Abstract
Multi-compartment samplers (MCSs) measure unsaturated solute transport in space and time at a given depth. Sorting the breakthrough curves (BTCs) for individual compartments in descending order of total solute amount and plotting in 3D produces the leaching surface. The leaching surface is a useful tool to organize, present, and analyze MCS data. We present a novel method to quantitatively characterize leaching surfaces. We fitted a mean pore-water velocity and a dispersion coefficient to each BTC, and then approximated their values by functions of the rank order of the BTCs. By combining the parameters of these functions with those of the Beta distribution fitted to the spatial distribution of solutes, we described an entire leaching surface by four to eight parameters. This direct characterization method allows trends to be subtracted from the observations, and incorporates the effects of local heterogeneity. The parametric fit creates the possibility to quantify concisely the leaching behavior of a soil in a given climate under given land use, and eases the quantitative comparison of spatio-temporal leaching behavior in different soils and climates.
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Abbreviations
- BTC:
-
Breakthrough curve
- CDE:
-
Convection-dispersion equation
- CV:
-
Coefficient of variation
- EC:
-
Electrical conductivity
- MCS:
-
Multi-compartment sampler
- RMSE:
-
Root mean square error
- SSDC:
-
Spatial solute distribution curve
- STDEV:
-
Standard deviation
- a D :
-
Fitting parameter
- a v :
-
Fitting parameter
- A :
-
Sample collection area (L2)
- b D :
-
Fitting parameter
- b v :
-
Fitting parameter
- B :
-
Beta function
- c D :
-
Fitting parameter
- c v :
-
Fitting parameter
- C :
-
Solute flux concentration (ML−3)
- C*:
-
Scaled solute flux concentration (T−1)
- C 0 :
-
Area under breakthrough curve BTC C (ML−3T)
- C f :
-
Dimensionless flux-averaged concentration (−)
- D :
-
Dispersion coefficient (L2T−1)
- F :
-
Solute flux density (ML−2T−1)
- F O :
-
Observed solute flux density (ML−2T−1)
- F P :
-
Calculated solute flux density (ML−2T−1)
- k :
-
Sampling time index
- n :
-
Number of cells (−)
- m :
-
Total number of sampling rounds
- p :
-
Probability of the Beta variate as a function of coordinate x
- q :
-
Water flux density (LT−1)
- \({\underline q}\) :
-
Water flux density matrix (LT−1)
- R :
-
Retardation factor (−)
- s :
-
Cumulative sampling area (L2)
- S :
-
Leaching surface (ML−2T−1)
- t :
-
Time (T)
- t k :
-
Time (T) at which the kth set of samples was retrieved
- v :
-
Pore-water velocity (LT−1)
- V :
-
Water volume (L3)
- x i :
-
Horizontal Cartesian coordinate (i is counter 1,…,n)
- y i :
-
Horizontal Cartesian coordinate (i is counter 1,…,n)
- z :
-
Depth below soil surface (L)
- α :
-
Positive shape parameter
- μ :
-
Degradation parameter (T−1)
- γ :
-
Production parameter (ML−3T−1)
- σ 2 :
-
Variance
- ζ :
-
Positive shape parameter
- C :
-
Solute flux concentration
- f :
-
Flux-averaged
- F :
-
Solute flux density
- i :
-
Index for spatial variable x
- j :
-
Index for spatial variable y
- k :
-
Sampling time index since solute application
- n:
-
Normalized
- nm:
-
Normalized mean
- t :
-
Time
- w :
-
Index for pseudo-spatial variable s
- s :
-
Cumulative sampling area
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Acknowledgments
This research is supported by the Research Council for Earth and Life Sciences (ALW) with financial aid from the Netherlands Organization for Scientific Research (NWO).
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Bloem, E., de Gee, M. & de Rooij, G.H. Parameterizing the Leaching Surface by Combining Curve-Fitting for Solute Breakthrough and for Spatial Solute Distribution. Transp Porous Med 92, 667–685 (2012). https://doi.org/10.1007/s11242-011-9927-2
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DOI: https://doi.org/10.1007/s11242-011-9927-2