surface runoff
DESCRIPTION
To estimate surface runoff this information is useful.TRANSCRIPT
# THE UNIT HYDROGRAPH
Surface hydrology
Surface runoff
Prof. W. Bauwens
Dpt. of Hydrology and Hydraulic Engineering
CONTENT
11INTRODUCTION
12DEFINITIONS & SYMBOLS
23HYDRODYNAMIC METHODS
34THE GENERAL HYDROLOGIC SYSTEM
34.1The general hydrologic system model
34.2Linear, time invariant systems
45RESPONSE FUNCTIONS OF LINEAR SYSTEMS
45.1The impulse response function
65.2The step response function
65.3The pulse response function
75.4Comments
86THE UNIT HYDROGRAPH
86.1Introduction
96.2Convolution
116.3 De-convolution
116.4 Standard unit hydrographs
116.4.1Introduction
126.4.2The standard unit hydrograph of Harms and Verworn
146.5The time-area method
167LINEAR RESERVOIR MODELS
167.1Introduction
167.2The single linear reservoir
177.3Reservoirs in series
197.4The linear channel
19REFERENCES
PRIVATE
1INTRODUCTION
The net rainfall over a river basin will produce the storm runoff hydrograph. As the storm runoff is generated from different locations within the basin, a time distribution of the storm runoff with time will be observed. To calculate the storm hydrograph in a location along the river, it is necessary to account for the transport of the water from within the river basin towards this location.
Although the transport mechanisms may be complex and consist of flow over the surface, flow within ditches and rivers and subsurface storm flow, this transport is here referred to as surface runoff.
This section provides an overview of different methods that can be used to this purpose:
Hydraulic methods
Linear models such as the unit hydrograph and linear reservoir models
Non- linear hydrologic methods
2DEFINITIONS & SYMBOLSSymbolUnit (e.g.)
HWater depthm
iPrecipitation intensity
Input ratemm / hour
IPrecipitation depth mm
nNet precipitation intensitymm / hour
NNet precipitation depthmm
p(t)Pulse response function
q(Storm) runoff rate
Response ratel/s ; m3/s
QRunoff volumel ; m3
s(t)Step response function
SStorage volumemm; m3
SmaxMax. storage capacitymm
SoSurface slope-
SfFriction slope-
SwWater surface slope-
tTimehour
tcConcentration timehour
TReturn periodyear
u(t)Impulse response function
xCo-ordinate
yCo-ordinate
zDepthm
3HYDRODYNAMIC METHODS
The surface runoff can be calculated by means of the equations for gradually varied flow of Barre de Saint Venant. More information on these equations is provided in the section on flood routing.
For use of the equations, the subbasin is divided in grid cells. Each cell is considered as a plane with given slopes in the x- and y-direction. The flow over such a plane is then calculated by the diffusive wave or cinematic wave approximation of the equations of de Saint Venant.
For the diffusive wave approximation, the equations are:
Conservation of mass (Continuity):
[3.1]
Conservation of momentum:
and
[3.2]
with
x & y
=the horizontal Cartesian co-ordinates [m]
H(x,y,t)
=the local water depth
[m]
n(x,y,t)
=the net rainfall intensity
[m/s]
Sox & Soy(x,y)
=the surface slope (x & y direction) [-]
Sfx & Sfy(x,y)
=the friction slopes [-]
t
=the time
[s]
u & v(x,y,t)
=the flow velocity (x & y direction) [m/s]
The relations between the flow velocities and the water depths are calculated by means of an equation for the calculation of the friction losses, e.g. the equation of Strickler-Manning
and
[3.3]
with
k(x,y)
= the Stickler roughness coefficient
[m0.33/s]
Swx & Swy(x,y)
= the slope of the water surface
[-]
4THE GENERAL HYDROLOGIC SYSTEM
4.1The general hydrologic system model
The change in time of the amount of water stored in a hydrologic system (a river basin, a reservoir, a river, a river reach,), S, is related to the rates if inflow and outflow by the continuity equation, which expresses the conservation of mass :
[4.1]
1In general, the storage can also be related to the inflow and outflow rates and to their derivatives with time. This relation is called the storage equation:
[4.2]
2where :
i(t)
= the inflow rate
( m3/s );
q(t)
= the outflow rate
( m3/s );
S(t)
= the storage
( m3 );
The function f in the latter equation is a function of the nature of the considered hydrological system (surface runoff, river routing,).
4.2Linear, time invariant systems
If the storage equation is of the linear type
[4.3]
with the parameters a and b constants, then the system is linear and time invariant.
The attribute time invariant indicates that the way the system processes input to output does not change with time.
The assumption of linearity involves that the principles of proportionality and superposition may be applied:
Proportionality: if q is the output of the system for input I, then c*q is the output for input c*i
Superposition: if q1 and q2 are the outputs of the system for the inputs i1 and i2 respectively, then q1+q2 will be the output for the input i1+i2.
5RESPONSE FUNCTIONS OF LINEAR SYSTEMS
Linear time invariant systems are completely and uniquely characterised by their response functions. The most common response functions are:
the impulse response function
the step response function
the pulse response function
5.1The impulse response function
The impulse response function describes the response of a linear system to a unit impulse. The latter is defined as an input of unit amount that is applied instantaneously.
Be ( the moment at which the impulse is applied. The response of the system at time t ( later than ( ) is described by u(t-(), where t-( is the time lag since the impulse was applied ( Fig. 5.1 ).
Fig.5.1: The impulse response function
Considering the principles of proportionality and superposition applicable to linear systems, the response of a combination of discrete pulses may be determined. E.g. the combined response q(t) of an impulse of amount 2 at time (1 and an impulse of amount 3 at time (2 is given by (see also Fig.5.2) :
q(t) = 2 u(t-(1) + 3 u(t-(2)
Fig.5.2: The response for 2 impulses: superposition and proportionality In analogy, a continuous input can be considered as a sum of infinitesimal impulses.
Let i(() represent the continuous input rate to the linear system. The amount of input concentrated between the time ( and (+d( after the start of the input may be considered as such an infinitesimal impulse (Fig.5.3). The latter amount equals i(() d(.
Fig.5.3 : ConvolutionThe response resulting from this impulse is i(() u(t-() d(.
The response to the continuous input rate may be found by integrating the responses to the pulses that constitute the input. An integral of this type is called a convolution integral.
[5.1]
5.2The step response function
The step response function describes the response of the linear system to a unit step input.
The unit step input is defined as
i(t) = 0 for t < 0
i(t) = 1 for t > 0
where i represents the input rate.
[5.2]
Applying Eq.5.1 with the latter input, the unit step response function is defined as
The step response function at time t thus corresponds to the integral of the impulse response function up to that time (Fig.5.4). By substituting l = t-( in Eq.5.2:
[5.3]
4Fig.5.4: The step response function
5.3The pulse response function
The pulse response function describes the response of the linear system to a unit pulse input.
The unit pulse input is defined as i(t) = 0
for t < 0
i(t) = 1/(tfor 0 M or for m = 1 to n if n < M.
The procedure is illustrated on Fig.6.1.
Fig.6.1: Discrete convolution
Remark
Note that the ordinates of the unit hydrograph have the dimensions L2/T. By multiplying the flows by (t and diving them by the basin area, they can be expressed as equivalent amounts of runoff per unit surface area, in mm. In this case, the U-values become dimensionless. Moreover, the sum of the U-values then equals 1.
6.3 De-convolution
De-convolution is the operation whereby the unit hydrograph is defined, based on (a) know net rain hyetograph(s) and (an) observed storm hydrograph(s).
Several techniques can hereto be used:
Gauss-elimination
Matrix-inversion
Linear regression
Linear or non-linear optimisation
The Gauss-elimination
Consider M net rainfall pulses and N values of the storm runoff. The following set of equations may be written:
[6.6]
U1 may be derived from the first equation. With U1 known, U2 can be derived from the second equation, etc.
The problem with the Gauss elimination method comes from the fact that the set of equations is over-determined: the set contains N equations for N-M+1 unknowns (Check this). Consequently, there is no unique solution to the problem.
Partly due to the de-convolution method and partly due to the approximate nature of the unit hydrograph method (definition of the net rainfall, linear system,) it is also often observed that the shape of the UH obtained by the Gauss method is not physically sound.
6.4 Standard unit hydrographs
6.4.1Introduction
If the UH cannot be determined by de-convolution due to lack of data, standard unit hydrographs can be used as an alternative. Hereby the (major) characteristics of the UH are determined, based on the knowledge of global characteristics of the river basin such as the surface area, the slope, the length of the river, Obviously, such standard UH rely on empirical data and their applicability is limited to basins with similar characteristics as the ones that were used to set up the empirical relations.
Well known methods are the Sneyder Unit Hydrograph (1938) equations derived from measurements in the Appalache mountains and the SCS Unit Hydrograph (1972).
As an illustration, the standard unit hydrograph of Harms and Verworn is presented.
6.4.2The standard unit hydrograph of Harms and Verworn
Harms and Verworn ( 1984 ) defined a standard unit hydrograph for European urban areas up to a few ha, with the following characteristics ( Fig.6.2 ) :
a linear increase up to the peak qp at the time tp;
an exponential recession, similar to the linear reservoir model;
end of the recession at 0.01 * qp
Fig.6.2 :The standard unit hydrograph of Harms and Verworn
The hydrograph can be made dimensionless by defining a dimensionless flow q' and a dimensionless time t' :
[6.7]
10
[6.8]
11and
[6.9]
where :
A= the area ( m2 )
tL= the inlet time (s)
q= the flow ( l/s )
I= the effective rainfall amount( mm )
k= the recession parameter ( 1/s ).
The analysis of about 20 dimensionless unit hydrographs for different catchments showed the following mean values for the dimensionless peak flow, time to the peak and recession parameter :
q'p = 0.96
t'p= 0.49
k'= 0.82
The latter values define the standard unit hydrograph. Using these values, the unit hydrograph for any given area can be reconstructed, using the transformations:
[6.10]
12
[6.11]
13
[6.12]
14The latter relation is used to certify a runoff volume of 1 mm. The time to peak should be rounded to a multiple of UH time base when calculating the recession constant k.
[6.13]
15The values of the rising limb of the hydrograph can be calculated by:
and the decreasing part
[6.14]
16The number of the ordinates is given by the minimum q for the decreasing part: q > 0.01 * qp.
The lag-time tL is calculated by empirical formulae :
for impervious areas :
[6.15]
with :
tL= the lag time
(minutes);
au= a calibration parameter
(default = 11 minutes );
A= the area
(ha);
L= the length of the subcatchment (m);
lf= the flow-path
(m).
for pervious areas:
[6.16]
17with :
tL= the lag time
(minutes);
ad= a calibration parameter
(default = 2.3 minutes);
ie= the effective rainfall intensity
(mm/min);
S0= mean surface slope
(%);
k= roughness coefficient
= 1/ n with n = Manning roughness.
6.5The time-area method
The time-area allow to define the UH, based on the construction of the isochrones within the river basin. The latter isochrones are lines that connect the points at an equal travel time from the basin outlet (Fig.6.3a).
Fig.6.3 : The time-area method
Knowing the isolines, a graph showing the cumulative basin area as a function of the travel time can be constructed (Fig.6.3b). It is further assumed that this curve represents the S-hydrograph of the river basin.
Finally, the UH is obtained by differentiating the S-hydrograph (Fig.6.3.c).
The definition of the isochrones requires a good understanding of the flow conditions within the river basin. Hereby, the surface flow, as well as the river flow has to be accounted for.
An approximate method consists of the drawing of the isolines that connect the points that are at the same flow distance from the outlet. In the latter case, the x-scale on Fig. 6.3b would be a distance scale. When assuming a uniform flow velocity over the basin, the distance scale can be transformed into a time scale by accounting for the travel time of the river basin.
7LINEAR RESERVOIR MODELS
7.1Introduction
For the reservoir models, the river basin is considered to act on the net rainfall as a reservoir or as a series of reservoirs in series or in parallel.
The linear reservoir models are based on the continuity equation
[7.1]
18and on a storage equation
[7.2]
19where :
i(t)
= the inflow rate
(m3/s);
q(t)
= the outflow rate
(m3/s);
S(t)
= the storage
(m3);
K
= the reservoir time constant
(s);
7.2The single linear reservoir
Combining Eqs.7.1 and 7.2, with x = 1 yields
[7.3]
20Starting the inflow at time t0 with outflow q0, the general solution of Eq.7.3 is :
[7.4]
21For t0 = q0 = 0 and for i = constant, Eq.7.4 reduces to :
[7.5]22The instantaneous unit hydrograph of this model can be expressed as :
[7.6]
Consider now a pulse with duration tp and intensity 1. For t ( tp equation 7.5 remains valid and thus:
[7.7]
For t > tp, i = 0. The general solution given by eq. 7.4 (with to = tp ) yields:
[7.8]
with qo the flow at time tp. Note that we hereby recognise the exponential recession discussed for the separation of the stormflow and the baseflow.Parameters
The model only requires the knowledge of the parameter K. If no other data are available for the determination of K, empirical relations can be used.
Viessman ( 1968 ) established the following empirical relation for K :
[7.9]
23where :
L= the maximum flow length
(m)
n= the Manning surface roughness coefficient (-)
s= the mean slope along the flow path
(-)
The equation is applicable to urbanised areas up to 4000 m2 and slopes from 1 to 8 %.
For 21 French urban catchments ( up to 100 ha ), Desbordes (1978) found:
[7.10]
24where :
K= the storage parameter
(min.);
A= the catchment area
( ha );
TR= the duration of the peak rainfall intensity
(min.);
ITR = the rainfall volume over TR
( mm );
a= area contributing to runoff / total area.
(-)
It should be mentioned that the presence of ITR in this relation makes the model nonlinear. Also, the empirical relation reflects both the surface runoff and the sewer flow.
7.3Reservoirs in series
If the shape of the hydrograph can not be represented by a single reservoir, two or more of these reservoirs can be put in series (Fig.7.1 ).
Cnsider a system at rest ( at time t0 = 0, q0=0 ). The response of the upper reservoir for a step input with intensity = 1 is given by eq. 7.5:
[7.11]25To calculate the outflow from the second reservoir, the outflow from the upper reservoir is considered as the input of the second reservoir.
The general equation for the outflow of the second reservoir (if the system is at rest at t=0) is obtained from eq.7.4:
[7.12]
Substituting eq. 7.11 in eq. 7.12 yields
[7.13]
etc.
Fig.7.1: Linear reservoirs in series
A special case of the reservoirs in series is the Nash cascade. Hereby, a catchment is conceptualised by a series of n identical reservoirs.
With K the storage parameter for the n reservoirs, the instantaneous unit hydrograph of this model may then be expressed as:
26[7.14]
Note that n does not have to be an integer and (n-1)! may be replaced by the Gamma function.
Exercise:
Prove that the IUH for the Nash cascade is given by the previous equation
7.4The linear channel
Reservoir models generate an immediate response to an input. For hydrologic systems, a delay is often observed between the input and the output. To represent this phenomenon, a linear channel model can be used to perform a simple translation between the input and the output:
[7.15]
27where :
i(t)
= the inflow rate
(m3/s);
q(t)
= the outflow rate
(m3/s);
t
= the translation time
(s).
The model is often used in combination with reservoir models, to delay the input to the reservoir or to delay the reservoir output.
REFERENCES
Chow, V.T., D.R. Maidment & L.W. Mays (1988). Applied hydrology, McGraw Hill, New York
Desbordes, M. (1978). Urban runoff and design storm modelling, Proc. Int. Conf. on Urban Storm Drainage, Southampton, p. 353-361.
Harms, R.W. & H.R. Verworn (1984). HYSTEM ein hydrologisches Stadtentwsserungsmodell, Teil I: Modellbeschreibung, Korrespondenz Abwasser, Heft 2, Hannover.
McCuen, R.H., S.L. Wong & W.J. Rawls (1984). Estimating urban time of concentration, J. of Hyd. Engng., A.S.C.E., Vol. 110, No. 7, pp. 887-904.
Radojkovic M. & C. Maksimovic (1987). On standardization of computational models for overland flow, Proc. Int. Conf. on Urban Storm Drainage, Topics in Urban Drainage Hydraulics and Hydrology, Lausanne.
Viessmann, W. (1968). Runoff estimation for very small drainage areas, Water Res. Res., Vol. 4, No. 1, pp. 87,.
Viessman, W., J.W. Knapp, G.L. Lewis & T.E. Harbaugh (1977). Introduction to hydrology, Harper Row, New York
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&A
Pagina &P
Blad8
000
000
000
000
000
000
000
000
000
000
3mm
2mm
4mm
TIME
q
Blad9
0
0
0
0
0
0
0
0
0
0
0
U
Blad10
000
000
000
000
000
000
000
000
000
000
N
Blad11
neerslag
homogeen.4;.8;2.6;.8;.4drempel = 0.45
000
0.158655259800.15865525980.0634621039
0.22082250650.158655259800.37947776630.2152532104
0.15979923650.22082250650.158655259800.53927700280.65308137520.08927700280.2030813752
0.11108360870.15979923650.22082250650.158655259800.65036061140.87333555740.20036061140.4233355574
0.07852233730.11108360870.15979923650.22082250650.15865525980.72888294870.77587394590.27888294870.3258739459
0.0568666480.07852233730.11108360870.15979923650.22082250650.6270943370.59055030340.1770943370.1405503034
0.04215321070.0568666480.07852233730.11108360870.15979923650.44842504120.4192992612
0.0319016880.04215321070.0568666480.07852233730.11108360870.32052749260.30158784180.74561489991.0928411818
0.02458592710.0319016880.04215321070.0568666480.07852233730.2340298110.2218563224
0.01925128790.02458592710.0319016880.04215321070.0568666480.17475876160.1667828733
0.0152859780.01925128790.02458592710.0319016880.04215321070.13317809160.1278214666
0.01228800280.0152859780.01925128790.02458592710.0319016880.10331288370.0996267489
0.00998690840.01228800280.0152859780.01925128790.02458592710.08139810410.0788041095
0.00819675410.00998690840.01228800280.0152859780.01925128790.06500893110.0631463332
0.00678716550.00819675410.00998690840.01228800280.0152859780.05254480870.0511830247
0.00566508820.00678716550.00819675410.00998690840.01228800280.0429239190.0419120561
0.00476302670.00566508820.00678716550.00819675410.00998690840.03539894290.0346360781
0.00403130310.00476302670.00566508820.00678716550.00819675410.02944333770.028860606
0.00343286370.00403130310.00476302670.00566508820.00678716550.02467944730.0242289943
0.0029397330.00343286370.00403130310.00476302670.00566508820.02083201480.0204800291
0.0029397330.00343286370.00403130310.00476302670.01516692660.0164074853
0.0029397330.00343286370.00403130310.01040389990.012002118
0.0029397330.00343286370.00637259670.0037249319
0.0029397330.0029397330.0011758932
debiet in m3/s elke 20 minutenQmax=0.3 m3:s
storm1storm2storm1+2instromingcumulatief volume
0000000
0.15865525980.31731051950.317310519520.772623421620.77262342160.31731051950.30.0031342745
0.37947776630.75895553250.7589555325550.7466390361571.51926245770.75895553250.30.0862336064
0.53927700281.07855400551.0785540055934.26480663741505.78406909511.07855400550.30.2272000249
0.65036061141.30072122291.30072122291200.86546744352706.64953653861.30072122290.30.408392448
0.72888294871.45776589751.45776589751389.3190769454095.96861348371.45776589750.30.6180196684
0.6270943371.25418867391.25418867391145.02640871445240.9950221981.25418867390.30.7907868227
0.44842504120.89685008230.8968500823716.22009881175957.21512100970.89685008230.30.8988535951
0.32052749260.64105498520.6410549852409.26598229356366.48110330320.64105498520.30.9606056373
0.2340298110.46805962210.4680596221201.67154647156568.15264977470.46805962210.30.9910348212
0.17475876160.34951752320.349517523259.42102789596627.57367767060.34951752320.31.0000005549
0.13317809160.26635618320.2663561832-40.37258010236587.20109756840.26635618320.30.9939089436
0.10331288370.20662576740.2066257674-112.04907910416475.15201846430.20662576740.30.9770024335
0.08139810410.16279620830.1627962083-164.64455009976310.50746836450.16279620830.30.9521600629
0.06500893110.13001786230.1300178623-203.97856525256106.5289031120.13001786230.30.9213827848
0.05254480870.105089617500.1050896175-233.89245904155872.63644407050.10508961750.30.8860919529
0.0429239190.08584783790.06346210390.1493099418-180.82806982455691.8083742460.14930994180.30.8588077341
0.03539894290.07079788580.21525321040.2860510962-16.73868453285675.06968971320.28605109620.30.8562821199
0.02944333770.05888667540.65308137520.7119680505494.36166065916169.43135037230.71196805050.30.930873812
0.02467944730.04935889470.87333555740.9226944521747.23334247036916.66469284260.92269445210.541
0.02083201480.04166402960.77587394590.8175379755621.04557061167537.71026345420.81753797550.811
0.01516692660.03033385320.59055030340.6208841566385.06098790177922.77125135590.62088415660.62088415661
0.01040389990.02080779970.41929926120.4401070609168.12847307048090.89972442630.44010706090.44010706091
0.00637259670.01274519340.30158784180.314333035317.19964231166627.570.31433303530.31433303531
0.0029397330.00587946590.22185632240.2277357883-86.71705405516540.85294594490.22773578830.30.9869157091
0.16678287330.1667828733-159.86055209026380.99239385470.16678287330.30.9627951714
0.12782146660.1278214666-206.61424013616174.37815371850.12782146660.30.9316202098
0.09962674890.0996267489-240.4479013675933.93025235160.09962674890.30.8953402608
0.07880410950.0788041095-265.43506858075668.49518377090.07880410950.30.8552901265
0.06314633320.0631463332-284.22440021345384.27078355740.06314633320.30.8124049665
0.05118302470.0511830247-298.58037040385085.69041315360.05118302470.30.7673537078
0.04191205610.0419120561-309.70553264244775.98488051120.04191205610.30.7206238305
0.03463607810.0346360781-318.4367062434457.54817426830.03463607810.30.6725765513
0.0288606060.028860606-325.36727274674132.18090152150.0288606060.30.6234835545
0.02422899430.0242289943-330.92520680943801.25569471220.02422899430.30.5735519496
0.02048002910.0204800291-335.42396513573465.83172957640.02048002910.30.5229415502
0.01640748530.0164074853-340.31101760963125.52071196690.01640748530.30.4715937685
0.0120021180.012002118-345.59745844712779.92325351980.0120021180.30.4194483428
0.00372493190.0037249319-355.53008175742424.39317176240.00372493190.30.3658042347
0.00117589320.0011758932-358.58892817752065.80424358490.00117589320.30.3116985929
&A
Pagina &P
Blad12
&A
Pagina &P
Blad13
2u3usum
Input2*u3*usum
0000
0000
0000
0000
0000
u0000
20200
00.15865525980.31731051950.3173105195
00.22082250650.4416450130.441645013
00.15979923650.3195984730.319598473
00.111083608730.222167217300.2221672173
00.07852233730.15704467460.47596577930.6330104539
00.0568666480.1137332960.66246751950.7762008155
00.04215321070.08430642140.47939770950.5637041309
00.0319016880.06380337590.3332508260.3970542019
00.02458592710.04917185420.23556701190.284738866
00.01925128790.03850257580.1705999440.2091025198
00.0152859780.0305719560.12645963210.1570315881
00.01228800280.02457600560.09570506390.1202810694
00.00998690840.01997381670.07375778120.093731598
00.00819675410.01639350820.05775386370.0741473719
00.00678716550.01357433090.0458579340.0594322649
00.00566508820.01133017640.03686400840.0481941848
00.00476302670.00952605350.02996072510.0394867786
00.00403130310.00806260630.02459026230.0326528686
00.00343286370.00686572750.02036149640.0272272239
00.0029397330.00587946590.01699526470.0228747306
0.01428908020.0142890802
0.01209390940.0120939094
0.01029859120.0102985912
0.00881919890.0088191989
00
00
00
&A
Pagina &P
Blad13
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
2*u
3*u
sum
TIME
Blad14
&A
Pagina &P
Blad15
&A
Pagina &P
Blad16
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
_1263966161.xlsChart5
0.30
0.60.20
0.750.40.4
0.540.50.8
0.420.361
0.270.280.72
0.120.180.56
00.080.36
00.16
0
3mm
2mm
4mm
TIME
q
Impuls
1
1lognimpuls
00
00
00
00
00
00
0.0001010
10.158655259800.1586552598
20.379477766300.2208225065
30.539277002800.1597992365
40.650360611400.1110836087
50.728882948700.0785223373
60.785749596700.056866648
70.827902807400.0421532107
80.859804495400.031901688
90.884390422500.0245859271
100.903641710400.0192512879
110.918927688300.015285978
120.931215691100.0122880028
130.941202599500.0099869084
140.949399353600.0081967541
150.956186519100.0067871655
160.961851607300.0056650882
170.96661463400.0047630267
180.970645937200.0040313031
190.974078800900.0034328637
200.977018533900.002939733
0.9770185339
&A
Pagina &P
Impuls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Step
000
0.31731051950.30.0031342745
0.75895553250.30.0862336064
1.07855400550.30.2272000249
1.30072122290.30.408392448
1.45776589750.30.6180196684
1.25418867390.30.7907868227
0.89685008230.30.8988535951
0.64105498520.30.9606056373
0.46805962210.30.9910348212
0.34951752320.31.0000005549
0.26635618320.30.9939089436
0.20662576740.30.9770024335
0.16279620830.30.9521600629
0.13001786230.30.9213827848
0.10508961750.30.8860919529
0.14930994180.30.8588077341
0.28605109620.30.8562821199
0.71196805050.30.930873812
0.92269445210.541
0.81753797550.811
0.62088415660.62088415661
0.44010706090.44010706091
0.31433303530.31433303531
0.22773578830.30.9869157091
0.16678287330.30.9627951714
0.12782146660.30.9316202098
0.09962674890.30.8953402608
0.07880410950.30.8552901265
0.06314633320.30.8124049665
0.05118302470.30.7673537078
0.04191205610.30.7206238305
0.03463607810.30.6725765513
0.0288606060.30.6234835545
0.02422899430.30.5735519496
0.02048002910.30.5229415502
0.01640748530.30.4715937685
0.0120021180.30.4194483428
0.00372493190.30.3658042347
0.00117589320.30.3116985929
TIME
FLOW (m3/s) or FILLING
Puls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Convolutie
1
1outputinputimpuls
00110
10.1586552598100.1586552598
20.3794777663100.2208225065Step response
30.5392770028100.1597992365
40.6503606114100.1110836087
50.7288829487100.0785223373
60.7857495967100.056866648
70.8279028074100.0421532107
80.8598044954100.031901688
90.8843904225100.0245859271
100.9036417104100.0192512879
110.9189276883100.015285978
120.9312156911100.0122880028
130.9412025995100.0099869084
140.9493993536100.0081967541
150.9561865191100.0067871655
160.9618516073100.0056650882
170.966614634100.0047630267
180.9706459372100.0040313031
190.9740788009100.0034328637
200.9770185339100.002939733
3011
4011
&A
Pagina &P
Convolutie
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
output
input
TIME
INPUT / RESPONSE RATE
Blad7
00000000.25
10.15865525980.158655259810.039663814900.03966381490.25
20.37947776630.379477766320.094869441600.09486944160.25
30.53927700280.539277002830.134819250700.13481925070.25
40.650360611400.650360611440.162590152900.16259015290.25
50.72888294870.15865525980.5702276894.0050.1625900.162590
60.78574959670.37947776630.406271830550.18222073720.03966381490.14255692220
70.82790280740.53927700280.288625804760.19643739920.09486944160.1015679576
80.85980449540.65036061140.20944388470.20697570190.13481925070.0721564512
90.88439042250.72888294870.155507473780.21495112380.16259015290.052360971
100.90364171040.78574959670.117892113690.22109760560.18222073720.0388768684
110.91892768830.82790280740.0910248809100.22591042760.19643739920.0294730284
120.93121569110.85980449540.0714111958110.22973192210.20697570190.0227562202
130.94120259950.88439042250.056812177120.23280392280.21495112380.0178527989
140.94939935360.90364171040.0457576433130.23530064990.22109760560.0142030443
150.95618651910.91892768830.0372588307140.23734983840.22591042760.0114394108
160.96185160730.93121569110.0306359162150.23904662980.22973192210.0093147077
170.9666146340.94120259950.0254120345160.24046290180.23280392280.007658979
180.97064593720.94939935360.0212465836170.24165365850.23530064990.0063530086
190.97407880090.95618651910.0178922819180.24266148430.23734983840.0053116459
200.97701853390.96185160730.0151669266190.24351970020.23904662980.0044730705
210.980.9666146340.013385366200.24425463350.24046290180.0037917317
220.9830.97064593720.0123540628210.2450.24165365850.0033463415
230.9850.97407880090.0109211991220.245750.24266148430.0030885157
240.9870.97701853390.0099814661230.246250.24351970020.0027302998
30110240.246750.24425463350.0024953665
40110300.250.250
400.250.250
3.9351.14634
&A
Pagina &P
Blad7
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
TIME
INPUT / RESPONSE RATE
Blad8
324
UH
0003mm2mm4mm0
10.110.300.3
20.220.60.200.8
30.2530.750.40.41.55
40.1840.540.50.81.84
50.1450.420.3611.78
60.0960.270.280.721.27
70.0470.120.180.560.86
80800.080.360.44
9900.160.16
101000
133
222
344
4
5
6
7
8
9
10
&A
Pagina &P
Blad8
000
000
000
000
000
000
000
000
000
000
3mm
2mm
4mm
TIME
q
Blad9
0
0
0
0
0
0
0
0
0
0
0
U
Blad10
000
000
000
000
000
000
000
000
000
000
N
Blad11
neerslag
homogeen.4;.8;2.6;.8;.4drempel = 0.45
000
0.158655259800.15865525980.0634621039
0.22082250650.158655259800.37947776630.2152532104
0.15979923650.22082250650.158655259800.53927700280.65308137520.08927700280.2030813752
0.11108360870.15979923650.22082250650.158655259800.65036061140.87333555740.20036061140.4233355574
0.07852233730.11108360870.15979923650.22082250650.15865525980.72888294870.77587394590.27888294870.3258739459
0.0568666480.07852233730.11108360870.15979923650.22082250650.6270943370.59055030340.1770943370.1405503034
0.04215321070.0568666480.07852233730.11108360870.15979923650.44842504120.4192992612
0.0319016880.04215321070.0568666480.07852233730.11108360870.32052749260.30158784180.74561489991.0928411818
0.02458592710.0319016880.04215321070.0568666480.07852233730.2340298110.2218563224
0.01925128790.02458592710.0319016880.04215321070.0568666480.17475876160.1667828733
0.0152859780.01925128790.02458592710.0319016880.04215321070.13317809160.1278214666
0.01228800280.0152859780.01925128790.02458592710.0319016880.10331288370.0996267489
0.00998690840.01228800280.0152859780.01925128790.02458592710.08139810410.0788041095
0.00819675410.00998690840.01228800280.0152859780.01925128790.06500893110.0631463332
0.00678716550.00819675410.00998690840.01228800280.0152859780.05254480870.0511830247
0.00566508820.00678716550.00819675410.00998690840.01228800280.0429239190.0419120561
0.00476302670.00566508820.00678716550.00819675410.00998690840.03539894290.0346360781
0.00403130310.00476302670.00566508820.00678716550.00819675410.02944333770.028860606
0.00343286370.00403130310.00476302670.00566508820.00678716550.02467944730.0242289943
0.0029397330.00343286370.00403130310.00476302670.00566508820.02083201480.0204800291
0.0029397330.00343286370.00403130310.00476302670.01516692660.0164074853
0.0029397330.00343286370.00403130310.01040389990.012002118
0.0029397330.00343286370.00637259670.0037249319
0.0029397330.0029397330.0011758932
debiet in m3/s elke 20 minutenQmax=0.3 m3:s
storm1storm2storm1+2instromingcumulatief volume
0000000
0.15865525980.31731051950.317310519520.772623421620.77262342160.31731051950.30.0031342745
0.37947776630.75895553250.7589555325550.7466390361571.51926245770.75895553250.30.0862336064
0.53927700281.07855400551.0785540055934.26480663741505.78406909511.07855400550.30.2272000249
0.65036061141.30072122291.30072122291200.86546744352706.64953653861.30072122290.30.408392448
0.72888294871.45776589751.45776589751389.3190769454095.96861348371.45776589750.30.6180196684
0.6270943371.25418867391.25418867391145.02640871445240.9950221981.25418867390.30.7907868227
0.44842504120.89685008230.8968500823716.22009881175957.21512100970.89685008230.30.8988535951
0.32052749260.64105498520.6410549852409.26598229356366.48110330320.64105498520.30.9606056373
0.2340298110.46805962210.4680596221201.67154647156568.15264977470.46805962210.30.9910348212
0.17475876160.34951752320.349517523259.42102789596627.57367767060.34951752320.31.0000005549
0.13317809160.26635618320.2663561832-40.37258010236587.20109756840.26635618320.30.9939089436
0.10331288370.20662576740.2066257674-112.04907910416475.15201846430.20662576740.30.9770024335
0.08139810410.16279620830.1627962083-164.64455009976310.50746836450.16279620830.30.9521600629
0.06500893110.13001786230.1300178623-203.97856525256106.5289031120.13001786230.30.9213827848
0.05254480870.105089617500.1050896175-233.89245904155872.63644407050.10508961750.30.8860919529
0.0429239190.08584783790.06346210390.1493099418-180.82806982455691.8083742460.14930994180.30.8588077341
0.03539894290.07079788580.21525321040.2860510962-16.73868453285675.06968971320.28605109620.30.8562821199
0.02944333770.05888667540.65308137520.7119680505494.36166065916169.43135037230.71196805050.30.930873812
0.02467944730.04935889470.87333555740.9226944521747.23334247036916.66469284260.92269445210.541
0.02083201480.04166402960.77587394590.8175379755621.04557061167537.71026345420.81753797550.811
0.01516692660.03033385320.59055030340.6208841566385.06098790177922.77125135590.62088415660.62088415661
0.01040389990.02080779970.41929926120.4401070609168.12847307048090.89972442630.44010706090.44010706091
0.00637259670.01274519340.30158784180.314333035317.19964231166627.570.31433303530.31433303531
0.0029397330.00587946590.22185632240.2277357883-86.71705405516540.85294594490.22773578830.30.9869157091
0.16678287330.1667828733-159.86055209026380.99239385470.16678287330.30.9627951714
0.12782146660.1278214666-206.61424013616174.37815371850.12782146660.30.9316202098
0.09962674890.0996267489-240.4479013675933.93025235160.09962674890.30.8953402608
0.07880410950.0788041095-265.43506858075668.49518377090.07880410950.30.8552901265
0.06314633320.0631463332-284.22440021345384.27078355740.06314633320.30.8124049665
0.05118302470.0511830247-298.58037040385085.69041315360.05118302470.30.7673537078
0.04191205610.0419120561-309.70553264244775.98488051120.04191205610.30.7206238305
0.03463607810.0346360781-318.4367062434457.54817426830.03463607810.30.6725765513
0.0288606060.028860606-325.36727274674132.18090152150.0288606060.30.6234835545
0.02422899430.0242289943-330.92520680943801.25569471220.02422899430.30.5735519496
0.02048002910.0204800291-335.42396513573465.83172957640.02048002910.30.5229415502
0.01640748530.0164074853-340.31101760963125.52071196690.01640748530.30.4715937685
0.0120021180.012002118-345.59745844712779.92325351980.0120021180.30.4194483428
0.00372493190.0037249319-355.53008175742424.39317176240.00372493190.30.3658042347
0.00117589320.0011758932-358.58892817752065.80424358490.00117589320.30.3116985929
&A
Pagina &P
Blad12
&A
Pagina &P
Blad13
2u3usum
Input2*u3*usum
0000
0000
0000
0000
0000
u0000
20200
00.15865525980.31731051950.3173105195
00.22082250650.4416450130.441645013
00.15979923650.3195984730.319598473
00.111083608730.222167217300.2221672173
00.07852233730.15704467460.47596577930.6330104539
00.0568666480.1137332960.66246751950.7762008155
00.04215321070.08430642140.47939770950.5637041309
00.0319016880.06380337590.3332508260.3970542019
00.02458592710.04917185420.23556701190.284738866
00.01925128790.03850257580.1705999440.2091025198
00.0152859780.0305719560.12645963210.1570315881
00.01228800280.02457600560.09570506390.1202810694
00.00998690840.01997381670.07375778120.093731598
00.00819675410.01639350820.05775386370.0741473719
00.00678716550.01357433090.0458579340.0594322649
00.00566508820.01133017640.03686400840.0481941848
00.00476302670.00952605350.02996072510.0394867786
00.00403130310.00806260630.02459026230.0326528686
00.00343286370.00686572750.02036149640.0272272239
00.0029397330.00587946590.01699526470.0228747306
0.01428908020.0142890802
0.01209390940.0120939094
0.01029859120.0102985912
0.00881919890.0088191989
00
00
00
&A
Pagina &P
Blad13
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
2*u
3*u
sum
TIME
Blad14
&A
Pagina &P
Blad15
&A
Pagina &P
Blad16
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
_1263966159.xlsChart4
0
0.1
0.2
0.25
0.18
0.14
0.09
0.04
0
9
10
U
Impuls
1
1lognimpuls
00
00
00
00
00
00
0.0001010
10.158655259800.1586552598
20.379477766300.2208225065
30.539277002800.1597992365
40.650360611400.1110836087
50.728882948700.0785223373
60.785749596700.056866648
70.827902807400.0421532107
80.859804495400.031901688
90.884390422500.0245859271
100.903641710400.0192512879
110.918927688300.015285978
120.931215691100.0122880028
130.941202599500.0099869084
140.949399353600.0081967541
150.956186519100.0067871655
160.961851607300.0056650882
170.96661463400.0047630267
180.970645937200.0040313031
190.974078800900.0034328637
200.977018533900.002939733
0.9770185339
&A
Pagina &P
Impuls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Step
000
0.31731051950.30.0031342745
0.75895553250.30.0862336064
1.07855400550.30.2272000249
1.30072122290.30.408392448
1.45776589750.30.6180196684
1.25418867390.30.7907868227
0.89685008230.30.8988535951
0.64105498520.30.9606056373
0.46805962210.30.9910348212
0.34951752320.31.0000005549
0.26635618320.30.9939089436
0.20662576740.30.9770024335
0.16279620830.30.9521600629
0.13001786230.30.9213827848
0.10508961750.30.8860919529
0.14930994180.30.8588077341
0.28605109620.30.8562821199
0.71196805050.30.930873812
0.92269445210.541
0.81753797550.811
0.62088415660.62088415661
0.44010706090.44010706091
0.31433303530.31433303531
0.22773578830.30.9869157091
0.16678287330.30.9627951714
0.12782146660.30.9316202098
0.09962674890.30.8953402608
0.07880410950.30.8552901265
0.06314633320.30.8124049665
0.05118302470.30.7673537078
0.04191205610.30.7206238305
0.03463607810.30.6725765513
0.0288606060.30.6234835545
0.02422899430.30.5735519496
0.02048002910.30.5229415502
0.01640748530.30.4715937685
0.0120021180.30.4194483428
0.00372493190.30.3658042347
0.00117589320.30.3116985929
TIME
FLOW (m3/s) or FILLING
Puls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Convolutie
1
1outputinputimpuls
00110
10.1586552598100.1586552598
20.3794777663100.2208225065Step response
30.5392770028100.1597992365
40.6503606114100.1110836087
50.7288829487100.0785223373
60.7857495967100.056866648
70.8279028074100.0421532107
80.8598044954100.031901688
90.8843904225100.0245859271
100.9036417104100.0192512879
110.9189276883100.015285978
120.9312156911100.0122880028
130.9412025995100.0099869084
140.9493993536100.0081967541
150.9561865191100.0067871655
160.9618516073100.0056650882
170.966614634100.0047630267
180.9706459372100.0040313031
190.9740788009100.0034328637
200.9770185339100.002939733
3011
4011
&A
Pagina &P
Convolutie
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
output
input
TIME
INPUT / RESPONSE RATE
Blad7
00000000.25
10.15865525980.158655259810.039663814900.03966381490.25
20.37947776630.379477766320.094869441600.09486944160.25
30.53927700280.539277002830.134819250700.13481925070.25
40.650360611400.650360611440.162590152900.16259015290.25
50.72888294870.15865525980.5702276894.0050.1625900.162590
60.78574959670.37947776630.406271830550.18222073720.03966381490.14255692220
70.82790280740.53927700280.288625804760.19643739920.09486944160.1015679576
80.85980449540.65036061140.20944388470.20697570190.13481925070.0721564512
90.88439042250.72888294870.155507473780.21495112380.16259015290.052360971
100.90364171040.78574959670.117892113690.22109760560.18222073720.0388768684
110.91892768830.82790280740.0910248809100.22591042760.19643739920.0294730284
120.93121569110.85980449540.0714111958110.22973192210.20697570190.0227562202
130.94120259950.88439042250.056812177120.23280392280.21495112380.0178527989
140.94939935360.90364171040.0457576433130.23530064990.22109760560.0142030443
150.95618651910.91892768830.0372588307140.23734983840.22591042760.0114394108
160.96185160730.93121569110.0306359162150.23904662980.22973192210.0093147077
170.9666146340.94120259950.0254120345160.24046290180.23280392280.007658979
180.97064593720.94939935360.0212465836170.24165365850.23530064990.0063530086
190.97407880090.95618651910.0178922819180.24266148430.23734983840.0053116459
200.97701853390.96185160730.0151669266190.24351970020.23904662980.0044730705
210.980.9666146340.013385366200.24425463350.24046290180.0037917317
220.9830.97064593720.0123540628210.2450.24165365850.0033463415
230.9850.97407880090.0109211991220.245750.24266148430.0030885157
240.9870.97701853390.0099814661230.246250.24351970020.0027302998
30110240.246750.24425463350.0024953665
40110300.250.250
400.250.250
3.9351.14634
&A
Pagina &P
Blad7
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
TIME
INPUT / RESPONSE RATE
Blad8
324
UH
0003mm2mm4mm0
10.110.300.3
20.220.60.200.8
30.2530.750.40.41.55
40.1840.540.50.81.84
50.1450.420.3611.78
60.0960.270.280.721.27
70.0470.120.180.560.86
80800.080.360.44
9900.160.16
101000
133
222
344
4
5
6
7
8
9
10
&A
Pagina &P
Blad8
000
000
000
000
000
000
000
000
000
000
3mm
2mm
4mm
TIME
q
Blad9
0
0
0
0
0
0
0
0
0
0
0
U
Blad10
000
000
000
000
000
000
000
000
000
000
N
Blad11
neerslag
homogeen.4;.8;2.6;.8;.4drempel = 0.45
000
0.158655259800.15865525980.0634621039
0.22082250650.158655259800.37947776630.2152532104
0.15979923650.22082250650.158655259800.53927700280.65308137520.08927700280.2030813752
0.11108360870.15979923650.22082250650.158655259800.65036061140.87333555740.20036061140.4233355574
0.07852233730.11108360870.15979923650.22082250650.15865525980.72888294870.77587394590.27888294870.3258739459
0.0568666480.07852233730.11108360870.15979923650.22082250650.6270943370.59055030340.1770943370.1405503034
0.04215321070.0568666480.07852233730.11108360870.15979923650.44842504120.4192992612
0.0319016880.04215321070.0568666480.07852233730.11108360870.32052749260.30158784180.74561489991.0928411818
0.02458592710.0319016880.04215321070.0568666480.07852233730.2340298110.2218563224
0.01925128790.02458592710.0319016880.04215321070.0568666480.17475876160.1667828733
0.0152859780.01925128790.02458592710.0319016880.04215321070.13317809160.1278214666
0.01228800280.0152859780.01925128790.02458592710.0319016880.10331288370.0996267489
0.00998690840.01228800280.0152859780.01925128790.02458592710.08139810410.0788041095
0.00819675410.00998690840.01228800280.0152859780.01925128790.06500893110.0631463332
0.00678716550.00819675410.00998690840.01228800280.0152859780.05254480870.0511830247
0.00566508820.00678716550.00819675410.00998690840.01228800280.0429239190.0419120561
0.00476302670.00566508820.00678716550.00819675410.00998690840.03539894290.0346360781
0.00403130310.00476302670.00566508820.00678716550.00819675410.02944333770.028860606
0.00343286370.00403130310.00476302670.00566508820.00678716550.02467944730.0242289943
0.0029397330.00343286370.00403130310.00476302670.00566508820.02083201480.0204800291
0.0029397330.00343286370.00403130310.00476302670.01516692660.0164074853
0.0029397330.00343286370.00403130310.01040389990.012002118
0.0029397330.00343286370.00637259670.0037249319
0.0029397330.0029397330.0011758932
debiet in m3/s elke 20 minutenQmax=0.3 m3:s
storm1storm2storm1+2instromingcumulatief volume
0000000
0.15865525980.31731051950.317310519520.772623421620.77262342160.31731051950.30.0031342745
0.37947776630.75895553250.7589555325550.7466390361571.51926245770.75895553250.30.0862336064
0.53927700281.07855400551.0785540055934.26480663741505.78406909511.07855400550.30.2272000249
0.65036061141.30072122291.30072122291200.86546744352706.64953653861.30072122290.30.408392448
0.72888294871.45776589751.45776589751389.3190769454095.96861348371.45776589750.30.6180196684
0.6270943371.25418867391.25418867391145.02640871445240.9950221981.25418867390.30.7907868227
0.44842504120.89685008230.8968500823716.22009881175957.21512100970.89685008230.30.8988535951
0.32052749260.64105498520.6410549852409.26598229356366.48110330320.64105498520.30.9606056373
0.2340298110.46805962210.4680596221201.67154647156568.15264977470.46805962210.30.9910348212
0.17475876160.34951752320.349517523259.42102789596627.57367767060.34951752320.31.0000005549
0.13317809160.26635618320.2663561832-40.37258010236587.20109756840.26635618320.30.9939089436
0.10331288370.20662576740.2066257674-112.04907910416475.15201846430.20662576740.30.9770024335
0.08139810410.16279620830.1627962083-164.64455009976310.50746836450.16279620830.30.9521600629
0.06500893110.13001786230.1300178623-203.97856525256106.5289031120.13001786230.30.9213827848
0.05254480870.105089617500.1050896175-233.89245904155872.63644407050.10508961750.30.8860919529
0.0429239190.08584783790.06346210390.1493099418-180.82806982455691.8083742460.14930994180.30.8588077341
0.03539894290.07079788580.21525321040.2860510962-16.73868453285675.06968971320.28605109620.30.8562821199
0.02944333770.05888667540.65308137520.7119680505494.36166065916169.43135037230.71196805050.30.930873812
0.02467944730.04935889470.87333555740.9226944521747.23334247036916.66469284260.92269445210.541
0.02083201480.04166402960.77587394590.8175379755621.04557061167537.71026345420.81753797550.811
0.01516692660.03033385320.59055030340.6208841566385.06098790177922.77125135590.62088415660.62088415661
0.01040389990.02080779970.41929926120.4401070609168.12847307048090.89972442630.44010706090.44010706091
0.00637259670.01274519340.30158784180.314333035317.19964231166627.570.31433303530.31433303531
0.0029397330.00587946590.22185632240.2277357883-86.71705405516540.85294594490.22773578830.30.9869157091
0.16678287330.1667828733-159.86055209026380.99239385470.16678287330.30.9627951714
0.12782146660.1278214666-206.61424013616174.37815371850.12782146660.30.9316202098
0.09962674890.0996267489-240.4479013675933.93025235160.09962674890.30.8953402608
0.07880410950.0788041095-265.43506858075668.49518377090.07880410950.30.8552901265
0.06314633320.0631463332-284.22440021345384.27078355740.06314633320.30.8124049665
0.05118302470.0511830247-298.58037040385085.69041315360.05118302470.30.7673537078
0.04191205610.0419120561-309.70553264244775.98488051120.04191205610.30.7206238305
0.03463607810.0346360781-318.4367062434457.54817426830.03463607810.30.6725765513
0.0288606060.028860606-325.36727274674132.18090152150.0288606060.30.6234835545
0.02422899430.0242289943-330.92520680943801.25569471220.02422899430.30.5735519496
0.02048002910.0204800291-335.42396513573465.83172957640.02048002910.30.5229415502
0.01640748530.0164074853-340.31101760963125.52071196690.01640748530.30.4715937685
0.0120021180.012002118-345.59745844712779.92325351980.0120021180.30.4194483428
0.00372493190.0037249319-355.53008175742424.39317176240.00372493190.30.3658042347
0.00117589320.0011758932-358.58892817752065.80424358490.00117589320.30.3116985929
&A
Pagina &P
Blad12
&A
Pagina &P
Blad13
2u3usum
Input2*u3*usum
0000
0000
0000
0000
0000
u0000
20200
00.15865525980.31731051950.3173105195
00.22082250650.4416450130.441645013
00.15979923650.3195984730.319598473
00.111083608730.222167217300.2221672173
00.07852233730.15704467460.47596577930.6330104539
00.0568666480.1137332960.66246751950.7762008155
00.04215321070.08430642140.47939770950.5637041309
00.0319016880.06380337590.3332508260.3970542019
00.02458592710.04917185420.23556701190.284738866
00.01925128790.03850257580.1705999440.2091025198
00.0152859780.0305719560.12645963210.1570315881
00.01228800280.02457600560.09570506390.1202810694
00.00998690840.01997381670.07375778120.093731598
00.00819675410.01639350820.05775386370.0741473719
00.00678716550.01357433090.0458579340.0594322649
00.00566508820.01133017640.03686400840.0481941848
00.00476302670.00952605350.02996072510.0394867786
00.00403130310.00806260630.02459026230.0326528686
00.00343286370.00686572750.02036149640.0272272239
00.0029397330.00587946590.01699526470.0228747306
0.01428908020.0142890802
0.01209390940.0120939094
0.01029859120.0102985912
0.00881919890.0088191989
00
00
00
&A
Pagina &P
Blad13
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
2*u
3*u
sum
TIME
Blad14
&A
Pagina &P
Blad15
&A
Pagina &P
Blad16
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
_1001155714.unknown
_1001155989.unknown
_1001160435.xlsChart1
2
7
13
24
33
36
TIME
AREA A
Sheet1
222
757
13613
241124
33933
36336
Sheet1
TIME
dA/dt
Sheet2
TIME
AREA A
Sheet3
_1001160436.xlsChart2
2
5
6
11
9
3
TIME
dA/dt
Sheet1
222
757
13613
241124
33933
36336
Sheet1
TIME
dA/dt
Sheet2
TIME
AREA A
Sheet3
_1001156464.unknown
_1001155976.unknown
_997699118.unknown
_997699448.xlsChart2
0000.25
0.039663814900.03966381490.25
0.094869441600.09486944160.25
0.134819250700.13481925070.25
0.162590152900.16259015290.25
0.1625900.162590
0.18222073720.03966381490.14255692220
0.19643739920.09486944160.10156795766
0.20697570190.13481925070.07215645127
0.21495112380.16259015290.0523609718
0.22109760560.18222073720.03887686849
0.22591042760.19643739920.029473028410
0.22973192210.20697570190.022756220211
0.23280392280.21495112380.017852798912
0.23530064990.22109760560.014203044313
0.23734983840.22591042760.011439410814
0.23904662980.22973192210.009314707715
0.24046290180.23280392280.00765897916
0.24165365850.23530064990.006353008617
0.24266148430.23734983840.005311645918
0.24351970020.23904662980.004473070519
0.24425463350.24046290180.003791731720
0.2450.24165365850.003346341521
0.245750.24266148430.003088515722
0.246250.24351970020.002730299823
0.246750.24425463350.002495366524
0.250.25030
0.250.25040
TIME
INPUT / RESPONSE RATE
Impuls
1
1lognimpuls
00
00
00
00
00
00
0.0001010
10.158655259800.1586552598
20.379477766300.2208225065
30.539277002800.1597992365
40.650360611400.1110836087
50.728882948700.0785223373
60.785749596700.056866648
70.827902807400.0421532107
80.859804495400.031901688
90.884390422500.0245859271
100.903641710400.0192512879
110.918927688300.015285978
120.931215691100.0122880028
130.941202599500.0099869084
140.949399353600.0081967541
150.956186519100.0067871655
160.961851607300.0056650882
170.96661463400.0047630267
180.970645937200.0040313031
190.974078800900.0034328637
200.977018533900.002939733
0.9770185339
&A
Pagina &P
Impuls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Step
000
0.31731051950.30.0031342745
0.75895553250.30.0862336064
1.07855400550.30.2272000249
1.30072122290.30.408392448
1.45776589750.30.6180196684
1.25418867390.30.7907868227
0.89685008230.30.8988535951
0.64105498520.30.9606056373
0.46805962210.30.9910348212
0.34951752320.31.0000005549
0.26635618320.30.9939089436
0.20662576740.30.9770024335
0.16279620830.30.9521600629
0.13001786230.30.9213827848
0.10508961750.30.8860919529
0.14930994180.30.8588077341
0.28605109620.30.8562821199
0.71196805050.30.930873812
0.92269445210.541
0.81753797550.811
0.62088415660.62088415661
0.44010706090.44010706091
0.31433303530.31433303531
0.22773578830.30.9869157091
0.16678287330.30.9627951714
0.12782146660.30.9316202098
0.09962674890.30.8953402608
0.07880410950.30.8552901265
0.06314633320.30.8124049665
0.05118302470.30.7673537078
0.04191205610.30.7206238305
0.03463607810.30.6725765513
0.0288606060.30.6234835545
0.02422899430.30.5735519496
0.02048002910.30.5229415502
0.01640748530.30.4715937685
0.0120021180.30.4194483428
0.00372493190.30.3658042347
0.00117589320.30.3116985929
TIME
FLOW (m3/s) or FILLING
Puls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Convolutie
1
1outputinputimpuls
00110
10.1586552598100.1586552598
20.3794777663100.2208225065Step response
30.5392770028100.1597992365
40.6503606114100.1110836087
50.7288829487100.0785223373
60.7857495967100.056866648
70.8279028074100.0421532107
80.8598044954100.031901688
90.8843904225100.0245859271
100.9036417104100.0192512879
110.9189276883100.015285978
120.9312156911100.0122880028
130.9412025995100.0099869084
140.9493993536100.0081967541
150.9561865191100.0067871655
160.9618516073100.0056650882
170.966614634100.0047630267
180.9706459372100.0040313031
190.9740788009100.0034328637
200.9770185339100.002939733
3011
4011
&A
Pagina &P
Convolutie
output
input
TIME
INPUT / RESPONSE RATE
Blad7
00000000.25
10.15865525980.158655259810.039663814900.03966381490.25
20.37947776630.379477766320.094869441600.09486944160.25
30.53927700280.539277002830.134819250700.13481925070.25
40.650360611400.650360611440.162590152900.16259015290.25
50.72888294870.15865525980.5702276894.0050.1625900.162590
60.78574959670.37947776630.406271830550.18222073720.03966381490.14255692220
70.82790280740.53927700280.288625804760.19643739920.09486944160.1015679576
80.85980449540.65036061140.20944388470.20697570190.13481925070.0721564512
90.88439042250.72888294870.155507473780.21495112380.16259015290.052360971
100.90364171040.78574959670.117892113690.22109760560.18222073720.0388768684
110.91892768830.82790280740.0910248809100.22591042760.19643739920.0294730284
120.93121569110.85980449540.0714111958110.22973192210.20697570190.0227562202
130.94120259950.88439042250.056812177120.23280392280.21495112380.0178527989
140.94939935360.90364171040.0457576433130.23530064990.22109760560.0142030443
150.95618651910.91892768830.0372588307140.23734983840.22591042760.0114394108
160.96185160730.93121569110.0306359162150.23904662980.22973192210.0093147077
170.9666146340.94120259950.0254120345160.24046290180.23280392280.007658979
180.97064593720.94939935360.0212465836170.24165365850.23530064990.0063530086
190.97407880090.95618651910.0178922819180.24266148430.23734983840.0053116459
200.97701853390.96185160730.0151669266190.24351970020.23904662980.0044730705
210.980.9666146340.013385366200.24425463350.24046290180.0037917317
220.9830.97064593720.0123540628210.2450.24165365850.0033463415
230.9850.97407880090.0109211991220.245750.24266148430.0030885157
240.9870.97701853390.0099814661230.246250.24351970020.0027302998
30110240.246750.24425463350.0024953665
40110300.250.250
400.250.250
3.9351.14634
&A
Pagina &P
Blad7
TIME
INPUT / RESPONSE RATE
Blad8
324
UH
0003mm2mm4mm0
10.110.300.3
20.220.60.200.8
30.2530.750.40.41.55
40.1840.540.50.81.84
50.1450.420.3611.78
60.0960.270.280.721.27
70.0470.120.180.560.86
80800.080.360.44
9900.160.16
101000
133
222
344
4
5
6
7
8
9
10
&A
Pagina &P
Blad8
000
000
000
000
000
000
000
000
000
000
3mm
2mm
4mm
TIME
q
Blad9
0
0
0
0
0
0
0
0
0
0
0
U
Blad10
000
000
000
000
000
000
000
000
000
000
N
Blad11
neerslag
homogeen.4;.8;2.6;.8;.4drempel = 0.45
000
0.158655259800.15865525980.0634621039
0.22082250650.158655259800.37947776630.2152532104
0.15979923650.22082250650.158655259800.53927700280.65308137520.08927700280.2030813752
0.11108360870.15979923650.22082250650.158655259800.65036061140.87333555740.20036061140.4233355574
0.07852233730.11108360870.15979923650.22082250650.15865525980.72888294870.77587394590.27888294870.3258739459
0.0568666480.07852233730.11108360870.15979923650.22082250650.6270943370.59055030340.1770943370.1405503034
0.04215321070.0568666480.07852233730.11108360870.15979923650.44842504120.4192992612
0.0319016880.04215321070.0568666480.07852233730.11108360870.32052749260.30158784180.74561489991.0928411818
0.02458592710.0319016880.04215321070.0568666480.07852233730.2340298110.2218563224
0.01925128790.02458592710.0319016880.04215321070.0568666480.17475876160.1667828733
0.0152859780.01925128790.02458592710.0319016880.04215321070.13317809160.1278214666
0.01228800280.0152859780.01925128790.02458592710.0319016880.10331288370.0996267489
0.00998690840.01228800280.0152859780.01925128790.02458592710.08139810410.0788041095
0.00819675410.00998690840.01228800280.0152859780.01925128790.06500893110.0631463332
0.00678716550.00819675410.00998690840.01228800280.0152859780.05254480870.0511830247
0.00566508820.00678716550.00819675410.00998690840.01228800280.0429239190.0419120561
0.00476302670.00566508820.00678716550.00819675410.00998690840.03539894290.0346360781
0.00403130310.00476302670.00566508820.00678716550.00819675410.02944333770.028860606
0.00343286370.00403130310.00476302670.00566508820.00678716550.02467944730.0242289943
0.0029397330.00343286370.00403130310.00476302670.00566508820.02083201480.0204800291
0.0029397330.00343286370.00403130310.00476302670.01516692660.0164074853
0.0029397330.00343286370.00403130310.01040389990.012002118
0.0029397330.00343286370.00637259670.0037249319
0.0029397330.0029397330.0011758932
debiet in m3/s elke 20 minutenQmax=0.3 m3:s
storm1storm2storm1+2instromingcumulatief volume
0000000
0.15865525980.31731051950.317310519520.772623421620.77262342160.31731051950.30.0031342745
0.37947776630.75895553250.7589555325550.7466390361571.51926245770.75895553250.30.0862336064
0.53927700281.07855400551.0785540055934.26480663741505.78406909511.07855400550.30.2272000249
0.65036061141.30072122291.30072122291200.86546744352706.64953653861.30072122290.30.408392448
0.72888294871.45776589751.45776589751389.3190769454095.96861348371.45776589750.30.6180196684
0.6270943371.25418867391.25418867391145.02640871445240.9950221981.25418867390.30.7907868227
0.44842504120.89685008230.8968500823716.22009881175957.21512100970.89685008230.30.8988535951
0.32052749260.64105498520.6410549852409.26598229356366.48110330320.64105498520.30.9606056373
0.2340298110.46805962210.4680596221201.67154647156568.15264977470.46805962210.30.9910348212
0.17475876160.34951752320.349517523259.42102789596627.57367767060.34951752320.31.0000005549
0.13317809160.26635618320.2663561832-40.37258010236587.20109756840.26635618320.30.9939089436
0.10331288370.20662576740.2066257674-112.04907910416475.15201846430.20662576740.30.9770024335
0.08139810410.16279620830.1627962083-164.64455009976310.50746836450.16279620830.30.9521600629
0.06500893110.13001786230.1300178623-203.97856525256106.5289031120.13001786230.30.9213827848
0.05254480870.105089617500.1050896175-233.89245904155872.63644407050.10508961750.30.8860919529
0.0429239190.08584783790.06346210390.1493099418-180.82806982455691.8083742460.14930994180.30.8588077341
0.03539894290.07079788580.21525321040.2860510962-16.73868453285675.06968971320.28605109620.30.8562821199
0.02944333770.05888667540.65308137520.7119680505494.36166065916169.43135037230.71196805050.30.930873812
0.02467944730.04935889470.87333555740.9226944521747.23334247036916.66469284260.92269445210.541
0.02083201480.04166402960.77587394590.8175379755621.04557061167537.71026345420.81753797550.811
0.01516692660.03033385320.59055030340.6208841566385.06098790177922.77125135590.62088415660.62088415661
0.01040389990.02080779970.41929926120.4401070609168.12847307048090.89972442630.44010706090.44010706091
0.00637259670.01274519340.30158784180.314333035317.19964231166627.570.31433303530.31433303531
0.0029397330.00587946590.22185632240.2277357883-86.71705405516540.85294594490.22773578830.30.9869157091
0.16678287330.1667828733-159.86055209026380.99239385470.16678287330.30.9627951714
0.12782146660.1278214666-206.61424013616174.37815371850.12782146660.30.9316202098
0.09962674890.0996267489-240.4479013675933.93025235160.09962674890.30.8953402608
0.07880410950.0788041095-265.43506858075668.49518377090.07880410950.30.8552901265
0.06314633320.0631463332-284.22440021345384.27078355740.06314633320.30.8124049665
0.05118302470.0511830247-298.58037040385085.69041315360.05118302470.30.7673537078
0.04191205610.0419120561-309.70553264244775.98488051120.04191205610.30.7206238305
0.03463607810.0346360781-318.4367062434457.54817426830.03463607810.30.6725765513
0.0288606060.028860606-325.36727274674132.18090152150.0288606060.30.6234835545
0.02422899430.0242289943-330.92520680943801.25569471220.02422899430.30.5735519496
0.02048002910.0204800291-335.42396513573465.83172957640.02048002910.30.5229415502
0.01640748530.0164074853-340.31101760963125.52071196690.01640748530.30.4715937685
0.0120021180.012002118-345.59745844712779.92325351980.0120021180.30.4194483428
0.00372493190.0037249319-355.53008175742424.39317176240.00372493190.30.3658042347
0.00117589320.0011758932-358.58892817752065.80424358490.00117589320.30.3116985929
&A
Pagina &P
Blad12
&A
Pagina &P
Blad13
2u3usum
Input2*u3*usum
0000
0000
0000
0000
0000
u0000
20200
00.15865525980.31731051950.3173105195
00.22082250650.4416450130.441645013
00.15979923650.3195984730.319598473
00.111083608730.222167217300.2221672173
00.07852233730.15704467460.47596577930.6330104539
00.0568666480.1137332960.66246751950.7762008155
00.04215321070.08430642140.47939770950.5637041309
00.0319016880.06380337590.3332508260.3970542019
00.02458592710.04917185420.23556701190.284738866
00.01925128790.03850257580.1705999440.2091025198
00.0152859780.0305719560.12645963210.1570315881
00.01228800280.02457600560.09570506390.1202810694
00.00998690840.01997381670.07375778120.093731598
00.00819675410.01639350820.05775386370.0741473719
00.00678716550.01357433090.0458579340.0594322649
00.00566508820.01133017640.03686400840.0481941848
00.00476302670.00952605350.02996072510.0394867786
00.00403130310.00806260630.02459026230.0326528686
00.00343286370.00686572750.02036149640.0272272239
00.0029397330.00587946590.01699526470.0228747306
0.01428908020.0142890802
0.01209390940.0120939094
0.01029859120.0102985912
0.00881919890.0088191989
00
00
00
&A
Pagina &P
Blad13
2*u
3*u
sum
TIME
Blad14
&A
Pagina &P
Blad15
&A
Pagina &P
Blad16
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
&A
Pagina &P
_1001155700.unknown
_997699391.xlsChart1
01
0.15865525981
0.37947776631
0.53927700281
0.65036061141
0.72888294871
0.78574959671
0.82790280741
0.85980449541
0.88439042251
0.90364171041
0.91892768831
0.93121569111
0.94120259951
0.94939935361
0.95618651911
0.96185160731
0.9666146341
0.97064593721
0.97407880091
0.97701853391
11
11
output
input
TIME
INPUT / RESPONSE RATE
Impuls
1
1lognimpuls
00
00
00
00
00
00
0.0001010
10.158655259800.1586552598
20.379477766300.2208225065
30.539277002800.1597992365
40.650360611400.1110836087
50.728882948700.0785223373
60.785749596700.056866648
70.827902807400.0421532107
80.859804495400.031901688
90.884390422500.0245859271
100.903641710400.0192512879
110.918927688300.015285978
120.931215691100.0122880028
130.941202599500.0099869084
140.949399353600.0081967541
150.956186519100.0067871655
160.961851607300.0056650882
170.96661463400.0047630267
180.970645937200.0040313031
190.974078800900.0034328637
200.977018533900.002939733
0.9770185339
&A
Pagina &P
Impuls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Step
000
0.31731051950.30.0031342745
0.75895553250.30.0862336064
1.07855400550.30.2272000249
1.30072122290.30.408392448
1.45776589750.30.6180196684
1.25418867390.30.7907868227
0.89685008230.30.8988535951
0.64105498520.30.9606056373
0.46805962210.30.9910348212
0.34951752320.31.0000005549
0.26635618320.30.9939089436
0.20662576740.30.9770024335
0.16279620830.30.9521600629
0.13001786230.30.9213827848
0.10508961750.30.8860919529
0.14930994180.30.8588077341
0.28605109620.30.8562821199
0.71196805050.30.930873812
0.92269445210.541
0.81753797550.811
0.62088415660.62088415661
0.44010706090.44010706091
0.31433303530.31433303531
0.22773578830.30.9869157091
0.16678287330.30.9627951714
0.12782146660.30.9316202098
0.09962674890.30.8953402608
0.07880410950.30.8552901265
0.06314633320.30.8124049665
0.05118302470.30.7673537078
0.04191205610.30.7206238305
0.03463607810.30.6725765513
0.0288606060.30.6234835545
0.02422899430.30.5735519496
0.02048002910.30.5229415502
0.01640748530.30.4715937685
0.0120021180.30.4194483428
0.00372493190.30.3658042347
0.00117589320.30.3116985929
TIME
FLOW (m3/s) or FILLING
Puls
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
TIME
INPUT MASS
RESPONSE RATE
Convolutie
1
1outputinputimpuls
00110
10.1586552598100.1586552598
20.3794777663100.2208225065Step response
30.5392770028100.1597992365
40.6503606114100.1110836087
50.7288829487100.0785223373
60.7857495967100.056866648
70.8279028074100.0421532107
80.8598044954100.031901688
90.8843904225100.0245859271
100.9036417104100.0192512879
110.9189276883100.015285978
120.9312156911100.0122880028
130.9412025995100.0099869084
140.9493993536100.0081967541
150.9561865191100.0067871655
160.9618516073100.0056650882
170.966614634100.0047630267
180.9706459372100.0040313031
190.9740788009100.0034328637
200.9770185339100.002939733
3011
4011
&A
Pagina &P
Convolutie
output
input
TIME
INPUT / RESPONSE RATE
Blad7
00000000.25
10.15865525980.158655259810.039663814900.03966381490.25
20.37947776630.379477766320.094869441600.09486944160.25
30.53927700280.539277002830.134819250700.13481925070.25
40.650360611400.650360611440.162590152900.16259015290.25
50.72888294870.15865525980.5702276894.0050.1625900.162590
60.78574959670.37947776630.406271830550.18222073720.03966381490.14255692220
70.82790280740.53927700280.288625804760.19643739920.09486944160.1015679576
80.85980449540.65036061140.20944388470.20697570190.13481925070.0721564512
90.88439042250.72888294870.155507473780.21495112380.16259015290.052360971
100.90364171040.78574959670.117892113690.22109760560.18222073720.0388768684
110.91892768830.82790280740.0910248809100.22591042760.19643739920.0294730284
120.93121569110.85980449540.0714111958110.22973192210.20697570190.0227562202
130.94120259950.88439042250.056812177120.23280392280.21495112380.0178527989
140.94939935360.90364171040.0457576433130.23530064990.22109760560.0142030443
150.95618651910.91892768830.0372588307140.23734983840.22591042760.0114394108
160.96185160730.93121569110.0306359162150.23904662980.22973192210.0093147077
170.9666146340.94120259950.0254120345160.24046290180.23280392280.007658979
180.97064593720.94939935360.0212465836170.24165365850.23530064990.0063530086
190.97407880090.95618651910.0178922819180.24266148430.23734983840.0053116459
200.97701853390.96185160730.0151669266190.24351970020.23904662980.0044730705
210.980.9666146340.013385366200.24425463350.24046290180.0037917317
220.9830.97064593720.0123540628210.2450.24165365850.0033463415
230.9850.97407880090.0109211991220.245750.24266148430.0030885157
240.9870.97701853390.0099814661230.246250.24351970020.0027302998
30110240.246750.24425463350.0024953665
40110300.250.250
400.250.250
3.9351.14634
&A
Pagina &P
Blad7
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
TIME
INPUT / RESPONSE RATE
Blad8
324
UH
0003mm2mm4mm0
10.110.300.3
20.220.60.200.8
30.2530.750.40.41.55
40.1840.540.50.81.84
50.1450.420.3611.78
60.0960.270.280.721.27
70.0470.120.180.560.86
80800.080.360.44
9900.160.16
101000
133
222
344
4
5
6
7
8
9
10
&A
Pagina &P
Blad8
000
000
000
000
000
000
000
000
000
000
3mm
2mm
4mm
TIME
q
Blad9
0
0
0
0
0
0
0
0
0
0
0
U
Blad10
000
000
000
000
000
000
000
000
000
000
N
Blad11
neerslag
homogeen.4;.8;2.6;.8;.4drempel = 0.45
000
0.158655259800.15865525980.0634621039
0.22082250650.158655259800.37947776630.2152532104
0.15979923650.22082250650.158655259800.53927700280.65308137520.08927700280.2030813752
0.11108360870.15979923650.22082250650.158655259800.65036061140.87333555740.20036061140.4233355574
0.07852233730.11108360870.15979923650.220822