46Process-based hydrological models have a long history dating back to the 1960s. 47Criticized by some as over-parameterized, overly complex, and difficult to use, a more 48 nuanced view is that these tools are necessary in many situations and, in a certain class of 49 problems, they are the most appropriate type of hydrological model. This is especially the 50 case in situations where knowledge of flow paths or distributed state variables and/or 51 preservation of physical constraints is important. Examples of this include: spatiotemporal 52 variability of soil moisture, groundwater flow and runoff generation, sediment and 53 contaminant transport, or when feedbacks among various Earth's system processes or 54 understanding the impacts of climate non-stationarity are of primary concern. These are 55 situations where process-based models excel and other models are unverifiable. This article 56 presents this pragmatic view in the context of existing literature to justify the approach where 57 applicable and necessary. We review how improvements in data availability, computational 58 resources and algorithms have made detailed hydrological simulations a reality. Avenues for 59 the future of process-based hydrological models are presented suggesting their use as virtual 60 laboratories, for design purposes, and with a powerful treatment of uncertainty. 61

[1] We investigated the control of postwildfire runoff by physical and hydraulic properties of soil, hydrologic states, and an ash layer immediately following wildfire. The field site is within the area burned by the 2010 Fourmile Canyon Fire in Colorado, USA. Physical and hydraulic property characterization included ash thickness, particle size distribution, hydraulic conductivity, and soil water retention curves. Soil water content and matric potential were measured indirectly at several depths below the soil surface to document hydrologic states underneath the ash layer in the unsaturated zone, whereas precipitation and surface runoff were measured directly. Measurements of soil water content showed that almost no water infiltrated below the ash layer into the near-surface soil in the burned site at the storm time scale (i.e., minutes to hours). Runoff generation processes were controlled by and highly sensitive to ash thickness and ash hydraulic properties. The ash layer stored from 97% to 99% of rainfall, which was critical for reducing runoff amounts. The hydrologic response to two rain storms with different rainfall amounts, rainfall intensity, and durations, only ten days apart, indicated that runoff generation was predominantly by the saturation-excess mechanism perched at the ash-soil interface during the first storm and predominantly by the infiltration-excess mechanism at the ash surface during the second storm. Contributing area was not static for the two storms and was 4% (saturation excess) to 68% (infiltration excess) of the catchment area. Our results showed the importance of including hydrologic conditions and hydraulic properties of the ash layer in postwildfire runoff generation models.

In the Colorado Front Range, forested catchments near the rain–snow transition are likely to experience changes in snowmelt delivery and subsurface water transport with climate warming and associated shifts in precipitation patterns. Snowpack dynamics are strongly affected by aspect: Lodgepole pine forested north‐facing slopes develop a seasonal snowpack, whereas Ponderosa pine‐dotted south‐facing slopes experience intermittent snow accumulation throughout winter and spring. We tested the degree to which these contrasting water input patterns cause different near‐surface hydrologic response on north‐facing and south‐facing hillslopes during the snowmelt period. During spring snowmelt, we applied lithium bromide (LiBr) tracer to instrumented plots along a north–south catchment transect. Bromide broke through immediately at 10‐ and 30‐cm depths on the north‐facing slope and was transported out of soil waters within 40 days. On the south‐facing slope, Br− was transported to significant depths only during spring storms and remained above the detection limit throughout the study. Modelling of unsaturated zone hydrologic response using Hydrus‐1D corroborated these aspect‐driven differences in subsurface transport. Our multiple lines of evidence suggest that north‐facing slopes are dominated by connected flow through the soil matrix, whereas south‐facing slope soils experience brief periods of rapid vertical transport following snowmelt events and are drier overall than north‐facing slopes. These differences in hydrologic response were largely a function of energy‐driven differences in water supply, emphasizing the importance of aspect and climate forcing when considering contributions of water and solutes to streamflow in catchments near the snow line. Copyright © 2012 John Wiley & Sons, Ltd.

Models are to be used, not to be believed in! Dooge (1972) Our models should be designed expressly to maximize the possibility of discovering that of which we are ignorant.Beck ( In the context of hydrology and deterministic-conceptual simulation, equifinality frequently refers to more than one parameter set providing an equally good (or poor) representation of the integrated response. Discussing the issue of equifinality, Savenije (2001) wrote as follows: Although we can consider equifinality as a nuisance since it implies that looking for more understanding through detailed distributed modelling is a dead-end track, it also offers an opening to the revival of larger-scale hydrological laws. Ill-Posed Problems and Model PerformanceNear-surface hydrologic response can be quantitatively analyzed for certain problems and scales, using physics-based mathematical models with meaningful (measurable) parameter estimates that are both spatially and temporally variable. Parameterization of a physics-based model, especially with sparse information, is no trivial task (see Bredehoeft, 2005). The inverse method of model parameterization, which involves determining the optimal parameter set by observing the dependent variable in the spatial and time domains, has been discussed by Neuman (1973), Carrera and Neuman (1986), Yeh (1986), and several others. When the number of unknowns is greater than the number of observations, the problem becomes ill-posed (Hadamard, 1902). For a given parameter set, the solution to an ill-posed problem is not necessarily unique or stable. Most, if not all, near-surface hydrologic-response problems are ill-posed. However, a problem being ill-posed does not imply, as pointed out by Allison (1979), that it is not worth solving.The issues that are associated with ill-posed problems in hydrology fall into three categories (Neuman, 1973; Carrera and Neuman, 1986; Khatibi et al., 2000): (i) identifiability, (ii) uniqueness, and (iii) stability. Identifiability requires that all the model parameters contribute meaningfully to the solution and that there is only one correct parameterization for a given site. Uniqueness requires that only one set of parameter values can be estimated from a given set of observations and that the set of parameters determined from one set of observations (from one time period) must also represent the observed behaviour at a different time period. While identifiability and uniqueness seem very similar, Carrera and Neuman (1986) distinguish between the two by associating identifiability with the forward solution and uniqueness with the inversion from observed data to model parameterization. The stability constraint demands that small errors in the observed data do not produce large changes in the calibration. Stability can also be taken to mean that slight changes in parameter values do not cause the model solution to be drastically different.The There are many valuable approaches for examining hydrologic processes. However, at the catchment scale, the most sensible framewor...

Distributed hydrologic models capable of simulating fully-coupled surface water and groundwater flow are increasingly used to examine problems in the hydrologic sciences. Several techniques are currently available to couple the surface and subsurface; the two most frequently employed approaches are first-order exchange coefficients (a.k.a., the surface conductance method) and enforced continuity of pressure and flux at the surface-subsurface boundary condition. The effort reported here examines the parameter sensitivity of simulated hydrologic response for the first-order exchange coefficients at a well-characterized field site using the fully coupled Integrated Hydrology Model (InHM ). This investigation demonstrates that the first-order exchange coefficients can be selected such that the simulated hydrologic response is insensitive to the parameter choice, while simulation time is considerably reduced. Alternatively, the ability to choose a firstorder exchange coefficient that intentionally decouples the surface and subsurface facilitates concept-development simulations to examine real-world situations where the surface-subsurface exchange is impaired. While the parameters comprising the first-order exchange coefficient cannot be directly estimated or measured, the insensitivity of the simulated flow system to these parameters (when chosen appropriately) combined with the ability to mimic actual physical processes suggests that the first-order exchange coefficient approach can be consistent with a physics-based framework.Enforcing simultaneous continuity of pressure between the surface and subsurface, typically accomplished implicitly using iterative boundary condition matching, is an alternative to the first-order exchange coefficient approach, predating it by decades

The comprehensive physics-based hydrologic-response model InHM was used to simulate 3D variably-saturated flow and solute transport for three controlled sprinkling experiments at the Coos Bay 1 (CB1) experimental catchment in the Oregon Coast Range. The InHM-simulated hydrologic-response was evaluated against observed discharge, pressure head, total head, soil-water content, and deuterium concentration records. Runoff generation, tensiometric/piezometric response in the soil, pore-water pressure generation, and solute (tracer) transport were all simulated well, based on statistical and graphical model performance evaluation. The InHM simulations reported herein indicate that the 3D geometry and hydraulic characteristics of the layered geologic interfaces at CB1 can control the development of saturation and pore-water pressures at the soil-saprolite interface. The weathered bedrock piezometric response and runoff contribution were not simulated well with InHM in this study, most likely as a result of the uncertainty in the weathered bedrock layer geometry and fractured-rock hydraulic properties that preclude accurate fracture flow representation. Sensitivity analyses for the CB1 boundary-value problem indicate that: (i) hysteretic unsaturated flow in the CB1 soil is important for accurate hydrologicresponse simulation, (ii) using an impermeable boundary condition to represent layered geologic interfaces leads to large errors in simulated magnitudes of runoff generation and pore-water pressure development, and (iii) field-based retention curve measurements can dramatically improve variably-saturated hydrologic-response simulation at sites with steep soil-water retention curves. The near-surface CB1 simulations reported herein demonstrate that physics-based models like InHM are useful for characterizing detailed spatio-temporal hydrologic-response, developing processbased concepts, and identifying information shortfalls for the next generation of field experiments. The field-based observations and hydrologic-response simulations from CB1 highlight the challenges in characterizing/simulating fractured bedrock flow at small catchments, which has important consequences for hydrologic response and landslide initiation.

We collected soil‐hydraulic property data from the literature for wildfire‐affected soils, ash, and unburned soils. These data were used to calculate metrics and timescales of hydrologic response related to infiltration and surface runoff generation. Sorptivity (S) and wetting front potential (Ψf) were significantly different (lower) in burned soils compared with unburned soils, whereas field‐saturated hydraulic conductivity (Kfs) was not significantly different. The magnitude and duration of the influence of capillarity during infiltration was greatly reduced in burned soils, causing faster ponding times in response to rainfall. Ash had large values of S and Kfs but moderate values of Ψf, compared with unburned and burned soils, indicating ash has long ponding times in response to rainfall. The ratio of S2/Kfs was nearly constant (~100 mm) for unburned soils but more variable in burned soils, suggesting that unburned soils have a balance between gravity and capillarity contributions to infiltration that may depend on soil organic matter, whereas in burned soils the gravity contribution to infiltration is greater. Changes in S and Kfs in burned soils act synergistically to reduce infiltration and accelerate and amplify surface runoff generation. Synthesis of these findings identifies three key areas for future research. First, short timescales of capillary influences on infiltration indicate the need for better measurements of infiltration at times less than 1 min to accurately characterize S in burned soils. Second, using parameter values, such as Ψf, from unburned areas could produce substantial errors in hydrologic modeling when used without adjustment for wildfire effects, causing parameter compensation and resulting underestimation of Kfs. Third, more thorough measurement campaigns that capture soil‐structural changes, organic matter impacts, quantitative water repellency trends, and soil‐water content along with soil‐hydraulic properties could drive the development of better techniques for numerically simulating infiltration in burned areas.

Wildfire can affect soil hydraulic properties, often resulting in reduced infiltration. The magnitude of change in infiltration varies depending on the burn severity. Quantitative approaches to link burn severity with changes in infiltration are lacking. This study uses controlled laboratory measurements to determine relations between a remotely sensed burn severity metric (dNBR, change in normalised burn ratio) and soil hydraulic properties (SHPs). SHPs were measured on soil cores collected from an area burned by the 2013 Black Forest fire in Colorado, USA. Six sites with the same soil type were selected across a range of burn severities, and 10 random soil cores were collected from each site within a 30-m diameter circle. Cumulative infiltration measurements were made in the laboratory using a tension infiltrometer to determine field-saturated hydraulic conductivity, Kfs, and sorptivity, S. These measurements were correlated with dNBR for values ranging from 124 (low severity) to 886 (high severity). SHPs were related to dNBR by inverse functions for specific conditions of water repellency (at the time of sampling) and soil texture. Both functions had a threshold value for dNBR between 124 and 420, where Kfs and S were unchanged and equal to values for soil unaffected by fire. For dNBRs >~420, the Kfs was an exponentially decreasing function of dNBR and S was a linearly decreasing function of dNBR. These initial quantitative empirical relations provide a first step to link SHPs to burn severity, and can be used in quantitative infiltration models to predict post-wildfire infiltration and resulting runoff.