The particle tracking method (PTM) module was added into the open source Full Shallow-Water equations for Overland Flow in a two-dimensional (FullSWOF_2D) program, which has coupled rainfall–runoff and infiltration modules to determine the time of concentration (T_c) for impervious (T_ci) and pervious (T_cp) surfaces. The updated program FullSWOF-PTM was tested using observed rainfall events with Nash–Sutcliffe efficiencies ranging from 0.60 to 0.95 (average of 0.75) for simulated runoff hydrographs. More than 400 impervious modeling cases with different surface slope (S₀), roughness coefficient (n), length (L), and rainfall intensity (i) combinations were developed and simulated to obtain the T_ci for developing the regression equation of T_ci as a function of the four input parameters. More than 700 pervious modeling cases with different combinations of S₀, n, L, i, and infiltration parameters including the saturated hydraulic conductivity, suction head, and moisture deficit were simulated to estimate the T_cp based on the travel time of 85% of particles arriving at the outlet and the ponding time. The regression equation of T_cp was developed as the sum of T_ci and additional travel time as a function of infiltration parameters and i. The T_cp equation can be applied to wide ranges of input parameters in comparison to Akan’s equation.

Time of concentration ($T_c$ ) is one of the most used time parameters in hydrologic analyses. As topographic slope ($S_o$ ) approaches zero, traditional $T_c$ estimation formulas predict large $T_c$ . Based on numerical modeling and a review of relevant literature, a lower bound for slope ($S_{lb}$ ) of 0.1% was identified as a threshold below which traditional $T_c$ estimation formulas become unreliable and alternate methods should be considered. In this study, slopes less than $S_{lb}$ are defined as low slopes. Slopes equal to or exceeding $S_{lb}$ are defined as standard slopes where traditional $T_c$ estimation formulas are appropriate. A field study was conducted on a concrete plot with a topographic slope of 0.25% to collect rainfall and runoff data between April 2009 and March 2010 to support numerical modeling of overland flows on low-sloped planes. A quasi-two-dimensional dynamic wave model (Q2DWM) was developed for overland flow simulation and validated using published and observed data. The validated Q2DWM was used in a parametric study to generate $T_c$ data for a range of slopes that were used to develop $T_c$ regression formulas for standard slopes ($S_o\ge 0.1\%$ ) and low slopes ($S_o<0.1\%$ ).

The time of concentration (T_c) is one of the important time parameters for hydrologic design, analysis, and modeling. More accurate estimation of T_c is necessary for the prediction of peak discharge(Q_p), which is important in hydrologic design. Even though T_c is conceptually defined as the time needed for the rain that falls on the most remote part of the catchment to travel to the outlet, most researchers have used an indirect method such as hydrograph analysis to estimate T_c. Using a validated quasi-two-dimensional diffusion wave model with particle tracking (DWMPT) for overland flow, a direct approach of determining the travel time of particles to reach the outlet is presented in the paper. Based on the percentage of particles arrived at the outlet of impervious surface, travel time for 100% particle arrival at the outlet is defined as T_c. Using 200 DWMPT numerical experiments for varying input variables like effective rainfall intensity (i), flow length (L), topographic slope (S₀), and flow resistance (n), a regression equation between T_c and its input variables is developed. Differences in numerical estimates of T_c due to conceptual differences in definition of T_c are also discussed.

Under the challenges of present and future population increase, urbanization, and global climate change, hydraulic analysis and design for water supply, drainage, and irrigation conveyance system are becoming increasingly important in order to solve the water management problem. Determination of critical and normal depths for irrigation and drainage channels is a classic but also important task for efficient hydraulic design, therefore, a significant number of researches have been done in this area. Unfortunately, there is no analytical solution to explicitly and directly compute critical and normal depths for most of channel cross-sections except for critical depth in rectangular and parabolic sections and critical and normal depths in triangular section. Designers may use a manual trial-and-error method, which is time-consuming and troublesome, or a chart method, which uses log-scale charts and has low accuracy in the solution. Various approximation equations have been developed for common open-channel sections with various degrees of estimation errors and limited application conditions. There are very limited researches for rounded-bottom or - corner sections. There are many hydraulic or drainage or stormwater computer programs (software packages) available that compute and report critical and normal depths for common cross-sections but there is very little information on what approximation equations or numerical methods are used (black-box approach to users). This study includes a comprehensive review and evaluation of different methods determining critical and normal depths for eight types of open-channel sections: circular, rectangular, trapezoidal, triangular, rounded-corner rectangular, rounded-corner trapezoidal, rounded-bottom triangular, and U- shaped. It also presents easy and efficient method to calculate critical and normal depths for these cross-sections using Solver function in Excel. General equations for geometric elements for these cross-sections are developed and used to create Excel worksheets determining critical and normal depths. Using the spreadsheet with Solver function designers not only get in-depth understanding on basic sectional geometry but also do not have to depend on commercial computer programs for computing basic hydraulic design parameters. We present a VBA code for repeated applications of Solver function that is useful for solving various problems in irrigation and drainage engineering. The method developing geometric equations for different depth ranges can be applied to more complex compound channel sections; and as long as we can develop equations computing geometric elements, then Solver can be used to determine critical and normal depths for the complex compound sections.

In southeast Texas, groundwater extraction has caused irreversible aquifer compaction that results in land subsidence. As this region continues to experience population growth and increased water demand, the evaluation of projected subsidence impacts is crucial for effective water resource planning. This study presents a scenario-based framework for investigating future flood hazards and quantifying economic damages associated with inland subsidence in the Spring Creek Watershed, Texas, United States (US). A 2D pluvial hydrologic and hydraulic (H&H) model, Hydrologic Engineering Center’s River Analysis System (HEC-RAS) 6.6, simulated flooding using two rainfall conditions for a Baseline scenario, containing 2020 conditions, and a subsidence with future development (SFD) scenario with projected 2070 conditions to assess flood risk. Modeling results for the 100-year event SFD scenario included expansion of the floodplain by over 1700 acres, increased streamflow, flood depth increases over 30 cm, and over 3700 flooded structures, the majority being residential. The greatest flood impacts were experienced downstream in the watershed rather than within the area of most projected subsidence. Economic losses were analyzed using the Go-Consequence tool and revealed the SFD scenario had over half a billion US dollars in additional losses for a single 100-year flood event relative to the Baseline. This work highlights the importance of long-term planning to minimize future flood damages in a flood-prone region.