A patch hierarchy approach to modeling surface and subsurface hydrology in complex flood‐plain environments

Geomorphology interacts with surface‐ and ground‐water hydrology across multiple spatial scales. Nonetheless, hydrologic and hydrogeologic models are most commonly implemented at a single spatial scale. Using an existing hydrogeologic computer model, we implemented a simple hierarchical approach to modeling surface‐ and ground‐water hydrology in a complex geomorphic setting. We parameterized the model to simulate ground‐ and surface‐water ?ow patterns through a hierarchical, three‐dimensional, quantitative representation of an anabranched montane alluvial ?ood plain (the Nyack Flood Plain, Middle Fork Flathead River, Montana, USA). Comparison of model results to ?eld data showed that the model provided reasonable representations of spatial patterns of aquifer recharge and discharge, temporal patterns of ?ood‐water storage on the ?ood plain, and rates of ground‐water movement from the main river channel into a large lateral spring channel on the ?ood plain, and water table elevation in the alluvial aquifer. These results suggest that a hierarchical approach to modeling ground‐ and surface‐water hydrology can reproduce realistic patterns of surface‐ and ground‐water ?ux on alluvial ?ood plains, and therefore should provide an excellent ‘quantitative laboratory’ for studying complex interactions between geomorphology and hydrology at and across multiple spatial scales. Copyright © 2004 John Wiley & Sons, Ltd.     

Advancing understanding of runoff and sediment transfers in agricultural catchments through simultaneous observations across scales

Our understanding of the effect of scale on runoff and sediment transfers within catchments is currently limited by a lack of available data. A multi‐scale dataset of 17 rainfall events collected simultaneously at four spatial scales within a small agricultural catchment in 2005–2006 is presented. Analysis using exploratory techniques and a two‐step, zero‐inflated lognormal mixed‐effects regression model, has demonstrated that event responses, and event response characteristics representing runoff and sediment peaks and area‐normalized yields, are scale dependent, and hence cannot be transferred directly between scales. Runoff and sediment yields increase as scale increases, and it is proposed that this effect, which differs from that observed in the few other studies of scale effects undertaken, is due to increasing connectivity within the catchment, and the dominance of preferential flow pathways including through macropores and field drains. The processes contributing to scale dependence in the data, and the possibility that certain processes dominate at particular scales, are discussed. The data presented here help to improve our spatial understanding of runoff and sediment transport in small agricultural catchments, and provide examples of the type of spatial dataset and the type of analysis that are essential if we are to develop models which are able to predict runoff and soil erosion accurately, and allow us to manage runoff and sediment transport effectively across scales. Copyright © 2011 John Wiley & Sons, Ltd.     

Soil moisture variability and scale-dependency of nonlinear parameterizations in coupled land–atmosphere models

Many of the relationships used in coupled land–atmosphere models to describe interactions between the land surface and the atmosphere have been empirically parameterized and thus are inherently dependent on the observational scale for which they were derived and tested. However, they are often applied at scales quite different than the ones they were intended for due to practical necessity. In this paper, a study is presented on the scale-dependency of parameterizations which are nonlinear functions of variables exhibiting considerable spatial variability across a wide range of scales. For illustration purposes, we focus on parameterizations which are explicit nonlinear functions of soil moisture. We use data from the 1997 Southern Great Plains Hydrology Experiment (SGP97) to quantify the spatial variability of soil moisture as a function of scale. By assuming that a parameterization keeps its general form the same over a range of scales, we quantify how the values of its parameters should change with scale in order to preserve the spatially averaged predicted fluxes at any scale of interest. The findings of this study illustrate that if modifications are not made to nonlinear parameterizations to account for the mismatch of scales between optimization and application, then significant systematic biases may result in model-predicted water and energy fluxes.     

Multi-scale heterogeneity of soil moisture following snow thawing in <Emphasis Type="Italic">Haloxylon ammodendron</Emphasis> shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.     

Multi-scale heterogeneity of soil moisture following snow thawing in Haloxylon ammodendron shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.     

Multi-scale heterogeneity of soil moisture following snow thawing in Haloxylon ammodendron shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.

     

Decadal variability and scales of the sea surface structure in the northern Ionian

The variability and scales of the sea surface structure of the northern Ionian Sea from January 1993 to December 2007 were studied by means of altimeter remotely-sensed weekly Sea Level Anomaly (SLA) objective maps. Variability in the sea surface structure was addressed by means of empirical orthogonal function (EOF) analysis and, assuming an exponential correlation model, scales of the SLA field were quantified as e-folding distances of the SLA autocorrelation function. The variability in the sea surface structure, described by the first three EOFs, which cumulatively explain 60.3% of the data set variance, is characterized by a large-scale structure with variability on a time scale of ∼10-13 years and, on shorter scales, an eddy system with variability on an annual scale. The variability in the large-scale structure describes an overturning of the SLA field, which took place in 1997, and determines a reversal of the geostrophic upper-layer circulation. As the large-scale circulation transition takes place, time-dependent spectral analysis of EOF coefficients shows a redistribution of the spectral energy from inter-annual to semi-annual and monthly components. Spatial scales display variability on an annual and inter-annual time scale. On the annual time scale, variability in spatial scales is characterized by longer values in summer-fall and shorter in winter-spring. Inter-annual variability in spatial scales is demonstrated by a remarkable drop in the values during fall in the period 1998-2000. We propose an explanation of the variability in horizontal scales in terms of the redistribution of water masses and related modifications of the vertical structure of the water column associated with different regimes of the basin-scale circulation.     

Beyond the semivariogram: Patterns,scale, and hydrology in a semi-arid landscape

As an alternative to geostatistical modeling, we characterized the hydrology of a semi-arid landscape in southeastern Washington state, USA, by coupling spatial patterns identified in the distributions of relative relief and vegetation with the influence each has on soil moisture storage and evapotranspiration at the appropriate scale. Gauging precipitation, soil moisture, and evapotranspiration over a two-year period while concurrently mapping relative relief and vegetation distributions at three scales ranging from centimeters to 90 m, we determined that soil moisture and soil moisture storage are significantly greater in topographic concavities than in convexities at the microrelief (20–50 cm) scale but are not significantly different in relief features at larger scales. A generalized microrelief surface produced using a two-dimensional Fourier transformation provided a good representation of the distribution of soil moisture within microrelief when scaled to soil moisture values. Applying a spatial point process analysis we determined that big sage are randomly distributed across the landscape at all scales, suggesting that lysimeter-derived sage evapotranspiration rates also be distributed randomly across the landscape. Where sage were not present, we applied an autoregressive moving-average model conditioned on grass lysimeter measurements to derive evapotranspiration rates. Combining these hydrologic spatial patterns derived from distributions in relief and vegetation with measured precipitation inputs and evapotranspiration outputs, we created a spatially distributed model of soil moisture which we tested against measured values over an eight-week period. The model provides accurate characterization of soil moisture, allows estimates of soil moisture between measurement points, permits extrapolation of soil moisture distributions outside the gauged area, and maintains small-scale variability when aggregating soil moisture to successively larger scales.     

Multi-scale analysis of meteorological drought risks based on a Bayesian interpolation approach in Huai River basin,China

A scheme for meteorological drought analysis at various temporal and spatial scales based on a spatial Bayesian interpolation of drought severity derived from Standardized Precipitation Index (SPI) values at observed stations is presented and applied to the Huai River basin of China in this paper, using monthly precipitation record from 1961 to 2006 in 30 meteorological stations across the basin. After dividing the study area into regular grids, drought condition in gauged sites are classified into extreme, severe, moderate and non drought according to SPIs at month, seasonal and annual time scales respectively while that in ungauged grids are explained as risks of various drought severities instead of single state by a Bayesian interpolation. Subsequently, temporal and spatial patterns of drought risks are investigated statistically. Main conclusions of the research are as follows: (1) drought at seasonal scale was more threatening than the other two time scales with a larger number of observed drought events and more notable variation; (2) results of the Mann–Kendall test revealed an upward trend of drought risk in April and September; (3) there were larger risks of extreme and severe drought in southern and northwestern parts of the basin while the northeastern areas tended to face larger risks of moderate drought. The case study in Huai River basin suggests that the proposed approach is a viable and flexible tool for monitoring meteorological drought at multiple scales with a more specific insight into drought characteristics at each severity level.     

Spatial patterns of frequent floods in Switzerland

This study investigates the spatial dependence of high and extreme streamflows in Switzerland across different scales. First, using 56 runoff time series from Swiss rivers, we determined the average length of high-streamflow events for different levels of extremeness. Second, a dependence measure that expressed the probability that streamflow peaks would meet or exceed streamflow peaks at a conditioning site was used to describe and map the spatial extent of joint streamflow-peak occurrences across Switzerland. Third, we analysed the spatial patterns of jointly occurring high streamflows using cluster analysis to identify groups that react similarly in terms of flood frequency at different sites. The results indicate that, on a coarse scale, high and extreme streamflows are asymptotically independent in the main Swiss basins. Additionally, mesoscale tributaries in the main basins show distinct flood regions across river systems.     

Effects of spatial aggregation of soil spatial information on watershed hydrological modelling

Many researchers have examined the impact of detailed soil spatial information on hydrological modelling due to the fact that such information serves as important input to hydrological modelling, yet is difficult and expensive to obtain. Most research has focused on the effects at single scales; however, the effects in the context of spatial aggregation across different scales are largely missing. This paper examines such effects by comparing the simulated runoffs across scales from watershed models based on two different levels of soil spatial information: the 10‐m‐resolution soil data derived from the Soil‐Land Inference Model (SoLIM) and the 1:24000 scale Soil Survey Geographic (SSURGO) database in the United States. The study was conducted at three different spatial scales: two at different watershed size levels (referred to as full watershed and sub‐basin, respectively) and one at the model minimum simulation unit level. A fully distributed hydrologic model (WetSpa) and a semi‐distributed model (SWAT) were used to assess the effects. The results show that at the minimum simulation unit level the differences in simulated runoff are large, but the differences gradually decrease as the spatial scale of the simulation units increases. For sub‐basins larger than 10 km² in the study area, stream flows simulated by spatially detailed SoLIM soil data do not significantly vary from those by SSURGO. The effects of spatial scale are shown to correlate with aggregation effect of the watershed routing process. The unique findings of this paper provide an important and unified perspective on the different views reported in the literature concerning how spatial detail of soil data affects watershed modelling. Different views result from different scales at which those studies were conducted. In addition, the findings offer a potentially useful basis for selecting details of soil spatial information appropriate for watershed modelling at a given scale. Copyright © 2011 John Wiley & Sons, Ltd.     

A review of continental scale hydrological models and their suitability for drought forecasting in (sub-Saharan) Africa

The aim of this review is to provide a basis for selecting a suitable hydrological model, or combination of models, for hydrological drought forecasting in Africa at different temporal and spatial scales; for example short and medium range (1–10 days or monthly) forecasts at medium to large river basin scales or seasonal forecasts at the Pan-African scale. Several global hydrological models are currently available with different levels of complexity and data requirements. However, most of these models are likely to fail to properly represent the water balance components that are particularly relevant in arid and semi-arid basins in sub-Saharan Africa. This review critically looks at weaknesses and strengths in the representation of different hydrological processes and fluxes of each model. The major criteria used for assessing the suitability of the models are (1) the representation of the processes that are most relevant for simulating drought conditions, such as interception, evaporation, surface water-groundwater interactions in wetland areas and flood plains and soil moisture dynamics; (2) the capability of the model to be downscaled from a continental scale to a large river basin scale model; and (3) the applicability of the model to be used operationally for drought early warning, given the data availability of the region. This review provides a framework for selecting models for hydrological drought forecasting, conditional on spatial scale, data availability and end-user forecast requirements. Among 16 well known hydrological and land surface models selected for this review, PCR-GLOBWB, GWAVA, HTESSEL, LISFLOOD and SWAT show higher potential and suitability for hydrological drought forecasting in Africa based on the criteria used in this evaluation.     

Intercomparison across scales between remotely-sensed land surface temperature and representative equilibrium temperature from a distributed energy water balance model

Abstract

Quantifying the reliability of distributed hydrological models is an important task in hydrology to understand their ability to estimate energy and water fluxes at the agricultural district scale as well the basin scale for water resources management in drought monitoring and flood forecasting. In this context, the paper presents an intercomparison of simulated representative equilibrium temperature (RET) derived from a distributed energy water balance model and remotely-sensed land surface temperature (LST) at spatial scales from the agricultural field to the river basin. The main objective of the study is to evaluate the use of LST retrieved from operational remote sensing data at different spatial and temporal resolutions for the internal validation of a distributed hydrological model to control its mass balance accuracy as a complementary method to traditional calibration with discharge measurements at control river cross-sections. Modelled and observed LST from different radiometric sensors located on the ground surface, on an aeroplane and a satellite are compared for a maize field in Landriano (Italy), the agricultural district of Barrax (Spain) and the Upper Po River basin (Italy). A good ability of the model in reproducing the observed LST values in terms of mean bias error, root mean square error, relative error and Nash-Sutcliffe index is shown.

Editor Z.W. Kundzewicz; Associate editor D. Gerten     

Application of hydrological models with increasing complexity to subarctic catchments

Many available complex models tend to demand far more input information than is afforded by subarctic remote regions, such as vast areas of North America and Eurasia. A suitable level of model complexity must be sought so that the model matches both the availability of data, but also the spatial and temporal scale at which the major hydrological processes occur. The present paper describes a method to seek a level of model complexity suitable for simulation of runoff for a particular environment at a particular scale, commensurate with the limited data availability in remote areas. Processes in a simple model are stepwise replaced by representations taken from a more complex model, to achieve a balance between data requirement and model complexity at different spatial and temporal scales. The results suggest that it is not always necessary to switch directly from a simple hydrological model to complex one, because at particular spatial and temporal scales, runoff may be sensitive to only a number of processes.     

HydroBlocks: a field‐scale resolving land surface model for application over continental extents

Land surface spatial heterogeneity plays a significant role in the water, energy, and carbon cycles over a range of temporal and spatial scales. Until now, the representation of this spatial heterogeneity in land surface models has been limited to over simplistic schemes because of computation and environmental data limitations. This study introduces HydroBlocks – a novel land surface model that represents field‐scale spatial heterogeneity of land surface processes through interacting hydrologic response units (HRUs). HydroBlocks is a coupling between the Noah‐MP land surface model and the Dynamic TOPMODEL hydrologic model. The HRUs are defined by clustering proxies of the drivers of spatial heterogeneity using high‐resolution land data. The clustering mechanism allows for each HRU's results to be mapped out in space, facilitating field‐scale application and validation. The Little Washita watershed in the USA is used to assess HydroBlocks' performance and added benefit from traditional land surface models. A comparison between the semi‐distributed and fully distributed versions of the model suggests that using 1000 HRUs is sufficient to accurately approximate the fully distributed solution. A preliminary evaluation of model performance using available in situ soil moisture observations suggests that HydroBlocks is generally able to reproduce the observed spatial and temporal dynamics of soil moisture. Model performance deficiencies can be primarily attributed to parameter uncertainty. HydroBlocks' ability to explicitly resolve field‐scale spatial heterogeneity while only requiring an increase in computation of one to two orders of magnitude when compared with existing land surface models is encouraging – ensemble field‐scale land surface modelling over continental extents is now possible. Copyright © 2016 John Wiley & Sons, Ltd.     

Spatial scale effects on sediment concentration in runoff during flood events for hilly areas of the Loess Plateau,China

The spatial scale effect on sediment concentration in runoff has received little attention despite numerous studies on sediment yield or sediment delivery ratio in the context of multiple spatial scales. We have addressed this issue for hilly areas of the Loess Plateau, north China where fluvial processes are mainly dominated by hyperconcentrated flows. The data on 717 flow events observed at 17 gauging stations and two runoff experimental plots, all located in the 3906 km² Dalihe watershed, are presented. The combination of the downstream scour of hyperconcentrated flows and the downstream dilution, which is mainly caused by the base flow and is strengthened as a result of the strong patchy storms, determines the spatial change of sediment concentration in runoff during flood events. At the watershed scale, the scouring effect takes predominance first but is subordinate to the downstream dilution with a further increase in spatial scale. As a result, the event mean sediment concentration first increases following a power function with drainage basin area and then declines at the drainage basin area of about 700 km². The power function in combination with the proportional model of the runoff‐sediment yield relationship we proposed before was used to establish the sediment‐yield model, which is neither the physical‐based model nor the regression model. This model, with only two variables (runoff depth and drainage basin area) and two parameters, can provide fairly accurate prediction of event sediment yield with model efficiency over 0·95 if small events with runoff depth lower than 1 mm are excluded. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination and integration of appropriate spatial scales for river basin modelling

Appropriate spatial scales of dominant variables are determined and integrated into an appropriate model scale. This is done in the context of the impact of climate change on flooding in the River Meuse in Western Europe. The objective is achieved by using observed elevation, soil type, land use type and daily precipitation data from several sources and employing different relationships between scales, variable statistics and outputs. The appropriate spatial scale of a key variable is assumed to be equal to a fraction of the spatial correlation length of that variable. This fraction was determined on the basis of relationships between statistics and scale and an accepted error in the estimation of the statistic of 10%. This procedure resulted in an appropriate spatial scale for precipitation of about 20 km in an earlier study. The application to river basin variables revealed appropriate spatial scales for elevation, soil and land use of respectively 0·1, 5·3 and 3·3 km. The appropriate model scale is determined by multiplying the appropriate variable scales with their associated weights. The weights are based on SCS curve number method relationships between the peak discharge and some specific parameters like slope and curve number. The values of these parameters are dependent on the scale of each key variable. The resulting appropriate model scale is about 10 km, implying 225–250 model cells in an appropriate model of the Meuse basin meant to assess the impact of climate change on river flooding. The usefulness of the appropriateness procedure is in its ability to assess the appropriate scales of the individual key variables before model construction and integrate them in a balanced way into an appropriate model scale. Another use of the procedure is that it provides a framework for decisions about the reduction or expansion of data networks and needs. Copyright © 2003 John Wiley & Sons, Ltd.     

Hydrological modelling uncertainty analysis for different flow quantiles: a case study in two hydro-geographically different watersheds

This study focuses on analysis of hydrological model parameter uncertainty at varying sub-basin spatial scales. It was found that the variation in sub-basin spatial scale had little influence on the entire flow simulations. However, the different sub-basin spatial scales had a significant impact on the reproduction of the flow quantiles. The coarser sub-basin spatial scale provided a better coverage of most prediction uncertainty in observations. However, the finer sub-basin spatial scale produced the best single simulation output closer to the observations. In general, the optimal sub-basin spatial scales (ratio to the entire watershed size) in the two test watersheds were found to be in the ranges 14–19% and 2–4% for good simulation of high and low flows, respectively. It is therefore worthwhile to put more effort into reproducing different flow quantiles by investigating an appropriate sub-basin spatial scale.