Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment"

CONHYD-03210; No of Pages 14 Journal of Contaminant Hydrology xxx (2016) xxx–xxx

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Erratum

Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment" Keith Loague a, Richard E. Green b, Thomas W. Giambelluca c, Tony C. Liang b, Russell S. Yost b a b c

Department of Soil Science, University of California, Berkeley, CA 94720, USA Department of Agronomy and Soil Science, University of Hawaii, Honolulu, HI 96822, USA Department of Geography, University of Hawaii, Honolulu, HI 96822, USA

a r t i c l e

i n f o

Article history: Received 7 December 1988 Received in revised form 10 May 1989 Accepted 10 May 1989 Available online xxxx

a b s t r a c t A simple mobility index, when combined with a geographic information system, can be used to generate rating maps which indicate qualitatively the potential for various organic chemicals to leach to groundwater. In this paper we investigate the magnitude of uncertainty associated with pesticide mobility estimates as a result of data uncertainties. Our example is for the Pearl Harbor Basin, Oahu, Hawaii. The two pesticides included in our analysis are atrazine (2-chloro-4ethylamino-6-isopropylamino-s-triazine) and diuron [3-(3,4-dichlorophenyl)-1,1-dimethylarea]. The mobility index used here is known as the Attenuation Factor (AF); it requires soil, hydrogeologic, climatic, and chemical information as input data. We employ first-order uncertainty analysis to characterize the uncertainty in estimates of AF resulting from uncertainties in the various input data. Soils in the Pearl Harbor Basin are delineated at the order taxonomic category for this study. Our results show that there can be a significant amount of uncertainty in estimates of pesticide mobility for the Pearl Harbor Basin. This information needs to be considered if future decisions concerning chemical regulation are to be based on estimates of pesticide mobility determined from simple indices.

1. Introduction The Pearl Harbor Basin (Fig. 1) is of great interest in Hawaii as it recharges the Pearl Harbor Aquifer, the most important source of freshwater on the island of Oahu. Trace amounts of organic chemicals have recently been discovered in the Pearl Harbor Aquifer (Oki and Giambelluca, 1987). Some of this pollution is thought to be the result of pesticides used by the pineapple industry over the past 30 years to control nematodes. The fumigants which have been detected in groundwater (e.g., DBCP, EDB) are now banned in Hawaii just as they are in many mainland states (e.g., California, Florida). Intuitive evaluations of potential pesticide leaching failed to predict their occurrence in Hawaiian groundwater before their discovery. The assumptions leading to faulty conclusions about the likelihood of fumigants reaching groundwater were that DOI of original article: http://dx.doi.org/10.1016/j.jconhyd.2016.04.003.

volatile and degradable chemicals would not be leached to groundwater with the relatively low recharge rates common to pineapple areas where water table depths exceed 100 m. Several authors (e.g., Rao et al., 1974) have suggested that near-surface solute transport in Hawaii is via preferential pathways in highly structured soils perhaps explaining the early appearance of some of the problem chemicals in groundwater. The majority of the vadose zone in Hawaii is made up of very permeable fractured basalt and some saprolite which is conducive to preferential flow and, therefore, rapid solute transport. The pressing question today is whether or not the chemicals currently used in Hawaii will leach to groundwater. Various mathematical models have been suggested (e.g., Oki, 1987; Or, 1987) for assessment of pesticide leaching. These models range from simple correlation procedures through comprehensive physics-based simulation algorithms. Analysis of the leaching problem with statistical correlation of soil properties with the incidence of groundwater contamination (e.g., Teso et al.,

http://dx.doi.org/10.1016/j.jconhyd.2016.04.003 0169-7722/

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

Fig. 1. Pearl Harbor Basin on the Island of Oahu.

1988) requires an extensive data base including both contaminated and uncontaminated wells, and is limited in prediction ability outside the area for which the correlations were derived. On the other hand, rigorous physically based prediction of pesticide leaching is limited both by a lack of accurate input data and by an inadequate representation of reality with existing analytical and numerical models. How then can decision makers regulate chemicals without banning everything? A rational approach is to use relatively simple indices, which describe processes more directly than correlation analysis and are less data-intensive than complex dynamic simulation models. Such indices should suffice to screen and rank the potential mobility of various chemicals. This may be the only level of information needed by a decision maker and, therefore, it can be very useful if the indices and the data are reliable. In this paper we illustrate how a simple pesticide mobility index, when combined with soil, hydrogeologic, climatic and chemical data, can be used to generate rating maps for various chemicals. Our example is for the Pearl Harbor Basin. The focus of our investigation, however, it not to make rating maps but to investigate the “magnitude of uncertainty” in pesticide mobility estimates resulting from data uncertainties. The two chemicals used in our example are currently employed by the pineapple growers in Hawaii. Both the public and state officials are concerned about the fate of these chemicals in the insular hydrogeologic environment of Hawaii. 1.1. AF index of pesticide mobility A simple index, known as the attenuation factor (AF), has been proposed by Rao et al. (1985) to rank pesticides with

respect to their potential to leach to groundwater. In essence, AF is simply the fraction of the initial mass of an applied pesticide to the mass remaining after a given time. Rao et al. (1985) point out that methods, such as the AF index, are needed by regulatory agencies to screen large numbers of pesticides to determine their potential to contaminate groundwater. The AF index is based upon some of the primary processes which control the rate of pesticide leaching. These processes are sorption, advection, and transformation. Sorption is incorporated into AF by way of a retardation factor (RF) defined as: RF ¼ 1 þ

ρb f oc K oc na K H þ θFC θFC

ð1Þ

where ρb foc Koc θFC na n ρp KH

soil bulk density (M L−3) soil organic carbon (mass fraction) pesticide sorption coefficient (L M−1) soil-water content at field capacity (volume fraction) soil air-filled porosity (fraction) [na = n − θFC] soil porosity (fraction) [n = 1 − (ρb/ρp)] soil particle density (M L−3) Henry's constant (dimensionless).

Advective transport is approximated in AF with an estimate of pesticide travel time given by: τ¼

d RFθFC q

ð2Þ

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx Table 1 Scales of pesticide mobility (Liang and Khan, 1987). The assignment of numerical values to the various classes is arbitrary, therefore the classes only indicate relative retardation (RF) and attenuation (AF). Index

3

Table 2 Component equations for AF uncertainty analysis. Uncertainty due to RF:

Classification

1

FC AF jSRF C 1 ¼ j −0:693dθ qt 1=2

RF =1.0 N1.0 and b2.0 ⩾2.0 and b3.0 ⩾3.0 and b10.0 ⩾10.0

Very mobile Mobile Moderately mobile Moderately immobile Very immobile

AF ⩾0.0 and b1.0 E − 4 ⩾1.0 E − 4 and b1.0 E −2 ⩾1.0 E − 2 and b1.0 E −1 ⩾1.0 E − 1 and b2.5 E − 1 ⩾2.5 E − 1 and ⩽1.0

Very unlikely Unlikely Moderately likely Likely Very likely

Uncertainty due to q: 1 0:693 dRFθFC t 1=2 AF

C2 ¼ j

2

ðqt 1=2 Þ

jSq

Uncertainty due to t1/2: 1

C 3 ¼ j 0:693 dRFθ2FC qAF jSt 1=2 ðqt 1=2 Þ

Uncertainty due to θFC: 1

dRFAF C 4 ¼ j −0:693 jSθFC qt 1=2

Uncertainty due to d: 1

RFθFC AF jSd C 5 ¼ j −0:693 qt 1=2

The AF index can now be defined by: where d q

AF ¼ expð−k  τ Þ: distance to the water table from the soil surface (L) net annual groundwater recharge (L T−1).

Pesticide transformation is accommodated in AF using a first-order degradation approximation. The pesticide half-life is related to the first-order relationship by: t 1=2 ¼ 0:693=k

ð3Þ

where k

first-order degradation rate coefficient (T−1).

ð4Þ

When Eqs. (2) and (3) are substituted into Eq. (4) the AF index is given as: " # −0:693d RFθFC : qt 1=2

AF ¼ exp

ð5Þ

As an index of pesticide mass emission from the vadose zone, AF is a relative index of the potential for the chemical to leach to groundwater (Rao et al., 1985). RF represents the retardation of pesticide leaching through soils because of sorption and pesticide partitioning between the solid, liquid,

Fig. 2. Diagrammatic representation of pesticide leaching-assessment methodology (modified from Loague et al., 1989a).

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx Table 3 Component equations for RF uncertainty analysis. Uncertainty due to foc: C 1:1 ¼ j ρb K oc jS f oc 1

θFC

Uncertainty due to θFC: C 1:2 ¼ j −ρb f2oc K oc − K2H þ 1

θFC

θFC

ρp ρb K H ðρp θFC Þ

2

jSθFC

Uncertainty due to ρb: 1

C 1:3 ¼ j f oc K oc − θFC

KH ρp θFC

jSρb

Uncertainty due to ρp: C 1:4 ¼ j θFC ρb K H2 jSρp 1

ðρp θFC Þ

Uncertainty due to Koc: C 1:5 ¼ j ρb f oc jSKoc 1

θFC

Uncertainty due to KH: 1

C 1:6 ¼ j

1 θFC

−

ρb ρp θFC

−1jSKH

and vapor phases (Rao et al., 1985). Both AF and RF are dimensionless. The range of possible values for AF is between 0 and 1. For nonsorbed, nonvolatile pesticides (Koc and KH = 0) RF = 1; with increasing Koc and/or KH, RF becomes larger. The assumptions inherent to the AF index are those associated with first-order kinetics, linear-reversible-equilibrium sorption, and uniformity with respect to the various input parameters of both AF and RF. In addition, the AF index does not account for pesticide transport resulting from hydrodynamic dispersion and is based on steady-state soil-water flow. The assumptions of AF are too restrictive to allow the index to be used for quantitative prediction of pesticide leaching. It should also be pointed out that the AF index does not account for varying application rates for different pesticides nor does it have any provision for characterizing variable recharge rates

contributing to the net annual recharge. The AF index should only be used as a first-cut method for comparing, in terms of likelihood, the approximate leaching potential of various chemicals at a given location or for ranking the vulnerability to leaching of different locations with variable soil properties. The RF index, on its own, is even less useful than AF for rigorous management of pesticides as it only indicates the relative mobility for a pesticide to leach out of the root zone with adequate recharge. The scales used to subdivide the AF and RF indices into ranges are, to date, essentially arbitrary. Liang and Khan (1987) have adopted the schemes shown in Table 1 for making relative assessments of pesticide mobility with AF and RF. The RF scale follows the classification scheme of Helling and Dragun (1980). The AF scale was first suggested by Khan et al. (1986). The two scales, although not carved in stone, are sufficient for the application in this study. Rao et al. (1985) have shown how multiple layers of differing soil properties could be accommodated with AF; however, data for the unsaturated zone below the solum are seldom available. In an ongoing study, we are evaluating single layer and multiple layer versions of the AF index by comparing them with a dynamic-conceptual solute transport model for a well-described field site. Jury et al. (1987) have developed a screening model that incorporates depth-dependent firstorder biodegradation. 1.2. AF, GIS and rating maps If pesticide mobility estimates are made over an area large enough so that soil, hydrogeologic, and climatic parameters change, then it is possible to construct maps which show the spatial variability of the estimates. Much, if not all, of the information needed to describe the spatial variability for the

Fig. 3. Water balance segments (after Giambelluca, 1983).

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

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Fig. 4. Occurrence of soil orders in the Pearl Harbor Basin (after McCall, 1975).

nonchemical AF input parameters can be included within a wellorganized geographic information system (GIS). We believe that a GIS which is based on soil survey has “potential” for generating rating maps of pesticide mobility. A preliminary effort (Khan et al., 1986) illustrated that the mechanics of linking the AF and RF indices to a GIS are well within reach. Khan et al. (1986) developed rating maps for the island of Oahu for several pesticides using the Hawaii Natural Resource Information System (HNRIS) as-the foundation. In the study by Khan et al. (1986), Oahu was discretized into a grid of square elements of approximately 0.1 km2 in area in which the soil series and mapping units were overlaid. The soil parameter inputs for the AF and RF calculations by Khan et al. (1986), were based on extrapolation of information at the great group soil taxonomic category. The soil properties assigned to a given grid element by Khan et al. (1986) were the average values for whatever soil great group dominated the element. In an earlier part of this study, Loague et al. (1989a) characterized the amount of uncertainty for calculated RF values in Hawaii due to data uncertainty by using first-order uncertainty analysis. The results of Loague et al. indicated that the RF index should be used with soil information from the lowest taxonomic category, and even then considerable uncertainty will exist in the predicted RF values used to screen

and rank pesticides. Loague et al. (1989a) also illustrated that the greatest uncertainty in RF was contributed by the uncertainty in estimates of foc and Koc indicating where future effort should be directed for improving soil and chemical data. Loague et al. (1989a) stress that “fuzzy” maps, showing the uncertainty in RF at different confidence levels, should be presented in parallel to any “crisp” RF map to provide useful information for decision makers concerned with the regulation of pesticides. Our perception of how pesticide rating maps should be developed is shown in Fig. 2. In this paper we illustrate how the uncertainty in AF and RF rating maps can be characterized.

2. Objective The objective of this work was to characterize the uncertainty in estimates of AF for the Pearl Harbor Basin resulting from uncertainties in soil, hydrologic, and chemical data. We employ first-order uncertainty analysis for soils delineated at the order taxonomic category. This study differs from the one reported by Loague et al. (1989a) in three ways: (1) the mobility index of central focus is AF not RF; (2) the soil taxonomic category of order is tested solely rather than all the

Table 4 Statistical properties for four soil parameters from the Hawaii soil data base for the five soil orders in the Pearl Harbor Basin. Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols a

ρb (kg m−3)

θFC (dimensionless)

foc (dimensionless) a

ρp (kg m−3)

n

Mean

SD

n

Mean

SD

n

Mean

SD

n

Mean

SD

88 42 55 41 14

0.09 0.02 0.03 0.04 0.02

0.05 0.01 0.01 0.01 0.01

34 16 16 24 7

0.41 0.37 0.43 0.04 0.42

0.09 0.06 0.06 0.05 0.03

47 23 18 25 8

688 1188 1107 1186 1281

239 112 142 182 103

32 20 17 10 7

2727 2862 3005 3170 2934

149 119 205 267 59

SD = standard deviation.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

Table 5 Statistical properties for recharge rates and water table depths for five soil orders and for miscellaneous land types in the Pearl Harbor Basin. q (m d−1)

Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols Miscellaneous land types

d (m)

n

Mean

SD

Mean

SD

69 11 100 23 20 50

5.4 E−4 3.7 E−4 7.4 E−4 3.7 E−3 3.7 E−4 3.2 E−3

5.2 E−4 1.2 E−4 6.9 E−4 1.8 e−3 1.5 E−4 31. E−3

0.5 0.5 0.5 0.5 0.5 –

0.0 0.0 0.0 0.0 0.0 –

Table 7 RF, SRF, AF, and SAF values for atrazine for the five soil orders in the Pearl Harbor Basin. Soil order

n

RF

SRF

AF

SAF

Inceptisols Mollisols Oxisols Ultisols Vertisols

88 42 55 41 14

25.9 12.1 11.7 19.3 8.5

21.0 7.8 8.2 10.9 5.6

~0.0 ~0.0 1.2 E−51 2.5 E−16 1.2 E−73

~0.0 ~0.0 1.8 E−49 1.8 E−14 1.9 E−71

Note: the equations for RF, SRF, AF, and SAF are (9), (11), (6), and (8), respectively.

Application of FOUA to RF gives: categories from order through family; and (3) the Pearl Harbor Basin is examined instead of the entire State of Hawaii.

1

RF ¼ 1 þ

3. Methodology

First-order uncertainty analysis (FOUA) is a well known technique for estimating the uncertainty in a deterministic model due to uncertainty in the parameters. Cornell (1972) describes the theoretical basis and the limitations of FOUA. Loague et al. (1989a) employed FOUA to characterize the uncertainty in estimates of RF for Hawaii soils at different soil taxonomic categories resulting from uncertainties in both soil and chemical data. Application of FOUA to AF yields: " # ̅ ̅ −0:693dRF θFC AF ¼ exp q ̅t 1=2 1

ð6Þ

1 indicates where the overbars designate mean values and ¼ equal in the first-order sense. The uncertainty in AF contributed by the ith parameter is given by:

  1 ∂AF  S C i ¼ ∂P i  Pi

ð7Þ

where SPi represents the standard deviation of the variable Pi. The total uncertainty in AF is: 1

" n X

#1=2 2

Ci

:

ð8Þ

i¼1

The number of parameters (n) contributing uncertainty to AF is five. The equations for the respective uncertainties for each of the AF parameters are listed in Table 2.

Table 6 Statistical properties for RF and AF chemical parameters for atrazine and diuron (from Rao and Davidson, 1982). Chemical

Atrazine Diuron

Koc (m3 kg−1)

ð9Þ

The uncertainty in RF contributed by the ith parameter is given by:

3.1. First-order uncertainty analysis

SAF ¼

ρb f oc K oc K H ρb K H þ − ‐K H : θFC θFC ρp θFC

Hh (dimensionless)

t1/2 (days)

Mean

SD

Mean

SD

Mean

SD

0.163 0.383

0.080 0.277

0.0 0.0

0.0 0.0

20 328

10 212

  1 ∂RF  S C 1;i ¼ ∂P i  Pi

ð10Þ

The total uncertainty in RF, at a given soil taxonomic category, is: 1

SRF ¼

" 0 n X

#1=2 2 C 1;i

:

ð11Þ

i¼1

The number of parameters (n′) contributing uncertainty to RF is six. The equations for the respective uncertainties for each of the RF parameters are listed in Table 3. One should note that the SRF estimates are input to the AF uncertainty analysis. 3.2. Soil taxonomy Taxonomic levels in the U.S. Soil Taxonomy (Soil Survey Staff, 1975) include: order, suborder, great group, subgroup, family, and series. This is a hierarchical classification system that establishes successive categories. For example, a single soil order is made up of several suborders in which, ideally, the variability of a given soil property is less within each of the suborders than it is for the order. There are ten separate orders in the U.S. Soil Taxonomy, all of which are found in Hawaii. Soil taxonomy and soil survey are separate entities. Where soil taxonomy is a classification scheme, soil survey is concerned with mapping and data collection. When combined, soil taxonomy and soil survey provide a procedure for estimating soil properties at unsampled locations. Essentially the “missing”

Table 8 RF, SRF, AF, and SAF values for diuron for the five soil orders in the Pearl Harbor Basin. Soil order

n

RF

SRF

AF

SAF

Inceptisols Mollisols Oxisols Ultisols Vertisols

88 42 55 41 14

59.5 27.2 26.2 44.1 18.6

58.4 23.0 23.5 34.3 16.2

1.3 E−21 3.5 E−13 1.1 E−7 6.8 E−3 1.8 E−10

9.3 E−20 1.1 E−11 2.7 E−6 3.8 E−2 4.7 E−9

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx Table 9 Uncertainty in AF contributed by each parameter in the index for atrazine for the five soil orders in the Pearl Harbor Basin. C2

C3

C4

C5

Soil order

C1 (RF)

(q)

(t1/2)

(θFC)

(d)

Inceptisols Mollisols Oxisols Ultisols Vertisols

~0.0 ~0.0 9.6 E−50 5.1 E−15 1.3 E−71

~0.0 ~0.0 1.3 E−49 4.4 E−15 8.3 E−72

~0.0 ~0.0 6.9 E−50 4.5 E−15 1.0 E−71

~0.0 ~0.0 1.8 E−50 1.0 E−15 1.7 E−72

0.0 0.0 0.0 0.0 0.0

7

Table 11 Uncertainty in AF contributed by each parameter in the index for diuron for the five soil orders in the Pearl Harbor Basin. C2

C3

C4

C5

Soil order

C1 (RF)

(q)

(t1/2)

(θFC)

(d)

Inceptisols Mollisols Oxisols Ultisols Vertisols

6.0 E−20 8.5 E−12 1.6 E−6 2.6 E−2 3.5 E−9

5.8 E−20 3.2 E−12 1.7 E−6 1.6 E−2 1.7 E−9

3.9 E−20 6.5 E−12 1.2 E−6 2.2 E−2 2.6 E−9

1.3 E−20 1.5 E−12 2.4 E−7 3.9 E−3 3.3 E−10

0.0 0.0 0.0 0.0 0.0

Note: The equations for C1, C2, C3, C4, and C5 are given in Table 2.

data is gleaned from information available at other sites having the same soil classification. The extrapolation technique described here has been employed by both Khan et al. (1986) and Loague et al. (1989a). In this study, estimates of the mean and variance for foc, θFC, ρb and ρp are determined for each soil order in the Pearl Harbor Basin using available information. The statistical characteristics of the four soil parameters are used to perform first-order uncertainty analyses for RF and AF estimates for each separate soil order. 3.3. Recharge estimates Recharge was estimated for discrete subdivisions of the basin using a modified Thornthwaite-type (Thornthwaite and Mather, 1955) water balance model. The modified model is described in detail by Giambelluca (1983). To account for soilwater exchanges within the root zone, a state variable xi is computed as: xi ¼ si−1 þ pi −r i −ei

ð12Þ

where the subscript i indicates the current time interval, and where s (L) is available soil water, p (L) is precipitation, r (L) is runoff, and e (L) is evapotranspiration. Recharge and end-of-interval soil water are determined using the following drainage rules: si ¼ 0 qi ¼ 0 ei ¼ si−1 þ pi −r i si ¼ xi qi ¼ 0 si ¼ ϕ qi ¼ xi −ϕ

for xi ≤ 0

Inceptisols Mollisols Oxisols Ultisols Vertisols

4. Data base The parameters which make up RF and AF can, in general, be divided into three groups: (1) soil properties ( foc, θFC, ρb, ρp); (2) hydrogeologic and climatic characteristic parameters (d, q); and (3) chemical coefficients (Koc, KH, and t1/2).

for 0 b xi ≤ ϕ 4.1. Soil properties

for xi N ϕ

Available data from 240 pedons located throughout the state of Hawaii were used to estimate statistical properties for

Table 10 Uncertainty in RF contributed by each parameter in the index for atrazine for the five soil orders in the Pearl Harbor Basin. Soil order

where q is groundwater recharge and ϕ is available soilwater capacity. Records from rain gauges within and near the basin were used to interpolate monthly precipitation for each basin subdivision. Daily precipitation was simulated by a simple disaggregation technique (Giambelluca, 1983). Runoff was estimated from streamflow records, where available, and with a modified version of the Soil Conservation Service curve number method (U.S. Department of Agriculture, 1972) elsewhere. Evapotranspiration was evaluated on the basis of evaporative demand, potential evapotranspiration, and soil-water availability. The rate of evapotranspiration was assumed to remain at the potential rate until soil water was depleted to a critical level dependent on root depth and evaporative demand. Below the critical level, evapotranspiration was assumed to decline linearly with decreasing soil-water content. The basin was subdivided along topographic divides, historic land-use boundaries, and according to the spatial patterns of climate, soil, and geology (Fig. 3). The model was employed independently for each subdivision using a daily time step. The 1946–1975 climatic record was used in each simulation. Mean annual recharge in each subdivision was derived from estimates of annual recharge for each of the 30 years in the climate record.

C1.1

C1.2

C1.3

C1.4

C1.5

C1.6

( foc)

(θFC)

(ρb)

(ρp)

(Koc)

(KH)

13.7 5.2 6.0 5.0 4.2

5.5 1.7 1.4 2.1 0.6

8.6 1.0 1.4 2.8 0.6

0.0 0.0 0.0 0.0 0.0

12.2 5.5 5.3 9.0 3.7

0.0 0.0 0.0 0.0 0.0

Note: The equations for C1.1, C1.2, C1.3, C1.4, C1.5, and C1.6 are given in Table 3.

Table 12 Uncertainty in RF contributed by each parameter in the index for diuron for the five soil orders in the Pearl Harbor Basin. Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols

C1.1

C1.2

C1.3

C1.4

C1.5

C1.6

( foc)

(θFC)

(ρb)

(ρp)

(Koc)

(KH)

32.3 12.3 14.1 11.7 9.8

12.9 4.0 3.3 5.0 1.4

20.3 2.5 3.2 6.6 1.4

0.0 0.0 0.0 0.0 0.0

42.3 18.9 18.3 31.1 12.8

0.0 0.0 0.0 0.0 0.0

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

Fig. 5. AF rating map for atrazine for the Pearl Harbor Basin.

the four near-surface soil-related parameters required to make calculations of RF and AF for the five soil orders (Inceptisols, Mollisols, Oxisols, Ultisols, Vertisols) located within the Pearl Harbor Basin. Fig. 4 illustrates the distribution of soils across the Pearl Harbor Basin. Measurements of foc were available for each of the 240 sites while data for θFC, ρb, and ρp were available, respectively, for only 40, 50 and 36% of the sites. The statistical properties for each of the soil parameters for each soil order are given in Table 4. These values represent only the top 0.2 m of the soil column. The Hawaii soil data base (Loague et al., 1989b) used

in this study is a revised and expanded version of the data reported, in part, by Loague et al. (1989a). 4.2. Hydrogeologic and climatic characteristics The depth to the water table in the Pearl Harbor Basin is extremely variable, ranging from the surface near the coast to 300 m or more towards the center of the island. Because our application of AF for a single near-surface layer we have elected to set d equal to 0.5 m across the entire basin. This is a very conservative tack as the source areas for pesticide contamination

Fig. 6. RF rating map for atrazine for the Pearl Harbor Basin.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

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Fig. 7. AF rating map for diuron for the Pearl Harbor Basin.

are in the upland areas where the water table is far deeper. For this study the uncertainty in AF due to uncertainty in d (set to zero) must be zero. The mean and standard deviation of the net annual recharge for each soil order listed in Table 5 were determined based on recharge estimates for natural land use. Figs. 3 and 4 were overlaid to estimate average recharge rates for each of the five soil orders. The recharge statistics for each soil order do not rigorously account for spatial variability because recharge estimates for the same soil order, possibly from much different rainfall areas, are averaged together in the simple approach used here.

4.3. Chemical coefficients The statistical properties for both diuron and atrazine for Koc and t1/2 (see Table 6) were taken, for this study, from the summary of Rao and Davidson (1982). The kind of data summarized by Rao and Davidson is, in general, scarce and therefore quite precious. It should be noted, however, that even though the t1/2 values used in this study are the result of field dissipation it is quite likely that these values would be different if measured in Hawaii and very conceivably would even vary between soil orders. The Koc values used here are for laboratory experiments. The KH parameter in RF was assumed to be zero

Fig. 8. RF rating map for diuron for the Pearl Harbor Basin.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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Fig. 9. AF + SAF rating map for atrazine for the Pearl Harbor Basin.

for both diuron and atrazine. This assumption is quite reasonable as both chemicals are nonvolatile. With KH set to zero, the third term in Eq. (1) is dropped and the uncertainty in RF due to uncertainty in ρp and KH is zero. 5. Results Tables 7 and 8 list the RF, SRF, AF, and SAF values for atrazine and diuron for each of the five soil orders. The uncertainty in AF and RF contributed by each parameter for each of the five soil orders is given in Tables 9 and 10 for atrazine and Tables 11 and 12 for diuron. Pesticide rating maps, based on the AF and RF indices, are shown in Figs. 5 and 6 for atrazine and Figs. 7 and

8 for diuron. Pesticide rating maps, which incorporate the uncertainty in AF and RF estimates based on data uncertainty, are shown in Figs. 9 and 10 for atrazine and Figs. 11 and 12 for diuron. Inspection of Tables 7 through 12 and Figs. 5 through 12 leads to the following generalized observations: (1) The RF values are greater for diuron than for atrazine due to the greater Koc value for diuron. (2) The AF values are smaller for atrazine than for diuron due to the greater t1/2 value for diuron. (3) The RF and AF estimates show considerable variability for the different soil orders for both atrazine and diuron.

Fig. 10. RF−SRF rating map for atrazine for the Pearl Harbor Basin.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

K. Loague et al. / Journal of Contaminant Hydrology xxx (2016) xxx–xxx

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Fig. 11. AF + SAF rating map for diuron for the Pearl Harbor Basin.

The magnitudes of the SRF and SAF values for each soil order are similar to the RF and AF values for both of the chemicals. (4) The two pesticides are shown to be least mobile for the Inceptisols soil order. (5) For diuron the parameter that contributes the most uncertainty to RF is Koc. The soil parameter that contributes the most uncertainty to RF for diuron is foc. For atrazine the uncertainty contributed to RF by Koc and foc is similar. (6) The uncertainty in q and t1/2 contributes similar levels of uncertainty to AF as are contributed by RF.

6. Discussion If the classification of RF and AF can be changed to a poorer category by accounting for plus (AF) or minus (RF) a single standard deviation, due to data uncertainties, then regulatory decisions will lack objectivity. The RF and AF rating maps generated, for example, by Khan et al. (1986) are preliminary and incomplete because they do not account for this uncertainty. Deterministically derived pesticide rating maps can be attractive to decision makers because they provide crisp boundaries that lead to yes or no interpretations of relative risk. In our view, however, pesticide rating maps that incorporate

Fig. 12. RF−SRF rating map for diuron for the Pearl Harbor Basin.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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existing knowledge describing data uncertainty are superior to those that do not because they provide decision makers with additional information. If RF and AF calculations are considered at various levels of confidence, then the boundaries of the resulting pesticide rating maps can have different levels of fuzziness. Fig. 5 illustrates that atrazine is ‘very unlikely’ to leach to a depth of 0.5 m for all five soil orders in the Pearl Harbor Basin. Fig. 7 illustrates that diuron is ‘very unlikely’ to leach to 0.5 m for all the soil orders except the Ultisols in which case leaching is ‘unlikely’. The AF values are considerably greater for diuron than atrazine due to the smaller half-life for atrazine. Fig. 6 shows that atrazine is classified as ‘very immobile’ for all the soil orders except the Vertisols for which it is classified as ‘moderately immobile’. Fig. 8 shows that diuron is classified as ‘very immobile’ for all five soil orders in the Pearl Harbor Basin. Although both chemicals are strongly retarded, diuron, relative to atrazine, is more strongly sorbed. This effect is due to the larger Koc value for diuron. Fig. 9 shows that atrazine is still ‘very unlikely’ to leach to 0.5 m for all five soil orders even with plus one standard deviation in AF superimposed on Fig. 5. Fig. 10 illustrates, however, that with minus one standard deviation in RF superimposed on Fig. 6 the classification for atrazine for each soil order has moved one class either from ‘very immobile’ to ‘moderately immobile’ (Inceptisols, Mollisols, Oxisols, Ultisols) or from ‘moderately immobile’ to ‘moderately mobile’ (Vertisols). Fig. 11 shows that diuron is still ‘very unlikely’ to leach to 0.5 m for all soil orders, except the Ultisols where leaching is still classified as ‘unlikely’ even when plus one standard deviation in AF is superimposed on Fig. 7. Fig. 12 illustrates, however, that with minus one standard deviation in RF superimposed on Fig. 8 the classification for all soil orders has changed: Inceptisols from ‘very immobile’ to ‘mobile’; Mollisols and Ultisols from ‘very immobile’ to ‘moderately mobile’; Oxisols and Vertisols from ‘very immobile’ to ‘moderately immobile’. The changes seen from Figs. 6 and 8 to Figs. 10 and 12, due to data uncertainties, are important to consider. Decisions made based on the pesticide ranking maps illustrated in Figs. 6 and 8 would be significantly different if the pesticide ranking maps in Figs. 10 and 12 were used. It is also worth pointing out that with either larger recharge rates or chemical half-lives, the uncertainties in RF for atrazine and diuron would propagate to the AF ranking maps in Figs. 9 and 11, respectively. 6.1. Limitations The shortcomings of the approach used in this study to generate pesticide rating maps for the Pearl Harbor Basin are considered here: (1) The Hawaii soil data base used to compile the statistics listed in Table 2 includes data from locations outside the Pearl Harbor Basin. Approximately 20% of the information in the Hawaii soil data base is from the Pearl Harbor Basin; therefore, there is obviously an element of uncertainty associated in our estimation of soil property statistics as the estimates are more heavily weighted from samples outside the region of interest than from within.

Table 13 AF classifications for atrazine and diuron for maximum and minimum recharge rates for the five soil orders in the Pearl Harbor Basin. Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols

AF (q max)

AF (q min)

Atrazine

Diuron

Atrazine

Diuron

Very unlikely Very unlikely Very unlikely Very unlikely Very unlikely

Unlikely Very unlikely Unlikely Unlikely Very unlikely

Very unlikely Very unlikely Very unlikely Very unlikely Very unlikely

Very unlikely Very unlikely Very unlikely Very unlikely Very unlikely

(2) The samples used to determine soil characteristics from each of the five soil orders are of different sizes. Ideally, the number of samples from each soil order should, based on the percentage of the total area represented, be equal. In this study, however, the data base was not compiled with this in mind. (3) The soil and chemical parameters used in the RF calculations ( foc, θFC, ρb, ρp, Koc) are assumed, as in the earlier analysis by Loague et al. (1989a), to be uncorrelated. The soil, climatic, hydrogeologic, and chemical parameters used in the AF calculations (θFC, q, t1/2) are also assumed to be uncorrelated. There is no effort to account for correlation between the RF and AF parameters. In an ongoing study we are examining what effect correlation within the soil data base has on calculated RF and AF values. The general mathematical formulation for FOUA with consideration for correlated parameters is given by Cornell (1972). (4) The AF calculations are made for a single soil layer that is 0.5 m thick. The water table is obviously not a constant and in general is much deeper in the upper reaches of the basin. The approach taken here is very conservative. (5) The recharge estimates given in Table 5 for each soil order are derived from averaging the recharge rates for areal units of various sizes which are coincident with the soil order distributions. The problem here is that the spatial variability of rainfall and evapotranspiration, which was included in the estimate of recharge, is lost when the recharge estimates are averaged by soil orders. Obviously, it is very probable that recharge estimates are either overestimated or underestimated depending upon the location of interest within the basin and the distribution of soil orders across the basin. The soil-order based recharge estimates are, however, superior to single values for the entire basin. Table 13 lists the AF classifications for both atrazine and diuron when the maximum and minimum annual recharge rates for each

Table 14 Estimates of mean recharge rates for irrigated land use for five soil orders in the Pearl Harbor Basin. Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols

q (m day−1) Pineapple (drip irrigation)

Sugarcane (furrow irrigation)

2.3 E−3 1.5 E−3 3.0 E−3 6.3 E−3 1.6 E−3

6.2 E−3 5.8 E−3 6.3 E−3 7.1 E−3 6.0 E−3

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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Table 15 AF classifications for atrazine and diuron for irrigated land use for five soil orders in the Pearl Harbor Basin. Soil order

Inceptisols Mollisols Oxisols Ultisols Vertisols

AF-pineapple

AF-sugarcane

Atrazine

Diuron

Atrazine

Diuron

Very unlikely Very unlikely Very unlikely Very unlikely Very unlikely

Unlikely Unlikely Moderately likely Moderately likely Unlikely

Very unlikely Very unlikely Very unlikely Very unlikely Very unlikely

Moderately likely Likely Likely Moderately likely Very likely

soil order are used instead of the average values. If reliable uncertainty estimates are to be made for pesticide mobility rating maps, then reliable recharge estimates are needed. Associated with the recharge estimates are uncertainties resulting from temporal and spatial variabilities in the parameters and variables used to calculate recharge. We feel that uncertainty analysis, as described here for pesticide mobility, should be incorporated into future recharge calculations. (6) The AF results presented throughout this paper for the Pearl Harbor Basin are based on recharge estimates only for natural land use. This is a simplifying assumption as there are obviously several other land uses in the Pearl Harbor Basin. Table 14 lists recharge estimates for drip-irrigated pineapple and furrow-irrigated sugarcane (Giambelluca, 1986). The recharge rates for both of these types of irrigated land use are greater than those given in Table 5 for natural land use. Table 15 summarizes AF classifications for atrazine and diuron for each of the five soil orders based on the recharge estimates in Table 14. The AF classes in Table 15 for diuron are greatly changed from those shown in Fig. 7 due to the higher recharge rates. The same changes in classification are not seen for atrazine (see Table 15 and Fig. 5) due to the smaller half-life used for atrazine. The example used here helps to illustrate the importance of correctly characterizing land use. The natural land use recharge rates used in this study are probably low overall. Therefore, we feel that the resulting AF estimates underestimate the leaching potential. (7) In Figs. 9 and 11, SAF values are added to AF values. In Figs. 10 and 12, SRF values are subtracted from RF values. If an AF or SAF value is large enough, then the AF + SAF could be greater than one. This did not happen in this study. However, AF− SAF can be less than zero and this did occur in our work. Similarly, RF − SRF can dip below one. At the start of this investigation we subjectively elected to set any AF ± SAF value greater than one or less than zero equal to one or zero respectively and any RF −SRF value less than one to one. For this study we did not attempt to characterize the statistical distributions for either mobility index or any of their parameters. We have added or subtracted standard deviations from mean values without regard to normality and the degrees of confidence that can be associated with one, two, or three standard deviations. It may be useful to think of our frequency distributions as uniform and truncated based on scale limits. The reader is reminded that the various classes for RF and AF are arbitrary.

7. Summary We believe that a simple pesticide mobility index, such as AF, when coupled with a soil-based GIS, such as HNRIS, can be used to generate useful pesticide rating maps. However, the data necessary to excite this approach are, in general, not available, or at least, less than totally reliable. Therefore, the uncertainty in pesticide rating maps due to data limitations must be considered and evaluated before potentially poor quality assessments are handed over to decision makers who may not recognize that uncertainty can exist in the maps. In this paper, we have given examples of pesticide rating and uncertainty maps for two chemicals. We did not use HNRIS in the analyses reported here. The reason for this is three-fold: (a) the archived data base bad only average values for each of the four soil parameters ( foc, θFC, ρb, ρp) and estimates of variance for each parameter are required for the uncertainty analysis reported in this study; (b) the locations and the sampling methods for the soils data were not contained within the system data base making it impossible to trace the origin and quality of information; and (c) the system data base was, to a large extent, derived from a single summary report which is now more than ten years old (U.S. Soil Conservation Service, 1976) and therefore failed to capture any of the information that has recently been collected. For this study it was not our intention to construct pesticide rating maps that would be used to make management or regulatory decisions. Rather, it was our desire to demonstrate the approach suggested by Loague et al. (1989a). Our ongoing investigation includes coupling the techniques described here to a GIS so as to produce pesticide mobility rating maps which include estimates of data uncertainty. Acknowledgments We are grateful to Suresh Rao, Mark Ingoglia, Haruyoshi Ikawa, Harry Sato, and Akram Khan for their interaction at various stages of the study. The manuscript was typed by Marlene Kuraoka and Terri DeLuca. The figures were drafted by April Kam. The research was funded by the Hawaii State Office of Environmental Quality Control and the U.S. Environmental Protection Agency. The opinions expressed in this paper do not necessarily represent those of the State of Hawaii or the EPA. References Cornell, C.A., 1972. First-order analysis of model and parameter uncertainty. In: Proc. Int. Symp. on Uncertainties in Hydrologic and Water Resources Systems, Tucson, Arizona, Vol. 3, pp. 1245–1274.

Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003

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Please cite this article as: Loague, K., et al., Erratum to "Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment", J. Contam. Hydrol. (2016), http://dx.doi.org/10.1016/j.jconhyd.2016.04.003