SOIL SUBMODEL

L.J. Hagen

TABLE OF CONTENTS

INTRODUCTION

Submodel Objectives

submodel Outputs

SUBMODEL COMPUTATION SCHEME

PROCESS EFFECTS ON SOIL TEMPORAL PROPERTIES

Ridge and Furrow Dike Height

Random Roughness Height

Crust

Crust Thickness

Crust Cover Fraction

Crust Stability

Loose Erodible Material on Crust

Dry Aggregate Stability

Aggregate Size Distribution

Bulk Density

Crust and Aggregate Density

REFERENCES

INTRODUCTION

The SOIL submodel is one of seven major science submodels included in the Wind Erosion Prediction System (WEPS). The objective of the SOIL submodel is to simulate the soil temporal properties which control wind erodibility of soil on a daily basis in response to various driving processes. On days when wind erosion or management activities occur, the EROSION and MANAGEMENT submodels also may update some of the same soil temporal variables.

The spatial domain affected by the SOIL submodel consists of the entire simulation region whose boundaries are specified by the user. The simulation region is assumed to be homogeneous in the horizontal direction, but not in the vertical direction. The SOIL submodel updates the relevant temporal variables in a series of soil layers by simulating the effects of both aggregation and deaggregation processes.

Symbols, definitions, and units used in this technical description are defined in the text and at the end of the chapter. The development of the SOIL submodel represents a new area in wind erosion research. In general, the variation in the temporal soil variables which control soil wind erodibility has not been widely investigated, so additional experimental research is ongoing for many of the topics addressed in this technical description. Updates and maintenance to this submodel will be necessary as new and more reliable data become available.

SOIL SUBMODEL COMPUTATION SCHEME

In selecting a computation scheme, we considered several characteristics of the problem. First, the temporal variable to be updated is generally a function of more than one driving process as well as intrinsic soil properties. Unfortunately, temporal properties at a point in time are often the result of a combination of prior processes, and thus, difficult to interpret. Moreover, researchers generally try to sort the field data and conduct laboratory experiments in order to determine the relationship between individual driving processes and a selected temporal soil variable. Two approaches were used in updating the soil erodibility variables.

For the first approach, a simple, typical case is illustrated in Fig S-1., where the individual effects of process A and process B on ridge height are known. In the field, however, these driving processes, A and B, may occur in many combinations of sequences. An example is illustrated by the arrow sequence of Fig S-1. Thus, the computation scheme must be able to accommodate the relationships which have been developed for single processes and combine them in a variety of sequences.

The approach used to update variables such as ridge height is illustrated in the following section. It was assumed that an explicit relationship [S-1] is known from field data or other experiments.

where

Y	=	a dependent soil temporal variable, and

Xj	=	an independent driving processes variable which changes Y.

Now, in principle, one can express Xj in terms of Y, i.e.,

Equation [S-2] often can be derived from [S-1] algebraically. However, some solutions may not be analytic, so numerical values for Xj must be obtained using an iteration scheme. Further, note that [S-2] should be single-valued. In the event that a process is not single valued in Y, i.e., causes both aggregation and deaggregation under different conditions, it is useful to separate the effects into separate aggregation and deaggregation equations and calculate the effects successively.

Now, in principle, one can express Xj in terms of Y, i.e.,

Because the dependent Y variable can be changed by several processes, updating the Y on a daily basis requires two steps. First, an "equivalent" value for the independent variable must be calculated, i.e.,

where,

Xi,j	=	the current "equivalent" value which the jth process would

have, if it alone had caused the current value of the dependent variable Yi; where 'i' refers to the day.

The second step is then to update the dependent variable using the equation

where,

Xj = the daily increment of the jth driving force.

A second approach used to update some of the variables was to determine the average and standard deviation of a given variable from field measurements. Prediction equations were then developed to relate these results to intrinsic soil properties such as the sand, silt, and clay fractions.

Next, each temporal variable for each soil was given a non-dimensional range of zero to one bounded by the average ± two standard deviations. Over the non-dimensional range, processes effects on individual variables were assigned. On a daily basis, the prior-day non-
dimensional variables were calculated and processes for the current day were applied to update the non-dimensional variables. Finally, the non-dimensional updated variables were converted to dimensional values for use by other submodels. Except when soils were frozen, the preceding approach constrained the temporal variables within the limits bounded by the average ± two standard deviations of the measured values.

Table S-1 presents a matrix of the temporal soil variables that are updated by SOIL and the driving processes that are currently considered in updating the temporal variables. Note that furrow irrigation and biological "glue" processes are not yet simulated.

Table S-1. Soil submodel variable and process matrix.

Soil

Temporal

Variables	Surface Processes	Layer Processes

Rain

Sprinkler

Irrigation

Snow

melt

Wet/dry

Freeze/

thaw

Freeze/

dry
Roughness:
Ridge Height	X	X	X
Dike Height	X	X	X
Random	X	X	X
Crust:
Depth	X	X	X
Cover fraction	X	X	X
Density	X	X	X
Stability	X	X	X	X	X	X
Loose mass	X	X	X
Loose cover	X	X	X
Aggregates:
Size distribution	X	X	X	X	X	X
Dry stability	X	X	X	X	X	X
Density	X	X	X	X	X	X
Bulk density	X	X	X

PROCESS EFFECTS ON SOIL TEMPORAL PROPERTIES

RIDGE AND FURROW DIKE HEIGHT

Ridges and dikes are degraded by both precipitation and wind erosion. In addition, the degradation rate depends on the relative ridge height. Hence, before an update for daily precipitation, the current height is used to calculate an apparent cumulative precipitation which could have produced that ridge height. Solving a modification of equation (S-6) for bare ridges gives:

where

CUMP = cumulative depth of snowmelt, rainfall and sprinkler irrigation

water (mm),

SZrg-1 = prior day ridge height (mm),

SZrgo = initial ridge height after tillage (mm), and

CF1rg = correction factor for ridge scale.

Then to update ridge height, an empirical equation developed by Lyles and Tatarko (1987) from field measurements was approximated, along with two empirical coefficients, as

where

DCUMP	= daily depth of snowmelt, rainfall and sprinkler irrigation water in mm,

SZrg	= updated ridge height (mm),

CF2cov	= correction factor for biomass cover, and

SVroc = surface layer soil volume of rock (fraction).

Ridges with various height/spacing ratios respond differently to precipitation. The ridges used to derive the response to precipitation in equation [S-5] ranged from 30 to 100 mm in height. Thus, the effect of scale for large ridges, such as lister ridges, was missing. An empirical correction factor for ridge scale was developed. Typical initial ridges (Lyles and Tatarko, 1987) had the relation

where

SXrg = ridge spacing (mm).

From geometric calculations, one can show that volume of soil which must be eroded to reach new height/spacing ratios is directly proportional to ridge height. The correction factor for ridge scale was estimated as

The correction factor for biomass cover sheltering the soil surface is estimated as

where

BFscv = fraction of biomass standing cover, and

BFfcv = fraction of biomass flat cover

Eq. [S-5] and [S-6] correspond to equations [S-3] and [S-4], respectively.

RANDOM ROUGHNESS

Random roughness can also be degraded by both precipitation and wind erosion. Similar to ridges, the degradatation rate depends on relative roughness height. Hence, prior day random roughness height is used to calculate an apparent cumulative precipitation which could have produced that roughness. Solving a modified version of equation (S-13) for a bare surface gives:

where

SZrr-1 = random roughness on prior day (mm),

SZrro = random roughness after last tillage using Allmaras et al. (1966) definition(mm), and

Arr, Crr = regression coefficients.

where

SFsan	=	soil fraction sand in first layer (kg/kg), and

SFsil	=	soil fraction silt in first layer (kg/kg).

Reduction in random roughness height is predicted for bare soil (Potter, 1990b; Zobeck and Onstad, 1987), but equation [S-13] also includes empirical cover factors for biomass and rock

where

SZrr	=	updated random roughness, respectively, using Allmaras' et al. (1966) definition (mm),

Arr, Crr	=	regression coefficients.

CRUST

The term 'crust' in WEPS refers to the near-surface consolidated zone which occurs after the addition of water to the surface or the puddling of surface soil when super-saturated. The equations which govern the changes in crust properties from addition of water will be presented in this section, and equations for the puddling effect will be included later in the layer process section.

CRUST THICKNESS

The apparent precipitation based on crust thickness is:

where

SZcr-1 = prior day crust thickness (mm), and

SFcla = soil fraction clay in top layer.

The basic structure for simulation of crust thickness is based on that reported by Farres (1978) and data of Zobeck (personal communication). The initial surface condition is aggregated, and the crust thickness grows toward limits imposed by intrinsic soil properties. An estimate of the crust thickness when water additions exceed 10 mm is

where

SZcr	= updated crust thickness (mm).

CRUST COVER FRACTION

The apparent cumulative precipitation based on crust cover fraction is:

where

SFcr-1 = prior day crust cover.

An empirical surface crust cover fraction after rainfall was developed from a 3-year study at Big Spring, Texas (Zobeck and Popham, 1992).

where

SFcr	= soil fraction crust cover,

DCUMP	= daily snowmelt, sprinkler irrigation, and rainfall (mm), and

CUMP	= prior cumulative snowmelt, sprinkler irrigation, and rainfall (mm).

CRUST STABILITY

Current data on crust stability show it may be less or close to that of the parent surface aggregates. Measured abrasion resistance on simulated crusts (Zobeck, 1991) found abrasion rates similar to that predicted for aggregates. Hence, crust stability will be estimated as

where

SEag	=	aggregate stability, ln(J/kg) of crushing energy of top layer, and

SEcr	=	crust stability, ln(J/kg) of crushing energy.

LOOSE ERODIBLE MATERIAL ON CRUST

The loose erodible material is defined as the single grains and water stable aggregates which occur on crusted surfaces after rainfall or sprinkler irrigation. Loose material on the crust was sampled using a vacuum system (Zobeck, 1989). Simulated crusts using two rainfall intensities on 13 mineral soils were tested (Zobeck, 1991). A prediction equation for maximum loose mass is:

with and upper limit of:

where

SFcce	=	soil fraction calcium carbonate equivalent (kg/kg),

SFom	=	soil fraction organic matter (kg/kg),

SMXlos	=	maximum loose erodible material on crust (kg/m2), and

SF84 = soil fraction less than 0.84 mm.

Equation [S-19] is valid only when cumulative rainfall and sprinkler irrigation (CUMSR) exceed 10 mm.

As precipitation accumulates the loose material mass slowly decreases as (Zobeck and Popham, 1992; Potter, 1990a)

where

SMlos = loose mass on surface crust (kg/m2),

SMlos-1 = loose mass on surface crust (kg/m2),

DCUMSR = daily sprinkler irrigation and rainfall (mm).

Another process which acts to consolidate loose material is snowmelt. Snow does not melt uniformly over the field, so we estimate about 1.0 mm of melt may consolidate about 10 percent of the loose material. An approximation for this process is:

where

HGsnom	=	daily snowmelt (mm)

The cover fraction of loose, erodible soil on the crust is estimated from the mass of loose soil and the height of the surface roughness elements. The geometric mean diameter of the loose material was assumed to be 0.5 mm, and the bulk density as 1.2 Mg m-3. For a smooth surface, the loose material was assumed to remain in a single layer until cover fraction was about 0.6 and then begin to overlap to give surface cover as:

where

SFXlos = soil fraction cover of loose material on crust, and

CRlos = correction coefficient for surface roughness.

In the presence of roughness elements, the wind tends to concentrate the loose material in sheltered areas and, thus reduce the surface cover. From geometric analysis, we found a depth of loose material equal 0.2 times the roughness height was needed to cover the roughness elements. For a rough surface, the loose surface cover coefficient was estimated as:

where

SZ = maximum of the ridge or 4 times random roughness height (mm).

DRY AGGREGATE STABILITY

Experimental results show abrasion coefficients are linearly related to natural log of dry aggregate crushing energy (Hagen, Skidmore, and Saleh, 1992). Because it is practical to measure from small field samples, the Ln of crushing energy will be used as the measure of dry aggregate stability in WEPS. From sampling 10 soils periodically over 3 years (Skidmore and Layton, 1992), the average aggregate stability was:

with the estimate

where

SEavgag = mean of natural log aggregate crushing energies, Ln(J/kg).

The mean coefficient of variation (CV) averaged over all soils was 0.16.

Several processes affect the aggregate stability including freeze/thaw, freeze/dry, wet/dry, overburden pressure, and biological (glue). Moreover, these processes may cause increases or decreases in stability depending upon soil and process conditions. We describe an approximate method to estimate dry aggregate stability. First, determine a maximum and a minimum aggregate stability for each soil as follows:

The soil aggregate and crust stabilities are modified by the layer processes defined in Table S-2.

Table S-2. Decision matrix for soil layer processes and states.

Daily

Processes

Simulated

Final State	Soil Temperature (0C) **
Current Day	Prior Day
Maximum Temperature	Minimum

Temperature	Maximum

Temperature
Wet	Unfrozen	> 0	> 0
Dry	Unfrozen	> 0	> 0
Wet + Freeze	Frozen	< 0	>0
Dry + Freeze	Frozen	< 0	>0
Thaw + Wet	Unfrozen	> 0	< 0
Thaw + Dry	Unfrozen	> 0	< 0
Freeze & Thaw

+ Wet	Unfrozen	> 0	< 0	> 0
Freeze & Thaw

+ Dry	Unfrozen	> 0	< 0	> 0
Wet while

Frozen	Frozen

< 0	< 0
Dry while

Frozen	Frozen

< 0	< 0

** Assumes minimum temperature in early A.M. and maximum temperature about 2 P.M.

???? What should happen at zero? (Code may have error at that point)

The measured range of dry stabilities was derived from the intrinsic soil properties. However, the updating processes are applied to non-dimensional stabilities for the prior day (SEag-1*) that are estimated as

In WEPS, wind-driven raindrop splash erosion is ignored, and erosion is simulated only for dry soils. Hence, when soil moisture is greater than wilting point, the simulated daily stability values (SEag1) are unmeasured, pseudo-stabilities that would increase to the measured dry stability, if the soil dried to equal or less than the wilting point moisture.

A non-dimensional average soil moisture for the prior day (Hrwc-1*) and the current day (HRwc1*) are also used in the updating processes.

where

HRwcs = gravimetric water content at soil saturation (kg kg-1), and

HRwcw = gravimetric water content at soil wilting~15 bar (kg kg-1).

Updating stability with unfrozen wetting is simulated as:

where

k4w = coefficient for wetting (1.0)

Updating stability with unfrozen drying using the drying coefficient (k4d) is:

where

SZlyd = depth to bottom of a soil layer from surface (mm).

By making the drying coefficient (k4d) a function of depth, stability of aggregates near the surface may be decreased, while at other depths stability may increased by a wetting and drying cycle as illustrated in Fig. S-2. A partial cycle will, of course, result in smaller changes in stability than shown in Fig. S-2.

Figure S-2. Simulated stability changes caused by wetting an aggregate with initial non-
dimensional stability of 0.8 to 0.85 field capacity and then drying the aggregate to wilting point at two different soil depths.

Updating stability for freezing process is done in two steps. First, there is expansion and water migration to freezing layer using current day relative water content:

Then solidifying (freezing):

where

k4fs = freezing solidification coefficient (4.25), and

k4f = water migration and freezing expansion coefficient (1.4).

Updating stability for freezing/thawing process is done in several steps. First is expansion and water migration to freezing layer using prior day relative water content:

Then solidifying (SEagf-1) using prior day water content:

The thawing process is also composed of two steps:

First, thaw

and then water migration and shrinkage using the after-thaw drying coefficient (k4td) is

Alternatively, if thawing occurs at a high moisture content [i.e., k4f (HRwc-1*) > 1.0], then soil puddling is simulated instead of thawing as

Change in relative stability caused by wetting while soil is frozen is simulated as

Change in relative stability caused by drying while soil is frozen is simulated as

The final step is to convert the non-dimensional stability to a quasi-stability or, if the soil is dry, to the real stability as

Non-dimensional dry aggregate stabilities for the prior day (SE-1*) and the current day (SE1*) for non-frozen soil are also calculated for use in simulating changes in the aggregate size distribution as

If soil is frozen, then

AGGREGATE SIZE DISTRIBUTION -ASD

Among the variables in the soil submodel, ASD is one of the most important. It is important, because it has strong influence on predictions of erosion (as in WEQ), and it varies widely in response to various processes. In addition to updating surface ASD, the SOIL submodel must also update ASD in all other soil layers. It is important that the SOIL submodel include aggregation processes which increase ASD in the tillage zone. Otherwise, after few iterations the deaggregation processes in the SOIL and MANAGEMENT submodels only return a minimum value of ASD to the EROSION submodel.

The aggregate size distribution of field soils generally fits an abnormal log-normal distribution, which is defined by four parameters - a geometric mean diameter (SLagm) and geometric standard deviation (S0ags), coupled with upper (SLagx) and lower (SLagn) limit parameters. The lower limit is about 0.001 to 0.015 mm, and varies as a function of soil intrinsic properties. The SOIL and MANAGEMENT submodels must update the SLagm, S0ags, and SLagx in response to the driving forces.

Similar to the representation of aggregate stability, aggregate mean geometric diameter was related to intrinsic soil properties. To begin, the average aggregate size fraction less than 0.84 mm diameter (SF84m) was calculated using a regression equation (Fryrear, et al., 1994) as:

with the following limits:

SF om ≤ 0.03, SF caco3 ≤ 0.20, SF cla ≤ 0.40, and SF san / SF cla ≤ 40.

Over time, weathering and tillage cause variations in SF84, and the standard deviation is approximately:

Next, a regression equation was developed for the geometric mean diameter as:

Finally, maximum and minimum values for geometric mean aggregate diameters were estimated as:

where

SLmin = minimum value for geometric mean aggregate diameter (mm), and

SLmax = maximum value for geometric mean aggregate diameter (mm).

The parameter that is updated is the prior day non-dimensional aggregate geometric mean diameter defined as

The processes that control aggregate stability, also affect aggregate size distribution. Hence, the non-dimensional aggregate stability is used to update the aggregate size distribution as follows:

When soil freezes (SE0* < 1.0 and SE1* > 1.0), the current day non-dimensional geometric mean diameter (gmd1) is estimated as

When frozen soil thaws (SE-1* > 1.0 and SE1* < 1.0), or the soil is at maximum stability the update estimates gmd1 based on SE1* as (Fig. S-3)

where

c4p = coefficient (0.6)

When the soil is not frozen and stability is not changing (SE0* = SE1*), the gmd1 moves slowly toward the average value (Fig. S-3) as

Figure S-3. Plot of equation (S-43) illustrating estimated average gmd1* as a function of SE1*.

Cumulative rainfall generally decreases gmd of	the surface layer of sandy soils (Zobeck and Popham, 1990). Hence, when the soil is not frozen, but stability is changing (SE0* SE1*), the gmd1 moves toward average values using the following empirical steps:

The companion equation is given by

Finally, the updated gmd1 is

and the dimensioned value is

at present, the S0ags will be linked to SLagm as

Finally, SLagx also will be linked to SLagm and S0 ags as

BULK DENSITY

In the SOIL submodel, the 'settled' bulk density (SD sblk) in any layer of mineral soil is estimated using the intrinsic properties of the soil layer as inputs to Rawls' (1983) prediction diagram.

Slow setting toward the settled bulk density is simulated on a daily basis as

where

SDblk1	=	current day layer bulk density (Mg/m3), and

SDblk-1	=	layer bulk density on prior day (Mg/m3).

The soil bulk density is further modified when water infiltration occurs in a given soil layer.

An initial value is assigned to a wet bulk density (SD wblk 1) as

Then, for each 5 mm of water infiltration in a layer, a new wet bulk density is calculated as

where the subscript i refers to the ith iteration.

Finally, a weighted bulk density for the current day is calculated as a weighted average of the dry and wet bulk densities as:

where

SZ wlyt = wetted depth thickness in layer (mm),and

SZ lyt = layer thickness (mm).

CRUST AND AGGREGATE DENSITY

In WEPS, the aggregate density is input as a constant

where

SDag = Soil aggregate density (Mg/m3).

As suggested by Zobeck (October 1991), the following equation is used for crust density:

where

SDblk 0 = Soil bulk density of the top layer (Mg m-3)

REFERENCES

Allmaras, R.R., R.E. Burwell, W.E. Larson, and R.F. Holt. 1966. Total porosity and random roughness of the interrow zone as influenced by tillage. USDA Cons. Res. Rpt. 7.

Farres, P. 1978. The Role of Time and Aggregate Size in the Crusting Process. Earth Surface Processes 3:243-254.

Hagen, L.J., E.L. Skidmore, and A. Saleh. 1992. Wind erosion: Predictions of aggregate abrasion coefficients. Trans. Amer. Soc. Agric. Engin. 35(6):1847-1850.

Lyles, Leon and J. Tatarko. 1987. Precipitation Effects on Ridges Created by Grain Drills. J. Soil and Water Conserv., 42(4): 269-271.

Potter, K.N. 1990a. Estimating wind-erodible materials on newly crusted soils. Soil Sci.150(5):771-776.

Potter, K.N. 1990b. Soil properties effect on random roughness decay by rainfall. Trans. Amer. Soc. Agric. Engin. 33(6): 1889-1892.

Rawls, W.J. 1983. Estimating Soil Bulk Density From Particle Size Analysis and Organic Matter Content. Soil Sci, 135(2): 123-125.

Skidmore, E.L. and J. Layton. 1992. Dry Soil Aggregate Stability as Influenced by Selected Soil Properties. Soil Sci. Soc. Amer. J. 56:557-561.

Zobeck, T.M. 1989. Fast-Vac A vacuum system to rapidly sample loose granular material. Trans. Amer. Soc. Agric. Engin. 32(4):1316-1318.

Zobeck, T.M. 1991. Abrasion of crusted soils: influence of abrader flux and soil properties. Soil Sci. Soc. Am. J. 55:1091-1097.

Zobeck, T.M. and T.W. Popham. 1990. Dry aggregate size distribution of sandy soils as influenced by tillage and precipitation. Soil Sci. Soc. Am. 54(1):198-204.

Zobeck, T.M. and T.W. Popham. 1992. Influence of microrelief, aggregate size, and precipitation on soil crust properties. Trans. Amer. Soc. of Agric. Engin. 35(2):487-492.

Zobeck, T.M. and C.A. Onstad. 1987. Tillage and rainfall effects on random roughness: a review. Soil and Tillage Research 9:1-20.

LIST OF SYMBOLS, DEFINITIONS, AND UNITS

-------------------------------------------------------------------------------------------------------------

SYMBOL	DESCRIPTION	UNIT
-1,1	subscripts indicating prior and current day values	---
Arr, Crr	regression coefficients for random roughness	---
BFscv	fraction of growing plant and residue biomass standing cover	m2/m2
BFfcv	biomass fraction of flat cover	---
c4p	coefficient (0.6)	---
CF2cov	correction factor for biomass cover	---
CF1rg	correction factor for ridge scale	---
CUMP	cumulative depth of snowmelt, rainfall and sprinkler irrigation water	mm
CUMSR	cumulative sprinkler irrigation and rainfall	mm
DCUMP	daily total depth of snowmelt, rainfall and sprinkler irrigation water	mm
DCUMSR	daily total sprinkler irrigation and rainfall	mm
gmd*	non-dimensional aggregate geometric mean diameter	---
HGsnom	daily snowmelt	mm
HRwca	available soil water content	kg/kg
HRwc	soil water content	kg/kg
HRwc*	non-dimensional soil water content	---
HRwcs	soil water content at saturation	kg/kg
HRwcw	soil water content at wilting point ( -1500 kPa)	kg/kg
k4d	coefficient for drying process as function of depth	---
k4f	coefficient for water migration and expansion freezing (1.4)	---
k4fs	coefficient for freezing and solidification (4.25)	---
k4td	coefficient for thaw then dry as function of depth	---
SDag	soil aggregate density	Mg/m3
SDsblk	settled bulk density of layer	Mg/m3
SDblk	soil bulk density	Mg/m3
SDblk 0	soil bulk density of top layer	Mg/m3
SEag	aggregate stability crushing energy	ln(J/kg)
SEcr	crust stability crushing energy	ln(J/kg)
SEavgag	mean of natural log aggregate crushing energies	ln(J/kg)
SEmaxag	maximum of natural log aggregate crushing energies	ln(J/kg)
SEminag	minimum of natural log aggregate crushing energies	ln(J/kg)
SF84m	average fraction < 0.84 mm diameter for given soil	---
SF84std	standard deviation of average fraction < 0.84 mm diameter	---
SFcce	soil fraction calcium carbonate equivalent	kg/kg
SFcla

SFcr	soil fraction clay

soil fraction crust cover	kg/kg

m2/m2
SFom	soil fraction organic matter	kg/kg
SFsan	soil fraction sand	kg/kg
SFsil	soil fraction silt	kg/kg
SFXlos	maximum loose soil cover on crust	m2/m2
SLagm	aggregate geometric mean diameter	mm
SLagx	maximum diameter of aggregate size distribution	mm
SLmax	maximum aggregate geometric mean diameter	mm
SLmin	minimum aggregate geometric mean diameter	mm
SMlos	loose, erodible mass on surface crust	kg/m2
SMXlos	maximum loose, erodible mass on crust	kg/m2
S0ags	standard deviation of aggregate size distribution	---
SVroc

SXrg

SZ	soil layer volume of rock > 2.0 mm diameter

ridge spacing

maximum of ridge height or 4 X random roughness	m3 m-3

mm

mm
SZcr	crust thickness	mm
SZlyd	depth to bottom of layer from surface	mm
SZlyt	layer thickness	mm
SZwlyt	wetted thickness in a layer	mm
SZrg	current ridge height	mm
SZrgo	initial ridge height after tillage	mm
SZrr, SZrro	current and initial (after tillage) random roughness	mm
Xj	daily increment of the jth driving force	---
Xj	an independent driving variable of the jth process	---
Xij	current value of the jth process variable	---
Y	a dependent soil temporal variabile	---