Transcript Diapositiva 1 - — CNR

WORLD ENVIRONMENTAL & WATER RESOURCES
CONGRESS
National Research Council
Research Institute for Geo-Hydrological Protection
Palm Springs, California – May, 22-26
G. Corato, F. Melone and T. Moramarco
Research Institute for Geo-hydrological Protection, National Research Council,
via Madonna Alta, 126 I-06128 Perugia (Italy) [email protected]
Introduction
Purpose Method Case Study Results Conclusions
Discharge measurements during floods are important for the assessment
and the accuracy of rating curves.
Introduction
Purpose Method Case Study Results Conclusions
Discharge is traditionally estimated by sampling velocity points in all parts
of the flow area.
Distance [m]
During a flood, velocity measurements can be difficult to carry
out and sometimes dangerous for the operators.
Introduction
Purpose Method Case Study Results Conclusions
1. Is it possible to assess the 2D velocity
distribution by using the maximum velocity in
order to estimate the mean flow velocity?
2. How accurate is this estimation?
umax
Monte Molino
Molino (Tiber
(Tiber River):
River): flood
flood event
event of
of November
November 2005
2005
Monte
Introduction Purpose Method Case Study Results Conclusions
To address velocity measurements during high
floods by sampling the maximum velocity only;
To assess the uncertainty related to the estimated
mean velocity.
Introduction Purpose Method Case Study Results Conclusions
The 2D velocity distribution can be simulated by using the entropic model
Chiu (1988):
u   
umax 
  0 
ln 1  eM  1

M



max
0



Algerian Rivers
Maximum velocity [m/s]
Mean velocity [m/s]
Mean velocity [m/s]
um
eM
1
  M   M

umax
e 1 M
Tiber River(Italy)
Maximum velocity [m/s]
Introduction Purpose Method Case Study Results Conclusions
Velocity profile (Moramarco et al., 2004):
umaxv (x) 


y
y
u ( x, y ) 
ln 1  eM  1
exp 1 

M
D
(
x
)

h
(
x
)
D
(
x
)

h
(
x
)





umaxv is sampled
The entropic paramater M:
• is caracteristic of the section
• is estimated through the historical sampled pairs
(um, umax) by using the linear entropic relation:
um    M  umax
Introduction Purpose Method Case Study Results Conclusions
Measurement time can be
drastically
reduced
by
sampling umax only and
modeling umaxv.
Maximum vertical velocity distribution (Moramarco et al., 2011):
2

 x  
umaxv (x)  umax 1  
 

 xbank  

with
0.5
1
 
xbank = xL or xbank = xR the distance of river bank to the y-axis.
elliptical
parabolic
Introduction Purpose Method Case Study Results Conclusions
Based on error analysis on vertical mean velocity umv
non gaussian
  X  1  1


g  X,    


ln  X  1
if
 0
if
 0
(Box and Cox, 1964)
gaussian
Procedure steps (Misirli et al., 2003)
z(x) = g(umv (x), )
1
Transformation
2
Error on z space
e(x) = zcomp(x) - zobs(x)
3
Confidence Bounds of z
z  (x)  zcom(x)  u /2s e
4
Confidence Bounds of umv

1

um
(
x
)

g
(
z
(x), )
v
5
Confidence Bounds of um
um

1

A
xrigth

xleft

umv dA
and
se= STD(e)
Introduction Purpose Method Case Study Results Conclusions
Forecast Range Error Estimate (FREE) (Misirli et al., 2003).

FREE 
where
Minimum
FREE
=
umv
dist x 0
number of dist x  0
u
 mv
dist x  
um
 v
Maximum data
inclusion
dist > 0
x
Constrains on umaxv distribution
umaxv(0) = umax

 umv
obs

dist x
obs
 umv
+


dist x 0
dist x
number of dist x  0
if
umv
obs
 umv
com
if
umv
obs
 umv
com
0
0
Minimum confidence bounds
width
umv|+
umv|+
and
umv observed
umv computed
umaxv(xbank) = 0
umv|-
Uncertainty on umaxv decreases near the river banks and the y-axis
distx < 0 u |mv
Section width is split in n parts depending on dimensionless position, x/xbank, of
vertical. In each part  is calibrated and the related se is computed
x
Introduction Purpose Method Case Study Results Conclusions
Basin Area
[km2]
Sampling period
1956
1982-2002
Velocity measurements
36
Sampled verticals
Discharge
Q
360
[m3/s]
3-171
Water level D
[m]
0.9-3.9
Section Width
[m]
31.6-36.3
umax depth h
[m]
0.06-0.56
Available data for each measurement
• observed velocity
• elevation from the bed
• position of sampled verticals
• hydrometric level
• mean flow velocity and discharge
Topographical surveys for whole sampling
period showed no significant changes in
the river section
Introduction Purpose Method Case Study Results Conclusions
M= 2.13
umax has always been observed in the
same portion of the flow area, wide ~7 m
Along the Tiber River
Brocca et al. (2010) found
M = 2.05-2.17
Maximum Vertical Velocity Error [%]
Introduction Purpose Method Case Study Results Conclusions
According to the constraints on umaxv distribution, confidence bounds are larger
between the y-axis and the river banks
Introduction Purpose Method Case Study Results Conclusions
Near the river banks a measured value of umaxv
is needed to reproduce velocity profiles
Velocity Measurement of 28th May 1984.
Mean Vertical Velocity Error [%]
Introduction Purpose Method Case Study Results Conclusions
Near the banks low velocities and low depths
give a minimum contribution in discharge
Introduction Purpose Method Case Study Results Conclusions
Introduction Purpose Method Case Study Results Conclusions
Calibration set of 16 velocity measurements
Validation set of 20 velocity measurements
Introduction Purpose Method Case Study Results Conclusions
25th October 1993, minimum water level (1.41 m)
30th January 2001, maximum water level (3.90 m)
Introduction Purpose Method Case Study Results Conclusions
95%
Calibration Set
Validation Set
90%
85%
80%
75%
70%
umaxv1 meas.
2
Parabolic
3
Elliptical
Introduction Purpose Method Case Study Results Conclusions
Calibration set
Validation set
Introduction Purpose Method Case Study Results Conclusions
The entropic method is suitable to accurately estimate the mean flow
velocity.
Using an elliptical spanwise distribution of umaxv it is possible to drastically
reduce the measurement time still obtaining a fairly accurate estimation
of the mean flow velocity.
In the preliminary results, the Box-Cox transformation
and the FREE statistic appear suitable to assess the
mean velocity uncertainty.
The procedure has a considerable potential application,
considering that "no contact" methods are available for
monitoring surface velocity, from which maximum
velocity can be estimated (Corato et al., 2011; Brocca
et al., 2010; Fulton & Ostrowski, 2008).
Box, G. E. P. and Cox, D. R. (1964). "An analysis of transformations". Journal of the Royal
Statistical Society, Series B 26(2): 211–252.
Brocca, L., Corato, G., Corradini, C., Melone F., Moramarco, T., (2010). “Stima della velocità
media in canali naturali attraverso il monitoraggio della velocità massima superficiale”,
Proc. 32° Convegno di Idraulica e Costruzioni Idrauliche, Palermo, Italia.
Chiu, C.L. (1988). Entropy and 2-D velocity distribution in open channels, J. Hydr. Engrg.,
ASCE, 114(7), 738-756,
Corato, G., Moramarco, T. and Tucciarelli, T. (2011). “Combining flow routing modelling and
direct velocity measurement for optimal discharge estimation”, Hydrol. Earth Syst. Sci.
Discuss., 8, 2699-2738, doi:10.5194/hessd-8-2699-2011.
Fulton, J. and Ostrowski, J. (2008). “Measuring real-time streamflow using emerging
technologies: Radar, hydroacoustics , and the probability concepts”, Journal of Hydrology,
357, 1-10.
Misirli, F., Gupta, H.V., Sorooshian, S., Thiemann, M., (2003). “Bayesian recursive estimation of
parameter and output uncertainty for watershed models”. In: Duan, Q.J., Gupta, H.V.,
Sorooshian, S., Rousseau, A.N., Turcotte, R. (Eds.), “Calibration of Watershed Models”.
Water Science Application No. 6, AGU, Washington DC, pp. 125-1132.
Moramarco T., Saltalippi C. and Singh V.P (2004). "Estimating the cross-sectional mean
velocity in natural channels using Chiu's velocity distribution", Journal of Hydrologic
Engineering, ASCE, 9(1), 42-50.
Moramarco T., Saltalippi C., Singh V.P. (2011). "Velocity Profiles assessment in natural channels
during high floods", Hydrology Research, 42(2-3), 162-170.