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DIVISION S-10—WETLAND SOILS

Logistic Modeling to Spatially Predict the Probability of Soil Drainage Classes

Lab. for Soil and Water, Faculty of Agricultural and Applied Biological Sciences, Katholieke Universiteit Leuven, Vital Decosterstraat 102, Leuven, B-3000, Belgium

* Corresponding author (Paul.Campling{at}sadl.kuleuven.ac.be)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
Logistic models were developed to spatially predict the probability of drainage classes in a humid tropical area (58900 ha) using sampled terrain attributes from a digital elevation model, and vegetation indices from a LANDSAT-5 Thematic Mapper image. Soil drainage classes were assigned on the basis of the local water table regime depth, determined by soil morphological indicators, to 295 pseudo-randomly selected soil auger hole observations (calibration data set) and 72 soil pedon observations (validation data set). Six drainage classes were identified: excessively (D1), well (D2), moderately well (D3), imperfectly (D4), poorly (D5), and very poorly (D6). A nested dichotomous modeling strategy of progressively separating the six drainage classes was adopted, and resulted in five multivariate logistic models. The best performing model, predicting the probability of nonhydric (D1D2) soils versus hydric (D3D4D5D6) soils had a concordance of 99%, and the worst performing model, predicting the probability of imperfectly (D4) drained soils versus moderately well (D3) drained soils had a concordance of 65%. The most important spatial determinants were: elevation, slope, distance-to-the-river channel (DC), and vegetation indices. The logistic models were combined in a geographic information system (GIS) to derive soil drainage class maps using the gridded data sets of the significant variables. The results showed that digital elevation models and vegetation indices from LANDSAT-5 Thematic Mapper provide complementary information for developing statistical models to spatially predict and map soil drainage classes.

Abbreviations: AIC, Akaike's information criterion • DC, distance-to-river channel • ESRI, Environmental System Research Institute • GIS, geographical informations system • NDVI, normalized difference vegetation index • PDI, profile darkness index • SC, Schwarz Criterion

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
THERE IS GROWING NEED to develop models that are able to predict the spatial extent of soil characteristics at a scale appropriate for environmental management. Soil-landscape modeling aims to develop explicit, quantitative, and spatially realistic models of the soil landscape continuum. Statistical models are used to investigate the correlation between soil characteristics (response variable) and terrain attributes and vegetation indices (explanatory variable) at field sampling points, and then spatial prediction is achieved by incorporating statistical models with gridded sets of significant explanatory variables. The underlying assumption is that the development of soil toposequences, and hence soil attributes, is a response to the way water moves through and over the landscape (Moore et al., 1993), and that vegetation indices provide indicators of prevailing edaphic factors (Levine et al., 1994). The increasing availability of spatially continuous explanatory variables from digital elevation models and satellite images encourages the development of this approach in favour of the interpolation of sampled data by kriging or triangulation, especially in regions that are sparsely surveyed (Gessler et al., 1995).

Predicting soil drainage conditions is important for both crop and hydrological modeling. Soil moisture conditions will influence the selection and performance of crops and will determine the propensity for rainfall-runoff.

Bell et al. (1994) used multivariate discriminant analysis to relate soil drainage class to eight landscape parameters in Pennsylvania, USA. Soil drainage probability maps were derived, and agreed at a level of 67% to the published soil drainage map. Sader et al. (1995) combined LANDSAT Thematic Mapper and GIS rule-based methods to delineate forest wetlands in Maine. They concluded that a combination of hybrid and GIS rule-based classification methods were the most appropriate. Cialella et al. (1997) on the other hand, combined normalized difference vegetation index (NDVI) data from advanced visible and infrared imaging spectrometer and digital terrain attributes to predict soil drainage class at a 6 by 4 km research site in Maine. Classification tree analysis, based on binary recursive partitioning of predictor variables, was used to arrive at increasingly homogeneous regions of drainage class areas. Merot et al. (1995) simply compared the mapped compound topographic index with a published soil drainage class map on the basis of a contingency table in Brittany, France. They found that the topogaphic index was able to predict the distribution of intensely waterlogged soils, provided that the relationship with bedrock type was established. At the soil-landscape level, Hurt and Brown (1995) identified hydric soil indicators that fit the definition of hydric soils and enabled the estimation of seasonal high water tables for all soils in Florida. Thompson et al. (1997) developed the profile darkness index (PDI) to assist in delineating the areal extent of hydromorphic soils. In a later paper, Thompson et al. (1998) emphasized the importance of landscape perspective when examining the relationships among soil hydrology, hydric soil conditions, and soil hydromorphic properties, as pedogenic processes are not restricted to a vertical soil profile.

We hypothesize that there is a relationship between drainage class and terrain and vegetation. The objective was to spatially predict soil drainage classes in tropical soils by expressing the relationship in a statistical model. Terrain is expressed by digital terrain attributes and vegetation by vegetation indices from a LANDSAT-5 Thematic Mapper Image. As drainage class is a categorical response variable, logistic modeling is used to develop the predictive model, which is validated against drainage classes assigned to reference pedons. The validated statistical models are combined to derive drainage class maps for the entire case study area and the accuracy of maps are determined.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
Study Site
The study area (58900 ha) traverses a section of the sandstone Udi Nsukka Cuesta and the shale Cross River Plains (Fig. 1) . The region is located in the transition zone between the Guinea-Congolian and Guinea Savanna ecoclimatological regions of South Eastern Nigeria. The mean annual precipitation is 1577 mm (max. = 2146 mm, min. = 901 mm) with a distinct dry season between November and March. Soils in the area exhibit contrasting soil drainage characteristics depending on the soil texture and the landscape position (Table 1; Gobin et al., 2000b). Hydric soils are defined as soils that form under conditions of saturation, flooding, or ponding long enough to develop anaerobic conditions in the upper part (Federal Register, 1994). In lowland shale areas (lower interfluve), high soil water tables occur during the wet season. The occurrence of plinthite and redoximorphic features indicate prolonged inundation (Table 1). In more upland shale areas (upper interfluve), the presence of ferric properties (Food and Agriculture Organization [FAO], 1998) is because of lateral subsurface flow and fluctuating water tables, respectively. Where ironstone occurs, usually at crests or at the top of slopes leading to incised streams, the high percentage of lag gravel increases infiltration and drainage. In the sandstone area, water tables are very deep (200–300 m) and the soils are nonhydric (Landon, 1991). At the steep slopes of the escarpment, the weak crumbly structure of the Quartzipsamments encourages excessive drainage. On the plateau, however, the better-structured Kandiustox retain water for longer periods.

View larger version (85K): [in this window] [in a new window]   Fig. 1. Study area with the position of the random auger hole observations (calibration data set), the reference profile pits (validation data set), and the local geology (1 = Udi Nsukka Cuesta, 2 = Cross River Plains).

Drainage classes were assigned on the basis of the depth and the duration of the local water table regime (Fig. 2) , which was assessed by examining the soil texture and the type, degree, and depth of soil mottling and gleying in the sampled soil. Gleyic properties occur when soils become completely saturated with groundwater for a period that allows reducing conditions occur and show a gleyic color pattern (FAO, 1998). The gleyic colour pattern reflects the preponderence of oximorphic and reductomorphic properties. Oximorphic properties reflect alternating reducing and oxidizing conditions, and are expressed by reddish brown (ferrihydrite) or bright yellowish brown (goethite) mottles. Reductomorphic properties, on the other hand, reflect permanently wet conditions and are expressed by neutral (white to black: N1/to N8/) or bluish to greenish (2.5Y, 5Y, 5G, 5B) colors in >95% of the soil matrix. Field evidence indicated that origin of the gleyic properties in the study area was from a combination of both run-on and groundwater, termed as amphigley by Brinkman and Blokhuis (1986).

View larger version (37K): [in this window] [in a new window]   Fig. 2. Soil drainage classes according to water regime, with associated soil morphological attributes (adapted from Landon, 1991).

Digital Terrain Modeling
The ANUDEM program (Hutchinson, 1989), was used to create a 25-m resolution digital elevation model (DEM) from digitized contour lines (at 50 interval), stream lines (scale—1:50000), lake polygon coverages (scale—1:50000), and spot heights. Preprocessing was carried out on the river lines to ensure that all the arcs had a down slope direction, that braiding was not represented in the valley bottomlands, and that a flow line passed through lake features. The DEM was processed iteratively to ensure that sinks were progressively removed.

In early work on quantifying land surface topography, Zevenbergen and Thorne (1987) fit a nine-term quadratic polynomial to a moving 3 by 3 square grid network (Fig. 3) to derive terrain attributes:

[1]

View larger version (21K): [in this window] [in a new window]   Fig. 3. The 3 by 3 grid elevation submatrix (Zevenbergen and Thorne, 1987).

[2]

[3]

[4]

[5]

[6]

Aspect was converted to radians. Contributing area, A_j, using the D8 algorithm (Jenson and Dominigue, 1988) indicates the upslope area that flows into each cell:

[7]

where a_i is the grid cell area, n_j is the number of grid cells draining into grid cell j, and b is the contour width approximated by the grid-cell resolution.

Three secondary terrain attributes in environmental modeling are the compound topographic index (Kirkby, 1975; O'Loughlin, 1981), the stream power index (Moore et al., 1991) and the slope-aspect index ():

[8]

[9]

[10]

The compound topographic index indicates the possible propensity of areas of the landscape to develop saturated conditions based on the shape of the topographic surface. The stream power index is a measure of the erosive power of water across the landscape, and the slope-aspect index provides an approximate method of examining the spatial distribution of radiation across a catchment (Moore et al., 1988).

Prior to creating the secondary terrain attributes, the slope gradient grid was checked for zero values, which would produce spurious results. Zero values were replaced by the mean value of the eight surrounding cells.

The distance-to-river-channel grid, DC_i, is a proximity attribute that provides information on the relative position of cells to the valley bottoms. The river channel grid is the digitized stream lines (from the 1:50000 topographic map) converted to 25-m grids. The euclidian distance from each cell i to location j on the river channel grid is:

[11]

Vegetation Indices from LANDSAT-5 Thematic Mapper
A LANDSAT-5 Thematic Mapper image was obtained on a cloud-free day in January 1987 when haze was minimal over the study area. The image was destriped and geometrically referenced to 1:50000 topographic maps (UTM) using resampling techniques to give a 25-m raster image. The advantage of using a dry season image of the area is that the vegetation present is a clear indicator of the seasonal variation in edaphic factors across the landscape. The visible red (Band 3: 0.63–0.69 µm), near-infrared (Band 4: 0.76–0.90 µm), and middle-infrared channels (Band 5: 1.55–1.75 µm and Band 7: 2.08–2.35 µm) were processed as they usually correspond best with the spectral characteristics of vegetation (Mather, 1995).

The NDVI was derived from the reflected solar radiation in the infrared and red wavelength bands via the algorithm (Tucker, 1979):

[12]

Where IR represents the near-infrared (Band 3: 0.76–0.90 µm) and R the red range of reflectance (Band 4: 0.63–0.69 µm). Alternative vegetation indices were constructed for other band combinations:

[13]

Where MIR(B5) represents the middle-infrared (Band 5: 1.55–1.75 µm) and NIR is the near-infrared (Band 4: 0.63–0.69 µm).

[14]

Where MIR(B7) represents the middle-infrared (Band 7: 2.08–2.35 µm). For visualization purposes, all vegetation indices were converted to 8 bit-scale with a two standard deviation contrast stretch.

Logistic Model Calibration
Logistic modeling is a generalized linear modeling technique that predicts the binary or ordinal response of categorical variables. A nested dichotomous modeling strategy of progressively separating the six drainage classes was adopted (Fig. 4) to predict the probabilities of soil drainage classes. Univariate and multivariate logistic models (Hosmer and Lemeshow, 1989) were constructed to define the independent variables that were important to predict the probability of drainage class. The binary logistic model takes the following form:

[15]

View larger version (31K): [in this window] [in a new window]   Fig. 4. Nested dichotomous modeling strategy for deriving drainage classes (D1, D2, D3, D4, D5, and D6).

The first logistic model, NONHYDRICMOD, predicted non-hydric (Y = 1) versus hydric (Y = 2) drainage classes, where nonhydric combines D1 and D2 and hydric combines D3, D4, D5, and D6 (Fig. 4). The second logistic model, EXCESSMOD, used only the nonhydric observations, to distinguish between the excessive (Y = 1) and well (Y = 2) drained classes. The third logistic model, POORMOD (Fig. 4), distinguished between poorly (D5) and very poorly (D6) drained soils combined together (Y = 1), and moderately well (D3) and imperfectly (D4) drained soils combined together (Y = 2). The fourth logistic model, VPOORMOD, distinguished between very poorly D6 (Y = 1), and poorly D5 (Y = 2) drained soils, and the fifth logistic model, IMPERFMOD, distinguished between imperfectly D4 (Y = 1) and moderately D3 (Y = 2) drained soils.

Prior to producing a multivariate model, collinearity was examined on the basis of parameter tolerance. Each predictor variable was regressed on all other variables in a weighted least square regression (i.e., adjusted by the weight matrix used in the maximum likelihood algorithm). The tolerance was computed as (1 - R²) and variables with values below 0.4 were removed until a satisfactory combination was obtained. The multivariate solution was fitted on the retained variables using a stepwise approach where thresholds of the residual ² were 0.15 for entry and 0.10 for removal. The likelihood ratio statistic (-2 lnL), based on the maximum likelihood estimates of B_k (where L = l [B_k]), has an asymptotic ²-distribution with p degrees of freedom (where p is the number of estimated parameters ß) under the global null hypothesis that all parameters (ß) equal zero. The likelihood ratio statistic (-2 lnL) was used to examine the significance of individual models and to compare competing models in conjunction with Akaike's Information Criterion (AIC) and Schwarz Criterion (SC). Both the AIC and SC are based on the likelihood ratio statistic but also take the number of observations into account. The Wald test was obtained by comparing the maximum likelihood of each individual slope parameter (ß) to an estimate of its standard error, and was used to keep individual variables in the model applying a ²-criterion of P < 0.10. The exponent of the slope coefficients, the odds ratio (e^ß), represents the percentage of change in the logit for a change of one unit of the independent variable (x). The association between predicted probabilities and observed responses was examined using percentages of concordant pairs, discordant pairs and the rank correlation index to summarize goodness-of-fit, according to:

[16]

Where C is the number of concordant pairs and D is the number of discordant pairs. A pair of observations is concordant if the predicted event probability is lower for an observation with a lower-ordered value of the observed response.

Logistic Model Validation
The models were used to compute predicted probabilities and to classify the 295 observations into one of the response levels following the nested modeling procedure. A bias-adjusted classification table was used to determine cut-off probabilities (SAS, 1990). Threshold probabilities were determined for each model on the basis of percentages correctly classified, false positive and false negative observations. For each model the probability level at which a maximum percentage of correctly classified observations was obtained and used to classify the validation dataset. Validation of the fitted models and respective cut-off probabilities was conducted by classifying the validation observations according to the best performing multivariate models. Predictors incorporated into the best performing models are spatially referenced drainage-class determinants.

Drainage Class Probability Mapping
To produce drainage class probability maps Eq. [15] was rewritten as:

[17]

Using Arc/Info GRID (Environment Systems Research Institute [ESRI], 2000), the logistic equation (Eq. [17]) was applied with input from the analysis of maximum likelihood estimates for each multivariate binary logistic model to the gridded data sets of significant variables. The mapping procedure followed the nested modeling strategy (Fig. 4), so that, for example, the EXCESSMOD algorithm was only applied to the nonhydric soils area, determined by the NONHYDRICMOD algorithm. The probability thresholds resulting in the highest number of correctly predicted grid cells were used to define the drainage class maps. To assess the overall accuracy of the drainage maps, Cohen's kappa () statistic (SAS, 1990) was calculated, which indicates the similarity between actual and predicted drainage classes.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
Logistic Model Calibration
NONHYDRICMOD predicted the probability of nonhydric soil drainage classes (Fig. 4). A comparison between different univariate models indicated that elevation (Z) was the best variable to predict nonhydric soils, followed closely by the DC (Table 2). Univariate models using VIB5B4 and tan ß were significant but had low measures of association (Table 2). These covariates were included in the multivariate model, after checking for collinearity, which achieved a very high association value ( = 0.99). The odds were positively associated (odds ratio >1) with Z, DC, and tanß, and were negatively associated (odds ratio <1) with VIB5B4 (Table 3). The odds ratio of DC was 1.546, which meant that one unit (the unit being 1000 m, Table 3), increase in distance from the river channel increased the odds by 55% of the soil being nonhydric. The areas that were increasingly further away from the river channel were therefore more likely to have nonhydric soils.

View this table: [in this window] [in a new window]   Table 3. Analysis of maximum likelihood estimates for multivariate binary logistic models predicting the probability of drainage classes (Odds ratio is eß for Z, , and , e0.01xß for Tanß, VIB5B4, VIB7B5, and , e1000xß for DC).

POORMOD (Fig. 4) predicted the probability of poorly (D5) and very poorly drained (D6) soils combined together. A comparison between different univariate models (Table 2) indicated that elevation (Z) was the best variable to predict poorly and very poorly drained soils, followed closely by the DC. Aspect (), VIB7B5, and the compound topographic index () also resulted in significant models but in all instances the association values () were below 0.3 (Table 2). The covariates meeting the stepwise 0.15 entry, 0.10 exit criteria were Z, VIB7B5, DC, , and . The odds were all negatively associated (odds ratio <1) (Table 3). The DC had the smallest odds, 0.386, which meant that a one unit increase in the distance from the river channel decreased the odds by 61% of the soils being either poorly or very poorly drained. There was therefore a high sensitivity in the degree of proximity to the river channel in predicting the wetter soils in the shale area.

VPOORMOD (Fig. 4) predicted the probability of very poorly drained soils (D6). A comparison between different univariate models indicated that VIB7B5 was the best variable to predict poorly drained soils, followed closely by VIB5B4 and elevation (Z) (Table 2). After checking for collinearity, the covariates meeting the stepwise 0.15 entry, 0.10 exit criteria were Z, VIB7B5, and (Table 2). The odds were positively associated with VIB7B5 (odds ratio >1) and negatively associated with Z and (odds ratio <1) (Table 3). The compound topographic index, , had a very low odds ratio, 0.137, which indicated that with a one unit increase in there was a 86% decrease in the odds of very poorly drained soils. High compound topographic index values are associated with river channels, and the soils on the floodplain are better drained than the soils located on the lower interfluve (Table 1). Thus relatively low values were used in this model to associate the D6 soils with areas not in close proximity to the river channel.

IMPERFMOD (Fig. 4) predicted the probability of imperfectly drained soils (D4). A comparison between different univariate models indicated that none of the univariate models were particularly successful in predicting the imperfectly drained soils, as no model achieved a value >0.26 (Table 2). The three covariates included in the multivariate model were tanß, , and VIB5B4. The odds were all positively associated (odds ratio >1) with tanß and VIB5B4 and negatively associated (odds ratio <1) with (Table 3), but the differences with unity were <20%, which indicated that none of the variables in IMPERFMOD were sensitive.

Logistic Model Validation
NONHYDRICMOD resulted in 97% correctly classified observations in the calibration data set (ncal = 295) at the 0.55 probability level (Table 4). At the 0.55 probability level the validation observations (nval = 72), 97% were correctly classified.

POORMOD correctly classified 85% of the calibration data set (ncal = 154) at the 0.45 probability level, and the validation observations (nval = 41) were 83% correctly classified. There were 6% false positive classifications and 9% false negative classifications in the calibration set, and in the validation set there were 7% false negative classifications and 10% false positive classifications.

VPOORMOD correctly classified 88% at a 0.70 probability level, and the validation observations (nval = 17) were 88% correctly classified, although a higher performance could be achieved (94%) at the 0.60 and 0.65 probability level.

IMPERFMOD only achieved a 65% correct classification for the calibration observations (ncal = 123) at the 0.50 probability level, and a 71% correct classification for the validation observations (nval = 24). The high false positive (13%) and false negative (22%) results indicated that there was higher degree of confusion between the drainage classes than other models where the false positive and negative percentages remained mostly below 10% (Table 4).

Drainage Class Probability Map
Drainage class probability maps were derived using the model parameters of the significant variables (Table 3), and the probability levels determined by the unbiased classification tables (Table 4). Maps were combined to produce drainage class maps at different stages in the modeling procedure for the entire study area (Fig. 5) . The nonhydric–hydric drainage map (Fig. 5a), achieved a kappa () of 0.918 (ASE = 0.021). The mapping of the nonhydric and hydric soils was least clear at the boundary between the escarpment and the Cross River Plains. The model was able to map the excessively drained hill slopes on the Cross River Plains. The three drainage classes map (Fig. 5b) had a of 0.818 (ASE = 0.024). The wettest soils (D5D6) were clearly mapped as being in closer proximity to the main river channels than the D3D4 soils. The area of wettest soils widened out below the confluence of the River Ebonyi and River Amanyi. The six drainage class map had a of 0.705 (ASE = 0.025), which meant that over 70% of predicted drainage classes were correct.

View larger version (122K): [in this window] [in a new window]   Fig. 5. (a) Nonhydric and hydric soil drainage classes map and (b) three-soil drainage classes map.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

The statistical analysis assessed the explanatory power of 14 variables individually (univariate analysis) and collectively (multivariate analysis). Distance-to-the-river channel was clearly an important explanatory variable (Fig. 6a) , as it featured in three of the five best multivariate models. It was particularly important in the NONHYDRICMOD and POORMOD models, as it had odds ratios of 1.546 and 0.386, respectively. Although DC is a proximity attribute, it can be regarded as a surrogate terrain variable as it integrates the terrain and landform information inherent to the measure of river channel proximity. Elevation (Z) and Slope (tanß) were the most important terrain variables (Fig. 6b,c) reflecting clearly the role that landscape plays in distinguishing between drainage classes. The study site is highly heterogeneous, having both sandstone and shale lithologies, which have undergone a prolonged period of denudation since the Tertiary. This accounts for the major contrasts in landform features, and hence the important role that primary terrain attributes such as elevation and slope have made in the analysis.

View larger version (110K): [in this window] [in a new window]   Fig. 6. (a) Distance-to-channel grid and (b) elevation grid. (c) Slope grid (tanß) and (d) Vegetation Index grid (VIB7B5).

The third derivative terrain models (, , and ) did not perform well in predicting drainage classes. This may be due to the resolution of the DEM (based on a 1:50000 topographic map), which does not provide enough terrain slope information to adequately differentiate between landscapes where soil water converges or diverges.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
Logistic modeling provided an explicitly quantitative approach to predict the spatial occurrence of soil drainage classes, by use of digital terrain attributes and vegetation indices from the LANDSAT-5 Thematic Mapper. A nested dichotomous modeling strategy was adopted to produce drainage class maps, and enabled the stepwise nature of the modeling procedure to be monitored. The model distinguishing between the nonhydric (D1D2) and hydric (D3D4D5D6) soils performed best ( = 0.91), followed by the three-drainage class model (D1D2, D3D4, D5D6) ( = 0.818), and then the six-drainage model ( = 0.704). The most important explanatory variables were DC, elevation (Z), slope (tanß), compound topographic index () and two vegetation indices (VIB7B5 and VIB5B4). In all cases, the multivariate models, which combined terrain and vegetation index information, performed better than the univariate models. It has been shown, therefore, that digital terrain models and satellite information have a complementary role as explanatory variables to predict drainage classes in humid tropical environments.

View larger version (75K): [in this window] [in a new window]   Fig. 5c. Six-soil drainage classes map.

	ACKNOWLEDGMENTS

Received for publication July 29, 2000.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 

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