1. HIERARCHICAL SET OF MODELS TO ESTIMATE SOIL THERMAL DIFFUSIVITY
Soil Science Faculty
Moscow State University
Moscow, Russian Federation
Tatiana Arkhangelskaya and Ksenia Lukyashchenko
Parameterization
Statistics
Model evaluation
Background and objectives
Thermal diffusivity is equal to thermal conductivity divided by volumetric heat capacity and reflects both the ability of soil to transfer heat and its ability to change temperature when heat is supplied or withdrawn. The higher thermal diffusivity is, the thicker is the soil/ground layer in which the diurnal and seasonal fluctuations of temperature are registered and the smaller is the phase shift of soil thermal waves compared to surface fluctuations. So thermal diffusivity affects soil thermal regime which in turn determines surface radiation balance, soil hydrology and respiration.
Soil thermal diffusivity depends on bulk and particle densities, texture, organic matter and moisture. Many authors (de Vries, 1963; Johansen, 1975; McCumber – Pielke, 1981; Campbell, 1985) suggested models relating soil thermal properties to basic soil properties. But all these models were based on very limited databases, and when applied to independent samples gave RMSEs of % (Peters-Lidard et al., 1998; Usowicz and Usowicz, 2004; Côte, Konrad, 2005).
The objective of this work was to develop and evaluate a set of grouping-based
models to estimate soil thermal diffusivity from readily available information on basic soil properties. k0 a q0
b/2 q
R=0.64
R=-0.56
R=0.52
R=-0.29
R=-0.71
R=0.68
R=-0.67
R=0.74
R=-0.59
R=-0.72
R=-0.35
R=0.38
R=-0.68
R=0.51
R=0.12
R=-0.18
Average curves
Objects and methods
RMSE, 10-7 m2 s-1
RRMSE, %
Average curves
1.20 36
Universal model
1.27 38
Sand range models
0.95 28
Textural class models
0.86 26
Regression models
Hierarchical set of multiple regression models was developed using 67 data sets obtained for individual soil samples. “Universal model” is a single set of equations relating k0, a, q0, b to basic soil properties, developed for the whole database. “Sand range models” include three sets of equations developed for samples grouped according to sand content: sand<15% (31 case), 15%<sand<65% (23 cases), sand>65% (13 cases). “Textural class models” include nine sets of equations for each textural class from our database, some of which are presented below.
The Universal model used exact textural fraction contents and was based on the widest possible predictors range, but turned out to be even less accurate than the Average curves model, which used textural class name as the only pedotransfer input. The accuracy of these two models was not high: 1.27 and 1.20×10-7 m2 s-1 with the mean k value in the validation base 3.53×10-7 m2 s-1.
Grouping soils by sand contents significantly increased model accuracy: RRMSEs for three groups were 28% for the whole validation base (10 samples, 107 k(q) pairs), 25% for most coarse soils, 30% for intermediate sand contents and 23% for soils with sand<15%.
The best results were obtained for the Textural class models based on multiple regression analysis within each textural class. RRMSEs varied from 10% for loamy sands,12% for silty clay loams and 15% for silty clays to 31% for clay loams and 36% for sandy loams.
It seems that combining the grouping approach with the non-linear regression analysis may be fruitful for the further model development.
0.1–6.4
0.1–6.5
C, %
2.58–2.73
2.52–2.78
rs, kg m-3
880–1740
860–1820
rb, kg m-3
2–49
1–52
Clay, %
4–74
2–80
Silt, %
1–95
1–97
Sand, %
Model validation (10 samples)
Model development (67 samples)
Range
Model predictors
Silty clays Silty clay loams Loams
No.
k0, 10-7 m2 s-1
a, 10-7 m2 s-1
q0, m3 m-3 b
SIlty clays 9
1.01
1.77
0.36
0.31
Silty clay loams 8
1.81
1.71
0.34
0.30
Clay loams 3
1.31
2.94
0.43
0.33
Sandy clay loams 2
1.84
2.67
0.16
Loams 11
2.00
1.94
0.37
0.38
Silt loams 19
2.29
0.59
Sandy loams
3.83
3.37
0.22
Loamy sands 5
3.34
3.98
0.62
Sands 7
2.46
5.08
1.13
Silt loams Loamy sands Sands
Unsteady-state* k(q) measurements on 77 intact soil samples were used. Sample height/diameter were 10/3.8 cm (53 cases) and 7/5 cm (14 cases).
*Parikh, R.J., Havens, J.A., Scott, H.D., Thermal diffusivity and conductivity of moist porous media. Soil Science Society of America Journal 43, 1050–1052.
Arhangelskaya, T.A., Thermal diffusivity of gray forest soils in the Vladimir Opolie region. Eurasian Soil Science 37 (3), 285–294.
The research is supported by the Russian Foundation for Basic Research (project № ).