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Uncertainty assessment of soil erodibility factor for revised universal soil loss equation
Catena 46 Ž2001. 1–14 www.elsevier.comrlocatercatena
Uncertainty assessment of soil erodibility factor for revised universal soil loss equation Guangxing Wang a , George Gertner a,) , Xianzhong Liu a , Alan Anderson b a
Department of Natural Resources and EnÕironmental Sciences, UniÕersity of Illinois, W503 Turner Hall, 1102 South Goodwin, Urbana, Il 61801 USA b USACERL, P.O. Box 9005, Champaign, Il 61820-1305 USA Received 10 November 2000; received in revised form 16 May 2001; accepted 5 June 2001
Abstract Soil erodibility accounts for the influence of the intrinsic soil properties on soil erosion and is one of six factors in the Revised Universal Soil Loss Equation ŽRUSLE., a most widely used model to predict long-term average annual soil loss. In a traditional soil survey, each of the soil types Žclasses. is assigned with a soil erodibility value that is assumed to be constant over time. However, heterogeneity of soil in time and in space tends to support the concept that soil erodibility depends dynamically and spatially on the set of properties of a specific soil. This study statistically compared the published soil erodibility values with those from a set of soil samples in terms of their differences. The published values tend to underestimate soil erodibility. This feature is also supported by the uncertainty assessment in difference maps of the published K values versus those from soil samples. Spatial prediction and uncertainty analysis of the soil erodibility from the set of soil samples was carried out using a sequential Gaussian simulation. The results show that the simulation produces a reliable prediction map of soil erodibility and can be recommended as a monitoring strategy to spatially update soil erodibility. Published by Elsevier Science B.V. Keywords: Uncertainty assessment; Spatial prediction; Soil erodibility; Simulation
1. Introduction Soil loss in the USA was estimated using the Universal Soil Loss Equation ŽUSLE. ŽWischmeier and Smith, 1978. before its modified version, and is currently predicted )
Corresponding author. Tel.: q1-217-333-9346; fax: q1-217-244-3219. E-mail address: [email protected] ŽG. Gertner..
0341-8162r01r$ - see front matter. Published by Elsevier Science B.V. PII: S 0 3 4 1 - 8 1 6 2 Ž 0 1 . 0 0 1 5 8 - 8
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using the Revised USLE ŽRUSLE. ŽRenard et al., 1994, 1997. for the purpose of agricultural, rangeland and environmental management. Both USLE and RUSLE are related to rainfall erosivity factor Ž R ., soil erodibility factor Ž K ., slope length factor Ž L., slope steepness factor Ž S ., cover management factor Ž C ., and support practice factor Ž P .. These equations consist of empirical model sets derived from an extensive database and their model parameters contain uncertainty when using these equations for a specific area. Moreover, these factors vary over space and time, depend on other variables, and may be correlated with each other. Additionally, errors in sampling, measuring, and modeling will lead to uncertainty in the estimate of these factors. The uncertainty may not be neglected and will be propagated in the prediction of soil loss. This uncertainty might be important when local estimates are required for management planning. Thus, there is a strong need to develop a general methodology for the spatial assessment of uncertainty for users of such systems. In recent years, we have been working on a large project related to the prediction and uncertainty analysis of soil erosion using the RUSLE. Our objectives are to develop a general procedure for spatially and temporally predicting soil loss, identifying various errors, modeling their propagation, and generating error budgets in order to provide guidelines for error reduction and management planning. As one part of the overall uncertainty analysis for soil loss prediction, this study reported here focuses on uncertainty assessment of soil erodibility factor K used in the RUSLE. The soil erodibility factor K measures the contribution of soil intrinsic properties to soil erosion. For major soil types and soil texture classes in the United States, the values of soil erodibility factor K have been published and can be obtained mainly from the USDA-Natural Resources Conservation Service ŽNRCS. ŽSWCS, 1995; Wischmeier and Smith, 1978.. Each soil type corresponds with a published soil erodibility value. The published values from USDA-NRCS are the average values within the soil types when the data were collected. They are assumed to be constant over time. However, heterogeneity of soil in time and in space tends to support the concept that soil erodibility depends dynamically and spatially on the properties of a specific soil. Soil properties influencing soil erodibility as used in RUSLE are grouped into two categories: Ž1. those that affect infiltration rate, movement of water through the soil, and water storage capacity; and Ž2. those that affect dispersion, detachability, abrasion, and mobility of soil particles by rainfall and runoff ŽWischmeier and Mannering, 1969; SWCS, 1995; Renard et al., 1997; Soil Survey Staff, 1997.. The important properties are texture, organic matter content, size and stability of structural aggregates in the exposed layer, permeability of the subsoil, and depth to a slowly permeable layer. Fine sand and silt soil particles are most susceptible to detachment and transport ŽWischmeier and Mannering, 1969.. Soil organic matter content affects soil aggregation, soil particle size distribution and soil infiltration capacity ŽStevenson, 1985.. Main factors considered in the soil erodibility calculation in the RUSLE include soil texture Ž%sand, %silt, %very fine sand and silt, and %clay., soil organic matter content, soil structure, and soil permeability ŽWischmeier and Mannering, 1969; Wischmeier et al., 1971; Wischmeier and Smith, 1978.. Because of the underling forces shaping the soils, the soil properties vary with time and space and are affected by climate, organisms, topography and parent materials interacting with time ŽJenny, 1941.. Climate
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factors, temperature and rainfall, affect soils as well as plants growing on those soils. Plant community succession due to the change of the soil physical environment is well observed and change in plant composition in turn affects the soil properties. The soil properties vary also in space because of the variation of soil formation factors. Thus, a soil erodibility value for a specific soil may vary dynamically and spatially. Using the soil erodibility values obtained previously from an extensive database to a specific area may lead to uncertainty. It is necessary to include the uncertainty on soil erodibility into the overall uncertainty analysis of soil loss and to improve methods for mapping the soil loss. Prediction methods to reliably estimate soil erodibility in space and time should be based on spatial variability of soil properties. Spatial statistical methods such as kriging interpolation and simulation have been used in spatial prediction, given a set of neighboring observations and assuming that there is a spatial correlation of a variable. These methods were developed in spatial geology and recently have been expanded to soil science. In soil management and soil remediation, for example, soil quality is evaluated and spatial distribution of soil nutrients andror chemicals is estimated by kriging ŽZhang et al., 1992; Smith et al., 1993; Hosseini et al., 1994; Chung et al., 1995; Gotway et al., 1996; Paz et al., 1996.. In studies by Istok and Rautman Ž1996., Rossi et al. Ž1993., and Mowrer Ž1997., sequential Gaussian simulations were applied to predict nitrate and DCPA concentrations in ground water, to estimate the rootworm density, and to generate estimation of variables for old growth forest conditions. Estimates by various kriging approaches are smoothed and may be best in local prediction. However, the kriging variances do not adequately reflect uncertainty of estimates because the variances depend only on the data configuration and not on the actual observed data. In spatial simulation, an estimate and variance obtained by a kriging method for a location are used as statistical parameters to determine a conditional cumulative density distribution. From the distribution, a value is drawn at random. This process can be repeated many times, which will result in many estimates at the location. From the estimates, an expected value and its variance can be derived. Thus, a set of the estimates at the location provides a visual and quantitative measure Žactually a model. of spatial uncertainty. The uncertainty depends on not only the data configuration but also on the data values. The study reported here discusses the use of published soil erodibility values from the national soil survey in spatial prediction of soil loss by traditional methods, and assess the uncertainty of the published values by comparing them with the soil erodibility values from a set of soil samples. A case study for spatial prediction and uncertainty analysis of soil erodibility was carried out by a sequential Gaussian simulation procedure in order to support a methodology recommendation for updating soil erodibility values as a monitoring strategy, and for providing spatial uncertainty information for an overall uncertainty analysis of soil loss prediction. 2. Materials and methods The study area is about 87,890 ha and located in Bell and Coryell Counties approximately 256 km southwest of Dallas, Texas USA. The climate is characterized by
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long, hot summers and short mild winters ŽTazik et al., 1993.. Average temperature ranges from 8 to 29 8C. Average annual precipitation is 81 cm. Elevations vary from 180 to 375 m above sea level. Most slopes are 2–5%. Soils are generally shallow to moderately deep and clayey, underlain by limestone bedrock. Soil samples were collected from 186 plots over the area and measured at a laboratory for soil properties including: %silt, %sand, %clay, %organic matter, and classes for structure and permeability. The soil erodibility factor K values of these soil samples were calculated using the following formula ŽWischmeier and Smith, 1978.: Ks
2.1 = 10y4 Ž 12 y OM . M 1.14 q 3.25 Ž S y 2 . q 2.5 Ž P y 3 .
, Ž 1. 7.59 = 100 where K is expressed in units of t ha h hay1 MJ 1.14 mmy1 , OM is soil organic matter content, M is Ž%silt q %very fine sand. Ž100 y %clay., S is soil structure code and P is permeability class. If soil organic matter content was greater or equal to 4%, OM was considered constant at 4%. Moreover, the influence of rock fragments on soil loss was accounted for by a subsurface component in the soil erodibility K factor ŽRenard et al. 1997.. The soil profile descriptions with permeability classes for all the soil samples in this study included the effect of rock fragments on permeability. The soil erodibility K factor and the subsurface component for effect of rock fragments were explained via an adjustment for permeability classes. The soil erodibility factor values obtained with the soil samples and Eq. Ž1. are denoted as A K sampleB. The sampled K values were used as a basis for comparison. A soil type map with the published soil erodibility K values for the case study area was obtained from USDA-Soil Conservation Service ŽUSDA-Soil Conservation Service, ŽSCS., 1985., now called USDA-Natural Resources Conservation Service ŽUSDANRCS.. According to the soil types obtained, these soil samples above were assigned with published K values, denoted as A K pubB. The K pub values were statistically compared with the K sample values in terms of the differences Ž K pub y K sample.. The spatial distribution of the differences was further displayed to visually examine possible underestimation and overestimation using the published K values. In addition, a map of the published soil erodibility K values was produced by a point-in-polygon method, that is, assigning the polygons with the published K values according to soil types in the soil map. The uncertainty of the published K values in prediction of soil loss using RUSLE was assessed. A spatial statistical procedure was applied for spatial prediction and uncertainty analysis of soil erodibility factor K using the K sample values. The procedure predicts a soil erodibility K value for an unknown location using the known K sample values and the existing estimates around the unknown location given a specified neighborhood. The description of this procedure follows. The K sample values were first de-clustered to obtain unequal weights for each sample location. The de-clustering led to less weight for the dense locations and more weight for the sparse locations. At the same time, the K sample values were transformed into normal scores as required by a sequential Gaussian simulation method. The spatial variability of the K sample values was then derived by calculating and modeling the experimental semivariogram. The semivariogram measures the spatial
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similarity of the soil erodibility factor given a separation vector or separation distance of data at a specific direction. The semivariogram is important because it is used to derive weights minimizing the covariance between sets of measured locations and unmeasured points, thus providing a minimum error estimate of the unknown values at these points. In addition, the anisotropy in spatial variability of soil erodibility was examined by obtaining semivariograms in different directions. If the anisotropy exists, the semivariograms from different directions must be fitted. For the study, sequential Gaussian simulation was used for spatial modeling and prediction. Briefly, if a study area is divided into N nodes of a grid, the steps used for the sequential Gaussian simulation are as follows ŽGoovaerts, 1997.: Ži. Define a random path visiting each node of the grid defined over the study area; Žii. At the ith node to be visited, model the conditional cumulative distribution function given the n original data and all Ž i y 1. simulated values at the previously visited locations, using simple kriging with the modeled semivariogram; Žiii. For the ith node, draw a realization from that conditional cumulative distribution function and this realization will become a conditional datum for all subsequent drawings; Živ. From the first node to be visited, repeat steps Žii. and Žiii. above until all N nodes are visited and each has received a simulated value. One realization consisting of the set of simulated values for the whole area is obtained when all N nodes of the grid have their simulated values. Repeating L times the entire sequential process with possibly different paths to visit the N nodes will result in L realizations. From the L realizations, an expected prediction map and conditional variance map can be derived. Using the sequential Gaussian simulation method can lead to a set of realizations providing a visual and quantitative measure Žactually a model. of spatial uncertainty. If a spatial feature, such as larger than a given value, exists on most of the L realizations, it is deemed certain, and otherwise uncertain. The simulation method thus reproduces model statistics, and it models spatial uncertainty. During the process of sequential Gaussian simulation, simple kriging is used to determine the mean and variance of the conditional distribution for each unknown location. The simple kriging is unbiased with minimum local error variance. For a detailed description of de-clustering, semivariogram, simple kriging and simulation methods mentioned above, readers can refer to Goovaerts Ž1997. and Deutsch and Journel Ž1998..
3. Results The total study area is composed of 25 soil types. A soil map is shown in the upper section of Fig. 1, and the soil characteristics are detailed in Table 1. All soil types have an organic matter content of less than 4% and are all well drained. The dominant soil types with counts greater than 10% in this area are BtC2, DrC, ErB and ReF. These are upland soils and formed on limestone, limestone and marl, or limestone and shale. BtC2
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Fig. 1. Soil map of the study area based on soil survey and published soil erodibility K factor map. Legend on left corresponds to the top map and legend on right corresponds to the bottom map. The unit for K factor is t ha h hay1 MJy1 mmy1 .
is a deep soil and the other three dominants are shallow soils. The soil textures for BtC2, DrC, ErB and ReF are, respectively, gravelly loam and clay loam, clay loam and gravelly clay loam, cobbly silty clay, and gravelly clay loam. Three co-dominant soil types with counts less than 10% but greater than 5% are NuC, EvB and KrB, on the low ridges, upland and terrace, respectively. The total of four dominant and three co-dominant soils occupy totally 83.4% of the area and four dominant soils type cover 63%. The soil erodibility map derived using a traditional point-in-polygon method in terms of the soil types and their published soil erodibility K values is given in the lower section of Fig. 1. The published K values vary from 0.0131 to 0.0488 t ha h hay1 MJy1 mmy1 , with 59.6% of values less than 0.0224 t ha h hay1 MJy1 mmy1 . The soil map leads to sharp-edged boundaries, that is, spatial discreteness of soil erodibility K values between the soil type polygons, and with the same estimates within each of the polygons. The spatial variability of soil erodibility over the whole area is noncontinuous and local variability within small areas disappears. The locations of soil samples and their estimated soil erodibility values are shown at the top of Fig. 2. The corresponding published K values for these sample locations and their differences between the published and sampled K values are also shown respectively in the middle and bottom of Fig. 2. The minimum and maximum soil erodibility K values from the soil samples are 0.0125 and 0.0589 t ha h hay1 MJy1 mmy1 and their corresponding published K values from soil survey are 0.0131 and 0.0488 t ha h hay1 MJy1 mmy1 . Higher soil erodibility K values from the soil samples are mainly located in the west and in a small section in the north, and lower values in other areas. Out of
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Table 1 Soil properties of 25 soil types covering the study area Soil Type
Cover Ž%.
BaB
0.5
BgB
0.1
Bo BtC2
3.3 22.1
ChB CoB2
2.1 0.7
CwB
0.1
DeB
0.0
DrC
14.6
EcB
0.2
ErB
14.4
EvB
6.2
Fr
0.4
HoB
0.0
KrB
5.3
LeB
1.7
LyB MnB
0.7 0.3
NuC
8.9
PrB ReF
0.3 11.9
SeC
0.4
SlB TpC
4.2 1.5
WsC2
0.1
a
Soil
Organic matter Ž%.
Depth
Position
Parent material
Bastsil fine sandy loam Bolar gravelly clay loam Bosque clay loam Brackett–Topsey associationa Cho clay loam Cisco fine sandy loam Crawford silty clay Denton silty clay Doss–Real complex a Eckrant cobbly silty clay Eckrant–Rock outcrop complex a Evant silty clay Frio silty clay Houston Black clay Krum silty clay Lewisville clay loam Lindy clay loam Minwells fine sandy loam Nuff very stony silty clay loam Purves silty clay Real–Rock outcrop complex a Seawillow clay loam Slidell silty clay Topsey–Pidcoke associationa Wise clay loam
-2
deep
terrace
alluvium
1–3
moderate
1–4 1–3
deep deep
convex knolls; ridge tops floodplain upland
1–2 -1
shallow deep
upland upland
limestoneq marl alluvium limestoneq shale sediment sediment
1–3
moderate
upland
limestone
1–4
deep
upland
1–3
shallow
upland
1–4
shallow
upland
clayer materials limestoneq marl limestone
1–4
shallow
upland
limestone
2–4
shallow
upland
1–4
deep
floodplain
...b
...b
...b
mare sediment old alluvial sediment ...b
1–3
deep
terrace
1–3
deep
terrace
old alluvial sediment Alluvium
...b -1
...b deep
...b terrace
...b Sediment
2–4
deep
low ridge
1–3 1–4
shallow shallow
upland upland
-1
deep
terrace
marlq limestoneqshale Limestone limestone q marl sediment
1–4 1–4
deep deep
upland upland
marine sediment Sediment
0.5–2
deep
upland
marlqsand
For soil complex or association, columns 4 to 6 are the properties of the first soil series, the predominant one within the complex or the association. b Information not available.
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Fig. 2. Location of field soil samples and spatial distributions of the soil erodibility K values derived from soil samples Žtop map., published K values Žmiddle map. and the differences between published and sampled K values Žbottom map.. The unit for K factor is t ha h hay1 MJy1 mmy1 .
186 sample plots, there are only 17 locations Že.g. 9.1%. where K values are less than 0.0224 t ha h hay1 MJy1 mmy1 . In the center of each of the maps, there is a blank area outlined where no samples were taken because sampling was not allowed. In the spatial distribution of published K values Žin the middle of Fig. 2., higher values at the west correspond with those at the same locations based on the soil samples Žat the top of Fig. 2.. However, some of higher published K values are also found in the east and close to the boundary of the northeast. From 186 sample locations, there are 88
Table 2 Statistical description of published soil erodibility K values Ž K pub. from USDA-Natural Resources Conservation Service ŽNRCS., from the soil samples Ž K sample., and differences between the published and sampled K values K pub from USDA-NRCS soil survey
Mean K sample
Stdv of K sample
Mean Diff
Stdv of Diff
Sample size
Calculated t value
BaB BgB Bo BtC2 ChB CoB2 CwB DrC EcB ErB EvB Fr KrB LeB LyB MnB NuC PrB ReF SeC SlB TpC WsC2 Overall
0.0316 0.0264 0.0369 0.0224 0.0369 0.0487 0.0422 0.0422 0.0198 0.0198 0.0422 0.0422 0.0422 0.0422 0.0198 0.0316 0.0224 0.0422 0.0132 0.0369 0.0422 0.0422 0.0487 0.0310
0.0361 0.0393 0.0491 0.0352 0.0382 0.0462 0.0270 0.0420 0.0318 0.0327 0.0289 0.0423 0.0345 0.0451 0.0412 0.0347 0.0381 0.0320 0.0277 0.0469 0.0337 0.0441 0.0485 0.0360
0.0074 0.0046 0.0071 0.0076 0.0079 0.0028 0.0105 0.0096 0.0061 0.0084 0.0069 0.0072 0.0091 0.0041 0.0103 0.0043 0.0091 0.0014 0.0082 0.0009 0.0153 0.0076 0.0134 0.0099
y0.0045 y0.0129 y0.0123 y0.0128 y0.0013 0.0025 0.0152 0.0001 y0.0120 y0.0129 0.0133 y0.0001 0.0076 y0.0029 y0.0215 y0.0030 y0.0157 0.0101 y0.0145 y0.0100 0.0084 y0.0020 0.0003 y0.0051
0.0074 0.0046 0.0071 0.0076 0.0079 0.0028 0.0105 0.0096 0.0061 0.0084 0.0069 0.0072 0.0091 0.0041 0.0103 0.0043 0.0091 0.0014 0.0082 0.0009 0.0153 0.0076 0.0134 0.0130
3 3 4 20 3 3 6 25 3 32 15 3 9 4 4 3 15 3 14 3 5 3 3 186
0.85 3.99 2.99 7.23 0.23 1.26 3.24 0.08 2.79 8.46 7.19 0.03 2.37 1.25 3.63 1.00 6.49 10.14 6.36 14.79 1.11 0.37 0.03 5.31
Significance level
- 0.1 - 0.1 - 0.001
- 0.05
- 0.001 - 0.001 - 0.05 - 0.05
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Soil type
- 0.001 - 0.001 - 0.001 - 0.01
- 0.001
Stdv sStandard deviation, Diff sdifference. The unit for K factor is t ha h hay1 MJy1 mmy1 . 9
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locations Že.g. 47.3%. where the published K values are less than 0.0224 t ha h hay1 MJy1 mmy1 . In the spatial distribution of the differences between the published K values and sample K values Žat the bottom of Fig. 2., the plus markers and triangles indicate positive and negative differences, respectively. From 186 sample locations, there are 21 locations Že.g. 11.3%. displayed in circles, implying the sample locations where the differences between the published K and sampled K values are not significantly statistically different from zero and not biased at the significant level of 0.05. A total of 116 sample locations are triangles and their differences are significantly negative, implying that most of the sample locations Ž62.4%. may be statistically underestimated by the published K values. The remaining 49 sample locations Že.g. 26.3%. are plus markers and may be statistically overestimated by the published K values. In Table 2, the published K values, sampled K values and their differences for each soil type are statistically described. As a whole, the number of soil samples for each soil type was proportional to its area. For most of the 25 soil types, the differences between the published and sampled K values within the soil types are significantly different from zero at the significance level of 0.1, and their mean differences are negative. Overall, the average of the differences between the published and sampled K values is negative and differs significantly from zero at significance level of 0.001. The differences between published and sample K values varied from y0.034 to 0.0296 t ha h hay1 MJy1 mmy1 . In Fig. 3, the relationship of the differences against the published K values exhibits a distinct separation. When these published K values are less than 0.04, most of the differences are negative, that is, underestimation occurs, and otherwise most of the differences are positive, indicating overestimation. Overall, most of the differences are negative. In this study area, the spatial variability of soil erodibility K values from the soil samples was examined in four directions: azimuths 08, 458, 908 and 1358. No significant anisotropy in the spatial variability was found. The prediction map of soil erodibility K values was derived using sequential Gaussian simulation and is presented at the top of
Fig. 3. The difference of K pub and K sample versus K pub. The unit for K factor is t ha h hay1 MJy1 mmy1 .
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Fig. 4. The variance image of the predicted K values and probability map for predicted K values are given at the middle and bottom of this figure. At center of the study area, there is an area without soil samples and the area was removed. The spatial distribution of the predicted K values based on the simulation was consistent with that of the soil erodibility K values based on the samples. That is, higher K values were predicted at the west and a small section of the north, and lower values at the other sections. There are only a few small areas where the predicted values were less than 0.0224 t ha h hay1 MJy1 mmy1 . At the sample locations, the simulation maintained the K values from the soil samples and the prediction variances were zero. The farther the predicted locations were away from the sample locations, the larger the prediction variances. Smaller variances occur in the areas where soil erodibility K values are lower and sampling density is higher. In addition, a threshold value, 0.042 t ha h hay1 MJy1 mmy1 , was selected only as an example and used to calculate probability for the predicted K values larger than the specified threshold value. That is, suppose that when soil erodibility K values are larger than this threshold value, soil loss might be considered to be serious. At the
Fig. 4. Using sequential Gaussian simulation, spatial prediction image Žtop map. of soil erodibility K values based on soil samples, variance image of the predicted values Žmiddle map., and probability map Žbottom map. for K values larger than 0.042. The unit for K factor is t ha h hay1 MJy1 mmy1 .
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bottom of Fig. 4, the probability for the predicted K values larger than the threshold value is the highest at the west and decreases from west to the east. The probability is less than 0.5 for most of the entire study area.
4. Discussion and conclusions The uncertainty of the published K values was documented in this paper. The methods used for assessing the uncertainty included statistically comparing the published and sampled soil erodibility K values in terms of their differences, analyzing error properties of the published K values, and performing spatial prediction and uncertainty analysis of the K values with the sample data using sequential Gaussian simulation. The results showed that unbiased estimation of soil erodibility K values using the published information was possible only at a few sample locations and for a few soil types. Biased estimation, especially underestimation, was observed at most of the sample locations, in most of the study area, and for most of the 25 soil types. For the whole area, using the published K values led to the underestimation of soil erodibility. Thus, the published soil erodibility K values should be used with care. This underestimation can be explained by the change of soil properties over space and time Žsee p.133, Hudson, 1995.. The published soil erodibility K values were determined 20 years ago using average values within the same soil series. In fact, the soil erodibility K values within a soil series varied within a certain range, and using an average value might thus result in uncertainty. On the other hand, the change of soil properties over time was caused by many factors such as plants, climate, human activities, and so on. Because off-road vehicular impact activities took place in recent years in this area, we looked into the correlation between the cumulative disturbance ŽDemarais et al., 1999. caused by the off-road vehicular impact activities and sampled soil erodibility K values, and their differences with the published K values. The correlations were found to be weak. That is, the soil erodibility increased due to many factors or their integrated effect, but not solely from these activities. Determining the soil erodibility factor Ž K . directly from soil loss data collected from repeat measurement plots measured over the long term Žover 20 years. is the most reliable method for assessing soil erodibility ŽWischmeier and Mannering, 1969; SWCS, 1995; Renard et al., 1997.. This method, however, is very expensive and can take a long time to obtain results, which can be impractical for many situations ŽRenard et al., 1997.. The second alternative is using the published soil erodibility K values by USDA-Natural Resources Conversation Service ŽUSDA-NRCS.. Its advantages include low cost and ease of acquisition of soil erodibility K values. However, the assumption that soil erodibility K values are constant over time and the use of an average K value for each soil type Žclass. introduces uncertainty into the estimate of soil erodibility. In addition, using the published K values introduces spatial discreteness in the soil erodibility values. Another alternative to determine soil erodibility K values is the application of geostatistical methods such as sequential Gaussian simulation with soil erodibility K
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values from soil samples, as used in this paper. The sequential Gaussian simulation produced not only a spatial prediction map of soil erodibility K values, but also, uncertainty measures, prediction variance images and probability maps for a specific feature such as soil loss larger than a given value. The spatial distribution of soil erodibility K values predicted using this method is very similar to that of the soil samples. The variance images and probability maps of the predicted values measured the uncertainty caused not only by the variation of the soil erodibility values based on the soil samples, but also by the spatial orientation of the sample plots. Thus, the procedure used in this paper for spatial prediction and uncertainty assessment of soil erodibility can be recommended as a potential monitoring strategy to periodically update soil erodibility K value maps. When this method is applied to all factors in the RUSLE, the uncertainties obtained can provide decision-makers with useful information to reduce the risks in soil and land management. Finally, as already mentioned, this study is only one part of a large study for developing a general methodology and framework of uncertainty assessment for a soil loss prediction system. The ongoing work will include developing spatial error budgets that systematically account for important sources of errors, and show how these errors propagate through the modeling systems. The variance maps presented here will be considered as one source of uncertainties in the development of these error budgets. The uncertainty in K values will not be neglected in the generation of the overall uncertainty analysis for soil loss predictions.
Acknowledgements We are grateful to Strategic Environmental Research and Development Program ŽSERDP. for providing support for the study, and to Ms. Tina Carrington, Mr. Eric Schreiber and Dr. Robert Darmody for collection of field data and laboratory work.
References Chung, C.K., Chong, S.K., Varsa, E.C., 1995. Sampling strategies for fertility on a Stoy silt loam soil. Commun. Soil Sci. Plant Anal. 26, 741–763. Demarais, S., Tazik, D., Guertin, P., Jorgensen, E., 1999. Disturbance associated with military exercises. In: Walker, L. ŽEd.., Ecosystems of the World 16: Ecosytems of Disturbed Ground. Elsevier, Amsterdam, pp. 385–396. Deutsch, C.V., Journel, A.G., 1998. Geostatistical Software Library and User’s Guide. Oxford Univ. Press, N.Y., p. 369. Goovaerts, P., 1997. Geostatistics for natural resources evaluation. Oxford Univ. Press, N.Y., p. 483. Gotway, C.A., Ferguson, R.B., Hergert, G.W., Peterson, T.A., 1996. Comparison of kriging and inverse-distance methods for mapping soil parameters. Soil Sci. Soc. Am. J. 60, 1237–1247. Hosseini, E., Gallichand, J., Marcotte, D., 1994. Theoretical and experimental performance of spatial interpolation methods in soil salinity analysis. Trans. ASAE 37, 1799–1807. Hudson, N., 1995. Soil Conservation. Iowa State University Press, Ames, IA, USA, p. 391. Istok, J.D., Rautman, C.A., 1996. Probabilistic assessment of ground-water contamination: Part 2. Results of case study. Ground Water 34, 1050–1064.
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Jenny, H., 1941. Factors of Soil Formation. McGraw-Hill Book, New York, p. 281. Mowrer, H.T., 1997. Propagating uncertainty through spatial estimation processes for old-growth subalpine forests using sequential Gaussian simulation in GIS. Ecol. Modell. 98, 73–86. Paz, A., Taboada, M.T., Gomez, M.J., 1996. Spatial variability in topsoil micornutrient contents in a one-hectare cropland plot. Commun. Soil Sci. Plant Anal. 27, 479–503. Renard, K.G., Foster, G.R., Yoder, D.C., McCool, D.K., 1994. RUSLE revisited: status, questions, answers, and the future. J. Soil Water Conserv. 49 Ž3., 213–220. Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K., Yoder, D.C., 1997. Predicting Soil Erosion by Water: A Guide to Conservation Planning With the Revised Universal Soil Loss Equation ŽRUSLE.. U.S. Department of Agriculture, Agriculture Handbook, 703, Government Printing Office, SSOP, Washington, DC, ISBN 0-16-048938-5, p. 404. Rossi, R.E., Borth, P.W., Tollefson, J.J., 1993. Stochastic simulation for characterizing ecological spatial patterns and appraising risk. Ecol. Appl. 3, 719–735. Smith, J.L., Halvorson, J.J., Papendick, R.I., 1993. Using multple-variable indicator kriging for evaluating soil quality. Soil Sci. Soc. Am. J. 57, 743–749. Soil Survey Staff, USDA-Natural Resources Conservation Service, Title 430-VI, 1997. National Soil Survey Handbook. U.S. Government Printing Office, Washington DC. Stevenson, 1985. Cycles of Soil. Wiley, N.Y., p. 380. SWCS, 1995. User Guide: Revised Universal Soil Loss Equation. Version 1.04. Soil and Water Conservation Society, p. 145. Tazik, D.J., Cornelius, J.D., Abrahamson, C.A., 1993. Status of the Black-capped Vireo at Fort Hood, Texas, Volume I: Distribution and Abundance USACERL Technical Report N-94r01 N-94r01. USDA-Soil Conservation Service ŽSCS., 1985. Soil Survey of Coryell County, Texas, p.129. Wischmeier, W.H., Mannering, J.R., 1969. Relation of soil properties to its erodibility. Soil Sci. Soc. Am. Proc. 33, 131–137. Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion loss: a guide to conservation planning. U.S. Department Agric. Washington D.C. Handb. No. 537, p. 58. Wischmeier, W.H., Johnson, C.B., Cross, B.V., 1971. A soil erodibility nomograph for farmland and construction sites. J. Soil Water Conserv. 26, 189–192. Zhang, R., Myers, D.E., Warrick, A.W., 1992. Estimation of the spatial distribution of soil chemicals using pseudo-cross-variograms. J. Soil Sci. Soc. Am. 56, 1444–1452.
Uncertainty assessment of soil erodibility factor for revised universal soil loss equation Guangxing Wang a , George Gertner a,) , Xianzhong Liu a , Alan Anderson b a
Department of Natural Resources and EnÕironmental Sciences, UniÕersity of Illinois, W503 Turner Hall, 1102 South Goodwin, Urbana, Il 61801 USA b USACERL, P.O. Box 9005, Champaign, Il 61820-1305 USA Received 10 November 2000; received in revised form 16 May 2001; accepted 5 June 2001
Abstract Soil erodibility accounts for the influence of the intrinsic soil properties on soil erosion and is one of six factors in the Revised Universal Soil Loss Equation ŽRUSLE., a most widely used model to predict long-term average annual soil loss. In a traditional soil survey, each of the soil types Žclasses. is assigned with a soil erodibility value that is assumed to be constant over time. However, heterogeneity of soil in time and in space tends to support the concept that soil erodibility depends dynamically and spatially on the set of properties of a specific soil. This study statistically compared the published soil erodibility values with those from a set of soil samples in terms of their differences. The published values tend to underestimate soil erodibility. This feature is also supported by the uncertainty assessment in difference maps of the published K values versus those from soil samples. Spatial prediction and uncertainty analysis of the soil erodibility from the set of soil samples was carried out using a sequential Gaussian simulation. The results show that the simulation produces a reliable prediction map of soil erodibility and can be recommended as a monitoring strategy to spatially update soil erodibility. Published by Elsevier Science B.V. Keywords: Uncertainty assessment; Spatial prediction; Soil erodibility; Simulation
1. Introduction Soil loss in the USA was estimated using the Universal Soil Loss Equation ŽUSLE. ŽWischmeier and Smith, 1978. before its modified version, and is currently predicted )
Corresponding author. Tel.: q1-217-333-9346; fax: q1-217-244-3219. E-mail address: [email protected] ŽG. Gertner..
0341-8162r01r$ - see front matter. Published by Elsevier Science B.V. PII: S 0 3 4 1 - 8 1 6 2 Ž 0 1 . 0 0 1 5 8 - 8
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G. Wang et al.r Catena 46 (2001) 1–14
using the Revised USLE ŽRUSLE. ŽRenard et al., 1994, 1997. for the purpose of agricultural, rangeland and environmental management. Both USLE and RUSLE are related to rainfall erosivity factor Ž R ., soil erodibility factor Ž K ., slope length factor Ž L., slope steepness factor Ž S ., cover management factor Ž C ., and support practice factor Ž P .. These equations consist of empirical model sets derived from an extensive database and their model parameters contain uncertainty when using these equations for a specific area. Moreover, these factors vary over space and time, depend on other variables, and may be correlated with each other. Additionally, errors in sampling, measuring, and modeling will lead to uncertainty in the estimate of these factors. The uncertainty may not be neglected and will be propagated in the prediction of soil loss. This uncertainty might be important when local estimates are required for management planning. Thus, there is a strong need to develop a general methodology for the spatial assessment of uncertainty for users of such systems. In recent years, we have been working on a large project related to the prediction and uncertainty analysis of soil erosion using the RUSLE. Our objectives are to develop a general procedure for spatially and temporally predicting soil loss, identifying various errors, modeling their propagation, and generating error budgets in order to provide guidelines for error reduction and management planning. As one part of the overall uncertainty analysis for soil loss prediction, this study reported here focuses on uncertainty assessment of soil erodibility factor K used in the RUSLE. The soil erodibility factor K measures the contribution of soil intrinsic properties to soil erosion. For major soil types and soil texture classes in the United States, the values of soil erodibility factor K have been published and can be obtained mainly from the USDA-Natural Resources Conservation Service ŽNRCS. ŽSWCS, 1995; Wischmeier and Smith, 1978.. Each soil type corresponds with a published soil erodibility value. The published values from USDA-NRCS are the average values within the soil types when the data were collected. They are assumed to be constant over time. However, heterogeneity of soil in time and in space tends to support the concept that soil erodibility depends dynamically and spatially on the properties of a specific soil. Soil properties influencing soil erodibility as used in RUSLE are grouped into two categories: Ž1. those that affect infiltration rate, movement of water through the soil, and water storage capacity; and Ž2. those that affect dispersion, detachability, abrasion, and mobility of soil particles by rainfall and runoff ŽWischmeier and Mannering, 1969; SWCS, 1995; Renard et al., 1997; Soil Survey Staff, 1997.. The important properties are texture, organic matter content, size and stability of structural aggregates in the exposed layer, permeability of the subsoil, and depth to a slowly permeable layer. Fine sand and silt soil particles are most susceptible to detachment and transport ŽWischmeier and Mannering, 1969.. Soil organic matter content affects soil aggregation, soil particle size distribution and soil infiltration capacity ŽStevenson, 1985.. Main factors considered in the soil erodibility calculation in the RUSLE include soil texture Ž%sand, %silt, %very fine sand and silt, and %clay., soil organic matter content, soil structure, and soil permeability ŽWischmeier and Mannering, 1969; Wischmeier et al., 1971; Wischmeier and Smith, 1978.. Because of the underling forces shaping the soils, the soil properties vary with time and space and are affected by climate, organisms, topography and parent materials interacting with time ŽJenny, 1941.. Climate
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factors, temperature and rainfall, affect soils as well as plants growing on those soils. Plant community succession due to the change of the soil physical environment is well observed and change in plant composition in turn affects the soil properties. The soil properties vary also in space because of the variation of soil formation factors. Thus, a soil erodibility value for a specific soil may vary dynamically and spatially. Using the soil erodibility values obtained previously from an extensive database to a specific area may lead to uncertainty. It is necessary to include the uncertainty on soil erodibility into the overall uncertainty analysis of soil loss and to improve methods for mapping the soil loss. Prediction methods to reliably estimate soil erodibility in space and time should be based on spatial variability of soil properties. Spatial statistical methods such as kriging interpolation and simulation have been used in spatial prediction, given a set of neighboring observations and assuming that there is a spatial correlation of a variable. These methods were developed in spatial geology and recently have been expanded to soil science. In soil management and soil remediation, for example, soil quality is evaluated and spatial distribution of soil nutrients andror chemicals is estimated by kriging ŽZhang et al., 1992; Smith et al., 1993; Hosseini et al., 1994; Chung et al., 1995; Gotway et al., 1996; Paz et al., 1996.. In studies by Istok and Rautman Ž1996., Rossi et al. Ž1993., and Mowrer Ž1997., sequential Gaussian simulations were applied to predict nitrate and DCPA concentrations in ground water, to estimate the rootworm density, and to generate estimation of variables for old growth forest conditions. Estimates by various kriging approaches are smoothed and may be best in local prediction. However, the kriging variances do not adequately reflect uncertainty of estimates because the variances depend only on the data configuration and not on the actual observed data. In spatial simulation, an estimate and variance obtained by a kriging method for a location are used as statistical parameters to determine a conditional cumulative density distribution. From the distribution, a value is drawn at random. This process can be repeated many times, which will result in many estimates at the location. From the estimates, an expected value and its variance can be derived. Thus, a set of the estimates at the location provides a visual and quantitative measure Žactually a model. of spatial uncertainty. The uncertainty depends on not only the data configuration but also on the data values. The study reported here discusses the use of published soil erodibility values from the national soil survey in spatial prediction of soil loss by traditional methods, and assess the uncertainty of the published values by comparing them with the soil erodibility values from a set of soil samples. A case study for spatial prediction and uncertainty analysis of soil erodibility was carried out by a sequential Gaussian simulation procedure in order to support a methodology recommendation for updating soil erodibility values as a monitoring strategy, and for providing spatial uncertainty information for an overall uncertainty analysis of soil loss prediction. 2. Materials and methods The study area is about 87,890 ha and located in Bell and Coryell Counties approximately 256 km southwest of Dallas, Texas USA. The climate is characterized by
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long, hot summers and short mild winters ŽTazik et al., 1993.. Average temperature ranges from 8 to 29 8C. Average annual precipitation is 81 cm. Elevations vary from 180 to 375 m above sea level. Most slopes are 2–5%. Soils are generally shallow to moderately deep and clayey, underlain by limestone bedrock. Soil samples were collected from 186 plots over the area and measured at a laboratory for soil properties including: %silt, %sand, %clay, %organic matter, and classes for structure and permeability. The soil erodibility factor K values of these soil samples were calculated using the following formula ŽWischmeier and Smith, 1978.: Ks
2.1 = 10y4 Ž 12 y OM . M 1.14 q 3.25 Ž S y 2 . q 2.5 Ž P y 3 .
, Ž 1. 7.59 = 100 where K is expressed in units of t ha h hay1 MJ 1.14 mmy1 , OM is soil organic matter content, M is Ž%silt q %very fine sand. Ž100 y %clay., S is soil structure code and P is permeability class. If soil organic matter content was greater or equal to 4%, OM was considered constant at 4%. Moreover, the influence of rock fragments on soil loss was accounted for by a subsurface component in the soil erodibility K factor ŽRenard et al. 1997.. The soil profile descriptions with permeability classes for all the soil samples in this study included the effect of rock fragments on permeability. The soil erodibility K factor and the subsurface component for effect of rock fragments were explained via an adjustment for permeability classes. The soil erodibility factor values obtained with the soil samples and Eq. Ž1. are denoted as A K sampleB. The sampled K values were used as a basis for comparison. A soil type map with the published soil erodibility K values for the case study area was obtained from USDA-Soil Conservation Service ŽUSDA-Soil Conservation Service, ŽSCS., 1985., now called USDA-Natural Resources Conservation Service ŽUSDANRCS.. According to the soil types obtained, these soil samples above were assigned with published K values, denoted as A K pubB. The K pub values were statistically compared with the K sample values in terms of the differences Ž K pub y K sample.. The spatial distribution of the differences was further displayed to visually examine possible underestimation and overestimation using the published K values. In addition, a map of the published soil erodibility K values was produced by a point-in-polygon method, that is, assigning the polygons with the published K values according to soil types in the soil map. The uncertainty of the published K values in prediction of soil loss using RUSLE was assessed. A spatial statistical procedure was applied for spatial prediction and uncertainty analysis of soil erodibility factor K using the K sample values. The procedure predicts a soil erodibility K value for an unknown location using the known K sample values and the existing estimates around the unknown location given a specified neighborhood. The description of this procedure follows. The K sample values were first de-clustered to obtain unequal weights for each sample location. The de-clustering led to less weight for the dense locations and more weight for the sparse locations. At the same time, the K sample values were transformed into normal scores as required by a sequential Gaussian simulation method. The spatial variability of the K sample values was then derived by calculating and modeling the experimental semivariogram. The semivariogram measures the spatial
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similarity of the soil erodibility factor given a separation vector or separation distance of data at a specific direction. The semivariogram is important because it is used to derive weights minimizing the covariance between sets of measured locations and unmeasured points, thus providing a minimum error estimate of the unknown values at these points. In addition, the anisotropy in spatial variability of soil erodibility was examined by obtaining semivariograms in different directions. If the anisotropy exists, the semivariograms from different directions must be fitted. For the study, sequential Gaussian simulation was used for spatial modeling and prediction. Briefly, if a study area is divided into N nodes of a grid, the steps used for the sequential Gaussian simulation are as follows ŽGoovaerts, 1997.: Ži. Define a random path visiting each node of the grid defined over the study area; Žii. At the ith node to be visited, model the conditional cumulative distribution function given the n original data and all Ž i y 1. simulated values at the previously visited locations, using simple kriging with the modeled semivariogram; Žiii. For the ith node, draw a realization from that conditional cumulative distribution function and this realization will become a conditional datum for all subsequent drawings; Živ. From the first node to be visited, repeat steps Žii. and Žiii. above until all N nodes are visited and each has received a simulated value. One realization consisting of the set of simulated values for the whole area is obtained when all N nodes of the grid have their simulated values. Repeating L times the entire sequential process with possibly different paths to visit the N nodes will result in L realizations. From the L realizations, an expected prediction map and conditional variance map can be derived. Using the sequential Gaussian simulation method can lead to a set of realizations providing a visual and quantitative measure Žactually a model. of spatial uncertainty. If a spatial feature, such as larger than a given value, exists on most of the L realizations, it is deemed certain, and otherwise uncertain. The simulation method thus reproduces model statistics, and it models spatial uncertainty. During the process of sequential Gaussian simulation, simple kriging is used to determine the mean and variance of the conditional distribution for each unknown location. The simple kriging is unbiased with minimum local error variance. For a detailed description of de-clustering, semivariogram, simple kriging and simulation methods mentioned above, readers can refer to Goovaerts Ž1997. and Deutsch and Journel Ž1998..
3. Results The total study area is composed of 25 soil types. A soil map is shown in the upper section of Fig. 1, and the soil characteristics are detailed in Table 1. All soil types have an organic matter content of less than 4% and are all well drained. The dominant soil types with counts greater than 10% in this area are BtC2, DrC, ErB and ReF. These are upland soils and formed on limestone, limestone and marl, or limestone and shale. BtC2
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Fig. 1. Soil map of the study area based on soil survey and published soil erodibility K factor map. Legend on left corresponds to the top map and legend on right corresponds to the bottom map. The unit for K factor is t ha h hay1 MJy1 mmy1 .
is a deep soil and the other three dominants are shallow soils. The soil textures for BtC2, DrC, ErB and ReF are, respectively, gravelly loam and clay loam, clay loam and gravelly clay loam, cobbly silty clay, and gravelly clay loam. Three co-dominant soil types with counts less than 10% but greater than 5% are NuC, EvB and KrB, on the low ridges, upland and terrace, respectively. The total of four dominant and three co-dominant soils occupy totally 83.4% of the area and four dominant soils type cover 63%. The soil erodibility map derived using a traditional point-in-polygon method in terms of the soil types and their published soil erodibility K values is given in the lower section of Fig. 1. The published K values vary from 0.0131 to 0.0488 t ha h hay1 MJy1 mmy1 , with 59.6% of values less than 0.0224 t ha h hay1 MJy1 mmy1 . The soil map leads to sharp-edged boundaries, that is, spatial discreteness of soil erodibility K values between the soil type polygons, and with the same estimates within each of the polygons. The spatial variability of soil erodibility over the whole area is noncontinuous and local variability within small areas disappears. The locations of soil samples and their estimated soil erodibility values are shown at the top of Fig. 2. The corresponding published K values for these sample locations and their differences between the published and sampled K values are also shown respectively in the middle and bottom of Fig. 2. The minimum and maximum soil erodibility K values from the soil samples are 0.0125 and 0.0589 t ha h hay1 MJy1 mmy1 and their corresponding published K values from soil survey are 0.0131 and 0.0488 t ha h hay1 MJy1 mmy1 . Higher soil erodibility K values from the soil samples are mainly located in the west and in a small section in the north, and lower values in other areas. Out of
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Table 1 Soil properties of 25 soil types covering the study area Soil Type
Cover Ž%.
BaB
0.5
BgB
0.1
Bo BtC2
3.3 22.1
ChB CoB2
2.1 0.7
CwB
0.1
DeB
0.0
DrC
14.6
EcB
0.2
ErB
14.4
EvB
6.2
Fr
0.4
HoB
0.0
KrB
5.3
LeB
1.7
LyB MnB
0.7 0.3
NuC
8.9
PrB ReF
0.3 11.9
SeC
0.4
SlB TpC
4.2 1.5
WsC2
0.1
a
Soil
Organic matter Ž%.
Depth
Position
Parent material
Bastsil fine sandy loam Bolar gravelly clay loam Bosque clay loam Brackett–Topsey associationa Cho clay loam Cisco fine sandy loam Crawford silty clay Denton silty clay Doss–Real complex a Eckrant cobbly silty clay Eckrant–Rock outcrop complex a Evant silty clay Frio silty clay Houston Black clay Krum silty clay Lewisville clay loam Lindy clay loam Minwells fine sandy loam Nuff very stony silty clay loam Purves silty clay Real–Rock outcrop complex a Seawillow clay loam Slidell silty clay Topsey–Pidcoke associationa Wise clay loam
-2
deep
terrace
alluvium
1–3
moderate
1–4 1–3
deep deep
convex knolls; ridge tops floodplain upland
1–2 -1
shallow deep
upland upland
limestoneq marl alluvium limestoneq shale sediment sediment
1–3
moderate
upland
limestone
1–4
deep
upland
1–3
shallow
upland
1–4
shallow
upland
clayer materials limestoneq marl limestone
1–4
shallow
upland
limestone
2–4
shallow
upland
1–4
deep
floodplain
...b
...b
...b
mare sediment old alluvial sediment ...b
1–3
deep
terrace
1–3
deep
terrace
old alluvial sediment Alluvium
...b -1
...b deep
...b terrace
...b Sediment
2–4
deep
low ridge
1–3 1–4
shallow shallow
upland upland
-1
deep
terrace
marlq limestoneqshale Limestone limestone q marl sediment
1–4 1–4
deep deep
upland upland
marine sediment Sediment
0.5–2
deep
upland
marlqsand
For soil complex or association, columns 4 to 6 are the properties of the first soil series, the predominant one within the complex or the association. b Information not available.
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Fig. 2. Location of field soil samples and spatial distributions of the soil erodibility K values derived from soil samples Žtop map., published K values Žmiddle map. and the differences between published and sampled K values Žbottom map.. The unit for K factor is t ha h hay1 MJy1 mmy1 .
186 sample plots, there are only 17 locations Že.g. 9.1%. where K values are less than 0.0224 t ha h hay1 MJy1 mmy1 . In the center of each of the maps, there is a blank area outlined where no samples were taken because sampling was not allowed. In the spatial distribution of published K values Žin the middle of Fig. 2., higher values at the west correspond with those at the same locations based on the soil samples Žat the top of Fig. 2.. However, some of higher published K values are also found in the east and close to the boundary of the northeast. From 186 sample locations, there are 88
Table 2 Statistical description of published soil erodibility K values Ž K pub. from USDA-Natural Resources Conservation Service ŽNRCS., from the soil samples Ž K sample., and differences between the published and sampled K values K pub from USDA-NRCS soil survey
Mean K sample
Stdv of K sample
Mean Diff
Stdv of Diff
Sample size
Calculated t value
BaB BgB Bo BtC2 ChB CoB2 CwB DrC EcB ErB EvB Fr KrB LeB LyB MnB NuC PrB ReF SeC SlB TpC WsC2 Overall
0.0316 0.0264 0.0369 0.0224 0.0369 0.0487 0.0422 0.0422 0.0198 0.0198 0.0422 0.0422 0.0422 0.0422 0.0198 0.0316 0.0224 0.0422 0.0132 0.0369 0.0422 0.0422 0.0487 0.0310
0.0361 0.0393 0.0491 0.0352 0.0382 0.0462 0.0270 0.0420 0.0318 0.0327 0.0289 0.0423 0.0345 0.0451 0.0412 0.0347 0.0381 0.0320 0.0277 0.0469 0.0337 0.0441 0.0485 0.0360
0.0074 0.0046 0.0071 0.0076 0.0079 0.0028 0.0105 0.0096 0.0061 0.0084 0.0069 0.0072 0.0091 0.0041 0.0103 0.0043 0.0091 0.0014 0.0082 0.0009 0.0153 0.0076 0.0134 0.0099
y0.0045 y0.0129 y0.0123 y0.0128 y0.0013 0.0025 0.0152 0.0001 y0.0120 y0.0129 0.0133 y0.0001 0.0076 y0.0029 y0.0215 y0.0030 y0.0157 0.0101 y0.0145 y0.0100 0.0084 y0.0020 0.0003 y0.0051
0.0074 0.0046 0.0071 0.0076 0.0079 0.0028 0.0105 0.0096 0.0061 0.0084 0.0069 0.0072 0.0091 0.0041 0.0103 0.0043 0.0091 0.0014 0.0082 0.0009 0.0153 0.0076 0.0134 0.0130
3 3 4 20 3 3 6 25 3 32 15 3 9 4 4 3 15 3 14 3 5 3 3 186
0.85 3.99 2.99 7.23 0.23 1.26 3.24 0.08 2.79 8.46 7.19 0.03 2.37 1.25 3.63 1.00 6.49 10.14 6.36 14.79 1.11 0.37 0.03 5.31
Significance level
- 0.1 - 0.1 - 0.001
- 0.05
- 0.001 - 0.001 - 0.05 - 0.05
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Soil type
- 0.001 - 0.001 - 0.001 - 0.01
- 0.001
Stdv sStandard deviation, Diff sdifference. The unit for K factor is t ha h hay1 MJy1 mmy1 . 9
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locations Že.g. 47.3%. where the published K values are less than 0.0224 t ha h hay1 MJy1 mmy1 . In the spatial distribution of the differences between the published K values and sample K values Žat the bottom of Fig. 2., the plus markers and triangles indicate positive and negative differences, respectively. From 186 sample locations, there are 21 locations Že.g. 11.3%. displayed in circles, implying the sample locations where the differences between the published K and sampled K values are not significantly statistically different from zero and not biased at the significant level of 0.05. A total of 116 sample locations are triangles and their differences are significantly negative, implying that most of the sample locations Ž62.4%. may be statistically underestimated by the published K values. The remaining 49 sample locations Že.g. 26.3%. are plus markers and may be statistically overestimated by the published K values. In Table 2, the published K values, sampled K values and their differences for each soil type are statistically described. As a whole, the number of soil samples for each soil type was proportional to its area. For most of the 25 soil types, the differences between the published and sampled K values within the soil types are significantly different from zero at the significance level of 0.1, and their mean differences are negative. Overall, the average of the differences between the published and sampled K values is negative and differs significantly from zero at significance level of 0.001. The differences between published and sample K values varied from y0.034 to 0.0296 t ha h hay1 MJy1 mmy1 . In Fig. 3, the relationship of the differences against the published K values exhibits a distinct separation. When these published K values are less than 0.04, most of the differences are negative, that is, underestimation occurs, and otherwise most of the differences are positive, indicating overestimation. Overall, most of the differences are negative. In this study area, the spatial variability of soil erodibility K values from the soil samples was examined in four directions: azimuths 08, 458, 908 and 1358. No significant anisotropy in the spatial variability was found. The prediction map of soil erodibility K values was derived using sequential Gaussian simulation and is presented at the top of
Fig. 3. The difference of K pub and K sample versus K pub. The unit for K factor is t ha h hay1 MJy1 mmy1 .
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Fig. 4. The variance image of the predicted K values and probability map for predicted K values are given at the middle and bottom of this figure. At center of the study area, there is an area without soil samples and the area was removed. The spatial distribution of the predicted K values based on the simulation was consistent with that of the soil erodibility K values based on the samples. That is, higher K values were predicted at the west and a small section of the north, and lower values at the other sections. There are only a few small areas where the predicted values were less than 0.0224 t ha h hay1 MJy1 mmy1 . At the sample locations, the simulation maintained the K values from the soil samples and the prediction variances were zero. The farther the predicted locations were away from the sample locations, the larger the prediction variances. Smaller variances occur in the areas where soil erodibility K values are lower and sampling density is higher. In addition, a threshold value, 0.042 t ha h hay1 MJy1 mmy1 , was selected only as an example and used to calculate probability for the predicted K values larger than the specified threshold value. That is, suppose that when soil erodibility K values are larger than this threshold value, soil loss might be considered to be serious. At the
Fig. 4. Using sequential Gaussian simulation, spatial prediction image Žtop map. of soil erodibility K values based on soil samples, variance image of the predicted values Žmiddle map., and probability map Žbottom map. for K values larger than 0.042. The unit for K factor is t ha h hay1 MJy1 mmy1 .
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bottom of Fig. 4, the probability for the predicted K values larger than the threshold value is the highest at the west and decreases from west to the east. The probability is less than 0.5 for most of the entire study area.
4. Discussion and conclusions The uncertainty of the published K values was documented in this paper. The methods used for assessing the uncertainty included statistically comparing the published and sampled soil erodibility K values in terms of their differences, analyzing error properties of the published K values, and performing spatial prediction and uncertainty analysis of the K values with the sample data using sequential Gaussian simulation. The results showed that unbiased estimation of soil erodibility K values using the published information was possible only at a few sample locations and for a few soil types. Biased estimation, especially underestimation, was observed at most of the sample locations, in most of the study area, and for most of the 25 soil types. For the whole area, using the published K values led to the underestimation of soil erodibility. Thus, the published soil erodibility K values should be used with care. This underestimation can be explained by the change of soil properties over space and time Žsee p.133, Hudson, 1995.. The published soil erodibility K values were determined 20 years ago using average values within the same soil series. In fact, the soil erodibility K values within a soil series varied within a certain range, and using an average value might thus result in uncertainty. On the other hand, the change of soil properties over time was caused by many factors such as plants, climate, human activities, and so on. Because off-road vehicular impact activities took place in recent years in this area, we looked into the correlation between the cumulative disturbance ŽDemarais et al., 1999. caused by the off-road vehicular impact activities and sampled soil erodibility K values, and their differences with the published K values. The correlations were found to be weak. That is, the soil erodibility increased due to many factors or their integrated effect, but not solely from these activities. Determining the soil erodibility factor Ž K . directly from soil loss data collected from repeat measurement plots measured over the long term Žover 20 years. is the most reliable method for assessing soil erodibility ŽWischmeier and Mannering, 1969; SWCS, 1995; Renard et al., 1997.. This method, however, is very expensive and can take a long time to obtain results, which can be impractical for many situations ŽRenard et al., 1997.. The second alternative is using the published soil erodibility K values by USDA-Natural Resources Conversation Service ŽUSDA-NRCS.. Its advantages include low cost and ease of acquisition of soil erodibility K values. However, the assumption that soil erodibility K values are constant over time and the use of an average K value for each soil type Žclass. introduces uncertainty into the estimate of soil erodibility. In addition, using the published K values introduces spatial discreteness in the soil erodibility values. Another alternative to determine soil erodibility K values is the application of geostatistical methods such as sequential Gaussian simulation with soil erodibility K
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values from soil samples, as used in this paper. The sequential Gaussian simulation produced not only a spatial prediction map of soil erodibility K values, but also, uncertainty measures, prediction variance images and probability maps for a specific feature such as soil loss larger than a given value. The spatial distribution of soil erodibility K values predicted using this method is very similar to that of the soil samples. The variance images and probability maps of the predicted values measured the uncertainty caused not only by the variation of the soil erodibility values based on the soil samples, but also by the spatial orientation of the sample plots. Thus, the procedure used in this paper for spatial prediction and uncertainty assessment of soil erodibility can be recommended as a potential monitoring strategy to periodically update soil erodibility K value maps. When this method is applied to all factors in the RUSLE, the uncertainties obtained can provide decision-makers with useful information to reduce the risks in soil and land management. Finally, as already mentioned, this study is only one part of a large study for developing a general methodology and framework of uncertainty assessment for a soil loss prediction system. The ongoing work will include developing spatial error budgets that systematically account for important sources of errors, and show how these errors propagate through the modeling systems. The variance maps presented here will be considered as one source of uncertainties in the development of these error budgets. The uncertainty in K values will not be neglected in the generation of the overall uncertainty analysis for soil loss predictions.
Acknowledgements We are grateful to Strategic Environmental Research and Development Program ŽSERDP. for providing support for the study, and to Ms. Tina Carrington, Mr. Eric Schreiber and Dr. Robert Darmody for collection of field data and laboratory work.
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