Groundwater recharge (R) from precipitation and discharge to rivers as baseflow (BF) are two of the main processes in the basin-scale water cycle. These processes vary with time and space. Effective management of water resources requires deep understanding of these processes. Due to the lack of data or the difficulties in measuring R and BF, however, our current knowledge and understanding of these complex processes are very limited, especially about their temporal and spatial variations. Various assumptions are made about spatial variations of R in existing studies and little attention has been given to temporal variations of R and BF. While it is difficult to measure R and BF, it is relatively easy to measure the water levels in observation wells (h) and runoff in rivers. Extensive groundwater level data sampled at various time intervals over periods of years or decades are often available. Fluctuations of the water table in a groundwater system are dynamic responses of the system to its recharge and discharge, and thus contain significant amount of information about the recharge and discharge. Our preliminary analyses of the observed water levels in seven monitoring wells at the Walnut Creek watershed of Iowa indicate that fluctuations of the groundwater levels is a temporal fractal whose fractal dimension (D) varies spatially. Baseflow from this and other four watersheds also behaves as a temporal fractal and, more importantly, has a transition time or break in scaling. Our objectives are: 1) to determine existence of fractal scaling of groundwater level and baseflow and their relationship with recharge; 2) to identify physical causes behind fractal scaling; 3) to study the effects of aquifers' physical heterogeneity on fluctuations of groundwater level, recharge, and discharge and on their scaling, and 4) to investigate the nature of groundwater recharge process. These objectives will be reached by testing six hypotheses. These hypotheses will be tested by collecting and analyzing the longterm groundwater level measurements in 42 monitoring wells in 6 groundwater regions and the streamflow at 58 gauge stations in 11 hydrological units over a period of 50 - 100 years at the USGG website, and by conducting an integrated hydrologic modeling (IHM), stochastic analyses, and numerical simulations. With data mining we will use the extensive data collected by USGS over the years to identify the existence of the temporal scaling. With IHM we will be able to assess impacts of temporal and spatial variations of P, ET, and ? on fluctuations of h and BF. With stochastic analyses and numerical simulations, we will investigate effects of spatial variations of aquifers' physical properties on the temporal variations of h and BF and their scaling as well as the nature of R process. The intellectual merits. The most important merits of this research are to find the temporal scaling of h and BF and to provide physical causes behind the scaling. Temporal scaling of h may be pervasive in many aquifers as we show in this proposal by the spectra of the longest water level data in 14 USGS wells. There may be a simple explanation for the scaling: fluctuations of groundwater levels are due to various contributing hydrological variables (e.g., P, ET, and ?) with differing time and/or spatial scales. As a result, there is no characteristic time scale in the head fluctuations! We are anxious to do further investigation. Whether processes in the natural world are dependent or independent of the scale at which they operate is one of the major issues in hydrologic science . (Sposito, 1998). There has been a significant effort in searching for scaling in hydrology since an invariance property across scales as a fundamental should guide data analysis and modeling methods (NRC, 1991). Significant progresses in searching spatial scale invariance have been made during the last decade in hydrology. However, less attention was given to temporal scaling of subsurface hydrological variables. We have proposed a relatively new direction of stochastic research, as summarized by the panel on the original proposal, and are trying to make a forward step in application of stochastic approaches. The broad impacts include: 1) use of abundant groundwater level and streamflow data in trying to understand the patterns of temporal variations of h and BF make the methods and results of the proposed research widely applicable, 2) the proposed research is closely related to the NSF initiative: Water Cycle Research, 3) the knowledge obtained in this research is needed in longterm management and planning of water resources and in dealing with climate changes, 4) A current Ph.D. student is working on this topic. Two new students (one graduate and one undergraduate) will participate in this project if the proposal is funded, 5) Several publications are expected from this research as two papers have been written (one published and another submitted recently) based on our preliminary results. Finally, we want to say that addressing the comments made by the reviewers and panel on the original and second-submission of this proposal has greatly improved the proposal.
