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1.
Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

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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.  相似文献   

4.
This paper compares artificial neural network (ANN), fuzzy logic (FL) and linear transfer function (LTF)‐based approaches for daily rainfall‐runoff modelling. This study also investigates the potential of Takagi‐Sugeno (TS) fuzzy model and the impact of antecedent soil moisture conditions in the performance of the daily rainfall‐runoff models. Eleven different input vectors under four classes, i.e. (i) rainfall, (ii) rainfall and antecedent moisture content, (iii) rainfall and runoff and (iv) rainfall, runoff and antecedent moisture content are considered for examining the effects of input data vector on rainfall‐runoff modelling. Using the rainfall‐runoff data of the upper Narmada basin, Central India, a suitable modelling technique with appropriate model input structure is suggested on the basis of various model performance indices. The results show that the fuzzy modelling approach is uniformly outperforming the LTF and also always superior to the ANN‐based models. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

5.
Because the traditional Soil Conservation Service curve‐number (SCS‐CN) approach continues to be used ubiquitously in water quality models, new application methods are needed that are consistent with variable source area (VSA) hydrological processes in the landscape. We developed and tested a distributed approach for applying the traditional SCS‐CN equation to watersheds where VSA hydrology is a dominant process. Predicting the location of source areas is important for watershed planning because restricting potentially polluting activities from runoff source areas is fundamental to controlling non‐point‐source pollution. The method presented here used the traditional SCS‐CN approach to predict runoff volume and spatial extent of saturated areas and a topographic index, like that used in TOPMODEL, to distribute runoff source areas through watersheds. The resulting distributed CN–VSA method was applied to two subwatersheds of the Delaware basin in the Catskill Mountains region of New York State and one watershed in south‐eastern Australia to produce runoff‐probability maps. Observed saturated area locations in the watersheds agreed with the distributed CN–VSA method. Results showed good agreement with those obtained from the previously validated soil moisture routing (SMR) model. When compared with the traditional SCS‐CN method, the distributed CN–VSA method predicted a similar total volume of runoff, but vastly different locations of runoff generation. Thus, the distributed CN–VSA approach provides a physically based method that is simple enough to be incorporated into water quality models, and other tools that currently use the traditional SCS–CN method, while still adhering to the principles of VSA hydrology. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

6.
《水文科学杂志》2013,58(4):725-740
Abstract

Appropriate representation of landscape heterogeneity at small to medium scales is a central issue for hydrological modelling. Two main hydrological modelling approaches, deductive and inductive, are generally applied. Here, snow-cover ablation and basin snowmelt runoff are evaluated using a combined modelling approach that includes the incorporation of detailed process understanding along with information gained from observations of basin-wide streamflow phenomena. The study site is Granger Basin, a small sub-arctic basin in the mountains of the Yukon Territory, Canada. The analysis is based on the comparison between basin-aggregated and distributed landscape representations. Results show that the distributed model based on “hydrological response” landscape units best describes the observed magnitudes of both snow-cover ablation and basin runoff, whereas the aggregated approach fails to represent the differential snowmelt rates and to describe both runoff volumes and dynamics when discontinuous snowmelt events occur.  相似文献   

7.
This paper presents a top–down approach for soil moisture and sap flux sampling design with the goal of understanding ecohydrologic response to interannual climate variation in the rain–snow transition watersheds. The design is based on a priori estimates of soil moisture and transpiration patterns using a physical distributed model, Regional Hydro‐Ecologic Simulation System (RHESSys). RHESSys was initially calibrated with existing snow depth and streamflow data. Calibrated model estimates of seasonal trajectories of snowmelt, root‐zone soil moisture storage, and transpiration were used to develop five hydrologic similarity indicators and map these at (30 m) patch scale across the study watershed. The partitioning around medoids‐clustering algorithm was then used to define six distinctive spatially explicit clusters based on the five hydrologic similarity indictors. A representative site within each cluster was identified for sampling. For each site, soil moisture sensors were installed at the 30‐ and 90‐cm depths and at the five soil pits and a sap flux sensor at the averaged‐size white fir tree for each site. The model‐based cluster analysis suggests that the elevation gradient and topographically driven flow drainage patterns are the dominant drivers of spatial patterns of soil moisture and transpiration. The comparison of model‐based calculated hydrological similarity indicators with measured‐data‐based values shows that spatial patterns of field‐sampled soil moisture data typically fell within uncertainty bounds of model‐based estimates for each cluster. There were however several notable exceptions. The model failed to capture the soil moisture and sap flux dynamics in a riparian zone site and in a site where lateral subsurface flow may not follow surface topography. Results highlight the utility of using a hypothesis driven sampling strategy, based on a physically based model, for efficiently providing new information that can drive both future measurements and strategic refinements to model inputs, parameters, or structure that might reduce these errors. Future research will focus on strategies for using of finer scale representations of microclimate, topography, vegetation, and soil properties to improve models.  相似文献   

8.
Hydrological models at a monthly time‐scale are important tools for hydrological analysis, such as in impact assessment of climate change and regional water resources planning. Traditionally, monthly models adopt a conceptual, lumped‐parameter approach and cannot account for spatial variations of basin characteristics and climatic inputs. A large requirement for data often severely limits the utility of physically based, distributed‐parameter models. Based on the variable‐source‐area concept, we considered basin topography and rainfall to be two major factors whose spatial variations play a dominant role in runoff generation and developed a monthly model that is able to account for their influences in the spatial and temporal dynamics of water balance. As a hybrid of the Xinanjiang model and TOPMODEL, the new model is constructed by innovatively making use of the highly acclaimed simulation techniques in the two existing models. A major contribution of this model development study is to adopt the technique of implicit representation of soil moisture characteristics in the Xinanjiang model and use the TOPMODEL concept to integrate terrain variations into runoff simulation. Specifically, the TOPMODEL topographic index ln(a/tanβ) is converted into an index of relative difficulty in runoff generation (IRDG) and then the cumulative frequency distribution of IRDG is used to substitute the parabolic curve, which represents the spatial variation of soil storage capacity in the Xinanjiang model. Digital elevation model data play a key role in the modelling procedures on a geographical information system platform, including basin segmentation, estimation of rainfall for each sub‐basin and computation of terrain characteristics. Other monthly data for model calibration and validation are rainfall, pan evaporation and runoff. The new model has only three parameters to be estimated, i.e. watershed‐average field capacity WM, pan coefficient η and runoff generation coefficient α. Sensitivity analysis demonstrates that runoff is least sensitive to WM and, therefore, it can be determined by a prior estimation based on the climate and soil properties of the study basin. The other two parameters can be determined using optimization methods. Model testing was carried out in a number of nested sub‐basins of two watersheds (Yuanjiang River and Dongjiang River) in the humid region in central and southern China. Simulation results show that the model is capable of describing spatial and temporal variations of water balance components, including soil moisture content, evapotranspiration and runoff, over the watershed. With a minimal requirement for input data and parameterization, this terrain‐based distributed model is a valuable contribution to the ever‐advancing technology of hydrological modelling. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

9.
A conceptual water‐balance model was modified from a point application to be distributed for evaluating the spatial distribution of watershed water balance based on daily precipitation, temperature and other hydrological parameters. The model was calibrated by comparing simulated daily variation in soil moisture with field observed data and results of another model that simulates the vertical soil moisture flow by numerically solving Richards' equation. The impacts of soil and land use on the hydrological components of the water balance, such as evapotranspiration, soil moisture deficit, runoff and subsurface drainage, were evaluated with the calibrated model in this study. Given the same meteorological conditions and land use, the soil moisture deficit, evapotranspiration and surface runoff increase, and subsurface drainage decreases, as the available water capacity of soil increases. Among various land uses, alfalfa produced high soil moisture deficit and evapotranspiration and lower surface runoff and subsurface drainage, whereas soybeans produced an opposite trend. The simulated distribution of various hydrological components shows the combined effect of soil and land use. Simulated hydrological components compare well with observed data. The study demonstrated that the distributed water balance approach is efficient and has advantages over the use of single average value of hydrological variables and the application at a single point in the traditional practice. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

10.
The hydrological sensitivities to long-term climate change of a watershed in Eastern Canada were analysed using a deterministic watershed runoff model developed to simulate watershed acidification. This model was modified to study atmospheric change effects in the watershed. Water balance modelling techniques, modified for assessing climate effects, were developed and tested for a watershed using atmospheric change scenarios from both state of the art general circulation models and a series of hypothetical scenarios. The model computed daily surface, inter- and groundwater flows from the watershed. The moisture, infiltration and recharge rate are also computed in the soil reservoirs. The thirty years of simulated data can be used to evaluate the effects of climatic change on soil moisture, recharge rate and surface and subsurface flow systems. The interaction between surface and subsurface water is discussed in relation to climate change. These hydrological results raise the possibility of major environmental and socioeconomic difficulties and have significant implications for future water resource planning and management. © 1997 John Wiley & Sons, Ltd.  相似文献   

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Although hydrologic responses to land cover changes are often studied using a paired watershed approach, it is not feasible to assess the hydrological effects of many different patterns of land cover alteration by empirical studies alone. An alternative is to use well validated, spatially explicit, physically based numerical models to estimate watershed storage and flux dynamics. The objectives of this study were to assess the sensitivity of watershed flow regimes to several spatial and temporal patterns of forest harvest and recovery in a snow‐dominated mountain watershed. The Distributed Hydrology Soil‐Vegetation Model (DHSVM) was parameterized using 1998–2007 climate data for the 28‐km2 Mica Creek Experimental Watershed (MCEW), a headwater catchment in the inland Pacific Northwest. The modelling experiment indicated that clear‐cutting the entire watershed would increase runoff volume by 79% and 5th percentile flows by 68%. Hydrologic recovery resulting from forest regeneration after clear‐cut harvesting is expected to take up to 25 years to return to baseline conditions, and 50 years to fully recover to preharvest conditions. A more realistic harvesting scenario where the watershed was gradually harvested in a series of clear‐cut blocks allowing for subsequent regeneration to occur was also assessed. This approach reduced the magnitude of hydrologic alteration. Analysis of several other scenarios, defined by aspect, elevation, and distance to the stream network, revealed that flow regime was more sensitive to the amount of alteration rather than pattern and landscape position of disturbance. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

13.
This study evaluates two (of the many) modelling approaches to flood forecasting for an upland catchment (the River South Tyne at Haydon Bridge, England). The first modelling approach utilizes ‘traditional’ hydrological models. It consists of a rainfall–runoff model (the probability distributed model, or PDM) for flow simulation in the upper catchment. Those flows are then routed to the lower catchment using two kinematic wave (KW) routing models. When run in forecast‐mode, the PDM and KW models utilize model updating procedures. The second modelling approach uses neural network models, which use a ‘pattern‐matching’ process to produce model forecasts.Following calibration, the models are evaluated in terms of their fit to continuous stage data and flood event magnitudes and timings within a validation period. Forecast times of 1 h, 2 h and 4 h are selected (the catchment has a response time of approximately 4 h). The ‘traditional’ models generally perform adequately at all three forecast times. The neural networks produce reasonable forecasts of small‐ to medium‐sized flood events but have difficulty in forecasting the magnitude of the larger flood events in the validation period. Possible modifications to the latter approach are discussed. © Crown copyright 2002. Reproduced with the permission of Her Majesty's stationery office. Published by John Wiley & Sons, Ltd.  相似文献   

14.
Soil moisture has a pronounced effect on earth surface processes. Global soil moisture is strongly driven by climate, whereas at finer scales, the role of non‐climatic drivers becomes more important. We provide insights into the significance of soil and land surface properties in landscape‐scale soil moisture variation by utilizing high‐resolution light detection and ranging (LiDAR) data and extensive field investigations. The data consist of 1200 study plots located in a high‐latitude landscape of mountain tundra in north‐western Finland. We measured the plots three times during growing season 2016 with a hand‐held time‐domain reflectometry sensor. To model soil moisture and its temporal variation, we used four statistical modelling methods: generalized linear models, generalized additive models, boosted regression trees, and random forests. The model fit of the soil moisture models were R2 = 0.60 and root mean square error (RMSE) 8.04 VWC% on average, while the temporal variation models showed a lower fit of R2 = 0.25 and RMSE 13.11 CV%. The predictive performances for the former were R2 = 0.47 and RMSE 9.34 VWC%, and for the latter R2 = 0.01 and RMSE 15.29 CV%. Results were similar across the modelling methods, demonstrating a consistent pattern. Soil moisture and its temporal variation showed strong heterogeneity over short distances; therefore, soil moisture modelling benefits from high‐resolution predictors, such as LiDAR based variables. In the soil moisture models, the strongest predictor was SAGA (System for Automated Geoscientific Analyses) wetness index (SWI), based on a 1 m2 digital terrain model derived from LiDAR data, which outperformed soil predictors. Thus, our study supports the use of LiDAR based SWI in explaining fine‐scale soil moisture variation. In the temporal variation models, the strongest predictor was the field‐quantified organic layer depth variable. Our results show that spatial soil moisture predictions can be based on soil and land surface properties, yet the temporal models require further investigation. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

15.
The analysis of the physical processes involved in a conceptual model of soil water content balance is addressed with the objective of its application as a component of rainfall–runoff modelling. The model uses routinely measured meteorological variables (rainfall and air temperature) and incorporates a limited number of significant parameters. Its performance in estimating the soil moisture temporal pattern was tested through local measurements of volumetric water content carried out continuously on an experimental plot located in central Italy. The analysis was carried out for different periods in order to test both the representation of infiltration at the short time‐scale and drainage and evapotranspiration processes at the long time‐scale. A robust conceptual model was identified that incorporated the Green–Ampt approach for infiltration and a gravity‐driven approximation for drainage. A sensitivity analysis was performed for the selected model to assess the model robustness and to identify the more significant parameters involved in the principal processes that control the soil moisture temporal pattern. The usefulness of the selected model was tested for the estimation of the initial wetness conditions for rainfall–runoff modelling at the catchment scale. Specifically, the runoff characteristics (runoff depth and peak discharge) were found to be dependent on the pre‐event surface soil moisture. Both observed values and those estimated by the model gave good results. On the contrary, with the antecedent wetness conditions furnished by two versions of the antecedent precipitation index (API), large errors were obtained. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
Integrated river basin models should provide a spatially distributed representation of basin hydrology and transport processes to allow for spatially implementing specific management and conservation measures. To accomplish this, the Soil and Water Assessment Tool (SWAT) was modified by integrating a landscape routing model to simulate water flow across discretized routing units. This paper presents a grid‐based version of the SWAT landscape model that has been developed to enhance the spatial representation of hydrology and transport processes. The modified model uses a new flow separation index that considers topographic features and soil properties to capture channel and landscape flow processes related to specific landscape positions. The resulting model is spatially fully distributed and includes surface, lateral and groundwater fluxes in each grid cell of the watershed. Furthermore, it more closely represents the spatially heterogeneous distributed flow and transport processes in a watershed. The model was calibrated and validated for the Little River Watershed (LRW) near Tifton, Georgia (USA). Water balance simulations as well as the spatial distribution of surface runoff, subsurface flow and evapotranspiration are examined. Model results indicate that groundwater flow is the dominant landscape process in the LRW. Results are promising, and satisfactory output was obtained with the presented grid‐based SWAT landscape model. Nash–Sutcliffe model efficiencies for daily stream flow were 0.59 and 0.63 for calibration and validation periods, and the model reasonably simulates the impact of the landscape position on surface runoff, subsurface flow and evapotranspiration. Additional revision of the model will likely be necessary to adequately represent temporal variations of transport and flow processes in a watershed. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

17.
Soil moisture is widely recognized as a fundamental variable governing the mass and energy fluxes between the land surface and the atmosphere. In this study, the soil moisture modelling at sub‐daily timescale is addressed by using an accurate representation of the infiltration component. For that, the semi‐analytical infiltration model proposed by Corradini et al. (1997) has been incorporated into a soil water balance model to simulate the evolution in time of surface and profile soil moisture. The performances of this new soil moisture model [soil water balance module‐semi‐analytical (SWBM‐SA)] are compared with those of a precedent version [SWBM‐Green–Ampt (GA)] where the GA approach was employed. Their capability to reproduce in situ soil moisture observations at three sites in Italy, Spain and France is analysed. Hourly observations of quality‐checked rainfall, temperature and soil moisture data for a 2‐year period are used for testing the modelling approaches. Specifically, different configurations for the calibration and validation of the models are adopted by varying a single parameter, that is, the saturated hydraulic conductivity. Results indicate that both SWBMs are able to reproduce satisfactorily the hourly soil moisture temporal pattern for the three sites with root mean square errors lower than 0.024 m3/m3 both in the calibration and validation periods. For all sites, the SWBM‐SA model outperforms the SWBM‐GA with an average reduction of the root mean square error of ~20%. Specifically, the higher improvement is observed for the French site for which in situ observations are measured at 30 cm depth, and this is attributed to the capability of the SA infiltration model to simulate the time evolution of the whole soil moisture profile. The reasonable models performance coupled with the need to calibrate only a single parameter makes them useful tools for soil moisture simulation in different regions worldwide, also in scarcely gauged areas. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

18.
The present study demonstrates a spatially distributed application of a field‐scale annual soil loss model, the modified‐MMF (MMMF), to a large watershed using hydrological routing techniques, remote sensing data and geospatial technologies. In this study, the MMMF model is implemented after incorporating the corrections suggested in recent literature along with appropriate modifications of the model to suit the agro‐climatological conditions prevailing in most parts of India. Sensitivity analysis carried out through an Average Linear Sensitivity approach indicates that the model outputs are highly sensitive to soil moisture (MS), bulk density (BD), effective hydraulic depth (EHD), ground cover (GC) and settling velocity for clay (VSc). During calibration and validation, the performance evaluation statistics are mostly in the range of very good to satisfactory for both runoff and soil loss at the watershed outlet. Even spatial validation of the results of intermediate processes in the water phase and the sediment phase, although qualitative, seems to be reasonable and rational. Furthermore, the soil erosion severity analysis for different land‐uses existing in the watershed indicates that about 90% of the watershed area, especially that occupied by agricultural lands, is vulnerable to the long‐term effects of soil erosion. Copyright © 2018 John Wiley & Sons, Ltd.  相似文献   

19.
A process‐based, spatially distributed hydrological model was developed to quantitatively simulate the energy and mass transfer processes and their interactions within arctic regions (arctic hydrological and thermal model, ARHYTHM). The model first determines the flow direction in each element, the channel drainage network and the drainage area based upon the digital elevation data. Then it simulates various physical processes: including snow ablation, subsurface flow, overland flow and channel flow routing, soil thawing and evapotranspiration. The kinematic wave method is used for conducting overland flow and channel flow routing. The subsurface flow is simulated using the Darcian approach. The energy balance scheme was the primary approach used in energy‐related process simulations (snowmelt and evapotranspiration), although there are options to model snowmelt by the degree‐day method and evapotranspiration by the Priestley–Taylor equation. This hydrological model simulates the dynamic interactions of each of these processes and can predict spatially distributed snowmelt, soil moisture and evapotranspiration over a watershed at each time step as well as discharge in any specified channel(s). The model was applied to Imnavait watershed (about 2·2 km2) and the Upper Kuparuk River basin (about 146 km2) in northern Alaska. Simulated results of spatially distributed soil moisture content, discharge at gauging stations, snowpack ablations curves and other results yield reasonable agreement, both spatially and temporally, with available data sets such as SAR imagery‐generated soil moisture data and field measurements of snowpack ablation, and discharge data at selected points. The initial timing of simulated discharge does not compare well with the measured data during snowmelt periods mainly because the effect of snow damming on runoff was not considered in the model. Results from the application of this model demonstrate that spatially distributed models have the potential for improving our understanding of hydrology for certain settings. Finally, a critical component that led to the performance of this modelling is the coupling of the mass and energy processes. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

20.
This paper reports results from field experiments and hydrological modelling on the dynamics of runoff generation in highly convergent parts of the landscape in a logged and burnt eucalypt forest in south‐eastern Victoria, Australia. Large‐scale rainfall simulation experiments were conducted to explore runoff generating mechanisms from harvested areas, and to assess the effectiveness of standard water quality protective measures, here a disturbed filter strip, in preventing accession of sediment to near‐stream areas. We then examined the likely effects of varying antecedent moisture conditions on surface and subsurface runoff generating mechanisms. Very small volumes of surface runoff were generated only at very high rainfall intensity rates that exceeded a 100 year recurrence interval event during the simulated experiments. There was little or no identifiable impact of either compaction from logging operations or fire‐induced hydrophobicity on surface infiltration or generation of surface runoff. Measured soil hydraulic properties and soil depths explained the paucity of surface runoff, and the dominance of subsurface storm flow as the prime runoff generating mechanism. Deep lateral subsurface flow was observed from the cut‐face of a fire access track and into a streamhead downslope of the experimental plots. Water balance modelling using Topog_Dynamic indicated the conditions under which saturated overland flow in this environment could be generated are rare, but that care should be taken in siting of roads and tracks in lower parts of convergent landscapes. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

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