Hillslope Velocities Research Articles

Modelling InSAR-derived hillslope velocities with multivariate statistics: A first attempt to generate interpretable predictions

Spatiotemporal patterns of earth surface deformation are influenced by a combination of the geologic, topographic, seismic, anthropogenic, meteorological and climatic conditions specific to any landscape of interest. These have been mostly modelled through machine learning tools. However, these influences are yet to be explored and exploited to train interpretable data-driven models and then make predictions on the deformation one may expect in space or time. This work explored this aspect by proposing the first multivariate model dedicated to InSAR-derived deformation data. The results we obtain are promising for we suitably retrieved the signal of environmental predictors, from which we then estimated the mean line of sight velocities for a number of hillslopes affected by seismic shaking. The importance of such models resides in its potential for opening an entirely new research line for slope instability modelling.

Hillslope Contribution to the Clark Instantaneous Unit Hydrograph: Application to the Seolmacheon Basin, Korea

In this study, the time–area curve of an ellipse is analytically derived by considering flow velocities within both channel and hillslope. The Clark IUH is also derived analytically by solving the continuity equation with the input of the derived time–area curve to the linear reservoir. The derived Clark IUH is then evaluated by application to the Seolmacheon basin, a small mountainous basin in Korea. The findings in this study are summarized as follows. (1) The time–area curve of a basin can more realistically be derived by considering both the channel and hillslope velocities. The role of the hillslope velocity can also be easily confirmed by analyzing the derived time–area curve. (2) The analytically derived Clark IUH shows the relative roles of the hillslope velocity and the storage coefficient. Under the condition that the channel velocity remains unchanged, the hillslope velocity controls the runoff peak flow and the concentration time. On the other hand, the effect of the storage coefficient can be found in the runoff peak flow and peak time, as well as in the falling limb of the runoff hydrograph. These findings are also confirmed in the analysis of rainfall–runoff events of the Seolmacheon basin. (3) The effect of the hillslope velocity varies considerably depending on the rainfall events, which is also found to be mostly dependent upon the maximum rainfall intensity.

Understanding the relative role of dispersion mechanisms across basin scales

Different mechanisms are understood to represent the primary sources of the variance of travel time distribution in natural catchments. To quantify the fraction of variance introduced by each component, dispersion coefficients have been earlier defined in the framework of geomorphology-based rainfall-runoff models. In this paper we compare over a wide range of basin sizes and for a variety of runoff conditions the relative role of geomorphological dispersion, related to the heterogeneity of path lengths, and hillslope kinematic dispersion, generated by flow processes within the hillslopes. Unlike previous works, our approach does not focus on a specific study case; instead, we try to generalize results already obtained in previous literature stemming from the definition of a few significant parameters related to the metrics of the catchment and flow dynamics. We further extend this conceptual framework considering the effects of two additional variance-producing processes: the first covers the random variability of hillslope velocities (i.e. of travel times over hillslopes); the second deals with non-uniform production of runoff over the basin (specifically related to drainage density). Results are useful to clarify the role of hillslope kinematic dispersion and define under which conditions it counteracts or reinforces geomorphological dispersion. We show how its sign is ruled by the specific spatial distribution of hillslope lengths within the basin, as well as by flow conditions. Interestingly, while negative in a wide range of cases, kinematic dispersion is expected to become invariantly positive when the variability of hillslope velocity is large.

Hydrological effects of within-catchment heterogeneity of drainage density

Local drainage density (dd) has been traditionally defined as the inverse of twice the distance one has to walk before encountering a channel. This formalization easily allows to derive raster-based maps of dd extracted straight off from digital elevation model data. Maps of local dd, which are continuous in space, are able to reveal the appearance of strong heterogeneities in the geological and geomorphological properties of natural landscapes across different scales. In this work we employ the information provided by these spatial maps to study the potential effects of the within-catchment variability of dd on the hydrologic response. A simple power law relationship between runoff yield at the local scale and the value of dd has been adopted; the hypothesis is supported by a large number of past empirical observations and modeling. The novel framework proposed (ddRWF) embeds this spatially variable runoff weight in the well-known Rescaled Width Function (RWF) framework, based on the more general geomorphological theory of the hydrologic response. The model is applied to four sub-basins in the Cascade Range Region (Oregon, USA) where strong contrasts in dissection patterns due the underlain geology have been broadly addressed in previous literature. The ddRWF approach is compared with the classic RWF in terms of shape, moments and peak of the simulated hydrograph response. Results hint that the variability of runoff yield due to the heterogeneity of dd (i.e. of hillslope lengths) determines a more rapid concentration of runoff, which implies shorter lag times, larger skewness and higher peak floods, especially in the case hillslope velocity is much smaller than channel velocity. The potential of the proposed framework relies on accounting for spatially variable losses related to geomorphologic heterogeneity in lumped rainfall–runoff models, still keeping the simple and robust structure of the IUH approach.

Rainfall organization control on the flood response of mild-slope basins

This study uses a long-term (8 years) dataset of radar-rainfall and runoff observations for the Tar River Basin in North Carolina, to explore the rainfall space–time organization control on the flood response of mild-slope (max slope <32 degrees) basins. We employ the concepts of “spatial moments of catchment rainfall” and “catchment scale storm velocity” to quantify the effect of spatial rainfall variability and basin geomorphology on flood response. A calibrated distributed hydrologic model is employed to assess the relevance of these statistics in describing the degree of spatial rainfall organization, which is important for runoff modeling. Furthermore, the Tar River Basin is divided into four nested sub-basins ranging from 1106 km2 to 5654 km2, in order to investigate the scale dependence of results. The rainfall spatiotemporal distribution represented in the analytical framework is shown to describe well the differences in hydrograph timing (less so in terms of magnitude of the simulated hydrographs) determined from forcing the hydrologic model with lumped vs. distributed rainfall. Specifically, the first moment exhibits a linear relationship with the difference in timing between lumped and distributed rainfall forcing. The analysis shows that the catchment scale storm velocity is scale dependent in terms of variability and rainfall dependent in terms of its value, assuming typically small values. Accordingly, the error in dispersion of simulated hydrographs between lumped and distributed rainfall forcing is relatively insensitive to the catchment scale storm velocity, which is attributed to the spatial variability of routing and hillslope velocities that is not accounted by the conceptual framework used in this study.

Re-Analysis of Clark Model Based on Drainage Structure of Basin

본 연구에서는 유역의 배수구조를 설명할 수 있는 폭 함수 기반의 Clark 모형을 제안하였다. 시간-면적곡선으로는 지표면과 하천에 대하여 개별적인 동수역학적 특성을 적용한 재조정된 폭 함수를 이용하였다. 선형저수지 추적의 경우 기존의 Clark 모형과 같이 차분화된 형태가 아니라 해석식을 적용하여 수행하였다. 본 연구에서 고려한 주요한 매개변수들로는 지표면평균이송속도 및 하천평균이송속도와 저류상수를 들 수 있다. 실제 매개변수의 추정 과정에는 전역최적화 기법 중의 하나인 SCE-UA 기법을 적용하였다. 또한 Clark 모형으로부터 유도된 순간단위도의 형상은 원점에 대한 1차모멘트와 면적중심에 대한 2, 3차 모멘트로 구분하여 평가하였다. 관측 수문사상의 통계모멘트들과 본 연구에서 추정된 통계모멘트들의 상관계수는 1차모멘트의 경우 0.995, 2차모멘트는 0.993, 3차모멘트는 0.983로 산정되었다. 평균과 분산에 대해서는 추정값과 관측값이 대체로 일치하는 경향을 보여주었다. 그러나 추정된 3차모멘트에 대한 결과는 다소 과대 평가되는 경향을 나타내었다. 제안된 Clark 모형은 순간단위도의 형상을 평균과 분산만을 고려하여 적용한 방법보다 수문곡선의 왜곡 및 첨두좌표의 모의와 관련된 한계점을 개선하였다. 이러한 결과로부터 본 연구에서 제시한 방법론은 배수경로의 이질성과 동적매개변수들의 영향을 적절하게 반영할 수 있음을 확인할 수 있었다. 본 연구에서 고려한 모멘트들의 변동성은 주로 저류상수의 영향이 크게 나타나고 있으며, 지표면평균이송속도보다는 하천평균이송속도가 크게 영향을 미치는 것을 확인할 수 있었다. 이로부터 저류상수와 하천평균이송속도가 Clark 모형으로부터 유도되는 순간단위도의 형상을 결정하는데 지배적인 역할을 하는 것으로 확인되었다. 따라서 두 매개변수는 모형의 적용 과정에서 중요하게 고려되어야 할 것으로 판단된다. This study presents the width function-based Clark model. To this end, rescaled width function with distinction between hillslope and channel velocity is used as time-area curve and then it is routed through linear storage within the framework of not finite difference scheme used in original Clark model but analytical expression of linear storage routing. There are three parameters focused in this study: storage coefficient, hillslope velocity and channel velocity. SCE-UA, one of the popular global optimization methods, is applied to estimate them. The shapes of resulting IUHs from this study are evaluated in terms of the three statistical moments of hydrologic response functions: mean, variance and the third moment about the center of IUH. The correlation coefficients to the three statistical moments simulated in this study against these of observed hydrographs were estimated at 0.995 for the mean, 0.993 for the variance and 0.983 for the third moment about the center of IUH. The shape of resulting IUHs from this study give rise to satisfactory simulation results in terms of the mean and variance. But the third moment about the center of IUH tend to be overestimated. Clark model proposed in this study is superior to the one only taking into account mean and variance of IUH with respect to skewness, peak discharge and peak time of runoff hydrograph. From this result it is confirmed that the method suggested in this study is useful tool to reflect the heterogeneity of drainage path and hydrodynamic parameters. The variation of statistical moments of IUH are mainly influenced by storage coefficient and in turn the effect of channel velocity is greater than the one of hillslope velocity. Therefore storage coefficient and channel velocity are the crucial factors in shaping the form of IUH and should be considered carefully to apply Clark model proposed in this study.

A parsimonious geomorphological unit hydrograph for rainfall–runoff modelling in small ungauged basins

In this study, a parsimonious hydrological modelling algorithm is proposed based on the automated DEM-based geomorphic characterization of runoff dynamics in scarcely monitored river basins. The proposed approach implements the instantaneous unit hydrograph (IUH) concept, estimated using the width function (WF), for characterizing the travel time distribution using just one parameter, the river network flow velocity. Hillslope velocities are defined using spatially-distributed empirical formulas based on slope and soil-use information extrapolated from digital topographic data. Case studies are presented for testing model performance and comparing simulated and observed hydrographs of 25 selected flood events, as well as investigating the differences with the geomorphological instantaneous unit hydrograph (GIUH) model results. The calibration of the WFIUH channel flow velocity parameter using the concentration time is investigated providing interesting insights for the use of such a method for hydrological prediction in ungauged basins. Editor D. Koutsoyiannis Citation Grimaldi, S., Petroselli, A. and Nardi, F., 2012. A parsimonious geomorphological unit hydrograph for rainfall–runoff modelling in small ungauged basins. Hydrological Sciences Journal, 57 (1), 73–83.

Effects of hillslope dynamics and network geometry on the scaling properties of the hydrologic response

This paper investigates the specific contributions of river network geomorphology, hillslope flow dynamics and channel routing to the scaling behavior of the hydrologic response as function of drainage area. Scaling relationships emerged from the observations of geomorphological and hydrological data and were reproduced in previous works through mathematical models, for both idealized self-similar networks and natural basins. Recent literature highlighted that scale invariance of hydrological quantities depends not only on the metrics of the drainage catchment but also on effective flow routing. In this study we employ a geomorphological width function scheme to test the simple scaling hypothesis adopting more realistic dynamic conditions than in previous approaches, specifically taking into account the role of hillslopes. The analysis is based on the derivation of the characteristic distributions of path lengths and travel times, inferred from DEM processing and measurements of rainfall and runoff data. The study area is located in the Tiber River region (central Italy). Results indicate that, while scaling properties clearly emerge when the hydrologic response is defined on the basis of the sole geomorphology, scale invariance is broken when less idealized flow dynamics are taken into account. Lack of scaling appears in particular as a consequence of the catchment to catchment variability of hillslope velocities.

Flow time estimation with spatially variable hillslope velocity in ungauged basins

The automated spatial estimation of the hillslope runoff dynamics is used as a valuable tool for the estimation of the travel time distribution (flow time), a major factor for the hydrologic prediction in ungauged basins. In fact, while the flow time function is usually obtained by rescaling the flow paths with constant channel and hillslope velocities, in this work a spatially distributed kinematic component, as a function of terrain features and in particular slope and land use, is implemented and its influence on the hydrologic response is tested by means of the Width Function Instantaneous Unit Hydrograph (WFIUH) framework. Hillslope surface flow velocities are evaluated by applying different uniform flow formulas within an automated DEM-based (terrain analysis) algorithm. A comparison test of the performances of the Manning, Darcy, Maidment and Soil Conservation Service uniform flow equations is performed for several case studies in Italy pertaining to different climatic and geomorphic conditions. Results provide new insights for a better understanding of the flow time function also introducing a more parsimonious and physically-based calibration scheme of the WFIUH.

Regional analysis of storm hydrographs in the Rescaled Width Function framework

Summary The kinematic parameters of the Width Function based Instantaneous Unit Hydrograph (WFIUH) are estimated for a variety of Italian basins. Different gauged catchments located within the Upper Tiber valley, some major tributaries of the Tiber river itself and the Amaseno river (Central Italy) were selected to perform a regional analysis of hillslope and channel velocities for catchments with different morphology and lithology. The analytical expressions adopted to determine the first and second moment of the WFIUH are revised taking into account the statistical dependence between hillslope and channel lengths. Velocities are estimated through a moment fitting procedure based on rainfall records, runoff data and on the metrics of the catchment. Larger lag times and travel time variances and smaller hillslope velocities are observed for catchments underlain by carbonaceous formations when compared to other basins. The values obtained for both hillslope and channel velocities appear always to maintain a physical meaning. Finally, the capability of the WFIUH as a tool for transferring hydrologic information and obtain the prediction of flow hydrographs in ungauged basins is evaluated. Two equations relating the kinematic parameters to some easily-available characteristics of the catchment (namely the average slope and the fraction of basin underlain by carbonaceous formations) are proposed.

Diagnosing peak-discharge power laws observed in rainfall–runoff events in Goodwin Creek experimental watershed

Observations from the Goodwin Creek experimental watershed (GCEW), Mississippi show that peak-discharge Q( A) and drainage area A are related, on average, by a power law or scaling relationship, Q( A) = αA θ , during single rainfall–runoff events. Observations also show that α and θ change between events, and, based on a recent analysis of 148 events, observations indicate that α and θ change because of corresponding changes in the depth, duration, and spatial variability of excess-rainfall. To improve our physical understanding of these observations, a 5-step framework for diagnosing observed power laws, or other space-time patterns in a basin, is articulated and applied to GCEW using a combination of analysis and numerical simulations. Diagnostic results indicate how the power laws are connected to physical conditions and processes. Derived expressions for α and θ show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between α and excess-rainfall duration, and an increasing and slightly convex relationship between θ and excess rainfall duration. These trends are consistent with observations only when hillslope velocity v h is given a physically realistic value near 0.1 m/s. If v h ≫ 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in α and θ can be impacted by the dependence of v h and link velocity v l on excess-rainfall rate.

Kinematic dispersion effects of hillslope velocities

When the flow parameters, such as celerity and hydrodynamic coefficient, are allowed to vary spatially within a basin, three mechanisms, namely, geomorphologic, kinematic, and hydrodynamic dispersion, contribute to the variance of the instantaneous response function. The relative contributions of the three dispersion mechanisms as a function of scale, or Strahler order of the basin, were studied earlier by Saco and Kumar [2002a, 2002b]. In this study we investigate the main mechanisms that are responsible for the variance when we take into account the hillslope dynamics. We use an approach similar to that derived by Saco and Kumar [2002a, 2002b], but for width functions, to compute the relative contributions of geomorphologic and kinematic dispersion due to hillslope celerities. We find that the kinematic dispersion due to hillslopes does not tend to reinforce the effect of geomorphologic dispersion; rather, it tends to counteract it. This means that the effect of hillslopes tends to “decrease” the variance induced by the geomorphology of the network. For hillslope celerities that are very small compared with channel celerities, the travel times in the hillslopes begin to be of the same order of magnitude as those in the network. If the celerity continues to decrease, all the variance is induced by the travel times at the hillslopes and the impact of geomorphologic dispersion becomes negligible.

Simulation of summer storms of differing recurrence intervals in a semiarid environment using a kinematic routing scheme

AbstractA kinematic flood routing procedure has been devised for a small dendritic headwater gully network on the Western slope of Colorado. the program is spatially‐distributed, incorporating lateral inflows from 103 field sites on the network for which channel geometry variables are known. This model, in which a lateral inflow algorithm for the sideslopes between each channel site is convoluted into a Freeze‐type (1978) numerical scheme, is fully developed in this paper.Although the field basis of the lateral inflow algorithm has been tested elsewhere (Faulkner, 1990), sensitivity tests were needed for the roughness and hillslope velocity estimates used in the routing procedure. After these successful tests, a suitably precalibrated run of the model was compared with a field‐monitored runoff event on the watershed, and results again were encouraging. However, peak attentuation downstream was more pronounced in reality than on the simulation, so the model was also modified by inclusion of allowances for transmission loss. the tendency that the model had displayed for peak size attenuation downstream was considerably enhanced.Using the model, the geomorphic role of the flashfloods which affect the watershed in the summer months is briefly considered by applying the model to existing records of local summer storm rainfall events as a basis for event simulation. These simulations show that downstream attenuation of the flood wave on concave networks in steep semiarid terrain was likely to be a common occurrence, possibly resulting in down‐net deposition and differences in geomorphic behaviour between upstream and downstream sites. the discussion is finally broadened to consider the relative importance of ‘common’ as compared to ‘freak’ watershed events in maintaining these differences.

Incorporating hillslope effects into the geomorphologic instantaneous unit hydrograph

Use of gamma distributions of stream holding times, rather than the traditional exponential distributions, results in geomorphologic instantaneous unit hydrographs (GIUHs) that better fit data‐based IUHs. In this paper, hillslope effects are incorporated into the gamma GIUH (GGIUH) model by assuming that the hillslope travel distance in an area of a given order is approximated by the inverse of twice the local drainage density and introducing a hillslope velocity term. A method of moments fitting procedure is developed to estimate the channel and hillslope velocity terms in the GGIUH model from the moments of rainfall input and basin discharge output. It was found that hillslope velocities are 2 orders of magnitude smaller than channel velocities. The values found for the latter are reasonable given the range of values given in the literature for channel velocities. Similarly, the hillslope velocity term found by the method of moments procedure matches macropore velocities reported in the literature.