###### April 15, 2007

# Estimating Hydraulic Properties of Volcanic Aquifers Using Constant- Rate and Variable-Rate Aquifer Tests1

By Rotzoll, Kolja; El-Kadi, Aly I; Gingerich, Stephen B

ABSTRACT:

In recent years the ground-water demand of the population of the island of Maui, Hawaii, has significantly increased. To ensure prudent management of the ground-water resources, an improved understanding of ground-water flow systems is needed. At present, large-scale estimations of aquifer properties are lacking for Maui. Seven analytical methods using constant-rate and variable-rate withdrawals for single wells provide an estimate of hydraulic conductivity and transmissivity for 103 wells in central Maui. Methods based on constant-rate tests, although not widely used on Maui, offer reasonable estimates. Step-drawdown tests, which are more abundantly used than other tests, provide similar estimates as constant-rate tests. A numerical model validates the suitability of analytical solutions for step-drawdown tests and additionally provides an estimate of storage parameters. The results show that hydraulic conductivity is log-normally distributed and that for dike- free volcanic rocks it ranges over several orders of magnitude from 1 to 2,500 m/d. The arithmetic mean, geometric mean, and median values of hydraulic conductivity are respectively 520, 280, and 370 m/d for basalt and 80, 50, and 30 m/d for sediment. A geostatistical approach using ordinary kriging yields a prediction of hydraulic conductivity on a larger scale. Overall, the results are in agreement with values published for other Hawaiian islands.(KEY TERMS: aquifer characteristics; aquifer pumping test; step- drawdown test; ground-water hydrology; kriging; Hawaii island aquifer; ground-water management.)

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

Between 1970 and 2000, the resident population on the island of Maui, Hawaii, increased more than 200% (State of Hawaii, 2000), and ground-water demand also increased significantly during this period. The consequence is over-pumping, saltwater upconing, and saltwater intrusion, especially in the Iao aquifer (Meyer and Presley, 2000). This is the most important aquifer on the island. Ground water provides about 99% of Hawaii's domestic drinking water (Gingerich and Oki, 2000), and this has led to concern over the long-term sustainability of groundwater withdrawals from wells in this and other aquifers in Hawaii. To ensure prudent management of the ground- water resources, an improved understanding of regional ground-water flow systems is needed. At present, no large-scale estimation of the formation properties has been completed for Maui. Groundwater flow and chemical transport depend mainly on aquifer characteristics such as storage properties and hydraulic conductivity or transmissivity. Numerous methods exist to estimate the hydraulic properties. In this article, aquifer tests were used to better constrain hydraulic property estimates. The results of this study will provide information needed to calibrate a numerical ground-water flow and transport model for central Maui in order to estimate the effects of selected recharge and withdrawal scenarios on ground-water availability.

Aquifer pumping tests involve posing artificial stress on the hydrologie system by pumping water from a well and measuring the changes in water levels in the pumped well and nearby observation wells. The response of the hydraulic head in the aquifer can be used to estimate transmissivity or hydraulic conductivity. In the absence of observation wells, estimating storage properties using analytical methods can be troublesome. However, numerical methods can be used to estimate storage properties.

Traditional methods used to estimate transmissivity from constant- rate aquifer tests include Theiscurve fitting (Theis, 1935), recovery fitting (Theis, 1935), and Cooper and Jacob (1946) straight- line fitting. For assumptions and limitations of the analytical solutions, the reader is referred to those publications or the comprehensive collection of Kruseman and de Ridder (1991). Williams and Soroos (1973) assessed the suitability of a few aquifer tests with observation wells using traditional methods on Hawaii volcanic aquifers. An important limitation of methods that provide estimates of transmissivity is that knowledge about aquifer thickness is required to determine hydraulic conductivity. Halford et al. (2006) found that hydraulic conductivity is better estimated with aquifer thickness rather than screen length in the case of partially penetrating wells in unconfined aquifers. However, the conversion from transmissivity to conductivity is difficult for Hawaii aquifers because the exact aquifer thickness is not physically defined. This is due to missing detailed lithologie information at depth. Therefore, either the aquifer is regarded bottomless or only parts of it can be considered to contribute to its effective thickness.

Variable-rate or step-drawdown aquifer tests relate steady-state drawdown to steps of increasing discharge. They are conducted as production tests, generally to establish the depth of pump setting or to define drawdown-yield relations. They are frequently ignored for evaluation of hydraulic properties. Jacob (1947) expressed the relationship between steady-state drawdown in the well and discharge as

s^sub s^ = BQ + CQ^sup n^ (1)

where s^sub s^ is the steady-state drawdown in the well (in m); Q is the discharge (in m^sup 3^/d); B is the aquifer-loss coefficient (in d/m^sup 2^); C is the well-loss coefficient (in d^sup 2^/m^sup 5^ for n = 2); and n is the well-loss exponent. The aquifer-loss term includes all laminar losses in the aquifer, while the well- loss term comprises all turbulent losses in the well.

Ample work has been done on the determination of the well-loss part of Equation (1). Jacob (1947) proposed n = 2, which was adopted by many authors, mainly to simplify the analysis. He adopted the similarity with turbulent flow in pipes, which implies that drawdown varies with discharge to some power with the square of velocity being an approximate upper limit (Mogg, 1969). Eden and Hazel (1973) strongly doubted whether any relationship that deviates from the quadratic proportion is justified. They stated that results for n > 2 should be interpreted with extreme caution due to the possibility of inaccurate data. Therefore, they suggested that n = 2 is an acceptable approximation for most step-drawdown tests under field conditions.

However, Rorabaugh (1953) disagreed on the quadratic exponent and suggested that n be evaluated individually for each test. Estimating n compensates partially for the transition from laminar to turbulent flow with increasing pumping rates (Uhl et al., 1975). Lennox (1966) reported values for n as high as 3.5. Soroos (1973) applied step- drawdown tests to estimate hydraulic conductivity for 72 wells on Oahu. He found that well-loss exponent values ranged from 1.1 to 8.9, with a mean value of 2.4. Although fitting n may occasionally give a better match with the data, Soroos attributed the higher values to errors in the field data or to the limited number of steps in the test.

Soroos (1973) did not include a broad comparison of hydraulic conductivity estimates obtained by traditional methods for the tested wells. The advantage of step-drawdown tests is that they provide a direct estimate of hydraulic conductivity, thereby eliminating uncertainty involved in the conversion with an unknown aquifer thickness. Furthermore, the analysis of step-drawdown tests includes a correction for well loss and does not depend on the subjectivity of the analyst in ignoring or incorporating wrong points in the analysis. Another advantage is that step-draw-down tests are more available in Hawaii.

Based on available point measurements, spatial distribution of hydraulic conductivity can be defined using a geostatistical estimation approach. Ordinary kriging was used in this study to predict hydraulic conductivity on a larger scale than available for single-well aquifer tests in central Maui. Ordinary kriging was favored over other kriging methods because it is assumed that spatial correlation among hydraulic conductivity estimates exists and local means are not necessarily closely related to the population mean. A detailed description of kriging methods can be found in geostatistical text books, e.g., Clark and Harper (2000), and a review is beyond the scope of this study. The concept of kriging has been widely used in connection with aquifer properties (e.g., Ahmed and Marsily, 1987; Ahmed et al, 1988; Razack and Lasm, 2005).

OBJECTIVES

The objectives of this study were to characterize aquifer parameters at different scales on Maui using single-well aquifer tests, to examine the usefulness of the Harr method and the step- drawdown tests, and to compare analytical and numerical estimation methods for step-drawdown tests. Seven analytical methods were applied to drawdown or recovery data obtained from constant- and variable-rate single-well aquifer tests. This allowed a direct comparison of the estimated hydraulic properties for the same well. On a larger scale, hydraulic conductivity estimates were correlated to geology. The point estimates were used in a geostatistical technique to estimate hydraulic conductivity distribution using \ordinary kriging. The validity of step-drawdown tests was assessed by a numerical inversion method.

SITE CHARACTERIZATION AND HYDROGEOLOGY

Maui is the second largest island of the state of Hawaii and consists of two shield volcanoes, which are shown in Figure 1. West Maui Volcano and East Maui Volcano have rift zones radiating from their center with numerous intrusive dikes (Stearns and Macdonald, 1942). West Maui Volcano is composed primarily of thin-bedded shield- stage Wailuku Basalt. The study area of East Maui Volcano consists mainly of thin-bedded shield-stage Honomanu Basalt overlain by thicker postshield-stage Kula Volcanics (Langenheim and Clague, 1987). Because lithologic information is scant, it was impossible to differentiate among the wells tapping Honomanu Basalt and Kula Basalt. An isthmus comprised of flank lavas overlain by Holocene marine and terrestrial sedimentary deposits connects the volcanoes. For a complete description of the geology of Maui, the reader is referred to Stearns and Macdonald (1942).

Ground water in Hawaii primarily occurs in the basal freshwater lens and in dike-impounded systems (Gingerich and Oki, 2000). More specific studies about hydraulic properties exist for the older island of Oahu. However, large-scale estimates for Maui are lacking. The hydraulic conductivity for three major stratigraphic units on Oahu ranges from 150 to 1,500 m/d in highly permeable dike-free flank lavas, 1 to 60 m/d in sedimentary deposits, and 0.05 to 1 m/d in the dike complex (Wentworth, 1951; Nichols et al., 1996). The low conductivity in the dike zone is an effective value used in numerical modeling to predict high-level ground water (50 to over 700 m above sea level), considering that conductivity within the individual dike compartments is considerably higher. The number of dikes can exceed 600 per kilometer in the center of the dike complex, but it sharply decreases in the outer part. However, single, widely scattered dikes can extend farther from the designated dike complex (Takasaki and Mink, 1985). The aquifers on the east side of West Maui Volcano are confined by a caprock (Meyer and Presley, 2000), whereas most of the remaining aquifers on Maui are unconfined.

METHODOLOGY

Analytical Solutions

A number of analytical solutions were used for single-well aquifer tests in this study. For estimating transmissivity, methods used for constant-rate aquifer tests were Theis-curve fitting (Theis, 1935), recovery fitting (Theis, 1935), and Cooper and Jacob (1946) straight-line fitting. A solution that was independently developed by Harr (1962) and Polubarinova-Kochina (1962) was used to estimate two hydraulic conductivity values from constant-rate tests and one value from step-drawdown aquifer tests. Step-drawdown tests were analyzed by the solution of Zangar (1953) to estimate hydraulic conductivity and by the solution of Thomasson et al. (1960) to estimate transmissivity. Details of various methods are provided below.

The traditional methods for constant-rate aquifer tests were strictly used as described in Kruseman and de Ridder (1991). In case a significant change in slope appeared in the semi-log plot of the Cooper-Jacob test (after ignoring the early-time drawdown), only the first slope was considered to eliminate boundary effects. Halford et al. (2006) claimed that transmissivity values from the Cooper-Jacob method in unconfined aquifers were overestimated by a factor of 2 due to subjectivity of the analyst, especially when late-time drawdown values were ignored. Considering that no evidence of leakage exists in aquifer tests from this study, transmissivity estimates are expected to be reliable.

Polubarinova-Kochina (1962) and Harr (1962) independently presented a solution that can be applied to constant-rate and variable-rate aquifer tests, even though it is not commonly used this way. The method estimates the hydraulic conductivity of a thick unconfined aquifer that is partially penetrated by a pumped well. The solution assumes a homogeneous and isotropic aquifer of infinite thickness. Spherical flow develops underneath the well bottom and the elliptic equipotentials of the well surface are substituted by an ellipsoid with the volume of a cylinder (Harr, 1962; Polubarinova- Kochina, 1962). The method combines well-construction and aquifer- test information and estimates hydraulic conductivity using

... (2)

where K is the hydraulic conductivity (in m/d); L is the active length or screened interval of the well (in m); and r is the radius of the pumped well (in m). Although the solution requires a condition of "steady-state drawdown," the study does not provide a suitable criterion for such a condition. The approach by Gingerich (1999) was adapted in this study by assuming that this condition is fulfilled when the drawdown per unit time becomes relatively small compared to early-time drawdown. According to Gingerich (1999), the drawdown per unit time is relatively small after 1 10^sup 4^ min for wells with high hydraulic conductivity. For wells with relatively low conductivity, the drawdown per unit time can still be large after 1 10^sup 4^ min. The steady-state drawdown was estimated from the Cooper-Jacob straight line, which is arbitrarily extended to 1 10^sup 4^ min and 1 10^sup 6^ min (Gingerich, 1999). This yields two hydraulic conductivity estimates that define a range of possible values from this method. For simplicity, the method for constant-rate test is hereafter referred to as the Harr method.

Zangar (1953) proposed an equation to estimate hydraulic conductivity based on the ratio of steady-state drawdown to discharge. He determined the equivalent hemispherical radius of a partially penetrating cylindrical well in a homogeneous and isotropic aquifer of infinite thickness and incorporated well construction information. The equation for hydraulic conductivity is

... (3)

where r^sub h^ is the hemispherical radius of pumped well (in m), which is defined as

... (4)

Soroos (1973) used Equation (1) to separate well-head losses from aquifer-head losses. In case the active length of the well is less than 20% of the aquifer thickness, the aquifer loss term from Equation (1) equals the steady-state drawdown (Soroos, 1973). Thus, the formula for hydraulic conductivity may be written as

... (5)

Isolating the aquifer-head loss from step-drawdown tests can be used in the same way for the Harr method (Harr, 1962; Polubarinova- Kochina, 1962). By using the same assumptions regarding the well and the aquifer and by replacing specific drawdown (s^sub s^/Q) in Equation (2) with the aquifer-loss coefficient, the solution reads:

... (6)

This method is hereafter referred to as the Polubarinova method to avoid confusion with the Harr method for constant-rate aquifer tests, even though it was derived by both authors.

The Thiem (1906) equilibrium equation for confined aquifers with a pumping well reads:

... (7)

where r^sub 2^ is the radius of influence (in m). Thomasson et al. (1960) reported that empirical values for the log-ratio of the radius of influence of the well to the effective well radius range from 2.5 to 4.2, with a mean of 3.2. The use of this ratio further simplifies Equation (7). Logan (1964) reported a similar value of 3.3, which is valid for 98 aquifer tests made in sand-and-gravel wells in Illinois.

Starting with Razack and Huntley (1991), numerous studies were conducted to define an empirical relationship between transmissivity and specific capacity (Q/s^sub s^). A good summary of the results can be found in Razack and Lasm (2005). Due to the comparable high hydraulic conductivity in coarse sediment and in basaltic rocks, the value of 3.3 has not been altered for this analysis. Well losses were neglected in Equation (7) (see Clark, 1977) but can be incorporated by replacing the specific drawdown with the aquifer- loss coefficient determined from step-drawdown tests. The solution that calculates transmissivity then reads:

... (8)

where T is transmissivity (in m^sup 2^/d). This method is hereafter referred to as the Thomasson method.

Calculation Scheme

Aquifer-loss and well-loss coefficients for step-drawdown tests were determined by fitting the observed drawdown in the well to Equation (1). An iterative procedure minimized the error for n, constrained to the range of 1.1 to 10, with increasing steps of 0.001. The coefficients B and C for each exponent were determined with least-square regression. Cases where the test produces a nonphysical hydraulic conductivity (i.e., negative values) or where the parabola is inverted were disregarded.

In total, 238 single-well aquifer tests were analyzed using the seven different solutions described above. Most of these tests were performed during pump installation and are documented in the files of the State of Hawaii's Department of Land and Natural Resources, Commission on Water Resource Management. Useful data were available for 72 constant-rate tests from 62 wells, for 74 recovery tests from 54 wells, and for 92 step-drawdown tests from 66 wells. The large number of step-drawdown tests is notable. When data from multiple tests of the same kind at the same well were available, the arithmetic mean for each method was used.

Hydraulic conductivity was obtained by dividing transmissivity by aquifer thickness. As mentioned earlier, the exact thickness of Hawaii aquifers is not physically defined. In this study the approach of Gingerich (1999) was adapted, which defines thickness as the distance from the well base to the water table. It was assumed that all wells are fully saturated from the water table above sea level to the bottom of the well below sea level. The aquifer thickness used in this study is the minimum thickness, because even though it certainly extends farther below supporting lithologic information at depth is unavailable. In addition, although the wells penetrate several layers of basalt flow\s and sedimentary deposits, a single aquifer was assumed because available lithologic information is insufficient to accurately define layers with different thicknesses.

Geostatistical Analysis

For statistical comparison, a t-test was used to determine whether the means of the two flank-lava populations are equal. The test assumes that the samples come from normal distributions with unknown and possibly unequal variances. A two-sample Kolmogorov- Smirnov test was useful for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions. The null hypothesis postulates that the samples come from the same population.

The geostatistical analyst, which is a toolbox in ESRI's ArcMap software package, was used for the geostatistical approach. A normal distribution improves the prediction (Ahmed et al., 1988). However, the logarithmic transformation of hydraulic conductivity used in kriging is problematic. Razack and Lasm (2005) indicated that the unbiasedness of the estimated value is lost when the estimate is back-transformed to hydraulic conductivity. These authors therefore questioned the necessity of a normal distribution in geostatistical analysis. Hence, the untransformed conductivity values were preferred. Investigation of statistical anisotropy with directional variograms was difficult in this study area. Horizontal hydraulic conductivity tends to be several times greater parallel to lava flows than perpendicular to the flows (Nichols et al., 1996). Since the study area encompasses two volcanoes with flows propagating from the caldera in all directions, the experimental variogram was expected to be omni-directional. To reduce complexity, only the spherical model to fit the experimental variogram was reported in this study. The equation of the model is

... (9)

where γ is the estimated variable (K); h is the lag or distance between the sampling points (in m); C^sub 1^ is the sill (in m^sup 2^); C^sub 0^ is the nugget (in m^sup 2^); and a is the range (in m) (e.g., Clark and Harper, 2000). A wide comparison of different kriging methods and the different fitting models is beyond the scope of this study.

Numerical Modeling

The validity of the analytical solution of step-drawdown tests was checked with a numerical simulation. A simple cylindrical three- dimensional finite-difference domain, representing an unconfined aquifer, was constructed. The solution was obtained using MODFLOW- 2000 (Harbaugh et al., 2000). The radius of the homogeneous cylinder was taken as 1,000 m to avoid effects at the boundary, and the grid size was refined toward the center. The grid size equaled the well diameter in the center and was gradually increased to 50 m at the edge of the cylinder. The model consisted of 10 layers with increasing thickness at depth to account for vertical flow due to the partial penetration of the well. The well penetrated 20% of the depth of the modeled aquifer to satisfy the assumption of partial penetration for step-drawdown tests (Zangar, 1953). The well diameter, the length of the open interval, and the aquifer thickness were adjusted based on well-construction properties. The ratio of vertical to horizontal hydraulic conductivity is 0.1, which is in the range of reported values (Nichols et al., 1996). The discharge corresponding to each step was used to produce a transient model. The hydraulic conductivity and storage parameters, i.e., specific storage and specific yield, were numerically estimated using the automated parameter estimation algorithm PEST (Doherty, 2000). PEST is a non-linear parameter estimator that iteratively minimizes the error between observed and computed water levels by adjusting selected aquifer parameters. The calculated aquifer loss in the well, based on Equation (1) was used for the automated calibration.

RESULTS AND DISCUSSION

The values of hydraulic conductivity based on data for all wells range between 1 and 2,500 m/d, characterizing a highly heterogeneous system. The variability of the highly permeable basalt is caused by fracture flow that exists on different scales. A normal probability plot of the log-transformed data is shown in Figure 2. The linear fit reflects a log-normal distribution of hydraulic conductivity, especially for the robust data between 0.1 and 0.9. The deviation from the fitted line in the lower part is attributed to the geologic origin of that specific data and will be discussed later.

The validity of nontraditional methods was evaluated by comparing the results of the Harr method and the step-drawdown tests to traditional methods. First, the mean hydraulic conductivity based on Theis and Cooper-Jacob tests is plotted vs. the mean conductivity of the two Harr estimates (Figure 3a). The correlation coefficient (R) is given for the log-log scale, which is acceptable due to the log- normal distribution. The R-value of 0.86 shows a strong relationship between hydraulic conductivity from traditional methods and the Harr method for constant-rate tests, indicating the usefulness of the Harr method.

The results of the step-drawdown test analysis indicate that fitting the exponent gives a better match to the observed data. The error is reduced for some wells by up to 100% and on average by 37%. Values for the exponent range from 1.1 to 6.2, with a mean of 2.9 and a median of 2.6. This raises the question of whether a result with high values of n is physically realistic. Projecting the curve further at higher pumping rates for such a large exponent would mean that a small increase of discharge results in an unrealistic large increase in drawdown. A higher exponent means more aquifer loss and less well loss, as indicated by a greater slope B, and this translates into a lower hydraulic conductivity estimate. One reason for large exponents is the limited number of steps. The range of n and the standard deviation (σ) drops gradually with increasing number of steps. While tests with three steps cover the full range of values for n up to 6.2 with σ = 2.0, tests with seven or more steps do not exceed an exponent of 2.7 with σ = 0.6. Due to the high uncertainty at higher exponents, the results reported in this study are all based on n = 2.

The hydraulic conductivity estimates based on step-drawdown tests are compared to those based on constant-rate tests. Figure 3b shows the relationship between constant-rate hydraulic conductivity and arithmetic-mean conductivity for three step-drawdown methods: Zangar, Polubarinova, and Thomasson. The R-value of 0.81 on a log- log scale stands for a strong correlation. This suggests that step- drawdown methods can also provide results with comparable accuracy to those based on traditional constant-rate tests. It can be concluded that both the Harr method and step-drawdown test are reasonable tools for estimating aquifer parameters in volcanic island aquifers.

Figure 4a, b, and c shows hydraulic conductivity values obtained from constant-rate tests, recovery tests, and step-drawdown tests, respectively. Figure 4d shows the combined results for all methods used for each well. When more than one method was used, the arithmetic mean is displayed in the figure. The analysis provides values of hydraulic conductivity for 103 wells in central Maui, and evidently, the values estimated from the aquifer tests are characterized by significant spatial variability. In the northwestern part of the isthmus, for example, low conductivity values are shown next to contrasting high conductivity values. This can be attributed to heterogeneity of the formation or the existence of different geologic units that are intersected by the well. Another reason could be the proximity of the dike zone, which does not have a well-defined boundary. Single dikes may occur beyond the marginal dike zone, causing boundary effects. Another source of uncertainty is related to the fact that development and clogging of once highly conductive wells can change over time. The time when the aquifer test was performed can be up to 60 years ago. This factor is not considered in this study.

The hydraulic conductivity for wells penetrating basalts ranges from 1 to 2,500 m/d, with an arithmetic mean value of 520 m/d, a geometric mean value of 280 m/d, and a median value of 370 m/d (Table 1). This is within the known range for dike-free lava on other Hawaiian islands. Only five shallow wells penetrate the sediment layer, for which mean hydraulic conductivity estimates range from 10 to 200 m/d. The arithmetic mean of 80 m/d, the geometric mean of 50 m/d, and the median of 30 m/d are also within the expected limit (Wentworth, 1951; Nichols et al., 1996). The deviation from the linear trend in Figure 2, mentioned earlier, is attributed to the presence of the sediment unit. In addition, some wells located in the marginal dike zone show a major change in slope based on the Cooper-Jacob test, which is typically associated with ground-water barriers related to dikes. However, no significant spatial trend can be observed from wells that show evidence of a boundary. In the absence of observation wells, it is difficult to locate these boundaries.

In order to link estimated conductivity values to the underlying geology, the Wailuku Basalt, Honomanu/Kula Basalt, and the sediment group are examined individually. One well in Iao Valley, indicated with parenthesis in Figure 4d, has a very low hydraulic conductivity of 6 m/d and a measured water table of 206 m above sea level. It is clearly located in the dike-zone complex and therefore excluded from the Wailuku Basalt flank lava group. A more detailed statistical description of each group is shown in a box and whisker diagram (Figure 5). The plot shows the minimum value, the 25% quartile value, the median value, the 75% quartile value, and the maximum value to provide more insight into the distribution. The sediment group is c\learly distinct from the flank lavas. Sediment hydraulic conductivities are one order of magnitude lower. The flank lava conductivities for Wailuku Basalt and Honomanu/Kula Basalt seem to be similar. The values for Honomanu/Kula Basalt are slightly higher then those for Wailuku Basalt, except for the median, which is the same for both. The main difference is the higher Honomanu/Kula Basalt standard deviation (Table 1), which can be attributed to a wider spread of the data.

The main question is whether differences between the Wailuku and Honomanu/Kula formations exist. The arithmetic mean can be ambiguous, considering the values of hydraulic conductivity span several orders of magnitude and are log-normally distributed. The t- test reveals that both samples have the same mean at the 99% confidence interval for both the log-transformed conductivity and the untransformed variable. The same is true for the two-sample Kolmogorov-Smirnov test, which shows that samples come from the same population at the 99% confidence interval. Therefore, the two basalt groups can be confidentially treated as one population in the geostatistical approach. The wells tapping the sediment and one well in the dike zone are excluded from the flank lava grouping.

The experimental variogram shows the spatial variability of hydraulic conductivity of the flank lava (Figure 6). The parameters for the spherical model are C^sub 0^ = 139,320, C^sub 1^ = 94,683, a = 9,571, and h = 1,000. The plateau is reached at a distance of 9.6 km. Beyond this, no significant correlation exists between points. The estimated hydraulic conductivity field using ordinary kriging is shown in Figure 7a. The distribution is contoured to simplify the illustration, considering that aquifer test results are generally reported to only one significant figure. In West Maui, two small areas of higher conductivity are apparent on both sides of the volcano. The area of the dike complex is masked, because no correlation between hydraulic conductivity in the flank lava and in the dike complex can be drawn. With only one sample from the dike complex, predictions are nonexistent. The isthmus has relatively low conductivity values, possibly because some wells that already belong to the West Maui marginal dike zone are mixed within the flank lava group. The flanks of East Maui Volcano show considerably higher conductivity values, with two larger clusters in the south and the north. The kriged standard error is illustrated in Figure 7b. As expected, the error is relatively small where the sample population is denser. The area of higher conductivity identified on the west side of West Maui Volcano has a greater standard error. This can be attributed to the fact that this area is influenced by only one sample point. The three other areas that show higher conductivity, mentioned earlier, come from a cluster of wells with consistently higher values.

Several wells were used to test analytical stepdrawdown tests against a numerical model. One well, which is typical for the dataset, was used to demonstrate the results. The separation of aquifer loss and well loss is shown in Figure 8. The figure also shows the aquifer-loss values obtained from the numerical model. The three hydraulic conductivity estimates for this well are 85, 92, and 84 m/d for the Zangar, Polubarinova, and Thomasson method, respectively. PEST determined the conductivity within that range, with a value of 85 m/d. The absolute mean difference between observed and calculated drawdown and the sum of squared differences were 0.03 m and 0.006 m^sup 2^, respectively. When compared to analytical methods, numerical methods have the advantage of providing estimates of storage parameters for single-well tests. PEST estimates for the specific storage and the specific yield were 6.4 10^sup -6^ m^sup -1^ and 0.073, respectively, which are typical values for Hawaii's unconfined aquifers. It can be concluded that comparable values for hydraulic conductivity are obtained by using analytical and numerical models. The numerical model has the extra advantage of providing values for storage parameters.

CONCLUSIONS

This study estimated aquifer properties for central Maui based on available aquifer test data. The analysis provides reasonable values of transmissivity and hydraulic conductivity for a large area in central Maui. Hydraulic conductivity is log-normally distributed. The Harr method and the often-disregarded step-drawdown tests are valuable tools for estimating hydraulic conductivity from single- well tests in volcanic island aquifers. The correlation coefficients for tests compared with traditional methods are 0.86 for the Harr method and 0.81 for the step-drawdown tests. Aquifer conductivities, which range over several orders of magnitude from 1 to 2,500 m/d, match expected values in dike-free volcanic rocks and the sediment. The mean and median values of hydraulic conductivity are respectively 520 and 410 m/d for basalt and 80 and 30 m/d for sediment. The two flank lava groups, Wailuku and Honomanu/Kula Basalts, are statistically from the same population. The sediment group is clearly distinct due to its geological nature, with hydraulic conductivities that are one order of magnitude lower than that of the basalts. Hydraulic conductivity is spatially correlated, and ordinary kriging provides an estimated hydraulic conductivity field on Maui for a larger scale compared to individual aquifer tests. The kriged standard error is low, and confidence in estimated values is relatively higher in areas where samples are more abundant. Numerically estimated step-drawdown test values agree with those estimated by analytical solutions. Numerical solutions have the advantage of estimating storage properties for single-well tests. The combination of different analytical solutions from different aquifer tests successfully yield hydraulic properties on a large scale. The values are consistent with estimates published for other Hawaiian islands. The aquifer parameters are needed when calibrating numerical ground-water flow and transport models for central Maui, which is important to manage ground-water resources and assess water quality.

ACKNOWLEDGMENTS

The senior authors thank the USGS Pacific Islands Water Science Center for funding the study under the Central Maui Ground-Water Availability Study. The authors are grateful to Charles Hunt, Delwyn Oki, and Todd Presley for helpful comments. We also thank Kevin Gooding of the Hawaii Department of Land and Natural Resources for providing data of numerous aquifer tests. One anonymous reviewer provided a critical and motivating review that helped improve the technical quality of this research. This is contributed paper CP- 2007-03 of the Water Resources Research Center at the University of Hawaii at Manoa.

Rotzoll, Kolja, Aly I. El-Kadi, and Stephen B. Gingerich, 2007. Estimating Hydraulic Properties of Volcanic Aquifers Using Constant- Rate and Variable-Rate Aquifer Tests. Journal of the American Water Resources Association (JAWRA) 43(2):334-345. DOI: 10.1111/j.1752- 1688.2007.00026.x

1 Paper No. J05159 of the Journal of the American Water Resources Association (JAWRA). Received October 8, 2005; accepted December 5, 2006. This paper originally was submitted for the Featured Collection on Sustainable Watershed Management, December 2006 (Vol. 42, No. 6). 2007 American Water Resources Association.

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Ahmed, S., G. Marsily, and A. Talbot, 1988. Combined Use of Hydraulic and Electrical Properties of an Aquifer in a Geostatistical Estimation of Transmissivity. Ground Water 26(1): 78- 86.

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Clark, I. and W.V. Harper, 2000. Practical Geostatistics 2000. Ecosse North America, Columbus, Ohio, 442 pp.

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Kolja Rotzoll, Aly I. El-Kadi, and Stephen B. Gingerich2

2 Respectively, Graduate Student and Associate Professor, Department of Geology and Geophysics and Water Resources Research Center, University of Hawaii, 1680 East-West Road, Honolulu, Hawaii 96822; Research Hydrologist, USGS Pacific Islands Water Science Center, 667 Ala Moana Blvd., #415, Honolulu, Hawaii 96813 (E-mail/ Rotzoll: [email protected]).

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