Probabilistic Flood Risk Mapping for National Highway Corridors in South Sudan: A Stochastic Hydrological Modelling and Bayesian Network Approach

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African Journal of Climate Science and Disaster Preparedness Manuscript 23 | Vol. 4, 2024 AFRICAN JOURNAL OF CLIMATE SCIENCE AND DISASTER PREPAREDNESS ISSN 2960-YYYY (Online) | Vol. 4, No. 1, 2024 | DOI: 10.XXXXX/ajcsdp.2024.23 Probabilistic Flood Risk Mapping for National Highway Corridors in South Sudan: A Stochastic Hydrological Modelling and Bayesian Network Approach Aduot Madit Anhiem Department of Civil Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak, Malaysia Correspondence: aduot.madit2022@gmail.com | rigkher@gmail.com ORCID iD: 0009-0003-7755-1011 | https://orcid.org/0009-0003-7755-1011 Received: 05 February 2024 | Revised: 28 March 2024 | Accepted: 10 April 2024 | Published: 22 April 2024 DOI: 10.XXXXX/ajcsdp.2024.0023 [Assign upon acceptance] ABSTRACT Flooding constitutes the most pervasive natural hazard threatening South Sudan's national road network, causing annual disruptions estimated at USD 27.8–45.8 million across five priority highway corridors. Despite this, no probabilistic flood risk mapping framework calibrated to South Sudan hydrological conditions has been documented in the peer-reviewed literature. This study develops and validates a probabilistic flood risk mapping methodology integrating stochastic hydrological modelling, two-dimensional hydraulic simulation, Bayesian network failure probability analysis, and multi-criteria risk indexing for five national highway corridors totalling 510 km. Daily discharge records from seven long-term gauging stations were fitted to Gumbel Extreme Value Type I (EV-I) distributions, and Monte Carlo uncertainty propagation (n = 10,000) was applied to quantify model parameter uncertainty. HEC-RAS 2D hydraulic simulations were executed for return periods of 2, 5, 10, 25, 50, 100, and 200 years to generate inundation extent and depth grids at 12-metre resolution using TanDEM-X terrain data. A Bayesian network with seven nodes was developed to model the conditional failure probabilities of road segments as a function of flood inundation depth, embankment height, drainage capacity, and structural vulnerability. Validation against satellite-derived flood extents from Sentinel-1 SAR imagery yielded overall accuracies of 82–91% with kappa coefficients of 0.70–0.81. The Malakal–Renk and Bor–Pibor corridors are classified as Extreme risk, with 66% and 54% of road segments at risk under the 100-year return period event respectively. First-Order Reliability Method (FORM) analysis demonstrates that embankment heights of 2.4–3.2 m above mean annual flood level are required to achieve the target reliability index of beta = 3.72 for South Sudan road design conditions. Projected flood damage costs under RCP 8.5 are estimated to increase 3.4-fold by 2055 relative to 2024 baseline levels. Five evidence-based policy instruments are recommended to reduce national flood exposure by 30–45% within a ten-year implementation horizon. Keywords: probabilistic flood risk mapping; South Sudan; highway corridors; Gumbel distribution; Bayesian network; HEC-RAS 2D; FORM reliability; Monte Carlo simulation; climate change; disaster preparedness; road vulnerability 1. INTRODUCTION South Sudan's road network underpins the delivery of humanitarian assistance, inter-state commerce, and national integration across a country of 11 million inhabitants spanning 644,329 km² of some of the most flood-susceptible terrain on the African continent. The vast central basin of the Sudd—one of the world's largest freshwater wetlands—together with the seasonal inundation dynamics of the White Nile, Sobat, Jur, and Bahr el-Ghazal river systems, creates a hydrological environment in which road infrastructure is annually exposed to inundation events of extraordinary spatial extent and duration (Sutcliffe & Parks, 1999; Ogilvie et al., 2020). The 2019–2022 flooding cycle, the most severe on record, inundated over 11,000 km² of floodplain and severed all primary road connections to Malakal, Bor, and Bentiu for cumulative durations exceeding 180 days, with direct infrastructure repair costs estimated at USD 480 million (OCHA, 2022). Probabilistic flood risk mapping constitutes the methodological foundation for evidence-based road design, investment prioritisation, and disaster preparedness planning. Unlike deterministic design approaches—which apply a single design flood without quantification of uncertainty—probabilistic frameworks explicitly acknowledge the aleatory uncertainty in hydrological extremes and the epistemic uncertainty in model parameters, yielding risk estimates expressed as probability distributions rather than point values (Apel et al., 2006; Beven & Binley, 1992). The integration of probabilistic hydraulic modelling with structural reliability analysis enables computation of failure probabilities for specific road segments as functions of flood characteristics and infrastructure conditions—information directly applicable to maintenance prioritisation, insurance premium setting, and climate adaptation investment allocation (Pregnolato et al., 2017; Dawson et al., 2018). The climate change dimension further amplifies the urgency of probabilistic flood risk assessment for South Sudan. IPCC AR6 projects increased frequency and intensity of extreme precipitation events across equatorial East Africa under all RCP scenarios, with East Africa expected to experience 15–30% increases in 100-year return period flood discharges by mid-century (IPCC, 2021). For a country where the entire paved road network is less than 3,600 km—and where road reconstruction costs in remote areas reach USD 2.8 million per kilometre—the implications of even marginal increases in flood frequency or severity for infrastructure lifecycle costs are severe (World Bank, 2023). Despite the critical importance of flood risk quantification for South Sudan road infrastructure, no peer-reviewed probabilistic flood risk mapping study specifically addressing national highway corridors has been published. Existing risk assessments are largely qualitative, employ coarse continental-scale hydrological datasets that do not resolve the complex dynamics of the Sudd, and are not spatially disaggregated to the level required for project-level investment decisions (MoRB, 2022; Peters et al., 2019). This study addresses this gap comprehensively, developing a replicable probabilistic flood risk mapping methodology calibrated to South Sudan hydrological conditions and validated against satellite-derived flood observations. 1.1 Research Objectives This study pursues the following primary research objectives: (i) to compile and quality-control long-period hydrological discharge records for seven gauging stations on rivers crossing or adjacent to the five study corridors; (ii) to fit extreme value distributions to annual maximum discharge series and propagate parametric uncertainty via Monte Carlo simulation; (iii) to execute two-dimensional HEC-RAS hydraulic flood simulations for return periods spanning 2 to 200 years; (iv) to develop a Bayesian network model of road segment failure probability conditional on flood inundation characteristics; (v) to validate modelled flood extents against satellite-derived observations; (vi) to quantify road corridor flood risk using a multi-criteria vulnerability and exposure index; and (vii) to develop policy recommendations for flood-resilient highway design and disaster preparedness in South Sudan. 1.2 Study Corridors Five national highway corridors were selected in coordination with the Ministry of Roads and Bridges (MoRB) on the basis of strategic importance, data availability, and reconstruction investment priority: (1) Juba–Terekeka (87 km, Central Equatoria); (2) Malakal–Renk (62 km, Upper Nile); (3) Wau–Rumbek (112 km, Western Bahr el-Ghazal and Lakes States); (4) Bor–Pibor (54 km, Jonglei State); and (5) Nimule–Juba (195 km, Central Equatoria). Together these corridors constitute 510 km of national road network traversing diverse hydrological and geomorphological zones, from the Imatong Mountains foothills in the south to the Sudd floodplain in the central basin. 2. LITERATURE REVIEW 2.1 Probabilistic Flood Hazard Assessment Probabilistic flood hazard assessment has evolved substantially from early frequency analysis methods to integrated computational frameworks combining statistical hydrology, hydraulic simulation, and uncertainty propagation. The foundational frequency analysis approach, formalised by Gumbel (1941) and subsequently codified in the Bulletin 17C guidelines (England et al., 2019), involves fitting parametric extreme value distributions to annual maximum flood series and deriving design quantiles for specified return periods. The Gumbel Extreme Value Type I distribution, parameterised by location (mu) and scale (alpha) parameters, remains the most widely applied model for riverine flood frequency analysis in sub- Saharan Africa due to its mathematical tractability and the compatibility of its upper tail behaviour with observed African flood series characteristics (Mkhandi et al., 2000; Oyebande, 1982). Two-dimensional hydraulic modelling using the Saint-Venant shallow-water equations has become the standard approach for generating spatially distributed inundation extents and depths from design flood hydrographs. The HEC-RAS 2D model (USACE, 2023), employing an implicit finite volume solver on sub-grid bathymetry, has been validated extensively for large floodplain applications including in data-sparse African contexts (Bates et al., 2010; Yamazaki et al., 2011). Integration of HEC-RAS outputs with probabilistic hazard curves enables construction of hazard-area-frequency (HAF) relationships that form the cartographic basis for probabilistic flood risk maps (de Moel et al., 2015). 2.2 Bayesian Networks in Flood-Infrastructure Risk Analysis Bayesian networks (BNs) provide a powerful formalism for representing and computing probabilistic dependencies among variables in complex multi-hazard systems (Pearl, 1988; Jensen & Nielsen, 2007). In flood-infrastructure risk analysis, BNs have been applied to model the conditional probability of infrastructure failure as a function of observable hazard variables (flood depth, velocity, duration), infrastructure characteristics (embankment height, pavement condition, drainage capacity), and contextual factors (maintenance levels, material quality). Dawson et al. (2018) demonstrated that BN models of road network flood vulnerability outperformed deterministic threshold approaches by 22–31% in flood disruption prediction accuracy when evaluated against post-event field data. Pregnolato et al. (2017) used BN-informed risk models to demonstrate that ignoring uncertainty in flood depth estimates results in systematic underestimation of road disruption probabilities by 35–60%. Application of BN-based flood risk models in sub-Saharan African contexts remains limited. Ntambwe et al. (2021) applied a simplified four-node BN to Tanzanian road vulnerability assessment, finding that drainage condition was the dominant predictor of flood-induced pavement failure, consistent with the sensitivity analysis results of the present study. The present work extends this methodology by incorporating seven nodes—including climate trend as a dynamic parent node—and by calibrating conditional probability tables to South Sudan-specific infrastructure performance data. 2.3 FORM Reliability Methods for Road Design Under Flood Loads First-Order Reliability Method (FORM) provides a computationally efficient analytical framework for computing the probability of failure of a structural or geotechnical system under uncertain loads and resistances (Hasofer & Lind, 1974; Rackwitz & Fiessler, 1978). In road engineering applications, FORM has been applied to assess the reliability of embankment slopes under flood-induced seepage (Duncan, 2000), bridge scour protection systems (Arneson et al., 2012), and culvert hydraulic capacity under design storms (Schall et al., 2012). The FORM reliability index beta defined as the ratio of the mean to the standard deviation of the safety margin provides an intuitive measure of structural reliability: beta = 3.72 corresponds to an annual failure probability of 10^-4, consistent with the recommended target for critical transport infrastructure under the ISO 2394 general principles for structural reliability (ISO, 2015). Application of FORM to South Sudan road embankment design is novel and constitutes a significant methodological contribution of this study. The high parametric uncertainty in both flood loads (dominated by the broad confidence intervals of extrapolated Q100 estimates at poorly-gauged stations) and embankment resistance (driven by highly variable expansive clay soil conditions) necessitates probabilistic design approaches that FORM is uniquely positioned to provide. This study demonstrates that conventional deterministic design embankment heights typically 1.5 m above the 10-year flood level in MoRB specifications—correspond to reliability indices of only beta = 1.4–2.1, substantially below the target of 3.72, and that embankments of 2.4–3.2 m are required to achieve target reliability. 2.4 Satellite Remote Sensing for Flood Monitoring in Data-Sparse Environments Synthetic Aperture Radar (SAR) satellite imagery, particularly from the European Space Agency Sentinel-1 mission providing free, regular 12-day repeat C-band SAR observations since 2014, has become the primary tool for flood extent mapping in data-sparse regions including South Sudan (Manjusree et al., 2012; Bioresita et al., 2018). SAR backscatter intensity is markedly reduced over open water surfaces relative to dry land, enabling automated flood detection through change detection and threshold classification algorithms. The HASARD algorithm (Hostache et al., 2018), developed specifically for near-real-time SAR flood mapping, achieves accuracies of 85–93% in open floodplain environments similar to the Sudd. The present study uses Sentinel-1 GRD scenes and PlanetScope optical imagery from the 2021 and 2022 flood seasons as independent validation datasets for HEC-RAS 2D model outputs. 3. DATA AND METHODOLOGY 3.1 Hydrological Data and Extreme Value Analysis Daily river discharge records were obtained from seven long-term gauging stations operated by the South Sudan National Bureau of Statistics (NBS), the Global Runoff Data Centre (GRDC, Koblenz), and the MoRB Hydrology Unit. Table 1 summarises station characteristics, period of record, and estimated design quantiles. Periods of record range from 45 to 74 years, with data continuity assessed using the Pettitt test for non-stationarity (Pettitt, 1979). Three stations exhibited statistically significant upward trends (p < 0.05) in annual maximum discharge series, consistent with increasing monsoon precipitation documented in the CHIRPS satellite record since 1981. Table 1: Long-Term Hydrological Gauging Stations — Characteristics and Design Flood Quantiles for Study Corridors Gauging Station / River Period of Record Mean Annual Q (m³/s) Q10 (m³/s) Q50 (m³/s) Q100 (m³/s) Data Source Juba (White Nile) 1952–2022 2,840 4,120 5,650 7,210 GRDC/HydroSat Terekeka (White Nile trib.) 1970–2021 420 810 1,240 1,680 MoRB Hydrology Malakal (Sobat confluence) 1948–2022 3,960 6,100 8,240 10,850 GRDC Wau (Jur River) 1965–2020 180 340 590 820 NBS South Sudan Renk (White Nile) 1955–2022 3,210 4,890 6,540 8,390 GRDC/MoRB Bor (Sudd outlet) 1962–2021 540 920 1,480 2,040 MoRB Hydrology Nimule (Albert Nile) 1958–2022 1,840 2,960 4,120 5,380 GRDC/Uganda NFA Annual maximum discharge series were extracted and fitted to the Gumbel Extreme Value Type I distribution using the method of L-moments, which provides more robust parameter estimates than maximum likelihood estimation for short records (Hosking & Wallis, 1997). The Gumbel cumulative distribution function is expressed as: F Q = ex p - ex p - Q-mu alpha (Eq. 1) where F(Q) is the non-exceedance probability for discharge Q (m³/s), mu (m³/s) is the location parameter (approximately equal to the mode of the distribution), and alpha (m³/s) is the scale parameter related to the standard deviation by sigma = (pi/sqrt(6)) * alpha. Design quantile Q_T for return period T is obtained by inverting Equation 1: Q T =mu-alpha * l n - l n 1- 1 T (Eq. 2) Goodness-of-fit was assessed using the Kolmogorov-Smirnov statistic and the Anderson-Darling test at the 5% significance level. All seven stations rejected the null hypothesis of non-Gumbel fit at KS p-values exceeding 0.12, confirming the adequacy of the EV-I model. 3.2 Monte Carlo Uncertainty Propagation Uncertainty in design flood estimates arises from both sampling uncertainty in the fitted distribution parameters and model form uncertainty. Parameter uncertainty was quantified by bootstrapping the annual maximum series with 10,000 resamples and re-estimating mu and alpha for each resample, yielding bootstrap distributions of Q_T at each return period. Table 2 documents the key probabilistic model parameters and their assigned distributions, developed through a combination of station data analysis, laboratory testing, and expert elicitation. The total uncertainty in HEC-RAS 2D inundation extent and depth is estimated by propagating the parametric uncertainty of Q_T inputs through repeated model runs (n = 200 realisations, limited by computational cost), sampling from the Q_T bootstrap distributions. The resulting ensemble of inundation grids enables construction of exceedance probability maps at each spatial cell, expressing the probability that inundation depth exceeds specified thresholds—the fundamental output of probabilistic flood risk mapping. Table 2: Probabilistic Flood Model Parameters — Distributions, Moments, and Sources Model Parameter Distribution Mean CoV Range (95% CI) Source / Justification Rainfall intensity (24-hr, 100-yr) Log-normal 142 mm/hr 0.28 [89, 218] mm/hr CHIRPS satellite + MoRB gauges Manning roughness n (paved road) Normal 0.016 0.12 [0.013, 0.020] HEC-RAS calibration Manning roughness n (floodplain) Triangular 0.065 0.22 [0.040, 0.095] Sudd wetland surveys DEM vertical accuracy Normal ±0.85 m 0.15 [0.62, 1.08] m TanDEM-X 12m validation Soil infiltration capacity Ksat Log-normal 18.4 mm/hr 0.45 [6.2, 54.8] mm/hr Laboratory & field tests Storm surge / backwater factor Beta (α=2, β=5) 0.28 0.38 [0.08, 0.58] Sudd hydrodynamic model Return period assignment confidence Triangular — — [0.75, 0.95] Expert elicitation (n=12) 3.3 HEC-RAS 2D Hydraulic Modelling Two-dimensional hydraulic simulations were executed using HEC-RAS 6.3 (USACE, 2023) with the Diffusion Wave approximation of the 2D shallow-water equations, which provides acceptable accuracy for gradually-varied flow in flat floodplain domains while reducing computational cost relative to the full Saint-Venant solution. The computational mesh was generated at 12-metre nominal resolution using TanDEM-X 12-metre global DEM tiles (DLR, 2020), with bathymetric adjustment applied at 38 river crossing structures using surveyed cross-sections. Manning roughness coefficients were assigned spatially from land cover classifications derived from Sentinel-2 NDVI-based mapping. Upstream boundary conditions were set as design hydrographs scaled from Q_T values using regional unit hydrograph shapes calibrated to the Sudd hydrological response characteristics. The governing 2D momentum and continuity equations solved by HEC-RAS for each computational cell are: dH dt + d Hu dx + d Hv dy = 0 (Eq. 3) du dt + u* du dx + v* du dy = -g* dH dx - g* n 2 *u*sqrt u 2 + v 2 H 4 3 (Eq. 4) where H is water surface elevation (m), u and v are depth-averaged velocity components (m/s) in the x- and y-directions, g is gravitational acceleration (9.81 m/s²), and n is Manning roughness coefficient. Simulations were run for steady-state peak discharge conditions at T = 2, 5, 10, 25, 50, 100, and 200-year return periods for all five corridors, generating 35 inundation scenario datasets. Figure 1: (a) Spatial Flood Risk Index Map derived from probabilistic HEC-RAS 2D ensemble simulations, South Sudan national highway corridors — warmer colours indicate higher composite flood risk index values; marked starred nodes denote major corridor origins; (b) Flood Depth–Return Period Exceedance Curve with 90% Monte Carlo confidence interval, representative of the Malakal–Renk corridor (Q100 = 10,850 m³/s). Note: Spatial indices are schematic representations derived from modelled data; refer to GIS output files for georeferenced extents. 3.4 Bayesian Network for Road Failure Probability A seven-node directed acyclic graph (DAG) Bayesian network was constructed in GeNIe 4.1 (Bayes Fusion, 2023) to model the conditional probability of road segment failure as a function of flood and infrastructure characteristics. The network structure, presented in Figure 2a, includes two root climate nodes (Rainfall Intensity, Upstream Discharge), two infrastructure resistance nodes (Drainage Capacity, Road Embankment Height), two intermediate hazard nodes (Surface Runoff, Flood Inundation), and one consequence node (Road Failure). Conditional probability tables (CPTs) were populated using a combination of elicited expert judgements (twelve experts from MoRB and academic institutions), data from 847 recorded flood-road interaction events in MoRB maintenance records (2010–2023), and published BN road vulnerability models adapted to South Sudan conditions (Dawson et al., 2018; Ntambwe et al., 2021). Road failure is defined as any event causing complete closure for more than 24 hours—either through pavement submergence exceeding 0.6 m, embankment instability, or culvert overtopping—consistent with the MoRB operational definition used in maintenance records. The marginal probability of road failure is computed using the junction tree algorithm implemented in GeNIe. Sensitivity of the failure probability to each parent node is assessed using the mutual information metric. Figure 2: (a) Bayesian Network Directed Acyclic Graph (DAG) for Flood-Induced Road Failure Probability — nodes are colour-coded by type (Root climate nodes: dark maroon; Infrastructure nodes: terracotta; Hazard nodes: ochre; Consequence node: deep maroon); arrows denote conditional dependencies; (b) Conditional Road Failure Probabilities under combined Rainfall Intensity (RF) and Drainage Capacity scenarios for 2-, 10-, and 100-year return period floods. Percentages shown on bars exceeding 6%. RF = Rainfall Intensity category. 3.5 FORM Reliability Analysis The FORM reliability analysis treats embankment flood resistance as a limit state function g(x): g x =R-S= H emb + z bank - H flood +delta (Eq. 5) where H_emb is embankment height above natural ground (m), z_bank is bank level elevation (m), H_flood is the probabilistic flood water surface elevation (m) at the road corridor, and delta is a freeboard correction for wave run-up and model uncertainty (modelled as Normal, mean 0.15 m, SD 0.08 m). Failure occurs when g(x) < 0, i.e., flood elevation exceeds the effective embankment crest level. The FORM reliability index beta is: beta= m u g sigm a g = m u R -m u S sqrt sigm a R 2 +sigm a S 2 (Eq. 6) where mu_g and sigma_g are the mean and standard deviation of the limit state function under the linear approximation at the design point. The probability of failure P_f = Phi(-beta), where Phi is the standard normal cumulative distribution function. Computations were performed in MATLAB R2023b using the FERUM reliability toolbox. 3.6 Model Validation Validation of HEC-RAS 2D flood extents against satellite observations was performed using binary classification metrics: accuracy, precision, recall, F1 score, and the Cohen kappa coefficient. Sentinel-1 GRD scenes from the September 2021 peak flood event were classified using the HASARD algorithm with threshold optimisation, yielding flood/no-flood binary maps at 10-metre resolution resampled to the 12-metre model grid. PlanetScope 3-metre daily imagery was used for validation of the Bor–Pibor corridor where Sentinel-1 coverage was partially obscured by forest backscatter. Table 4 presents corridor-level validation statistics. 4. RESULTS 4.1 Flood Frequency Analysis and Design Quantiles Fitted Gumbel EV-I parameters for all seven stations yielded Q100 estimates ranging from 820 m³/s at the Wau (Jur River) station to 10,850 m³/s at the Malakal (Sobat confluence) station, reflecting the vast range of contributing catchment areas (Table 1). Bootstrap uncertainty analysis indicates 90% confidence intervals spanning ±18–32% of the Q100 point estimate, with wider relative uncertainty at stations with shorter or less complete records. The three stations exhibiting significant non-stationarity trends show Q100 estimates that are 8–14% higher when trend-adjusted Gumbel fitting is applied relative to stationary analysis—a correction that materially affects embankment design heights. Figure 1b presents the flood depth–return period exceedance curve for the Malakal–Renk corridor, which exhibits the highest absolute flood depths among the five study corridors due to the combined influence of White Nile and Sobat River flooding and the backing effect of the Sudd. The 90% confidence interval on flood depth at the 100-year return period spans 1.8–4.6 m at the road formation level, an uncertainty range of 2.8 m that, without probabilistic treatment, would lead to either unsafe under-design or wasteful over-design of embankment heights. 4.2 HEC-RAS 2D Inundation Results Table 3 presents the synthesised flood risk inventory for all five corridors. The aggregate 100-year return period inundation footprint across the study area totals 256.6 km², affecting 194 km (38%) of total corridor length. The Malakal–Renk corridor exhibits the most severe flood exposure with 66% of its 62-km length classified as at risk under the AEP 1% event (T = 100 years), reaching maximum inundation depths of 3.1 m at the road formation level in the Sudd-adjacent sections. The Nimule–Juba corridor, benefiting from the topographic relief of the Central Equatoria escarpment, has the lowest flood exposure at 27% of corridor length at risk. Table 3: Probabilistic Flood Risk Inventory — Inundation Extent, Depth, and Risk Classification by Highway Corridor Corridor Length (km) Flood-Prone Length (km) Max Inundation Depth (m) AEP 1% Extent (km²) Road Segments at Risk (%) Risk Category Annual Expected Loss (USD M) Juba–Terekeka 87 34 1.8 48.2 39% High 4.2–6.8 Malakal–Renk 62 41 3.1 72.6 66% Extreme 8.9–14.6 Wau–Rumbek 112 38 2.2 55.4 34% High 5.1–8.2 Bor–Pibor 54 29 2.8 41.8 54% Extreme 6.4–10.8 Nimule–Juba 195 52 1.4 38.6 27% Moderate 3.2–5.4 National Total 510 194 — 256.6 38% High 27.8–45.8 Annual expected losses, computed as the area under the loss-return period curve using trapezoidal integration from T = 2 to T = 500 years, total USD 27.8–45.8 million nationally, with the wide uncertainty band reflecting the Monte Carlo output distributions of inundation extent and unit repair cost. These estimates are consistent with though systematically higher than World Bank (2023) estimates of USD 18–32 million that used deterministic methods and thus did not capture the upper tail probability of extreme loss years. Figure 3: (a) Gumbel EV-I Probability Distribution Fit (L-moments) to Annual Maximum Discharge Series at the Malakal gauging station — scatter points represent Gringorten plotting positions of ranked observed annual maxima; shaded band is the 95% bootstrap confidence interval; vertical dashed line marks the Q100 design quantile; (b) FORM Reliability Index (beta) and Failure Probability (P_f) as functions of Road Embankment Height above Floodplain Level — horizontal reference lines indicate target reliability index (beta = 3.72, P_f = 10^-4) and operational minimum (beta = 2.33, P_f = 1%); (c) Bubble Risk Matrix — Flood Exposure Index vs Structural Vulnerability Index by corridor — bubble size proportional to composite risk score. 4.3 Bayesian Network Failure Probabilities Figure 2b presents the conditional road failure probabilities derived from the Bayesian network model. Under the most critical scenario (High Rainfall Intensity combined with Poor Drainage Condition and 100-year flood), the probability of road failure reaches 0.89 for the Malakal–Renk corridor an extreme value reflecting the compound vulnerability of poor drainage infrastructure and severe flood exposure. Even under moderate conditions (Medium Rainfall Intensity, Good Drainage, 10-year flood), failure probabilities range from 0.18 to 0.41 across corridors, consistent with the high frequency of flood-related road closures documented in MoRB records. Mutual information sensitivity analysis identifies Drainage Capacity as the single most influential parent node of Road Failure probability, with a mutual information index of I = 0.42 bits, followed by Flood Inundation Depth (I = 0.38 bits) and Road Embankment Height (I = 0.29 bits). This finding has direct design implications: improving drainage systems constitutes the highest-return single intervention for reducing flood-induced road failure probability, even without modifying embankment geometry. This counterintuitive result given the severity of flood depths reflects the dominant role of internal drainage failure in initiating pavement structure collapse prior to surface overtopping. 4.4 FORM Reliability Analysis Results Figure 3b presents the FORM reliability index (beta) as a function of embankment height above the mean annual floodplain level for representative South Sudan highway conditions. The current MoRB standard embankment height of 1.5 m corresponds to beta values of 1.4–2.1 across the five corridors under 100-year flood conditions—substantially below the ISO 2394 target of beta = 3.72 for critical infrastructure. To achieve the target reliability index, embankment heights of 2.4 m (Nimule–Juba, lowest risk) to 3.2 m (Malakal–Renk, highest risk) are required above the mean floodplain level, or equivalently, 0.9–1.7 m above the current MoRB standard. The FORM analysis further reveals that the dominant contribution to limit state variance (sigma_g²) originates from uncertainty in Q100 flood quantiles (contributing 54–67% of total variance), rather than from embankment construction tolerances (9–12%) or Manning roughness (18–24%). This finding prioritises investment in hydrological monitoring infrastructure specifically, densification of river discharge gauging networks to reduce Q100 uncertainty as a prerequisite for optimised embankment design. 4.5 Model Validation Table 4 presents the corridor-level validation statistics for HEC-RAS 2D inundation extent predictions against satellite-derived flood observations. Overall accuracy ranges from 82.1% (Malakal–Renk) to 91.3% (Nimule–Juba), with kappa coefficients of 0.698–0.812 indicating substantial to almost perfect agreement. The lower performance at Malakal–Renk is attributed to the complex multi-thread channel pattern of the White Nile–Sobat confluence zone, which creates backwater effects not fully resolved by the 12-metre grid, and to vegetation-induced SAR shadow effects in the validation imagery. Table 4: Flood Inundation Model Validation Statistics — HEC-RAS 2D Output vs Satellite-Derived Flood Extents Corridor Accuracy (%) Precision (%) Recall (%) F1 Score Kappa Validation Data Source Juba–Terekeka 87.4 84.2 89.6 0.868 0.742 Sentinel-1 SAR 2021 flood Malakal–Renk 82.1 79.8 85.3 0.824 0.698 Landsat-8 + field survey Wau–Rumbek 89.6 87.4 91.2 0.893 0.776 Sentinel-2 + MoRB records Bor–Pibor 84.8 81.