The different imaging strategies of stem cell trafficking and guide to finding the appropriate molecular imaging modalities
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\r\n\tWhile two-dimensional (2D) thin crystals limit the physical phenomena into a plane, in a one-dimensional (1D) quantum structure (nanowires, nanotubes, and nanoribbons (NRs)), charge carriers and excitations have only one degree of freedom. These crystal structures have been the focus of interest due to their unique properties such as the very high electronic density of states, enhanced exciton binding energy, diameter-dependent bandgap, increased surface scattering for electrons and phonons, and chirality-dependent electronic band structure.
\r\n\tNanoribbons (NRs), made of single- or few-atom-thick lamellar crystals, are novel forms of 1D nanoscale materials and are ideal systems for investigation of the size and dimensionality dependence of the fundamental properties. After the successful synthesis of many 2D monolayer materials, their 1D NR form came into prominence due to their necessity in nanoscale applications. In this context, this book will cover the synthesis techniques, characterization methods, fundamental properties, and state-of-the-art applications on NRs of recent 1D/2D materials such as graphene, transition metal dichalcogenides (TMDs) (MoS2, WS2, ReS2, and TiSe2), mono-chalcogenides (GaS, GaSe, ZnSe, and SnSe), tri-chalcogenides (TiS3 and ZrS3), black phosphorus, group-IV, III–V binary compounds, superstructures and so on. The proposed book is intended for academia, professionals, scientists and Graduate & Undergraduate students without any geographical limitations.
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The main objective of stem cell therapy is to repair the tissue with functional cells differentiated from stem cells, and contribute to the lost organ function together with the remaining functional native cells. Nevertheless, there also remain important questions unanswered, regarding the engraftment, viability, biology and safety of transplanted stem cells, as well as interaction with the environment. Consequently, novel molecular imaging techniques are necessary for investigating the behaviors and the ultimate feasibility of cell transplantation therapy of stem cell.
Along with the rapid development of sensitive, noninvasive technologies, several molecular imaging approaches have been implicated to track the fate of stem cells
Molecular imaging is a rapidly emerging biomedical research discipline that provides integrated information on specific molecules of interest within the cells of
A wide variety of stem or progenitor cells, including adult bone marrow stem cells, endothelial progenitor cells, mesenchymal stem cells (MSCs), resident cardiac stem cells, and embryonic stem cells, have been shown to have positive effects in preclinical studies and therefore hold promise for treating and curing debilitating and deadly diseases. Several of these types of stem cells have been tested in early-stage clinical trials, such as MSCs [10], human embryonic stem (hES) cells [11]. However, to realize the full therapeutic potential of stem cell technology, it will be necessary to develop novel and improved quality assessments that can be used readily to determine the exact cellular state of the transplanted cells.
After the systemic or local administrating, stem cells may be able to proliferate, migrate and repopulate in pathologic sites to bring tremendous therapeutic effect. However, the transplantation success is companied with risks of the stem cell misbehavior after delivered, especially embryonic stem cells [6, 12]. Consequently, real-time visualization of the fate of the transplanted cells over time
The ability to label and track stem cells in humans would provide a method to answer some of the ongoing, unsolved issues in the field. The most efficacious route of delivery, the appropriate choice of stem cell type(s), the optimal cell population for treatment in a chronic setting and the favorable time-point of cell delivery, however, is still unknown and requires further study. A safe, noninvasive, and repeatable imaging modality that could identify injected stem cells would be able to answer questions about cell viability and retention in future clinical trials of stem cell therapies, as well as provide the ability to adjust the assessment of bioactivity on the basis of actual delivered doses of cells. With the desire to monitor stem cells long-term continuously with high temporal resolution and good biocompatibility, which have the properties of differentiation and self-renew over long periods of time, stem-cell-derived regeneration still faces in its efforts to improve.
Despite significant progress in molecular imaging, no single technique meets all the stem cell tracking criteria. Combined imaging modalities, such as PET-CT, are already well accepted and offer high sensitivity and anatomical detail [14]. Multimodality imaging approaches are likely to play an important role in illuminating different aspects of stem cell biology
A number of methods are available to track stem cells by molecular imaging. In general, there are two methods to label the cells: [1] direct labeling method, which physically introduce marker(s) into the cells before transplant; [2] indirect labeling method, which genetically introduce reporter gene(s) into the cells before transplant. The current noninvasive imaging approaches for tracking stem cells
Conceptual basis for noninvasive imaging of transplanted stem cells in living animals. It shows imaging techniques including magnetic resonance imaging, radionuclide imaging, quantum dots imaging and reporter gene imaging. Abbreviations: Gd-DTPA, gadolinium-diethylenetriamine penta-acetic acid; SPIO, superparamagnetic iron oxide; 99mTc, 99mTc-hexamethylpropylene amine oxime; 111In-Oxine, 111In-oxyquinoline.
Imaging of stem cell therapy requires the selection of a molecular target, an imaging probe, and an imaging system. Specific molecular targets along with advances in imaging modalities increase the sensitivity and specificity of stem cell imaging. The commonly used labeling methods are discussed below.
Possessing the advantages of high spatial resolution (ranging from 50μm in animal and up to 300μm in whole body clinical scanners) and high temporal resolution, magnetic resonance imaging (MRI) is widely used for
Radionuclide imaging techniques, including positron emission tomography (PET) and single-photon emission computed tomography (SPECT), allow the imaging of radiolabeled makers and their interaction with biochemical processes in
However, these cell-labeling techniques have some significant disadvantages. They are limited by concerns such as the potential transfer of radiotracer to nontargeted cells and potential adverse effects of the radiotracer on stem cell viability, function, and differentiation capacity. Thus, the effects of labeling on the capacity to differentiate stem cells of various origins are needed to be studied.
QDs are emerging as an important class of fluorescent agents. Luminescent colloidal QDs are inorganic semiconductor particles with physical properties that enable them to emit fluorescent light from 525 to 800 nm. The nanoparticles are consisting of an inorganic core, a shell of metal and an outer organic coating. The total diameter of quantum dots is 2–10 nm [17], depending on the physical properties of the material due to the quantum nature of QDs. With the capability of being excited by one single wavelength and emission light of different wavelengths, QDs are ideal probes for multiplex imaging. By contrast, conventional organic labeling agent cannot be easily synthesized to emit different colors and have narrow excitation spectra and broad emission spectra, making it difficult to use these dyes for multiplexing. Due to their extreme brightness and resistance to photobleaching [18], QDs are appropriate for live stem cells imaging, which requires long-term observation under the excitation light source. The approaches of QDs entering stem cells include passive loading, receptor-mediated endocytosis or transfection. Passive loading has been found to be the most effective method owning to the high label efficient and limited damage to surrounding cells. QDs are capable of single quantum dot tracking, multiplex imaging, and 3-D imaging reconstruction.
Unquestionable, quantum dots represent a novel strategy to tracking stem cells
Reporter gene imaging has been commonly applied to the non-invasive imaging of stem cell therapy by studying the survival, localization, and functional effects of exogenously administered stem cells. Imaging of gene expression in
In the fields of stem-cell-driven regeneration, some conventional reporter genes, such as green fluorescent protein (GFP) [7], firefly luciferase [23], renilla luciferase [24], and HSV1-tk [25] allow for localization in some small
Stem cell therapies offer enormous potential for the treatment of a wide range of diseases and injuries including neurodegenerative diseases, cardiovascular disease, diabetes, arthritis, spinal cord injury, stroke, and burns. More research teams are accelerating the use of other types of adult stem cells, in particular neural stem cells for diseases where beneficial outcome could result from either in-lineage cell replacement or extracellular factors. At the same time, the first three trials using cells derived from pluripotent cells have begun [12]. These early trials are showing roles for stem cells both in replacing damaged tissue as well as in providing extracellular factors that can promote endogenous cellular salvage and replenishment [26].
Clinical trials have demonstrated that stem cell therapy can improve cardiac recovery after the acute phase of myocardial ischemia and in patients with chronic ischemic heart disease [10]. Nevertheless, some trials have shown that conflicting results and uncertainties remain in the case of mechanisms of action and possible ways to improve clinical impact of stem cells in cardiac repair [27]. The public clinical trials database http://clinicaltrials.gov shows 238 clinical trials using MSCs for a very wide range of therapeutic applications. Although early clinical trials of stem cell therapy have showed positive effect, there remains much controversy about which cell type holds the most promise for clinical therapeutics and by what mechanism stem cells mediate a positive effect, and further research should be able to answer these questions.
Embryonic stem cells (ESCs) are pluripotent stem cells capable of self-renewal and differentiation into virtually all cell types [28]. Various lineages have been derived from human and mouse ESCs, including cardiomyocytes, neurons, hematopoietic cells, osteogenic cells, hepatocytes, insulin-producing cells, keratinocytes, and endothelial cells. Given their unlimited self-renewal and pluripotency capacity, ESCs have been regarded as a leading candidate source for novel regenerative medicine therapy. So far, ESCs transplantation has been widely investigated as a potential therapy for cell death-related heart disease, ischemic diseases, CNS disorders and diabetes. However, the bottleneck of application of ESC driven regeneration is high risk of teratoma formation
The concurrent development of accurate, sensitive, and noninvasive technologies capable of monitoring ESCs engraftment
Mesenchymal stem cells (MSCs) are a heterogeneous subset of stromal stem cells that can differentiate into cells of the mesodermal lineage, such as bone, fat and cartilage cells, but they also have endodermic and neuroectodermic differentiation potential. The use of MSCs for clinical purposes takes advantage of their poor immunogenicity
The versatility of the molecular imaging method could allow cellular tracking using single or multimodal imaging modalities. These single methods include direct labeling of cells for transplantation with iron oxide particles for MRI, with 18F-hexafluorobenzene or 18F-FDG for PET, or with 111In-oxine or 111In-tropolone for SPECT. Noninvasive MRI is fast becoming a clinical favorite, though there is scope for improvement in its accuracy and sensitivity. In that, use of superparamagnetic iron-oxide nanoparticles (SPION) as MRI contrast enhancers may be the best select for tracking MSC treatment delivery and monitor outcome [42, 43]. Indirect labeling relies on the expression of imaging reporter genes transduced into cells before transplantation. A classic example of using reporter gene tracing MSCs transplantation is the research by Zachary Love, et al. They have used a triple-fusion reporter system (fluc-mrfp-ttk) for multimodal imaging to monitor hMSCs transplanted into NOD-SCID mice. Signals from the cubes loaded with reporter-transduced hMSCs were visible by BLI over 3 mo, meanwhile, PET data provided confirmation of the quantitative estimation of the number of cells at one spot (cube) [44]. The reporter gene approach resulted in a reliable method of labeling stem cells for investigations in small-animal models by use of both BLI and small-animal PET imaging.
Neural stem cells (NSCs)-driven regeneration has been proposed as a promising potential treatment option for CNS-related disease processes, including everything from cerebrovascular disease to traumatic brain injury to degenerative diseases of the CNS. Grafted NSCs differentiated into neurons, into oligodendrocytes undergoing remyelination and into astrocytes extending processes toward damaged vasculatures [45]. At present, Applications of NSCs therapy of neurological diseases, including Alzheimer’s disease, Huntington disease, stroke, spinal cord injuries in preclinical researches have raised intense interest and the hope of radical new therapies in clinical.
In contrast to most tissues in adults, the central nervous system has a low regenerative activity, and neural stem cells reside in regions of the adult brain that are difficult to access by most imaging modalities [5] owning to tissue depth and the blood-brain barrier(BBB). The most promising techniques for monitor the fate of NSCs
Hematopoiesis is described to be the production of all types of fully differentiated daughter blood cells from ancestral great-grandmother hematopoietic stem cells (HSCs). HSCs studies and clinical applications have historically been ahead of other tissue stem cells and have generated most stem cell biology models. However, hematopoiesis is arguably among the most difficult of the mammalian stem-cell systems to image real-time
Endothelial progenitor cells (EPCs) recruitment is often involved in the tissue injury triggered reparative processes, and contribute to healing ischemic tissues. Transplantation of EPCs offers the potential for targeted treatment of ischemic diseases such as myocardial [55], hind-limb ischemia [56], and renal injury [57]. Considerable efforts have been made to monitor the fate of endothelial progenitor cells fate
Currently, none individual imaging modalities can fill the bill of flawless, without limitations in the spatial and/or temporal resolution or the time span and/or volume that can be observed in a single experiment. The use of direct labeling, with labeling agent such as SPIO or 18F-FDG is hindered by signal decrease, as a result of radio-decay or cell division or cell dispersion. Additionally, the label may become dissociated from the exogenous stem cell. Thus, direct labeling may not be a reliable means of monitoring long-term cell viability. On the contrary, this approach is a valid method to observing the stem cell delivery and homing properties. Meanwhile, Reporter gene imaging offers unique capabilities for noninvasive and longitudinal measurement to determine cell biology and cell viability.
Fundamentally, the choice of modality depends on the questions being addressed (
\n\t\t\t\t | \n\t\t
The different imaging strategies of stem cell trafficking and guide to finding the appropriate molecular imaging modalities
Stem-cell-driven regeneration offers tremendous approach for the treatment of intractable diseases. Tracking the fate of implanted cells is vital to monitor the delivery and viability of the grafts over extended periods of time. Molecular imaging represents one such tool that can provide insight into cell survival and proliferation following transplantation into the tissue. The greatest potential for optimizing imaging approaches for regeneration research probably lies in applying new insights from stem-cell biology and the development of molecular imaging. As experimental techniques and molecular imaging technologies progress, the potential benefits of regenerative medicine should be a strong motivation to continuously improve imaging technology that will enable stem-cell-driven regeneration in mammals to be more understood. Efforts now should focus on the development of novel labeling agent and multimodality approaches to increase perception of regenerative medicine, and promote the clinical translation of these techniques.
This work was partially supported by grants from the National Basic Research Program of China (2011CB964903), National Natural Science Foundation of China (31071308), and Tianjin Natural Science Foundation (12JCZDJC24900).
The authors indicate no potential conflicts of interest.
Numerical simulation is increasingly used for studying overland flows. Since runoff drives soil erosion and landscape evolution, the runoff models provide a foundation for modeling soil erosion, rill erosion, and related processes at the watershed scale [1, 2]. Models involving different levels of abstraction have been proposed [3, 4, 5]. Two commonly used models are the diffusion wave (DW) and kinematic wave (KW) models [6, 7, 8, 9]. The KW models set the friction slope to be equal to the bed slope and ignore the inertial terms [10]. The method has been successfully used to describe overland flows [11, 12, 13, 14]. The governing equations are highly nonlinear and do not have general analytical solutions, so one has to solve them numerically for practical cases [15]. The models based on full Saint-Venant (SV) equations have also been applied and produced better results.
Two-dimension models are generally used for cases with irregular domains. A distributed rainfall-runoff model using the KW approximation solved by an implicit finite difference scheme was developed [16], but channel flows are computed using a separate KW model. Fully two-dimensional shallow water equations are being utilized for modeling overland flows in late 1980s [17]. A two-dimensional finite difference (FD) runoff model was developed by solving 2D SV equations [18]. Shallow water equation-based 2D models [19] were used for runoff over an irregular topography of experimental scale with infiltration processes considered and in rural semiarid watersheds for overland flows generated by storms [20].
In addition to finite difference method (FDM), the two-dimensional finite element (FEM) and finite volume methods (FVM) have been used for overland flow simulations. A FEM KW model was developed by Liu et al. [21] for simulating runoff generation and concentration over an irregular bed and reproduced experimental results. Tests [15] indicated that the FVM-based 2D SV model performed better than that of FDM. Costabile et al. [22] solved the shallow water equations using the FVM and applied the resulting model to simulate a real event on a watershed of 40 km2. Nunoz-Carpena et al. [23] solved the KW equation using the Petrov-Galerkin method. Venkata et al. [24] developed a Galerkin DW FEM and applied it to a small watershed. Singh et al. [25] simulated runoff processes by solving the 2D shallow water equations with a shock-capturing scheme and the FVM. Shirmeen et al. [26] showed results of a validated, FEM 2D model in predicting runoff from a flat agricultural watershed.
In order to check numerical models’ mathematical correctness and physical applicability, the developed computational models have been tested with analytical solutions, experimental, and field data. Iwagaki [27] studied runoff using analytical methods and experimental data; several specific solutions were developed based on the characteristic method. Govindaraju et al. [28] developed analytical solutions using KW and DW approximations. Comparisons of analytical solutions, numerical solutions, and experimental data were discussed. Singh [29] detailed the KW model’s analytical and numerical solutions and their wide applications. Cea [30] tested FVM using an experimental watershed with a complex shape. These overland flow models use simplified equations and need to specify pre-existing channel networks, which make it difficult to simulate soil erosion cases with hill-slope evaluation and mixed sheet-channel flow conditions.
CCHE2D is a physically based model, which treats the entire watershed including the channels and ditches as one continuous domain. One does not need to differentiate overland sheet flow and channel flow calculation areas using grid cells and 1D channel networks as is done in GSSHA [31], WASH123D [32], NIKE-SHE [33], and SHETRAN [34]. It is also not necessary to employ arbitrarily shaped sub-watersheds and 1D channel networks as is done in the CCHE1D model [35]. In these models, 2D DW equations or KW equations are solved for the overland flow using finite difference methods, and the 1D SV equation is solved in the prescribed channel networks. In contrast to these models, in CCHE2D, hydrodynamics over the entire watershed is simulated using only 2D equations discretized on an irregular quadrilateral finite element mesh, which is generated using digital elevation model (DEM) data. The simulated overland sheet flow and channel flow are seamlessly connected everywhere in the domain and the channel network is formed automatically. This method may be more applicable when sediment transport, rill erosion, or gully erosion processes in watersheds are considered.
In this study, the CCHE2D model is modified and applied to simulate watershed hydrological processes. CCHE2D is a general hydrodynamic model for unsteady, turbulent free flows, sediment transport, and pollutant transport. It has been validated and applied widely to simulations of channel flow, flooding, coastal flow, bed topographic change, and chemical contamination in aquatic environments [36, 37, 38, 39, 40].
The major objectives of the present paper are to assess the accuracy and the effectiveness of this FEM in predicting overland runoff processes, and its applicability to practical agricultural watersheds with ditches and natural stream channels. The approach of the study followed the recommendations of [41] for quality assurance that numerical models have to be verified and validated using analytical solutions, physical experimental data, and field data. The validated numerical model was used to simulate and characterize the hydrological processes of an agricultural watershed in the Mississippi River alluvial plain where farm fields are drained and separated by ditches and stream channels. A limitation was found in the interpolation method when it is applied to the water surface elevation of the sheet runoff. A numerical scheme was developed and implemented for improving the bilinear interpolation. The present study focused on watershed surface flow processes over bare soils; interception, evapotranspiration, and infiltration were not considered.
Surface runoff due to precipitation is typically quite shallow and can be aptly represented by the 2D shallow water equations within the CCHE2D model [36, 38]. The water surface elevation of the runoff flow,
in which
in which
The full Eqs. (1)–(3) are applicable for general flow conditions. In realistic cases where runoff and channel flow conditions coexist, a general flow model is necessary. Under the sheet flow condition, the advection and turbulence stress terms in the momentum equations vanish because the dominant forcing for the overland flow is the gravity and bed shear stress. The water depth is very small, and water surface slope and bed slope become almost the same:
in which
in which
CCHE2D uses a partially staggered method: the velocities are solved at collocation points and the pressure (water surface) is solved at cell centers [36]. A bilinear interpolation method is used to interpolate the water surface elevation solution to the collocation nodes where the momentum equations are solved. The bilinear interpolation works well for general channel flow simulations because the water depth is large in comparison with the variation of bed surface and the mesh size. When overland sheet runoff is simulated; however, the water depth is very small; it is often less than the microelevation variation of bed topography represented in an element. In this case, the interpolated water surface elevation may be lower than the bed if the bed is concave down and vice versa. This is a limitation of the interpolation method. In the concave down case, dry nodes are created artificially; in the concave up case, artificial masses of water could be erroneously created. Figure 1 illustrates this problem in one dimension. The problem occurs whenever irregular bed topographies are encountered. A correction is therefore necessary to the interpolation over the surface runoff area.
The error of underestimation and overestimation caused by linear interpolation of water surface elevation from cell centers to collocation nodes.
A numerical scheme has been developed and implemented in CCHE2D to correct the interpolation error [43]. Figure 2 illustrates how the scheme is formulated in one dimension with an exaggerated vertical scale. Eq. (7) is the formulation to compute the correction value
Definition sketch for the formulation of the correction (
where
Two analytical solutions were obtained by solving a one-dimensional kinematic equation analytically for rain-generated runoff by [44, 45]. The solution of sustained rains for the runoff to reach a steady state [44] and the solution for rainfall that stops before the runoff becomes steady [45], including the tailing stage solution after rainfall stops, were provided. The governing one-dimensional kinematic equation for deriving these solutions is:
in which
Figure 3 shows the comparisons of the simulated runoff and the analytical solutions for the sustained rain collected at the four cross sections. Hydrographs at each cross section indicate that equilibrium runoff (steady state) is reached before the rain stops at
Comparisons of the simulated runoff hydrographs and analytical solutions. The sustained rain stopped at
Figure 4 shows a case in which the rainfall stops before runoff reaches steady state (
Comparisons of the simulated runoff hydrographs and analytical solutions. The rain stopped at
CCHE2D model was validated using experimental data sets collected from the literature. All of these cases were carried out on impervious overland flow planes. The only quantity measured in these experiments was the downstream runoff discharge.
Morgali and Linsley [46] obtained two sets of experimental runoff data. Their tests were carried out over a straight turf surface of 21.95 m long with a constant slope (0.04) and width. The Manning’s coefficient,
Comparisons of measured data with analytical solution, results of CCHE2D, and other numerical models.
Figure 5 also compares the simulation results of CCHE2D and the model results by Govindaraju et al. [28]; the two numerical solutions agree well for the case with the higher rain (1A), but the fit of their solutions based on the SV equations does not correspond well for the case with the smaller rainfall (1B). The results of CCHE2D also outperform the analytical solution of the DW approximation [28].
Cea et al. [30] conducted three runoff experiments of complex topography and simulated these cases using a 2D unstructured FVM. The experimental watershed was a rectangle (2 × 2.5 m) made by three planes of stainless steel, each of them with a slope of 0.05 (Figure 6). Two dikes (1.86 and 1.01 m in length) were placed in the watershed to vary the topography. Rainfall intensity, duration, and runoff hydrographs were measured. As a result, the runoff direction, distribution, and pattern of the hydrograph were affected. The runoff was accumulated and became channel flows along intercepting lines of slopes and dikes. Since both overland flow and channel flow are involved, faithful simulation requires solving full governing Eqs. (1)–(3). The rainfall applied to each test case was different. In the first test (2A), the rainfall intensity was 317 mm/h for 45 s. In the second test (2B), the rainfall intensity was 320 mm/h for 25 s; then it was stopped for 4 s and restarted for an additional 25 s with the same intensity. In the third test (2C), rainfall intensity was 328 mm/h. The rainfall was applied for 25 s; then it was stopped for 7 s and then restarted for another 25 s.
Topography of the experimental watershed [
In this study, CCHE2D was applied and the numerical results were compared with experimental data. The watershed was modeled using an irregular structured mesh with the cell size ranging from 0.034 to 0.009 m; the mesh was refined near the main channel and the outlet for improving results. The Manning’s roughness coefficient was set equal to 0.009 m−1/3s. The simulation time was 120 s for each case. The channel flow and runoff sheet flow coexisted: the runoff from the watershed surface was accumulated in the bottom of the watershed channel with a triangle-shaped cross section formed by the side slopes. Results of cases 2A and 2C are shown in Figures 7 and 8, respectively.
Comparison of measured and simulated hydrographs using rainfall with one peak (Case 2A).
Comparison of measured and simulated hydrographs using rainfall with two peaks (Case 2C).
Figure 7 shows the comparison between the numerical solution and experimentally observed runoff hydrograph of Case 2A. The solution of the CCHE2D model agrees very well with the experimental results. The flow discharge increased continuously once the rain started. The peak discharge occurred at the time the rainfall stopped (at 45 s). Although the rising and the falling limbs of the hydrograph were slightly overestimated, the shape of the hydrograph and the peak discharge were aptly predicted.
Figure 8 shows the comparison between the numerical and experimental runoff hydrographs of Case 2C. The shape of the hydrograph was successfully predicted. The interval between the two rainfall peaks was 7 s. The first runoff peak discharge occurred at the time the rainfall stopped, at 25 s. The runoff discharge decreased for approximately 10 s and then increased. The second runoff peak discharge occurred at approximately 57 s. The simulated processes and the observed physical processes showed a good general agreement; it also matched well with the model results of [30].
Figure 9 shows the simulation results at t = 54 s (the peak of the second rainfall) for Case 2C: (a) simulated water depth contour distribution, (b) simulated flow unit discharge pattern and (c) velocity vector distribution in the watershed. The distributions indicate how the overland sheet flow, under the influence of dikes and topography, concentrates into channels and flows out of the watershed. The flows over the slopes are sheet runoff, but complex recirculations are developed in the main channel. The water surface is no longer parallel to the bed surface. These flows cannot be represented by KW, DW, and SV models.
Distributions of simulated (a) water depth contours (b) flow (unit discharge) distribution and (c) velocity vectors at
This section presents the application of CCHE2D to a sub-watershed of the Howden Lake watershed, an 18 km2 agricultural watershed in the Mississippi River alluvial plain (Figure 10). In this region of low relief, watersheds are configured by farm fields drained by culverts, ditches, and intermittently flowing streams called bayous. During periods between runoff events, the channels contain standing water. The studied sub-watershed was upstream of a gaging station on an intermittently flowing bayou. The average annual precipitation in this region is about 1440 mm. Precipitation occurs as intense thunderstorms or low-intensity rains associated with major frontal movements. The latter type of events may stretch over several days of drizzle and sporadic showers. During growing seasons, channels experience some flow and stage fluctuation due to irrigation withdrawals and return flows.
Location and topography of the Howden Lake watershed. Dashed curve encloses the runoff simulation area, and the dark closed curve is the gaged watershed.
Watershed topography was surveyed by airborne LiDAR with a 1.5 m horizontal resolution. The vertical accuracy was 15.0 cm RMSE or better. The watershed elevation ranges from approximately 43.89–48.99 m. A nearly uniform fine mesh (mesh spacing = 3.76–4.98 m) was generated for the simulation with the ditches and small streams between the plots further refined locally. Cultivated fields are connected to the streams and ditches with drainage culverts, which often convey water from one sub-watershed to another. The locations of culverts in the study watershed were identified in a field survey and incorporated in the numerical mesh.
Soil data were obtained from the Soil Survey Geographic (SSURGO) database [47]. The watershed is covered mostly by soils with high clay content, which is typical of the region [48]. Infiltration is, therefore, negligible and was not considered in the simulation. Precipitation and flow stage data were measured by field instrumentation. Because the stream instrumented with the gage station has complex conditions, it was difficult to collect reliable velocity data during a rain event. Only stage data were available. As a result, the gage station does not have a discharge-stage rating curve. Development of a rating curve using simulations and measured data for this site would be helpful for understanding the hydrologic processes in these watersheds.
Because the Howden Lake watershed is of low-relief, it was often difficult to determine the boundaries between sub-watersheds in field surveys or on topographic contour maps. For example, the runoff from a piece of field may flow in two directions into two sub-watersheds, and the location of the divide line might be identified only from the runoff flow distribution during a simulation. Normally, the outline of a watershed is a given condition for a hydrology study. In this study, the exact boundary outline was not firmly established even after field surveys. A larger area containing the studied watershed was simulated, and the watershed boundary and area were finally defined by the simulated runoff and channel flow patterns. The boundary outline of the studied watershed (Figure 11) contributing to the gage was identified by visually checking the simulated overland flow directions of CCHE2D.
Numerical simulation identified watershed for the gage station. Simulation results in the dashed rectangle area are shown in
In the simulations, the streams and ditches between farming plots were represented using DEM elevations like flat surface areas. No channel networks were prescribed, but the simulated surface runoff flowed logically to the ditches and to the stream channel. No other watershed analysis tools were needed. Although the study results presented later are for this identified watershed, the spatial domain of numerical simulations was several times larger (Figure 10). The northern side of the stream channel had been blocked by farmers, so the overland flow from the watershed entered the stream in the middle and flowed in a southwesterly direction (Figure 11). The water from this identified watershed pasted the gage, while runoff from the region outside this watershed was discharged from the simulation domain via other ditches and streams. The area of this watershed, including cultivated land, drainage ditches and a stream segment, was found to be 973,700 m2. In this area, the topographic elevation ranges from approximately 46.77–47.49 m in one plot and from 47.27 to 48.09 m in another. The mean slope of the fields is 0.0097 and 0.0098, respectively.
Several observed storm events were selected for the model application. To reduce minor losses of water due to evaporation, soil wetting and infiltration, etc., only large rain events were considered. The rainfall event in April 2011 (Table 1) was first used for simulation. Figure 12a shows the detailed ground elevation contour of a small simulation area (dashed rectangle area in Figure 11). The elevation of this area ranges from about 46.8 to about 47.4 m. Figure 12b shows the direction vectors of the runoff near the end of the simulation. Because the water is very shallow, the flow direction is highly affected by the ground topography. Figure 12c and d shows the direction vectors and water depth distribution at the peak time of the rainfall.
Event | Measured rainfall (mm) | Runoff volume* (m3) | |||
---|---|---|---|---|---|
4/27–4/28/2011 | 88.39 | 85,817 | 2.4 | 1.223 | 0.45 |
10/30–11/4/2013 | 53.59 | 52,182 | 1.9 | 4.24 | 0.78 |
11/21–25/2011 | 62.99 | 61,333 | 1.4 | 1.613 | 0.45 |
5/20–24/2013 | 48.77 | 47,483 | 1.0 | 1.436 | 0.59 |
9/25–27/2011 | 52.32 | 50,946 | 1.8 | 5.211 | 0.48 |
Parameters of selected runoff events for numerical simulations.
Computed from the main bulk of the rain event.
Information and simulation results in an area indicated in
Although the variation of the bed surface topography is very small, the simulation shows how the runoff is controlled by microtopography (Figure 12a). At the peak time of the rainfall, the overall water depth in this area (Figure 12d) is much deeper, and the flow directions (Figure 12c) are less affected by the local microtopographic features. The flow on the right side of the domain is still sheet runoff under the KW condition; while on the left side, the water depth is more than 0.2 m, and the flow is no longer governed by the KW condition. This model provides the outflow hydrograph as well as the temporal and spatial distribution of the water depth and flow velocity, which can be used for studying soil erosion, agro-pollutant transport, and water quality.
The gage station (Figure 11) recorded the channel water surface elevation at regular time intervals, but velocities were generally too low for accurate measurement, and therefore, water discharge was not measured. In order to better understand the watershed hydrology, a rating curve of the form:
was developed using simulated discharge, in which
in which
Attempts were made to fit all simulated curves using a single set of values for
Manning’s roughness coefficient (
Sensitivity of simulated hydrograph to Manning’s coefficient.
The total observed rainfall volume for the April 27–28, 2011 event (Figure 13) was approximately 86,000 m3 (88.32 mm). The total simulated runoff volume is about 80,600 m3 (83.78 mm), which is reasonable because the hydrograph recession limb extended past the simulation termination at 47 h. There were several small rain events that occurred before the event shown in Figure 13, so the runoff volume based on the observed water surface elevation may include recession of the earlier events.
Figure 14 compares the discharge hydrographs of several additional runoff events computed using Eq. (12) and that of the numerical simulations. The identified parameters for these events,
Comparisons of simulated runoff and
As noted above, the watershed has multiple field ditches that convey runoff into the channel (Figures 10 and 11). Ditch and channel flow were simulated together with the overland sheet runoff. Figure 15 shows the simulated flows in the channel network of the watershed. The contours represent the distribution of the unit flow discharge. The vectors in the ditches and in the stream formed a channel network indicated by the large velocity vectors; those in the runoff area are too small to be seen. The flows in the stream are turbulent when the rainfalls are large. Because no velocity data were acquired, the simulated velocity results in the channel were not validated.
Simulated flow in the network of drainage ditches and the stream in the watershed.
The numerical model CCHE2D was used to model sheet runoff from watersheds, large and complex enough to include both overland and channel flow processes. The model was systematically verified and validated using analytical solutions and experimental data due to steady and unsteady rainfall intensity, and applied to a real world watershed. Good agreement between the analytical solutions, experimental data, and numerical simulations were obtained. For the experimental cases involving complex watershed shapes, the numerical model has the ability to simulate runoff over the slope surfaces and the channel flows.
A numerical scheme was developed to correct the bilinear interpolation of the water surface elevation from its solutions at the staggered cell centers to the collocation nodes. The scheme was necessary and effective for obtaining good sheet runoff simulation results in watersheds with irregular topography. One would have to smooth the ground topography if a model requires the interpolation of water surface solution under this condition.
The model was applied to an agricultural watershed in the Mississippi River alluvial plain. It was useful to identify the boundary of the monitored watershed and develop the rating curve at the gage station of the watershed. Several significant runoff events were selected for simulation. Each of the simulated runoff hydrographs and the rating curves agreed well with those observed in the field. The sensitivity of the model to overland sheet flow friction was studied. An increase in the bed surface friction coefficient significantly diminishes the peak of runoff discharge, delaying its time of arrival. Values of
This work is supported in part by USDA Agriculture Research Service under the Research Project No. 6060-13000-025-00D (NCCHE) monitored by the USDA-ARS National Sedimentation Laboratory (NSL). Support is also in part by the Southeast Region Research Initiative (SERRI) project and the University of Mississippi (UM).
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