Mathematical Models in Flood Modelling - Case Study Example

Urban storm water Your name Name of Assignment 4th November, 2016 Table of Contents Introduction 3 Plan of subdivision 3 Plan for sub-areas 4 Longitudinal section 4 References 12 Introduction The main aim is to design rainfall water to avoid flood in residential area. The data used is for 3 year to accurately predict the volume of water, design pits, times of concentration and required time. To begin with determining peak runoff rates as well as runoff volumes is essential in the models that are used in determining pipe velocities, capacity and invert levels. This is information can also be used in designing water and soil conservation in flooding areas. The base flow and direct runoff information is usually recorded from the area of study and calculated from automatic recorders that are put there. This paper is going to study flood mathematical models that are used in flood modeling Plan of subdivision Plan for sub-areas Longitudinal section Calculation Time of Concentration         1. Surface Description (Table 3-1)         2. NRCS Curve Number 52       3. S = 1000/CN - 10 9.23       4. Hydraulic Length, Lh 163 m     5. Watercourse Land Slope, Y (%) 0.6135 %     6. La = Lh0.8 * (S + 1)0.7 / (1900 * Y0.5) 0.20 hr     7. Tc = 1.67 * La 0.34 hr = 20.18 min Calculation to determine land slope:         Elevation of high point = 26.0 m     Elevation of low point = 25.0 m     Difference in Elevation = 1.0 m     Slope (based on cell B9, Hyd Length) = 0.006135 m/m = 0.613497 % Head Loss -Pipes Flowing Full                                 Pipe Length (l) = 83 m                       Pipe Span (d) = 1 m         Pipe Rise (d) = 1 m         Manning's n = 0.036           Pipe Flow (Q) = 0.80 cubic m/second                     Upstream Invert = 4.80 m         Downstream Invert = 4.30 m         Slope (s) = 0.0060                         Head Loss = 712022.54 m - based on velocity                   Head Loss = 711661.08 m - based on Q                     Velocity (V) = 0.20 fps - based on physical slope     Head Loss = 0.50 feet - based on velocity and slope   Q = 0.00 cfs - pipe flowing full                   Using the data provided, the observed data event has been separated base flow and direct runoff separately. This has been done to provide losses associated to the rainy water. In determining the base flow, it is assumed that the gradient does not affect the base of river. This is comparable to dry season when the flow rate is different. If we look at the initial SDM one can note that a small change leads to increase in flow rate per second. Rainfall/runoff model treats each catchment as a single unit, allowing some of the model parameters to be evaluated from physical catchment data. Rainfall/runoff model shows the SDM as well as the actual evapotranspiration and the runoff components such as interflow, base flow and overland flow. This shown below From the figures above the discharge shows that cease to a high flow was a common occurrence period under study and not month that does not high flow rate. The groundwater recession curve is a characteristic of the particular catchment in which it was recorded, and some part of this curve will be a constituent of the total hydrograph. It is possible to attempt to relate the runoff component of the record of discharge against time and the fraction of the rainfall hyetograph (called the net or effective rainfall) that produced it. In order to estimate the net (effective) rainfall from the total it is necessary to separate out the quantity of rainfall that becomes evapotranspiration, infiltration and surface detention in pools. In view of the difficulties in obtaining separate measurements of these components they are often referred to collectively as losses. Hence: Net precipitation = total precipitation – losses (2) Where the volume of net precipitation = the total volume of runoff. Estimation of the losses for a storm on a particular catchment is usually based on the analysis of existing rainfall and record of discharge against time. Direct runoff and Base flow hydrographs developed in this paper have no much difference with other mathematically developed models although this was related to a specific case. A table of pit sub catchment details- total lot area and the road reserve area to each pit. area cumul. inlet pipe slope Length increment area time tC i Qdes Dpipe Dstd* (Vfull = 1) Line m ha ha C min min mm/hr m3/s mm mm m/m x6-46 9 0.0088 0.008775 0.35 10 20 122.37 0.01 750.0 825 0.001387 pit 9-1 9 0.0081 0.02 0.35 10 20.1 122.35 0.03 675.0 750 0.001575 pit 9-2 9 0.0074 0.02 0.35 20 20.2 122.33 0.04 675.0 675 0.001812 pit 9-3 9 0.0074 0.03 0.35 15 20.3 122.31 0.05 675.0 675 0.001812 pit 9-4 9 0.0074 0.04 0.35 10 20.3 122.29 0.06 675.0 675 0.001812 pit 9-5 9 0.0074 0.05 0.35 20 20.4 122.28 0.07 600.0 675 0.001812 pit 9-6 9 0.0054 0.05 0.35 15 20.5 122.26 0.08 375.0 375 0.003968 pit 9-7 9 0.0054 0.06 0.35 10 20.5 122.24 0.09 375.0 375 0.003968 pit 9-8 9 0.0054 0.06 0.35 15 20.6 122.23 0.09 300.0 375 0.003968 pit 9-9 9 0.0054 0.07 0.35 10 20.7 122.21 0.10 375.0 375 0.003968 pit 9-10 9 0.0054 0.07 0.35 20 20.8 122.19 0.11 300.0 375 0.003968 pit 9-11 9 0.0054 0.08 0.35 15 20.8 122.17 0.12 300.0 300 0.005343 pit 9-12 9 0.0054 0.08 0.35 16 20.9 122.16 0.13 300.0 300 0.005343 pit 9-13 9 0.0054 0.09 0.35 20 21.0 122.14 0.13 300.0 300 0.005343 surface slope Vfull Qfull tpipe Ground Elev, m Invert Elev, m Cover Depth, m m/m m/s m3/s min upper lower upper lower upper lower 0.00222 1.637905 0.88 0.1 36.62 36.60 34.295 34.283 2.18 1.49 0.03333 1.819894 0.80 0.1 37.49 37.19 35.240 35.226 1.35 1.21 0.00778 1.926947 0.69 0.1 38.51 38.44 36.335 36.319 1.34 1.45 0.12111 2.047381 0.73 0.1 39.90 38.81 37.725 37.709 2.46 0.43 0.00778 2.047381 0.73 0.1 39.18 39.11 37.005 36.989 1.64 1.45 0.00778 2.047381 0.73 0.1 39.31 39.24 37.135 37.119 1.67 1.45 0.00778 2.047381 0.23 0.1 37.79 37.72 35.915 35.879 2.12 1.47 0.00778 2.047381 0.23 0.1 37.96 37.89 36.085 36.049 1.78 1.47 0.01778 2.047381 0.23 0.1 38.18 38.02 36.305 36.269 1.65 1.38 0.00778 2.047381 0.23 0.1 38.23 38.16 36.355 36.319 1.59 1.47 0.13667 2.047381 0.23 0.1 39.51 38.28 37.635 37.599 2.24 0.31 0.00556 2.047381 0.14 0.1 38.44 38.39 36.640 36.592 2.08 0.00 0.02778 2.047381 0.14 0.1 38.77 38.52 36.970 36.922 1.35 0.00 0.01 2.047381 0.14 0.1 39.01 38.92 37.210 37.162 1.09 0.00 derivation of IDF equation [i = a/(b + )] for T = 100 years, 10 min <  < 30 min:     , min 1/i, hr/mm i, mm/hr     10 0.00833 120 slope = 0.000016 = 1/a   5 0.00769 130   20 0.00800 125 a = 1/slope = 63901   15 0.00769 130   10 0.00769 130 intercept = 0.0079 = b/a   20 0.00794 126   15 0.00794 126 b = a*intercept = 502.2   10 0.00781 128   5 0.00741 135   10 0.00769 130   20 0.00769 130   15 0.00735 136   5 0.00741 135   5 0.00769 130 I have attached excel for file for calculation The models more closely approximated the observed ones in the Southern Australia catchment than in the Lagan catchment. In all the observed hydrographs, the base flow was separated by first plotting the recession limb on semi-logarithmic paper and the end of the direct runoff contribution was marked at the point where the recession curve changed to a straight line. The use of the SCS curve number model with curve numbers determined using storm rainfall and runoff data, gave satisfactory results compared to the poor results from curve numbers derived from catchment characteristics documented in the literature. The success of the model in the catchment showed that the model can be easily extrapolated into neighboring catchments for estimating runoff volumes. However, the model requires some rainfall-runoff data for parameter estimation. The use of the method of moments in the Nash model for parameter estimation was found satisfactory in the catchment while in the Lagan catchment geomorphic relationships were found superior. Although the former required some data, the latter enabled the model to be applied in ungauged catchments. The kinematic wave model performed well in the southern Australia but less satisfactorily in the Lagan. This indicated that it required calibration in a catchment where it is intended for use. Although both models can be used for direct runoff hydrograph generation, the Nash model seemed more accurate and versatile than the kinematic wave model as indicated by the results of this study. References Clewett, J. F., N. M. Clarkson, et al. 2003. RainmanStreamFlow (version 4.3): A comprehensive climate and streamflow analysis package on CD to assess seasonal forecasts and manage climatic risk., Department of Primary Industries, Queensland. Connell Wagner Pty Ltd, 2001. Flood investigation of the communities of Beswick, Mataranka, Djilkminggan and Elsey – Study Report, unpublished. Dooge, J. C. I. 1977. Problems and methods of rainfall-runoff modelling. Ciriani, T.A., Maione, U. and Wallis, J.R. (Eds) Mathematical Models for Surface Water Hydrology. Proceedings of the Workshop held at the IBM Scientific Center, Pisa, Italy. Wiley, London.pp 71-108. Institute of Hydrology, 1999.Flood Estimation Handbook.Institute of Hydrology, Wallingford, UK. Gaffield, Stephen, J., Goo, Robert, L., Richards, Lynn, A., and Jackson, Richard, J. “Public Health Effects of Inadequately Managed Stormwater Runoff.” American Journal of Public Health 93. 9 (2003): 1527-1533. Print. Wilson, E M. 1990. Engineering Hydrology. London: MacMillan. Read More