metadata: authors: 0: author: Espinet Alegre,Xavier
1: author: Rozenberg,Julie
2: author: Rao,Kulwinder Singh
3: author: Ogita,Satoshi
count: World
docna: 0: docna: Piloting the use of network analysis and
            decision-making under uncertainty in transport operations :
            preparation and appraisal of a rural roads project in
            Mozambique under changing flood risk and other deep uncertainties
docty: Policy Research Working Paper
theme: Natural disaster management,Climate change
majtheme: Social protection and risk management,Environment and natural resource management
subtopic: Natural Disasters,Transport Services,Food Security,Hydrology,Intelligent Transport Systems
teratopic: Environment,Agriculture,Transport,Water Resources
abstracts: cdata!: This paper presents a methodology to
            identify key priority areas for transport investments. The
            methodology uses a geospatial data-driven approach and then
            proposes an innovative economic analysis for project
            appraisal.  The two main steps involve (i) prioritization of
            road interventions based on a set of economic, social, and
            risk reduction criteria; and (ii) assessment of monetized
            and nonmonetized costs and benefits of road interventions
            under many scenarios covering the uncertainty on future
            risks and other factors. This methodology is used at
            different stages of project preparation for a rural roads
            lending operation to the Government of Mozambique. In the
            two regions of Mozambique considered, the analysis
            prioritizes regions along the coast when combining
            agriculture, fisheries, poverty, network criticality, and
            hazard risk criteria. With a limited budget of US$15 million
            per district, the results show that investing in repairing
            and rehabilitating culverts and bridges is the intervention
            that performs better under most of the scenarios.
repnme: repnme: Piloting the use of network analysis and
            decision-making under uncertainty in transport operations :
            preparation and appraisal of a rural roads project in
            Mozambique under changing flood risk and other deep uncertainties
display_title: Piloting the use of network analysis
            and decision-making under uncertainty in transport
            operations : preparation and appraisal of a rural roads
            project in Mozambique under changing flood risk and other
            deep uncertainties
listing_relative_url: /research/2018/06/30187741/piloting-use-network-analysis-decision-making-under-uncertainty-transport-operations-preparation-appraisal-rural-roads-project-mozambique-under-changing-flood-risk-other-deep-uncertainties
topicv3: Agriculture and Food Security m1326205 435,Water m1326522 137,Transport m1326661 135,Flood m1503315 3216,Traffic Management m1583399 4231
publishtoextweb_dt: 2018-06-21T00:00:00Z
historic_topic: Environment,Agriculture,Transport,Water Resources
no_of_pages: 52
author_keys: 0: author_key: 1464311
1: author_key: 1296276
2: author_key: 1110678
3: author_key: 1165774
model_extractions: WPS8490 Policy Research Working Paper 8490 Piloting the Use of Network Analysis and Decision-Making under Uncertainty in Transport Operations Preparation and Appraisal of a Rural Roads Project in Mozambique under Changing Flood Risk and Other Deep Uncertainties _Xavier Espinet Julie Rozenberg Kulwinder Singh Rao Satoshi Ogita_ Sustainable Development Chief Economist Office & Transport and Digital Development Practice June 2018
Policy Research Working Paper 8490

# **Abstract**

This paper presents a methodology to identify key priority areas for transport investments. The methodology uses a geospatial data-driven approach and then proposes an innovative economic analysis for project appraisal. The two main steps involve (i) prioritization of road interventions based on a set of economic, social, and risk reduction criteria; and (ii) assessment of monetized and nonmonetized costs and benefits of road interventions under many scenarios covering the uncertainty on future risks and other factors. This methodology is used at different stages of project preparation for a rural roads lending operation to the Government of Mozambique. In the two regions of Mozambique considered, the analysis prioritizes regions along the coast when combining agriculture, fisheries, poverty, network criticality, and hazard risk criteria. With a limited budget of US$15 million per district, the results show that investing in repairing and rehabilitating culverts and bridges is the intervention that performs better under most of the scenarios.

This paper is a joint product of the Sustainable Development Chief Economist Office and the Transport and Digital Development Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at xespinetalegre@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
**Piloting the Use of Network Analysis and Decision-Making under Uncertainty in Transport Operations**

**PREPARATION AND APPRAISAL OF A RURAL ROADS PROJECT IN MOZAMBIQUE UNDER CHANGING FLOOD RISK AND OTHER DEEP UNCERTAINTIES**

**Xavier Espinet**<sup>**1**</sup> **, Julie Rozenberg**<sup>**2**</sup> **, Kulwinder Singh Rao**<sup>**3**</sup> **and Satoshi Ogita**<sup>**4**</sup>

# **JEL** : O13, O18, O19, O22,

**Keywords** : transport planning; climate change; robust decision making; geospatial analysis; rural development; Mozambique; rural roads prioritization

> 1 Transport Specialist, Chief Economist Office for Sustainable Development, The World Bank, <u>xespinetalegre@worldbank.org, +12024732994</u>

> 2 Economist, Chief Economist Office for Sustainable Development, The World Bank

> 3 Senior Highway Engineer, Transport & Digital Development, The World Bank

> 4 Senior Transport Specialist, Transport & Digital Development, The World Bank
# **Introduction**

Many of the poorest countries in the world depend heavily on the agriculture sector. In Mozambique, for example, agriculture sector employs about 70 percent of the workforce and generates about 25 percent of its GDP (E. Baez and Olinto 2016). However, the agriculture production is low in comparison with neighboring Sub-Saharan Africa countries due to low market-oriented farming, limited use of agricultural technology, and poor rural access, among others (The World Bank 2017). In fact, as stated by the International Fund for Agriculture Development, providing reliable connectivity to farmers is key for achieving sustainable growth (IFAD 2016). In the Zambezia and Nampula provinces, the poorest provinces in Mozambique, rural accessibility is very low and most farmers practice subsistence agriculture (Iimi et al. 2016). Improving farmers’ connectivity to markets, through transport investments, would increase their revenues and reduce poverty, while also improving the national economy (by reducing food import needs for instance) (Bell and van Dillen 2012).

But the benefits of transport investments also depend on transport reliability under extreme and unexpected events (Cervegini et al 2016). Mozambique is affected by river floods and storm surges that repeatedly damage the transport infrastructure and create disruptions in the road network (World Bank 2016). Since the Mozambican road network has a low redundancy, those disruptions sometimes isolate communities for months, and thus have a significant detrimental impact on their local economics. Incorporating components of climate adaptation and natural hazard risk reduction in transport investments is therefore critical to ensure transport reliability, particularly in areas with low road redundancy and high exposure to climate events.

Additionally, in a budget-constrained scenario, and with many roads in need of rehabilitation or repair, it is important to prioritize the rural road interventions that will trigger the highest socio-economic benefits, and ensure the reliability of the transport network under disruptive weather events.

This paper addresses the challenges raised above and proposes a method to: (i) identify critical and vulnerable roads, and (ii) assist decision-makers on the selection of interventions which can ensure the reliability of the road network for rural communities. The methodology is applied to a feeder roads project in two provinces in Mozambique: Nampula and Zambezia. The paper is divided in two sections.

The first section defines the methodology to identify critical and vulnerable roads. In this section, we analyze the criticality of the roads, based on metrics of network performance and socio-economic attributes. Then, we assess the exposure and the vulnerability of the road network to river floods and storm surges and calculate disruption risk in each district under multiple future scenarios. Finally, we combine criticality and risk to identify which districts should be a priority for investment. The methodology is applied to Zambezia and Nampula provinces in northern Mozambique with the goal of selecting the top three districts in each province. The method proposed in this first section supports investments prioritization in a quantitative and transparent manner.

In the second section, we present the method to select climate resilience interventions. We begin by identifying several sets of investments based on stakeholder consultations in each of the districts selected in the previous section. We then assess the robustness of those road interventions using a cost-benefit analysis under thousands of possible future scenarios. The benefits include risk reduction expressed in terms of reduced expected damage to the infrastructure and reduced expected user losses due to road disruptions. This method can be used for the economic analysis of transport projects required during project appraisal. The paper ends with a discussion on the benefits of using this method in World Bank operations in transport project and other infrastructure investment.

2
# **Background**

Roads, bridges and culverts are the most vulnerable elements of a transport system to adverse weather conditions (EEA 2014; Nemry and Demirel 2012; NRC 2008). Disruption of those elements may have severe cascading reactions along the entire transport system, isolating rural villages or towns and disrupting trade or business operations (Koetse and Rietveld 2009). Climate change is exacerbating these risks, increasing the frequency of disruptions along the transport systems, and is challenging every single step of the transport planning process. Transport infrastructure has become one of the most vulnerable sectors to climate change in the civil infrastructure realm (Bollinger et al. 2014; Meyer et al. 2010).

The frequency and magnitude of future floods, storms and other extreme weather events fostered by climate change pose challenges to transport engineering design, maintenance, rehabilitation scheduling, and disaster preparedness plans. The current design standards, practices and building codes have become obsolete as they were developed based on historical weather patterns (Lisø 2006). Failing to update standards, practices and codes for new and existing transport projects will lead to an increase of maintenance, repair and rehabilitation budgets in almost every road administration agency around the world (Espinet et al. 2016, Schweikert et al. 2014), all contributing to negative impacts on transport users (Bruin et al. 2009; Hambly et al. 2013; Keener 2013; McBeath 2003).

In response to these recognized threats to transport infrastructure, many professionals and stakeholders in the transport field are moving to incorporate climate change considerations into transport planning, engineering and design (Ebinger and Vandycke 2015, Henning et al 2017). This approach aims at lowering infrastructure degradation rates, life-cycle costs and negative social impacts, creating a more sustainable transport asset management system and overall increasing the resilience of the transport system to natural disasters (EEA 2014; Meyer et al. 2010; Meyer and Weigel 2011).

As part of a sustainable transport asset management system, a network-level approach is required to fully capture the vulnerability of the transport system and to evaluate the real impact of the disruption (Berdica 2002; D’este and Taylor 2003). When a bridge is disrupted due to extreme floods, users will use an alternative route to reach their original destination. If that alternative route leads to a much longer travel time, or if there is no alternative route available, the disruption cost can be very high. Network-level analyses allow identifying the most vulnerable segments (in terms of highest lack of redundancy) and test the resilience of the overall transport network (Knoop et al 2012; Jenelius et al. 2015).

A complex challenge that arises while quantifying both the project-level impact and the network-level impact of future weather events is the uncertainty associated with climate change projections (Dessai et al. 2007; Hallegatte 2009). In fact, climate change is an example of “deep uncertainty” (Fankhauser et al. 1999; Jones 2000; Lempert et al. 2004; Yohe and Neumann 1997). Deep uncertainty arises when decision-makers cannot agree on (i) the models to describe the system, (ii) the probabilities and interdependencies of the inputs of the model and (iii) how to measure the desirability of the model outcomes (Lempert et al. 2004). This deep uncertainty adds complexity to the prioritization process of interventions, and can lead to poor decisions in a traditional deterministic cost-benefit approach (Fankhauser and Soare 2013; Pittock et al. 2001).

Pushed by the need to effectively prioritize infrastructure projects under climate change, researchers have been developing a set of new methods and techniques to support decision-makers under situations of deep uncertainty (Hallegatte et al. 2012). All these techniques fall under the umbrella of _Decision-Making under Deep Uncertainty_ (DMDU or sometimes simply DMU). These methods have been applied to different types of infrastructure projects but mostly are used in the water management context. There are still very few 3
examples of DMDU applied to transport infrastructure projects even though transport planning is facing most of the same challenges and issues.

This paper builds upon these two concepts; network-level analysis and decision-making under deep uncertainty techniques. It presents the integration of these two concepts into a prioritization study (in section I) and economic analysis (in section II) of different road interventions in rural Mozambique. The methodology presented in this paper captures network-level climate adaptation co-benefits in the costbenefit analysis. Additionally, the methodology presents an approach, grounded in a robust decisionmaking framework, that properly deals with the large range of plausible future scenarios in which the investments will operate.

# **Section I: Prioritization of roads and districts**

The goal of this first section is to present a comprehensive methodology for prioritization of districts for roads interventions based on geospatial data, network analysis and risk assessment. The prioritization is based on two pillars; (i) socio-economic criticality and (ii) current and future hazard risk to the roads. Socioeconomic criticality is a composite indicator based on (1) lack of network redundancy, (2) proximity to potential agriculture clusters, (3) proximity to potential fishery clusters, (4) current agriculture production and (5) poverty rate in the district. The second pillar, hazard risk, is calculated using flood maps, for current floods and under climate change scenarios, and damage functions for the different pieces of infrastructure in the road system. The hazard risk is calculated as expected annual damage to the infrastructure using 10 return periods, in four climate scenarios (current climate, low, medium and high climate change).

The following sections describe in detail each of the two pillars and its components and present the results for two provinces in central and northern Mozambique; Zambezia and Nampula.

# **Methodology**

## **Criticality**

To help decision makers prioritize investment in Mozambique, we identified the most critical links in the road network. Here we define the criticality of a link as the loss of network performance if this link is removed from the network (Rozenberg et al. 2017). The metrics for evaluating the performance are:

- Cumulated Road user cost or RUC, defined as $-vehicle and based on road condition (IRI) and data from the HDM4 model

- Total kilometers traveled

- Total travel time, based on average speed from HDM4 based on road condition (IRI) (we assumed free flow speed in all the network – traffic congestion was not considered as traffic volumes are very low in the study area, under 2,000 AADT).

We first calculate these three variables in a baseline with the complete existing network. We then remove each of the links one by one and we recalculate the performance of the network with respect to these three indicators based on the assumption that travelers will take the secondary best route when the optimal route is disrupted (see Figure 1 for an example of the approach). The optimal and second best routes are the routes that minimize the total road user cost between the origin and destination. The additional cost, time and length of travel due to the disruption of a link are aggregated over all Origin-Destination pairs and assigned to the disrupted link to determine its criticality.

4
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collected on the field for some roads. Our estimation seems to be very conservative and a larger number of culverts is more realistic.

For bridges and culverts, the damage is modeled as a % of total replacement cost based on the difference between the observed water level and the water level the structure was designed for. The following simplistic damage equation is used:

- WLd = water level design comes from the design standard of 20 yr for culverts and 100 yrs for bridges on primary and secondary roads (probability is based on past events)

- WLcci = water level for climate change projection for return period _i_

- Dc = drainage capacity rate

- Cr = condition rate

- Rc = replacement cost

We add two factors, drainage capacity rate (dc) and condition rate to be applied to the damage. Drainage capacity rate is set at 0.7 (as default), and it reduces the total amount of water that the structure can actually drain. Condition rate is applied directly to the damage as a multiplying factor, to account for the fact that structures in poor condition will incur more damage than structures in excellent condition. The condition rates are set to 0.7, 0.5 and 0.3 for good, fair and poor condition.

The damage cost on road surface is based on 3 thresholds; 0.2, 0.5 and 1.5 meters of water above surface. It is assumed that roads are built at ground level (no embankments). For each of the three water level thresholds we assigned a % of total replacement cost if surpassed, different for paved or unpaved: [1, 2, 20%] for paved and [20,50,100%] for unpaved.

# **Risk to the infrastructure (Expected Annual Damage to the infrastructure)**

The final step is to combine the hazards, vulnerability and exposure to estimate the flood risk that each district faces annually, expressed in terms of damage to the infrastructure.

Damages are calculated for flood events with 10 different intensities (5, 10, 20, 50, 75, 100, 200, 250, 500, 1,000 return period), and for four different climate scenarios (one based on past climate and 3 climate change projections), in each of the river basins in the two provinces. Individual events are then aggregated, for each climate scenario, into expected annual losses (EAD). To calculate the EAD the trapezoidal rule was used, using the losses associated to each event and its probability of occurrence as the inverse of the return period.

Where _i_ is an integer between 1 and 10, _Ti_ is the i<sup>th</sup> return period, and _Di_ is the damage to the infrastructure corresponding to _Ti_ .

For the prioritization process we use only the risk expressed in terms of damage to the infrastructure and we do not calculate the risk for users. The risk in terms of user costs will be used for assessing the benefits of interventions. This is because the risk in terms of damage to the infrastructure can easily be calculated at the link level and then aggregated at the district level, while the risk to users has to be calculated at the country level – since trips crossing the flooded area can come from all over the country – and is not relevant at the district level.

6
## **Prioritization**

The prioritization is a combination of the criticality identified before and the risk to the infrastructure. A prioritization matrix is built to combine criticality and risk, and displayed below in Table 1, giving a 1 to a very low risk road and a 5 to a very high risk road. For example, a district identified as low priority will have a low risk, and will be low priority for investment, no matter the level of risk. On the other side of the spectrum a road identified as highly critical will range from medium to very high priority and therefore will be a priority for investment, as any disruption will cause a huge burden for users and the local economy.

_Table 1: Risk Matrix_

|||**Risk to the**<br> <br>|**infra**<br>|**struct**<br>|**ure**<br>|
|---|---|---|---|---|---|
|||**1**<br>**2**|**3**|**4**|**5**|
||**1**|1<br>1|1|1|2|
|**lity**|**2**|1<br>2|2|2|3|
|**tica**|**3**|2<br>2|3|3|4|
|**Cri**|**4**|3<br>3|4|4|5|
||**5**|3<br>4|4|5|5|

# **Results: Zambezia and Nampula**

## **Baseline Network Model**

We first selected the nodes and roads of Mozambique’s network that were useful for the analysis. Even if we focused on Nampula and Zambezia, we modeled the national network since trips from and to those provinces have origins and destinations in the entire country. The road national administration (ANE) provided the classified road network, and we completed it with an assessment of the conditions of unclassified roads in the provinces of Nampula and Zambezia using an innovative smartphone-based technique (Wang and Guo 2016, Espinet et al. 2017). This last set of roads was merged into the classified roads to obtain a complete transport network. The clean new network is composed of 798 links containing paved and unpaved roads, and primary, secondary, tertiary and unclassified roads (Figure 2).

We identified, in consultation with local authorities, 138 major Origin/Destination nodes including major population clusters, seaports, airports, border crossings and, of special interest for this study, agriculture production clusters in the provinces of Nampula and Zambezia (see Figure 16 in the annex). The agriculture clusters where identified based on the results from an agriculture production potential model, SPAM, developed by the International Food Policy Research Institute (IFPRI). The underlying data can be found in the annex.

The road network contains information on the traffic volume – provided by ANE and collected in the field for unclassified roads – and is shown in Figure 17 using annual average daily traffic (AADT). Using the measured traffic volumes and a simplified travel demand model, we estimated the traffic between each OD pair (see detailed methodology in the annex). A few roads – 275 km - where left out of the analysis as they did not give access to any of the identified nodes (a map highlighting these roads can be found in the annex).

7
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# **Section II: Cost-Benefit Analysis under deep uncertainties**

In this second section, we present a methodology to calculate the costs and benefits of road interventions under deep uncertainty, using a robust decision-making framework (Lempert et al. 2006). The methodology is tested on five different investment scenarios in each of the districts selected above. The investment scenarios were defined based on discussions with local stakeholders during two workshops held in January 2017 in Quelimane and Nampula. Each investment scenario was constrained to a total of approximately US$15 million. Each investment was a combination of five engineering solutions that would lead to four kinds of cost savings: reduction of flood risk for the users, repair and rehabilitation costs, maintenance expenditure and daily road user costs. The results are presented in detail for the district of Murrumbala in Zambezia to illustrate the method. A summary of the results for the other 5 districts is presented at the end of this section.

# **Methodology**

The road interventions that are being analyzed in this study aim to improve farmers’ access to markets and adapt the road network to climate change. The main impact of climate change on the roads is through riverine flood events combined with sea level rise. For that reason, the cost-benefit analysis includes flood risk reduction as a benefit in the selection of interventions. To assess this benefit, we first estimate flood risk in a baseline scenario with no intervention.

## **Definition of a baseline**

In the baseline, it is assumed that no intervention is made, and the existing infrastructure is maintained with a low standard of routine and periodic maintenance – allowing IRI up to 16 for gravel and 18 for earth. That translates to yearly routine maintenance and periodic maintenance every 8 years (for earth roads) – these are average values based on interviews with local authorities. The existing bridges and culverts, including the ones destroyed by floods, are not rehabilitated nor reconstructed.

Traffic is expected to grow because of economic growth, at a rate of 3% per year. However, this rate is highly uncertain, and we vary this assumption later. The correlation between IRI and road user cost can be found in the annex and was obtained through the HDM4 calibrated for Mozambique (Iimi 2016). We have assumed that all traffic falls under the category of light trucks (based on discussion with locals and visual assessment).

The road network is exposed and vulnerable to floods, and we can estimate flood risk as the expected annual losses caused by floods. The probability distribution of flood events varies with climate change; thus, flood risk has to be estimated in multiple climate change scenarios.

Expected annual losses (EAL) have two components: the cost of repairing or rebuilding the damaged infrastructure ( _D_ ) and the increased road user cost that users in a district must pay when they are forced to make a detour due to flood disruptions ( _U_ ). In the results section the two components are shown in separate graphs, the first one labeled as ‘avoided damage’ and the second one as ‘reduced flood risk’.

To calculate these user losses, it is assumed that the roads and bridges are impassable when the water level on the road (����� ����∗��) is higher than 0.5 meter. Each drainage structure has a certain level of water that it can drain before water starts to accumulate on the surface of the road. Here, multiple links can be disrupted at the same time (unlike in the criticality analysis) since we simulate flood events. This means that the secondary best route identified previously may be disrupted as well. In this case user losses are associated with the use of a third best route, or fourth best, etc. In some cases, no route is available between 13
two nodes. We are thus unable to calculate an increase in road user cost, but we calculate the number of isolated trips as an additional decision metric.

The rerouting is assumed to happen until the original route is reopened to traffic. Therefore, repair time is a major driver of user losses.

User losses are calculated for 10 different flood events (5, 10, 20, 50, 75, 100, 200, 250, 500, 1,000 return period), and for 4 different climate scenarios (one based on past climate and 3 climate change projections), in each of the river basins in the two provinces. So, it is assumed that for a given flood event all the roads in the same basin are exposed to the flood simultaneously. Individual events are then aggregated, for each climate scenario and in each basin, into expected annual user losses (EAUL). To calculate the EAUL the trapezoidal rule was used, using the losses associated to each event and its probability of occurrence as the inverse of the return period.

Where _i_ is an integer between 1 and 10, _Ti_ is the i<sup>th</sup> return period, and _Ui_ is the increased user cost corresponding to _Ti_ . _Ui_ is defined as: Where _RUCOD,i_ is the road user cost for the OD pair under flood _i_ , _RUCOD,no disruption_ is the road user cost for the same OD pair in the absence of disruption, _ri_ is the repair time after flood _i_ , and _tOD_ is traffic on this OD pair.

The repair time depends on the severity of the flood but also on the capacity of the local road agency. We thus treat this parameter as an uncertainty in the next steps.

Total expected annual losses (EAL) are the sum of the EAD (Equation 2) and the EAUL (Equation 3).

# **Impacts of Road Interventions – Costs and Benefits**

Following consultations with local authorities, we assessed the economic performance of five different road interventions:

- Upgrade to surface treatment

- Upgrade to gravel road

- Rehabilitation of earth roads

- Clean and repair bridges

- Replace culverts

These five interventions have four kinds of benefits: reduction of flood risk for the users, reduction of flood risk for the road agency (lower repair and construction costs after flood events), reduction of road user costs due to improvement of road conditions and reduction of maintenance expenditure due to improvement of road conditions.

The reduction of flood risk for users is calculated as the difference between EAUL in the baseline scenario and EAUL with the intervention (using Equations 3 and 4). Some interventions prevent disruptions or allow a faster restoration of service; thus, the risk is lower. Also, if secondary roads are improved, even if the first-best road is disrupted, the detour can be less costly.

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The decrease in flood risk for the road agency is calculated as the difference between EAD in the baseline scenario and EAD with the intervention (using Equations 1 and 2). Following interventions, the repair and rehabilitation cost (after floods) will be reduced, as damage will be lower or avoided in some cases.

With some of the interventions, a major intervention on the road surface is assumed to take place. As the condition of the surface improves, the road user cost is reduced independently from flood events. The benefits will be incurred by the road users daily and will depend on traffic. This benefit is calculated as traffic multiplied by the difference between RUC (aggregated over all OD pairs) between the baseline and intervention scenario, in the absence of floods. Similarly, because of a major intervention on the road surface the routine maintenance expenditure will be reduced giving additional annual benefits to the road agency (the maintenance savings are detailed in the annex and are obtained from RONET model).

Finally, a recent study by the World Bank finds a correlation between reduction of transport cost and increase of agriculture production in Mozambique (Iimi, forthcoming). The agriculture production is found to increase by 2.7% for a reduction of 10% in transport costs. This study is used to calculate the increase in agriculture production following a decrease in road user costs. In addition, we assume that traffic growth increases by 1 percentage points when agriculture production increases by 1%. There is a lot of uncertainty in this elasticity, so we used a range of elasticity from 0.5 to 1.5. The traffic increase is defined with the following equation and is based on the above-mentioned assumptions, where ���<sup>�</sup> is traffic volume in year _y_ , �� is national traffic increase, ��� is agriculture to traffic elasticity, ��� is transport cost to agriculture production elasticity ���� is baseline road user cost and ∆���<sup>�</sup> is reduction of road user cost by intervention i.

We detail below the benefits attributed to each of the interventions.

# **Upgrade of surface treatment**

When roads are paved, the road user cost is assumed to be 0.23 $/km (equivalent to an IRI of 4). When the paved road is close to an agriculture cluster, it is assumed that agriculture production increases by 2.7 points for each 10 point of decrease on road user cost and that the traffic will increase following equation 5 introduced above.

Disruptions are reduced as new drainage structures (culverts) have been put in place to accommodate the new paved road. For instance, an unpaved road was disrupted with 50cm of water on top of the road surface while the paved road can drain 80cm before the road is disrupted (as it is assumed that a new culvert can drain the rainfall from a 20-year return period event). Damages from floods on the infrastructure are considerably lower and so is the repair cost as it is assumed that the condition rate (used in equation 1) is set to 1.

# **Upgrade to gravel road**

Here it is assumed that damaged roads are rehabilitated to restore the initial design. Most of the roads in Zambezia and Nampula are in poor or bad condition due to deficient maintenance and periodic maintenance so this intervention would upgrade the earth road to a gravel one in good conditions. The road user cost is thus assumed to be 0.27$/km (equivalent to an IRI of 7). The surface and class type are not changed. Like the previous intervention, when the gravel road is close to an agriculture cluster it is assumed that agriculture production would increase using the 2.7/10 relation and thus traffic increases using an elasticity that ranges from 0.5 to 1.5.

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Flood damage on the infrastructure is slightly lower as the condition of the road is higher and the costs of repair are lower as it is assumed that the condition rate (used in equation 1) is set to 1. Disruptions caused by flood are not reduced as no intervention on the culverts or bridges is done.

# **Rehabilitation of earth roads**

Here the road user cost is reduced to 0.3$/km because of improving the condition of the roads through better maintenance and reducing its IRI to 9. When the earth road is close to an agriculture cluster, it is assumed that agriculture production increases by 2.7 and thus we assume traffic increases using an elasticity that ranges from 0.5 to 1.5.

This intervention includes cleaning up culverts as part of rehabilitation procedures. Most culverts have a deficit in maintenance and the drainage capacity is dramatically reduced due to sedimentation or growth of vegetation both up and downstream the culvert. Damage from flood and consequent disruption are thus assumed to be lower as the drainage capacity of culverts is maximized as a consequence of cleaning up the culverts. The drainage capacity is set to the original design standard so that more water can go on the road before it is disrupted. The damage on the surface will be consequently lower as the water level on top of the road is reduced thanks to the increase in drainage capacity.

# **Clean and repair bridges**

It is important to keep bridges in good condition to reduce repair cost after a flood event. However, most bridges in those areas are in poor or bad condition due to the lack of regular and periodic maintenance. They are thus more vulnerable to floods and will suffer more damages than good or fair condition bridges. Here it is assumed that damage from flood onto the bridges can be considerably reduced because of restoring the original condition of the bridge. Disruption is significantly reduced as well because of cleaning up the bottom of the bridge, maximizing the drainage capacity of the bridge to design standards. For example, a bridge currently has a clearance of 170 cm, after this intervention the bridge will be able to drain up to 200cm (equivalent to a 50-year event – the design standard) because of cleaning the sediments/debris that were taking up to 30 cm. Here the road user cost is unchanged as it is assumed that this intervention does not have any impact on the surface of the road.

This section assumes that bridges are designed properly and therefore they do not collapse or are not washed away. At the same time, it simplifies the possible damages, as it only considers damage from water level overtopping the bridge superstructure; it does not include possible failure due to scour or damage on the abutments. This simplicity goes accordingly to the amount of collected data on the bridges – it was not possible to obtain any information regarding the condition of the bridges. We acknowledge that this model is simplistic and can lead to optimistic results. Field experience in Mozambique has demonstrated that many bridges have failed due to poor design on either the piles, abutments or connections between piles and beams with water level that the bridge should be able to withstand if designed properly.

# **Replacing culverts**

Damage from flood on the infrastructure is considerably reduced as new culverts are put in place. The new culvert is assumed to have a design standard twice as large as the original culvert. Disruption is significantly lower as the new culvert can take higher levels of flood. Most culverts are designed for a 10-year event, the new culverts will be able to drain a 20-year event rainfall. In this intervention, the road user cost is unchanged as it is assumed that this intervention does not have any impact on the surface of the road.

The unit cost for each intervention can be found in the annex.

# **Cost-benefit analysis**

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A net present value is calculated for each intervention. The decreased number of isolated trips is calculated as well but it is not included in the net present values as it is challenging to give a dollar value to disrupted trips. The net present value (NPV) for intervention _i_ follows the equation below: Where ME is maintenance expenditure, EAD is expected annual damage, RUC is road user cost, TR is traffic volume, EAUL is expected annual user losses, CI is capital cost of intervention, d is the discount rate and _y_ the years going from 1 to 20. The cost is different for each of the interventions. Each of the interventions includes periodic and recurrent maintenance that happens at different times during the lifecycle. For instance, a surface treatment road will include periodic maintenance every 9 years, while a gravel road will be maintained every year and an earth road every 4 years (values can be found in the annex and were provided by ANE). The benefits are calculated every year as described in the previous section.

To capture the uncertainty that may affect the performance of some of the interventions, we calculate the NPV of each intervention in 2,000 scenarios, combining values on:<sup>5</sup>

- Climate projections: current, low, medium and high

- Flood duration, -50% to +50% increase compared to the results of the hydrological model<sup>6</sup>

- Traffic growth in the absence of interventions, 0 to 6%<sup>7</sup>

- Traffic growth to agriculture increase elasticity, 0.5 to 1.5

- Discount rate, ranging from 3 to 12%

- Repair time, -50% to +50% of original

- Capital Cost, -50% to +50% of original

- Bridge Repair, -50% to +50% of original

Each of the selected districts has different characteristic and vulnerabilities. For this reason, each district may require a unique combination of the five interventions above in each of its link of the road network, that will maximize the net present value and increase robustness of the road network. Some of these combinations will be: (1) surface treatment to the most vulnerable road and ensure proper maintenance on the rest, (2) repair bridges in most critical link and rebuilt culverts in secondary roads, (3) upgrade to gravel the most critical road and ensure maintenance on secondary road, (4) upgrade to gravel secondary roads only or (5) repair and replace culverts in most critical links only – other combinations may be suggested here by the team.

Once we calculate the NPV of several investment combinations for each of the 2,000 scenarios, we will look for those conditions that are the most robust, that is that have a high NPV under many future conditions.

# **Robustness analysis**

There are many ways of testing the robustness of an investment plan:

> 5 We use a Latin Hypercube Sampling (LHS) method for generating the 2,000 scenarios.

> 6 SSBN developed the flood maps and the hydrological model that calculated water levels and flood duration (more details about the model are in the annex). Flood durations are however difficult to assess in the hydrological model, so we assume it can vary.

> 7 The projected GDP growth for 2018 in Mozambique (Mahdi et al. 2016) is calculated at 6.5%. Traffic and agriculture are expected to grow at a similar rate as GDP. The range of uncertainty applied in these variables is intended to capture the uncertainty on GDP growth.

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regret(i,s) = max(NPV(i',s) — NPV(i,s)) ur — (max(regret(i,s))) L s i ~~(=max(regret(i,s))—_-)~~
<!-- Start of picture text --> Ps SS To —_<br>. gmSy. 0 12.5 25 50 Kilometers<br>£ eFe) Pas naue Milenge yo 1 1<br>e Wry a i as<br>& bg, Lugela<br>—— 1-T7025<br>pars IN A A<br>genire: Ny,<br>= o>,82. a<br>iS h zHamanjavira<br>7 La 2%<br>¢ § PSP og AT une<br>~* 2 Derre = Mocuba ra<br>cls Zaheria EPa ae. 4,<br>€ 8 Zr<br>&4 E/_ Ring,Morrumbela 3 Sp<br>~~€ _Megaza 4 Coa ]<br>oe) oo,<br>a he a<br>3 SS ss<br>iS & Legend<br>: © Morrumbal<br>Mt jorrumbala ’ .<br>[B.N322-T7017 ay anal "70n.», mm Culvert Se,<br>Tere 2, 7;79 << Bridge<br>LaeN322-TS¥a =e que Primary Paved jcurral<br>\ Primary Unpaved<br>7 le N17} Secondary Unpaved ,<br>h !} ~ ' Tertiary Unpaved }<br>\ & : meres dala<br>ie 5 as Mopata 3 Unclassified Unpaved<br>fal are<br><!-- End of picture text -->
_Table 3: Summary of investment scenarios_

|||||**Murrumbala**|||||
|---|---|---|---|---|---|---|---|---|
|||**Paving**|**Gravel**|**Partial Rehab**|**Bridge**|**Culverts**|**Initial**<br>**Capital**<br>**Cost**|**Life-**<br>**Cycle**<br>**Cost**<br>**(Median)**|
|**Investment 1**|RoadID|N322<br>(partial<br>–<br>45km)||N322 (rest),<br>R652, R1107,<br>R650 (rest),<br>R1110, R1109,<br>NC|||||
||Length|45|0|551|0|0|15|18|
|**Investment 2**|RoadID|R652<br>(partial<br>–<br>60km)||N322, R652<br>(rest), R1107,<br>R650, R1110,<br>R1109, NC|||||
||Length|66|0|530|0|0|15|19|
|**Investment 3**|RoadID|||N322, R652,<br>R1107, R650,<br>R1110, R1109,<br>NC|N322,<br>R652,<br>R1107,<br>R650,<br>R1110,<br>R1109,<br>NC|N322,<br>R652,<br>R1107,<br>R650,<br>R1110,<br>R1109,<br>NC|||
||Length|0|0|596|13|17|22|24|
|**Investment 4**|RoadID||R650 (partial<br>– 150km) and<br>R652 (partial<br>– 60km)|N322, R652<br>(rest), R1107,<br>R650 (rest),<br>R1110, R1109,<br>NC|||||
||Length|0|213|383|0|0|11|19|
|**Investment 5**|RoadID||N322, R652<br>(rest), R1107,<br>R650 (rest),<br>R1110,<br>R1109, NC|R650 (partial –<br>150km) and<br>R652 (partial –<br>60km)|||||
||Length|0|383|213|0|0|18|29|

We calculated the net present value for each of the five investment combinations in 2,000 scenarios following equation 6 above.

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initial capital investment, recurrent and periodic maintenance. The five interventions initial investment costs are around US$15 million, with investment 3 being the highest. When this initial investment is aggregated with the recurrent and periodic maintenance over the 20 years, investment 5 is substantially more expensive than the others. The reason is that gravel roads require more frequent periodic maintenance in order to maintain the initial condition set to a high standard.

Figure 12 (right panel) shows the number of avoided isolated trips for each intervention, divided by the cost of the intervention. Here the third intervention is also the one that reduces the highest number of isolated trips per dollar spent.

Investment 3 is the best (i.e. has the highest NPV) under 98% of the scenarios, and it has a positive NPV under 95% of the scenarios. We look for the conditions under which investment 3 has a positive NPV using a scenario discovery technique called PRIM (Bryant and Lempert 2010). We find that the NPV of investment 3 is positive if three of the conditions are met together: (i) if the discount rate is lower than 10.5%, (ii) the cost of bridges is greater than 60% of current estimates and (iii) the capital cost does not exceed 140% of the current estimate. 100% of the scenarios that meet those criteria have a positive NPV, and 70% of the scenarios that have a positive NPV meet these criteria.

The explanations for these results are as follows. The main benefits of investment 3 come from avoided flood disruption risk (reduction of EUAL) and the reduction of damage to the infrastructure (EAD). On the other side, most of the cost comes from repair, cleaning and retrofitting of bridges. Most of the expenditure happens upfront while the benefits are distributed across the 20 years of the life-cycle, therefore high discount rates will lead to lower net present values. If this is combined with low cost of repairing bridges, the discounted benefits from avoided cost after floods will be much smaller, as it may be more beneficial to repair the bridge after a flood than invest proactively upfront. Finally, the capital cost variable affects not only bridges but all the other interventions. So, if lower benefits due to (i) and (ii) happen together with higher capital cost, the NPV of investment 3 may become negative.

As explained before, even if we cannot say much about the likelihood of all these uncertainties, it is unlikely that the cost of repairing bridges will decrease dramatically over the next decade, while other costs increase, therefore under reasonable conditions investment 3 is always a good option.

To go further, we calculate the regret that each investment can bring in each of the scenarios. The regret is calculated as the difference between the NPV of the investment and the NPV of the best investment under this particular scenario. Figure 13 shows that investment 3 brings the lowest maximum regret, meaning that even when it is performing less well than investment 5 the loss is minimal. The maximum regret of investment 5 is higher because this investment misses the potentially very high benefits of investment 3 in terms of avoided risk (reduction of EUAL and EAD) under some scenarios. These results mean that it is better to invest in investment 3 under conditions more suitable for investment 5, than the other way around. The analysis above therefore suggests that investment 3 is the most robust investment for Murrumbala.

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Given the limited budget per district (approx. US$15 million) cleaning and repair of bridges together with upgrading the culverts seems to be the most robust intervention in almost every district. Cleaning and repair of bridges and upgrading culverts has a lower capital cost and returns a high benefit mostly in terms of avoided damage to the infrastructure due to flood events. The other types of investment, paving, graveling or rehabilitating, have a higher capital cost and with the constrained budget of US$15 million very few kilometers of road can be upgraded. Additionally, the low traffic volumes in these regions of the country make it harder to justify these last interventions.

_Table 5: Summary of most robust intervention in each of the 6 selected district_

|**Province**|**District**|**Investment**|**Description**|**Robustness**|
|---|---|---|---|---|
|Zambezia|Murrumbala|Inv 4|Clean and repair all<br>bridges and upgrade<br>all culverts|Very high|
||Maganja|Inv 2|Clean<br>and<br>repair<br>bridges in N324|Medium (good only if climate<br>change is high)|
||Pebane|Inv 3 + Inv<br>4|Clean<br>and<br>repair<br>bridges in N324 +<br>upgrade all culverts|High for Inv 4, medium for inv<br>3|
|Nampula|Memba|Inv 3|Clean and repair all<br>bridges and upgrade<br>all culverts|Very high|
||Namapa/Erati|Inv 2|Clean and repair all<br>bridges and upgrade<br>all culverts|Very high|
||Monapo|Inv 3 + Inv<br>4|Paving R700 & R1153<br>+ Clean and repair all<br>bridges and upgrade<br>all culverts|Very high for Inv 4, medium<br>for Inv 3 (good only if traffic<br>growth is high)|

In order to better understand the robustness of the interventions across each of the provinces, we have plotted together the distribution of net present values for each of 5 interventions in each of the 3 districts (Figure 14 and Figure 15) – with each color corresponding to a district. The distributions of NPV are shown in the boxplot using the left axis. The initial investment or capital cost for each intervention is plotted with a blue star and using the right axis.

In the province of Zambezia (Figure 14), investment 1B in Murrumabala is an addition to the ones previously described and represents the pavement of the entire N322. The initial investment is US$30 million approximately, so outside the initial budget limitation. The reason to add this investment is to test 25
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travel disruption costs, it presents a new method to quantify the systemwide benefits of improving the resilience of the transport network. Using a network approach, it quantifies the road user cost benefits from upgrading second-best routes. It quantifies as well non-monetized benefits in terms of reduction of isolated trips. Second, it presents an innovative method, embedded in decision-making under uncertainty techniques, to deal with deep uncertainty in many economic factors. This method identifies combinations of variables that make investments fail and it helps decision-makers select interventions that are robust to a range of future conditions.

This new methodology is applied to road interventions in rural Mozambique. Five different sets of interventions are proposed for each of the six districts selected for the analysis. Among the different interventions in the study area, and given the limited budget per district, investing in bridges and culverts is always the most robust option. In some cases, paving seems to be the best option when the paved road is long (but in this case the cost is higher than the available budget, like investment 1B in Murrumbala). When incorporating systemwide benefits, paving or graveling secondary routes to increase redundancy is not always profitable, as traffic volumes are low and alternative routes may get flooded as well. In some districts the NPV of interventions is positive only under some conditions (e.g. high climate change), however we have demonstrated that they could be justified using non-monetized benefits, such as reduction of isolated trips.

Incorporating network benefits has proven to be very effective to identify interventions that improve the overall performance of the network under adverse conditions – like interventions that increase the redundancy of the network. These interventions increase the resilience of the network because they improve second-best routes when the main one is disrupted. This type of benefit would not have been taken into consideration with a traditional project-level economic analysis.

Decision-making under uncertainty techniques are particularly useful in the context of transport investment. Climate change is not the only factor in the transport economic analysis which is a deep uncertainty: traffic demand forecasting and traffic growth play a major role in the analysis and are uncertain and fluctuant during the lifecycle of the intervention. DMDU techniques, as demonstrated in this paper, help identify the most robust interventions. DMDU identifies the combinations of factors that would make the interventions fail. With all the information provided through the different components of the DMDU method, the decision-maker can suggest possible alternatives to the current interventions analyzed, with the goal to improve their performance under the conditions identified as risky.

# **Acknowledgments**

We acknowledge the assistance received by counterparts in Mozambique; ANE ( _Administração Nacional de Estradas_ ) and _Fundo de Estradas_ that did an excellent job preparing the field collection and provided all the needed equipment and additional data. We also wish to thank other members of the World Bank for their support and suggestions: Marianne Fay, Atsushi Iimi and Laura Bonzanigo. This work was funded by the Korean Green Growth Trust Fund.

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