mm (smooth surfaces). Past studies have focused on scales of 5–50 mm and have reported a decrease in miccroroughness. Findings in this study show a consistent increase in microroughness under rainfall action for initial length scales of 2 mm. Thus, rainfall–surface interactions can be different for smooth and rough surfaces.
Manuel Tijera, Gregorio Maqueda, and Carlos Yagüe
Nonlin. Processes Geophys., 23, 407–417, https://doi.org/10.5194/npg-23-407-2016, https://doi.org/10.5194/npg-23-407-2016, 2016
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This work investigates the possible correlations between the integral scale of the turbulent stratified flows in the atmospheric boundary layer and parameters characterizing topological features of the wind velocity field, such as fractal dimension and its stability properties, studied through the bulk Richardson number. Fractal dimension and the integral scale of the horizontal (u') and vertical (w') velocity fluctuations have been calculated using the mean wind direction as a framework.
José Manuel Mirás-Avalos, Emiliano Trigo-Córdoba, Rosane da Silva-Dias, Irene Varela-Vila, and Aitor García-Tomillo
Nonlin. Processes Geophys., 23, 205–213, https://doi.org/10.5194/npg-23-205-2016, https://doi.org/10.5194/npg-23-205-2016, 2016
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The current study aimed to describe the dynamics of soil water content at three depths in a vineyard under rain-fed and irrigation conditions and to assess the multifractality of these time data series. Soil water content data series obeyed power laws and tended to behave as multifractals. Our results suggest that singularity spectra were useful for characterising temporal variability of soil water content, distinguishing patterns among series registered under rain-fed and irrigation treatments.
V. K. Gupta and O. J. Mesa
Nonlin. Processes Geophys., 21, 1007–1025, https://doi.org/10.5194/npg-21-1007-2014, https://doi.org/10.5194/npg-21-1007-2014, 2014
Cited articles
Biswas, A. and Si, B. C.: Scales and locations of time stability of soil water storage in a hummocky landscape, J. Hydrol., 408, 100–112, https://doi.org/10.1016/j.jhydrol.2011.07.027, 2011a.
Biswas, A. and Si, B. C.: Identifying scale specific controls of soil water storage in a hummocky landscape using wavelet coherency, Geoderma, 165, 50–59, https://doi.org/10.1016/j.geoderma.2011.07.002, 2011b.
Biswas, A. and Si, B. C.: Revealing the Controls of Soil Water Storage at Different Scales in a Hummocky Landscape, Soil Science Society of America Journal, 75, 1295-1306, https://doi.org/10.2136/sssaj2010.0131, 2011c.
Biswas, A. and Si, B. C.: Identifying effects of local and nonlocal factors of soil water storage using cyclical correlation analysis, Hydrol. Process., 26, 3669–3677, https://doi.org/10.1002/hyp.8459, 2012.
Biswas, A., Chau, H. W., Bedard-Haughn, A. K., and Si, B. C.: Factors controlling soil water storage in the hummocky landscape of the Prairie Pothole Region of North America, Canadian Journal of Soil Science, 92, 649-663, 10.4141/cjss2011-045, 2012a.
Biswas, A., Cresswell, H. P., and Si, B. C.: Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review, in: Fractal Analysis and Chaos in Geosciences, edited by: Ouadfeul, S.-A., InTech, Croatia, 109–138, 2012b.
Biswas, A., Zeleke, T. B., and Si, B. C.: Multifractal detrended fluctuation analysis in examining scaling properties of the spatial patterns of soil water storage, Nonlin. Processes Geophys., 19, 227–238, https://doi.org/10.5194/npg-19-227-2012, 2012c.
Caniego, F. J., Martí, M. A., and San José, F.: Rényi dimensions of soil pore size distribution, Geoderma, 112, 205–216, 2003.
Chhabra, A. and Jensen, R. V.: Direct determination of the f(α) singularity spectrum, Phys. Rev. Lett., 62, 1327–1330, 1989.
Entin, J. K., Robock, A., Vinnikov, K. Y., Hollinger, S. E., Liu, S. X., and Namkhai, A.: Temporal and spatial scales of observed soil moisture variations in the extratropics, J. Geophys. Res.-Atmos., 105, 11865–11877, https://doi.org/10.1029/2000jd900051, 2000.
Evertsz, C. J. G. and Mandelbrot, B. B.: Self-similarity of harmonic measure on DLA, Physica A, 185, 77–86, https://doi.org/10.1016/0378-4371(92)90440-2, 1992.
Fang, X. and Pomeroy, J. W.: Modelling blowing snow redistribution to prairie wetlands, Hydrol. Process., 23, 2557–2569, https://doi.org/10.1002/hyp.7348, 2009.
Feddes, R. A., Kowalik, P. J., and Zaradny, H.: Simulation of field water use and crop yield., John Wiley & Sons Inc., New York, 1978.
Grassberger, P. and Procaccia, I.: Characterization of Strange Attractors, Phys. Rev. Lett., 50, 346–349, 1983.
Gray, D. M., Landine, P. G., and Granger, R. J.: Simulating infiltration into frozen Prairie soils in streamflow models, Can. J. Earth Sci., 22, 464–472, 1985.
Grayson, R. B., Western, A. W., Chiew, F. H. S., and Bloschl, G.: Preferred states in spatial soil moisture patterns: Local and nonlocal controls, Water Resour. Res., 33, 2897–2908, 1997.
Grego, C. R., Vieira, S. R., Antonio, A. M., and Della Rosa, S. C.: Geostatistical analysis for soil moisture content under the no tillage cropping system, Scientia Agricola, 63, 341–350, 2006.
Hayashi, M., van der Kamp, G., and Rudolph, D. L.: Water and solute transfer between a prairie wetland and adjacent uplands, 2. Chloride cycle, J. Hydrol., 207, 56–67, 1998.
Hu, Z. L., Islam, S., and Cheng, Y. Z.: Statistical characterization of remotely sensed soil moisture images, Remote Sens. Environ., 61, 310–318, 1997.
Kachanoski, R. G. and de Jong, E.: Scale dependence and the temporal persistence of spatial patterns of soil water storage, Water Resour. Res., 24, 85–91, https://doi.org/10.1029/WR024i001p00085, 1988.
Kim, G. and Barros, A. P.: Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data, Remote Sens. Environ., 83, 400–413, 2002.
Koster, R. D., Dirmeyer, P. A., Guo, Z. C., Bonan, G., Chan, E., Cox, P., Gordon, C. T., Kanae, S., Kowalczyk, E., Lawrence, D., Liu, P., Lu, C. H., Malyshev, S., McAvaney, B., Mitchell, K., Mocko, D., Oki, T., Oleson, K., Pitman, A., Sud, Y. C., Taylor, C. M., Verseghy, D., Vasic, R., Xue, Y. K., Yamada, T., and Team, G.: Regions of strong coupling between soil moisture and precipitation, Science, 305, 1138–1140, https://doi.org/10.1126/science.1100217, 2004.
Liu, H. H. and Molz, F. J.: Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res., 33, 2483–2488, https://doi.org/10.1029/97WR02188, 1997.
Mandelbrot, B. B.: The fractal geometry of nature, W. H. Freeman and Company, San Francisco, 1982.
Mascaro, G., Vivoni, E. R., and Deidda, R.: Downscaling soil moisture in the southern Great Plains through a calibrated multifractal model for land surface modeling applications, Water Resour. Res., 46, W08546, https://doi.org/10.1029/2009WR008855, 2010.
Meneveau, C., Sreenivasan, K. R., Kailasnath, P., and Fan, M. S.: Joint multifractal measures: Theory and applications to turbulence, Phys. Rev. A, 41, 894–913, 1990.
Montero, E. S.: Rényi dimensions analysis of soil particle-size distributions, Ecol. Model., 182, 305–315, https://doi.org/10.1016/j.ecolmodel.2004.04.007, 2005.
National Wetlands Working Group: The Canadian wetland classification system, University of Waterloo, ON, 1997.
Pomeroy, J. W. and Gray, D. M.: Snowcover, accumulation, relocation, and management, in: NHRI Science Report No. 7, Environment Canada, Saskatoon, SK, 144 + xiii pp., 1995.
Pomeroy, J. W., de Boer, D., and Martz, L. W.: Hydrology and water resources, in: Saskatchewan: Geographic Perspectives, edited by: Thraves, B., CRRC, Regina, SK, Canada, 2007.
Quinn, P.: Scale appropriate modelling: representing cause-and-effect relationships in nitrate pollution at the catchment scale for the purpose of catchment scale planning, J. Hydrol., 291, 197–217, https://doi.org/10.1016/j.jhydrol.2003.12.040, 2004.
Rodriguez-Iturbe, I., Vogel, G. K., Rigon, R., Entekhabi, D., Castelli, F., and Rinaldo, A.: On the spatial-organization of soil-moisture fields, Geophys. Res. Lett., 22, 2757–2760, https://doi.org/10.1029/95gl02779, 1995.
Schertzer, D. and Lovejoy, S.: Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res.-Atmos., 92, 9693–9714, https://doi.org/10.1029/JD092iD08p09693, 1987.
Sivapalan, M.: Scaling of hydrologic parameterizations, 1. Simple models for the scaling of hydrologic state variables, examples and a case study, Center for Water Research, University of Western Australia, Nedlands, WA, Australia, 1992.
van der Kamp, G., Hayashi, M., and Gallen, D.: Comparing the hydrology of grassed and cultivated catchments in the semi-arid Canadian prairies, Hydrol. Process., 17, 559–575, https://doi.org/10.1002/hyp.1157, 2003.
Voss, R.: Fractals in nature: From characterization to simulation, in: The Science of Fractal Images, edited by: Peitgen, H.-O., and Saupe, D., Springer, New York, 21–70, 1988.
Western, A. W., Grayson, R. B., Bloschl, G., Willgoose, G. R., and McMahon, T. A.: Observed spatial organization of soil moisture and its relation to terrain indices, Water Resour. Res., 35, 797–810, 1999.
Zeleke, T. B. and Si, B. C.: Scaling properties of topographic indices and crop yield: Multifractal and joint multifractal approaches, Agron. J., 96, 1082–1090, 2004.
Short summary
We measure soil water at points (point scale) and try to understand how they vary over the landscape. Previous studies identified a statistical relationship between these scales only at the surface and not at depths. This study found that the relationship stands at different depths. The relationship was very similar at different depths in drier season or in late summer and fall. A less similar relationship was observed between surface and subsurface layers in spring or in wetter seasons.
We measure soil water at points (point scale) and try to understand how they vary over the...
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