R temporal VARIABILITY of
p™ped watershed behaviour and
EVALUATING AVERAGED PERFORMANCE OF A 
HYDROLOGIC MODEL
W.M.D Wijesinghe,
Research Assistant pepartment of Civil Engineering, University of Morahiwa) 
(email: dulanjanw@gmail.com)
N.T.S. Wijesekera,
Senior Professor Pepartment of Civil Engineering, University of Moratuwa) 
(email: sohan@civil.mrt.ac.lk)
Abstract: Majority of watersheds associated with civil engineering infrastructure projects are 
ungauged and most commonly used method to determine streamflow in ungauged basins is 
mathematical modelling with the use of Synthetic Unit Hydrograph (SUH) technique. Mathematical 
models require watershed characteristics to be spatially and temporally averaged. The SUH is an 
event based model which estimates direct runoff. Hence model calibration and verification requi: : 
event based evaluations with a baseflow separation effort or a method incorporating a baseflow model 
to combine with the SUH model and generate total runoff. In this study, a rainfall runoff model 
developed using SUH and a linear baseflow concept while selecting the watershed of Attanagalu Oya 
at Karasnagala as the study area. Other than the SUH parameters to be identified, the conceptual 
model used for this work consisted of 5 model parameters to be optimised. The main objective of this 
research was to identify the issues during calibration and verification of this five parameter model. 
Model calibration was carried out for 30 datasets, selecting the Mean Ration of Absolute Error 
(MRAE) as the objective function. Optimum model parameters for each event were determined and 
the most probable range of values for each parameter was computed. Using 30 datasets, model 
verification was carried out by assuming that the average of each range would lead to a representative 
watershed model. A successful calibration produced a good match of observed and calculated 
streamflows with a MRAE of 0.34. Parameter optimisation revealed the inability to obtain an average 
initial moisture level for the entire watershed while catering both wet and dry conditions. The runoff 
coefficients and rainfall thresholds also indicated the need of further investigations. Event based 
modelling approach in this work provides an insight to the watershed behaviour and to the 
appropriateness of model parameters, however in order to identify the spatially and temporally 
ged parameters it is necessary to carryout optimisations using a lengthy data series together with
an appropriate model.
ires
was
avera
selection. Model calibration. Rainfall-runoffSynthetic unit hydrograph, ParameterKeywords: 
modelling, Sri Lanka
Incorporation of mathematical models either 
physical, empirical in nature or their 
combinations is the most commonly used 
method for streamflow estimations.
1. Introduction
from ungaugedestimationsStreamflow 
watersheds is a challenge faced > m*n) 
engineers, hydrologists and v\ aters e 
managers. The world over, majority of strea 
reaches which require streamflow 1 orma ^on 
are ungauged (Young, 2006), n ri 
of 103 major basins only 13 gauging static*> are 
in existence (Hydrological Annual, )• 
streamflow
Though there are many watershed models 
which facilitate the estimation of watershed 
runoff, the most sought models are those which 
be used to estimate runoff generation from 
ungauged watersheds. Sherman (1932) 
introduced the theory of Unit Hydrograph 
OJH) for the generation of direct runoff from a
catchment, which is still considered as one
the most important contributions to hydrology
can
central
for water resource and water 
and management.
is aInformation on 
component 
quality engineering 85
-2012h for Industry Symposium (CERIS)
Civil Engineering Researc#
and a linear storage concept to 
conceptualise the baseflow
(ii) Identify optimum model parameters to 
predict streamflows from a particular 
rainfall dataset
(iii) Evaluate parameter behaviour with 
individual events and make
model
especially with work on ungauged watersheds. 
Synthetic Unit Hydrograph (SUH) is the only 
available UH derivation method for direct 
runoff estimation from ungauged watersheds.
Mathematical modelling of watersheds require 
conceptualisation of the reality to suit a 
particular requirement whether it is flood 
control water management or design of water 
infrastructure. Watersheds and their porous 
soil mass covered with vegetation demonstrate 
a wide spatial heterogeneity and a temporal 
variability. Lumped watershed models attempt 
to aggregate both spatial and temporal 
variability in order to capture the requisite 
watershed behaviour, while spatially 
distributed modelling try to incorporate a lesser 
aggregation of spatial variability. In case of 
calibration, a model would identify a set of 
parameters that would reproduce the 
streamflow variations over a significant time 
period or reproduce a set of selected sections 
from a hydrograph spanning over a longer 
duration.
forrecommendations
development
Methodology3.
Identification of 
Objectives
I
Literature Survey
*> r
Watershed
Demarcation
UH> Spreadsheet
Model
J Rainfall / 
/ Data /
DRH Runoff 
Hydro graphTheissen
Averaged Rainfall >The calibration and verification of direct runoff 
models require either a baseflow separation 
from the observations or a baseflow generation 
model coupled to the direct runoff generation 
model. Modelling of direct runoff is an event 
based task and hence a modeller is required to 
calibrate individual events which take place at 
various stages in the annual hydrological cycle. 
In this task the modeller has to consider the 
temporal variation of watershed parameters 
such as initial storage, runoff coefficient, 
baseflow coefficient etc.
The most common method of handling such 
variations is to conceptualise threshold 
parameter values in order to represent 
circumstances such as wet and dry conditions, 
flat and hilly terrain, change of monsoonal 
winds etc. In this backdrop the present work 
carried out the development of a conceptual 
watershed model with a UH concept coupled to 
a baseflow generation component in order to 
estimate streamflows for selected sections of 
rainfall time series. Selected sections were 
chosen to represent peakflows that occurred at 
the gauging point.
Streamflow
Data
Event
Selection Total Runoff 
Hydrograph 
Development
T >
Calibration of the 
Model
J
Verification of Model
Comparison
I
Discussion and
Figure 1: Methodology Flowchart
The methodology used for the present work 
(Figure 1) included a literature survey, 
identification and checking of data, model 
development, model calibration and 
verification.
There are several methods that are popularly 
used for unit hydrograph model development. 
They are the Rational method (Ponrajah, 1984), 
US Soil Conservation Service (SCS) method 
(Chow, Maidement and Mays, 1988), and 
Snyders method (Mays, 2004). Though, there
Objectives
The following tasks were undertaken as the 
objectives of the present work.
(i) Develop a hydrologic model having a 
UH concept to represent direct runoff
2.
* 86Civil Engineering Research for Industry Symposium (CERIS) - 2012
are several publications on the comparison of 
results generated with the use of these 
methods, it is still not clear which method 
could be recommended for a
Linear storage concept is widely used to 
present watershed baseflow behaviour (US 
Army, 1980, Wijesekera, 2000). Model 
calibration and verification techniques for 
Parameter optimisation use several objective 
funrtons (WMO, 1986). Among them the 
mostly used indicator is the Mean Ratio of 
Absolute Error (MRAE) (Wijesekera and
2003, Nandalal and Rathnayake, 
2010, Perera, 2011). The MRAE which provides 
guidance on the degree of matching with 
respect to two datasets consider the _. 
deviation of model predictions (Equation 1),
_ • y K=71 —c?2 j 
n -52
where, is usually the calculated data while qi 
is the observed data, n is the number of data in 
each data set
particular
watershed or for a particular purpose. In the 
published literature there are only limited 
pertaining to applications in the Sri Lankan 
context. Among them there are two on the 
application of SCS method. Wijesekera (2000) 
in a comparison of SCS and other UH 
applications for small urban watersheds have 
indicated
cases
wide variation of outputs.
and meanBatuwitage,
Wickramasuriya (1986) applied Rational 
Method, Snyder's Method, SCS Methods for 
peak flow estimation and compared the results 
with the outputs from the Statistical Methods. 
Zlatunova, Gergov and Littlewood (2002) 
developed a UH based flow simulation model 
for five Bulgarian Rivers, discussing the 
potential of the UH approach in assisting with 
regional surveys and
Manchanayake
MRAE (1)
4. Data
Present work selected the Karasnagala 
watershed of Attanagalu Ova due to the 
availability of a lengthy gauged data series. 
Attanagalu Ova is one of the 103 major rivers of 
Sri Lanka, located in the Western Province. 
Watershed at Karasnagala (Figure 2) is located 
at the upper most section of the river basin. 
Streamflow measurement of Attanagalu Oya 
had been carried out from 1970 to 1982 at the
water resources
In this model, a preliminarymanagement, 
assessment of the suitability of a UH-based 
modelling methodology for application to small 
and medium-sized rivers in south-east Europe 
has been carried out. Yen and Lee (1997) used 
the Geomorphic Instantaneous UH Method for 
two hilly watersheds in the Eastern United 
States and two flat-slope watersheds in Illinois, 
where a comparison between the simulated and 
observed hydrographs for a number of 
rainstorms has indicated its potential in 
watershed rainfall-runoff analysis.
Different techniques have been used for 
modelling the watersheds whose watershed 
parameters are spatially distributed. Saghafian, 
Julien and Rajale (2002) used variable isochrone 
techniques to simulate the runoff hydrographs 
for a 15.6 ha pilot watershed in West Africa. 
This work had utilised a raster based runoff 
simulation of rainfall intensity and infiltration 
rate to model the watershed.
Karasnagala gauging station. Since 2005, the 
gauging station had been moved from 
Karasnagala to Dunamale which is further 
downstream of the river. Annual average 
rainfall and streamflow values for the 
considered study period are 1433mm and 242 
MCM, respectively. Karasnagala Watershed 
has an area of 52.8 km2. Gauged streamflow 
data of this basin has been checked extensively 
during previous studies (Prerera, 2010, 
Wijesekera and Perera, 2012). Prior to 
modelling, the entire rainfall and streamflow 
data series was plotted and checked for any 
visual inconsistencies. The topographic survey 
sheets of 1:10,000 published by the Survey 
Department of Sri Lanka were used for the 
watershed delineation. Length of the longest 
stream of the watershed is 9.8km and the slope 
of the watershed along the longest stream is 
The watershed is at a rural setting with 
a very small urban area. The main land use 
classes are paddy, forest, scrub and commercial 
cultivations like rubber, tea and coconut. Field 
visits were undertaken to observe the 
tershed and drainage characteristics.
Several sub watershed approaches have been 
cited to incorporate spatial heterogeneity.
distributed model 
had used
Maidment, (1993) applying 
integrating a cell based system 
isochones for sub watershed division. Perera 
and Wijesekera, (2010) carried out a study to 
identify the spatial variability of runoff 
coefficients of three wet zone watersheds of Sn 
Lanka featuring a GIS analysis where mo 
calibration and verification has been earned ou 
This work had been based on the
BASIN model
2.34%.
satisfactorily, 
development of a 
consisting of 18 sub watersheds.
wa
MIKE
87
-2012Research for Industry Symposium (CERIS)
# Civil Engineering
direct runoff, would infiltrate to enhance 
groundwater storage and later appear as 
baseflow. Accordingly the infiltration amount 
is Rt(l-Ct). Since baseflow was taken as directly 
proportionate to the watershed storage (St), the 
amount of baseflow from the watershed is aS 
where a is the coefficient of proportionality. 
The parameter m, was taken as the model 
parameter representing the initial moisture 
content of the system.
SCS UH equations were used for the 
determination of UH. In the U(t) a standard UH 
was determined first for a standard rainfall 
duration of tr. Time to peak, Tp and the peak 
discharge, QP of the standard UH were 
computed following Equations (2) to (5) 
(Maidemnt, 1994).
(2)Tc=0.002L°-77S'0-395 
Tp- 0.7TC 
tr = 0.133 Tp 
Qp = (0.208A)/TP 
tp-Tp- tr/2
tpR = tp+(tR-tr)
TPR = tpR- tp/2 
QpR = 0.375A/2TPr
(3)
(4)
(5)
(6)
(7)
Figure 2: Karasnagala Watershed (8)
(9)
5. Modelling
Basin lag of the standard UH, tp can be 
calculated by Equation (6). According to Mays 
(2004), the basin lag of the UH of required 
duration, tR is calculated by Equation (7). The 
required duration was selected as 1 day, since 
the computational resolution of the model is 1 
day. Time to peak, Tpr and the Peak discharge, 
Qpr of the 1 day UH were calculated using 
equations (8) to (9). In the equations Length of 
the longest watercourse, L, Watershed slope, S 
and Watershed Area, A are watershed 
parameters.
curvilinear UH using the SCS dimensionless 
parameters (Chow, Maidment and Mays, 1988). 
The area under the UH was checked for unity. 
In the case of discrepancy, the noted minor 
differences were adjusted by distributing the 
error proportionate to the hydrograph 
ordinates.
The work described in this paper 
conceptualised the entire watershed as a single 
lumped system (Figure 3), where the direct 
runoff from effective rainfall is combined with 
linear baseflow storage to generate the Total 
Runoff (TRO). In this model, the only input is 
rainfall (Rt) and the outputs are Direct Runoff 
(DR) and Baseflow (BF).
Since the measured rainfall values are available 
in daily resolution, computational time 
resolution was taken as one day. In this 
particular time interval, the amount of effective 
rainfall is QRt where, the fraction of rainfall 
converted to direct runoff is indicated by the 
runoff coefficient, G. The model incorporated 
two runoff coefficient thresholds to represent 
the runoff variation during high and low 
rainfall events. These two runoff coefficients, 
Cl and Ch were taken as two model parameters 
to be calibrated. Cl denotes the coefficient for 
low rainfall values while Ch is the coefficient 
for high rainfall values. Demarcation of the 
boundary of runoff coefficients was done with 
the use of a rainfall threshold value, Ro which is 
also a model parameter, 
computations were based on the Unit 
Hydrograph model [lift)] using effective 
rainfall as input. It was assumed that the 
amount of rainfall which does not contribute to
The UH was converted to
OR, .DUOU(t)
Tolal
Runof
Direct runoff
£tvra'gv, Sj- [ y' • IBF+4 aSt
Figure 3: Schematic Diagram of the Model
# 88Civil Engineering Research for Industry Symposium (CERIS) - 2012
After examining the observed streamflow and 
rainfall time series, 60 data sets were separated 
from the selected date series. Thirty were used 
for model calibration and the other 30 
used for verification.
Time to peak and 
Standard peak discharge of the
r ? ™
t0 a' m'' C«' ^ and Ro 
for the 3° calibration datasets are shown in the
Table 1 and Figure 5. The parameter values 
were categorised to identify the most frequently 
occurring ranges and the average values of each 
most frequent range for a, mh C* Cl, and Ro are 
0.01, 265mm, 0.296, 0.126, 67.67mm
respectively.
Unit
were
Optimisation of 
parameters Of/ Cl, Ro, cc and mi. was done using 
a systematic trial and error methodology by 
minimising the MRAE.
Results6.
The MRAE value for each event during 
calibration showed good matching with an 
overall average value of 0.3423 for the 30 
events. Two calibrated data sets with one 
showing a good matching and the other 
showing a relatively poor matching are shown 
in the Figure 6.
ire
Hydrograph of Karasnagala Watershed 100000
10000Table 1: Conceptual Model Parameters of 
Calibration Dataset 1000
-Eveht'NQi; Cri Ro | MRAE
5S 1 0.3915
m, CLa I1 0.01 450 0.16 1000.43 ai2 0.001 50 | 0,141611300 0.1 0.23
| 103 0.1 75 0.85 0.41 56 02543 ora4 0.05 85 0.01 05 20 0.4496
2 1 135 0.01 700 0.57650.9 0.52 20 o6 0.004 1400 032 0.0005 74 0.1643 o 0-17 0.82640.4 0.01 0.88 934
a0.26208 0.48 660.02 600 0.1
75 0.01 V032550.17 0.8S 929 0.02 350 >
0.09590.2 SO10 0.20.001 2000 t0.0010.0356690.12 0.1411 0.001 6100
03985660.80.14512 0.01 850 0.00010.1842630.0090.1813 0.002 3550 Cl RoChmia
0.25490.99 1370360.02 20514
0.4393670.576 0.1415 0.1 Parameter0.1078490.170.0916 1500.03
0.1025390.250.4731017 0.02 Figure 5: Conceptual Model Parameters of 
Calibration Dataset
The average set of calibration parameters 
used with the verification data set. In general, 
the matching of hydrographs were not 
successful and the MRAE values reflected the 
poor performance. Outputs showed that four 
verification data sets were very poorly matched 
by model predictions with average datasets. 
These four datasets, which had problems with 
the initial moisture levels, produced excessively 
high peak runoff values leading to MRAE 
values of 4.1875,2.8628,2.0386 and 3.994. Other 
than these four events the other 26 venhcatton 
data sets produced an average MRAE value of 
0.4901 which still falls in the category of poor 
performance.
0.46791770.10.710018 0.01
0321435030.3628019 0.01 were0.1455910.30310000.00320
0.4718580.2920.2710021 0.045
0.1974500.430.2113000.00122
0.2338560.440.75900.0823
0.4211200.60.018524 0.05
0.1987200320,97000.0125
0.1043740.0010.312600.0226 1.1198930.780.01427 0.4 0.0443660.380.16000.0228 03070920.780.1735029 0.02 0.0141800.10.220000.00130.
v
■ 0.400,
Minimum -Q.0Q1
0,04?/:
0.010 j
1502 :1- I 0.407 | V \
The curvilinear one day Unit hydrograph of 
Karasnagala watershed is shown in Figure 4.
Av
89
Research for Industry Symposium (CERIS) - 2012
# Civil Engineering
results showed that such averaging does not 
lead to representative streamflow estimates.Raiiifhli (mm) 
Calculated Discharge 
----- Observed Discharge Parameter Value Variations 
During model calibration, the Initial moisture 
level (mi), expressed as a per unit area value 
varied between 4mm and 11,300mm. This wide 
variation of values noted during calibration is 
an indication of the inappropriateness of using 
mi as a model parameter to be averaged over 
The mismatch of initial streamflow
o10 7.2■!9
$8
- 40 w
o a?6
c5?4
80 -S'
I8 :-,20aCO 2
time.
values during model verification demonstrated 
the incapability of using an average m/ to reflect 
the varying watershed behaviour between wet 
and dry conditions.
i
4—f- +H—I—h H—i—l- r 1600
*-« fH —4 •—« f—« f-H -H ►“« *—1
r- r- r- r* r- r** r* r*- r-
• i i i i i i i i i i i 
*1**-***~m*1*********m{*
111111111111 
'OhCoaOHri^T^Wf' 
h < n ri n ri ri ri ri ri
Time in Days00
Watershed runoff coefficients change with the 
magnitude of the rainfall and also with the 
wetness of the watershed. Conceptualisation in 
the model ignores the direct runoff generation 
due to saturation overland flow and assumes 
that any runoff increase due to catchment 
rainfall would occur only by increased 
baseflow. In the search for a simple watershed 
model, the saturation overland flow component 
was not considered in the present work.
C/3 .1...
n ri n ri n n n
i" r- i" r-» r~ r- r
g. z z i z is *op o o c o o o
o -< ri rr, rf ir. \0
O O O O O O The model used in this work made an attempt 
to simplify the variation of watershed runoff by 
using a rainfall threshold value as a parameter 
to reflect two rainfall dependent runoff 
coefficients which were also optimised as 
parameters. Two runoff coefficients Cl and Ch 
varied in the range of 0.01-0.9 and 0.0005-0.99 
respectively. Threshold rainfall value Ro varied 
between 20.18 to 177.13mm. The ranges of 
runoff coefficient variation in case of both 
parameters show that the values occupy the full 
range available for fluctuation. Results from 
verification dataset showed that the peaks 
estimated by the model were significantly 
different to the observed streamflow peaks. It 
was observed that on many occasions the 
predictions were out of phase indicating the 
incapability of averaged values to effect a 
suitable delay in the response.
The dimensionless baseflow coefficient (a) 
varied from 0.001 to 0.4. This parameter has a 
upper limit which is a relatively high value for 
the baseflow. This reflects the problem of sub 
surface runoff prediction with a single 
coefficient catering to both baseflow and 
interflow. The indication is that the catchment 
wetness fluctuations do not permit an averaged 
coefficient to represent the entire watershed 
spatially and temporally.
Another factor that could be attributed to the 
parameter fluctuation is the assumption of a
(b) Time in Days
Figure 6: Hydrograph Matching for Calibration 
Date Sections (a) C008 (Relatively Poor) and (b) 
C016 (Good)
7. Discussion
7.1 Spatial and Temporal Averaging of
Parameters
The present work attempted to average the 
watershed behaviour by identifying the 
performance of model for each calibration 
dataset. Parameter optimisation corresponding 
to each calibration dataset showed very good 
matching reflecting the representativeness of 
the conceptual model which was used to 
mathematically model the Karasnagala 
watershed. The matching of each individual 
event with a low MRAE is 
demonstration of the ease of spatially lumping 
the hydrological processes for individual events 
of short duration. The variability observed 
with each parameter shows the difficulty that 
would be faced by a modeller when attempting 
to model the temporal variability of watershed 
responses. This work identified the parameters 
of most frequently experienced events in order 
to obtain a temporally averaged set of spatially 
averaged parameters. Poor model verification
good
♦ Civil Engineering Research for Industry Symposium (CERIS) 90-2012
uniform rainfall over the entire catchment and 
the resolution of base data being 1 day 
duration. These factors cause difficulties in the 
reproduction of streamflows from a watershed 
which has a significant heterogeneity.
Parameter Outliers 
A study of baseflow coefficient variation during 
calibration showed that the values reached 0.4 
only in two occasions. Investigation of these 
two data sets revealed that the streamflow 
value at the start of the dataset is small 
compared to that of other datasets. This 
requires the mi values to be kept low but a need 
arose to match the direct runoff at subsequent 
time intervals, 
coefficient required an increase. The model 
showed a need to incorporate the direct runoff 
increase that could be noted with an increased 
saturation of soil.
The runoff coefficient for low rainfall (Cl) 
varied between 0.001 and 0.9, however values 
closer to 0.9 were found only in the case of four 
events. These four events have recorded lesser 
rainfall values when comparing with other 
events generating similar streamflows. Since 
the baseflow component is not adequate to 
represent the fluctuations in the total 
hydrograph, direct runoff component in the 
calculated hydrograph required an increase. A 
higher Cl values was given for the purpose of 
obtaining a higher direct runoff at lower rainfall 
conditions.
The runoff coefficient for High Rainfall (Ch) 
reached a value closer to unity only in one 
rainfall event. In all other events the values 
were much lower. When the behaviour of the 
model was evaluated, it could be noted that 
major contribution has been from the larger 
rainfall datasets which assigned larger values 
for the high rainfall-runoff coefficient.
°-thl.parameter usase to fulfil the modelling 
objechves^ However using individual and 
speofic datasets for model calibration and 
verification does not provide 
modeller to opportunity for a the full potential of calibration 
parameters for temporal and 
spatial averaging of watershed behaviour. The 
present work revealed difficulties with the 
initial moisture level, the incorporation of 
runoff coefficients and the issues of threshold 
rainfall event. Therefore the calibration of 
individual events could only be used to 
understand the watershed behaviour for a 
modeller to subsequently carry out continuous 
modelling to arrive at
use
to optimise the7.3
representativeAccordingly the baseflow parameters.
5. Conclusions
1. Calculated streamflow of selected data 
sets representing hydrograph peaks could be 
matched with observed streamflow from the 
developed model with an accuracy of 0.34 
MRAE for the calibration dataset
2. Considering the highest probable 
parameter values obtained from 30 events, the 
averaged values for the baseflow coefficient 
(a), Runoff coefficient for low rainfall (Cl), 
Runoff Coefficient for High Rainfalls (Ch), 
Rainfall threshold value (Ro) and Initial soil 
moisture level (mj) were identified as 0.01, 
0.126, 0.296, 67.67mm and 265mm
Present work revealed that the selected 
event based modelling provides an insight to 
the watershed behaviour and to the 
appropriateness of model parameters, but in 
order to identify the spatially and temporally 
averaged parameters it is necessary to 
carryout optimisations using a lengthy 
data series together with an
3.
continuous 
appropriate model.In one event the threshold rainfall reached a 
high value when compared with the others. 
This is due to the incompatibility noted in the 
rainfall data and the associated streamflow 
Tire initial moisture level
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91
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Acknowledgement
This research was supported by University of 
Moratuwa Senate Research Committee (SRC) 
Grant under the title "Analysis of Parameter 
Sensitivity and Sub Watershed Delineation 
when Flood Modelling with Spatially 
Distributed Hydrographs"
(SRC/LT/2011/15). The authors would like to 
express their sincere thanks to International 
Centre for Geoinformatics Applications and 
Training (ICGAT) of University of Moratuwa 
for the
UnitWijesekra, N.T.S., "A Comparison of Peak 
Flow Estimates for Small Ungauged Urban 
Watersheds", Transactions, Annual Sessions of 
the IESL, Institution of Engineers, Sri Lanka, 
October 2000
support and use of facilities.
* Civil Engineering Research for Industry Symposium (CHRIS) 92-2012