Notes on simple water accounting of the Karkheh Basin
Mac Kirby and Mohammed Mainuddin
May 2006
1. Introduction
In this note, we describe a demonstration simple water account for the Karkheh Basin.
It must be emphasised that this is a demonstration water account. The main
purpose is to aid understanding of how the basin works, and to point to areas where
improved data would help further that understanding. We have used values for
rain, landuse, flow, etc., supplied to us, but we think some of these values are
questionable. The models linking rain to flow are tentative in many sub-catchments.
Nevertheless, if used with great care (and scepticism and testing of the results) the
account may aid understating of how the basin works.
The Karkheh Basin Focal Project of the Challenge Program on Water and Food aims to
explore threats, opportunities and trade-offs in water access and impact on agricultural
productivity and hence poverty / livelihoods and environment.
To address the aims, they want a model that integrates hydrology with social uses and
benefits of water. It must be quick and easy to develop, modify and run, and must run
using the limited data available in the Karkheh. It must be capable of looking at the tradeoffs amongst uses, opportunities such as increased irrigation, and threats to the water
resource such as land use change and climate change.
Here, we describe a demonstration level water account part of an overall model. It is
based on a similar water account of the Mekong, developed in a companion Basin Focal
Project. The Karkheh demonstration water account is in Excel.
If this demonstration is seen as valuable, the account can be improved with better data
and calibration. The calibration methods are built into the Excel spreadsheet.
2. Basic hydrology and outline of simple water account
Basic hydrology, irrigation and land use
The Karkheh Basin covers about 60,000 km2, and is drained by the River Karkheh and its
tributaries. Near the downstream end of the Karkheh is a major dam, built recently for
irrigation supply. Downstream of the dam, the river discharges into a swamp, where most
of the remaining water is consumed as evapotranspiration. Presumably, there is discharge
form the swamp into the Tigris-Euphrates during extreme floods.
The rainfall is around 400 mm per year in much of the catchment, falling mainly in the
winter (November to March), with almost no rain in the late summer. The flow, like the
rain, is seasonal, but without the pronounced peaks, as shown in the figure below.
Doab flow and rain
400
Flow
Rainfall, mm
300
Rain
200
100
0
0
50
Month
100
150
Simple water account
The simple water account is a mixture of data and model. Climate and flow data constrain
the water balance in and between subcatchments, but do not give all the elements in the
water balance nor account for the transfers and storages within and between elements of
the water balance. Simple, physically plausible models are used to account for the
transfers and storages, and thus complete the water balance (to the level of resolution of
interest – which is lumped by subcatchment and monthly). The data are not regarded as
without error (we will point out where there are problems for further investigation), and
the physically plausible transfer and storage models also balance out inconsistencies in
the data (which may or may not be errors, and in any event it is not always clear faced
with inconsistencies where the error may be).
The development of the simple, physically plausible models for storages and transfers is
essentially performed manually, subcatchment by subcatchment. This demands a good
appreciation of the data.
The simple water account has two parts:
- a hydrological account of the water flowing into the basin (primarily rain), flows
and storages within the basin, and water flowing out of basin (primarily as
evapotranspiration and discharge to the sea);
- a further partitioning of the evapotranspiration into the proportion of
evapotranspiration accounted for by each vegetation type or land use, including
evapotranspiration from wetlands and evaporation from open water.
The simple hydrological account is based on a monthly timestep, this being considered
adequate for our purpose.
The account is a top-down model (Vertessy et al around 2000), based on simple lumped
partitioning of rainfall into evapotranspiration and runoff. This is done at the catchment
level, with no spatial separation into different vegetation types. Runoff flows into the
tributaries and into the Karkheh, with downstream flow calculated by simple water
balance. During high flows, some of the flow is stored in the channels. Inflows are stored
in Lake Karkheh, and are balanced by evaporation and discharge at the dam. Water is
spilled if the capacity of the dam is exceeded.
Units:
Rain, evapotranspiration and potential evapotranspiration are given in mm.
River flows and storages, and lake storage, are given in mcm (million cubic metres). 1
mcm is equivalent to one metre over one square kilometre. 1000 mcm = 1 bcm (billion
cubic metres) = 1000 m over 1 km2 = 1 km3.
Rainfall / evapotranspiration / runoff
The partitioning is based on an idea of Lu Zhang, which in turn is derived from the
reasoning of Budyko (which applies to average annual runoff), with the addition of a
storage of which varies from month to month. Rainfall (P) plus irrigation (Ir) is first
partitioned at the surface into the runoff (Ro) and infiltration (I), where conservation must
be observed:
P  Ir  I  Ro  0
(1)
Rainfall plus irrigation is the supply limit, whereas the unfilled portion of a generalised
storage, Ssmax, is the capacity limit governing the partition and includes soil storage and
small surface stores. A Budyko-like equation is used to smooth the transition from the
supply limit to the capacity limit:
1
 P  Ir  S s max a1  a1

(2)
 
a1 
S s max




1

P

Ir

S
s
max


The following figure shows that this equation makes a sharper transition from the supply
limit to see capacity limit with larger values of the parameter a1.
I


1.2
Supply limit, P +Ir
Capacity limit, S s max
1
5
I / Ss max
0.8
2
0.6
1
0.4
0.5
0.2
0
0
0.5
1
1.5
2
2.5
3
(P +Ir ) / S s max
Figure. Behaviour of the runoff infiltration partition equation with different values of the
parameter a1.
The evapotranspiration depends on the potential evapotranspiration (ETpot, capacity limit)
and the surface storage (Ss, supply limit). Although soil and other surface stores are not
differentiated, the implication is that evaporation occurs from small ponds, puddles, and
the soil surface, whereas transpiration comes from deeper soil storage. A similar equation
to the above, with a second adjustable parameter a2, is used to smooth the transition from
the supply limit to the capacity limit:



1
a2

 a2
S st t  I ET pot
ET


(3)

a2 
t


t

ET pot
1

S

I
ET
s
pot


This equation also behaves as shown by the figure with the obvious changes to the
parameters.





The surface storage is increased by the infiltration and decreased by the
evapotranspiration and a drainage-to-baseflow component, DB:
S st  S st  t  I  ET  DB
(4)
Baseflow is negligible in most of the tributaries of the Karkheh, so the drainage-tobaseflow component was mostly assumed to be zero. The lower part of the Black
Karkheh has a small baseflow, and there DB was assumed to be proportional to the
surface storage (that is, it varied from month to month).
River flow and storage
River flow is modelled as a series of reaches, with mass balance observed between
reaches.
Thus, the reach outflow, Qo, is given by the inflow, Qi, plus any tributary flows, Qt, plus
the runoff, Ro (as calculated above), plus a baseflow component, Bf, less any diversion
(for industrial or agricultural use), less any losses (evaporation, seepage), plus the change
in reach storage Sr:
Qo  Qi  Qt  Ro  B f  D  L  S r
(5)
The reach storage is taken to be a function of the inflow:
c2
(6)
S r  c1Qi
where c1 and c2 are parameters. The change in reach storage is the difference between
reach storage at two timesteps:
(7)
S r  S rt  S rt t
The reach storage is recovered as river flow during recession. Reach storage is not
particularly important in the Karkheh, and we have set C1 to zero everywhere, thus
setting reach storage to zero.
The monthly baseflow, Bf, was ignored here. It appears not to be important in the
Karkheh, with river flows often falling to near zero during the late summer.
Small storages
We suspect that there is considerable small storage capacity within the Karkheh basin.
Firstly, there is a considerable area of irrigation in each subcatchment and, since the
irrigation is (presumably) out of phase with the rain, water must be stored. Secondly, the
flows are much smoother than the rainfall and generally lag the rainfall, and this can only
happen if water is stored in the winter and released later. The soil and channel storage
referred to above do not provide adequate storage to account for this and, in any event, do
not smooth the rainfall to mimic the flows. We do not necessarily assume that the
catchment storage is in the form of managed reservoirs.
We assume small storages, SD, that fill and empty according to:
S Dt  MIN S D,Max , S Dt t  Ro  E  S r  D  c3 S Dt t



(8)
The maximum function gives the capacity limit of the storages. The other terms are
inputs and output, defined above expect for the evaporation, E. The final term gives a
slow leakage (or controlled release) from storage, at a rate governed by the adjustable
parameter, c3. This final term is a working hypothesis which gives the right form of
behaviour. Whether it is physically reasonable in the Karkheh we do not know, nor
do we know if the values of the parameters are plausible. We have assumed that
enough water must be supplied from the dam not just to satisfy diversion demand, but
also to fill the river storage by the amount implied by the irrigation diversion flow. The
evaporation is given by:
(9)
E  c4 ET0 S Dc5
The term c4ET0 accounts for evaporation demand from open water, and c4 is often
assumed to be 0.7. The term SDc5 is the conversion from storage volume to surface area
and c5 will often be around 2/3 (because volume is proportional to the cube of the depth,
whereas the evaporating surface area is proportional to the square of depth).
Karkheh dam
The Karkheh dam became operational in 2000. This is after the period for which we have
climate and flow data. Therefore we are not able calibrate a model for the dam.
Xxxxxxxxxxxxxxxxx add stuff about dam?
Balance checks
The spreadsheet has two checks of the overall water balance for each sub-basin. The first
check is that the sum of the monthly rain over the full period equals the sum of the
monthly evapotranspiration plus the sum of the monthly runoff plus the difference in the
surface storage, Ss, between the beginning and end of the period.
The second check is that for each sub basin the sum of the monthly inflows equals the
sum of the monthly losses to discharge, evaporation from storages and diversions plus the
difference in storages between the beginning and end of the period.
In the present version of the spreadsheet, we have not checked the balances carefully.
Some gaps in the flow data and some other modifications to the spreadsheet have led to
slight errors and inconsistencies in the balance checks. These have yet to be sorted out.
Note also that annual averages reported in the spreadsheet do not always compare as they
should because of gaps: the flow data, for example, sometimes have gaps, and the
average measured flow data is thus not always for the same period as the average
calculated flow data.
Irrigation demand and supply
The spreadsheet can, in principle, handle many irrigated crops, limited only by the
column capacity of Excel. The area of irrigated crops is also limited by the total land area
in a sub-basin, and by the volume of water available.
We use a crop factor approach, in which the crop factor, KC, is 0 when there is no crop, or
takes a value often about 1 when there is a crop. The basis of this approach is given in
FAO 56 (Allen et al.) and companion publications. We assume here that crops are always
well watered, and that the area cropped is limited when water supply is limited. Thus,
decreases in crop production result from reduced area, not reduced yield. The crop water
demand per unit area for n crops is:
IrrDemand  K c1 ET0  K c 2 ET0  ...... K cn ET0
(12)
where KC1…n are the crop factors for each crop. The irrigation demand is summed for the
following 12 months, in order that a full year's demand may be compared with a full
year's supply.
The total area, ATI, that may be supplied for all irrigated crops is given by:

SD 

(13)
ATI  MIN  ATI max ,
IrrDemand 

where the MIN function limits the area irrigated. The individual area for crop i is:
AiI

ATI
Ai max
(14)
ATI max
and the volume, Di, diverted to supply crop i is:
An I ( K cn ET  Pen )
A1I ( K c1 ET0  Pe1 ) A2 I ( K c 2 ET0  Pe 2 )
(15)
Di 

 ......
IE1
IE 2
IE n
where IE1….n is the total irrigation efficiency (ie accounting for all losses between the
diversion point and the use of water by the crop) and Pe1….n is the effective rainfall. The
individual diversions, Di, to each crop are summed to give the total diversion, D:
D  D1  D2  ...... Dn
(16)
Partitioning of dryland evapotranspiration by land use / vegetation type
Equation (3) gives an estimate of the monthly evapotranspiration for each catchment
which is constrained by and consistent with the measured outflows. This can be
partitioned into the evapotranspiration from each land use / vegetation type in several
ways, using vegetation water use modelling principles. The FAO CROPWAT model is a
suitable candidate, since it is a simple model closely based on observed crop water use,
and has been applied all over the world. Andah et al (2003) used SWAP. As well as
providing a better estimate of the partition, it would also provide an independent check of
the rainfall-evapotranspiration-runoff partitioning of the simple hydrological model. At
this stage, we have used a simple pro-rata partitioning based on some country land use
statistics.
AiD
ETiD 
ETTD
(17)
ATD
where AiD is the ith dryland land use, and ATD is the total dryland area.
We emphasise that this simple partitioning is not a restriction in the spreadsheet
accounting. It is merely an expedient used here for this demonstration. Using something
like the FAO CROPWAT approach is quite easy to implement.
3. Data used
This is a brief summary only of the input data. Input data were based what was to hand as
simple, consistent datasets.
- Rainfall and potential evapotranspiration were supplied by Mobin.
- Reach flows supplied by Mobin.
- Some basic statistics for areas of forest, grassland and cropping (dryland and
irrigation) were supplied by Mobin.
Problems
The water account has several problems, none of which prevent it fulfilling the main aim
of aiding understanding of how the basin works. Most of the problems are in the
individual subcatchments and will be dealt with in section 4. The balance checks should
be improved.
Using the spreadsheet
The spreadsheet is developed by adding extra worksheets for extra catchments or
subcatchments. On a new worksheet, the rain and flow are first added, and the overall
catchment, irrigation and dryland areas are added.
The calculations are then done in two stages. Firstly, the runoff parameters a1 and a2
(cells L10 and L11) are adjusted so that the summed calculated discharge equals the
summed observed discharge. This is based on the requirement that, over a long period
when storages can be ignored, the locally generated discharge from a subbasin must
approximately equal the runoff less any local diversions and open water evaporation
losses. In the small screen-grab below, a1 and a2 are manually adjusted so that
sumcalcdisch approximately equals sumobsdisch.
Parameters
Smax 0.5
a1 0.84
a2 0.84
a3 0
Totals
Fitting: adjust the parameters so
sumobsdisch 5197
<------------ this cell equals
sumcalcdisch 5245
<------------ this cell
years 1990-2000, not 1994approximately is good enough
Next, the c3 parameter is adjusted to minimise sum dev - the summed squared deviations
between observed and calculated discharge. The parameter is adjusted using Solver. We
expected Smax also to be important, but it turns out to only weakly influence the summed
squared deviations between observed and calculated discharge, and solver usually does
not change it.
Parameters
c1
c2
c3
Smax
c4
0.2
0.6
0.342468948
1000
0.7
Totals
Fitting: minimise
sum dev
135623 <------------ this cell
sums (o-e)^2
subject to the parameters
years 1990-2005, not 1994
c5
0.67
Closs
1.00
4. Components and results in detail
We were given climate and flow records for 15 subcatchments in the Karkheh basin. We
added the marshes at the base of the basin as a 16th area. The subcatchments and flow
gauge points are shown in the figure below.
Doab
The Doab subcatchment has an area of 7514 km2, including 1676 km2 of irrigated land;
the flow gauge is 21-115.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
600
mcm/mo
discharge calc
400
200
0
0
50
Months
100
150
The main mismatch between observed and calculated flow is missing the peak in the third
year – this will be seen in several other records in the northern part of the basin.
Calculating water use amongst the land uses is problematic. The irrigation area of 1676
km2 would, at full irrigation (ie actual ET = potential ET) and an irrigation efficiency of,
say 50 % (including losses to evaporation from storages), require on the order of 3000
mcm, which is approximately equal to all the rain falling on the catchment. Clearly,
either the area is not all irrigated at once, or it is irrigated at a very small supplemental
rate of perhaps 50 – 100 mm per year.
We have assumed a very small supplemental rate of irrigation and that most of the
irrigated area is of summer crops, but we do not know what the actual rates and
area are.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Forest etc
Irrigation
Grazing
Dryland
Pole Chehr
The Pole Chehr subcatchment has an area of 3015 km2, including 390 km2 of irrigated
land; the flow gauge is 21-127.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
800
discharge calc
mcm/mo
600
400
200
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Discharge
Grazing
Dryland
Irrigation
Note that here, and in several other catchments, the discharge is a larger proportion of the
water balance than might be expected based on worldwide catchment behaviour. This
might be because the winter dominance of the rain leads to a greater saturation excess
runoff than is usually seen, or might point to inconsistencies in the data.
Doabe Merek
The Doabe Merek subcatchment has an area of 1241 km2, including 109 km2 of irrigated
land; the flow gauge is 21-133.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
150
mcm/mo
discharge calc
100
50
0
0
50
Months
100
150
The flow peak of the third last year is not captured, as well as that of the third year (as
mentioned in Doab).
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Discharge
Grazing
Irrigation
Dryland
Ghor Baghestan
The Ghor Baghestan subcatchment has an area of 3937 km2, including 538 km2 of
irrigated land; the flow gauge is 21-143.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
400
discharge calc
mcm/mo
300
200
100
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Forest etc
Irrigation
Grazing
Dryland
Holilan
The Holilan subcatchment has an area of 4240 km2, including 302 km2 of irrigated land;
the flow gauge is 21-147.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
1500
mcm/mo
discharge calc
1000
500
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Grazing
Discharge
Dryland
Irrigation
Dartoot
The Dartoot subcatchment has an area of 2573 km2, including 112 km2 of irrigated land;
the flow gauge is 21-157.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
300
mcm/mo
discharge calc
200
100
0
0
50
Months
100
150
The behaviour of this small catchment is very different to that of nearby catchments. The
flow is less smooth, and there appears to be a modest base flow.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Irrigation
Forest etc
Dryland
Grazing
Tang Sazin
The Tang Sazin subcatchment has an area of 2881 km2, including 87 km2 of irrigated
land; the flow gauge is 21-159.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
2000
discharge calc
mcm/mo
1500
1000
500
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Forest etc
Irrigation
Grazing Dryland
Kaka Reza
The Kaka Reza subcatchment has an area of 1133 km2, including 133 km2 of irrigated
land; the flow gauge is 21-169.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
300
mcm/mo
discharge calc
200
100
0
0
50
Months
100
150
Two features of the data for this catchment are problematic:
- the peak flow for the third winter occurs about three months later than the peak
rainfall. This is the only year in which that happens. No plausible model can account
for this.
- the observed discharge is a very high proportion of the rainfall (almost 2/3), which
is very unlikely. See also the pie chart below.
Futhermore, getting the base flow right for this catchment required a rather higher deep
drainage from the soil than is likely.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Grazing
Discharge
Dryland
Irrigation
Cham Anjir
The Cham Anjir subcatchment has an area of 1634 km2, including 106 km2 of irrigated
land; the flow gauge is 21-175.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
300
mcm/mo
discharge calc
200
100
0
0
50
Months
100
150
Again, this catchment has a very high observed discharge (see pie charts below). Getting
the base flow right for this catchment required a rather higher deep drainage from the soil
than is likely.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Discharge
Grazing
Dryland
Irrigation
Pole Dokhtar
The Pole Dokhtar subcatchment has an area of 6762 km2, including 441 km2 of irrigated
land; the flow gauge is 21-183.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
1000
mcm/mo
discharge calc
500
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Forest etc
Irrigation
Grazing
Dryland
Jelogir
The Jelogir subcatchment has an area of 4115 km2, including 158 km2 of irrigated land;
the flow gauge is 21-185.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
3000
mcm/mo
discharge calc
2000
1000
0
0
50
Months
100
150
Apart from the peak in the third summer, the match here is good.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Discharge
Forest etc
Irrigation
Grazing
Dryland
Pole Zal
The Pole Zal subcatchment has an area of 332 km2, including 1 km2 of irrigated land; the
flow gauge is 21-189.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
300
mcm/mo
discharge calc
200
100
0
0
50
Months
100
150
The data for this catchment are problematic:
- the observed discharge is greater than the rainfall (almost twice as much), which
obviously is very impossible.
In estimating the contribution of this catchment to downstream, we used the observed
flow data, assuming that the error lies elsewhere.
The calculated water use for the main land uses and for the discharge is shown below.
losses
Forest etc
Irrigation
Dryland
Grazing
(evaporation
etc)
Discharge
This is essentially fictitious and should be ignored.
Paye Pol
The Paye Pol subcatchment has an area of 2678 km2, including 28 km2 of irrigated land;
the flow gauge is 21-191.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
3000
mcm/mo
discharge calc
2000
1000
0
0
50
Months
100
150
The discharge for this catchment is higher than is likely – see also pie chart below.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc)
Forest etc
Discharge
Grazing
Irrigation
Dryland
Abdol Kha
The Abdol Kha subcatchment has an area of 1872 km2, including 371 km2 of irrigated
land; the flow gauge is 21-193.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible. The
irrigation supply is based on small storages, whereas in this catchment they could be
taken run-of-river: this is an area for future improvement of the water use account.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
discharge calc
mcm/mo
3000
2000
1000
0
0
50
Months
100
150
Note the missing flow records for the first four years.
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
etc) Discharge
Forest etc
Irrigation
Grazing
Dryland
The discharge for this catchment is less than the inflow from upstream. In terms of water
use, therefore, this catchment consumes more water than falls as rain, and discharge is
not a component of the rainfall. We show discharge as zero.
Hamidieh
The Hamidieh subcatchment has an area of 931 km2, including 295 km2 of irrigated land;
the flow gauge is 21-199.
As mentioned in section 2 on small storages, we do not know whether our
assumptions regarding small storages within the catchment are plausible. The
irrigation supply is based on small storages, whereas in this catchment they could be
taken run-of-river: this is an area for future improvement of the water use account.
The calculated and measured flow record is shown below.
Discharge
Discharge obs
discharge calc
mcm/mo
3000
2000
1000
0
0
50
Months
100
150
The calculated water use for the main land uses and for the discharge is shown below.
losses
(evaporation
Discharge
etc)
Forest etc
Grazing
Dryland
Irrigation
The discharge for this catchment is less than the inflow from upstream. In terms of water
use, therefore, this catchment consumes more water than falls as rain, and discharge is
not a component of the rainfall. We show discharge as zero.
End / marshes
The end (discharge) subcatchment has an area of 6709 km2, and includes some of the
Horal Azim (spelling as per supplied jpg map, but other spellings seem preferred
elsewhere) wetland. We have not been given figures for the area of irrigation, but have
assumed that it is 295 km2 (as for Hamidieh). There is no flow gauge.
We have been given few data of land use for this subcatchment, so we have assumed:
- that there is 1000 km2 of irrigation;
- that the marshes occupy up to 2000 km2, and have a capacity of up to 20000 mcm (ie
are 10 m deep when full to capacity);
- that the relationship between volume, Vm, and area, Am is non-linear with the volume
falling more rapidly than the area, given by
c6
 V 
Am  Am max  m 
(18)
 Vm max 
where Vmmax, is the maximum volume and Ammax is the maximum area, c6 is a constant,
taken to be 0.1 The evaporation from the marshes is given by
E  c 4 ET0 Am
(19)
which is the same as equation (9) but with the area of the marshes taken directly.
The calculated flow record is shown below.
Discharge
Discharge obs
400
mcm/mo
discharge calc
200
0
0
50
Months
100
150
The calculations show that the marshes may well have discharged a small volume of
water into the Tigris in wet years. The annual average was, according to this calculation,
about 180 mcm per year (0.18 km3). This figure should not be treated as relaiable, since
we have assumed the areas and other parameters for the marshes and the irrigated area,
but it gives a feel for the behaviour.
The calculated water use for the main land uses and for the discharge is shown below.
Discharge
Irrigation
losses
(evaporation
etc)
Dryland
Grazing
Forest etc
Note that the evaporation from the marshes is a large component of the water use in this
catchment.
5. Example use
As a demonstration, we examine the consequences of the Karkheh dam. The dam has a
capacity of 7800 mcm and is just above Paye Pol. The dam will be used to supply
irrigation districts of up to 3200 km2, which is about 1600 km2 more than we have
assumed was developed prior to the dam. We assume that the dam discharge equals the
demand from the irrigation areas downstream (which is in turn calculated from the area,
the crop factor, the potential ET, and an irrigation efficiency, as given by equations (12)
to (16)), plus volumes in excess of the storage capacity. The downstream irrigation
districts take from the river what they require, subject to the available flow. (To see how
this is done, refer to the spreadsheet.)
We emphasise that this example is for demonstration only. We have assumed far too
much for this to be treated as realistic. We have assumed no allowance of flows
(either volume or timing) to the marshes.
- Furthermore, it has been done quickly and not properly checked.
The flow for Paye Pol (ie dam discharge) is shown below.
Discharge
Discharge obs
3000
mcm/mo
discharge calc
2000
1000
0
0
50
Months
100
150
The flow is obviously substantially changed from that calculated previously (above),
which matched the observed flow reasonably well. The calculated flow at Hamidieh is
shown below, and again is substantially changed from the previous picture.
Discharge
Discharge obs
discharge calc
mcm/mo
3000
2000
1000
0
0
50
Months
100
150
The discharge from the marshes is now zero in all years except a tiny discharge (7 mcm)
in one month in the fourth year), as shown below.
Discharge
Discharge obs
400
mcm/mo
discharge calc
200
0
0
50
Months
100
150
The water use in the final catchment shows that the irrigation water use has increased
substantially, and the evaporation from the marshes has dropped substantially (from an
annual average of 3258 mcm to 1531 mcm). The area of the marshes is also calculated to
diminish substantially.
losses
Discharge
(evaporation
etc)
Forest etc
Grazing
Dryland
Irrigation
6. Next
- more work on model
- Link with social issues
- Use!
7. Conclusions
A very simple spreadsheet model with few adjustable parameters has produced plausible
runoff and river flow behaviour in the Karkheh Basin. If desired it could be further
developed.
8. Acknowledgements
9. References