Ecosystem Services Assessment and Valuation of Proposed
Investments for the Upper Tana-Nairobi Water Fund
A Technical Appendix to the Upper Tana-Nairobi Water Fund Business Case
Benjamin P. Bryant
The Natural Capital Project
Stanford University
Author contact: [email protected]
March 2015
Contents Preface .......................................................................................................................................................... 3
Acknowledgments ......................................................................................................................................... 3
Introduction .................................................................................................................................................. 4
What question are we trying to answer? ................................................................................................. 4
A fundamental assumption regarding interpreting “the intervention” ................................................... 4
Model structure and documentation overview ............................................................................................ 5
Detailed documentation: Costs .................................................................................................................... 5
Investment costs ....................................................................................................................................... 6
Net additional costs .................................................................................................................................. 7
Detailed documentation: Benefits ................................................................................................................ 7
Sediment-related benefits over time ........................................................................................................ 8
Benefits to agricultural producers and value-chain members ................................................................. 8
Source of agricultural benefits .............................................................................................................. 8
Agricultural benefits over time ............................................................................................................. 9
Potentially omitted impacts on agricultural producers ...................................................................... 10
Benefits to KenGen ................................................................................................................................. 10
Changes in generation ........................................................................................................................ 10
Avoided dredging costs for small upstream dams .............................................................................. 14
Improved generation (or value capture) due to increased storage capacity ..................................... 14
Potential negative value of preserved storage capacity ..................................................................... 14
Nairobi City Water and Sewerage Company benefits ............................................................................ 15
Avoided flocculant costs and avoided electricity costs ...................................................................... 15
Net revenue from saved process water .............................................................................................. 17
Scaling up for meeting demand .......................................................................................................... 17
Drinking water for those outside municipal water supply service ......................................................... 17
Preface This appendix details the model and assumptions used to translate biophysical output from SWAT
modeling of RIOS portfolios into monetary units and other biophysical metrics of more direct
stakeholder interest. Agricultural yield benefits are primarily discussed in the FutureWater technical
appendix,1 though this document provides additional detail on how they were utilized within the
broader return-on-investment analysis.
This document assumes the reader has read the primary business case report,2 and therefore does not
provide significant background on the Upper Tana context, nor does it recapitulate the modeling and
economic analysis results. Rather, the goal is to make the underlying modeling transparent and
reproducible. It is therefore oriented around the model itself and data sources, with important
contextual points and assumptions discussed or referenced where relevant.
Acknowledgments The author would like to thank Johannes Hunink of FutureWater for extensive discussions regarding
proper interpretation of the SWAT modeling results. Adrian Vogl and Stacie Wolnie of the Natural
Capital Project provided helpful guidance on proper interpretation of the RIOS portfolios. Thanks are
also due to Colin Apse of the Nature Conservancy, and many helpful individuals based in Kenya,
including Fred Kihara and George Njugi of the Nature Conservancy (Nairobi office), Heather Mason,
Mathews Murgor, Philip Githinji, and all members of the Water Fund Steering committee.
1 Hunink and Droogers (2015). Impact Assessment of Investment Portfolios for Business Case Development of the Nairobi Water Fund in the
Upper Tana River, Kenya. FutureWater Report 133.
2 TNC (2015). Upper Tana-Nairobi Water Fund Business Case. Version 2. The Nature Conservancy: Nairobi, Kenya.
Introduction
What question are we trying to answer?
The fundamental question this analysis seeks to answer is whether the benefits to watershed
investments that may be undertaken by a Water Fund are likely to outweigh the costs associated with
them. This provides an assessment of whether the fund is an economically “worthwhile” investment
from the social perspective. Secondary to this, we also seek to gain an understanding of how the
benefits will be distributed, as well as a sense of how completely we have captured benefits and what
potentially significant benefits are being omitted. Because the first question essentially requires
assessing whether total benefits are above a certain threshold, it is possible to answer it without
definitely answering the latter distributional questions.
Before proceeding further, please note that while this report covers the analysis provided in the
business case document, it is intended primarily to document and justify the detailed modeling choices
made, and does not provide sufficient context to serve as a standalone document. It is assumed that the
reader will have good familiarity with the “Benefits analysis” chapter of the Business Case, and
preferably the chapters leading up to it as well.
A fundamental assumption regarding interpreting “the intervention”
The economic value of the conservation investments under consideration are based on the difference in
outcomes between what would happen with the Water Fund and what would happen without. It is
assumed that the Water Fund will make investments guided by outputs of the Resource Investment
Optimization System (RIOS). Importantly, RIOS identifies suggested interventions to make at the pixel
level of a landscape – in this analysis, 15 meters. These interventions are defined at a generic level,
including activities such as “agroforestry” and “riparian management.” These activities are then
translated into changes in parameters at higher units (the Hydrologic Response Unit in SWAT -- “HRU”),
based on response curves in the literature, which are described in Section 2.3.2 of the FutureWater
companion report. The process of translating RIOS interventions at the pixel level into HRU parameters
involves a series of assumptions related to parameters describing particular land cover characteristics
(independent of spatial orientation), how land cover within the HRU is distributed, and how that
distribution of land cover translates to parameter changes.
Therefore, when making statements regarding the magnitude of benefits associated with implementing
RIOS portfolios, we are making an assumption that implementation will occur in a manner that produces
approximately equivalent biophysical changes at approximately equivalent costs – these may or may not
be the same exact interventions specified by the RIOS outputs, as the assumption is that on the ground
specialists will utilize the RIOS outputs as guidance for implementing the water fund. Deviation from the
RIOS outputs could result in higher or lower returns than those modeled here. Additional research will
explore this relationship more closely to assess relevant sensitivities in this complex link between model
outputs and implementation realities. For additional discussion see “Addressing uncertainty during
implementation” on page 24 of the main body report.
Model structure and documentation overview The ultimate assessment of overall cost effectiveness is completed in an Excel spreadsheet, drawing on
modeling outputs from multiple other sources (eg, SWAT, statistical models in R, and other data). Here,
we explain the model structure by working backward from the final summary outputs that are
presented in the report. The model references the Excel implementation, though every attempt has
been made to specify the model mathematically. In some cases this results in rather trivial equations
that add little beyond the verbal description, but this is done in part to serve assist in verification that
the model is implemented as specified. Notationally, bolded italics with complete names indicate a
conceptual variable, while similarly formatted abbreviated terms with underscores indicate named
variables in Excel (for example “exchange rate for investment” and “exrate_for_inv”).
We utilize Net Present Value as the main summary metric, contained on the “Summary” sheet which
assembles all the different benefit streams.
On the summary sheet, all costs and benefits are calculated in KSh, though may be summarized
elsewhere (and in the final summary lines) in M KSh or M USD. If units are not specified in the
spreadsheet, KSh should be assumed.
NPV summarizes net benefits over time, utilizing a discount rate, according to the following equation:
Net Present Value = ∑ [ (1/𝑟𝑡𝑇𝑡=1 ) × Investment cost in year t ]
Where T is the time horizon (assumed to be 30 years), and r is the real discount rate (assumed to be
5%). See Page 16 and Footnote 22 of the main business case document for justification of these values.
Net Annual Benefits are in turn simply defined as:
Net Annual Benefit in Year t = Annual Benefit in Year t – Annual Cost in Year t
We now step through the individual sources of costs, followed by the individual sources of benefits.
Detailed documentation: Costs Total cost is simply considered to be investment cost plus net additional cost, because all other benefit
streams are assumed to be net of costs borne by the beneficiaries.
Total cost in year t = Investment cost in year t + Net additional cost in year t
As discussed in the main business case (p23), net additional cost encompasses all additional costs and
benefits besides upfront implementation cost – the most obvious of these are any maintenance or
reinvestment costs required to preserve the biophysical benefits flowing from the change in land use.
There may also be additional costs in terms of labor or altered farming practices, and these costs may
also be offset by co-benefits (with fodder provision by Napier grass being a prime example).
Investment costs
In the analysis used to prepare the business case document, the user specifies an aggregate budget,
which is assumed to be disbursed evenly over a given number of years, which can also be specified by
the user. Formally, this is implemented according to the following rules:
If project year is less than or equal to total years to invest, then:
Investment cost in year t = [Exchange rate for Investment] ×
[Total investment cost in USD]/[years to invest]
Otherwise,
Investment cost in year t = 0
Total investment cost in USD (inv_total) is entered on the Dashboard sheet. As of v17 of the CBA
spreadsheet, changing investment cost does not adjust the benefits, it only varies costs independently.
Depending on needs in later analysis, the model could be adjusted with a switch to allow independent
variation of the cost, or one that appropriately scaled benefits by interpolating between benefits
produced by the different portfolios.
The default length of time to make the investments (inv_years) is taken to be 10 years. That is, spending
occurs evenly over 10 years, and there is no distinction between the type of benefits that arise. The
current (v17) implementation should be robust to specifying any timeline of investment between 1 and
30 years, subject to the caveat that benefits produced after the 30 year time horizon will not be
captured. Also, currently (v17) the agricultural benefits are only calculated appropriately up to a
maximum of 20 cohorts (see “Agriculture benefits over time.”)
The analysis is conducted in units of Kenyan shilling and converted back to US dollars for summary
purposes where convenient. Because almost all of the cost considered for the investment are
opportunity costs borne within the Kenyan economy, fluctuating exchange rates should not have a
significant impact on the economic viability of the project within Kenya, in terms of consumption
opportunities for Kenyan beneficiaries. Exchange rates do matter for how money is raised and managed
within the fund however, and this will need to be given attention by the governors of the Water Fund. It
will also matter for the agricultural yield benefits, which were based on economic water productivity
estimates developed for export values.
The exchange rate for investment (exrate_for_inv) is specified as a separate exchange rate from the
primary exchange rate used in the model because the portfolios were developed by converting per-area
costs in KSh at a particular point in time (February 2014) to USD. The exact rate used was 84.918
KSh:USD. Under the assumption that implementation costs are most accurately priced in local currency
(as they are mostly a function of local labor and local currency), a rise in the strength of the dollar
(above the ~85 that was used) implies that a given portfolio can be implemented today for fewer USD
than at the time the portfolio was developed. However, the default analysis for the March 2015
business case does not utilize a different exchange rate, out of the interest of conservatism, and
pragmatism: Rather than assessing the exchange rate dependence of every parameter utilized in the
model and how it has changed from the date of estimation, we utilize a constant rate throughout. Other
values that may in fact be exchange-rate dependent include economic water productivity statistics
(which reference export values), and avoided generation costs for KenGen, which may depend on oil
prices and Kenya’s purchasing power.
Net additional costs
As implemented for the business case analysis, net additional cost is specified as a fraction of the
investment cost that has come before it, defined by the parameter maint_frac:
Net additional cost in year t =
Net additional cost as fraction of investment × ∑𝑡−11 Investment cost in year t
This formulation allows the manifestation of maintenance cost over time to accurately track changes to
the implementation timeline. One caveat is that the assumption of a constant scalar implies that the
average net additional costs are manifested immediately in the year after implementation. This would
not be the case if project implementation was front-loaded with particularly high or low maintenance
interventions, or if net additional costs included factors besides maintenance that took time to manifest
themselves. For example, for some interventions, immediate maintenance may be required, but co-
benefits not captured in other benefit streams may not manifest for multiple seasons or time-periods.
Detailed documentation: Benefits Monetized benefits are considered for four different sets of stakeholders, each of which has at least one
benefit stream, and sometimes more than one:
Agricultural producers (including others in the value chain)
Nairobi City Water and Sewerage Company (NCWSC)
KenGen
Household abstracters of raw water for drinking
Background on these stakeholders is given in the main body of the business case, so this text focuses
only on technical issues surrounding implementation of their benefit streams.
In the spreadsheet, annual benefits are first aggregated to the level of the stakeholder, and then the
stakeholder benefits are summed to identify the total benefits in a given year, according to the simple
summation (with an implied subscript for the year):
Annual benefit = Total ag benefits + NCWSC benefits + KenGen benefits + Raw water users benefits
Before discussing each individual beneficiary and benefit stream, we discuss some general points about
the manifestation of benefits over time.
Sediment-related benefits over time
Benefits related to the sediment retention (eg, sediment concentration benefits for the water supply,
and sediment deposition benefits for KenGen) depend on upstream interventions taking effect. A first
requirement for consistency in modeling the timing of benefits is to ensure that the model does not
allow benefits to materialize prior to interventions being made. A second requirement is to allow that
there may be some delay between undertaking an intervention and significant sediment retention (if,
for example, sediment retention depends on development of above ground vegetation and/or root
structure).
These requirements are enforced in the model by use of a year-specific sediment benefit scalar, which
scales down the steady-state benefits in a sediment-related benefit stream according to the following
formula:
sediment dependent benefit in year t = sediment benefit scalar in year t × long run benefit
Where:
sediment benefit scalar in year t = ∑𝑡−(1+𝑠𝑒𝑑 𝑏𝑒𝑛𝑒 𝑑𝑒𝑙𝑎𝑦)1 [investment costt ]/[Total investment cost]
(and zero if sed_bene_delay ≥ t).
Here, sed_bene_delay refers to the parameter sediment benefit delay, which indicates the number of
years between investment and realization of steady-state sediment retention benefits. (In the
spreadsheet this is implemented in two rows using the offset function in Excel.)
The default value for sed_bene_delay is taken to be three years, based on hydrologist judgment with an
intent to be somewhat conservative – however, the choice of this parameter is currently not informed
by specific data, and could vary significantly for different interventions (for example, benefits from
terracing may be near-immediate, while benefits that rely on tree cover and tree root structures could
take longer).
Benefits to agricultural producers and value-chain members
Source of agricultural benefits
The details of the modeling of agricultural benefits are described in the FutureWater technical appendix
(Chapter 6), with additional details of the economics considerations described in the main body of the
business case document. Briefly, the increase in yields is assumed to be derived from avoided soil losses,
which lead to higher soil productivity than would occur without the project. The effect of soil depth on
yields is modeled through the use of a productivity index function, which relates relative yields to soil
depth. Rather than using yields directly however, the approach estimates changes in revenue by
assuming an equivalent relative change in evapotranspiration, which is multiplied by published values of
crop-specific economic water productivity.
This approach was chosen for feasibility and data availability, though an alternative approach based on
yields and crop budgets would likely better track what fraction of the change in revenue is captured as
profit by the farmer, captured as profit elsewhere in the export and domestic value chains, and what
fraction is used to cover costs associated with the increase in production. For the business case analysis,
we do not attempt to disentangle these distributional effects, except to recognize that there is a
difference between the true economic benefit and the modeled change in revenue. By default, we scale
down the benefits by 50% (Yield benefits scalar, named ag_bene_scalar in Excel), which is admittedly a
somewhat arbitrary point, grounded simply as the midpoint between the bounds of 0 and 100 percent.
In perfectly complete and competitive markets with all domestic consumption, the fraction of altered
revenue that would count as a benefit would be closer to zero, because resources to move products
through the value chain are close to fully employed, and therefore incur a higher opportunity cost. By
contrast, the more “excess capacity” exists in the value chain, the lower the marginal cost of marketing
the higher yields, which in turn means that a higher fraction of the revenue change is a true benefit.
Besides the yield benefits scalar, the only other spreadsheet parameters related to the agricultural
benefits regard the timing of how benefits are realized, discussed next. (There are of course many other
parameters involved, but these are described in the FutureWater technical appendix. The return on
investment analysis treats the outputs of the FutureWater modeling as inputs.)
Agricultural benefits over time
Agricultural yield benefits are distinct from most others (except hydro sedimentation) in that they are a
function of cumulative action: Sediment accumulates over time, which, accounting for soil productivity
dynamics, leads to a concave-down curve for yield increase over time. The FutureWater report provides
these values for years 5, 10 and 15 from the time of full sediment retention capability. As with the
sediment retention benefits, we allow for some delay between implementation and the beginning of
yield benefits. Essentially, the yield benefit trajectory is shifted back in time. Because there is a
trajectory associated with the implementation that occurs in each year, it is more appropriate to track
these by “cohort” and sum across cohorts in a given year to get the total ag benefits in that year. These
calculations are performed on the “Ag – cohorts” sheet of the Excel CBA workbook.
Specifically:
We first establish the reference trajectory of yield benefits over time, assuming benefits start
immediately, and are implemented for the entire portfolio. This is simply linear interpolation between
the values provided in the future water report. This is implemented mathematically as
𝑈𝐴𝐵�̂̂� = 𝑈𝐴𝐵̅̅ ̅̅ ̅̅𝑡− +
�̂� − 𝑡−
𝑡+ − 𝑡−× (𝑈𝐴𝐵̅̅ ̅̅ ̅̅
𝑡+ − 𝑈𝐴𝐵̅̅ ̅̅ ̅̅𝑡−)
Where “UAB” stands for Unscaled Ag Benefits (that is, the output of the FutureWater modeling),
overbar indicates outputs from FutureWater, the hat indicates time relative to implementation for that
cohort, and t+ and t- indicate the nearest time periods on either side of �̂� for which FutureWater provided
values (0, 5, 10 and 15 years).
We then identify unscaled benefits adjusted for the lag in implementation:
𝑈𝐴𝐵𝑡 = 𝑈𝐴�̂�[�̂�=𝑡−𝐴𝐵𝐷]
Where UABt is the actual unscaled benefit in that year, and ABD stands for “ag benefits delay” –
assumed to be 3 years in the reference case. (in Excel, the time lag is implemented using the OFFSET
function).
Then, to identify the value in a given year for a given cohort, we scale down the unscaled benefits by
dividing by the years to implement.3
𝐴𝐵𝑡 =𝑈𝐴𝐵𝑡
𝑇𝑖𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡
Where 𝐴𝐵𝑡 indicates “actual benefits,” 𝑇𝑖𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡 is the years to implement (years_to_imp in Excel).
Finally, we delay each cohort’s benefits by one year per cohort, and sum for each of the cohorts. In
Excel, this lag is implemented by referencing the cell above and to the left. Mathematically, it is making
the statement that the value to be assigned to cohort i in year j is the value assigned to cohort (i-1) in
year (j-1). To estimate total ag benefits in a given year, the summation is performed across cohorts (by
row in the spreadsheet). In the spreadsheet, cohort-specific values are always calculated for 20 cohorts,
but the summation is adjusted to draw only the first years_to_imp cohorts.
Potentially omitted impacts on agricultural producers
In at least some regions of the world, irrigators actually benefit from nutrient and sediment content in
surface water that is applied to their fields. In theory, these irrigators could suffer impacts from reduced
sediment in the water. Our discussions with WRMA and other groups have not suggested that there
would be significant loss in this case. Furthermore, since most sediment is trapped in Masinga reservoir,
any potential negative impact of the interventions beyond Masinga can be assumed minimal.
Benefits to KenGen
Benefits to Kengen derive from avoided service interruptions and (more significantly) increases in water
yield. We also attempted valuing the change in Masinga reservoir storage, but challenges and
uncertainties involved in such valuation were quite high, and so that value stream was omitted from the
business case document, though some of the challenges are discussed below.
Changes in generation
As essentially all benefits are related to increased (or avoided losses of) generation, we focus on
estimating changes in generation for each benefit stream first, and then finally discuss issues of valuing
the increase in generation.
3 Note that this formulation does not reference budget actually spent by year, but rather matches the assumption of even disbursement over
time. If that assumption is relaxed elsewhere, it needs to be relaxed here as well, but adjusting the formula to utilize the “Cumulative
Investment Fraction” discussed in section on sediment-related benefits over time.
Estimating changes in generation – increased yields4
The largest source of benefits comes from the increase in water yield flowing into Masinga reservoir, the
majority of which is assumed to flow through the Seven Forks cascade and generate electricity. To
estimate the change in generation, we can apply the standard physics-based equations based on change
in potential energy and efficiency of conversion to energy fed to the grid:
𝐸𝑔𝑒𝑛 = 𝜂𝑚𝑔ℎ
where η is the efficiency of energy conversion, reported by KenGen as between 90 and 93%. m is the
mass of one cubic meter of water (assumed to be 1000 kg, ignoring minor temperature and pressure
deviations), g is the gravitational acceleration (9.8 m/s/s), and h is the effective head (meters). This is
the formula we use to estimate power generation in the Seven Forks Cascade downstream of Masinga
dam.
For Masinga dam specifically, we were able to utilize data provided by KenGen5 describing efficiency as a
function of surface height (h), expressed as cubic meters of water required to produce a megawatt of
electricity. This greatly simplifies the calculation of increased generation to simple division:
𝐸𝑔𝑒𝑛 = 𝑉/𝛾(ℎ)
Where V is the volume and γ is the efficiency expressed in volume per unit energy. To choose γ, we must
identify a representative surface height (h). For this we simply used the average of daily surface heights
in Masinga for the 10 year period from 1 October 2001 to 30 September 2013. (KenGen provided data
for a slightly longer period, but we chose this interval rather than the entire dataset in order to avoid
bias from seasonality issues.) The average dam height and associated efficiency are 1051.505 meters
and the associated efficiency from the KenGen data of 9500.9 cubic meters per megawatt-hour, or .1053
kwh/m3.
However, if a significant fraction of the additional water yield is not used consumptively by irrigators or
other users within the Seven Forks cascade, then it will provide benefits at the downstream generating
stations as well.6 The total height of dams within the Seven Forks cascade, not counting Masinga, is
222.3 meters.
Dam Height (m)
Masinga 69.5
Kamburu 56
4 The calculations described here are mostly performed on the “Hydro – background calcs” sheet, as of v18.
5 Extracted from a report prepared by Soluziona consulting group.
6 In reality, this could be represented by a parameter representing the fraction of increased yields that actually generate electricity within the
Seven Forks cascade. The distribution of benefits to KenGen would be linearly sensitive to this parameter, though total benefits produced
would be less sensitive, as presumably abstracted water would be going to produce economic benefits, just in a different use. The error in
total benefits would be a function of the difference in value of water between hydropower and the competing use.
Gitaru 30
Kindaruma 24.3
Kiambere 112
total height = upper bound on head 291.8
total height = upper bound on head, not counting Masinga 222.3
Masinga average head to height ratio .626
Implied average head for remainder of cascade 139.2
We know, however, that the effective head is not equivalent to the dam height, but did not have the
same detailed data on the other dam surface heights as we did for Masinga. Therefore, we add a
parameter specifying average head as a function of surface height. For the reference case, we set this
equal to the same ratio as in Masinga reservoir.7 The total height of all the dams provides an upper
bound for this head.
We can use the physics-based equation based on potential energy to identify the kwh/m3 generated by
the rest of the cascade. Because the generation is linear in so many real (or implicit) parameters,
(efficiency, head, fraction of increased water yield traveling the whole cascade), in the model
implementation we capture this value as a single scalar expressing benefits as a multiple of generation
through Masinga dam (the “water yield benefits multiplier”). Under our reference case parameter
values, one cubic meter flowing the through Masinga dam will generate on average .105 kwh, and one
cubic meter flowing through the remainder of the cascade will generate .32 kwh. Therefore, for the
reference case, we multiply the Masinga generation by [(.105 + .32)/.105] = 4.06 to estimate generation
through the entire cascade. That is:
Long-run average annual value of water yield = water yield benefits multiplier × increased generation
at Masinga
Adjustments to this multiplier can capture any of the other uncertain parameters mentioned above as
part of sensitivity analysis. In the spreadsheet implementation of the model (as of v18), the increased
generation at Masinga is calculated as a product on the “Dashboard” sheet itself, using parameters
identified in background calculations.
Note that consumptive losses prior to and within the Seven Forks cascade would of course reduce this
benefit, however these would need to be consumptive losses of the increased water supply brought
about by the intervention. Also, note that (not accounting for changes in efficiency as a function of
head), the sensitivity to consumptive loss has a linear upper bound for impact. If 10% of the additional
water is lost between the priority watersheds and the lower portion of the Seven Forks Cascade,
generation is reduced by at most 10%, since it is unlikely all of the water will be lost to consumptive use
prior to flowing through Masinga reservoir – some will flow through at least some generating stations.
7 Given that Masinga reservoir is used to regulate the levels of the other dams, this may be a conservative estimate.
Avoided generation losses due to decreases in shutdown time
There are multiple smaller power plants upstream of Masinga that are likely to experience fewer
operational interruptions due to reduced sediment concentrations (for locations, see Figure 4 in the
main business case document). For example, on a visit to the 20MW Tana power station, we were told
operations must interrupted periodically to deal with sediment accumulation near the intake, and also
potentially sediment-related damage to turbine seals. Furthermore, each interruption removed
generators from service for about two weeks. If the frequency of interruptions is approximately
proportional to the sediment concentration, then this translates to fewer interruptions and lower
forgone generation. There is unfortunately very limited data to calibrate this relationship, but we were
told that two years may be considered a reference time period for needing to undertake such
maintenance. So as an example, halving sediment reduction would reduce interruptions to every four
years.
The avoided loss of generation associated with an individual shutdown event is simply:
GENloss = capacity × capacity factor × shutdown duration
At Tana for example, if we assume a capacity factor of .5, then two weeks offline translates to
20000 kw × .5 × (24 hours/day × 14 days) = 3336000 kwh
The undiscounted average annual benefit associated with a change in frequency of interruptions is:
(1
τ𝑜𝑙𝑑−
1
𝜏𝑛𝑒𝑤) × 𝐺𝐸𝑁𝑙𝑜𝑠𝑠
Where τ is the period of interruption (years between events). With the example of doubling the
frequency from 2 years to 4, one is essentially avoiding a service interruption every fourth year on
average.
Our nominal figures above were based on approximate benefits for Tana. Besides the assumption of
capacity factor, we make the assumption that scaling up by capacity is the best available approximation
for the benefits that would apply to the other power stations. As shown in the table below, this means
increasing the benefits by another 56% above those of Tana alone.
Power station Capacity (MW)
Mesco 0.38
Sagana (Falls) 1.5
Wanjii 7.4
Ndula 2
Tana 20
Total upstream of Masinga 31.28 Multiplier relative to Tana power station 1.564
Avoided dredging costs for small upstream dams
While do know that dredging occurs for a subset of the dams upstream of Masinga, we were unable to
acquire data on volume or frequency of that dredging. In general, the calculation would be similar as
that for avoided interruptions described above, where a given volume of dredging (or dredging event)
results in a periodic cost. Reduced sedimentation would either reduce the volume of dredging per
dredging event, or the frequency of dredging events.
Improved generation (or value capture) due to increased storage capacity
One of the primary benefits anticipated for KenGen was the preservation of reservoir storage volume.
While many dams (including Masinga) are designed with a finite useful life based on assumed
sedimentation rates, reducing sedimentation can extend the lifetime of the dam, reduce spillage events,
and allow for closer to optimal control of the water resource. Also, in the case of Masinga,
sedimentation is occurring faster than assumed during the design stage.
This analysis does not attempt valuing changes in the useful life of the dam, because the time to lose
even half the reservoir volume with or without the conservations interventions are both over 100 years,
which was deemed well beyond the relevant time horizon for this analysis – it would be difficult to make
assessments about the marginal value of hydro production for energy technologies 100 years in the
future.
However, in the near term, the impacts of sedimentation can still affect the bottom line for KenGen.
Masinga reservoir at the top of the Seven Forks Cascade – while the Masinga Power Station represents a
relatively small portion of the total generation, the storage capacity of the reservoir is used to balance
generation across the cascade. Capturing the marginal value of storage capacity on such an integrated
system would require detailed engineering information unavailable to us, as well as careful study of
inflow characteristics. We continue to examine alternative approaches to bound this benefit. One
avenue explored was to consider changes in spillage and associated lost generation capacity, assuming
the same historic inflow and outflow patterns. While this approach can be used to provide an upper
bound if the benefit stream is small, it cannot be used to establish the actual magnitude of the benefit
stream because it assumes no response by the dam operator, who would in fact take measures to
reduce losses, violating the assumption of managing to produce the same outflow as was done in the
past.
Potential negative value of preserved storage capacity
Conversely, there are potentially some benefits from sedimentation, which we identified as small: In
theory sedimentation could raise the effective head of the dam, by effectively displacing water upwards.
We checked the potential impact of this by assessing the marginal increase in volumetric generation
efficiency as a function of height (numerically estimating 𝑑[𝛾(ℎ)]/𝑑ℎ) assuming a linear response), and
multiplied it by the long-run change in surface height that might be expected under sediment
accumulation in the baseline case, with no change in flow: We find that the efficiency of generation
would lead to approximately 500,000 kwh extra per year all else equal. Even so, this amounts to an
annual loss of approximately 17600 USD, which is negligible. These calculations are detailed on the
“Hydro – background calcs” sheet.
Valuing the increase in generation is done at 3.06 Ksh/kwh based on the average generation cost.8 In
reality, the financial value to KenGen and the social value to Kenyans as a whole will depend on the time
and conditions of generation, as well as the details of the power-purchase agreements to which KenGen
is party. In the near term at least, it is quite likely that the value of increased generation is higher
especially during the dry season, when KenGen will rely on expensive fossil generation to cover low
hydropower production (though costs are largely passed through to consumers). However, this dynamic
of reliance on fossil fuel is likely to be reduced in the coming decades as increasingly large amounts of
geothermal come online and with increasing integration of the East African power pool. Also reducing
gains is that fact that the efficiency of hydro generation will presumably be lower in the dry season due
to the lower heads – though this efficiency difference is on the order of 10%, which is small compared to
the differences in marginal cost when moving from hydro to fossil fuel.
Nairobi City Water and Sewerage Company benefits
As described in the main business case document, reduced sediment concentrations to NCWSC have
multiple benefits, including:
Avoided flocculant costs
Avoided electricity costs
Avoided loss of revenue from saved process water
It is also likely that NCWSC’s operations will benefit from increased dry season baseflow, allowing
cheaper or improved reliability. In addition, the (future) costs associated with wet sludge disposal will be
lower (after NCWSC implements a wet-sludge disposal system), as wet sludge volume to be disposed is
approximately directly proportional to sediment concentration intake. Here we focus only on the
primary calculations of the three bulleted items above.
Avoided flocculant costs and avoided electricity costs
We group the explanation of these because they are both based on similar regressions of turbidity
against cost data for the Ngethu treatment plant. In each case, we were given access to historical
turbidity data, plant process volumes, and energy use or flocculant use.
For energy use, we estimated an equation of the form
𝐸𝐿𝐸𝐶 𝐶𝑂𝑆𝑇 = 𝛽0 + 𝛽1 log(𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒) + 𝛽2𝑝𝑒𝑎𝑘𝑡𝑢𝑟𝑏 + 𝛽3𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦
Where security is a dummy variable marking the date of transition to a new security system at the plant
which had a significant increase in continuous energy usage.9
The results of the above regression (which was chosen for fit based on several alternatives) was as
follows:
8 Kenya Electricity Generating Company Limited. 2014 Annual Report & Financial Statements
9 Personal communication with NCWSC.
Coefficients: Estimate Std. Error t value Pr(>|t|) Beta 0: (Intercept) 3008143.16 274108.37 10.974 3.80e-15 *** Beta 1: I(log(discharge_m3)) -145225.46 16815.48 -8.636 1.27e-11 *** Beta 2: peak_turb 105.25 25.66 4.101 0.000145 *** Beta 3: security 349007.77 50599.26 6.897 7.21e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Multiple R-squared: 0.8359, Adjusted R-squared: 0.8264 F-statistic: 88.28 on 3 and 52 DF, p-value: < 2.2e-16
The marginal effect on the peak_turb parameter identifies the change in monthly cost that would be
realized for a unit reduction in peak turbidity. We have data demonstrating that peak turbidity is highly
correlated with average monthly turbidity as measured at Ngethu, and also have shown that at the
monthly level, sediment concentration and turbidity are nearly directly proportional (see Chapter 4 of
the FutureWater appendix). Mean monthly sediment concentration reductions (averaged acrossed
simulated years) ranged from 55 to 58 percent (see Figure 11 of the business case report). Therefore,
while a more precise month by month estimate of the cost savings could be made by tracking the SWAT
outputs through the regression above, for simplicity and conservativism, we chose to estimate savings
based on average 50% reduction in peak turbidity. Based on this assumption, we calculate the
approximate long-run annual average savings as follows:
months per year × fraction reduction in sediment concentration × maximum average monthly
spending attributable to variation in electricity expenses
Maximum average monthly spending attributable to variation in electricity expenses is based on
multiplying the peak turbidity coefficient from the regression by the aggregate of NTU-months
contained in the peak turbidity column of the dataset.
A similar approach is taken to estimate flocculant savings.
𝐹𝐿𝑂𝐶 𝐶𝑂𝑆𝑇 = 𝛽0 + 𝛽1𝑖𝑛𝑓𝑙𝑜𝑤𝑠 + 𝛽2𝑖𝑛𝑓𝑙𝑜𝑤𝑠2 + 𝛽3𝑡𝑢𝑟𝑏 + 𝛽4𝑡𝑢𝑟𝑏2 + 𝛽5𝑖𝑛𝑓𝑙𝑜𝑤𝑠 ∗ 𝑡𝑢𝑟𝑏
Coefficients: Estimate Std. Error t value Pr(>|t|) Beta 0: (Intercept) 4.505e+06 8.389e+06 0.537 0.593 Beta 1: I(inflows) 7.138e-02 1.501e+00 0.048 0.962 Beta 2: I(inflows^2) 1.973e-08 6.738e-08 0.293 0.771 Beta 3: I(month_ave) 2.000e+05 1.229e+05 1.628 0.109 Beta 4: I(month_ave^2) 3.056e+01 1.180e+02 0.259 0.796 Beta 5: month_ave:inflows -1.118e-02 9.984e-03 -1.120 0.267 Multiple R-squared: 0.5179, Adjusted R-squared: 0.4797 F-statistic: 13.54 on 5 and 63 DF, p-value: 5.709e-09
Here, because the response is nonlinear in the monthly average turbidity, we actually do need to run the
changes in turbidity through the statistical cost function identified above. That is: Predict the cost by
month, under with-out project and with-project turbidities, where again a linear relationship is assumed
between sediment concentration and turbidity.
Net revenue from saved process water
The largest source of benefit to NCWSC that we were able to calculate is that of saved process water
and the associated improvement in revenue capture. This benefit did not rely directly on changes in
sediment concentrations identified by SWAT, but were rather based on statements from NCWSC
employees that the change in sediment concentrations brought about by the Water Fund
implementations would allow them to reduce lost water from 5% to 3.5% – a major cause of this is the
need to use already-processed water to backflush sand filters – this is water that could otherwise be
delivered to NCWSC customers, providing a benefit to them, and improved revenue to NCWSC. The
benefits to NCWSC from this savings are calculated by multiplying the saved process water volume by an
adjustment to the volumetric tariff accounting for efficiency considerations. A “commercial efficiency”
(of 62%) accounts for the translation of revenue to financial benefit within NCWSC, while in the
reference case a further factor is used to reduce benefits by 25% based on any potential costs
associated with the increase in water delivery. We were unable to identify the precise source of the
commercial efficiency figure, and applied this extra scalar to be conservative. If the system is truly rife
with extra capacity to deliver this saved water, then potentially neither of these reductions in total
benefit would be necessary. Specifically, the formula used to calculate steady-state benefits is:
commercial efficiency × value per unit of process water saved × change in fraction of process water
used for backwash × annual water intake at Ngethu
The value of process water saved (to KenGen) was taken to be 14.025 KSh/m3 in the reference case
(allowing for further loss, relative to the tariff of 18.7 KSh/m3), with daily intake assumed to be the
conservative low value of 400,000 m3/day (multiplied by 365.25 days per year).
Scaling up for meeting demand
Our detailed cost accounting data was available primarily for the Ngethu treatment works, which are
currently the largest treatment works serving NCWSC. Unfortunately, even accounting for other existing
treatment works in the system, significant demand in Nairobi goes unmet. However, we assume that by
the time the full effect of the sediment retentions has occurred, additional infrastructure will be in place
to meet the existing unmet demand, and therefore scale-up the long-run cost savings benefits by the
demand shortfall. For the level of satisfied demand, we use 482000 m3/day, and a long-run demand of
650000 m3/day, which does not account for project demand from population growth, but is rather a
lower estimate for total demand.
Drinking water for those outside municipal water supply service As noted in the main body report (“Other co-benefits and stakeholders”), many residents of the Upper
Tana do not have access to treated water. We estimate that on the order of half a million residents
outside Nairobi will see improved water quality as well. According to 2009 census figures, there were
approximately 606,000 people within the catchment districts whose primary water source was raw
water from streams.10 This number is calculate on the “Raw water – census calcs” sheet, using data from
Table 8 of Volume II of the census (“Households by main Source of Water and District”). Household
10 The 2009 Kenya Population and Housing Census, Volume II.
counts are used to identify fractions of each household in each class of source drinking water, and then
multiplied by total population within the district. Assessment of whether a particular district was
relevant was based on visual inspection of the district locations relative to priority sub-watersheds.
There are reasons this number may be an under estimate or over estimate of the true number of people
affected, though chances are better it is an underestimate.11 However, the impact will also vary spatially,
with those upstream of many interventions not seeing as much change, while those far down will see
the impact diluted by sediment contributions from other sub-catchments that are not part of the
intervention.
11 The districts counted are not 100% contained within the priority watersheds, which biases the number upward. However, the population in
downstream districts is not counted at all. The figures also do not include those who listed “Pond/Dam” or “Lake” as their water source, even
though they will likely experience some increase in water quality as well.
