Estimating Channel Storage and Discharge Hydrographsof Flooding
Shoji FUKUOKA 1, Akihide WATANABE 2

To estimate channel storage and reduction of peak discharge—uniqueproperties of flood flows—the authors performed intense, fully planned
observation of flooding in a 7-km section of the Edo River and carried out adetailed investigation of the longitudinal distribution of discharge and water level
hydrographs. Then, the water level hydrographs by this temporally and spatiallyintense observation were used to estimate storage and discharge hydrographs of theobserved flood flow in accordance with a two-dimensional unsteady flow analysis
technique developed by the authors. The accuracy of flood flow observation was
examined through intense observation and analysis and recommendations are madefor a method of flood observation that should prove useful in estimating channel
storage and reduction in peak discharge.

1. Introduction
In a compound channel, discharge decreases in the rising-water phase, as floodwaters
flow into the flood channel, and increases in the receding-water phase, as floodwaters flow
back into the main channel from the flood channel. Consequently, discharge in a compoundchannel during flooding varies longitudinally with distance downstream, such that peakdischarge decreases with distance downstream. Laboratory studies have shown that peakdischarge decreases particularly when the main channel meanders or the flood channel has ahigh roughness coefficient1), 2), 3). Field observation3) and numerical analysis4) of floodhydrograph transformation and channel storage in actual rivers is being carried out to arrive at
a method for estimating longitudinal changes in the discharge hydrograph and reduction inpeak discharge in such compound channels because such a method would be highly
significant with regard to river planning and flood safety assessment. This paper discusses theanalysis of temporal and spatial changes in water surface profile and discharge of flood flow
as determined by intense observation in a 7-km section of the Edo River (between the 39 km
and 46 km points) and presents a method for estimating the discharge hydrograph from
Observed flood level hydrographs for the Edo River and a two dimensional unsteady flow
analysis. Then, the accuracy of intense observation is discussed, and a method for flood
observation is proposed.
Dense vegetation

Discharge
observation point
45
46 km
km

(m)
100

Main channel

Athletic ground

43 km
44
km

50

42

41

40

Discharge
observation point Levee
39 km

Flood channel

0

100

200

300

400

500

600

700

Levee

800
(m)

Fig.1 Planform of the Edo River section observed (46.0km – 39.0km)

1Professor, Department of Social and Environmental Engineering, Graduate School of Engineering, Hiroshima
University, Japan, ph.+81-824-24-7821, fax +81-824-24-7821, sfuku@hiroshima-u.ac.jp
2
Associate Professor, Department of Social and Environmental Engineering, Graduate School of Engineering,
Hiroshima University, Japan, ph.+81-824-24-7819, fax +81-824-24-7821, awata@hiroshima-u.ac.jp

2. Analysis of Channel Storage and Reduction in Peak Discharge
Figure 1 shows the planform and ground cover condition of the Edo River section
observed. The flood channel of this section, located between upstream and downstream
discharge observation sections, is primarily grassland, with other, more substantive vegetation
distributed sparsely over a large area. Vegetation growth is dense between the 42.5 km and 44
km points. Some parts of the flood channel are used as athletic grounds, and a golf course
exists on the right bank, on a site whose upstream boundary is near the 41 km point. In theanalysis, velocity was calculated using the following equations of motion in the generalcoordinate system:
~
~
~
¶V
¶U
¶q x
¶q x
~ ¶U ~ ~ ~~ ¶U ~ ~ ~hx ¶V} - t zx
h + Uh{ ~ - J (V - U cosq hx ) ~ } + Vh{ ~ - J (V - U cosq hx ) ~ } = - gh{ ~ + cosq
¶h~
¶t
¶h
¶h
¶x
¶x
¶x
+

1 ¶ Jh ~¶ Jh ~¶q x ~¶q x~[ ( t xx ) +( t xh )] - J h(-t~xx cosq hx + t~xh ) ~ - J h(-t~xh cosq hx + t~hh ) ~J ¶x dx
¶h dh
¶h
¶x

(1)

where the shear stress term t zx represents bottom shear stress and the fluid resistanceresulting from the vegetation. This is determined as follows using the Manning roughness
coefficient n and the vegetation permeability coefficient K, revealing the difference inresistance variance according to depth:
gn 2

t zx = ( 1 / 3 +
h

gh
K

2

~ ~
~~
~
~
) u 2 + v 2 U ， u 2 + v 2 = J 2 (U 2 - 2UV cosq hx + V 2 )(2)Table 1 Coefficients of Manning roughness and vegetation permeability
Place
Main channel
Flood channel ground
Right bank46.0-43.0 km
Left bank
Right bank43.0-42.0 km
Left bank
Right bank42.0-40.5 km
Left bank
Right bank40.5-39.0 km
Left bank

Roughnesscoefficient
0.029
0.031
0.044
0.038
0.049
0.049
0.044
0.044
0.038
0.038

Place
46.0-43.5 km
43.5-42.5 km
42.5-42.0 km
42.0-40.5 km
44.5-43.0 km
43.0-42.0 km
42.0-41.0 km

Right
bank
Left
bank

Vegetation
permeability
coefficient (m/sec)
60.0
30.0
40.0
60.0
45.0
50.0
60.0

The Manning coefficients for main channel and flood channel roughness andvegetation permeability used in the analysis were determined so that the calculated discharges
and surface profiles would generally match the observed values; these assumed values arelisted in Table 1. Because the vegetation could not be precisely positioned in the calculation
mesh, an average vegetation permeability coefficient for the entire flood channel was usedwith the roughness coefficient. Figure 2 shows the cross-sectional shape of the 39–46 km
section used in the analysis. In this section, the main channel is 80–120 m wide; the distance
between levees, roughly 400 m. Flooding was observed over a 48-hour time period lastingfrom 12:00 a.m. September 11 to 12:00 a.m. September 13. Thus, the start time in thecalculations is also 12:00 a.m. on the 11th.

10
Height (m)86Section 39km
Section 40km
Section 41km
Section 42km

4
2
0

50

100

150

200

250

(a) 39km - 42km

300
350
400
Lateral distance (m)10Height (m)86Section 43km
Section 44km
Section 45km
Section 46km

4
2
0

50

100

150

200

250

(b) 43km - 46km
Fig. 2 Cross-sectional shape (39km - 46km)

400
350
300
Lateral distance (m)In ordinary unsteady flow analysis, discharge at the upstream end and water level atthe downstream end is given, and temporal change in discharge and water level is calculated.
During observation of Edo River flooding on September 11, discharge at the upstream anddownstream ends was observed nearly every hour. Water level was observed on the left andright banks roughly each hour at intervals of 0.25 km in the 46–41 km section and at 0.5 km
intervals in the 41–39 km section. However, as discussed below, the values for upstream anddownstream end discharge observed each hour contained error that resulted in a large
difference in discharges, thus failing to satisfy the continuity conditions.
In general, error in observed discharge is considered to be greater than error in the
profile of water level observed at multiple points. In the authors' analysis, because observed
water level is assumed to have the greater accuracy, water level at the upstream anddownstream ends is given, and roughness is adjusted so that the calculated discharge for the
upstream end matches the corresponding observed discharge.
Figure 3 is a flowchart of the overall analysis procedure. As it shows, the first step isto create the boundary conditions from the observed values by interpolating time series datafor upstream and downstream end water level. In this stage, one cycle of flood calculations is
performed while measuring error and adjusting upstream and downstream water levels as in amodel experiment so as to eliminate error, so that calculated water level for each specified
location at each time point agrees with the observed values. Next, the calculated dischargehydrograph and calculated temporal variation in the longitudinal distribution of water levelare compared with the observed results, after which the absolute value and relative
distribution of the coefficients of roughness and vegetation permeability are altered so as tobring the observed and calculated results closer to agreement. Flood flow calculations arerepeated until the calculations obtained match the observed results. Because discrepancy
between the calculations and the observed results can also results from poor accuracy in theobservations, care is required to determine whether such discrepancy is due to unadjusted dataor to observation error.

Observed
water level anddischarge

Topography data(planform and sectional
form)

Create boundary conditions(time series for upstream anddownstream end water level)

Createcalculation mesh
Distribution ofroughness andvegetation permeability
coefficients

Analyze water leveland discharge

Compare upstream
water levels

Adjust upstream
water level

Compare downstream
water levels

Adjust downstream
weir height
Reverse analysis ofroughness coefficient

Results
Discharge hydrographLongitudinal
distribution of water
Compare with observed
discharge

Adjust absolute valueof resistanceCompare with observed
surface profile

Groundcover data

Adjust distributionof resistanceFig 3 Flowchart of overall analysis.
13.0

Water level (m)

12.5
12.0
11.5
11.0
left bank 45.00km
left bank 45.50km
right bank 45.00km
right bank 45.50km

10.5

left bank 45.25km
left bank 45.75km
right bank 45.25km
right bank 45.75km

10.0
0

5

10

15

20
25
30
Time (hour)

35

40

45

Fig.4 Temporal change in observed water level in an upstream part

Figure 4 shows temporal changes in observed water level in an upstream part (45–45.75 km) of the observed section. The considerable variation in observed water level at theleft and right banks in this upstream section is believed to reflect considerable observation
error. With the calculation mesh positioned so that the right bank water level at the 45 km
point corresponds to the right bank at the mesh's 45 km point, water level at the downstream
end discharge observation point was used as the average downstream end water level for the

13

2500

12
11
Water level (m)Discharge (m 3/s)

2000
1500
1000

5

10

15

20
25
30
Time (hour)

3540

Fig.5 Comparison between the observedand calculated discharge

845.00km observed water level39.25km observed water level45.00km calculated water level39.25km calculated water level45.00km cross-sectional shape

6
5

0
0

9

7

observed upstream end discharge
observed dow nstream end discharge
calculated upstream end discharge
calculated dow nstream end discharge

500

10

45

4
0

5

10

15

20

25

30

35

40

45

Time（hour）

Fig.6 Observed and calculated water levels for the
upstream and downstream ends and crosssectional shape at the 45km point

calculation mesh. In the calculations, water levels at the upstream and downstream ponds inthe mesh are automatically adjusted so that the observed and calculated water levels for these
sections agree3).
Figure 5 shows the calculated and observed discharges for the upstream anddownstream end discharge observation points. Figure 6 shows the observed and calculated
water levels for the 45 km point (upstream) and the downstream end discharge observation
point, along with the channel's cross-sectional shape at the 45 km point. The figures show thatthe upstream and downstream water levels roughly satisfy the given boundary conditions. At
12:00 a.m. on the 11th (the analysis start time), water level at the 45 km point is 9.5 m, withroughly 1 m of water in the flood channel. The observed section's flood channel also exhibits
the same amount of water levels. As for discharge, because the analysis is synchronized to thedischarge at the upstream end in the rising-water phase, calculated upstream discharges in therising-water phase agree well with observed discharges. However, calculated discharges at thedownstream end are larger than the observed values. Comparison of calculated and observed
discharges shows that at the time of peak water level, observed discharge upstream has
already dropped considerably even though water level has continued to rise. Such a state isinconceivable in light of the continuity relationship of water level. On the other hand, theupstream and downstream end discharges in the receding-water phase present no problem
within the range of observation accuracy. Although further investigation is needed, it isbelieved that there was some problem with discharge observation accuracy at the upstream
end in the rising-water phase. Ordinarily, there should be almost no difference between peakdischarges upstream and downstream, and the difference between calculated discharge andobserved upstream end discharge at the peak should be almost the same as that during thereceding-water phase. However, this difference is more than 100m3/s, suggesting thatobserved discharge during the rising-water phase was probably overestimated.

3. Results of Analysis and Consideration
As Figure 5 shows, calculated discharge changes slightly with distance downstream,
but peak discharge hardly decreases at all. Peak discharge falls less than 0.5% (10[m3/s]/2100[m3/s]) roughly 6.5 km downstream from its occurrence. Because temporal change
in discharge in the Edo River is very gradual, peak discharge and water level both continued
for 3–4 hours in the observed section, as shown in Figures 5 and 6. Considering that the flood
travel time in the observed section is 1–2 hours, discharge and water level remained nearlyconstant at and around the peak. This is believed to explain the low amount of storage
associated with the flood flow's unsteadiness. Similar results for storage can be expected solong as agreement with observed water level profiles is sought in water surface profile
analysis, regardless of what values are used for the discharge or roughness coefficients. For
this section to have an unsteady flow characteristics and thus make considerable channel
storage of the floodwaters possible would require the type of flood hydrograph that precludes
steady flows, i.e., a time scale that is one-third to one-fourth of this particular flood's timescale. Flood hydrographs in the Maruyama River do have a time scale that is conducive tosuch unsteady flows4), and this is believed to explain the significant decrease in discharge that
occurs there. Figure 7 shows the longitudinal distribution of observed and calculated waterlevel in the rising-water phase (7a), at peak water level (7b), and in the receding-water phase(7c). Excepting the 43 km point, the calculated values generally agree with the observed
values. Although the water level increase near the 43 km point is attributable to vegetation,
increasing the resistance of the vegetation in the calculations does not yield as great anincrease as was observed there; in fact, only a local rise in surface slope occurs, such that
overall agreement in surface profile is lost. In addition, 22 hours after the start of flooding (i.e.,
at peak), observed water level on the left bank of the 46–43 km section was 20 cm higher thanthe calculated water level and the observed water level on the right bank. However, because it
Lef t bank observ ed water lev el

13.0

Right bank observ ed water lev el
Calculated water lev el 6h

Water level (m)12.5

Calculated water lev el 8h
Calculated water lev el 10h

12.0

Calculated water lev el 12h
Calculated water lev el 14h

11.5

Calculated water lev el 16h

11.0
10.5
10.0
9.5
9.0
39

Fig.7(a)

40

41

42

43

Time (hour)

44

45

46

Longitudinal distribution of observed and calculated
water level (rising-water phase)

13.0

Water level (m)

12.5
12.0
11.5
11.0
10.5

Left bank observed w ater level

10.0

Calculated w ater level 18h

Right bank observed w ater level
Calculated w ater level 22h

9.5

Calculated w ater level 26h

9.0
39

40

41

42

43

44

45

Time (hour)Fig.7(b)Longitudinal distribution of observed and calculated
water level (peak-water level phase)46

Left bank observed w ater level
Right bank observed w ater level
Calculated w ater level 28h
Calculated w ater level 32h
Calculated w ater level 36h
Calculated w ater level 40h

13.0
12.5

Water level (m)

12.0
11.5
11.0
10.5
10.0
9.5
9.0
39

40

41

42

43

44

45

46

Time (hour)Fig.7(c) Longitudinal distribution of observed and calculated water level(receding-water phase)is inconceivable that the left bank water level could be higher at the peak—when discharge isroughly constant—this is likely a result of observation error. The preceding shows that
temporal change in surface profile can be easily tracked using numerical methods.
In the 45.75–39.5 km section, cross-section-averaged water levels were calculated forobserved and calculated values by averaging the left and right bank water levels; these
averages, weighted by each section's water surface area, are shown in Figure 8. (Note that thedata are presented in 2-hour increments.) Multiplying a section's surface area by the change inwater level in Figure 8 produces the amount of storage, which is time-differentiated to yield
the storage per unit time. The temporal change each 2 hours in mean storage rate in thesection as calculated from the values in Figure 8 is shown in Figure 9, along with thedifference between calculated and observed values for upstream and downstream discharge.
Figure 8 shows that the calculations can reproduce floodwater storage in the observed
section. The differences at peak in Figure 8 are, as already shown in Figure 4, due to thehigher observed water level upstream on the left bank at peak. The agreement, seen in Figure
9, between the storage rate (dS/dt) determined from observed and calculated water surface
profile and the storage rate determined from the calculated discharge differential (Qin–Qout)
12.0

Water level (m)

11.5
11.0
10.5
10.0

observed water level9.

calculated water level

9.

0

5

10

15

20
25
30
Time (hour)

35

40

45

Fig.8 Temporal change in average water level in the observed section

Storage rate (m3/s)

400
dS/dt observation
Qin-Qout observation
dS/dt
calculation
Qin-Qout calculation

300
200
100
0
-100
-200

0

5

10

15

20
30
25
Time (hour)

35

45

40

Fig.9 Temporal change in storage rate

indicates the numerical method's high reproducibility with regard to actual floodwater storage.
The storage rates are low: 100 m3/s in the rising-water phase and –40 m3/s in the recedingwater phase. These low storage rates, along with the small difference in shapes between therising- and receding-water phases, indicate that extensive storage did not occur and thatdischarge hydrograph transformation was consequently low in this flood. On the other hand,the storage rate determined from observed discharge exceeds the actual storage rate in therising-water phase but is less than the actual storage rate in the receding-water phase.
Because the reduction in discharge over a section of several kilometers is on the orderof at most several percentage points relative to peak discharge, discharge must be measured
correctly to be accurate at a percentage level. However, as the results of these calculations
show, if the accuracy of field observation is to be taken into account, then the quantitative
reduction in peak discharge can be determined more accurately with a method that tracks
temporal change in profile than it can be with observed discharge. In other words, the detailed
observation of water levels is the superior method for assessing channel storage in actual
rivers.

Discharge (m 3/s)

2500

2000

1500

1000

500

8

8.5

9

9.5
10
Water level (m)

10.5

11

Fig.10 Calculated water level and discharge relationship for thedownstream end discharge observation point (39.25km)

The calculated water level–discharge curve for the downstream end discharge
observation point (Figure 10) is a clockwise-looping curve. However, the loop is extremely
narrow, almost overlapping at the peak, indicating particular small unsteadiness near the peak.
Because the degree of unsteadiness depends on the relationship between flood travel time(itself determined by flood flow velocity and section length) and the duration of the steadyphase at peak, either the time scale of the flood hydrograph is shortened, yielding a sharp
discharge hydrograph, or a longer observed section is chosen to increase the effect of
unsteadiness, i.e., to manifest the effect of the channel storage of floodwaters.
The Edo River flood considered in this paper had poor unsteadiness, particularly near
the peak, so that there is almost no decrease in discharge with distance downstream. In
addition, variation in channel storage and peak discharge can be estimated by adjusting the
calculated surface profile at each point in time to the observed surface profile. Accurate
estimations of a discharge hydrograph require accurate values for observed discharge, but thetemporal change in discharge between its low and high values can be back-calculated withmeasurements from only several points therebetween; such a technique should be especially
useful for estimating peak discharge. The accuracy of discharge estimated by this technique isdirectly determined by the accuracy of observed discharge. Observed discharge used by theauthors contained error on the order of 100 m3/s because of the relatively short section at
whose upstream and downstream ends discharge was measured and because of detailed
measurements of surface profile. The authors were able to assess this error quantitatively byobserving upstream and downstream discharge and by tracking surface profile. An error of
100 m3/s corresponds to merely 5% of peak discharge in the Edo River. The degree of error
depends on the accuracy of the discharge observation technique, and although accuracy isdifficult to improve, the observation technique used by the authors in the Edo River makes it
possible to determine the degree of error in observed discharge. For a slow-moving flood suchas the one considered herein, an effective means of determining the transformation of adischarge hydrograph over a long distance is to define a long section (i.e., one on the order oftens of kilometers long), establish therein multiple sections for the intense observation ofdischarge and water level, use the observed results to validate calculated discharge, and track
the temporal change in surface profile over a long range using observation point water leveland other data.
Discharge hydrograph transformation and peak discharge reduction have been shownto occur in cases where discharge changes over a short time scale as in the Maruyama River
study, in which the observation section legnth (5 km), river width (250 m), discharge, andwater level change were similar4). The time required for peak discharge to decrease 50% wassignificantly longer in the Edo River (peak discharge 2,100 m3/s) than in the Maruyama River(peak discharge 2,500 m3/s): 10 times longer in the rising-water phase and 6–7 times longer inthe receding-water phase. The Edo River's hydrograph overall is a U-shaped curve, whereasthat of the Maruyama river is an inverted U-shaped curve in the receding water phase becauseof the sharply dropping discharge. Flood flow unsteadiness affects hydrograph shape and timescale and has a great effect on the tendency of peak discharge to decrease with distancedownstream. However, even when discharge changes this abruptly, tracking of temporalchange in surface profile makes it possible to estimate peak discharge (from surface form) andchanges in peak discharge without the need for intense observation of discharge.
Although automation of discharge observation is still difficult in view of current
technology and accuracy considerations, automated water level and surface profile
observation is possible. Therefore, it should be possible to estimate temporal change indischarge accurately and with less labor-intensive discharge observation by using a method inwhich temporal change in discharge is estimated by numerical analysis and by the tracking of
temporal change in surface profile, with the data necessary for computational calibration
provided by a small number of discharge observation points. However, as already stated, theaccuracy of discharge values depends on the accuracy of discharge observation.
Furthermore, in both the Edo and Maruyama River studies, observation began after
waters had already started to flow into the flood channel, but because the channel storage rateincreases greatly when water enters the flood channel, measurements for the longitudinaldistribution of water level should, at the very least, begin before this point. When surface
profile has been tracked, discharge and roughness calibration can be performed to generate adischarge hydrograph for that period. In this respect, too, it is hoped that water level
observation will be automated to the degree that longitudinal change in surface profile can be
determined.

4. Issues for Future Consideration
Channel storage of a flood flow and the decrease in peak discharge vary depending on
the observed section's flood hydrograph properties (e.g., unsteadiness and peak discharge) andon channel properties (e.g., planform, cross-sectional form, and flood channel roughness). For
the Edo River, the relationship between the temporospatial distribution of rainfall in thedraining basin and the hydrographs of previous floods should be thoroughly investigated todetermine what type of flood hydrographs should be anticipated in the flood control planning.
Further, now that this research has essentially established a practical method for the unsteadyflow analysis of flood flows, the next step is to assess this method's accuracy by calculating
the downstream transformation of discharge hydrographs and storage through twodimensional unsteady flow analysis using the water level hydrographs from all automaticwater level observation points in a long river section and using discharge data on channel
cross-sectional form and planform taken at 200-m intervals. The next task is to thus establish
a method for assessing storage and peak discharge reduction in river sections and to
appropriately incorporate such storage rate quantities into planning throughout a river
extension.

References(1)Shoji Fukuoka, Akihide Watanabe, Hirokazu Okabe and Koh-tarou Seki (2000) : Effects of
Unsteadiness, Planform and Cross-Sectional Form of Channels on HydraulicCharacteristics of Flood Flow, Annual Journal of Hydraulic Engineering, JSCE,
Vol.44.pp.867-872.
(2) Shoji Fukuoka, Koh-tarou Seki and Daisuke Kurisu (2000) : Flood Flow Storage and Peak
Discharge Attenuation in Channels, Advances in River Engineering, Vol.6, pp.31-36.
(3)Akihide Watanabe, Shoji Fukuoka, Alex George Mutasingwa and Masaru Ota (2002) : The
Unsteady 2D Flow Analysis on the Deformation of Hydro-Graph and the Flood Flow
Storage in Compound Meandering Channels, Annual Journal of Hydraulic Engineering,
JSCE, Vol.46.pp.427-432.
(4)Shoji Fukuoka, Daisuke Kurisu, Alex George Mutasingwa, Tsuyoshi Nakamura andMasanori Takahashi (2002) : Effect of Levee and Main Channel Alignments and Flood
Channel Width on Water Storage During Flood Flow, Annual Journal of HydraulicEngineering, JSCE, Vol.46.pp.433-438.