789

AbstractThe 137Cs technique has been widely used to provide soil redistribution estimates since the 1970s. However, most 137Cs-conversion models remain theoretical and largely unvalidated. Our objectives were to validate the four widely used conversion models, examine model parameter sensitivity, and evaluate the potential of using kriging to improve soil redistribution estimation. Soil loss was measured from a 1.6-ha plot since 1978. Winter wheat (Triticum aestivum L.) was grown primarily under conventional tillage. Soil samples in a 10-m grid were taken from the plot to estimate the 137Cs inventory. Soil redistribution rates were estimated using four models and were further interpolated using ordinary kriging. The parameter sensitivity analyses at the 95% confidence limits showed that reference inventory had the most impact on estimated water erosion, followed by particle size correction for erosion and tillage depth, with minimal impacts from mass depth, bulk density, and particle size correction for deposition. Compared with the measured water erosion, the relative errors of the mean net water erosion estimates across the entire plot without and with kriging were 28 and −17% for the proportional model (PM), 141 and 106% for the simplified mass balance model, 133 and 100% for the improved mass balance model (MBM2), and 109% for the extended MBM2 with tillage erosion (MBM3). Results indicated that the PM performed better than the mass balance models under the study conditions and that kriging improved mean soil redistribution estimates. However, the full potential of the MBM2 and MBM3 needs to be further evaluated under conditions where loss of newly deposited 137Cs exists.

Evaluation of Cesium-137 Conversion Models and Parameter Sensitivity for Erosion Estimation

X. C. (John) Zhang,* G. H. Zhang, X. Wei, Y. H. Guan

The fallout radionuclide 137Cs is an anthropogenic radioisotope that was released from atmospheric nuclear bomb testing, primarily in the 1950s and 1960s, and was

largely brought back to the earth surfaces in wet fallout. It has been widely used as a sediment tracer to provide soil redistribu-tion estimates for individual sampling points in the past 40 yr (Ritchie and McHenry, 1990; Zapata, 2010). This tracing tech-nique represents a complement to conventional measurement techniques such as erosion plots and pins. The technique is based on the key assumption that 137Cs fallout is initially uniformly distributed in space at a local scale (Walling and Quine, 1992). Based on this assumption, soil redistribution at any sampling point can be estimated by directly comparing the 137Cs inventory at that point with the mean reference inventory estimated in a nearby reference site experiencing neither erosion nor deposi-tion. The ability to retrospectively estimate long-term mean soil redistribution for individual points across a landscape using a single sampling campaign is deemed a key advantage of the 137Cs technique (e.g., Walling and Quine, 1992; Walling et al., 1995; Walling and He, 1998; Zapata, 2010). Furthermore, the tech-nique provides soil redistribution data that integrate the effects of all processes leading to soil redistribution, which normally cannot be achieved using conventional measurement methods (Mabit et al., 2008; Mabit et al., 2013).

The 137Cs tracing technique requires conversion models that translate the amounts of 137Cs inventory changes to the amounts of soil losses or gains (referred to here as soil redistribution rates) at individual sampling points. Numerous 137Cs conversion models have been proposed under various assumptions of the fate and behavior of 137Cs in soils and across landscapes, as well as for different profile distributions of 137Cs in soils as affected by land use, tillage operations, and other management practices. Based on the distinct characteristics of the 137Cs vertical distributions in soil profiles, two groups of 137Cs conversion models have been proposed: one for cultivated soils and another for uncultivated soils. In each group, the 137Cs conversion models can generally be divided into two categories: empirical and theoretical models.

Abbreviations: CI, confidence interval; MBM, mass balance model; MBM1, simple mass balance model; MBM2, improved mass balance model; MBM3, extension of improved mass balance model with tillage erosion; PM, proportional model.

G.H. Zhang and X. Wei, State Key Lab. of Earth Surface Processes and Resource Ecology, Beijing Normal Univ., Beijing, China; X.C. Zhang, USDA–ARS Grazinglands Research Lab., El Reno, OK; and Y.H. Guan, College of Resources and Environment, State Key Lab. of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest A&F Univ., Yangling, Shaanxi, China. Assigned to Associate Editor Robert Malone.

Copyright © American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. 5585 Guilford Rd., Madison, WI 53711 USA. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. J. Environ. Qual. 44:789–802 (2015) doi:10.2134/jeq2014.09.0371 Received 3 Sept. 2014. Accepted 29 Dec. 2014. *Corresponding author (John.Zhang@ars.usda.gov).

Journal of Environmental QualityLANdSCAPE ANd WATERSHEd PROCESSES

TECHNICAL REPORTS

790 Journal of Environmental Quality

The former are regression-type equations developed between soil erosion rates and relative changes in 137Cs inventories (Zhang, 2015). The latter are mathematical relationships derived based on mass conservation, as well as understanding and simplification of the physical processes of the fate, behavior, and characteristics of 137Cs in soils.

Most conversion models are theoretical and were developed based on various simplification assumptions. However, those assumptions on which all conversion models rest are essentially untested, and the models remain largely unvalidated (Porto et al., 2004; Porto and Walling, 2012a). The main reason is the lack of suitable long-term, spatially distributed soil loss data that are compatible with the capability of 137Cs conversion models to generate long-term, spatial soil redistribution patterns. Li et al. (2010) evaluated the performance of four conversion models using soil redistribution rates predicted with an erosion model along a hillslope. In the literature, several theoretical conversion models were validated with only a few years of soil loss data measured in cultivated plots (Porto et al., 2003a; Porto and Walling, 2012b) and in small forested watersheds (Porto et al., 2001, 2003b, 2004, 2009; Wakiyama et al., 2010). The general results of those studies showed that the 137Cs-estimated soil losses agreed well with the measured soil losses. Nevertheless, there were two shortcomings with all those validation studies, namely, (i) there were gross mismatches in space and time between measured and 137Cs-estimated soil loss, and (ii) many model parameters were not directly measured and were often taken from the literature. Most of those studies had only a few years of measured soil loss data, while the 137Cs technique simulated soil loss since 1954 or since the initiation of the first tillage. For validation at the watershed scale, measured sediment data existed only at the watershed outlets, but the 137Cs technique estimated spatially distributed loss or deposition. Spatially distributed long-term erosion data are needed for rigorous evaluation. Despite the lack of ideal validation data sets, Walling and Quine (1990) stressed the importance of validating the theoretical models and stated that any information capable of affording some degree of calibration or validation should be fully utilized.

A great advantage of using the 137Cs tracer for erosion estimation is its unique ability to characterize the spatial behavior or pattern of soil redistribution (Zapata, 2010). Geostatistics like kriging have been specifically developed to characterize the spatial structure of a variable and to predict the values of this variable between sampled points to minimize estimation errors (Sterk and Stein, 1997). However, only a few researchers have taken advantage of those good geostatistical tools to characterize the spatial pattern of 137Cs-estimated soil redistribution (Chappell, 1998; van der Perk et al., 2002; Schuller et al., 2003; Chappell and Warren, 2003; Mabit et al., 2008; Navas et al., 2013, 2014). The ability of geostatistical tools to improve spatial soil redistribution needs to be further elucidated.

Large differences in soil redistribution estimates among various 137Cs conversion models necessitate detailed model validation and comparison. Walling and Quine (1990) demonstrated for a hypothetical site that the erosion rates estimated from a given depletion percentage of 137Cs could vary by more than two orders of magnitude among the 17 models tested. Such large differences in soil redistribution rates cast doubt on the usefulness of the tracing technique, hindering

some researchers from using the technique or making use of the data it generated. To date, serious efforts are still needed to verify the assumptions on which the theoretical models rest and to validate the 137Cs-estimated soil redistribution rates against those measured under different environments to gain the widespread acceptance and to realize the full potential of the technique (Porto and Walling, 2012a). The objectives of this study were to conduct a thorough validation of the four widely used conversion models using the long-term measured soil loss data from a 1.6-ha homogeneous unit watershed, to examine model parameter sensitivity, and to evaluate the potential of using kriging to improve spatial soil redistribution estimation.

Materials and MethodsSite Description

One experimental plot or unit watershed, located at the Grazinglands Research Laboratory, 7 km west of El Reno, OK, was used in this study. The plot, situated on a gentle slope, is 80 m wide and 200 m long (downslope), with a drainage area of 1.6 ha. The average longitudinal slope is approximately 5% at the top and 1% at the bottom (Fig. 1). The plot is surrounded by earthen berms, which were constructed with soil outside the plot area. An H-flume with a float and mechanical water-level recorder is used to measure flow levels. The stage height in the flume is converted to water discharge using a calibrated rating table for the flume. A pump-type sediment autosampler has been used to collect sediment concentration samples at predetermined intervals (more frequent at the beginning of each storm) since 1978 (Zhang et al., 2014). Nearly 0.45-L samples are pumped from a small hole in the flume wall 2.5 cm above the flume bed. Sediment transport rates are calculated by multiplying the sediment concentration by the corresponding discharge rates in a continuous concentration manner. Soils (fine, mixed, thermic Udertic or Pachic Paleustolls) are primarily silt loam, with an average of 23% sand and 56% silt in the tillage layer. Four tipping bucket rain gauges (20.3-cm-diameter catch) are used to record precipitation data at the site. The climate at the location is characterized as semiarid to subhumid. The annual precipitation varies greatly from year to year, with a mean of about 886 mm (Table 1). Soil loss measurements were incomplete after 2001 due to a malfunction of the sediment sampler. Linear regressions between monthly soil loss and monthly runoff were established for each calendar month and for both no-till and conventional tillage winter wheat using the historical data measured from other paired plots on the same site (Fig. 1). The overall averaged coefficient of determination (r2) was 0.57, with most regressions being significant at a = 0.01. Those relationships were used to estimate soil loss between 2001 and 2004. Linear regression between annual soil loss and annual runoff was also developed for perennial grass and was used to estimate the annual soil loss under perennial cool-season grass between 2005 and 2012 using the measured annual runoff. The coefficient of determination for the regression was 0.103, which was significant at a = 0.003. The lower r2 value was partially due to the very low annual soil loss under native tallgrass prairie.

The mean monthly precipitation is bimodal, with the primary peak occurring in May to June and a secondary peak in August to October (Fig. 2). The greatest soil loss occurred

www.agronomy.org • www.crops.org • www.soils.org 791

during the secondary peak when the ground was bare under the conventional tillage system. Lesser soil losses during the primary peak were due to the maximum wheat canopy cover before harvest in June (Zhang and Garbrecht, 2002).

The annual maximum tillage depths and cropping systems of each year are listed in Table 1. The native tallgrass prairie was turned under in 1978. The conventional tillage (also referred as clean and intensive tillage), which comprised one primary tillage of a deep moldboard plow or chisel plow and two to four passes of secondary tillage including disking and harrowing, was used from 1978 to 1998, while no-till was primarily used afterward. Annual winter wheat was grown before 2003, and a cool-season perennial grass was raised for grazing afterward.

Sampling DesignTo fully capture the spatial variability, a 10-m grid was

used to sample the plot area (Fig. 1). Six samples in a row were taken across the slope, and 18 rows were made downslope. To minimize border effects, 5-m strips along the top and the two side borders were not sampled but were included in kriging interpolation. The sampling depth was 30 cm, below which a preliminary study confirmed that 137Cs activity was negligible. The vertical distributions of 137Cs activity were measured along three transects at 30, 100, and 170 m from the bottom berm (Fig. 1). Six cores were taken along each transect and were composited by depth at 5-cm intervals. For reference samples, a transect along a flat ridgetop under the undisturbed permanent native tallgrass prairie vegetation was chosen for sampling (Fig. 1). A total of 21

Fig. 1. Aerial photo of the study site and digital elevation map of the homogeneous unit watershed (plot), showing the reference site, small subplot locations, and sampling points (photo is cropped from Google Earth).

792 Journal of Environmental Quality

samples along the transect at 5- to 10-m intervals was taken to a depth of 30 cm. Lance et al. (1986) showed that 20-cm-deep cores were sufficient to sample the entire 137Cs profile on the native tallgrass prairie of the study site. A hydraulic probe with an inner diameter of 5.2 cm was used for all samplings. All samples were taken in 2012.

Cesium-137 MeasurementAll samples were air dried, ground, and sieved through

a 2-mm sieve. The 137Cs mass activity of all samples was measured by g spectrometry at 661.62 keV using a high-purity germanium coaxial detector (50% efficiency and a resolution of full width at half maximum of 2.2 keV at 1.3 MeV) coupled to a multichannel analyzer. The measuring cup, made of polyethylene, was 6.5 cm tall with a uniform inner diameter of

7.0 cm. An approximately 400-g mass was used for each sample. The counting times were typically in the range of 8 to 24 h, providing a relative measurement error of ±10% at the 95% level of confidence.

Conversion ModelsTheoretical conversion models were improved by Walling

and He (1999), and an Excel add-in program was developed for standardized applications of those models by Walling et al. (2011). Those improved models have been widely used since their release. Four theoretical models for cultivated soils were evaluated in this study, namely, the proportional model (PM), a simplified mass balance model (MBM1), an improved mass balance model (MBM2), and an extended MBM2 with tillage erosion (MBM3). The first three models were evaluated in detail

Table 1. measured annual precipitation, surface runoff, soil loss, maximum tillage depth, land use type, and management practices in the 1.6-ha experimental plot.

Year Precipitation Runoff Soil loss† Tillage depth Land use and management————— mm ————— Mg ha−1 yr−1 m

1977 730 9.6 0.025 no tillage native tallgrass prairie1978 709 13.0 0.005 0.20 CT‡ winter wheat (grain)–summer fallow1979 870 35.0 0.802 0.20§ CT winter wheat (grain)–summer fallow1980 682 12.8 0.239 0.20§ CT winter wheat (grain)–summer fallow1981 940 27.6 0.527 0.20§ CT winter wheat (grain)–summer fallow1982 823 51.0 0.044 0.20§ CT winter wheat (grain)–summer fallow1983 1155 180.5 3.764 0.25 CT winter wheat (grain)–summer fallow1984 801 53.2 1.538 0.20 CT winter wheat (grain)–summer fallow1985 985 154.7 13.401 0.25 CT winter wheat (grain)–summer fallow1986 1222 259.3 33.758 0.25 CT winter wheat (grain)–summer fallow1987 1137 192.3 11.196 0.20 CT winter wheat (grain)–summer fallow1988 781 63.1 0.517 0.20 CT winter wheat (grain)–summer fallow1989 1068 133.2 10.350 0.18 CT winter wheat (grain)–summer fallow1990 990 200.0 1.063 0.20 CT winter wheat (grain)–summer fallow1991 923 16.4 0.419 0.20§ CT winter wheat (grain)–summer fallow1992 974 112.4 2.760 0.20§ CT winter wheat (grain)–summer fallow1993 1092 286.1 1.029 0.20§ CT winter wheat (grain)–summer fallow1994 918 181.2 0.665 0.20§ CT winter wheat (grain)–summer fallow1995 1099 241.4 0.044 0.20§ CT winter wheat (grain)–summer fallow1996 739 6.4 0.052 0.18 CT winter wheat (grain)–summer fallow1997 1173 264.7 6.234 0.18 CT winter wheat (grain)–summer fallow1998 768 121.6 0.445 0.18§ CT winter wheat (grain)–summer fallow1999 923 255.5 0.639 no-till graze-out winter wheat2000 908 139.6 0.264 no-till graze-out winter wheat2001 611 80.9 0.432 no-till graze-out winter wheat2002 829 137.8 0.242 no-till graze-out winter wheat2003 515 3.1 0.200 0.30 CT graze-out wheat–summer fallow2004 921 16.7 1.067 0.20 planted perennial cool-season grass2005 772 0.1 0.014 no-till grazed perennial cool-season grass2006 674 0 0 no-till grazed perennial cool-season grass2007 1449 330.9 0.058 no-till grazed perennial cool-season grass2008 1009 52.8 0.021 no-till grazed perennial cool-season grass2009 785 0 0 no-till grazed perennial cool-season grass2010 724 0.6 0.014 no-till grazed perennial cool-season grass2011 619 0.1 0.014 no-till grazed perennial cool-season grass2012 566 0 0 no-till grazed perennial cool-season grass

† Soil loss from 2001 onward was estimated from monthly runoff.

‡ CT, conventional tillage including a primary tillage of moldboard plow or chisel and multiple passes of offset disk.

§ Tillage depth was not recorded and was estimated from tillage tool and type.

www.agronomy.org • www.crops.org • www.soils.org 793

regarding model parameter sensitivity and kriging interpolation. The PM as a linear model is probably the most commonly used theoretical model for cultivated soils (Walling et al., 2011). The mean annual soil loss rate (Y, Mg ha−1 yr−1) is estimated as

D L10100B D X

YTP

= [1]

where BD is the average bulk density of soil (in kg m−3), DL is the average tillage depth (in m), X is the depletion percentage and is calculated as 100(Am

ref − Aisam)/Am

ref (where Amref is the

mean reference inventory [in Bq m−2] and Aisam is the sample

inventory at the ith point [in Bq m−2]), T is the time elapsed since the commencement of the 137Cs fallout or tillage, and P is the particle size correction for erosion and is defined as the ratio of the 137Cs concentration of the mobilized sediment to that of the original soil. This model assumes that the fallout 137Cs input was instantaneously and homogenously mixed within a tillage layer of fixed depth. The instantaneous mixing assumption would generally lead to overestimation of soil loss because the freshly deposited 137Cs might have been lost before being incorporated by tillage. The fixed depth assumption ignores the tillage dilution by progressive incorporation of soil below the original plow depth and thus causes underestimation of soil erosion. The mean annual deposition rate (Y¢, Mg ha−1 yr−1) is estimated as

¢¢=

¢D L10

100B D X

YTP

[2]

where X¢ is the percentage gain in 137Cs inventory and is calculated as 100(Ai

sam − Amref )/Am

ref, and P¢ is the particle size correction for deposition and is defined as the ratio of the 137Cs concentration of the deposited sediment to that of the mobilized sediment. The deposition rate Y¢ is calculated independently of the upslope erosion processes.

The simplified mass balance model (MBM1) was originally proposed by Zhang et al. (1990) and Kachanoski (1993) without the particle size correction factor P. For an eroding site, the improved MBM1 (Walling and He, 1999) takes the form of

-é ùæ öê ú÷ç= - - ÷çê ú÷çè øê úë û

1/( 1963)D L10

1 1100

tB D XYP

[3]

where t is the sampling year. This model assumes that the total fallout input occurred in 1963 and was instantaneously mixed in the plow layer. Compared with models using 1954 as the initial fallout year, the model overestimates soil loss due to the assumptions of instantaneous mixing and the one-time fallout input in 1963. Nevertheless, this model does account for the tillage dilution. For a depositional site, a constant deposition rate (R¢, kg m−2 yr−1) is estimated as

( ) ( )-¢=é ù¢ ¢ ¢-l -ê úë ûò

0

sam refm

d exp d

it

t

A AR

C t t t t [4]

where l is the decay constant for 137Cs (in yr−1), t0 is the beginning year of 137Cs deposition (1963 for MBM1), and Cd(t¢) is the 137Cs concentration of the sediment deposited in the t¢ year (in Bq kg−1) and can be calculated as

( ) ( )¢ ¢ ¢= òò

d e1

dd S

S

C t P C t R SR S

[5]

where S is the upslope contributing area (in m2), R is the average erosion rate in the upslope eroding area (in kg m−2 yr−1), and Ce(t¢) is the 137Cs concentration of mobilized sediment from the eroding area (in Bq kg−1) and can be estimated as

( ) ( )¢-æ ö÷çé ù¢ ¢ ÷= l - -ç ÷ê úçë û ÷çè ø

1963ref

e mm m

exp 1t

P RC t A t t PD D

[6]

where Dm is the cumulative mass depth of tillage (in kg m−2). Conceptually, the deposited 137Cs concentration is affected by the 137Cs concentration of sediments mobilized in the upslope eroding areas and their associated soil erosion rates (cf. Eq. [5]).

Fig. 2. monthly mean precipitation amounts and soil loss rates in the study unit watershed during 1977 to 2012.

794 Journal of Environmental Quality

The MBM2 is an improved model that further considers the temporal fallout 137Cs input and the fate of the freshly deposited fallout before being incorporated into the plow layer by tillage. For an eroding point, MBM2 takes the form of

( )( ) ( ) ( )

æ ö÷ç ÷= -G - l+ç ÷ç ÷çè ø

samsam

m

d1

di

iA t RI t P A t

t D [7]

where G is the percentage of the freshly deposited 137Cs fallout removed by erosion before being incorporated into the plow layer, and I(t) is the annual 137Cs deposition flux (in Bq m−2 yr−1). Equation [7] is solved for R numerically. The 137Cs concentration of mobilized sediment Ce(t¢) can be calculated as

( )( ) ( )¢ ¢é ùæ ö- ÷çê ú¢ = g - +÷ç ÷çê úè øë û

sam

em

1 exp iI t A tRC t P PR H D

[8]

where g is the proportion of the annual 137Cs input susceptible to erosion loss, and H is the relaxation mass depth of the initial profile distribution of fresh fallout in the soil (in kg m−2), reflecting the mobility of fresh fallout 137Cs in the soil. The deposition rate R¢ is calculated with Eq. [4] and [5] in the same way as in MBM1.

The MBM3 is an extension of MBM2 with tillage erosion incorporated. For an eroding point, MBM3 takes the form of

( )( ) ( ) ( ) ( )

( ) ( )

= -G + -

- -l

sam

t,in t,in t,out t,out

samw w,out

d1

di

i

A tI t R C t R C t

tR C t A t

[9]

where Ct,in and Ct,out are the 137Cs concentrations in the tillage influx and outflux sediment for the ith sample and are assumed to equal the 137Cs soil concentrations of the respective segments at time t, Cw,out is the 137Cs concentrations in water-eroded sediment, Rt,in and Rt,out are tillage influx and outflux rates (in kg m−2 yr−1), respectively, and Rw is the water erosion rate (in kg m−2 yr−1). The two tillage erosion fluxes are calculated as

b=t,in

sin i

i

kR

L [10a]

-b= 1

t,outsin i

i

kR

L [10b]

where k is a tillage translocation constant related to tillage practice (in kg m−1 yr−1), b is the slope angle, and Li is the slope length for the ith segment or sample. For more detailed definitions of the

relevant variables as well as the equations for a deposition point, see Walling and He (1999).

Parameter EstimationApproximately 1.4% of the total 137Cs fallout input in the

United States occurred after 1978 when tillage was initiated in this experiment. Because soil erosion under the permanent tallgrass prairie before 1978 was negligible (see data below), the parameters of I(t), g, and H were largely inconsequential. However, they were estimated and used in the Excel add-in program in this study. A default value of 4 kg m−2 for H was used. The annual I(t) at the study site was estimated by scaling the annual inputs measured in Alabama to match the local mean reference inventory after decay correction. The value of g was estimated to be 0.39 based on the ratio of the total runoff-producing rainfall in the summer months during which most erosion occurred to the total precipitation during 1978 to 2012. The remaining parameters that are more relevant to this study were estimated as follows. The tillage depth DL varied each year, mostly ranging from 0.2 to 0.3 m (Table 1). To calculate a representative depth, the deepest mixing depths, which were taken as 0.20, 0.25, and 0.30 m for the years of 1978 to 1982, 1983 to 2002, and 2003 to 2012, respectively, were weighted by the magnitudes of the soil losses of each year. The overall weighted tillage depth for the study period was 0.252 m. A uniform probability distribution between 0.2 and 0.3 m was assumed to compute the 95% confidence limits for DL in Table 2.

Twenty-three soil cores were used to estimate the average soil bulk density of the top 0.25-m layer. The mass tillage depth Dm was calculated using the independently generated tillage depth and bulk density data (note that a uniform probability distribution was assumed for DL and a triangular probability distribution for BD). For estimating the particle size correction factor P for erosion, two small runoff plots (20 and 40 m long by 5 m wide) were set up in the upper segment of an adjacent watershed in 2013 (Fig. 1). The soil was rotor tilled, and a composite sample of 30 surface soil subsamples was taken with a small ring (4-cm i.d. and 2.5-cm height) from each plot and was analyzed for 137Cs activity. The total runoff and sediment from each plot were collected in a big barrel, and the sediment from each runoff event was separated and processed for 137Cs measurement. In total, 20 sediment samples were collected from the two small subplots and three from the H-flume at the outlet of the watershed, and the P factor was calculated for each sediment sample or storm. Despite the P values for the three events calculated for the watershed being slightly greater than those for the small subplots, they were combined in the analyses.

Table 2. Statistics of the model parameter values estimated for the data sets used in this study.

Factor Tillage mass depth Tillage depth Bulk density

Particle size correction for

erosion

Particle size correction for

deposition

Reference 137Cs activity

kg m−2 m kg m−3 Bq m−2

Nominal mean 347.8 0.252 1380 2.003 0.634 1621.9Standard error 10.1 0.021 22.9 0.135 0.027 33.1Sample size 20 2 23 23 3 2195% lower limit† 328.0 0.212 1335 1.738 0.581 1557.195% upper limit† 367.6 0.292 1425 2.267 0.686 1686.8

† 95% confidence limits for the estimated means, calculated with a normal assumption for each mean.

www.agronomy.org • www.crops.org • www.soils.org 795

For estimating the size correction factor P¢ for deposition, a fine mesh screen was laid flat on the ground in the lower segment to catch fresh sediment deposition (Fig. 1). Three samples of deposited sediment, including one from the H-flume bed, were collected. The P¢ value was calculated as a ratio of the 137Cs concentration in the deposit to that in the mobilized sediment of the same storm, and the estimated P¢ values were fairly close, with a mean of 0.634. For tillage constant k, an average of 235 kg m−1 yr−1 was estimated for the tillage tools and operations according to Govers et al. (1994). However, a value of 200 kg m−1 yr−1 was used in the MBM3 runs because Eq. [9] had no solution when k was >200 kg m−1 yr−1 under the study conditions. The means, standard errors, and 95% lower and upper limits for the means for the key parameters are shown in Table 2.

Kriging Interpolation of Soil Redistribution EstimatesAn ordinary kriging method was used to estimate soil

redistribution rates for unsampled points using the neighboring sampled locations. A spherical model was used to fit the semivariogram curve, and the standardized root mean square error was about 1.1. A standard neighborhood search was used to include seven (at least four) sampled locations. The estimate at any unknown target location was calculated as a linear sum of the weighted values known at the sampled locations. The optimum weight at each sampling distance was estimated by the sampling distance and the degree of autocorrelation for the distance (determined from the spherical model). The ordinary kriging method, known as the best linear unbiased estimator, has the great advantage of best utilizing the semivariogram information. The interpolation was made for each of the 0.5-m grid cells to minimize the overall estimation error for soil redistribution in the study area. All 108 sampling points were used in kriging.

Model ExecutionThe Excel add-in program of Walling et al. (2011) was used

for all predictions. The four conversion models (PM, MBM1, MBM2, and MBM3) in the program were executed for each of the six downslope transects individually. The four models were run for a baseline scenario with all parameters set at their nominal values. In addition, three of the models (except MBM3) were run for (i) the lower and upper 95% confidence limits of each parameter (Table 2) while the remaining parameters were held at their nominal values and (ii) worst case scenarios in which a combination of the 95% confidence limits of all parameters produced either the most or the least net soil erosion.

Statistical TestsNearing (2000) proposed a statistical test method that allows

erosion model evaluators to take natural, within-treatment variability of erosion plots into account when validating soil erosion models. The basis for the method is that if the difference between a model prediction and a measured plot soil loss value lies within the population of differences between pairs of measured plot erosion values, then the prediction is considered acceptable. Data from replicated plot pairs for 2061 storms, 797 annual erosion measurements, and 53 multiyear erosion totals were used to calculate the relative differences (Rdiff ) between the paired erosion measurements as (Nearing et al., 1999)

-=

+2 1

diff2 1

M MR

M M [11]

where M1 and M2 are the paired soil loss values from two replicate plots. The 95% confidence limits of Rdiff were calculated in groups as a function of measured soil loss rates. For erosion model evaluation, the relative differences in erosion were calculated as (Nearing, 2000)

diffP MRP M-

=+

[12]

where P is the predicted erosion value and M is the measured value. If the calculated Rdiff falls within the range of the 95% confidence limits, then the model prediction is considered acceptable. It needs to be mentioned that this test is based on the paired data of erosion plots that are 22 m long and 2 to 8 m wide. However, our study plot was 200 m long and 80 m wide. The applicability or transferability of the test method to a much larger plot is unknown at this point. Thus, the test result must be seen as a guide rather than an absolute.

Results and DiscussionIt is necessary to elaborate on several assumptions made in

this study that may potentially affect the accuracy of the 137Cs estimates. First, soil loss under tallgrass prairie was assumed negligible before the first tillage in 1978. This assumption was corroborated by measured soil losses from cultivated plots and paired native prairie plots between 1983 and 1997 at the study site. For example, the average soil loss between 1983 and 1997 was 5779 kg ha−1 yr−1for a cultivated plot and only 32 kg ha−1 yr−1 for a native prairie plot (Zhang and Garbrecht, 2002). Given the low soil loss rates under the native tallgrass prairie, it is reasonable to assume that the 137Cs loss before 1978 was negligible. Under this assumption, soil losses predicted with the conversion models would be representative of the total losses that occurred between 1978 and 2012, which were compared with the soil losses measured during the same period. However, it should be noted that neglect of the minor soil losses before 1978 may lead to overestimation of soil erosion rates by all 137Cs models because some 137Cs might have been lost with sediment due to the greatest 137Cs concentration being at the undisturbed soil surface.

Second, wind erosion was assumed negligible during the period. The study location has a subhumid to subarid climate, with a mean annual precipitation of 886 mm in the past 35 yr, which was the longest and wettest period in the 100-yr records. Given the relatively wet conditions, wind erosion was believed very low in the area. This was corroborated by visual observations, which showed that wind erosion was of little importance at the study site compared with water erosion since the monitoring began in 1978.

Third, 137Cs loss through vegetation removal was assumed to be equal at both reference and measuring sites, and consequently no correction was made for differential removal of 137Cs from the two sites. Before the establishment of the plots in 1977, the two sites were part of a large pasture and were grazed evenly. From 1978 to 1998, wheat was harvested for grain, and wheat straw

796 Journal of Environmental Quality

was returned to the cultivated plot, while the native prairie on the reference site was grazed by cattle. Although there were no experimental data to quantify 137Cs removal by grain harvest vs. grass grazing, it was believed that the removals were comparable. From 1999 to 2012, the cultivated plot was planted to winter wheat or perennial cool-season grass (Table 1) and was grazed by cattle, while the native prairie on the reference site was continuously grazed by cattle each year.

Fourth, the sampling and 137Cs measurement errors were within 20% and were not explicitly included in the analysis. Fifth, the downward movement of 137Cs by infiltrating water was negligible, as evidenced by the fact that 137Cs activity was extremely low below the 30-cm sampling depth (Fig. 3). The 137Cs inventories above the 30-cm depth accounted for 98.2, 98.6, and 97.8% of the total inventories in the soil profiles for the upper, middle, and lower transects, respectively, and the mixing depths for the bulk inventories were 20, 25, and 30 cm, respectively.

Sixth, all 137Cs models assume a constant erosion rate during the entire simulation period; however, the actual soil loss rates varied greatly from year to year and from annual winter wheat to perennial grass (Table 1). Clearly, the assumption of a constant erosion rate in all models would result in certain estimation errors due to the decay loss of 137Cs in soil with time. Seventh, although intensive tillage operations were used in 1978 and the ensuing years, 137Cs was unlikely to have been mixed uniformly in the tillage layer. The nonuniform mixing would give rise to a certain uncertainty in the soil erosion estimates.

Mean Soil RedistributionThe Excel add-in program was executed for each individual

downslope transect to account for the effects of upslope erosion on downslope deposition. Soil redistribution rates calculated for each sampling point at the nominal values of all input parameters (i.e., the baseline scenario) were used to compute mean erosion rates for all eroding points, mean deposition rates for all deposition points, and mean net erosion rates for all points (Table 3). In this particular study, since the first tillage occurred in 1978, all conversion models predicted soil erosion between 1978 and 2012. Since the 137Cs fallout had almost vanished after 1978, MBM2 had no advantage over MBM1. Under the condition of this particular study, MBM1 and MBM2 were almost identical in process representation and therefore behaved rather similarly. The MBM3 model is an extended version of MBM2 with tillage erosion incorporated. The overall net water erosion predicted by MBM3 was fairly close to that of MBM2, being about 11% less. The MBM3 model also predicted a mean net tillage erosion rate of −1.3 Mg ha−1 yr−1. Taken together, the total mean net erosion predicted by MBM3 was 6% greater than that of MBM2. The modeling concepts for water erosion were similar among the three mass balance models (MBMs) but differed from the PM. That is, the former considers tillage dilution as well as the effect of upslope erosion on downslope deposition, while the latter does not. The distinctive conceptualization leads to the different model structures. As a result, the net water erosion estimates were similar for the three MBMs and rather different from that of the PM (Table 3). Compared with the PM, the three MBMs slightly overestimated mean water erosion rates but considerably underestimated mean deposition rates and consequently substantially overestimated mean net water erosion

rates. The slight overestimation of water erosion was expected because tillage dilution is simulated in the three MBMs. The minor differences in water erosion between the MBMs and PM were partially because (i) the tillage dilution effects were limited due to the low soil erosion rates on the site (a total loss of about 6-mm depth in the eroding area) and (ii) no 137Cs loss occurred from fallout before 1978. The underestimation of deposition was the major contributor to the overestimation of the mean net water erosion rates. Sediment deposition rates are dependent on the upslope water erosion rates in the MBMs but remain independent in the PM. This is the major conceptual difference between the MBMs and PM in the context of this study.

The measured mean net erosion rate during 1978 to 2012 was −2.7 Mg ha−1 yr−1 (or a total of 91.6 Mg ha−1), which translated to a 18.3% coefficient of variation (CV) using Nearing’s regression

Fig. 3. Vertical distributions of 137Cs mass activity at the upper, middle, and lower transects in the unit watershed.

www.agronomy.org • www.crops.org • www.soils.org 797

equation (Nearing et al., 1999). A relative error of 36% was estimated at the 95% confidence level for the 18.3% CV under a normal assumption with one replicate. In light of the 36% relative error associated with the measured soil erosion, the Nearing’s test showed that the predictions of the net water erosion were different from the measured value for all three MBMs, but the prediction of the PM was considered acceptable (Table 3). In comparison with the measured mean, the relative errors of the estimated mean water erosion rates for the same period were 28, 141, 133, and 109% for the PM, MBM1, MBM2, and MBM3, respectively. Because all the models used the same nominal values of the same input parameter set (Table 2), the differences in the relative errors resulted largely from the differences in the model structures or concepts, implying that a sizable structural error may exist with MBMs in the deposition algorithms. It is worth noting that this work may not provide the definite validation of the deposition processes because the total deposition in the plot was not explicitly measured.

Given the gentle slopes (5% in the upper segment and <1% in the lower segment), the tillage erosion predicted by MBM3 was somewhat substantial, with mean net erosion of −1.3 Mg ha−1 yr−1. Because the plot was surrounded by berms, it was impossible to have net tillage erosion loss from the plot. It is difficult to explain the fate of the 71 Mg of net tillage erosion from the 1.6-ha plot during the 34-yr period, casting doubt on the accuracy of the tillage erosion estimates. Given that the water erosion predicted by MBM3 was similar to those predicted by MBM1 and MBM2, MBM3 was excluded from further kriging interpolation and parameter sensitivity analyses.

Large spatial variability of the 137Cs inventory necessitates a large sample size to obtain reliable estimates of the 137Cs inventory and subsequently soil erosion estimates (Zhang, 2015). Spatial variability of the 137Cs inventory comprises a systematic variability resulting from soil erosion and an intrinsic random variability caused by 137Cs redistribution during the transfer processes of the fallout 137Cs. A large number of independent replicate samples are needed to statistically separate the two components for better assessment of soil redistribution rates (Zhang, 2015). It is practically infeasible to take an exhaustive number of soil samples. Fortunately, geostatistical tools like kriging can be used to overcome this limitation and to extend soil erosion estimates from the known sampling points to unknown

locations (Mabit et al., 2008; Sterk and Stein, 1997). In this study, the sampling points in the 10-m grid were interpolated to those in a 0.5-m grid using ordinary kriging. The absolute soil loss and deposition rates averaged after kriging were much lower than those averaged across the original sampling points (Table 3). The average net erosion rates after kriging were closer to the measured mean of −2.7 Mg ha−1 yr−1 for all models, with relative errors of −17, 106, and 100% for the PM, MBM1, and MBM2, respectively. In comparison with the 36% relative error for the measured value, the interpolated prediction of the PM was acceptable, while those of MBM1 and MBM2 were not (Table 3). The somewhat improved estimates with kriging demonstrate its potential to improve the mean estimates of soil redistribution. Given the large spatial variations in both 137Cs inventories and estimated soil redistribution rates, the smoothing over and interpolating between the sampled points with kriging would reduce the spatial variability, minimize estimation errors, and therefore improve the mean estimates. The kriging-interpolated soil redistribution surfaces are shown in Fig. 4 for the three conversion models. The three models predicted similar spatial patterns for the relative soil redistribution magnitudes in the plot. That is, the predicted soil erosion rates increased from the upper border to maxima near the 50-m slope position and then gradually decreased to about zero near the 170-m slope position, at which point sediment deposition began and progressively increased toward the end of the slope. This spatial pattern is consistent with the topographic features. The erosion rates increased as slope length increased in the upper steep section and then decreased as slope steepness decreased in the middle-lower section (Fig. 1), while deposition occurred in the low-lying bottom section and the deposition rate increased toward the end of the plot. Although the three models predicted similar spatial patterns of soil redistribution, MBM1 and MBM2, compared with the PM, predicted more erosion in the top section but less deposition in the bottom section (Fig. 4).

Soil erosion occurred at 80% of the sampling points (Table 3). The sediment delivery ratios of water erosion, calculated across all sampling points, were 45, 73, 73, and 70% for the PM, MBM1, MBM2, and MBM3, respectively. Compared with the PM, the MBMs consistently predicted more erosion but less deposition, resulting in a higher sediment delivery ratio. The sediment delivery ratios after kriging were 54, 88, and 88% for

Table 3. mean soil redistribution rates estimated by the proportional model (Pm), the simple mass balance model (mBm1), the improved mass balance model (mBm2), and the mBm2 extended to include tillage erosion (mBm3) at the baseline nominal values of the input parameters, with the mean rates calculated either at the sampling points or after kriging interpolation.

Variablemeans across sampling points means after kriging

Pm mBm1 mBm2mBm3

Pm mBm1 mBm2Water Tillage

Erosion†, Mg ha−1 yr−1 −9.6 −11.2 −10.8 −10.1 −3.5 −5.3 −7.5 −7.3Deposition‡, Mg ha−1 yr−1 20.7 12.0 11.5 11.9 7.3 9.3 4.9 4.7Net erosion§, Mg ha−1 yr−1 −3.5 −6.5* −6.3* −5.6* −1.3 −2.3 −5.6* −5.4*Delivery ratio, % 45.1 72.6 72.9 69.9 57.7 53.7 87.7 87.9Relative error, % 28 141 133 109 NA¶ −17 106 100

* Different from the measured value at a = 0.05 using Nearing’s test.

† Mean erosion rate at all eroding points.

‡ Mean deposition rate at all deposition points.

§ Mean net soil loss across all points.

¶ NA, not applicable.

798 Journal of Environmental Quality

the PM, MBM1, and MBM2, respectively, indicating a 20% increase over the original estimates for the three models. The increase is because larger surface areas were predicted to undergo soil erosion following the kriging interpolation (data not shown). The sediment delivery ratios after kriging were believed to be more representative due to the smoothing effects.

Soil Redistribution at 95% Confidence LimitsSoil redistribution rates at the 95% confidence limits

were estimated for each parameter (one at a time) while the remaining parameters were held at their nominal values. Given the confidence limits established in this experiment (Table 2), the widths of the 95% confidence interval (CI) for the net soil redistribution rates calculated with the PM, MBM1, and MBM2 showed that the reference inventory had the most impact, followed by the particle size correction for erosion P and the tillage depth DL, with minimal impacts from mass depth Dm, bulk density BD, and particle size correction for deposition P¢ (Table 4). An increase in the reference inventory substantially increased the soil erosion estimates at the eroding points, while it decreased sedimentation at the depositional points, resulting in much greater increases in the mean net soil erosion rates. An increase in P considerably decreased the soil erosion estimates for the three models and also reduced the deposition rates for MBM1 and MBM2 but had no effect on the PM. For the PM, deposition rates as determined by Eq. [2] were unaffected by upslope erosion, and therefore the deposition estimates for the lower and upper confidence limits of P are the same (Table 4). In contrast, deposition calculated using MBM1 and MBM2 is affected by upslope erosion using Eq. [4–5]. For a given P and P¢, a long-term lower upslope erosion rate yields higher 137Cs concentrations in the soil, mobilized sediment, and deposits with time. A higher 137Cs concentration in the deposits means a lower sedimentation rate. This result indicates that the upslope erosion rates are positively correlated to the downslope deposition rates in the MBMs. An increase in DL leads to increases in both erosion and deposition. The increased deposition for the PM is because deposition rates are positively related to DL using Eq. [2]. The increased deposition for MBM1 and MBM2 were the results of increased upslope erosion rates and the positive correlation as discussed above. The impact of DL might be somewhat inflated because a small sample size of two was assumed and a wide CI of 8 cm was used in the calculation. As expected, the impacts of P¢, BD, and Dm on soil redistribution estimation were limited, partially because of the narrow CI ranges for these parameters as measured or generated in the study. The BD and Dm are generally easy to measure and often have small estimation errors, leading to small uncertainty in soil loss estimates.

The worst case scenarios, which used a combination of the upper or lower confidence limits of each parameter to produce the maximum or minimum estimate of net soil erosion, were used to indicate the largest possible ranges of the mean soil erosion estimates. The net erosion ranged from 0.6 to −9.5 Mg ha−1yr−1 for the PM, from −2.7 to −12.6 Mg ha−1yr−1 for MBM1, and from −3.0 to −10.8 Mg ha−1yr−1 for MBM2 (Table 4), showing a wide range of possible outcomes of net erosion estimates for each conversion model. The differences between the maximum and minimum net mean erosion estimates ranged approximately from 7 to 10 Mg ha−1 yr−1, which is close to the tolerable soil

Fig. 4. Kriging-interpolated spatial patterns of soil redistribution rates (mg ha−1 yr−1) simulated for each sampling point at the nominal values of all input parameters (i.e., the baseline scenario) using the Excel add-in program for the (A) proportional model, (B) simplified mass balance model, and (C) improved mass balance model. A negative number denotes erosion and a positive number signifies deposition.

www.agronomy.org • www.crops.org • www.soils.org 799

loss rate recommended for use in most parts of the United States. The positive net erosion and negative delivery ratio (noted as NA in Table 4) for the PM indicated that the arbitrary combination of the selected confidence limits may sometimes be physically implausible in the real world.

The soil redistribution estimates at the 95% confidence limits at all 108 sampling points were interpolated to a 0.5-m grid using kriging. In general, the absolute mean erosion rates in the eroding area and the mean deposition rates in the deposition area after kriging (Table 5) were much lower than those without kriging (Table 4), indicating a smoothing (averaging) effect on the estimated means. More importantly, the net soil erosion estimates at the 95% confidence limits were also lower, and the widths of

the 95% CI tended to be narrower and converge or shift toward the measured mean soil loss of −2.70 Mg ha−1 yr−1after kriging. These results demonstrate that kriging interpolation can produce better soil redistribution estimates and reduce uncertainty by smoothing the prediction surfaces, provided that the statistical sampling design is sound and the semivariogram function is well defined for the study area.

ImplicationsThe random component of 137Cs spatial variation on both

reference and sampling sites is the major setback for producing accurate soil redistribution estimates using the 137Cs tracing technique (Zhang, 2015). To overcome this obstacle, a large

Table 4. Estimated mean soil redistribution rates at the lower and upper limits of the 95% confidence interval of each parameter, while the rest were held at their nominal values, using the proportional model (Pm), the simple mass balance model (mBm1), and the improved mass balance model (mBm2).

VariableLower limit of 95% confidence interval for the mean upper limit of 95% confidence interval for the mean

Pm mBm1 mBm2 Pm mBm1 mBm2

Tillage depth, DL DL = 0.21 m (ne = 86, nd = 22) DL = 0.29 m (ne = 86, nd = 22) Erosion†, Mg ha−1 yr−1 −8.16 −9.51 −9.22 −11.14 −12.98 −12.50 Deposition‡, Mg ha−1 yr−1 17.53 10.19 9.77 23.92 13.91 13.27 Net erosion§, Mg ha−1 yr−1 −2.93 −5.50 −5.35 −4.00 −7.51 −7.25 Delivery ratio, % 45.1 72.6 72.9 45.1 72.6 72.8Bulk density, BD BD = 1335 kg m−3 (ne = 86, nd = 22) BD = 1425 kg m−3 (ne = 86, nd = 22) Erosion, Mg ha−1 yr−1 −9.33 −10.88 −10.50 −9.96 −11.61 −11.20 Deposition, Mg ha−1 yr−1 20.04 11.65 11.15 21.39 12.43 11.89 Net erosion, Mg ha−1 yr−1 −3.35 −6.29 −6.09 −3.58 −6.71 −6.50 Delivery ratio, % 45.1 72.6 72.8 45.1 72.6 72.9Particle size correction for erosion, P P = 1.738 (ne = 86, nd = 22) P = 2.267(ne = 86, nd = 22) Erosion, Mg ha−1 yr−1 −10.84 −12.95 −12.46 −8.52 −9.93 −9.56 Deposition, Mg ha−1 yr−1 20.72 13.88 13.23 20.72 10.64 10.14 Net erosion, Mg ha−1 yr−1 −4.41 −7.49 −7.23 −2.57 −5.74 −5.54 Delivery ratio, % 51.1 72.6 72.8 37.8 72.6 72.9

Particle size correction for deposition, P¢ P¢ = 0.581 (ne = 86, nd = 22) P¢ = 0.686 (ne = 86, nd = 22) Erosion, Mg ha−1 yr−1 −9.65 −11.24 −10.83 −9.65 −11.24 −10.83 Deposition, Mg ha−1 yr−1 22.34 12.99 12.40 19.36 11.25 10.74 Net erosion, Mg ha−1 yr−1 −3.13 −6.31 −6.10 −3.74 −6.66 −6.44 Delivery ratio, % 40.8 70.4 70.7 48.7 74.4 74.6Reference activity, Am

ref Amref = 1557.1 Bq m−2 (ne = 80, nd = 28) Am

ref = 1686.8 Bq m−2 (ne = 88, nd = 20) Erosion, Mg ha−1 yr−1 −8.59 −9.93 −9.57 −11.06 −13.01 −12.53 Deposition, Mg ha−1 yr−1 22.27 12.80 12.22 15.69 9.26 8.84 Net erosion, Mg ha−1 yr−1 −0.59 −4.04 −3.92 −6.11 −8.88 −8.57 Delivery ratio, % 9.3 54.9 55.3 67.8 83.8 84.0Mass tillage depth, Dm Dm = 328.0 kg m−2 (ne = 86, nd = 22) Dm = 367.6 kg m−2 (ne = 86, nd = 22) Erosion, Mg ha−1 yr−1 −10.23 −11.44 Deposition, Mg ha−1 yr−1 10.85 12.14 Net erosion, Mg ha−1 yr−1 −5.93 −6.64 Delivery ratio, % 72.9 72.9

Worst case scenario DL = 0.21, BD = 1335, P = 2.267, P¢ = 0.581, Amref = 1557.1,

Dm = 328 (ne = 80, nd = 28)DL = 0.29, BD = 1425, P = 1.738, P¢ = 0.686, Am

ref = 1686.8, Dm = 367.6 (ne = 88, nd = 20) Erosion, Mg ha−1 yr−1 −6.22 −7.19 −8.00 −15.61 −18.29 −15.60 Deposition, Mg ha−1 yr−1 20.18 10.25 11.29 17.55 12.32 10.42 Net erosion, Mg ha−1 yr−1 0.63 −2.67 −3.00 −9.47 −12.62 −10.78 Delivery ratio, % NA¶ 50.1 50.6 74.4 84.7 84.8

† Mean erosion rate at all eroding points (ne).

‡ Mean deposition rate at all deposition point (nd).

§ Mean net erosion across all points.

¶ NA, not applicable.

800 Journal of Environmental Quality

sample size and proper geostatistical treatment are needed to separate the random spatial variation in the 137Cs inventory from the systematic spatial variation that is a true result of soil erosion. Geostatistical analysis such as kriging can be used to estimate soil redistribution rates at unsampled points and therefore improve the overall estimation by effectively increasing

the sample size without exhaustive sampling, as demonstrated here and elsewhere (Chappell, 1998; van der Perk et al., 2002; Schuller et al., 2003; Chappell and Warren, 2003; Mabit et al., 2008). Kriging is useful for smoothing out the effect of the random error component of 137Cs spatial variation on erosion estimation and therefore for improving estimation of mean

Table 5. Kriging interpolated mean soil redistribution rates for the lower and upper limits of the 95% confidence interval of each parameter, while keeping the rest at their nominal values, using the proportional model (Pm), the simple mass balance model (mBm1), and the improved mass balance model (mBm2).

VariableLower limit of 95% confidence interval for the mean upper limit of 95% confidence interval for the mean

Pm mBm1 mBm2 Pm mBm1 mBm2

Tillage depth, DL DL = 0.21 m DL = 0.29 m Erosion†, Mg ha−1 yr−1 −4.87 −6.46 −6.24 −6.18 −8.69 −8.48 Deposition‡, Mg ha−1 yr−1 9.04 5.37 4.97 10.46 6.17 6.99 Net erosion§, Mg ha−1 yr−1 −1.88 −4.26 −4.18 −2.82 −6.43 −6.18 Delivery ratio, % 51.6 83.6 84.4 53.6 86.9 83.8 Erosional area, % 79.3 83.5 83.6 78.5 84.4 83.5Bulk density, BD BD = 1335 kg m−3 BD = 1425 kg m−3

Erosion, Mg ha−1 yr−1 −5.58 −7.36 −7.13 −5.94 −7.88 −7.61 Deposition, Mg ha−1 yr−1 10.02 5.93 5.87 11.04 6.56 6.26 Net erosion, Mg ha−1 yr−1 −2.00 −4.51 −4.39 −2.73 −6.18 −5.96 Delivery ratio, % 52.0 84.1 83.8 51.6 83.6 83.8 Erosional area, % 78.9 83.6 83.6 79.3 83.5 83.6Particle size correction for erosion, P P = 1.738 P = 2.267 Erosion, Mg ha−1 yr−1 −6.39 −8.80 −8.43 −4.96 −6.71 −6.47 Deposition, Mg ha−1 yr−1 10.90 6.63 6.54 9.77 5.27 5.00 Net erosion, Mg ha−1 yr−1 −2.94 −6.16 −5.95 −1.55 −4.73 −4.57 Delivery ratio, % 57.4 84.5 84.6 40.7 84.4 84.7 Erosional area, % 80.0 82.9 83.5 76.9 83.4 83.5

Particle size correction for deposition, P¢ P¢ = 0.581 P¢ = 0.686 Erosion, Mg ha−1 yr−1 −5.65 −7.55 −7.28 −5.85 −7.69 −7.41 Deposition, Mg ha−1 yr−1 11.29 6.95 6.64 10.09 5.86 5.60 Net erosion, Mg ha−1 yr−1 −1.95 −5.09 −4.93 −2.69 −5.52 −5.34 Delivery ratio, % 44.1 81.2 81.4 57.3 85.4 85.7 Erosional area, % 78.2 83.0 83.1 80.2 84.0 84.0Reference activity, Am

ref Amref = 1557.1 Bq m−2 Am

ref = 1686.8 Bq m−2

Erosion, Mg ha−1 yr−1 −4.02 −5.57 −5.38 −7.75 −9.48 −9.13 Deposition, Mg ha−1 yr−1 10.00 7.83 7.58 7.74 4.35 4.16 Net erosion, Mg ha−1 yr−1 0.76 −2.79 −2.72 −5.25 −7.84 −7.56 Delivery ratio, % NA¶ 63.1 63.6 80.8 93.8 93.9 Erosional area, % 65.9 79.2 79.5 83.9 88.1 88.2Mass tillage depth, Dm Dm = 328.0 kg m−2 Dm = 367.6 kg m−2

Erosion, Mg ha−1 yr−1 −6.95 −7.77 Deposition, Mg ha−1 yr−1 5.71 6.40 Net erosion, Mg ha−1 yr−1 −4.87 −5.44 Delivery ratio, % 83.8 83.8 Erosional area, % 83.5 83.5

Worst case scenario DL = 0.21, BD = 1335, P = 2.267, P¢ = 0.581, Am

ref = 1557.1, Dm = 328DL = 0.29, BD = 1425, P = 1.738, P¢ = 0.686,

Amref = 1686.8, Dm = 367.6

Erosion, Mg ha−1 yr−1 −3.22 −3.85 −4.30 −11.13 −13.42 −11.44 Deposition, Mg ha−1 yr−1 7.29 6.51 7.17 9.08 6.46 5.47 Net erosion, Mg ha−1 yr−1 1.73 −1.72 −1.94 −8.15 −11.01 −9.40 Delivery ratio, % NA 56.1 56.8 85.9 93.4 93.4 Erosional area, % 52.9 79.4 79.5 85.2 87.9 87.9

† Mean erosion rate at all eroding points.

‡ Mean deposition rate at all deposition point.

§ Mean net erosion across all interpolated points.

¶ NA, not applicable.

www.agronomy.org • www.crops.org • www.soils.org 801

soil redistribution. A statistical sampling design (e.g., grid or transect) and proper sampling size are strongly recommended to allow a meaningful kriging analysis. Generally, 100 to 150 samples are needed for kriging interpolation (Pennock and Appleby, 2002). This study showed that the overall mean soil loss rates after kriging, compared with those without kriging, were much closer to the measured mean, indicating the potential of using kriging to smooth out random spatial variations in the 137Cs inventory and therefore to improve mean soil redistribution estimation.

Because soil loss estimates for a given 137Cs depletion with different conversion models can vary by more than two orders of magnitude (Walling and Quine, 1990), model selection is critical for successful use of the 137Cs technique. Models are developed based on different assumptions and simplifications or even concepts and are expected to perform differently under different circumstances. The PM, which assumes that downslope deposition is independent of upslope erosion, predicted mean net erosion rates better than the MBMs did in this study, indicating a need for further examining the dependency relationship assumed in the MBMs. It should also be noted that because no soil erosion and 137Cs loss were assumed under the tallgrass prairie before the first tillage in 1978, MBM2 and MBM3 had no advantage over the other two models. To fully assess the potential of MBM2 and MBM3, they should be evaluated under more complex conditions in which temporal loss of newly deposited 137Cs fallout exists.

Theoretically, the MBMs are superior to the PM. In this particular study, however, the relative errors, compared with the measured mean net soil erosion, were much smaller with the PM than with the MBMs both with and without kriging interpolation (Table 3). Because the four models use nearly identical input parameter values for water erosion estimation in this particular study and thus possess similar overall parametrical uncertainty, the differences in the relative errors between the models are attributable to the model structural errors, suggesting that the MBMs may have more structural errors than the PM. This conclusion runs counter to the common wisdom that more complex models should have smaller structural errors but greater parametrical errors (Zhang et al., 2015). We don’t have a definitive explanation here. One possible source of the structural error may be the dependency assumption between erosion and deposition for the MBMs. That is, given a constant P and P¢, a greater long-term mean erosion rate would be accompanied by a greater long-term mean deposition rate and vice versa (Table 4). This positive association is inconsistent with the common belief that the relative magnitude of the erosion and deposition rates is largely controlled by the local topography and thus must be validated explicitly using measured deposition data.

ConclusionsThe four widely used conversion models for cultivated soils

were thoroughly evaluated with the measured parameter values and soil loss data of 34 yr collected in a unit experimental watershed. Compared with the measured net soil erosion, the relative errors of the estimated mean net soil erosion by water were 28, 141, 133, and 109% for the PM, MBM1, MBM2, and MBM3, respectively. Nearing’s test showed that the prediction

of the PM was considered acceptable, indicating that the PM performed better than the MBMs under the simplistic conditions in this study. Compared with the PM, the MBMs slightly overestimated mean water erosion rates in the eroding areas but considerably underestimated mean soil deposition rates in the deposition areas and consequently overestimated mean net soil loss rates for the entire watershed. This result indicated that the prediction errors among the four models were similar for the erosion predictions but were rather different for the deposition predictions between the MBMs and PM. The sizable underestimation of deposition may be caused by the assumed conceptual dependency between upslope erosion and downslope deposition in the MBMs, which warrants further examination. Our results also demonstrated that kriging interpolation tended to improve soil redistribution estimates without exhaustive sampling. The relative errors for the mean net erosion rates were reduced to −17, 106, and 100% for the PM, MBM1, and MBM2 by kriging interpolation, advocating the use of the geostatistically based grid sampling designs that allow effective kriging interpolation and smoothing. The 95% CI analyses for the net soil redistribution rates calculated with the PM, MBM1, and MBM2 showed that reference inventory had the most impact on erosion estimation, followed by particle size correction for erosion P and tillage depth DL, with minimal impacts from mass depth Dm, bulk density BD, and particle size correction for deposition P¢.

AcknowledgmentsThe work was partially funded by the open project: Tracking soil redistribution on hillslopes (Project no. 2011-KF-12) funded by the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University.

ReferencesChappell, A. 1998. Using remote sensing and geostatistics to map 137Cs-

derived net soil flux in south-west Niger. J. Arid Environ. 39:441–455. doi:10.1006/jare.1997.0365

Chappell, A., and A. Warren. 2003. Spatial scales of 137Cs-derived soil flux by wind in a 25 km2 arable area of eastern England. Catena 52:209–234. doi:10.1016/S0341-8162(03)00015-8

Govers, G., K. Vandaele, P. Desmet, J. Poesen, and K. Bunte. 1994. The role of tillage in soil redistribution on hillslopes. Eur. J. Soil Sci. 45:469–478. doi:10.1111/j.1365-2389.1994.tb00532.x

Kachanoski, R.G. 1993. Estimating soil loss from changes in soil cesium-137. Can. J. Soil Sci. 73:629–632. doi:10.4141/cjss93-060

Lance, J.C., S.C. McIntyre, J.W. Naney, and S.S. Rousseva. 1986. Measuring sediment movement at low erosion rates using cesium-137. Soil Sci. Soc. Am. J. 50:1303–1308. doi:10.2136/sssaj1986.03615995005000050044x

Li, S., D.A. Lobb, K.H.D. Tiessen, and B.G. McConkey. 2010. Selecting and applying cesium-137 conversion models to estimate soil erosion rates. J. Environ. Qual. 39:204–219. doi:10.2134/jeq2009.0144

Mabit, L., C. Bernard, M. Makhlouf, and M.R. Laverdiere. 2008. Spatial variability of erosion and soil organic matter content estimated from 137Cs measurements and geostatistics. Geoderma 145:245–251. doi:10.1016/j.geoderma.2008.03.013

Mabit, L., K. Meusburger, E. Fulajtar, and C. Alewell. 2013. The usefulness of 137Cs as a tracer for soil erosion assessment: A critical reply to Parsons and Foster (2011). Earth Sci. Rev. 127:300–307. doi:10.1016/j.earscirev.2013.05.008

Navas, A., M. Lopez-Vicente, L. Gaspar, and J. Machin. 2013. Assessing soil redistribution in a complex karst catchment using fallout 137Cs and GIS. Geomorphology 196:231–241. doi:10.1016/j.geomorph.2012.03.018

Navas, A., M. Lopez-Vicente, L. Gaspar, L. Palazon, and L. Quijano. 2014. Establishing a tracer based sediment budget to preserve wetlands in Mediterranean mountain agroecosystems. Sci. Total Environ. 496:132–143. doi:10.1016/j.scitotenv.2014.07.026

802 Journal of Environmental Quality

Nearing, M.A. 2000. Evaluating soil erosion models using measured plot data: Accounting for variability in the data. Earth Surf. Processes Landforms 25:1035–1043. doi:10.1002/1096-9837(200008)25:9<1035::AID-ESP121>3.0.CO;2-B

Nearing, M.A., G. Govers, and L.D. Norton. 1999. Variability in soil erosion data from replicated plots. Soil Sci. Soc. Am. J. 63:1829–1835. doi:10.2136/sssaj1999.6361829x

Pennock, D.J., and P.G. Appleby. 2002. Site selection and sampling design. p. 15–40. In: F. Zapata, editor, Handbook for the assessment of soil erosion and sedimentation using environmental radionuclides. Kluwer Acad. Publ., Dordrecht, the Netherlands.

Porto, P., and D.E. Walling. 2012a. Using plot experiments to test the validity of mass balance models employed to estimate soil redistribution rates 137Cs and 210Pbex measurements. Appl. Radiat. Isot. 70:2451–2459. doi:10.1016/j.apradiso.2012.06.012

Porto, P., and D.E. Walling. 2012b. Validating the use of 137Cs and 210Pbex measurements to estimate rates of soil loss from cultivated land in southern Italy. J. Environ. Radioact. 106:47–57. doi:10.1016/j.jenvrad.2011.11.005

Porto, P., D.E. Walling, and G. Callegari. 2004. Validating the use of caesium-137 measurements to estimate erosion rates in three small catchments in southern Italy. IAHS Publ. 288:75–83.

Porto, P., D.E. Walling, G. Callegari, and A. Capra. 2009. Using caesium-137 and unsupported lead-210 measurements to explore the relationship between sediment mobilization, sediment delivery and sediment yield for a Calabrian catchment. Mar. Freshwater Res. 60:680–689. doi:10.1071/MF08050

Porto, P., D.E. Walling, and V. Ferro. 2001. Validating the use of caesium-137 measurements to estimate soil erosion rates in a small drainage basin in Calabria, southern Italy. J. Hydrol. 248:93–108. doi:10.1016/S0022-1694(01)00389-4

Porto, P., D.E. Walling, V. Ferro, and C.D. Stefano. 2003b. Validating erosion rate estimates provided by caesium-137 measurements for two small forested catchments in Calabria, southern Italy. Land Degrad. Dev. 14:389–408. doi:10.1002/ldr.561

Porto, P., D.E. Walling, V. Tamburino, and G. Callegari. 2003a. Relating caesium-137 and soil loss from cultivated land. Catena 53:303–326. doi:10.1016/S0341-8162(03)00084-5

Ritchie, J.C., and J.R. McHenry. 1990. Application of radioactive fallout cesium-137 for measuring soil erosion and sediment accumulation rates and patterns: A review. J. Environ. Qual. 19:215–233. doi:10.2134/jeq1990.00472425001900020006x

Schuller, P., A. Ellies, A. Castillo, and I. Salazar. 2003. Use of 137Cs estimate tillage- and water-induced soil redistribution rates on agricultural land under different use and management in central-south Chile. Soil Tillage Res. 69:69–83. doi:10.1016/S0167-1987(02)00129-0

Sterk, G., and A. Stein. 1997. Mapping wind-blown mass transport by modeling variability in space and time. Soil Sci. Soc. Am. J. 61:232–239. doi:10.2136/sssaj1997.03615995006100010032x

van der Perk, M., O. Slavik, and E. Fulajtar. 2002. Assessment of spatial variation of cesium-137 in small catchments. J. Environ. Qual. 31:1930–1939.

Wakiyama, Y., Y. Onda, S. Mizugaki, H. Asai, and S. Hiramatsu. 2010. Soil erosion rates on forested mountain hillslopes estimated using 137Cs and 210Pbex. Geoderma 159:39–52. doi:10.1016/j.geoderma.2010.06.012

Walling, D.E., and Q. He. 1998. Use of fallout 137Cs measurements for validating and calibrating soil erosion and sediment delivery models. IAHS Publ. 249:267–278.

Walling, D.E., and Q. He. 1999. Improved models for estimating soil erosion rates from cesium-137 measurements. J. Environ. Qual. 28:611–622. doi:10.2134/jeq1999.00472425002800020027x

Walling, D.E., Q. He, and T.A. Quine. 1995. Use of caesium-137 and lead-210 as tracers in soil erosion investigations. IAHS Publ. 229:163–172.

Walling, D.E., and T.A. Quine. 1990. Calibration of caesium-137 measurements to provide quantitative erosion rate data. Land Degrad. Rehabil. 2:161–175. doi:10.1002/ldr.3400020302

Walling, D.E., and T.A. Quine. 1992. The use of caesium-137 measurement in soil erosion surveys. IAHS Publ. 210:143–152.

Walling, D.E., Y. Zhang, and Q. He. 2011. Models for deriving estimates of erosion and deposition rates from fallout radionuclide (caesium-137, excess lead-210, and beryllium-7) measurements and the development of user friendly software for model implementation. In: Impact of soil conservation measures on erosion control and soil quality. IAEA-TECDOC-1665. Int. Atomic Energy Agency, Vienna. p. 11–33.

Zapata, F. 2010. Handbook for the assessment of soil erosion and sedimentation using environmental radionuclides. Kluwer Acad. Publ., Dordrecht, the Netherlands.

Zhang, X., D.L. Higgitt, and D.E. Walling. 1990. A preliminary assessment of the potential for using caesium-137 to estimate rates of soil erosion in the Loess Plateau of China. Hydrol. Sci. J. 35:243–251. doi:10.1080/02626669009492427

Zhang, X.C.J. 2015. New insights on using fallout radionuclides to estimate soil redistribution rates. Soil Sci. Soc. Am. J. 79:1–8. doi:10.2136/sssaj2014.06.0261

Zhang, X.-C.J., and J.D. Garbrecht. 2002. Precipitation retention and soil erosion under varying climate, land use, and tillage and cropping systems. J. Am. Water Resour. Assoc. 38:1241–1253. doi:10.1111/j.1752-1688.2002.tb04345.x

Zhang, X.-C., J.D. Garbrecht, J.L. Steiner, and R.L. Blazs. 2014. Upper Washita River experimental watersheds: Sediment database. J. Environ. Qual. 43:1273–1279. doi:10.2134/jeq2013.07.0288

Zhang, X.C., G.H. Zhang, and X. Wei. 2015. How to make 137Cs erosion estimation more useful: An uncertainty perspective. Geoderma 239-240:186–194. doi:10.1016/j.geoderma.2014.10.004