[1] Traditional analysis of aquifer tests uses the observed drawdown at one well, induced by pumping at another well, for estimating the transmissivity (T) and storage coefficient (S) of an aquifer. The analysis relies on Theis' solution or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well is screened in a low-permeability zone while the pumping well is located in a high-permeability zone, the resulting situation contradicts the homogeneity assumption in the traditional analysis. As a result, what does the traditional interpretation of the aquifer test tell us? Using numerical experiments and a first-order correlation analysis, we investigate this question. Results of the investigation suggest that the effective T and S for an equivalent homogeneous aquifer of Gaussian random T and S fields vary with time as well as the principal directions of the effective T. The effective T and S converge to the geometric and arithmetic means, respectively, at large times. Analysis of the estimated T and S, using drawdown from a single observation well, shows that at early time both estimates vary with time. The estimated S stabilizes rapidly to the value dominated by the storage coefficient heterogeneity in between the pumping and the observation wells. At late time the estimated T approaches but does not equal the effective T. It represents an average value over the cone of depression but influenced by the location, size, and degree of heterogeneity as the cone of depression evolves.

Abstract:In this paper, we perform an inverse method to simultaneously estimate aquifer parameters, initial condition, and boundary conditions in groundwater modelling. The parameter estimation is extended to a complete inverse problem that makes the calibrated groundwater flow model more realistic. The adjoint state method, the gradient search method, and the least square error algorithm are combined to build the optimization procedure. Horizontal two-dimensional groundwater flow in a confined aquifer is exemplified to demonstrate the correlation between unknowns, the contribution of observation, as well as the suitability of applying the inverse method. The correlation analysis shows the connection between storage coefficient and initial condition. Besides, transmissivity and boundary conditions are also highly correlated. More observations at different location and time are necessary to provide sufficient information. A time series of unsteady head is requested for estimation of storage coefficient and initial condition. Observation near boundary is very effective for boundary condition estimation. The observation at pumping well mostly contributes to the estimation of transmissivity. According to all observations, it is possible to identify parameters, initial condition, and boundary condition simultaneously. Furthermore, the results not only illustrate the traditional assumption of known boundary condition but also initial condition, which may cause an incorrect estimation.

Abstract:A model describing the three-dimensional matrix flow along a slope with rock fragments or impermeable blocks was developed. The model was combined with modified Picard's iteration to ensure mass conservation in the unsaturated flow. We found that rock fragments obstruct water flow along the slope. The groundwater table must be raised to provide a sufficient pore water pressure gradient to facilitate water flow, but higher pore water pressure may induce slope failure. We also conducted a benchscale laboratory flume experiment to examine the effects of impermeable blocks on downstream seepage flow. In addition, a numerical experiment was conducted to examine how different arrangements of impermeable blocks affect downstream seepage flow and pore water pressure. This research demonstrated that the hydraulic phenomena were affected when impermeable blocks were present, and pore water pressure increased as the position of impermeable blocks was lowered.

The multivariate relationships between hourly surface wind and rainfall observations during typhoons affecting Taiwan have been investigated with maximum covariance analysis (MCA). Historical surface observations from 1987 to 2004 are used when typhoon centers were located inside the domain of 198-288N, 1178-1278E. The three leading MCA modes explain 70%, 20.6%, and 7.6% of the squared covariance fraction, and the correlation coefficients are 0.59, 0.48, and 0.49, respectively. The wind directions of the three leading positive modes are 1) northwesterly flow perpendicular to the Snow Mountain Range (SMR), 2) southwesterly flow toward the river valleys of the southwestern Central Mountain Range (CMR) and the southern SMR, and 3) easterly flow toward the northeastern SMR and the northern CMR. The rainfall patterns of the three principal modes reveal the contrast between the windward and the leeward sides of the mountain ranges. Based on the MCA singular vectors, historical typhoon surface wind patterns are categorized into major types. The results show that the three major wind types consist of 53% of the data, with 25%, 9%, and 19%, respectively, for these wind types. Furthermore, the analyses of the corresponding surface air temperatures, relative humidities, and air pressures also reveal contrasting patterns between the windward and leeward sides.

This paper introduces a quality control (QC) program for the real-time hourly land surface temperature observation developed by the Central Weather Bureau in Taiwan. There are three strategies involved. The first strategy is a range check scheme that inspects whether the observation falls inside the climatological limits of the station to screen out the obvious outliers. Limits are adjusted according to the station’s elevation. The second strategy is a spatial check scheme that scrutinizes whether the observation falls inside the derived confidence interval, according to the data from the reference stations and the correlations among the stations, to judge the reliability of the data. The scheme is specialized, as it employs the theorems of unbiased and minimum error estimators to determine the weights. The performance evaluation results show that the new method is in theory superior to the spatial regression test (You et al.). The third strategy is a temporal check scheme that examines whether the temperature difference of two successive observations exceeds the temperature variation threshold for judging the rationality of the data. Different thresholds are applied for the data observed in different times under different rainfall conditions. Procedurally, the observation must pass the range check first and then go through the spatial or the temporal check. The temporal check is applied only when the spatial check is unavailable. Post-examinations of the data from 2014 show that the QC program is able to filter out most of the significant errors.