FE 537 Hillslope and Watershed Hydrology
Lab 3: Catchment Scale
Takahiro Sayama
1. Hydrograph Separation
Calculate the fraction of total stream flow contributed by old water and new water from the observed data
at the Maimai 15 Catchment (McGlynn et al. 2004). Remember that the equation to compute the old
water fraction of stream flow (Qo / Qt) is:
18
18
Qo  O stream   O

Qt
18 O old  18 O
where 18 O (stream) , 18 O (old) and 18 O are oxygen-18 compositions of streamflow, old water and event
water, respectively.
The input data is provided with excel file (FE537_HydroSep.xls). Use both standard weighting and
incremental mean methods to compute 18 O values of event water. Note that the standard weighting
method determines 18 O by the following equation.
n
 P
18
 O
18
i
i 1
Oi
n
P
i
i 1
where Pi and 18 O i are the precipitation depth (mm) and oxygen-18 composition collected over period
or i (i = 1, … , n). The incremental mean is the same, except the values used in the above equation are
from the beginning of the event to the time of stream sampling j:
j
 P
18
 Oj 
18
i 1
i
Oi
j
P
i 1
i
where 18 O j is the incremental mean of 18 Oi (i = 1, …, j) of event water at the time step j. For
additional explanation of weighting procedures, see McDonnell et al. (1990).
Questions:
1. Plot the hydrograph with old / new water separation lines calculated by both weighting methods.
2. Briefly discuss your findings.
3. What is the reason for the high old water contribution in this steep catchment (next to the Mosley
Maimai catchment) with shallow soils?
Reference
1) McDonnell, J.J., Bonnell, M., Stewart, M.K., Pearce, A.J. : Deuterium variations in storm rainfall:
implications for stream hydrograph separation, Water Resources Research, Vol. 26, No. 3, pp. 455 –
458, 1990.
2) McGlynn, B.L., McDonnell, J.J., Seibert, J., Kendall, C.: Scale effects on headwater catchment runoff
timing, flow sources, and groundwater-streamflow relations., Water Resources Research, Vol. 40,
W07504, 2004
2. Transit Time Analysis
Determine transit time distribution function and its parameters that fit for the given data (spring data in
Wimbach Valley Catchment). The input data and sample fitting are provided with excel file
“FE537_TransitTime.xls”.
The first sheet “dO_in” in the excel file contains the input dataset as well as the calculation of
amount-weight precipitation  in (t ) based on the following equations.
G 
   s Ps    w Pw
  Ps   Pw
 in (t ) 
N i Pi
N
 P
i 1
 i   G    G
i i
where  g is the isotopic composition of ground water,  is the infiltration coefficient equal to ratio of
summer to winter infiltration ( = 0.1 indicates that the winter recharge exceeds the summer recharge by
ten time),  s and  w are isotopic compositions in summer and winter seasons, Ps and Pw are
precipitation depth (mm) in summer and winter seasons. N is the number of time periods for which
precipitation is corrected (i = 1, …, N).
The second sheet “Conv” contains convolution calculation. Remember that the equation for the
convolution calculation is:

 out t   g t  *  in t      g ( ) in t   d
0
where  out t  is stream flow composition,  in t    is input composition in the past at time t   , and
g   is transit time distribution (TTD).
The “Conv” sheet, yellow cells (G2:DA2), contain the TTD that you can replace with your function
values. The following grey cells (G3:DA3) representing the normalized TTD (probability distribution
function) will be automatically recalculated. The convolution results will appear on the light blue cells
(E105:E161) which can be compared with the observed ones shown in (D127:D160). The third sheet
“Conv Results” shows the fitting plot.
Questions:
1. Find two different functions and their parameters that reasonably fit with the measured oxygen-18
composition. Plot the results.
2. Calculate the mean transit time from the proposed two functions and interpret the results.
Reference
1) McGuire, K.J., McDonnell, J.J.: A review and evaluation of catchment transit time modeling, J. of
Hydro., 330, pp. 543– 563, 2006.
3. Rainfall-Runoff Modeling
Develop a Rainfall-Runoff model for Maimai 8 catchment by Tank Model approach. The input data and
the sample model are given in “FE537_RR-Model.xls”. The sample model has two tanks representing
surface storage and sub-surface storage. As you can see from the output figure, the hydrograph simulated
by the sample model closely approximates the observed streamflow measurements. However, most of the
discharge is contributed by surface flow by this model structure, which is something not ever observed in
the steep Maimai 8 catchment with highly transmissive soils.
R E
Q1
Q12
Q2
Questions:
1.
2.
With your knowledge of the Mosley paper and runoff processes discussed in class, try out different
model structures (i.e. having more tanks perhaps or different assemblages of tanks) and parameters to
obtain a model that performs well with right reasons.
- Construct your own tank model and plot the simulation results.
- Illustrate your model and explain your perceptions of the model struccture.
Briefly discuss the problems of your model and possible approaches to overcome these problems.
The sample calculation applies a simple numerical solution for solving set of ordinary equations. You can
use the same numerical solution with the excel file, but note that more sophisticated approach may be
required to obtain more accurate simulation results. Note that original tank model of Sugawara (1972)
assumes the linear relationship between storage depth and runoff, the sample model in this exercise
assumes a non-linearity relationship between storage depth and runoff. The purpose of this exercise is not
to develop a complete Tank Model of the Maimai catchment but to develop a simple numerical model
that matches your perception of runoff generation at the site.
Reference
1) Sugawara, M..: Tank Model, in Computer Models of Watershed Hydrology, ed. Singh., V.P., 1995.