Basin Scale Water Infrastructure
Investment Evaluation and Crop selection
guidance considering Climate Risk
Upmanu Lall and Yasir Kaheil
Columbia Earth Institute
Draft Report
Submitted to the
Asian Development Bank
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Abstract
Water storage infrastructure has historically been a primary means of addressing vulnerability to climate
risk. Rainfall, and streamflow fluctuate at many time scales, rendering supply unreliable unless a
mechanism for surface or subsurface storage is provided. Irrigated agriculture typically provides
dramatically higher yields relative to rain fed agriculture, by ensuring a regular, when needed water
supply. Irrigation is also typically the dominant water user in most parts of the world. Addressing
storage-irrigation infrastructure needs is thus a critical piece in developing a strategy for regional water
and food security in the face of a changing climate.
In the 20th century, large reservoir and canal system projects were funded and developed in many
regions. It is argued that these played a significant role in facilitating the Green Revolution in India,
Pakistan and elsewhere. However, this notion has been challenged, and many negative environmental
and socio-economic impacts of such projects have been highlighted. Governance and maintenance of
such hydraulic infrastructure has also been a challenge.
In the last decade or so, considerable interest has been directed towards local or on-farm decentralized
storage development, i.e., towards small scale reservoir and use systems where governance may be less
of an issue. There has been government support of such activities in countries such as India, leading to a
rapid proliferation of such systems in some areas. Questions about the effect of such development on
the regional hydrologic balance and as to their resilience in a changing climate arise.
Further, in the spirit of IWRM, one needs to consider the potential use of water as well as the
development and management of supply. In the current context, a central question that can be posed is
the identification of the best mix of centralized and decentralized storage, and the associated spatial
distribution of crops in a river basin, such that issues of governance, equity, income are properly
resolved while addressing climate risk. This is the question addressed in this paper, with the qualification
that we do not consider the use of groundwater storage. The integration of that important aspect is left
for future work. Water balance and economic calculations parametric to a specified climate scenario
are used to assess the relative hydro-economics of the system. Environmental and social impacts can be
situation dependent, and would require customization of the model presented here.
A mathematical modeling system and associated software systems (in the open source package R) are
presented that allow the development of climate scenarios for a given region using a variety of sources
of climate information; specification of cropping pattern scenarios, and parameters for the centralized
and decentralized storage system provision. A hydrologic balance analysis is then conducted in a
spatially distributed framework (a digital elevation model of the river basin is needed so that flow
pathways can be automatically identified), so that spatial supply efficiency, income and cost
distributions, and reduction in climate risk associated with a proposed configuration of cropping
patterns and/or centralized and decentralized storage can be assessed. The modeling system and
scenario analysis capability can be used by regional planners or investors to assess both policy and
investment proposals in a participatory IWRM framework, as part of a formal approach to climate
change adaptation with water and food security goals.
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Table of Contents
Contents
Abstract ......................................................................................................................................................... 2
Table of Contents .......................................................................................................................................... 3
Introduction .................................................................................................................................................. 4
Background Literature and Framing ............................................................................................................. 6
Assumptions................................................................................................................................................ 10
Model Details .............................................................................................................................................. 11
Catchment delineation ........................................................................................................................... 11
Algorithm description ................................................................................................................................. 12
Initialization............................................................................................................................................. 13
Agricultural water demand ..................................................................................................................... 13
Flow accounting for centralized/decentralized schemes ....................................................................... 14
Notation .............................................................................................................................................. 14
Cost-revenue accounting ........................................................................................................................ 15
Cost ......................................................................................................................................................... 15
Revenue .................................................................................................................................................. 15
Preparation of input files ............................................................................................................................ 15
Catchment definition file ........................................................................................................................ 15
Catchment area file................................................................................................................................. 16
Meteorological data................................................................................................................................ 16
Input parameters file .............................................................................................................................. 17
Crop properties and reservoir files ......................................................................................................... 17
Running the model.................................................................................................................................. 18
References .................................................................................................................................................. 19
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Introduction
Most anthropogenic climate change simulations project increased variability in rainfall, as well as
changes in the mean value, intermittence and seasonality. These changes pose a significant stress on the
reliability and resilience of regional water supplies, impacting both drinking water and irrigation needs,
which often rely on spatially distributed storage and conveyance elements.
Water resource planners have historically considered project level analysis of infrastructure. For
instance, river basin development used to focus on the identification of a few sites where major
reservoirs could be sited, and then an optimal combination of these with distribution canals to provide
use in selected areas was investigated. Recently, the relative inefficiency, high losses, and inequity of
these centralized storage and canal systems has been highlighted, and NGOs and others have advocated
decentralizes solutions such as rainwater harvesting structures and “watershed management”. Private
investment in groundwater usage has also increased substantially, driven primarily by the availability of
energy sources and the desire to be free of reliance on a system that may not reliably deliver services.
While small personal storage units provide access to the user, they may also incur high evaporative and
other losses and their aggregate performance under climatic exigencies is unclear.
Further, while large centralized storage based irrigation schemes supply only those below the dam
(Figure 1a), providing limited to no services to those above a dam, the small, distributed storage systems
provide services to those developing these sources (Figure 1b), but potentially negatively impacting
those downstream of them. In many Asian countries, even where planned centralized dam and canal
systems were developed, an unplanned development of small on-farm or community storage systems
has emerged as demands have increased (Figure 1c). Sometimes, these infrastructure elements have
emerged as part of a state funded push for “watershed management”. However, even in these cases, by
and large there is no macro level planning or prior hydrologic assessment of the cumulative effect of a
large number of distributed storage elements. As a result, while the initial impact of the “watershed
management” projects may be positive, in that the residence time of water in the basin is increased,
services are provided to those immediately connected, and baseflow in small ephemeral streams is
increased, eventually, the state of development can reach a point where downstream water users and
stream ecology are adversely impacted. Such chronic effects are rarely appreciated until after the
development has taken place and it is politically difficult to undo or regulate. Unregulated groundwater
development and use is also a significant contributor to the overall problem due to its impact on the
regional water balance through surface water interactions. The argument that the small storage
structures contribute to groundwater recharge and hence provide additional services is valid, but is
again a function of the stage of development.
The public infrastructure debate is usually over whether the small storage elements should be
developed vs a large dam or canal system, and the associated groundwater development is not
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considered. Especially in Asian areas with high population density and intensity of agriculture, a
coordinated approach to integrated river basin management is essential. Planning the density and
location of small storage systems to develop, in association with the evaluation of a proposal for a large
dam and canal system, conjunctively with a strategy for groundwater extraction is essential. Such a plan
needs to also consider active monitoring of the state of surface and groundwater systems, including
water quality considerations, to inform active management of the total water resource for individual
and community benefit. The resulting system (Figure 1d) could work in conjunction with a spatially
specific strategy for crop planting (e.g., rice in lowlands, and beans in highlands) that improves the
economic and physical (water and land) productivity of the region.
(a)
(c)
(b)
(d)
Figure 1. Alternate possibilities for river basin storage and water use development: a) Large dam and
canal system that serves a restricted downstream area (green); b) Unplanned, spatially distributed small
storage and groundwater wells constructed as needed by individuals (green represents the area served,
red are the wells, and blue the storage elements); c) evolution of small storage and wells on top of
previous large dam and canal system leading to reduction in effectiveness of the dam/canal system; and
d) planned implementation and management of small storage, wells and large dam/canal system so that
most pumping is moved to the lowlands area where upstream recharge can promote sustainability, and
small storage is concentrated with a density that works to promote equitable use across the basin
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without significantly impacting downstream dam and use.
We realize that such integrated river basin management requires institutional controls and effectiveness
that may be difficult to achieve in most cases. However, recognizing that such processes can be
informed by analyses that clarify the outcomes, we pursue the development of a simulation model that
allows an assessment of the performance of a proposed mix of large and small storage and distribution
elements for agriculture, parametric on a climate scenario and on specified cropping patterns. Thus,
both agricultural policy and changing climate implications for the proposed design can be assessed in
terms of a variety of socio-economic and physical performance indicators. Weather/climate data are
readily available either from archival records or from stochastic simulations linked to seasonal climate
forecasts or to climate change scenarios. Soil and topographic information are also readily available
from public sources, at varying spatial resolution. However, aquifer characteristics (depth of different
layers, their hydraulic conductivity etc) are usually not readily available and are also highly spatially
variable. Similarly, existing infrastructure (small) and use information is not usually readily available.
Consequently, as an initial effort we considered an idealized evaluation where groundwater dynamics is
not considered in the model, and a basin scale evaluation is done with a proposed large dam /canal
system considered, along with small storage capacity allocation by sub-basin. The river drainage
network and the associated sub-basins are derived automatically from the digital elevation data for the
purpose. Since many existing attributes are not explicitly incorporated in our initial model, its purpose is
to primarily facilitate a conceptual evaluation or initial screening of how a mix of small and large projects
may perform as we consider a changing climate and crop choices in a river basin. In this context, the
model developed can be used to assess win-win strategies to resolve water development conflicts
between upstream and downstream users in the river basin through appropriate controls on density of
development, cropping and water delivery while recognizing the climatic attributes.
Since rather limited formal work has been done on assessing how a mix of small, distributed storage and
irrigation systems and a centralized storage and distribution system can be expected to perform in the
face of changing climate, this first order simulation toolkit that can help inform various aspects of
performance of such systems, with a view to supporting decision processes for regional processes for
investment in water resource development. We recognize that climate and water demands vary by time
and space scales and hence the development of a universal modeling system for the purpose is
challenging. A simplified analysis that attempts to resolve this issue at appropriate scales is attempted
through a hierarchical prescription for analysis. At the outset we recognize that developing a
comprehensive universally applicable, multi-scale hydrologic model is an open challenge, and take a
simpler approach that is consistent with the goals of screening development options given relatively
limited data sources in a region.
Background Literature and Framing
The most relevant past work that provides a background for the work presented here is a seminal
contribution by van der Zaag and Gupta (2008). They specifically consider the physical and governance
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attributes of small vs large water storage systems in the context of a policy analysis of choice between
the two types of systems. They develop four indicators to understand the scale issues and their
governance as well as biophysical and socio-economic implications. These are:
1) The residence time of water in a reservoir: used as a proxy for the spatial scale of the catchment
area, and hence of the biophysical impact of the reservoir
2) The water provision capacity: Relative to water supply or population measures, this is used as an
indicator of the size of the demand that may be supplied
3) Cost effectiveness of providing reliable access to water per beneficiary: this is an economic
efficiency measure computed over the service area
4) The number of beneficiaries and loser compensation: this adds an equity dimension.
The framing of their discussion is that of large vs small infrastructure, rather than the development
of an optimal mixture across the two types of infrastructure. They consider agricultural use as the
dominant use category given its dominance in the water balance. Given their governance and equity
interests, van der Zeeg and Gupta define people upstream of a storage project as benefactors, those
directly served by the project through canals or a distribution system as direct recipients, and those
who may benefit from the storage and irrigation activity by receiving augmented return flows
and/or base flow or increased groundwater levels as indirect recipients. In their context, the
benefactors may deserve compensation by the recipients of the benefits of a storage project,
especially for the large storage + canal project. Their discussion is focused on the complications
introduced into governance as the physical and temporal scale of the water enterprise to be
managed increases. They note that there is a growing recognition that there is neither an optimal
scale nor an optimal level at which environmental and water issues can be managed. Structured
arguments as to jurisdictional and governance issues as well as a variety of social interactions that
develop in the use of these systems are offered to support this observation. Both physical and social
externalities that result from water resource development and the alteration of natural flows are
cited.
The four metrics of performance offered are discussed in this context. They advocate the residence
time of water as a useful measure of the spatio-temporal scale of its impacts and a recognition of
both the level of water use and the associated reliability of supply since both contribute to the
storage requirements relative to both the average inflow and the nature of its temporal variation.
The basic idea is that a small reservoir would refill more often, i.e. have a smaller residence time,
and potentially lower reliability. However, they don’t quite connect the reliability of a collection of
small reservoirs, or the equivalent residence time of storage in such a system. Given the topology of
a river drainage network, the derivation of an equivalent residence time is not obvious. Surely, it is
not a simple average or related statistic of the residence time of a single small reservoir. They do
acknowledge this factor implicitly, by illustrating that the impact of changing residence time or
storage of the main project (they are equivalent in a sense) is nonlinear on downstream flood flows
and also on the base flow in the dry season at downstream locations. They note that if the residence
time of a reservoir is greater than 3 to 6 months then it has a significant biophysical impact on
downstream flows. Through this assertion they exhibit a preference for small storages. However,
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the inability to assess the equivalent residence time of a collection of small storage units, as well as
the evaporative and other losses from such units, especially in the semi-arid settings that are often
the targets of development, leads to an inability to meaningfully use this metric.
The second measure discussed by them is the ratio of the reservoir storage to the area to be
irrigated. The idea is that if this is small (e.g., 0.1 to 0.2m) then the reservoir (system) is primarily
being used for supplemental irrigation, whereas large values (>1m) would represent use for full
scale irrigation. As this ratio increases they expect higher levels of natural disruption (as may be
expected also with higher residence times/larger storage). This is an intuitively useful measure as to
the service provided by a reservoir. However, in the absence of the consideration of evaporative
losses (these could be as high as 1 to 2 m per unit reservoir surface area) and the cumulative effect
of a system of small shallow storage units vs a large deep unit, it is not clear how the equivalent
comparison of a system of small vs a large project can be achieved.
The third measure looks at cost effectiveness in terms of the ratio of the total investment cost
divided by the total number of beneficiaries. This is an interesting measure (as an alternative to
dividing the investment by irrigated area) since it aims to measure equity of application of
investment relative to the investment an average user may have to come up with to receive this
benefit. The measure is most useful where the beneficiary population is relatively homogeneous in
terms of the actual irrigation benefit received. A concern is that for a large project, a large number
of potential beneficiaries could be indicated, with a low probability that the ones downstream
actually receive benefits, or alternately even for a collection of small projects, indirect beneficiaries
who really do not derive proportional benefits are indicated. The economies of scale that exist
between small and large storage projects and in the design of a mixes system may not be ideally
captured by such a measure.
The final measure they introduce is further motivated directly by an equity consideration. They
define the measure as the ratio of the total population to the number of beneficiaries (i.e., the
inverse of the % of actual to potential beneficiaries). They note that distributed small reservoirs will
in general have a large number of beneficiaries, and that these will have relatively small effects both
in terms of benefits and adverse impacts. As reservoir size increases, the number of people
impacted increases dramatically, but without necessarily a proportional increase in the number of
beneficiaries. While they do not directly measure the inequity or the variance in the benefits
received by the population, their argument implicitly addresses this issue through the potential for
increasing negative impacts and lack of service if only a large project is constructed.
In summary, the authors have a very thoughtful and useful characterization of some of the factors
that have been cited consistently in the large vs small system debate. The measures or indices they
propose are not without problems in practical analysis, as is invariably the case when such indices
are specified. The most significant issue is that it is difficult to map spatial considerations directly
into the analysis of the aggregate effect of a set of small systems (this limitation is in evidence in
their generally insightful comparative example of individual farm tanks, distributed tank systems,
and a centralized reservoir system). As a result, their analysis tends to self-validate that “small is
beautiful”. However, in the face of climate uncertainty, where the provision of storage is a key
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aspect of climate risk mitigation, one needs to extend their analysis to consider spatial effects as
would be needed in the real setting. This provides the motivation for the work reported here.
Recognizing that much of the development of small storage infrastructure in a river basin is typically
unplanned by a central authority, and may not be even mapped raises an interesting challenge in
terms of assessing the potential impact of extensive amounts of such storage on basin hydrology,
especially in the context of strategic development of storage systems for climate risk management.
Consequently, given the discussion in van der Zaag and Gupta, and the interest in assessing how the
total storage infrastructure (small and large) in a river basin may be best utilized through
recommendations for appropriate cropping strategies and enhancement through storage, we
decided to develop a simulation strategy that could address the following aspects:
1. What is the performance of a prescribed mix of small storage elements and a large
reservoir/canal system in a river basin in terms of the following measures:
a. Equity in terms of irrigation water provided per unit area at a given reliability across the
river basin. This is measured by the uniformity of the spatial distribution of water
provided, or if different cropping patterns are assumed by the uniformity of the
reliability in meeting the designated crop water demand for a subset of the area served.
Alternately, one can measure the imbalance in equity by prescribing a demand for each
sub-area and computing the spatial distribution of reliability (deficit) in meeting this
demand. The tighter this distribution is the more equitable the setting.
b. Economic efficiency in terms of the aggregate annual water provided at a specified
reliability across the river basin, per unit total annualized public (and private)
investment. Given prices for crops and yield information the economic efficiency can
also be computed in terms of the ratio of the potential annual crop value to investment.
2. How does a climate scenario impact the performance of a selected mix of small and large
infrastructure in terms of:
a. Resilience of the system to climate variability. This is measured by the duration and
severity of the aggregate failure of the system relative to a specified cropping pattern
and spatial distribution of use, and target reliability.
b. Reliability relative to design reliability. This is measured by the frequency of failure of
supply to individual users and can be represented as a frequency distribution. The
application is designed so that the frequency distribution of failure is considered for a
historical climate represented by stochastic sequences of weather corresponding to the
period of record. The analysis is then repeated with a proposed climate scenario (e.g.,
2050 climate downscaled to a stochastic weather generator) with the same cropping
pattern and use distribution. The two frequency distributions can then be compared to
assess the spatially distributed impacts of a changed climate scenario on the
performance of a specified mix of infrastructure and cropping pattern.
3. How does the choice of a specific cropping pattern impact the performance of the system. This
assessment is done in terms of each of the measures indicated above.
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Relative to van der Zaag and Gupta, we do not explicitly consider the governance issues that they
discuss. However, the measures computed by our analysis can be used as part of the type of analysis
they recommend. An overlay of user information and attributes would be necessary to accomplish this.
At present, the model we have developed considers an analysis at a certain scale of aggregation dictated
by the topographic, soils and land use data available and does not embody a mapping of actual practices
or users. Thus, it offers a generic evaluation tool rather than a tool that can be directly applied to a
specific social setting.
Assumptions
We consider the following assumptions to guide the design of the simulation algorithm.
1. Infrastructure elements. We assume that there are a finite number of choices and sizes of
storage and conveyance elements that are known a priori. For instance, candidate large
reservoir sites have been located and their storage-area relationship is known. Similarly, we
assume that a prototype storage-area relationship for a small water retention structure and its
associated catchment area is known a priori.
2. Computational representation: We consider that the watershed can be divided into distinct
elements or sub-basins. Using a digital elevation model derived from satellite or ground based
maps, a drainage network is established across the watershed elements. Each element is
considered a node on this network, and the arcs that connect the different elements of a
network are derived and recorded in an arc-node or node-node incidence matrix (source
element is -1, destination element is +1, and no connection is 0). Since the drainage network
typically has a dendritic structure, multiple sources can go to the same destination, but each
source can go to only one destination. In a future version of the algorithm we will consider the
division of flow from a source element to multiple destination elements.
3. Hydrological Model: Each element is considered to have a proposed amount of storage of each
type, and an indigenous demand from that storage. In the case of the small storage elements,
the demand is that of a user or set of users who are directly connected to it. No additional
supply beyond what could be generated by the endogenous catchment for this storage unit is
assumed feasible. In the case of the large storage unit, a connection through a canal is
presumed to the demand point. The priority order or “link distance” reflecting the relative
position of the demand node on the canal system is also recorded in this case. The large storage
unit can receive all the flow from the contributing drainage area that has not been appropriated
by the small storage units. Water demands and their temporal distribution are assumed to be
known, and do not depend on crop choice etc. They are a policy variable in that the investigator
can propose certain demands to be satisfied.
4. Climate/meteorology: We consider two main climatic parameters, precipitation and
temperature. Water supply is driven by stochastic fluctuations in the former, and evaporation
and transpiration are assumed to be determined by the latter. These two variables are
simulated at a daily time step using a stochastic weather generator. The parameters of the
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weather generator depend in turn on a climate variable, either from a historical or a future
climate scenario that is simulated by a GCM or RCM.
5. Economics: The user specifies an annualized cost function for each type of storage and
conveyance system that is related to the capacity and size and includes an assumption as to the
appropriate discount rate. Benefits may also be computed on an annualized basis if prices for
each crop are provided. A simple crop yield and revenue model is included. Extensive soil water
and chemistry calculations or yield modeling contingent on fertilizer or pesticide or other input
expenses are not considered. These may be viewed as fixed costs that apply to either type of
storage and conveyance system and hence do not necessarily enter the comparison of the small
and large system mix.
Model Details
The component level details of the general purpose model developed are described in this section.
Consider the example river basin as illustrated in Figure 2. It is first divided into sub-catchments based
on topography, or equivalently using the drainage network. A certain fraction of each subcatchment is
proposed as a collection area for water and the balance for agricultural use. The height of the small
storage infrastructure is user specified, thus specifying the max storage capacity that may be installed
for small infrastructure in that subcatchment, as well as the associated surface area for evaporation. If
this storage is filled given rainfall, the surplus is allowed to overflow along the drainage network to the
topographically downstream subcatchment and is available for storage there. Crops are specified by the
user at a subcatchment level, with a default of the same crop pattern over the entire basin, or
segregated by 1st order and 2nd order catchments etc, so that position preference for crops can be
explored.
The user needs to provide a proposed “large storage and canal based conveyance system configuration.
A network representation of the canal delivery system to each sub-catchment connected to it needs to
be provided starting from the main reservoir. Flow routing takes place on the entire river basin along the
channels /drainage network identified with water stored in all reservoirs (large or small) up to capacity,
and consumed directly from each reservoir for evaporation, and by deliveries needed for deficit (relative
to precipitation) irrigation as per the crop water requirements. Crop yield is computed proportional to
satisfaction of water requirements, and storage and crop economics are computed, followed by the
performance measures indicated above. Stochastic weather sequences of a desired length are provided
so that reliability and probabilistic economic outcomes can be assessed if needed. The scheme is
illustrated in Figure 3.
Catchment delineation
The publicly available package TauDEM was used to perform the catchment delineation analysis. To
guarantee transferability of the analysis, a given Digital Elevation Model, (DEM) was analyzed with a set
of initial conditions that allows different catchment areas, different stream orders. The outputs of this
analysis are the shapefile of catchment areas and its table of attributes, which contains information on
stream order, catchment dependency table, catchment areas,…etc. the catchment dependency table is
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used to generate the “catchment definition file”, described later in this manual, whereas the catchment
areas make the “catchment area file”.
¯
Legend
Nodes
Streams
0
2,500 5,000
10,000
15,000
Meters
20,000
Figure 2 A hypothetical case study map, depicting catchments (of different sizes), streams (of different
orders) and nodes.
Algorithm description
The algorithm starts with the basic inputs: DEM, meteorological input, and crop choices and properties.
Each component in the following flowchart, whether it is file, process, or module, is described separately
in this document. The user is advised to follow the flowchart in order to further understand the
progression of the input file preparation as well as the model calculations.
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Start: prepare
input files
Digital elevation model
Catchment areas
Catchment
delineation:
TAUDEM
Start/end
Crops: crop definition,
properties.
Meteorological input:
Precipitation and
temperature
document/file
Stream order and
catchment
dependency table
DEM
Select crop
type per each
catchment
process
module
Add columns:
CrID, AcolFr,
AstFr
End: output profit/
catchment
Catchment
definition file
Reservoirs: definition,
properties.
Select mode:
1- hist. 2- m.d.
3- climate
1- Potential ET
accounting
(Blaney-Criddle).
Flow and storage
accounting
Storage cost
accounting
Calculate
profit/catchment
Crop yield and
revenue
accounting (Ky)
2- Crop water
requirement (Kc)
Figure 3 Algorithm flow chart
Initialization
Meteorological data were obtained to force the flow accounting model, and calculate crop water
requirements. The meteorological variables are assumed to be constant spatially; i.e. at time t, all
catchments have the same precipitation and temperature.
Agricultural water demand
Three different crop choices may be defined along with their characteristics. The crops selected for
illustration are corn, sugar cane, and cabbage. The three crops have different cash values, different
water requirements, and different planting seasons.
The Blaney-Criddle method was used to estimate the potential evapotranspiration (ET0). The crop
parameters required to implement the Blaney Criddle method were selected to be representative of
South-Eastern Asia.
Each crop has a defined Kc (crop coefficient curve) which determines the factors by which ET0 values
should be multiplied across the crop season in order to estimate the given crop water requirement at
which the yield is maximal. The collection and storage area fractions are read into the model as part of
the catchment definition file, described later in this document. Considering these fractions, the model
only calculates the agricultural water demand over the area not used for rain harvesting.
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Flow accounting for centralized/decentralized schemes
In this section, the word catchment is replaced with the word “element”. The equations are written with
subscripts “i” to represent element and “t” to represent time step.
Notation
Pt= precipitation at time t.
r= runoff coefficient, assumed constant at all time for all elements.
Each element is characterized by the following parameters:
Acoli= rainfall harvesting area.
Si = storage capacity installed in that element. The storage area is referred to as Asi
Qit =basic demand for water. (The amount of water that is “asked for”)
Dit = water demand. (The amount of water that is actually delivered)
Wit= the amount of water available at time t at element i.
Fitin = the flow into element i at time t from other elements.
Fitout = the flow out of element i at time t. this is the “overflowing” of water beyond the storage capacity
at the element.
Ritin= the external flow into element i at time t, but not from other elements. This can take into account
surface flow which is not from releases upstream, for example, or flow through a channel entering our
watershed.
For each element “i” at a given time step “t”:
The model first checks if there is a reservoir centered over the given ith catchment. Given the reservoir
file –described in a later section of this document-, if there exists a reservoir at the ith catchment, the
model takes into account the existing initial storage, and calculates the incoming flow into the reservoir
from the upstream catchments at each time step t. At the given time step, the model also sums up the
water demand at the catchments the reservoir is serving. The reservoir then releases the required
agricultural demand or the available storage at that time step, whichever is less. In either case, the
water released is distributed according to the proportion of the agricultural demand at each catchment
relative to the sum of the demand at all catchments being served by the reservoir. If the water released
does not satisfy the demand entirely, the amount that is left over is deferred to the decentralized
scheme, described below.
The incoming water is the summation of outgoing water from elements directly upstream of element I
as well as water that infiltrated from precipitation on that element at time t.
out
Ftin =
+ Rt, j elements directly upstream of i
jFt
Rt= P.r.(Acoli-Asi)+ P.(1-r).(Ai-Acoli)
The amount of water that is delivered at time t, is the available water at time t or the amount of water
demanded, whichever is less.
Dit=Min[Wit, Qit]
Qit=Kcit.ET0 t
The amount of water available at the next time step is the amount of water available at the current time
step plus the incoming water less the water delivered both at the current time step.
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Wit+1 = Wit + Fitin – Dit
If Wit+1 exceeds the element storage, then the excess water leaves the element.
Fi,t+1out = Max[Wit+1 - Si , 0]; Wit+1 = min(Si, Wit+1)
Cost-revenue accounting
Cost
For each element i, Si is the storage required to sustain agricultural demand. Storage volume is divided
among a storage unit of (8m2x2.4m) each costs $800.
Asi= Si/2.4; Ci=800.Asi/8. The cost of storage in a reservoir (centralized storage) is assumed to be $30/m3- Please refer to: Lall and Miller (1988).
Revenue
Crop yield is calculated for each element by discounting the maximum yield/unit volume of water (Eyi),
which corresponds to Qit according to Kyit.
Maximum yield (Ym) and Actual yield (Ya) for each element is estimated as follows
Ymit=(Eyi. Qit)
Yai=
t(Kyit.Eyi.
Dit)
Revenue for each element is the multiplication of Ya and the price of a unit mass of the yield.
Revi= Pri. Yai
Therefore the profit of each element is revenue less the cost.
= Revi-Ci
Preparation of input files
The input files include catchment properties, definition, and dependency; meteorological inputs such as
rainfall and temperature; crop properties; and reservoir properties. The following sections describe the
preparation of these files and their formats.
Catchment definition file
The catchment definition file is an output of terrain analysis on a given DEM. The process is described in
detail in the first section of this document. TAUDEM produces a DEM net file in comma separated vector
format. Three columns have been added to the csv table. The first one is labeled CRID to set the crop
choice for each catchment. The crop ID should refer to one of the defined crops in the crop properties
file whose format is outlined in one of the following sections. The second column is labeled AcolFr to set
the fraction of the collection area relative to the total area of the catchment. The last column, SAFr, is to
set the storage area fraction relative to the collection area. In the provided case study the catchment
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definition file is named (demwApr22.csv). Figure 1 shows a snapshot of the file. It is important to note
that column WSNO (watershed number) provides the unique ID per each catchment.
Figure 1. catchment definition file format.
Catchment area file
The catchment area file is a simple csv table calculated with ArcMap from the attribute table of raster
catchment dataset. The “Value” column provides the ID for each catchment—that is to be linked with
WSNO in the aforementioned file. The COUNT column provides the number of grid cells in each
catchment. The third column, labeled as AREA, is the multiplication of the preceding COUNT column
with the grid cell area, Figure 2. The file in the case study is named WSArApr22.csv.
Figure 2. Catchment area file format.
Meteorological data
The meteorological data used to force the model are precipitation and temperature. There are three
modes for the model to operate: a) historical mode; b) multi-decadal mode; and c) climate change
mode. The folder “inputdata” contains the three different folders corresponding to the three modes.
Within each folder there are two tab-delimited text files (precip.txt and temp.txt) containing daily
timeseries of precipitation and temperature, respectively. The date format is in mm-dd-yyyy.
Precipitation units are in mm, whereas temperature is in degree Celsius, Figure 3.
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(a)
(b)
Figure 3. (a) Meteorological data folder structure and content; (b) tab-delimited precip/temp file format.
Input parameters file
The input parameters file is a simple R script file to set the settings of other input files. Through this file,
the user can specify file names and paths of the different aforementioned input files. The user can also
set the mode (historical, multidecadal, or climate) in the last line of this file. To be in line with R syntax,
the user is required to surround filenames such as precip.txt with either single or double quotations,
such as precip.txt becomes ‘precip.txt’. The input parameters file is named inputpars.R. The user cannot
change this name.
Crop properties and reservoir files
Both these files are simple R script files. The user can only change the content of these files but not the
filenames.
The crop properties file defines the properties of each crop each as a list then the variable ‘crops’
combines all these lists. In each crop property list, say sugarcane or sc in the crops.R example:
sc<- list(id=1,name="sugarcane",L=c(35,60,190,120),pd=as.Date("01-012001","%m-%d%Y"),kc=c(0.4,NA,1.25,0.75),ky=c(0.75,NA,0.5,0.1),Ey=0.8,p=0.135/0.45359237)
#Ey in m3/kg. price in $/Kg
sc is the list variable name which contains all the properties associated with the crop: a) the ID of this
crop, which is used to set the CRID in the catchment definition file; b) the name of the crop; b) the
length of its growth stages; c) the planting date in format mm-dd-yyyy; d) the crop coefficient for each
growth stage—notice that the second growth stage does not have a constant kc value because in the
vegetative stage the value is being interpolated; e) the yield values which reflect how influential each
stage is on the yield; f) the Ey which is the amount of water required to get a unit of yield in m 3/Kg; g)
the price in $/Kg. The user has to follow the code convention in order to change the values of these
variables or add a new crop. If the user was to add a new crop, the IDs have to be consecutive in an
increasing order.
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In the reservoir file, the user can simply add a reservoir by adding a list variable such as:
R1<- list(id=1,at=8,serving=c(8,7,6,5),initSt=5e4,size=6e4)
R1 is the reservoir variable name and is equal to the list, which contains the reservoir ID, reservoir
location (which WSNO it is stationed at), which WSNOs it is serving, its initial storage in cubic meters,
and finally its size in cubic meters. If the user was to add a new reservoir, the IDs have to be consecutive
in an ascending order. After a list of these reservoir property lists have been added, the variable ‘Res’ is
defined which is a list of lists. In the given case study, the file reservoir.R contains 3 reservoirs. In
defining the variable Res, two of them (R2 and R3) have been remarked to take them offline to take
offline:
Res<-list(
R1
#,R2
#,R3
)
Running the model
The user needs to download and install R (2.60 or higher) from http://cran.r-project.org/. After setting
up the input files, the user can change the working directory to the folder that contains the script files,
by going to File/Change dir… Then, the user can open the script file start.R, select all the text, and press
Ctrl+R to run the algorithm. Once the program finishes running, a bar plot depicting the $/m2 profit per
catchment appears. The user can further manipulate the main script file (currently: scriptJune24final.R)
for more outputs.
Example Results
Simulation results from selected experiments are presented in this section. We consider the following
matrix of simulations.
Climate:
1. Historical rainfall and temperature data
2. A climate change scenario with rainfall variance increased by 10% coupled with a warming of 2°
C as is typical in current IPCC projections for S and SE Asia, for a 2050 scenario.
Infrastructure:
1. A large dam and canal system that serves approximately half the river basin.
2. A small infrastructure system with a storage height of xxx m, and a collection area of xxx % of
sub-catchment for each sub-catchment
3. A combination of 1. And 2.
4. A combination of 1. With the size of 2. Increased to achieve approximate equity in terms of
reliability of meeting demand.
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Cropping Pattern:
1. Uniform crop pattern across the entire area (different crops by season but fixed pattern)
2. Less water using crops prescribed in 1st order sub-catchments (either conservation or crop
choice)
Selected results for the performance measures indicated earlier are presented for these choices below
with a view to exposing some of the key trends that result from the specifications above.
References
1. van der Zaag, P., and J. Gupta (2008), Scale issues in the governance of water storage projects,
Water Resour. Res., 44, W10417, doi:10.1029/2007WR006364.
2. Lall, U., and C. W. Miller, An optimization model for screening multipurpose reservoir systems,
Water Resour. Res., 24(7), 953–968, 1988.
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