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Tropical Storm Erika was a weakly organized tropical storm when its center of circulation passed more than 150 km north of the island of Dominica on August 27, 2015. Hurricane hunter flights had difficulty finding the center of circulation as the storm encountered a high shear environment. Satellite and radar observations showed gyres imbedded within the broader circulation. Radar observations from Guadeloupe show that one of these gyres formed in convergent mid-level flow triggered by orographic convection over the island of Dominica. Gauge-adjusted radar rainfall data indicated between 300 and 750 mm of rainfall on Dominica, most of it over a four hour period. The result was widespread flooding, destruction of property, and loss of life. The extremity of the rainfall on steep watersheds covered with shallow soils was hypothesized to result in near-equilibrium runoff conditions where peak runoff rates equal the watershed-average peak rainfall rate minus a small constant loss rate. Rain gauge adjusted radar rainfall estimates and indirect peak discharge (IPD) measurements from 16 rivers at watershed areas ranging from 0.9 to 31.4 km2 using the USGS Slope-Area method allowed testing of this hypothesis. IPD measurements were compared against the global envelope of maximum observed flood peaks versus drainage area and against simulations using the U.S. Army Corps of Engineers Gridded Surface/Subsurface Hydrologic Analysis (GSSHA) model to detect landslide-affected peak flows. Model parameter values were estimated from the literature. Reasonable agreement was found between GSSHA simulated peak flows and IPD measurements in some watersheds. Results showed that landslide dam failure affected peak flows in 5 of the 16 rivers, with peak flows significantly greater than the envelope curve values for the flood of record for like-sized watersheds on the planet. GSSHA simulated peak discharges showed that the remaining 11 peak flow values were plausible. Simulations of an additional 24 watersheds ranging in size from 2.2 to 75.4 km2 provided confirmation that the IPD measurements varied from 40 to nearly 100% of the envelope curve value depending on storm-total rainfall. Results presented in this paper support the hypothesis that on average, the peak discharges scaled linearly with drainage area, and the constant of proportionality was equivalent to 134 mm h−1, or a unit discharge of 37.22 m3 s−1 km−2. The results also indicate that after the available watershed storage was filled after approximately 450–500 mm of rain fell, runoff efficiencies exceeded 50–60%, and peak runoff rates were more than 80% of the peak rainfall rate minus a small constant loss rate of 20 mm h−1. These findings have important implications for design of resilient infrastructure, and means that rainfall rate was the primary determinant of peak flows once the available storage was filled in the absences of landslide dam failure.

Summary Process-based hydrological models have a long history dating back to the 1960s. Criticized by some as over-parameterized, overly complex, and difficult to use, a more nuanced view is that these tools are necessary in many situations and, in a certain class of problems, they are the most appropriate type of hydrological model. This is especially the case in situations where knowledge of flow paths or distributed state variables and/or preservation of physical constraints is important. Examples of this include: spatiotemporal variability of soil moisture, groundwater flow and runoff generation, sediment and contaminant transport, or when feedbacks among various Earth’s system processes or understanding the impacts of climate non-stationarity are of primary concern. These are situations where process-based models excel and other models are unverifiable. This article presents this pragmatic view in the context of existing literature to justify the approach where applicable and necessary. We review how improvements in data availability, computational resources and algorithms have made detailed hydrological simulations a reality. Avenues for the future of process-based hydrological models are presented suggesting their use as virtual laboratories, for design purposes, and with a powerful treatment of uncertainty.

Summary Vadose zone flow problems are usually solved from the Richards equation. Solution to the Richards equation is generally challenging because the hydraulic conductivity and diffusivity in the equation are strongly non-linear functions of water content. The finite water-content method was proposed as an alternative general solution method of the vadose zone flow problem for infiltration, falling slugs, and vadose zone response to water table dynamics based on discretizing the water content domain into numerous bins instead of the traditional spatial discretization. In this study, we develop an improved approach to the original finite water-content method (referred to as TO method hereinafter) that better simulates diffusive effects but retains the robustness of the TO method. The approach treats advection and diffusion separately and considers diffusion on a bin by bin basis. After discretizing into water content bins, we treat the conductivity and diffusivity in individual bins as water content dependent constant evaluated at given water content corresponding to each bin. For each bin, we can solve the flow equations analytically since the hydraulic conductivity and diffusivity can be treated as a constant. We then develop solutions for each bin to determine the diffusive water amounts at each time step. The water amount ahead of the convective front for each bin is redistributed among water content bins to account for diffusive effects. The application of developed solution is straightforward only involving algebraic manipulations at each time step. The method can mainly improve water content profiles, but has no significant difference for the total infiltration rate and cumulative infiltration compared to the TO method. Although the method separately deals with advection and diffusion, it can account for the coupling effects of advection and diffusion reasonably well.

Stream hydrograph separation using naturally occurring geochemical tracers holds great potential for elucidating mineral weathering and solute transport. This study addresses a critical need to characterize catchment runoff generation in the humid tropics using multiple natural tracers for hydrograph separation and concentration/discharge (C/Q) hysteresis analysis. We use hydrometric and geochemical data collected at the start of the wet season from three small, steep catchments located in the humid seasonal tropics of central Panama that differ primarily in land cover. We apply a dual source hydrograph separation model between two end-members: new event water precipitation and pre-event water stored in the catchment. We compare the effectiveness of electrical conductivity (EC) and stable water isotopes (δD and δ18O) tracers for identifying precipitation event water in stream runoff using across forested (1.43 km2), mixed land use ‘mosaic’ (1.82 km2) and pasture (0.42 km2) catchments. Hysteretic C/Q loops are analyzed for flowpath interpretation using δD, Ca2+, Mg2+, Na+, K+, Cl−, and SO42−. During a medium-large magnitude event on May 23, 2013, forest and mosaic stream δD, Ca2+, Mg2+, and Na+ exhibited clockwise hysteresis, SO42− exhibited anticlockwise hysteresis, and K+ and Cl− each showed no hysteresis. EC as a surrogate for total dissolved solids agrees acceptably with stable water isotope hydrograph separations during small peak runoff events ( 10 mm/h) in the mosaic catchment. Early wet-season events indicate lower event water fractions than events farther into the wet season. Despite previous work showing land cover strongly controls storm runoff efficiencies, hydrograph separation and hysteresis analyses only indicate weak event water delivery differences between the paired forest and mosaic catchments.

Summary Numerical solution of the Richards’ equation (RE) in variably saturated soils continues to be a challenge due to its highly non-linear behavior. This is particularly true as soils approach saturation and the behavior of the fundamental partial differential equation changes from elliptic to parabolic. In this paper, a finite volume predictor–corrector method with adaptive time-stepping was developed to solve the 1D vertical RE. The numerical method was mass-conservative and non-iterative. In the predictor step, the pressure head-based form of the RE was solved using the cell-centered finite volume method and the pressure head was updated. In the corrector step, the soil water content was calculated by solving the mixed form RE. Five different schemes to evaluate the inter-cell hydraulic conductivity were investigated. The robustness and accuracy of the numerical model were demonstrated through simulation of experimental tests, including free drainage, field infiltration into wet and dry soils, and laboratory infiltration with falling water table. Numerical results were compared against laboratory measurements, simulation results from the Hydrus-1D program, or analytical solution when available. Results showed that the developed scheme is robust and accurate in simulating variably saturated flows with various boundary conditions. The arithmetic mean and Szymkiewicz’s mean of inter-cell hydraulic conductivity performed better than other methods especially in the case of infiltration into very dry soil.

Summary Tropical hydrology is poorly understood for a number of reasons. Intense biological activity in the tropics introduces complexities to the hydrologic process. Bioturbation, rapid rates of decay, and intensive insect activity all tend to promote rapid flow paths in the upper soil. Aggressive weathering leads to clays depleted of light cations and deep soil profiles. Processes in the seasonal tropics are further complicated by seasonal transitions, and very large changes in catchment storage between seasons. Beginning in 2005, we installed a suite of hydrologic sensors in a 16.7 ha first-order catchment in the Panama Canal Watershed to observe hydrologic variables and identify the dominant streamflow generation processes. The site is located near the village of Gamboa, which is located on the east bank of the Panama Canal at the confluence of Lake Gatun and the Chagres River. The study catchment is located on the north side of a ridge off the eastern flank of a 230 m tall hill known as Cerro Pelado, and is covered by 70–120 year old re-growth triple-canopy forest. Measurements included: rainfall above the canopy, throughfall, stemflow, evapotranspiration, shallow groundwater levels and streamflow. Deep groundwater storage was not measured. This paper describes measurements made, data collected, and the worth of those data in estimating the mass balance closure of a first-order catchment during the wet season. We compare measurements of the different components of the water cycle with observations from other published studies from the tropics. Data analysis results indicate water balance closure errors of approximately 8%.

The TalbotOgden model is a mass conservative method to simulate flow of a wetting liquid in variably-saturated porous media. The principal feature of this model is the discretization of the moisture content domain into bins. This paper gives an analysis of the relationship between the number of bins and the computed flux. Under the circumstances of discrete bins and discontinuous wetting fronts, we show that fluxes increase with the number of bins. We then apply this analysis to the continuous case and get an upper bound of the difference of infiltration rates when the number of bins tends to infinity. We also extend this model by creating a two dimensional moisture content domain so that there exists a probability distribution of the moisture content for different soil systems. With these theoretical and experimental results and using a Dynamic Data Driven Application System (DDDAS), sensors can be put in soils to detect the infiltration fluxes, which are important to compute the proper number of bins for a specific soil system and predict fluxes. Using this feedback control loop, the extended TalbotOgden model can be made more efficient for estimating infiltration into soils.

Summary HBV is a conceptual hydrological model extensively used in operational hydrological forecasting and water balance studies. In this paper, we apply the HBV model on the 1924 km 2 semi-humid Leaf River catchment near Collins, Mississippi. We analyze individual sensitivity of the parameters by calibrating the model using the Multi-Objective Shuffled Complex Evolution (MOSCEM) algorithm, perform Monte-Carlo based identifiability analysis and investigate the dynamic behavior of the parameters using the Dynamic Identifiability Analysis (DYNIA) approach in reference to the hydrological process in the catchment. The sensitivity analysis using two objective measures showed that there are distinct groups of parameters that control total runoff volume errors and errors from the high-flow series. The DYNIA analysis revealed that parameters have specific periods where they show higher identifiability and play a crucial role in representing the predicted stream flow. Temporal changes of parameter optima were observed due either to inadequacies in the model structure or possible time-varying catchment response subject to unsteady hydrodynamic and hydroclimatic conditions.

This research develops a one-parameter model of saturated source area dynamics and the spatial distribution of soil moisture. The single required parameter is the maximum soil moisture deficit within the catchment. The concept behind the development of the model comes from the fact that the complexity of topographically-driven runoff generation can be reduced through the use of geomorphological scaling relations. The scaling formulation allows the prediction of the dynamics of saturated source areas as a function of basin-wide soil moisture state. This model offers a number of potential advantages. Firstly, the model parameter is independent of topographic index distribution and its associated scale effects. Secondly, it may be possible to measure this single parameter using field measurements or perhaps remote sensing, which gives the model significant potential for application in ungauged basins. Finally, the fact that this parameter is a physical characteristic of the basin, estimation of this parameter avoids regionalization and parameter transferability problems. The model is tested using rainfall–runoff data from the 10.4 ha experimental catchment known as Tarrawara in Australia, the 37 km2 Town Creek catchment in U.S.A., and the 620 km2 Balaphi and the 850 km2 Likhu sub-catchments of the Koshi river in Nepal. In sub-catchments of Koshi river, the simulation results compare favorably against the calibrated TOPMODEL both in terms of direct runoff and the spatial distribution of soil moisture state. In the Tarrawara and Town Brook catchments, simulation results compare favorably against observed storm runoff using all observed data, without calibration.

The Upper Rio Chagres drains 414 km2 of steep, mountainous terrain in central Panama. A tropical air mass thunderstorm on 10 July 2007 produced a flood across the basin that peaked at 720 m3 s− 1 at a headwaters gage draining 17.5 km2 and 1710 m3 s− 1 at a downstream gage draining 414 km2. The storm also triggered numerous landslides in the upper basin, which facilitated the formation of large logjams along portions of the channel where transport capacity of wood was reduced by a change in channel geometry such as a bend or channel expansion. During field work in February 2008, we characterized three jams with surface areas of 400–2450 m2; two of these jams resulted in storage of substantial (1100–8200 m3) sediment wedges upstream. We returned to these sites in March 2009 to document changes in the logjams and sediment storage. Drawing on observations made in the basin since 2002, and site visits during 2008 and 2009, we suggest that jams such as these last two years or less. We propose that wood dynamics in the Upper Chagres alternate between brief periods of moderate wood load in the form of large logjams and much longer periods of essentially no wood load, a situation that contrasts with the more consistent wood loads in catchments of similar size in temperate environments and with limited studies of more consistent wood load in tropical catchments with no landslides.

Summary The worth of archival, long-term, high spatial and temporal resolution radar-rainfall estimates for hydrologic modeling has not yet been established. In particular, uncertainties remain regarding accuracy at the event time-scale, which is a modeling requirement for mass conservation. To explore this issue, an archival radar-rainfall precipitation dataset produced from the National Reflectivity Composite for the GEWEX Continental-Scale International Project (GCIP) and US National Weather Service, Weather Surveillance Radar 1988-D (WSR-88D) Stage III (SIII) data were compared with data from 982 National Climatic Data Center (NCDC) rain gages throughout the Mississippi River Basin. These two datasets are derived from the same radar-reflectivity observations but they are different. The GCIP dataset was developed from low resolution (5 dBZ bins) national radar mosaic imagery using a systematic procedure that employed one climatologically-derived reflectivity-rainfall relationship, while the SIII radar-rainfall estimates are produced using a processing algorithm developed by the US National Weather Service that employs near-real time adjustment and varied parameterizations in different River Forecast Centers around the Mississippi River Basin. Statistical analyses were performed to compare both radar-rainfall datasets with rain gage data on an event time-scale for the entire year of 1997. The investigation shows that the GCIP dataset, given a change in the equation used to calculate rainfall from reflectivity, has a lower root mean square difference for the majority of gages in four of the five river forecast centers that cover the Mississippi River Basin compared to SIII in 1997.

The objective of this research is to explore the relationship between small catchment properties and the temporal growth and decay of saturated source areas (SSA). A simple physics-based hydrologic model, which we call the Sandbox model, is developed for this purpose. A thorough sensitivity analysis is undertaken to evaluate model response to variations in model parameters. Sandbox model output is compared to that from the semi-distributed conceptual model, TOPMODEL, a model with a wide spread acceptance. Plotting the temporal evolution of the extent of saturated source area versus catchment average soil water content during a number of wetting and drying cycles shows a wide variety of trajectories or hysteretic loops. A parametric analysis was performed to quantify the impact of hypothetical catchment properties on the relationship between saturated area extent and basin-average soil water content, revealing hysteretic behavior. It is shown that this hysteresis is the result of changes in groundwater table slope, which is usually less than, and seldom equal to, the land-surface slope in non-saturated areas.

Rainfall rates estimated from polarimetric weather radar measurements of a convective rainstorm are used as input to a two-dimensional physically based rainfall-runoff model. The correlation length of the input rainfall field LS is 2.3 km. Runoff simulations are performed on two semi-arid watersheds covering 32 km2 and 121 km2 at basin data grid sizes LM of 125 m and 200 m, respectively. The characteristic basin length scale LW is taken as the square root of the watershed area. Rainfall data at resolutions LR of 1, 2, 3, 4, 6 and 8 km serve as model input to determine the effect of precipitation data spatial resolution on computed outflow hydrographs. Two dimensionless length parameters are identified which describe the similarity of the effect of rainfall data aggregation on both basins. The first parameter, L R L S , describes ‘storm smearing’, and the second parameter, L R L W , describes ‘watershed smearing’. Results from simulations without infiltration show storm smearing occurring as LR → LS. Watershed smearing causes more significant deviations from simulations using the finest-resolution data when L R L W exceeds 0.4. Results with infiltration reveal that excess rainfall volumes decrease with increasing L R L W . Additionally, excess rainfall volumes do not converge as L R L W is decreased to the practical lower limit provided by contemporary weather radars, which is of the order of 1 km.