Evaluation of models for description of wet aggregate size distribution from soils of different land uses

Figures & data

Table 1 Average soil physical and chemical properties by the land use types

Land use types
	Dry farmland (n = 300)			Rangeland (n = 300)			Forestland (n = 400)
Soil properties^†	Mean	Min–Max	SD	Mean	Min–Max	SD	Mean	Min–Max	SD
pH	8.32	8.2–8.4	0.0957	8.20	8–8.3	0.1732	7.08	6.8–7.5	0.2714
EC (dS m^−1)	1.08	0.89–1.56	0.3244	1.57	0.87–2.56	1.20	1.26	0.87–2.4	0.5145
CCE (%)	16.04	10.5–23.2	5.414	5.25	0–15.15	8.5816	3.51	0–16.36	6.4384
SOC (%)	1.36	1.2–1.62	0.2435	2.79	2.65–2.93	0.1401	2.83	2.62–3.23	0.2067
Sand (%)	18.25	10–41	15.196	21	12–36	13.077	16.86	6–40	12.144
Silt (%)	36.75	31–46	6.898	35	34–36	1.041	38.86	31–50	6.067
Clay (%)	45	27–59	13.880	44	29–52	13	44.28	29–53	8.40
MWD (mm)	1.73	1.26–2.16	0.5171	3.85	3.80–3.92	0.0625	4.14	3.69–4.90	0.4861

^†EC: electrical conductivity, CCE: calcium carbonate equivalent, SOC: soil organic carbon, Min–Max: minimum and maximum values of soil parameters by the samples, SD: standard deviation of data for the samples, n: number of soil samples; MWD: mean weight diameter.

Table 2 Average values of goodness of fit criteria from the six models for each type of land use

Land use types
		Dry farmland (n = 300)		Rangeland (n = 300)		Forestland (n = 400)
Models		R^2	SSE	R^2	SSE	R^2	SSE
J	Mean	0.9612	0.040	0.9478	0.057	0.9493	0.055
	Min–Max	0.9455–0.9894	0.012–0.052	0.9282–0.9666	0.035–0.085	0.9344–0.9601	0.045–0.063
N	Mean	0.8909	0.098	0.9805	0.018	0.9814	0.017
	Min–Max	0.8735–0.9092	0.086–0.108	0.9790–0.9821	0.016–0.022	0.9560–0.9924	0.008–0.040
LN	Mean	0.9847	0.014	0.9726	0.025	0.9695	0.029
	Min–Max	0.9777–0.9942	0.006–0.019	0.9659–0.9785	0.020–0.029	0.9588–0.9775	0.020–0.035
R	Mean	0.9723	0.026	0.9517	0.045	0.9503	0.047
	Min–Max	0.9603–0.9902	0.010–0.033	0.9415–0.9591	0.037–0.051	0.9313–0.9608	0.038–0.058
FL	Mean	0.9808	0.014	0.9849	0.012	0.9851	0.012
	Min–Max	0.9718–0.9921	0.007–0.020	0.9830–0.9861	0.011–0.015	0.9811–0.9896	0.009–0.014
FR	Mean	0.9641	0.038	0.9969	0.003	0.9981	0.002
	Min–Max	0.9189–0.9827	0.018–0.091	0.9947–0.9983	0.002–0.006	0.9918–0.9996	0.0005–0.009

Models: Jaky (J), normal (N), log-normal (LN), Rosin-Rammler (R), Fredlund (FL); fractal (FR); R²: coefficient of determination; SSE: sum of square error; n: number of soil samples.

Figure 1 Comparative fit of six models on examples of wet sieving data for (a) dry farmland, (b) rangeland, (c) forestland. The models: FR (fractal model), FL (Fredlund model), R (Rosin-Rammler model), N (normal model), LN (log-normal model), J (Jaky model).

Figure 2 An example of appropriate fitting of the normal (N) or log-normal (LN) models on wet sieving data from dry farmland (Df) and forest (F).

Table 3 Average values of Mallows statistics (C_p) and Akaike’s information criterion (AIC) calculated for all of the soils from the five comparison models (normal model was the reference model)

Models
	J		LN		R		FL		FR
Statistics	Cp	AIC	Cp	AIC	Cp	AIC	Cp	AIC	Cp	AIC
Mean	13.87	−20.15	5.52	−24.38	12.00	−19.55	1.48	−27.17	−5.59	−42.35
Min	−6.17	−32.06	−4.61	−36.51	−4.34	−31.83	−2.54	−32.76	−6.69	−60.64
Max	46.78	−14.40	21.68	−20.22	37.17	−16.84	5.83	−22.68	−0.72	−13.80
SD	17.14	4.38	8.97	4.29	13.49	4.04	2.99	2.52	1.52	14.20

Models: Jaky (J), log-normal (LN), Rosin-Rammler (R), Fredlund (FL); fractal (FR). Mean, Min, Max and SD are respectively average, minimum, maximum and standard deviation of C_p and AIC values for all WASD data sets. Underlined mean values denote the optimum model in all of the studied soils (FR was the optimum model with the lowest C_p and/or AIC values).

Figure 3 Relative superiority of the comparison models in all of the study soils using Mallows statistics (Cp) and Akaike’s information criterion (AIC) statistics. The number above bars indicates the number of soils for which a model can be accepted instead of the normal model (N). The comparison model: FR (fractal model), FL (Fredlund model), LN (log-normal model), J (Jaky model), R (Rosin-Rammler model).