Abstract A main component of hydrographs is due to geomorphology that is a direct contribution of surface runoff. This is in turn affected by vegetation canopy which in middle latitudes has considerable seasonal dynamics. The present investigation tested the evidence of a variable canopy cover on a hydrograph, comparing observed data to a semiempirical 3 parameters model. The strong simplifications, introduced to allow model inclusion in a non linearfitting procedure, permitted to fit satisfactorily discharge events recorded from Centonara watershed (with a surface of 2 km 2 and located in a hilly area in Italy, mean slope 28%). The small scale contributed to reveal the seasonal differentiation of surface storage, together with an estimate of base flow routing

G Vitali

M Vignudelli

P Rossi Pisa

CiteSeerX

ISCO 2004  - 13th International Soil Conservation Organisation Conference –  Brisbane, July 2004 
Conserving Soil and Water for Society: Sharing Solutions   
 
Paper  No. 732            page 1 
 
SEASONAL EFFECT OF CANOPY DISTRIBUTION ON RUNOFF FROM HYDROGRAM 
ANALYSIS IN A SMALL CATCHMENT  
 
G. Vitali, P. Rossi Pisa, M. Vignudelli 
Department for Agro-Environmental Sciences and Technology, Bologna, Italy. 
 
Abstract 
A main component of hydrographs is due to geomorphology that is a direct contribution of surface runoff. This is 
in turn affected by vegetation canopy which in middle latitudes has considerable seasonal dynamics. The present 
investigation tested the evidence of a variable canopy cover on a hydrograph, comparing observed data to a semi-
empirical 3 parameters model. The strong simplifications, introduced to allow model inclusion in a non linear-
fitting procedure, permitted to fit satisfactorily discharge events recorded from Centonara watershed (with a surface 
of 2 km2 and located in a hilly area in Italy, mean slope 28%). The small scale contributed to reveal the seasonal 
differentiation of surface storage, together with an estimate of base flow routing. 
 
Additional Keywords: hydrograph, runoff, model, non-linear fitting 
 
Introduction  
Hydrological system outflow is currently investigated by two major tools. The former, based on the unit 
hydrograph theory (Sherman, 1932; Rodriguez-Iturbe and Valdez, 1979) is oriented to define general behaviours 
and features (as scaling laws). A second, based on simulation models, is oriented to integrate any physical law 
ruling system dynamics (e.g. Beven and Kirkby, 1979; Todini and Ciarapica, 2001). As a model is considered valid 
when it explains most of the variability of data (system output), any model with a correct structure (shape and 
dynamics) and a sufficient number of degrees of freedom is valid when the it fits recorded values. 
 
The unit hydrograph method, based on the assumption that the discharge is built up from single rainfall events, also 
tells us that when original information (contained in event features) is coupled to geomorphology, a lot of  
information is lost, because of the stochastic mixing at the physical base of the process. In practice, information 
contained in the hydrograph is less than that required to determine parameter values of almost any deterministic 
model for simulation of hydrology, and so such models are too complex to be included in a automated fitting 
procedures. These are the reasons why the present investigation introduces a simplified model to verify the 
information content of a hydrograph and eventually to recognize the incidence of vegetated surfaces on model 
parameters. 
 
The Model 
The basic idea of the unit hydrograph theory 
approach, a reference model for surface hydrology, is 
that discharge can be represented as a time-
convolution of rainfall distribution with a basin-
dependent dispersion function (Gupta et al., 1980). In 
practice each rainfall event can be seen as made of 
pulses (with an amplitude corresponding to recorded 
values), each participating to basin outflow by a flow 
distribution function, which is basically the same, but 
its weight and delay derive from magnitude and 
recording time of originating pulse. 
 
Such a distribution function collects hydrological 
(channels), geomorphological (surface runoff) and 
base flow (the underground flow contribution due 
both to subsurface and water-table). The components 
have usually different weights when working at 
different scales. At lower scales the dispersion 
function, similar to a Poisson distribution, can be 
approximated by an exponential one, as it can be seen 
looking at a simple event (Figure 1).  
 
 
Figure 1. Simple rainfall event (vertical bars) and 
generated hydrograph (line) from Ozzano data-set.  
ISCO 2004  - 13th International Soil Conservation Organisation Conference –  Brisbane, July 2004 
Conserving Soil and Water for Society: Sharing Solutions   
 
Paper  No. 732            page 2 
 
It follows that the expression describing a single pulse contribution is: 
 
F (t ; k) = qo(k) e  - Dr (t - tk - Tr)   t >  tk +Tr  
 (1) 
F (t ; k) = 0 otherwise 
 
where tk is the recording time [d] , k (1 .. N) is the pulse index for the considered event, Tr is discharge delay (from 
rainfall pulse to the beginning of discharge peak) [d], Dr is dumping factor [1/d],. The discharge peak value qo (k) 
[m3/d] can be obtained integrating the expression (1): 
  
qo (k) =  Dr A ρ p’(k) 10-3 (2) 
 
where A [m2] is the watershed area and ρ the discharge ratio, the fraction of the surface contributing to the flow,  
p’(k) is  the total amount of effective precipitation event [mm], obtained subtracting from total rainfall p the total 
canopy interception hc  also called canopy storage [mm]: 
 
hc = Σ k=1,N  [ p(k) - p’(k)] (3) 
 
The total amount of surface flow QR (t) can now be expressed as: 
 
QR (t) = Qoff Σ k=1,N  F(t;k)  (4) 
 
where Qoff is the discharge rate at the beginning of the event, and whose contribution is supposed to be constant. 
 
The model has not meant to be an explanatory one: it does not include explicitly phenomena such as surface 
storage, infiltration and evapo-transpiration, oversimplifies phenomena as interception and infiltration, and 
completely neglects others like percolation. With respect to widely used model as Topmodel (Beven and Kirkby, 
1979), it also neglects any (even lumped) geographic information, while includes the proportionality between 
surface and total flow, as in SCS method (USDA-SCS, 1985), here parameterised by the partition coefficient ρ, 
which value is affected significantly from the simplifications introduced, and has been excluded from discussion. 
 
The model described above has been 
translated into algorithm and inserted in 
a non-linear fitting (NLF) procedure. 
Given the complexity of the curves to be 
fitted, which in general contains multiple 
peaks, a generic steepest-descent 
procedure were ineffective, so it has 
been improved by a start-up estimating 
procedure (based on a random search of 
parameter driven by extreme values 
supplied by user). Standard algorithms 
are designed to accept the trial 
parameters suggested by steepest-descent 
method only if SSQ be decreasing: this 
rule has been also removed so as to 
allow the trials to overcome local 
maximum, and a stopping criterion has 
been introduced on search radius. 
 
 
 
Figure 2.  Change of Cover index as a difference between 
summer and winter values. 
ISCO 2004  - 13th International Soil Conservation Organisation Conference –  Brisbane, July 2004 
Conserving Soil and Water for Society: Sharing Solutions   
 
Paper  No. 732            page 3 
 
Data Records 
Discharge records are from Centonara watershed, a small watershed (2 km2) located in a hilly region of Italy (mean 
slope 28%). The basin of Centonara is largely vegetated and cropped.  Its vegetal canopy changes considerably 
from the cold season (winter) to the warm one (summer). Figure 2 displays the geographical distribution of the 
change of a cover index, (an estimate of LAI) during the season.  Events from 3 year records where considered but 
many did not give a detectable discharge, and others were rejected because of low values and of base-flow 
fluctuations. The remaining events have been successively classified by complexity and magnitude (total discharge 
volume - V), using 3 classes for both. Magnitude limit values has been obtained from the steps evidenced 
displaying sorted values (Figure 3 - left). Complexity was expressed in term of peaks number. For this investigation 
only events of low complexity (number of peaks less than 4) have been used: huge events (V > 3 105 m3), also 
related to an high complexity, have been excluded because of the simplifications introduced in the models, and 
partly because of the complexity induced into parameter search surface (inherently to NLF routine).  Displaying 
events by date (Figure 3 – right), it is also possible to observe that those of higher magnitude occurred in middle 
seasons, namely spring (from 60th to 150th day of year) and autumn (from 240th to 330th day of year) when in the 
Centonara region, precipitation duration is longer (during summer events are intense and of short duration). 
 
1.E+03
1.E+04
1.E+05
1.E+06
1 5
 
0N
m3
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0 60 120 180 240 300 360
DOY
m3 
 
 
 
 
 
 
 
 
 
 
Figure 3. Observed discharges ordered by value (left) and by day of occurrence (right)  
 
Results 
The efficiency of the fitting procedure on the selected events, in terms of R2 can be observed in Figure 4, where a 
ramp-like distribution shows that about 60% of events have been fitted rather successfully, that is with a R2 > 0.5. 
In Table 1 it is possible to see the sensitivity of parameters to the fit. The parameters on which the model induces to 
focus our attention are surface storage hc and dumping factor Dr, whose seasonal variation is shown in Figure 5. 
The discharge delay time Tr also shows a certain seasonal dependency, but with a rather visible growing trend from 
autumn to winter, when in the region watertable refills and soil saturation increases, making reasonable to conclude 
that in that period a notable component of base flow occurs and that the model hypotheses are no longer valid. 
 
Table 1.  Mean values of the estimates and variations 
Parameters Mean Variation 
hc 1.01 7.64 
Tr 0.048 0.175 
Dr 8.55 32.33 
 
 
Conclusions 
This preliminary investigation on the possibility to extract canopy status information from hydrographs has given 
encouraging results. In fact, even if the parameter chosen to model the system were not directly related to 
vegetation dynamics, a visible seasonal component has been found, together with an estimate of base flow water 
routing. Model enhancement are required to get an even rough estimate of the portion of the surface interest to the 
processes while major progresses on interpretation are expected improving the NLF procedure. 
ISCO 2004  - 13th International Soil Conservation Organisation Conference –  Brisbane, July 2004 
Conserving Soil and Water for Society: Sharing Solutions   
 
Paper  No. 732            page 4 
 
 
 
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 6 11 16 21 26 31 36
R2
 
0.01
0.1
1
0 60 120 180 240 300 360
DOY
Tr [d]
 
Figure 4. Values of R2 from the NLF outputs (LEFT) and of  discharge delay Tr  (right). 
 
0
2
4
6
8
10
12
0 60 120 180 240 300 360
 
1
10
100
0 60 120 180 240 300 360
DOY
Dr [1/d]
 
Figure 5. Estimated values of hc (canopy storage) (left) and of Dr (dumping factor) (right). 
 
 
References 
Beven K.J., and Kirkby M.J. (1979). A physically based variable contributing area model of basin hydrology. Hydrol.Sci.Bull. 24(1):43-69. 
Gupta V.J., E.Waymire E., and Wang C.T. (1980). A representation of an IUH fom geomorphology. Water Resour.Res., 16, 885-892. 
Rodriguez-Iturbe, I., and Valdes B. (1979). The geomorphologic structure of hydrologic response, Water Resour.Res., 15, 877-886. 
Sherman, L.K. (1932). Streamflow from rainfall by the unit-graph method. Eng.News Record, 108, 501-505. 
Todini E. and Ciarapica L. (2001). The Topkapi model – Mathematical models of large watershed hydrology, Chapter12.ed.Singh et al., 
Water Resoures Pub.Littleton, Colorado. 
USDA-SCS (1985). National engineering handbook – Hydrology. Washington D.C., USDA-SCS. 


SEASONAL EFFECT OF CANOPY DISTRIBUTION ON RUNOFF FROM HYDROGRAM ANALYSIS IN A SMALL CATCHMENT

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SEASONAL EFFECT OF CANOPY DISTRIBUTION ON RUNOFF FROM HYDROGRAM ANALYSIS IN A SMALL CATCHMENT

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