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GIS in determination of the discharge hydrograph generated by surface runoff for small basins

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A hydrograph model is proposed in which the watershed is decomposed into subareas represented by individual cells. The watershed response is found for each cell and these responses are convoluted to produce the watershed runoff hydrograph. The cell to cell flow path to the watershed outlet is determined from a digital elevation model. A flow velocity for each cell is calculated using Manning's formula and used in determining the travel time of water through each cell. In this paper a simplified approach is used: the rainfall intensity is considered constant thorough the rainfall event. The velocity field, considered spatially varying but time invariant, and the flow path to the outlet are used to determine the runoff time from each cell to the outlet of the watershed. The responses of each cell with the same travel time to the outlet are summed to produce the hydrograph. An example is shown for the 11 km2 Pârâul Mare watershed in the Apuseni Mountains.
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GIS IN DETERMINATION OF THE DISCHARGE HYDROGRAPH
GENERATED BY SURFACE RUNOFF FOR SMALL BASINS
M. Domniţa1, A. I. Crăciun1, I. Haidu1
ABSTRACT:
A hydrograph model is proposed in which the watershed is decomposed into subareas
represented by individual cells. The watershed response is found for each cell and these
responses are convoluted to produce the watershed runoff hydrograph. The cell to cell flow
path to the watershed outlet is determined from a digital elevation model. A flow velocity
for each cell is calculated using Manning’s formula and used in determining the travel time
of water through each cell. In this paper a simplified approach is used: the rainfall intensity
is considered constant thorough the rainfall event. The velocity field, considered spatially
varying but time invariant, and the flow path to the outlet are used to determine the runoff
time from each cell to the outlet of the watershed. The responses of each cell with the same
travel time to the outlet are summed to produce the hydrograph. An example is shown for
the 11 km2râul Mare watershed in the Apuseni Mountains.
Keywords: hydrograph, runoff, small basin, GIS, rational method
1. INTRODUCTION
The unit hydrograph is a traditional method of representing the response at a watershed
outlet to a rainfall event over the watershed. This method suffers from the limitation that
the response function is considered constant over the watershed and does not consider the
spatially distributed nature of the watershed properties (Maidment, 1996).
The representation of a watershed as a grid of cells allows the user to calculate the
characteristics that determine a certain response for each cell of the grid. The question
examined in this paper is how to extend the hydrograph method in order to use the spatially
distributed characteristics of the watershed in calculating the response of the watershed to
the rainfall event.
A GIS allows the user to determine the base characteristics of flow through the
watershed using standard functions implemented in the system. Therefore, the flow path
from each cell to the outlet can be determined and the flow length can be calculated easily.
The only thing that needs special calculations is the speed of water passing through each
cell and the time that the water needs to pass through this cell.
Using the flow path and the time of translation through each cell total time of runoff to
the watershed outlet can be easily calculated. The response at the outlet at a certain time can
be determined using the total time of runoff from each cell and the quantity of water runoff
from each cell. The discharge at the outlet is calculated according to the intensity and
duration of the rainfall event and the behavior of runoff in the watershed during and after
this event.
The initial state of the watershed is considered to be a dry state and the discharge at the
outlet is calculated without taking into account the discharge existing at the beginning of
1 „Babeş-Bolyai” University, Faculty of Geography, 400006 Cluj-Napoca, Romania.
12 Geographia Technica, no.2, 2009
the rainfall. If the actual discharge before the rainfall can be measured, the result of this
study can be summed with the measured discharge to obtain the estimation of total
discharge during the rainfall.
The usage of this model is presented on the
Pârâul Mare watershed in the Apuseni
Mountains. This watershed is located in the
south-western region of the Cluj county, about
30 km west of Cluj-Napoca. This watershed is a
small part of the Căpuş watershed and represents
a zone with an area of ~11 km2 . The location of
the Pârâul Mare watershed related to the Cluj
county and the Căpuş catchment can be seen in
fig. 1.
The relief of the catchment is characteristic
to low altitude mountains, with the land covered
by forests and meadows. The altitude of the
basin varies from 609 to 910 m (Fig. 3a). The
slope of the hillslopes in the basin varies from 0
to 40 degrees (Fig. 3b).
The catchment does not include any major
towns or communes, and the main landuse is
characteristic to regions at this altitude. The land
cover includes agricultural areas, broad-leaved
and coniferous forests and pastures.
The rainfall event was a hypothetical storm event with a uniform rainfall intensity ower
a known period of time.
The catchment and three subwatersheds were selected to calculate the hydrographs.
The location and these subwatersheds are shown in fig. 2. The hydrographs were calculated
for all four of the watersheds and shown on the same figure for comparison.
Fig. 1 Location of the Pârâul
Mare watershed.
Fig. 2 Subwatersheds used for
calculating the hydrographs
M. Domniţa et colab. / GIS IN DETERMINATION OF DISCHARGE…________
13
After the functions used in calculating and plotting the hydrographs were implemented,
four of these hydrograph comparisons are presented with different rainfall intensities and
different storm duration.
2. METHODOLOGY
2.1. Initial data processing
The data needed to apply the method described above was obtained from
georeferencing and digitizing maps available for the zone where the model is applied. The
most important piece of data that is needed to create any hydrological model is the digital
representation of elevation (DEM).
A DEM can be obtained from different sources. The SRTM data offers worldwide
elevation data at 90m resolution and USA elevation data at 30m resolution (NASA SRTM
site). Another good source is the ASTER Global Digital Elevation Model (GDEM) released
to the public in June 2009, which offers 30m resolution for the entire world. Also, different
maps can be digitized to obtain a good DEM.
The DEM used in this study was obtained from digitizing the 1:25000 topographic
maps of Romania. The digitized contours were converted to a GRID DEM with a 10m cell
size. This DEM was used to obtain the slopes of the terrain in the studied region. The
obtained DEM and the slopes of the region can be seen in fig. 2.
a. b.
Fig. 3 DEM (a) and slope (b) of the Pârâul Mare watershed
Using the DEM, the terrain slope and the streams digitized in the area, some of the
characteristics of the watershed can be calculated. Using a grid DEM cell to cell flow paths
through the terrain can be defined by any common GIS. The most used algorithm is the 8
direction pour point algorithm which defines the flow from a cell to be in the direction of
14 Geographia Technica, no.2, 2009
the steepest descent to one of its eight neighbors (Fig. 4). Using the flow direction, the flow
path and length can be determined directly from the terrain with other GIS functions (Fig.
3). Using the flow direction grid the watershed corresponding to the user defined outlet
can be delineated. The outlet defined for this watershed was placed at the confluence
between Pârâul Mare and the Căpuş River, so the location where the model was applied
includes all the surface of the Pârâul Mare watershed.
128
1
2
8
16
32 64
4
1
122
3754
24 7 1
20 1
24 35
a.
b. c.
Fig. 4 Flow direction (a), flow direction grid (b), flow path (c)
(after D. R. Maidment)
The calculation of runoff speed and runoff curve numbers also requires data about the
types of soil and the land use types in the watershed.
The curve number index (CN) was determined according to the land use and the
hydrologic soil group. The land use was obtained from the CORINE Land Cover Databas
(CLC2000), created by the European Environment Agency. CLC data is available at 100
meters resolution for most European countries and offers data about land use. (CLC main
page). The determined curve number index can be seen in fig. 5b.
The soils were digitized from the 1:200.000 topographic map and separated in 4
hydrologic soil groups (HSG) according to the infiltration capacity. The hydrologic soil
groups were marked in the following way: Group A is sand, loamy sand or sandy loam
types of soils. It has low runoff potential and high infiltration rates (>7.62 mm); Group B is
silt loam or loam. It has a moderate infiltration rate when thoroughly wetted (3,81-7,62
mm); Group C soils are sandy clay loam. It has low infiltration rates when thoroughly
wetted (1,27-3,81 mm); Group D soils are clay loam, silty clay loam, sandy clay, silty clay
or clay. It has very low infiltration rates when thoroughly wetted (0-1,27 mm).
The runoff coefficient (α) is a parameter that will be used in the final calculation of
discharge. The GRID that represents this parameter was generated according to the land
use, slope and soil texture (Frevert tables) and can be seen in fig. 5a. The creation of this
GRID was made using different spatial analysis functions available in GIS (raster
reclassification, map algebra, conversions from shapefiles to raster). Some of the recent
studies that deal with the spatial representation of the α coefficient include: Păcurar (2005),
Crăciun , (2007), Magyari-Saska (2008), Bilaşco (2008).
M. Domniţa et colab. / GIS IN DETERMINATION OF DISCHARGE…________
15
a. b.
Fig. 5 Runoff coefficient (α) (a) and curve number index (b)
2.2 Travel time computation
The calculation of traveling time to the outlet from any cell needs information about
the runoff speed through each cell. The runoff speed can be calculated using Manning’s
formula for open streamflow.
The Manning Equation is the most commonly used equation to analyze open channel
flows. It is a semi-empirical equation for simulating water flows in channels and culverts
where the water is open to the atmosphere, i.e. not flowing under pressure, and was first
presented in 1889 by Robert Manning. The Manning Equation was developed for uniform
steady state flow.
The GaucklerManning formula states:
V = 1/n * Rh2/3 * S1/2 (1)
- where:
V - the cross-sectional average velocity (m/s)
N - Manning’s roughness coefficient
S is the slope of the water surface (m/m)
R is the hydraulic radius (ft, m)
Manning’s roughness coefficient (a coefficient for quantifying the roughness
characteristics of the channel) can be obtained from tables available in literature according
to the terrain on which the water flows (ex: Chow, 1988).
On the hillslopes, mean flow depth is used as an approximation of the hydraulic radius
because the flow width is significantly larger than the flow depth (Michaelides Katerina,
2002)
The runoff speed on the hillslopes was calculated using the Gauckler-Manning formula
in each cell. First, the Manning’s n number was calculated according to the landuse and soil
properties (Fig. 6a).
16 Geographia Technica, no.2, 2009
a. b.
Fig. 6 Manning’s n number (a), runoff travel time (b)
Once the flow velocity through each cell is known, the travel time through each cell
can be estimated as
t = D / V (2)
-where
t is the travel time through any given cell (s)
D is the distance traveled through that cell (m).
V is the equilibrium flow velocity through the same cell (m/s).
For orthogonal flow, the flow distance is the cell width (10 m), while for diagonal
flow, it is the 2 times cell width which yields 14.41 m in this study.
At this point, the travel time through each cell, the flow direction and the flow path are
all known. The cumulative travel time grid can be found by summing the travel times along
the path of flow.
The calculation of the cumulative travel time and the flow velocity through each cell
according to the flow length and Manning’s equation was implemented in a SAGA GIS
module by Victor Olaya (Olaya, 2004). This function was used to calculate the flow speed
and total travel time through the watershed (Fig. 6b)
Using the calculated Manning’s n number, the formula was applied for an average
rainfall intensity of 12 mm/h (0.2 mm/min) and 60mm/h (1 mm/min). This allowed the
calculation of the flow speed through each cell.
After applying Manning’s formula, the cells which had a calculated flow speed lower
than 0.05 m/s were automatically set at this value to avoid errors in calculating the
M. Domniţa et colab. / GIS IN DETERMINATION OF DISCHARGE…________
17
isochrones. The travel time through each cell led to easy calculation of the isochrones on
the studied area.
When the travel time from each cell to the outlet is known, the isochrones can be
determined by classifying the travel time grid in classes with a defined time interval (Fig.
7).
a. b.
Fig.7 15 min isochrones for I= 0.2 mm/min (a) and 1 mm/min (b)
When the travel time from each cell is known, the isochrones can be calculated by
classifying the travel time grid in classes representing a defined time interval. In fig 7
isochrones are shown for a rainfall intensity of 0.2 mm/min and 1 mm/min for the whole
watershed.
2.3 Discharge calculation
Calculation of the discharge from the watershed was made using the rational equation.
The Rational Method was first introduced in 1889. Although it is often considered
simplistic, it still is appropriate for estimating peak discharges for small drainage areas of
up to about 200 acres (80 hectares) in which no significant flood storage appears. The
Rational equation is the simplest method to determine peak discharge from drainage basin
runoff.
The rational method is appropriate for small watersheds (< 20 km2) where the intensity
of the rainfall can be considered constant in space and time (Şerban and colab., 1989;
Diaconu, Şerban , 1994).
In this case, the rational method was applied according to the equation (Păcurar,
2005):
18 Geographia Technica, no.2, 2009
izmiziz
iSQ
α
= 167,0
(3)
- where:
QizPeak discharge for each isochrone (m3/s)
SizIsochrone area (ha)
ImRainfall intensity (mm/min)
α izRational method medium runoff coefficient
Using the grid that represents the isochrones and the runoff coefficient grid, the area of
each isochrone and the medium runoff coefficient (α) for each isochrone was extracted. To
obtain these values, the zonal statistics function from ArcView wto generate the tables
containing the values automatically.
3. RESULTS
The discharge corresponding to each isochrone was determined using equation (3) and
the tabular data obtained with Zonal Statistics, as presented. The tabular data was imported
in Matlab to make the necessary operations and to plot the results.
The surfaces that contributes to runoff in each isochrone can be seen in the Time-Area
Diagram (Fig. 8 a,b). The Time-Area diagrams were generated in OpenOffice.org.
The examples show the TAD for a hypothetical rainfall intensity of 10 mm/h (a) and
60 mm/h (b).
a.
M. Domniţa et colab. / GIS IN DETERMINATION OF DISCHARGE…________
19
b.
Fig. 8 Time Area Diagrams for a rainfall intensity of 10 mm/h (a) and 60 mm/h (b)
The calculation of the final hydrographs was made by accumulating the discharge
from each isochrone during the rainfall event. After the rain stops, the value of the
discharge in each isochrone does not change anymore and the isochrones are eliminated in
chronological order.
The calculated values of the cumulated discharge for certain points in time
represent defined points within the hydrograph. These points are then interpolated to obtain
the hydrograph corresponding to the associated rainfall.
Examples are presented in fig. 9 a,b,c,d for different rainfall intensities and
rainfall durations. The hydrograph values from the watershed and the three subwatersheds
are plotted on the same figure for comparison.
a.
20 Geographia Technica, no.2, 2009
b.
Fig. 9 Discharge hydrograph, 0.2 mm rainfall for 60 min (a) and 90 min (b)
a.
M. Domniţa et colab. / GIS IN DETERMINATION OF DISCHARGE…________
21
b.
Fig. 9 Discharge hydrograph, 1 mm rainfall for 60 min (c) and 90 min (d)
4. CONCLUSIONS
This paper allowed us to use and understand the hydrological functions that exist in
different GIS packages and their usage. Different GIS packages offer different sets of
functions that can be used in hydrological modelling of any kind.
Some of these functions were presented and used through this study to obtain the
desired results (the hydrographs). The main data needed for the result was obtained in GIS
using these functions as presented but the data needed some processing in other software
packages to obtain the plots.
The data obtained by running the model (as shown in the last section) may be used
effectively by regional authorities for taking decision on certain water resources projects.
These include small structures on the river mainly for the use of the local community.
Some examples could be:
Bridges, Culverts, and Aqueducts, which need knowledge about the
anticipated high flood level
Levees for flood protection, whose design can be made with results of
this simulation and data about the shape of the stream bank.
The result of this study can be completed by adding some other parameters in
calculation.
The first parameter that has to be taken into account is the soil antecedent moisture
condition (AMC). This parameter affects the quantity and behavior of runoff on the
hillslopes.
The second parameter should be related to the rainfall. Although the basin is small, the
rainfall is never uniform in time and space. The rational method used is only appropriate for
rainfall which is constant in both space and time, so using this parameter requires changing
the main method of computing the discharge.
22 Geographia Technica, no.2, 2009
The model is oriented towards the use of regional level managers for taking a decision
on local water resources related projects or estimating different events.
REFERENCES
Bilaşco Şt., Haidu I., (2006), The Valuation of Maximum Runoff on Interbasinal Areas, Assisted by
GIS, Geographia Technica, ISSN 1842-5135, No.2, pag. 1-6, Cluj-Napoca.
Bilaşco Şt., (2008), Model G.I.S de estimare a coeficientului de scurgere adaptat după Frevert,
Geographia Napocensis, Nr. 1, pag. 38-45.
Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK,
2nd edition, ISBN 978 0 7506 5978 9
Chow, V. T., Maidment, D. R. & Mays, L. W. (1988) Applied Hydrology. McGraw-Hill, New York
Crăciun, A. I., (2007), Use G.I.S to establish some parameters useful to measure the time of
concentration and runoff coefficient, Geographia Technica, ISSN 1842-5135, No.2, pag. 12-19,
Cluj-Napoca.
Diaconu C., Şerban P., (1994), Sinteze şi regionalizări hidrologice, Edit. Tehnică, Bucureşti.
Maidment, D. R. (1993) Developing a spatially distributed unit hydrograph by using GIS, Application
of Geographic Information Systems in Hydrology and Water Resources Management (ed. by K.
Kovar & H. P. Nachtnebel), IASH Publ., 211, pag. 181-192.
Magyari-Saska Zs., (2008), Dezvoltarea algoritmilor S.I.G pentru calculul riscurilor geografice
naturale. Aplicaţie la Bazinul Superior al Mureşului, Teză de doctorat, UBB Cluj-Napoca.
Michaelides Katerina, Wainwright, J. (2002) Modelling the effects of hillslope-channel coupling on
catchment hydrological response, Earth Surface Processes and Landforms, 27, pag. 1441-1457.
Olaya, V. Hidrologia computacional y modelos digitales del terreno. Alqua. 536 pp. 2004
Păcurar V. D., (2005), Utilizarea Sistemelor de Informaţii Geografice în modelarea şi simularea
proceselor hidrologice, Edit. Lux Libris, Braşov.
Şerban P., Stănescu Al. V., Roman P., (1989), Hidrologie dinamică, Editura Tehnică Bucureşti.
Official NASA SRTM site - http://www2.jpl.nasa.gov/srtm/
Corine Land Cover main page - http://dataservice.eea.europa.eu/dataservice/
Open Channel Flow and Pressure Pipe Flow - http://www.lmnoeng.com/literature.htm
Acknowledgements:
“Investing in people”! PhD scholarship, Project co-financed by the European Social Fund,
SECTORAL OPERATIONAL PROGRAMME HUMAN RESOURCES DEVELOPMENT
2007 2013, Babeş-Bolyai University, Cluj-Napoca, Romania.
This work was also supported by Grant PN-II-ID-No.517 of CNCSIS Romania.
... Several studies concerning the risk of flash floods in the Apuseni Mountains (Romania), have described the initial versions and the evolution of a hydrological GIS model adapted for very small watersheds as the ones conducted by Domnița et al., 2009, Domnița et al. 2010a, 2010b, Crăciun, 2011Domnița, 2012, Gyori, 2013 The flow path and travel time can be easily computed based on velocity, this latter parameter being the only one that requires exclusive estimations (Domnița et al., 2009). Based on the travel time, the time-area diagram (TAD) can be derived, by dividing the watershed into zones of constant travel time (isochrones) and the excess runoff for each isochrones can then be routed to the catchment outlet. ...
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A new two-dimensional hydrological model has been developed that accounts for dynamic interactions between hillslope and channel flows. The model is specifically designed for semi-arid areas dominated by Hortonian overland flow, and has a dynamically active channel belt. Sensitivity analyses of the model have been carried out to assess the relative importance of topographic linkages, surface characteristics and rainfall characteristics on catchment hydrological response. Attribute sensitivity analyses suggest that hillslopes are more sensitive than floodplains to all parameters except surface roughness. However, decoupling through the presence of floodplains or other barriers will reduce the relative importance of the sensitivity of hillslope parameters. Spatial sensitivity analysis suggests that sensitivity to the spatial variability of infiltration decreases with an increase in the magnitude of the runoff event. On the other hand, variability in output discharge at the catchment outlet increases with an increase in the spatial variability of infiltration. Rainfall intensity is thus an important factor in controlling the overall coupling characteristics. Catchment runoff production is affected by a complex interaction of topographic, surface and rainfall characteristics. Copyright © 2002 John Wiley & Sons, Ltd.
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English Preface The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.arnoldpublishers.com/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est" ( ).
dataservice/ Open Channel Flow and Pressure Pipe Flow
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Official NASA SRTM site -http://www2.jpl.nasa.gov/srtm/ Corine Land Cover main page -http://dataservice.eea.europa.eu/dataservice/ Open Channel Flow and Pressure Pipe Flow -http://www.lmnoeng.com/literature.htm
Dezvoltarea algoritmilor S.I.G pentru calculul riscurilor geografice naturale. Aplicaţie la Bazinul Superior al Mureşului
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Use G.I.S to establish some parameters useful to measure the time of concentration and runoff coefficient
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