GIS-based modeling of runoff source areas and pathways

GIS-based modeling of runoff source areas and pathways The application of runoff modeis that rely on calibration to future land use and cümate conditions is restncted to situations where the reaction of Hydrologic Response Units to environmental change is known. This limitation and the ensuing uncertainty of model results can be avoided when a risk-based approach to landscape and runoff analysis is taken. GIS-based landscape analysis provides the possibüity of assessing the risks associated with non-linear responses of Hydrologic Response Units to changing rainfall and land use. In this paper, a runoff module designed for IDRISI-Andes to calculate runoff amount and routing for Single or multiple rainfall events on a hülslope at small catchment scale is presented. The module is raster-based and uses layers with topographic and hydrological parameters to calculate a spatially distributed Output layer of surface runoff. Conceptually, the module extrapolates point data of Infiltration capacity onto a field or hülslope. A spatially distributed runoff map is calculated based on the addition of layers with rainfaü data and the routing of runoff through pathways connecting pixels in a digital elevation model. Unlike outlet-based runoff modefing, the need for parameterization of the catchment is kept to a minimum. The application of the RUNOFF module in a test area in the Eifel region of Germany indicated that runoff from grassland is sensitive to small increases in rainfall intensity and soü compaction. The spatial patterns of infiltration capacity also contnbute significantly to the non-linearity of the test area reaction to changing rainfall and soü hydrologic properties.


Introduction
In large parts of the world, frequency of rainfall events with extreme intensity and duration are likely to increase in the 21st Century (Intergovernmental Panel on Climate Change, IPCC, 2007). Such change in rainfaü characteristics represents a particular problem for modeling runoff, erosion and off-site water pollution because they often cause a non-linear reaction within fields, along hülslopes or small catchments, which will be referred to here as Hydrologic Response Units (HRUs) (Dünne & Aubry 1986). The runoff generating area increases with amount and intensity of rainfall, or both, and a larger part of a watershed becomes connected to the Valley Channel (Dünne & Black 1970). Conventional rainfall-runoff modeling, based on a relationship between rainfall and response unit outlet data, does not integrate these changes in HRU internal functioning (Beven & Binley 1992). Cümate and land use change will cause a quasi-permanent change of the relevant hydrologic properties and dominating processes in many HRUs in the 21st Century (Kuhn 2006). This condition of transition exacerbates the problems associated with the use of rainfallrunoff modeis, especially those relying on calibration using data sets collected under current or past climate and land use. Planning and management of the impact of Environmental Change therefore rely increasingly on so called Reduced Complexity Models (RCMs), developed to address a specific issue associated with Environmental Change (Schulz & Beven 2003;Van Oost et al. 2004). However, RCMs stül have to rely on empirical relationships based on past or present rainfall-runoff Observation. Their application to future conditions therefore may constitute an extrapolation beyond the ümits of the data set and may therefore often be restricted to situations where the reaction of HRUs to environmental change is known.
The systematic assessment of the risks associated with the impact of climate and land use change on runoff generation within HRUs offers an alternative to rainfaü-runoff modeis (e.g. Agnew et al. 2006). Instead of focusing on the prediction of discharge at a given catchment outlet point, the changes in rainfall-surface interaction, runoff generation and routing can be examined on a hülslope scale for different rainfall and land use scenarios. Conceptuaüy, this approach is based on upscaüng point data ofinfiltration capacity and the routing of runoff using a digital elevation model (DEM).
Unlike outlet-based runoff modeüng, the need for parameterization of the catchment is kept to a minimum. GIS-based runoff modeling and topography analysis provides the possibiüty of assessing the risks of changing HRU behavior by examining the spatial patterns of runoff generation and runoff routing within HRUs.
The objective of the work presented in this paper was to design and implement a module into the IDRISI GIS package for calculating runoff amount and routing for Single or multiple rainfall events on a hülslope and small catchment scale. The new RUNOFF tool is raster-based and uses topographic and hydrologjcal Parameters represented by different layers to calculate values for a spatially distributed Output layer of surface runoff. The underlying hydrologic model and the procedures followed for the identification of runoff pathways from the DEM, and a case study examining the risks of runoff generation on grassland from the Eifel region of Germany are presented.

Hydrologic model in RUNOFF
In this study, raster layers were used both to provide the input parameters and to represent the results. The basic hydrologic model for calculating surface runoff during a rainfall event used here is: Rainfall during event I Infiltration during event Infiltration was divided into two components: the final infiltration rate and absorption. Absorption includes aü the water which is either retained by the surface or infiltrates at a rate higher than the final infiltration rate (Figure 1). The simplicity of the model ümits its application to events where surface runoff dominates. Furthermore, the duration of the event has to be sufficiently long so that the entire runoff wave can reach the HRU outlet. The model was transferred into a raster GIS environment with the foüowing input layers (see also Figure 2):  Ienson and Domingue (1988). A pixel has eight neighboring pixels to interact with to form runoff, four of them are connected horizontally and vertically, and four others diagonally ( Figure 2). Assuming that aü pitfalls in a DEM have been removed, a pixel may receive runoff from up to seven of its eight neighbors. These neighbors must be upper neighbors with elevation values not less than that of the receiving pixel. A pixel can only contribute runoff to one of its neighbors, which is either lower or equal in elevation. Accounting for all possible scenarios for a pixel, the net amount of runoff a pixel carries to its lower neighbor pixel is given in equation 3: Where Qu is the runoff from adjacent upper pixels, Q0 is obtained using equation 2, and Qx is the runoff the current pixel passes on to its lower neighbor. The max Operator ümits Qx to a non-negative value when Q0 + Qu < 0. The interpretation of Qx is that a pixel may contribute runoff to a lower neighbor; it may take some or aü of the runoff it receives from its upper neighbors, 3.1 Removal of pitfalls The process of accumulating runoff assumes that a surface flow continues moving downward into one of its eight neighbors before it flows out of the study area or totally infiltrates if there is no more runoff. Within a watershed, any surface flow should get to the outlet of the watershed if it is not infiltrated on its pathway. A pitfall in a DEM is a local elevation minimum with no lower neighbors which prevents runoff from continuing flowing into any of its neighbors. Such pitfaüs cause erroneous runoff results because they act as unnatural sinks in the model. They therefore have to be removed from the DEM before runoff is calculated.
There are three Steps involved in this pitfall removal process. The first step is to identify pitfalls. Pixels located at the pitfalls are identified as those with elevation values at a local minima. The second step is to identify an optimal drainage path connecting a pitfall to its outlet, which would be a pixel on its path and with a lower elevation value than the pitfall pixel. A priority-first search algorithm (Sedgewick 1992 (modified) is that when there is a tie according to the first criterion, the path with a shorter distance has a higher priority. Finally, the third step is to lower the elevation of all pixels along the Optimum drainage path to create a consistent downward gradient between the original pit pixel and the outlet pixel. When the pitfaü removal process is completed, the resulting surface image ensures that any cell in the image can follow along a path to the edge of the image. A path consists of cells that are adjacent horizontally, vertically, or diagonally in the raster grid and decrease monotonically in value.

Identification of flow pathways
Flow pathways are derived from the pitfall-clear surface image using the approach described by Ienson and Domingue (1988). The example in Figure 2 shows the flow direction for a 3 x 3 pixel surface. One of the eight neighboring pixels is identified as the lower neighbor to flow into. Using the flow direction image, any pixel in the test area can find its path to get to the boundary of the study area. If the study area is a complete watershed, then all of the runoff should go through the outlet of the watershed. The outlet is located on the boundary of a watershed and it should have the lowest elevation value of the watershed.
3.3 Runoff calculation Every pixel in the study area is examined in a strict order. Whether a pixel is ready to be processed depends on all of its upper neighbors. If aü of its upper neighboring pixels have been processed, then the pixel's runoff value can be calculated using equation 2 and 3. Naturally, the starting pixels for a runoff process are those located either at the top of hiüs or ridges. A simplified example is illustrated in Figure 2 to demonstrate the methodology. 4 Potential impact of land use and climate change on runoff from grassland in the Eifel region, Germany

Study area
The new RUNOFF module was tested using data from a 3.45 ha grazing area near the town of Oberkail in the Eifel region of Germany ( Figure 3). The soil in the area is a silty Luvisol which has developed on upland plateaus formed by Triasic Muschelkalk (Werle 1978).
The area was chosen because it represents a typical upland part (350 to 400 m a.s.l.) of first order catchments contributing to the Mosel river, which has one of the highest flood frequencies of all rivers in Germany. The study area was split into seven units after a farmland consolidation scheme in the 1960s. Today, aü seven units have been amalgamated and are used by one farmer as meadow for silage production and grazing. The test area is surrounded by paved roads, which lie lower than the field and thus collect all the runoff from the field and provide a rapid connection to drainage Systems and the creek (Kailbach) in the main Valley. Understanding the interaction between surface and rainfall is of critical importance for assessing flood risk in the future. Currently, annual rainfall averages 920 mülimeters per year. Maximum daüy rainfall reaches 60 mm, and the maximum amount of event rainfall, i.e. during consecutive days with rain, is up to 220 mm in 10 days. Rainfall is rarely continuous over more than a few hours, however, information on rainfall intensity is scarce. The highest rainfall intensities are associated with convective thunderstorms. Local observations showed that amounts of up to 45 mm rainfall can faü in 30 minutes (May 13th 1993, pers. comm. D. Gerten), and peak intensities of 1.6 mm per minute (17.6.2005, N.J. Kuhn, unpublished data) have been observed. These intensities are sufficient to overcome the infiltration capacity of intensively used grassland, which in current planning is generally considered as not-contributing to surface runoff during summer thunderstorms (Maniak 2005). However, the magnitude and frequency of high intensity rainfall events will increase in the next 100 years (Intergov- Furthermore, consoüdation of farmland and the trend towards high-intensity fodder production for diary farming bear the risk of reducing infiltration capacity through soü compaction (Hörn et al. 1995) and removal of barriers between land use units. Therefore, the probabüity of surface runoff during summer thundershowers is ükely to increase. The results reported here aim at ülustrating the methodologjcal approach on one field, but could easüy be expanded to a larger area, for example aü fields connected to roads leading into the town of Oberkaü.

DEM, infiltration and initial absorption
The new RUNOFF module offers the possibiüty to assess the risk of surface runoff associated with extreme rainfall events and land use change. A DEM of the field near Oberkail was produced by digjtizing elevation from the 1:5000 orthophoto. Areas outside the test field were masked and excluded from the analysis (Figure 4). Elevation of a rim of one pixel width surrounding the field was reduced by 1 m to ensure that the effect of the lower lying roads on runoff routing was fully represented in the DEM. The roads did not receive any rainfall, their infiltration was set to 0 and absorption to 1 mm. Infiltration data collected along the grass field were used to produce infiltration and absorption layers for the RUNOFF module. Infiltration was measured along a five-point transect across the test field, with three repücates along a 100 m Une on each point. Tests were conducted using a spray nozzle mounted 2 m above the soil surface, supplied from a 500 üter pump barrel hooked to a tractor. The rainfall had an intensity of 5 mm per minute and covered a circle of 2.5 m diameter. In the center of the wetted circle, a 0.5 by 0.5 meter plot was separated and runoff was coüected in a trough. Infiltration tests were conducted on field fresh soil moisture conditions to ensure similar effects of soil moisture on infiltration capacity. The Urning of the infiltration tests simulates a scenario where a high intensity thunder shower follows a short wet spell, which is a typical weather pattern caused by mid-latitude cyclones during the summer. Soil moisture can be easüy corrected for differences relative to field capacity based on preceding weather conditions. Based on these tests, infiltration curves were calculated for each site. Final infiltration was relatively uniform across the test field (1.5 mm min4), while absorption was lowest at the steeper mid-slope section (6 mm) in comparison to the upland plateau (12 mm) and the Hat lower section of the testfield (8 mm).

Rainfall scenarios
The aims of the simulations conducted with RUNOFF were twofold. First, to identify how total runoff from the grassland would increase with rainfall intensity and reduced infiltration and absorption, and second, how source area distribution and Connectivity within the test field would change for the simulated scenarios.
The peak event magnitudes and intensities observed between 1988 and 2003 were used as a baseline rainfall event, set for a duration of 30 minutes at an intensity of 1.5 mm per minute. These values correspond to both the highest observed amount of rainfaü in 30 minutes and the peak rainfaü intensity during thundershowers. From this baseline scenario, rainfall intensity, infiltration, and absorption were modified to assess the sensitivity of runoff to future climatic conditions and soil compaction. In addition, runoff during three consecutive ten-minute intervals with different rainfall intensity and gradually Alling absorption was tested.The füll details of the simulated scenarios are given in Table 1.
Total runoff from the test area was calculated from the accumulated mülimeter of rainfall value of the lowest lying pixel. The value of the pixel was converted into liters by multiplying the accumulated milfimeters of rainfaü by the size of the pixel. The size of a pixel was determined by dividing the size of the field by the number of pixels in the field. One pixel had an area of 0.16 m2. Accordingly, a mülimeter of rainfall on a pixel corresponds to 0.16 liters. The amount of runoff that would be generated on the roads during the simulated events was used as a reference for the significance of the grassland contribution to surface runoff. area occurred for scenario C4, when infiltration and absorption had been reduced to 50% of their observed values. The greatest increase in runoff coefficient and relative importance of grassland contribution to total runoff developed during scenarios D2 and D3 when preceding rainfall had saturated the absorption capacity of the soil. Overall, contributions from the grassland exceeded road runoff for scenario A3 (double rainfall intensity), B3 (50% infiltration), C3 and C4 (reduced absorption and infiltration), and D2 and D3 (saturation of absorption during preceding showers). Overall, it is noteworthy that small changes in infiltration and absorption caused equal or greater increase in runoff than increasing rainfall intensity. While the test field generated up to nearly three times more runoff than the road, the effect was not linearly related to changes in rainfall intensity, infiltration and absorption. For example, increasing rainfall intensity by 20% between scenarios AI and A2 led to a 48-fold increase of runoff. The non-linearity is attributed to the Saturation of the absorption layer and effects of the spatial pattern of absorption on runoff generation and continuity. The runoff patterns in the Output images explain the non-linearity. For scenario AI, most runoff originates from the steeper middle sections of the slope (Figure 5), while the upper and lower sections do not contribute significantly. A further increase of rainfall intensity (scenario A2) fills up absorption in the lower slope section, effectively reducing infiltration capacity, and now both the upper and lower sections of the slope generate runoff. Calculating runoff using a spatially averaged absorption value confirms the significance of using spatially varying absorption (Table 3). For most scenarios, an average absorption value leads to an overestimation of runoff, in particular for the events with only small increase in intensity or decrease of absorption or infiltration. The overestimation is attributed to ignoring the sink in the lower section of the slope. The underestimation for events D2 and D3 (3%) is caused by a slight difference in the actual surface area of the grass field and the surface area of the masked DEM used by RUNOFF.

Conclusions
The new RUNOFF module in IDRISI provides an integrated tool for analyzing the risks associated with Hydrologic Response Unit reaction to environmental change. By adding layers for rainfall intensity and duration, the impact of changes in event magnitude of future rainfall on patterns of runoff generation, routing and Connectivity within HRUs can be simulated. The results of the study conducted on the Eifel grass field demonstrate the use of RUNOFF. Non-linear responses of runoff are closely related to the spatial pattern of runoff source and sink areas. Runoff on Eifel grassland appears to be more sensitive to a reduction of infiltration and absorption, and thus land management practices, than rainfall intensity. While certainly preliminary, the results demonstrate the use of RUNOFF in risk assessment studies by indicating that the study area appears to be close to becoming a Scenario Q(i) in rainfall intensity coincide.
The new RUNOFF offers the possibiüty to use directly measured infiltration data. While any direct measurement provides only a benchmark value for the area it represents, the approach has the benefit of being directly observed, rather than derived indirectly from outlet data and soü and land use information (e.g. United States Department of Agriculture (USDA) curve approach). This has several advantages. First of all, the effects of land management, for example soil conservation practices, can be incorporated directly into the infiltration and absorption layer, rather than being ignored or estimated using empirical approaches.
Second, infiltration measurements can be combined with remotely sensed data and further landscape analysis to determine the extent of areas with similar infiltration and absorption (e.g. Jensen 2007). Embedding a runoff model in a GIS also aüows a relatively easy integration of man-made runoff pathways, such as roads, ditches, separating walls and hedges, into the surface DEM. Finally, the ünk between infiltration test and change in patterns and pathways of runoff generation is much more direct and transparent than for outletdata based runoff modeis. This is of particular importance when stakeholders have to be informed about the effects of climate and land use change on runoff.
Further studies using RUNOFF wül involve studying the effects of changing rainfall characteristics, the reduction of soü storage capacity due to compaction by heavy machinery and inappropriate tülage practices.
Special attention will be gjven to the use of remotely sensed data in combination with infiltration tests. These studies wül also allow the Separation of climate from land cover/land management change signal in runoff.
ity of assessing the risks associated with non-linear responses of Hydrologic Response Units to changing rainfall and land use. In this paper, a runoff module designed for IDRISI-Andes to calculate runoff amount and routing for Single or multiple rainfall events on a hülslope at small catchment scale is presented. The module is raster-based and uses layers with topographic and hydrological parameters to calculate a spatially distributed Output layer of surface runoff. Conceptually, the module extrapolates point data of Infiltration capacity onto a field or hülslope. A spatially distributed runoff map is calculated based on the addition of layers with rainfaü data and the routing of runoff through pathways connecting pixels in a digital elevation model. Unlike outlet-based runoff modefing, the need for parameterization of the catchment is kept to a minimum. The application of the RUNOFF module in a test area in the Eifel region of Germany indicated that runoff from grassland is sensitive to small increases in rainfall intensity and soü compaction.
The spatial patterns of infiltration capacity also contnbute significantly to the non-linearity of the test area reaction to changing rainfall and soü hydrologic properties.
La carte du ruissellement est alors basee sur Taddition des couches de donnees de pluviometne ainsi que sur l'orientation des ecoulements ä travers des chenaux dans un modele numenque de terrain. Contrairement ä la modelisation du ruissellement basee sur les exutoires, la necessite de parametrer la portion de terrain est reduite au minimum. Lapplication du module RUNOFF sur une zone test de la region de l'Eifel en