GEO3280 Assignment#7 Page |1
University of Florida
Department of Geography
GEO 3280
Assignment 7
Excess Precipitation, Runoff and Storage at Electriona
Solar
Radiation
Precipitation
SubSurface Surface Vegetation
EvapoTranspiration
Interception
Effective
Precipitation
Evapo-transpiration
Excess
Precipitation
Direct Runoff
Infiltration
Storage
Drainage Basin
Sub-surface Runoff
Runoff
INTRODUCTION: In the previous assignment, the calculated mean monthly Excess
Precipitation for the entire Tiribí basin above Electriona was allocated to either Runoff or
Storage, simply by subtracting the observed mean monthly runoff from the calculated Excess
Precipitation to derive ΔStorage as a residual. If the ultimate aim of the procedures outlined in
the lab manual is to develop a method by which estimates of available runoff (discharge) can be
made at locations for which no historic data exist, a way must be determined to disentangle the
seasonally changing partitioning of Excess Precipitation between these two. As elsewhere in
the lab manual, progress is made by noting the behavior of the observed phenomenon,
determining a physically reasonable mathematical procedure by which to represent the
observations, and then testing the proposed procedure against the real world.
GEO3280 Assignment#7 Page |2
A. What Is the Graphical Relationship between Excess Precipitation and Δ
Storage?
1.
 Produce one (1) simple vertical bar graph depicting mean monthly estimates of both
Excess Precipitation and ΔStorage at Electriona.
(2 Marks)
2.
Produce an X-Y scatter (joined by lines) plot of these two variables with Excess
Precipitation as the x-variable and ΔStorage as the y-variable. Identify each point on the
above X-Y scatter plot as a particular month.
(3 Marks)
 Make a closed loop of these data by repeating the first pair of coordinates (January)
after the last pair (December), making a total of 13 pairs of coordinates.
3.
Divide the graph into four quadrants around the origin (0,0) of the graph. Starting in
the top left quadrant and moving clockwise, identify each quadrant from I to IV.
i)
In which months and quadrant are the hydrologic stores emptying in the basin
even though Excess Precipitation is being produced?
ii)
In which months and quadrant are the hydrologic stores filling in the basin while
Excess Precipitation is being produced?
iii)
In which months and quadrant are the hydrologic stores emptying in the basin
and Excess Precipitation is negative (overall evapotranspiration losses)?
iv)
In which months and quadrant are the hydrologic stores filling in the basin,
despite net losses of precipitation through evapotranspiration?
(2 Marks)
N.B. We will return to this question at the end of the next section.
B. How Can This Complex Relationship between Excess Precipitation,
Runoff and Storage be represented Numerically?
Hydrologic stores are often viewed as analogous to big rain barrels with an outlet at the base. A
series of scenarios of increasing complexity, based on this idea, follow. These introduce the
concept of stores and the ways in which this may be used to solve the problem.
In Scenario 1 the rain barrel starts (time = 0) with an initial storage volume of 500
units. The barrel is a perfect cylinder, so depth (mm) may be viewed as an indicator of volume.
The spigot is opened, the water flows out at the base and is recorded for twelve time periods
(e.g. the next twelve months, 1,.2. ...., 12). The rate of outflow is related to the volume of water
stored in the barrel. In a rain barrel, the greater the depth, the greater the pressure the stored
GEO3280 Assignment#7 Page |3
water exerts in exuding liquid from the base. In nature, stored water likewise flows more easily
the greater the moisture present.
The rate at which the outflow volume declines, or recedes, with each successive time
period is called the “recession rate” and will vary depending upon the nature of the hydrologic
store (for instance, imagine how fast water would come out of a rain barrel which had
previously been filled with fine gravel). The recession rate indicates the proportion of the
water stored at the beginning of the time period that will flow out during the subsequent time
period. This is related to the concept of time lags in the responses of various components of the
hydrologic system.
In Scenario 1, the recession rate is set at 0.35. This means that 35% of the 500mm will
flow out in the first time period (500mm x 0.35 = 175mm). Leaving 325mm (500mm -175mm)
in storage at the end of the first period. Thirty-five percent of this figure flows out in the second
period (325mm x 0.35 = 113.75), leaving 211.25 in storage, etc. In Scenario 2 the recession
rate is reset at 0.20 in order to illustrate the control that the recession rate exerts upon the
Scenario 1: Initial Storage = 500
Recession = 0.35
Storage
Outflow ?
outflow “hydrograph” of stores which are merely left to drain through time.
 1. Compute storage levels AND outflows for 12 successive time periods for Scenario 1
(recession rate 0.35) and Scenario 2 (recession rate 0.20). Graph, on a single line and
symbol graphs, both sets of outcomes - time on the x-axis, commencing at 0, and
storage/outflow on the y-axis. Outflow values will always commence at time period 1,
whereas storage will be at its initial level (500 in both cases here) at time period 0.
(4 Marks)
Check: The first values of outflow and storage under scenario 1 have been calculated for
you in the preceding explanation.
 2. All other things being equal, will a basin with a higher recession rate
experience higher or lower ranges (high flows minus low flows) in outflows during a
year? Explain your answer.
(2 marks)
GEO3280 Assignment#7 Page |4
 3. Convert the storage values from Scenarios 1 and 2 to a natural logarthmic scale.
See EXCEL How-To #33
Using the REGRESSION option, compute the best fit line (time on x-axis and LN(x) on yaxis) and record the slopes for both scenarios separately. Convert the respective slopes back
from natural logarithms to REAL numbers.
(4Marks)
See EXCEL How-Tos #34 and 35
 4. What is the relationship between the recession rates employed and the
exponents of the slopes derived?
(2 Marks)
Hint: The following table includes two additional values of recession rates and corresponding
exponents of slopes in lines of the natural logs. Insert you estimated values. Hopefully these
four pairings will help you to see the numerical relationship.
Recession
Rate
Exponent
of slope
0.1
0.9
0.2
0.35
0.6
0.4
The months of December-April all experience negligible rainfall within the basin, and fall
within quadrant IV in your diagrams. They therefore represent times that closely resemble
scenarios 1 and 2. The observed runoff in these months, in all likelihood, reflects the drawing
down, or draining, of the groundwater store in the Tiribí basin, as discussed in Assignment 6.
5.
Plot these five monthly values of mean runoff (y-axis) versus months since November
(x-axis), i.e. December = 1, and April = 5. Take the natural log of the runoffs and
compute the slope of the best fit straight line to these points. What is the approximate
value of the recession rate in this basin estimated from monthly flows?
(3 Marks)
GEO3280 Assignment#7 Page |5
Most natural stores do not simply lose water by drainage alone as we have assumed above, but
also gain or lose water, simultaneously, from other sources (positive/negative excess
precipitation). In Scenario 3, water is removed from the top of the store at a constant rate (20
mm per month). The monthly loss of water is subtracted from the storage level before the
monthly outflow is computed. This is analogous to months during the dry season when the rain
barrel (basin) is constantly losing water or experiencing negative excess precipitation
(Evaporation exceeding precipitation). Note the similarities here to Assignment 4, Part D on
seasonal inputs, outputs, and stores on, below and above the surface of the Tiribí.
- 20/ month
Scenario 3: Initial Storage = 500
Recession = 0.35
Constant Excess Rain -20/month
Storage
Outflow ?
 6. Compute and graph the differences in outflows under Scenario 3 with those of Scenario
1 for 5 (five) months. Compute the expected recession constant of the basin from the
outflows under scenario 3. Describe and explain the nature of the changes in outflows and
recession rate made to outflows brought about by removing a constant input.
(4 Marks)
See EXCEL How-To #36
 Note: Net losses, or months of negative Excess Precipitation when Evaporation exceeds
Effective Precipitation, can be entered under the input column as negative inputs.
! Warning: Don’t forget to subtract the inputs to the system before computing the outflow, otherwise you will
get different answers.
GEO3280 Assignment#7 Page |6
-10
/month
+ 200/
month
Scenario 4: Initial Storage = 500
Recession = 0.35
-10, Months 1-4, 11 and 12
+200, Months 5-10
Storage
Outflow ?
Scenario 4
600
Storage
Flow
Storage/Outflow
500
400
300
200
100
0
0
2
4
6
8
10
12
Time
Figure 7.2. Time series of storage and outflow values under the inputs and storage capacity
specified in Scenario 4. Dry season (negative excess precipitation) November-April; Rainy
season (positive excess precipitation) May-October.
GEO3280 Assignment#7 Page |7
Overflow
Begins
600
Storage Capacity
Storage/Flow
500
400
300
Storage
Flow + Overflow
Flow
200
Initial Storage
100
0
2
4
6
8
10
12
Time
Figure 7.3. Time series of storage values, outflow and overflow under the constant inputs and
storage capacity specified in Scenario 6.
+ 350/ month
Overflow
Storage
Scenario 6: Initial Storage = 150
Storage Capacity = 550
Recession = 0.35
Constant Excess Rain 350/month
Outflow ?
GEO3280 Assignment#7 Page |8
Natural stores, like rain barrels, can be viewed as having a finite capacity (note the
hydrologic concept of saturation) which once exceeded produces overflow. In Scenario 6,
(Figure 7.3) the barrel is given a storage capacity of 550mm. Water stored in excess of this will
over flow directly to the outflow, and storage in the barrel reset to 550mm. The monthly
outflow from the base of the store is calculated based on the maximum capacity of 550mm.
The total flow in that month is the sum of the overflow and the basal outflow. Figure 7.3,
illustrates what happens to the outflows when initial storage is set at 150 mm and input is a
constant 350mm per month (Scenario 6).
In Scenario 7, Excess Precipitation values have been distributed to reflect the constantly
changing precipitation pattern seen in the Pacific watershed of Costa Rica (Table 7.1). Initial
Storage is set to 150mm to represent the dry season of January and Storage Capacity is
550mm. For comparative purposes, Figure 7.4 (upper) displays the daily discharge regime of
the Río Candelaria, which is located on the Pacific Slope immediately to the south and east of
the Río Tiribí. The monthly Excess Precipitation values listed in Table 7.1 (and 7.2) are to be
regarded as the monthly inputs to the basin.
Month
Excess P
Month
Excess P
Month
Excess P
1 -10
5 180
9 320
2 -15
6 300
10 500
3 -20
7 120
11 50
4 -10
8 190
12 -5
Table. 7.1 Monthly values of excess precipitation into a simple hydrologic store designed to
reflectedthe typical hydrologic regime of the Pacific watershed of Costa Rica, under
Scenario 7.
GEO3280 Assignment#7 Page |9
M
J
J
A
S
O
N
D
J
F
M
A
250
Río Candelaria
Pacific Slope
661.4 km2
200
Mean
+/- 1 Standard
Deviation
150
CDaily Discharge (m3s-1)
100
50
0
0
30
M
60
J
90
J
120 150 180 210 240 270 300 330 360
A
S
O
N
D
J
F
M
A
450
Río Sarapiquí
Caribbean Slope
2
820.9 km
400
350
300
250
200
150
100
50
0
0
30
60
90
120 150 180 210 240 270 300 330 360
Days since April 30th
Figure 7.4. Observed mean daily discharges on the nearby Río Candelaria (upper) and Río
Sarapiquí (lower), representing examples of Pacific slope and Caribbean slope regimes
respectively. (From Quesada and Waylen, 2004)
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 10
 Example: Using IF (... , ...., ....) to evaluate Scenario 6. An explanation of steps is provided on the next page.
A
B
C
D
E
F
Input
G
Computed
Storage
Outflow
Overflow
3 IF(C3>$F$16,
(B2+F3)-D3
step 
(B2+F3)*$F$15
step 
IF(C3>$F$16,
(C3-$F$16), 0)
step 
350
E3+D3
step 
2
4 step  COPY
step  COPY
step COPY
step  COPY
350
step  COPY
3
5
Time
1 Storage
0
2 150 step 
1
$F$16, C3)
step 
.
.
.
F15 = 0.35
(recession rate)
.
.
.
.
....
....
Total Flow
F16 = 550
(max store)
......
1 12
4
1
5
Recessio
n
Rate
st
ep 
0.35
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 11
 Explanation of steps:
Parameters are terms that describe the overall behavior of the mathematical model, variables
are aspects of the model which change with time, t. Recession Rate and Storage
Capacity are therefore parameters, they are fixed for any specific scenario regardless of
time, but we can change them to describe different scenarios, rain barrels, or drainage
basins. Precipitation Input, Storage level, Outflow, Overflow and Total Flow, are all
variables, which potentially change with each time period
1.
Parameters describing the system (Recession Rate and Stage Capacity) and initial
conditions (Initial Storage, t = 0), are set to the prescribed values.
2.
Outflow, t, at the base of store is calculated as the product of [Storage in previous time
period (t-1), plus precipitation Input (t)] and the Recession Rate.
3.
New Computed Storage (t) is estimated as [Storage in previous time period (t-1), plus
precipitation Input (t)] minus Outflow at base, t.
4.
Check to see whether New Computed Storage, t, exceeds designated Storage Capacity.
If it does, then the Storage, t, is reset to the Storage Capacity. If not, then Storage, t, is
reset to the New Computed Storage, t.
5.
Check to see whether New Computed Storage, t, exceeds designated Storage Capacity.
If it does, then the Overflow, t, is calculated as the difference of New Computed
Storage, t, and the Storage Capacity. If not, then Overflow, t, is set to zero.
6.
The Total Flow, t, from the rain barrel (basin), from both Outflow at the base and
Overflow, is calculated as the sum of these two variables at time t.
7.
Having set these equations up properly, ensuring that the appropriate fixed and relative
addresses have been used, they can be copied for all time periods on interest and the
simple mathematical model yields values of the variables at any and all time periods.
Having established the way in which the mathematical model operates conceptually, and
translated that to mathematical terms and a simple form of “programming” using Excel, one can
change values of inputs, initial conditions and/or barrel (basin) parameters and simulated
expected states of the other variables through time very quickly.
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 12
Because the regional mountain chains run roughly at right angles to the dominant precipitation
bearing winds in Costa Rica, basins located on the Caribbean slope of the country show the
reverse pattern of excess precipitation to those basins of the Pacific slope. Figure 7.4 (lower)
illustrates the Caribbean regime observed in the Río Sarapiquí, which drains the Caribbean
slope of the Cordillera Central to the north of the Tiribí basin. The consistent trade winds off of
the Caribbean produce a) higher Initial Storage (450mm) and b) no period of negative excess
precipitation. Table 7.2 hypothesizes some equivalent figures for a basin (rain barrel) in the
Caribbean watershed of Costa Rica. This along with a Storage Capacity of 550 mm, constitute
Scenario 8
Month Excess P
Month Excess P
Month Excess P
1 390
5 70
9 210
2 425
6 150
10 120
3 330
7 450
11 270
4 170
8 500
12 310
Table 7.2. Monthly values of excess precipitation into a simple hydrologic store designed to
reflect a typical hydrologic regime of the Caribbean watershed of Costa Rica, under
Scenario 8.
 7.
Compute and graph the storage levels, flow and {flows + overflows} (see Figure 7.3)
under Scenario 7 and 8. Compare and contrast the expected Total Flow regimes and
fluctuations of Storage in the Pacific and Caribbean “rain barrels”, with each other, and
with the observed data shown in Figure 7.4. Try to connect the observed and expected
regimes to the regional seasonal hydro-climatology discussed in Assignment 2.
(8 Marks).
 Note: Don’t forget that the value of Initial Storage is 150mm for the Pacific example
(Scenario 7) and 450 mm for the Caribbean (Scenario 8).
 8. Now that you have a better understanding of; recession rates, the timing
of positive and negative Excess Precipitation inputs to stores, storage capacity and
overflows reconsider the figure created in question A2.
Discuss the nature of the partitioning of inputs to storage and runoff in each of the 5
seasons used in the manual.
(10 marks)
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 13
 Hint: Start our discussion in May/June, assuming that storage reached its minimum level at
the end if the preceding season (Jan, Feb, Mar, Apr). Remember Question 1, parts J and
K in assignment #2, which drew attention to the peculiar relationship between seasonal
rainfalls before and after the veranillos, and runoffs in the same periods.
You might find this easier to conceptualize if you view each season graphical as below:
Max.
INPUT
OUTPUT
STORAGE
XS Precip.
Runoff
Min.
Changing the width of the arrows to indicate the seasonal magnitudes of inputs and outputs, and
filling the storage box from bottom (minimum) to top (maximum) with each season
C. Is it Possible to Incorporate all these Ideas and Estimate their Appropriate
Values, in a Single Numerical Representation of the Tiribí Basin?
A series of progressively more complex conceptual and mathematical representations
have been developed in section B. Figure 7.5 reproduces the model with the additional idea that
a certain percentage of the excess precipitation will flow directly to the stream without entering
the Soil/Groundwater system (through precipitation directly into streams, ponds etc. and by
means of overland flow as in the partial and variable contributing area hypotheses.
Varying levels of storage, storage capacity and storage recession have been shown to
influence the way in which a regime of excess precipitation is converted to regimes of storage
and runoff. These parameters and the proportion of excess precipitation going to direct runoff
need to be estimated for the Tiribí basin to permit simulation of responses to differing inputs
(inter-annual variability in precipitation and evaporation resulting from ENSO), or the effects of
various future land use scenarios, or the behavior of smaller spatial units (sub-basins) within the
study area.
The monthly regime of excess precipitation in the entire basin has been calculated and
patterns of monthly runoff observed. A computer program evaluates the many tens of
thousands of combinations of values of the four unknown parameters to see which combination
most successfully converts the calculated regime of inputs (Excess Precipitation) to the
observed monthly runoffs. Values of the four parameters are tried in the following ranges:
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 14
Proportion of direct runoff:
Storage Capacity (mm):
Initial Storage (mm)
Storage Recession constant
0.01 - 0.99 in steps of .01
2 - 800 in steps of 2
2- 500 in steps of 2
0.01 - 0.99 in steps of .01
The “best fit” between the predicted Total Flows and observed monthly runoffs was
determined by calculating a number called the “Root Mean Square Error” (R.M.S.E.).In
order to calculate the RMSE the following steps are taken:
a. The predicted Total Flow in a month is subtracted from the observed runoff to obtain the
error in the proposed model for that month. (Error)
b. That difference is squared to get rid of potential negative signs (predicted could be greater
than or less than the observed - either way it is an error). (Squared)
c. This squared difference is totaled for each of the twelve months and divided by twelve to
obtain the average, or mean, of the squared monthly errors. (Mean)
d. The square root is then taken of this value to get rid of the inflated values derived from
squaring the error initially. (Root)
The resulting number is an indicator of the average monthly error (in units of mm of runoff in
this case) that each possible combination of parameter values tried in the model yields. The
smaller the RMSE the better the combination of parameters performs in reproducing observed
behavior.
One condition was added, which was that the lowest monthly forecast runoff could not be any
lower than three-quarters of the observed minimum monthly runoff. In this way the “best”
model would not give unrealistically low (or even negative) flows in the low flow season.
! Important note: For the sake of convenience and convention, the calculations started with
the month of May. Observed runoffs are at their minimum in March/April at the end of the
dry season, so storage levels will also be at their lowest. This is conventionally defined as
the beginning of the “Water Year” in Costa Rica, which begins at the start of the month
after the month of lowest mean runoff (our case May 1) and ends on the last day of the
month with the lowest mean runoff (our case April 30). Note x-axes in Figure 7.4.
AND THE PARAMETRIC WINNERS ARE!
Proportion of direct runoff:
Storage Capacity (mm):
Initial Storage level (mm):
Storage Recession constant:
0.05
563 mm
222 mm
0.21
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 15
 1. Discuss the degree to which these parameter estimates appear to be
physically reasonable, and explain potential causes of differences. Specifically
? In Assignment #4, 50 of the 265 cells within the basin were classified as Urban,
how does this relate to the estimated Proportion of Direct Runoff? How might the
concept of variable contributing area be useful here?
? Table 6.3 shows the monthly change in storage and cumulative changes in storage,
how do these relate to the range between the Initial Storage Level and the Storage
Capacity?
? How does your answer to question B4, relate to the derived Storage Recession
constant. How might your answer to question B5 provide some logic for the disparity?
(6 Marks)
2. A flowchart (Figure 7.6) shows the steps that must be followed to convert the observed
monthly regime of excess precipitation to a monthly regime of runoff. An explanation
of each variable name follows the chart. Using the parameters listed above and the
twelve monthly values of excess precipitation calculated in the class so far (Assignment
6) follow the steps to derive 12 monthly values of predicted runoff. Report the 12 values
derived. (6 Marks)
! Warnings:
Start these calculations with the initial conditions, parametric values and the inputs for
May. The last (12th) month will be April. It will be helpful to take some scrap paper and
simply write each step out with the variables name and the new computed value as you
proceed. If you have any computer programming abilities, you can try to write a program
based on the flow chart.
The value of Storage (STORE) at the end of the computation for each individual month
becomes the new Initial Storage value at the beginning of the following month.
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 16
Figure 7.5 Conceptual approach linking mean monthly Excess Precipitation inputs to the basin
to mean monthly Runoff.
Excess
Rain
Direct
Runoff
"?"
Infiltration
"?"
Storage
Soil/Groundwater
System
Capacity
"?"
Initial Storage
Level
Saturation
Excess
Flow
"?"
Storage
Storage
Recession
"?"
Parameters needing
to be estimated.
Subsurface
Flow
Runoff
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 17
 Check: To start you going: Here is a run through the calculations for the first month, May.
Start:
ISTORE = 222 (given)
M = 1 (first month, May)
XS = 168.7 (computed previously for May)
Is XS positive? Yes
DIRQ = XS*DIRATE = 168.7* 0.05 (given and constant throughout all months)=8.44
STORE = XS * (1-DIRATE) = 168.7* (1- 0.05) = 160.27
STORE = ISTORE + STORE = 222 + 160.27 = 382.27 (Most of Excess P topping up the
depleted Store)
Is STORE > WHC? No
SATXSQ = 0
SUBQ = STORE * K = 382.27 * 0.21 (given and constant throughout all months) = 80.28
RUNOFF(1) = DIRQ+SATXSQ+SUBQ = 8.44 + 0 + 80.28= 88.68
STORE (1) = STORE - SATXSQ - SUBQ = 382.27 - 0 – 80.28 = 301.99
ISTORE = 301.99
Next month
M = 2 (June)
XS = ....................................................... and so on BUT REMEMBER that when you put the
June XS precipitation values in the ISTORE value was recalculated to 301.99 as the last step in
the May calculations …. Do not reuse the Initial value of 222, once you have progressed
beyond May!


3. Produce a bar graph showing the twelve monthly values of observed and predicted
runoff.
(2 Marks)
4. Produce a scatter plot of the monthly observed runoff (x-axis) and predicted runoff (yaxis), using symbols only (no connecting lines). Identify each point by the month it
represents. Place a 1:1 line on this graph. Record the slope and r2.
(2 Marks)
5. Using the steps outlined in the introduction to section C, calculated the RMSE of this
prediction method.
(1 Mark)
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 18
6. On the basis of all the above information (scatter plot and fitted line, RMSE, absolute
errors and % errors) comment on how well the model and estimated parameters forecast
the runoff. Can you see any systematic errors? Are there some seasons when the model
performs better than others?
(3 Marks)
DEFINITION OF TERMS USED IN FLOWCHART
ISTORE
Initial soil/groundwater storage at the start of each month (Initial value:
222mm, but only to be used in May, After that use the recalculated value
of ISTORE, which is the last step in each monthly iteration through the
flow chart)
M
Month under evaluation (1, 2, ....., 12)
XS
Excess Precipitation - [Precipitation-Interception-Evaporation] (mm)
DIRQ
Direct Runoff (mm)
DIRATE
Proportion of excess precipitation going to Direct Runoff. (Value: 0.05)
STORE
Temporary calculation of water stored in the Soil/Groundwater system
(mm)
WHC
Maximum storage capacity of the Soil/Groundwater system (mm)
(Value: 563 mm)
SATXQ
Saturation Excess Runoff (mm)
SUBQ
Subsurface Runoff (mm)
K
Soil/Groundwater Recession Rate (Value: 0.21)
RUNOFF(M) Total Runoff computed for month, M ,(mm).
STORE(M) Water stored in the Soil/Groundwater system at the end of month, M,
(mm)
Flowchart appears on the following page.
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 19
Figure 7.6. Flowchart by which values of mean monthly runoff may be calculated from values
of mean monthly excess precipitation
Start
Initial Storage
ISTORE
Repeat for Month
M = 1, .., 12
Input Excess
Rainfall, XS
DIRQ = 0
No
XS
Positive?
Yes
DIRQ
= XS * DIRATE
STORE = XS
* (1-DIRATE)
STORE = XS
STORE =
ISTORE +STORE
SATXSQ
=0
No
STORE
> WHC?
Yes
SUBQ =
STORE * K
RUNOFF (M) =
DIRQ + SATXSQ + SUBQ
STORE (M) =
STORE - SATXSQ - SUBQ
ISTORE = STORE(M)
Next Month
Stop
SATXSQ
= STORE - WHC
SUBQ =
WHC * K
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 20
Assignment #7 – Submission checklist:
 A1. Bar graph showing mean monthly Excess Precipitation and mean monthly
change in Storage.
 A2. X-Y scatter (joined by lines) of Excess Precipitation (x-axis) and Change in
Storage (y-axis), months identified and quadrants inserted.
 A3. Discussion of changing relationship between Excess Precipitation and
Change in Storage throughout the year.
 B1. Graphical summary of monthly storage and outflows under scenarios 1 and
2.
 B2. Graphical summary of storages under scenarios 1 and 2, when converted to
natural logarithms.
 B3. Graph of natural logs of observed mean monthly runoffs, Dec-April, versus
time (months 1-5) on the Tiribí, plus interpretation.
 B4. Graphical summary of scenario 3 with brief comment.
 B5. Graphical comparison of outflows from scenarios 4 and 5, with
interpretation.
 B6. Graphical comparison of outflows from scenarios 7 and 8, with
interpretation.
 C1. Discussion of potential physical meaning of computed parameters
 C2. Tabulation of the 12 computed mean monthly runoffs using the flowchart
provided.
 C3. Bar chart of calculated and observed mean monthly runoffs (month on xaxis).
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 C4. Scatter plot of observed mean monthly runoff (x-axis) and calculated mean
monthly runoff (y-axis), with one to one line and months identified.
 C5. Calculations of Root Mean Square Error.
 C6. Discussion of model performance.
G E O 3 2 8 0 A s s i g n m e n t # 7 P a g e | 22
What you should take away from Assignment #7.

An appreciation for the complex seasonal interaction between inputs, stores
and outputs to the hydrologic system, which gives rise to the “nonlinearities” highlighted elsewhere.

An introductory understanding for the ways in which hydrologic stores are
represented mathematically in many models.

The benefits of formulating mathematical models correctly in order to
provide simulations of “what if” scenarios.

The difference between Parameters and Variables, and how the same model
may be used in a variety of geographic locations, merely by changing the
parameters appropriately.

The benefit of having physically interpretable parameters which then allow
you to summarize the way in which the hydrologic system varies in its
operation over geographic space.

A second standard means by which the performance of a model or
mathematical representation of part of the hydrologic system, may be
compared to the real world.