Jeremy T. White

Scripting MODFLOW model development using Python and FloPy

Graphical user interfaces (GUIs) are commonly used to construct and postprocess numerical groundwater flow and transport models. Scripting model development with the programming language Python is presented here as an alternative approach. One advantage of Python is that there are many packages available to facilitate the model development process, including packages for plotting, array manipulation, optimization, and data analysis. For MODFLOW-based models, the FloPy package was developed by the authors to construct model input files, run the model, and read and plot simulation results. Use of Python with the available scientific packages and FloPy facilitates data exploration, alternative model evaluations, and model analyses that can be difficult to perform with GUIs. Furthermore, Python scripts are a complete, transparent, and repeatable record of the modeling process. The approach is introduced with a simple FloPy example to create and postprocess a MODFLOW model. A more complicated capture-fraction analysis with a real-world model is presented to demonstrate the types of analyses that can be performed using Python and FloPy.

Quantifying the predictive consequences of model error with linear subspace analysis

All computer models are simplified and imperfect simulators of complex natural systems. The discrepancy arising from simplification induces bias in model predictions, which may be amplified by the process of model calibration. This paper presents a new method to identify and quantify the predictive consequences of calibrating a simplified computer model. The method is based on linear theory, and it scales efficiently to the large numbers of parameters and observations characteristic of groundwater and petroleum reservoir models. The method is applied to a range of predictions made with a synthetic integrated surface-water/groundwater model with thousands of parameters. Several different observation processing strategies and parameterization/regularization approaches are examined in detail, including use of the Karhunen-Loeve parameter transformation. Predictive bias arising from model error is shown to be prediction specific and often invisible to the modeler. The amount of calibration-induced bias is influenced by several factors, including how expert knowledge is applied in the design of parameterization schemes, the number of parameters adjusted during calibration, how observations and model-generated counterparts are processed, and the level of fit with observations achieved through calibration. Failure to properly implement any of these factors in a prediction-specific manner may increase the potential for predictive bias in ways that are not visible to the calibration and uncertainty analysis process.

A python framework for environmental model uncertainty analysis

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification. pyEMU is a python framework for model-independent uncertainty analysis and supports highly-parameterized inversion.pyEMU exposes several methods for data-worth analysis for designing observation networks and data collection activities.pyEMU can be used to estimate parameter and forecast uncertainty before inversion.pyEMU can be used to design objective functions and parameterizations.

MODFLOW-Based Coupled Surface Water Routing and Groundwater-Flow Simulation.

In this paper, we present a flexible approach for simulating one- and two-dimensional routing of surface water using a numerical surface water routing (SWR) code implicitly coupled to the groundwater-flow process in MODFLOW. Surface water routing in SWR can be simulated using a diffusive-wave approximation of the Saint-Venant equations and/or a simplified level-pool approach. SWR can account for surface water flow controlled by backwater conditions caused by small water-surface gradients or surface water control structures. A number of typical surface water control structures, such as culverts, weirs, and gates, can be represented, and it is possible to implement operational rules to manage surface water stages and streamflow. The nonlinear system of surface water flow equations formulated in SWR is solved by using Newton methods and direct or iterative solvers. SWR was tested by simulating the (1) Lal axisymmetric overland flow, (2) V-catchment, and (3) modified Pinder-Sauer problems. Simulated results for these problems compare well with other published results and indicate that SWR provides accurate results for surface water-only and coupled surface water/groundwater problems. Results for an application of SWR and MODFLOW to the Snapper Creek area of Miami-Dade County, Florida, USA are also presented and demonstrate the value of coupled surface water and groundwater simulation in managed, low-relief coastal settings.

Use of general purpose graphics processing units with MODFLOW

To evaluate the use of general-purpose graphics processing units (GPGPUs) to improve the performance of MODFLOW, an unstructured preconditioned conjugate gradient (UPCG) solver has been developed. The UPCG solver uses a compressed sparse row storage scheme and includes Jacobi, zero fill-in incomplete, and modified-incomplete lower-upper (LU) factorization, and generalized least-squares polynomial preconditioners. The UPCG solver also includes options for sequential and parallel solution on the central processing unit (CPU) using OpenMP. For simulations utilizing the GPGPU, all basic linear algebra operations are performed on the GPGPU; memory copies between the central processing unit CPU and GPCPU occur prior to the first iteration of the UPCG solver and after satisfying head and flow criteria or exceeding a maximum number of iterations. The efficiency of the UPCG solver for GPGPU and CPU solutions is benchmarked using simulations of a synthetic, heterogeneous unconfined aquifer with tens of thousands to millions of active grid cells. Testing indicates GPGPU speedups on the order of 2 to 8, relative to the standard MODFLOW preconditioned conjugate gradient (PCG) solver, can be achieved when (1) memory copies between the CPU and GPGPU are optimized, (2) the percentage of time performing memory copies between the CPU and GPGPU is small relative to the calculation time, (3) high-performance GPGPU cards are utilized, and (4) CPU-GPGPU combinations are used to execute sequential operations that are difficult to parallelize. Furthermore, UPCG solver testing indicates GPGPU speedups exceed parallel CPU speedups achieved using OpenMP on multicore CPUs for preconditioners that can be easily parallelized.

A model-independent iterative ensemble smoother for efficient history-matching and uncertainty quantification in very high dimensions

Abstract An open-source, scalable and model-independent (non-intrusive) implementation of an iterative ensemble smoother has been developed to alleviate the computational burden associated with history-matching and uncertainty quantification of real-world-scale environmental models that have very high dimensional parameter spaces. The tool, named pestpp-ies, implements the ensemble-smoother form of the popular Gauss-Levenberg-Marquardt algorithm, uses the pest model-interface protocols and includes a built-in parallel run manager, multiple lambda testing and model run failure tolerance. As a demonstration of its capabilities, pestpp-ies is applied to a synthetic groundwater model with thousands of parameters and to a real-world groundwater flow and transport model with tens of thousands of parameters. pestpp-ies is shown to efficiently and effectively condition parameters in both cases and can provide means to estimate posterior forecast uncertainty when the forecasts depend on large numbers of parameters.

Potential effects of alterations to the hydrologic system on the distribution of salinity in the Biscayne aquifer in Broward County, Florida

To address concerns about the effects of water-resource management practices and rising sea level on saltwater intrusion, the U.S. Geological Survey in cooperation with the Broward County Environmental Planning and Community Resilience Division, initiated a study to examine causes of saltwater intrusion and predict the effects of future alterations to the hydrologic system on salinity distribution in eastern Broward County, Florida. A three-dimensional, variable-density solute-transport model was calibrated to conditions from 1970 to 2012, the period for which data are most complete and reliable, and was used to simulate historical conditions from 1950 to 2012. These types of models are typically difficult to calibrate by matching to observed groundwater salinities because of spatial variability in aquifer properties that are unknown, and natural and anthropogenic processes that are complex and unknown; therefore, the primary goal was to reproduce major trends and locally generalized distributions of salinity in the Biscayne aquifer. The methods used in this study are relatively new, and results will provide transferable techniques for protecting groundwater resources and maximizing groundwater availability in coastal areas. The model was used to (1) evaluate the sensitivity of the salinity distribution in groundwater to sea-level rise and groundwater pumping, and (2) simulate the potential effects of increases in pumping, variable rates of sea-level rise, movement of a salinity control structure, and use of drainage recharge wells on the future distribution of salinity in the aquifer. Results from the simulation of historical conditions indicate that the model generally represents the observed greater westward extent of elevated salinity in the central part of the intruded area relative to the northern and southernmost parts of the intruded area. Results of sensitivity testing indicate that the extent of elevated salinity is most sensitive to pumping in areas where the source of saltwater is largely offshore, from the Atlantic Ocean, and is most sensitive to sea-level rise in areas where the source of salinity is downward leakage of brackish water from canals. Simulations of future scenarios indicate that increases in pumping near the existing interface may cause the interface to advance and decreases in pumping may cause it to retreat. Climatic effects, such as periods of prolonged drought or high precipitation, may augment or counteract long-term effects of changes in pumping on aquifer salinity at well fields. With increasing rates of sea-level rise, the freshwater-saltwater interface advances progressively inland, and flow-averaged salinities at well fields near the existing interface increase commensurately. Hypothetical southeastward (downstream) re-positioning of the existing G–54 salinity-control structure may prevent the interface from moving northwestward along and near the North New River canal, but beneficial effects are localized. Implementation of freshwater recharge wells in the city of Hallandale Beach may also have only a localized freshening effect in the aquifer and little appreciable effect on the freshwater-saltwater interface or on concentrations of salinity at well fields. Model accuracy and use are limited by uncertainty in the physical properties and boundary conditions of the system, uncertainty in historical and future conditions, and generali zations made in the mathematical relationships used to describe the physical processes of groundwater flow and transport. Because of these limitations, model results should be considered in relative rather than absolute terms. Nonetheless, model results do provide useful information on the relative scale of response of the system to changes in pumping distribution, sea-level rise, and mitigation activities. 2 Potential Effects of Alterations to the Hydrologic System on the Distribution of Salinity in the Biscayne Aquifer Introduction Saltwater intrusion of the Biscayne aquifer in Broward County, Florida (fig. 1), is a challenge for water-supply management. This issue is expected to persist, given current predictions of climate change, sea-level rise, and continued population growth. The Biscayne aquifer in Broward County is particularly susceptible to saltwater intrusion because of its high permeability, low hydraulic gradient, and proximity to an unlimited source of saltwater in the Atlantic Ocean. Additional factors that contribute to saltwater intrusion include groundwater pumping, rising sea level, anthropogenic alterations to the hydraulic system, and natural climatic variations. The Biscayne aquifer is a shallow, unconfined to semiconfined aquifer composed of highly transmissive limestone situated on top of a large, flat carbonate platform that composes the Florida peninsula. In Broward County, estimated transmissivity values in the surficial aquifer system, of which the Biscayne aquifer is the most transmissive unit, are as high as 900,000 square feet per day (ft2/d; Fish, 1988). The groundwater and surface-water systems are closely connected, and the groundwater system reacts quickly and markedly to precipitation. Average annual precipitation between 1981 and 2010 was about 58 inches (in.), and generally ranged from about 2 inches per month (in/mo) in December to almost 9 in/mo in June. Land surface elevations are typically less than 20 feet (ft) in eastern Broward County (appendix fig. 1–3), and topographic relief is minimal. The Biscayne aquifer is in contact with the Atlantic Ocean offshore. The onshore potentiometric head gradient drives fresh groundwater toward the Atlantic, whereas differences in fluid density force the denser saltwater from the Atlantic Ocean into the deeper parts of the aquifer, beneath overlying freshwater-bearing parts of the aquifer (fig. 2). The Biscayne aquifer is the primary source of water supply in Broward County, and groundwater withdrawals from the aquifer have steadily increased since the early 1900s. Groundwater extraction via pumping lowers groundwater levels in the aquifer, increasingly allowing saltwater to intrude the aquifer from the east. Groundwater pumping has been cited as a substantial cause of saltwater intrusion at several locations along the Atlantic coast (Lacombe and Carleton, 2002; Monti and others, 2009; Payne, 2010; Langevin and Zygnerski, 2013). Rising sea level in the Atlantic Ocean reduces the eastward potentiometric gradient in the Biscayne aquifer, thereby elevating groundwater levels between the recharge areas and the coast. The reduced onshore potentiometric gradient allows saltwater to enter the aquifer more readily. Local mean sea level has risen approximately 0.5 ft since 1950 (fig. 3). Numerous studies indicate that sea level in the North Atlantic has been rising for thousands of years; for example, Fairbanks (1989) indicates it has risen hundreds of feet in the past 18,000 years, and Kemp and others (2011) indicates it has risen nearly 10 ft in the past 2,500 years. The local hydrologic system has been substantially altered to allow urban development in southeastern Florida, including the eastern part of Broward County. An extensive network of canals has been constructed over decades to promote drainage and route excess water to the Atlantic Ocean during major precipitation events. Drainage tends to lower the water table and reduces the seaward movement of fresh groundwater. During the dry season (October to May), the canals are used to control saltwater intrusion by providing a source of freshwater that leaks into the Biscayne aquifer and maintains water-table elevations in the aquifer. Broward County faces the possibility of increased saltwater intrusion. Population growth in the county is expected to continue, potentially increasing groundwater pumping (fig. 4), reducing groundwater levels, and increasing saltwater inflow to the aquifer. Sea-level rise has been predicted to continue, potentially reducing the eastward potentiometric gradient in the Biscayne aquifer and in tidal canals, and driving additional saltwater into the aquifer. In response to rising sea level, alterations to surface-water management are being considered to adapt to increased coastal flooding during major storm events. Such alterations are likely to affect salinity distribution in the aquifer, given the strong connection between the surface-water and groundwater systems. To address these concerns, the U.S. Geological Survey (USGS) in cooperation with the Broward County Environmental Planning and Community Resilience Division, initiated a study to examine causes of saltwater intrusion and predict the potential effects of future alterations to the hydrologic system on salinity distribution in eastern Broward County. Purpose and Scope The purpose of this report is to (1) evaluate controls on the salinity distribution from 1950 to 2012, and (2) to simulate potential effects of possible future alterations to the hydrologic system on salinity distribution in the Biscayne aquifer in the southern and central parts of eastern Broward County. The simulated area extends from the area just east of the Atlantic coastline to the area just west of the major canals separating the Everglades from the urbanized part of the county, and from the C–14 basin in the north to the C–9 east and west basins in the south (fig. 1). Historical and future hydrologic conditions affecting saltwater intrusion in the northeastern part of the county were studied previously (Langevin and Zygnerski, 2013). The study period represents the timeframe during which the greatest alterations to the hydrologic system were made and for which records are available to quantify the alterations. The study period also extends 50 years into the future, during which time proposed hypothetical changes to management of the hydrologic system might occur. Of particular interest are production well-field areas that potentially will be most affected by