The Effect of Surface Texture on Evaporation, Infiltration and Storage Properties of Paved Surfaces

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1 The Effect of Surface Texture on Evaporation, Infiltration and Storage Properties of Paved Surfaces M. Mansell* and F. Rollet School of Engineering and Science, University of the West of Scotland, Paisley PA1 2BE, Scotland, UK *Corresponding author, ABSTRACT This paper concerns an investigation of evaporation, infiltration and detention storage on paved surfaces and the effect of surface texture and microtopography on these processes. A numerical model has been developed which represents the evaporation and infiltration processes on a nominally impervious surface as well as the depression storage due to the surface microtopography. The model was applied to semirandomly generated surfaces and the results show the relationship between surface microtopography and initial storage losses. KEYWORDS Depression storage; water balance; evaporation; initial losses. INTRODUCTION It is well known that the initial part of a rainstorm is lost in wetting the ground and filling depression storage. The amount and spatial distribution of depression storage is already recognised as being important in soils because of the effect on the yield of crops Moore and Larson (1979). However, in the water balance of urban areas evaporation is normally neglected and attention is normally focussed on the runoff from short duration rainfall. A constant runoff coefficient is often used and the initial depression storage is usually estimated using a regression of runoff against rainfall or from a simple empirical equation such as that used in the Wallingford Procedure (Hydraulics Research (1983)) where Depth of initial losses (D) = k / slope (1) and k is a coefficient reflecting the surface type and microtopography. Suggested values for k are m for paved and roof surfaces and m for pervious surfaces (Wallingford_Software (2004)). These methods will often overestimate runoff and underestimate the recharge to groundwater (Ragab, Rosier et al. (2003)) and do not reflect the complex pattern of urban water balance in the long term. Rodriguez, Morena et al. (2005), for example, have shown that there is a considerable variation in the runoff coefficient with different rainfall conditions while Davies and Hollis (1981) showed that when the water balance is considered over a long period, evaporation, infiltration and depression storage may be more significant than runoff. The amount of initial losses from rainfall depends partly on the surface texture and microtopography of the surface, which inhibits runoff and traps surface water and partly on the potential evaporation and infiltration. Evaporation, surface wetting and infiltration are a result of the dynamic interaction between the microclimate above the Mansell et al. 1

2 surface and the distribution of moisture on and within the surface. A typical sequence of events following rainfall on a surface with depressions is shown in Figure 1. rainfall (a) rainfall evaporation (b) infiltration rainfall (c) (d) Figure 1. Runoff Processes showing (a) initial surface wetting, (b) runoff accumulating in depression areas, (c) depression areas beginning to overflow, (d) areas progressively drying 2 Mansell at al

3 At the start of rainfall some moisture infiltrates into the top few millimetres of the surface material (surface wetting), which occurs in both permeable and notionally impermeable materials. Once this has occurred runoff tends to flow to local depressions, where some evaporation and infiltration through cracks and joints occurs. These depressions begin to progressively overflow and form larger depression areas, eventually leading to runoff. After the rain has ceased, some water will remain in the depressions and will continue to evaporate. Evaporation will also occur from the upper layer of the surface material when there is no surface water (surface drying). This study is concerned with modelling the development of runoff from both impermeable and permeable paved surfaces in a way which includes all the above processes. The modelling of the runoff process was divided into (i) the processes of evaporation and infiltration on a small area of surface and (ii) the storage and routing of the resulting runoff due to the surface microtopography. SURFACE PROCESSES The processes of evaporation and infiltration were modelled by a single tank storage model which is a simplified version of the three tank model described by Mansell and Rollet (2007). In this model the surface is represented by a storage tank with a capacity Smax mm. Water infiltrates into the surface at a rate given by I = ki * (1 S/Smax) where ki is an empirical coefficient and S is the storage (mm) at any time. If there is no surface water, water evaporates from the surface at a rate given by E = ke* E o * S/Smax where E o is the grass reference evapotranspiration derived from the Penman Monteith equation (Allen, Pereira et al. (1998)). Where there is rainfall the evaporation is assumed to be E = kr*e o It is often assumed that there is no evaporation during rainfall events but since the rainfall is aggregated over one hour time intervals, it is likely that evaporation will occur during short periods of no rainfall within this interval. Where there is no rainfall but there is some surface storage of water, it assumed that the evaporation will be E = kd*e o (where kd > ke). These processes are summarised in Figure 2 below. This model was calibrated with observed runoff from a concrete slab (Mansell and Rollet (2007)). Figure 3 shows the comparison between observed and modelled runoff and Table 1 shows the empirical coefficients. Mansell et al. 3

4 rainfall evaporation = kr*e o evaporation = kd*e o evaporation = ke*e o *S/Smax infiltration = ki*(1-s/smax) infiltration = ki*(1-s/smax) (a) (b) (c) Figure 2. Surface Process Model (a) with rainfall, (b) surface storage but no rainfall, (c) no storage or rainfall Observed and Model Runoff model obs cumulative runoff (mm) Time (hours) Figure 3 Table 1 Calibration of Surface Process Model Calibration Coefficients parameter calibrated value evaporation coefficient (kr) 0.3 evaporation coefficient (kd) 1.0 evaporation coefficient (ke) 0.02 infiltration coefficient (ki) 0.02 mm/hr storage depth 2.0 mm 4 Mansell at al

5 SURFACE ROUTING PROCESSES Several models have been developed to simulate the flow between cells of varying elevations. In each case the amount and direction of flow from a given cell is determined by the difference in the elevation between that cell and the adjoining cells. In some models eight flow directions (i.e. including diagonal directions) are permitted: others permit only four orthogonal directions. In both cases, where a cell is lower than any of its neighbours it becomes a depression cell. In some models the flow travels to one of the lower neighbouring cells with a probability which is proportional to the difference in height and in others the flow is distributed between lower neighbouring cells proportional to the power of the difference in heights. In this study a single direction drainage model based on the work of Moore and Larson (1979) was used, which assumes that flow from a cell travels to the lowest of four neighbouring cells. Thus each cell has only one outlet, unless it is a depression cell, but may have up to three inlets (four for a depression cell). The flow was calculated using a simple balance with no allowance for depth or velocity of flow. Intuitively it can be postulated that the amount of depression storage depends on the mean slope, the variability of the surface levels and the connectivity between depressions. In order to examine the effect of surface microtopography on depression storage a series of surfaces were generated with specific properties. The variables used to define a given surface were 1) the mean slope 2) the correlation between the levels of adjacent cells 3) the standard deviation of the levels The levels at the grid points were determined using a first order autoregressivemoving average process where the cell level was related to the mean of the four surrounded cell levels (z ) by a correlation coefficient (α) and a random component was also included using a normally distributed random variable (F) and a standard deviation (). e.g. the level of cell i,j is 2 z, ( i j = z + α z z) + Fσ 1 α where 1 z = i+ 1, j i 1, j i, j ( z + z + z z ) i, j 1 ž is the level generated on a plane with a slope m in the y direction. i.e. z = z + min n. dy. m where n is an integer (1, 2, 3,..N x ) The lower boundary elevations were all set to a minimum arbitrary level (z min ) and the edge boundaries were set to the mean slope. The cells outside the edge and top boundaries were set at a high value to prevent flow across these boundaries. The effect of the correlation between cells can be seen in Figure 4. Figure 4(a) shows a typical surface with zero correlation between adjacent cells while Figure 4(b) shows a similar surface with a correlation coefficient of 0.9. A value of 1 for the correlation coefficient would lead to a perfectly plane surface, regardless of the standard deviation (as would a standard deviation of zero). Mansell et al. 5

6 slope alpha sigma (a) slope alpha sigma (b) Figure 4. The Effect of Correlation, showing a generated surface with (a) zero correlation, (b) correlation of 0.9 between grid points. Each depression cell represents the focal point of a local depression or drainage sub area, which is defined by the cells draining to the depression cell. Each depression area will eventually overflow and drain to an adjacent area. The overflow levels between two areas were determined by the minimum levels of adjacent cells on the boundary between the areas. It was assumed that all the flow from a depression sub area will pass to only one area downstream (the area with the lowest overflow level) i.e. each area has only one outlet (Figure 5). The storage depth for each depression area is determined as the volume required to cause overflow to the adjacent 6 Mansell at al

7 (downstream) area. Some cells will drain directly to outlet cells and such areas were assumed to have no storage Figure 5. Individual Cells grouped to form depression areas The drainage areas can thus be linked together in a sequence of drainage runs forming a typical dendritic drainage pattern with outlets along the lower boundary. Spatially uniform rainfall was applied to each cell and the excess water from each depression area was added to the volume for the downstream area until an outlet was reached. For an outlet area the flow was counted as outflow. Since the outflow was assumed to occur almost instantaneously, it is implied that the time for overland flow is short compared with the rainfall time step. MODEL RESULTS The model was initially run using a generated surface 10m wide and 20m long with a 1m x 1m grid with slopes ranging from 1/200 to 1/2000 and standard deviations from 0 to 50mm and correlation coefficients from 0 to 0.7. For each combination 10 separate surfaces were generated with different sets of random numbers. The standard deviation can be regarded as the average depth of surface texture e.g. 50mm would be coarse gravel. Figure 6 shows the variation of depression storage with the reciprocal of slope for different values of standard deviation. Also shown on the graph is the relationship proposed by the Wallingford Procedure (Eq. (1)). It can be seen that there is a wide scatter of data within the 10 surfaces because of the difference in flow patterns, although the trend lines are fairly consistent. As would be expected, increasing the variability increases the depression storage but the mean slope is only significant at slopes steeper than about 1/1000. Mansell et al. 7

8 depression storage (mm) /slope sd=50mm wallingford model sd=20mm sd=10mm sd=5mm sd=2mm Figure 6. The variation of depression storage with surface variability The variation of depression storage with the correlation of grid points is shown in Figure 7. It can be seen that the correlation coefficient only has a significant effect at high values of correlation coefficient. As has been mentioned, a correlation coefficient of 1 would, in principle, give zero depression storage. 1.2 depression storage (mm) /slope c=0 c=0.2 c=0.5 c=0.7 Figure 7. The variation of depression storage with correlation coefficient The model was also run for a period of observed rainfall when other climatic variables were also observed and the reference evapotranspiration was calculated using the Penman Monteith equation. A typical output is given in Figure 8 which shows a period of rainfall followed by a short dry period. The runoff closely follows the 8 Mansell at al

9 rainfall and the effect of the evaporation and the change in moisture content in the upper layer of the material in the dry period can also be seen rain storage evap outflow depth (mm) hours Figure 8 A typical water balance showing evaporation and the variation in storage within the material COMMENTS AND CONCLUSIONS The investigation has shown that surface infiltration and evaporation can be significant components of the runoff process even for nominally impervious surfaces and the surface variability and the correlation between adjacent grid points both have a significant effect on the amount of depression storage. The standard deviation of the surface should be seen in the context of the grid size (1 metre). Thus a standard deviation of 50mm in 1metre would be the equivalent 0.5mm in a 10mm grid. A typical gravel texture might have a vertical variation of around 2mm with a grid scale of about 5mm (i.e. 400mm at a 1m grid). The effect of surface texture could therefore be investigated using these results although the units of depression storage would have to be adjusted. It should also be noted that increasing the correlation between adjacent grid points effectively increases the smoothing and therefore increases the horizontal scale of the variations. In principle the model could be applied on scales from metres to hundreds of metres but applying this model on a grid basis to a large urban catchment would require allowance to be made for the velocity of overland flow. Mansell et al. 9

10 REFERENCES Allen, R. G., L. S. Pereira, et al. (1998). Crop Evapotranspiration - Guidelines for Calculating Crop Water Requirements, Food and Agricultural Organisation. Davies, H. and T. Hollis (1981). Measurements of Rainfall-Runoff Volume and Relationships and Wtaer Balance for Roofs and Roads. Second Int. Conf. on Urban Storm Drainage, Illinois, USA. Hydraulics Research (1983). Design and Analysis of Urban Storm Drainage, Hydraulics Research. Mansell, M. G. and F. Rollet (2007). The Water Balance of Paved Surfaces in Urban Areas. SUDSnet Conference, Coventry. Moore, I. D. and C. L. Larson (1979). "Estimating Micro-Relief Surface Storage from Point Data." Trans. A.S.C.E. 20: Ragab, R., P. Rosier, et al. (2003). "Experimental study of water fluxes in residential areas: 2 Road infiltration, runoff and evaporation." Journal Hydrological Processes 17: Rodriguez, F., F. Morena, et al. (2005). "Development of a distributed hydrological model based on urban databanks - production processes of URBS." Water Science and Technology 52(5): Wallingford_Software (2004). InfoWorks Manual, Wallingford Software. 10 Mansell at al

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