physio-geographic regions in Karnali: Low Hills, Middle Hills, High Hills, and Mountains. These charges aggregate materials, labor, management, and administrative expenses. We followed the government’s practice as described by RAP in an August 2018 interview, allocating per-kilometer budget charges to road segments based on their length and the majority geography of the district they primarily fell within. Thus Mountain roads were 33% more expensive than Low Hill roads. The values that were used are provided in Table 2.

Table 2: Average per-kilometer budget charge associated with different physio-geographic regions. Values were provided in NPR and converted to USD using an exchange rate of 120 NPR to 1 USD (2 May 2020).

|Geography|Road cost<br>(NPR / km)|Road cost<br>(USD / km)|
|---|---|---|
|Low Hills|15 million|126 thousand|
|Middle Hills|17 million|143 thousand|
|High Hills|18 million|151 thousand|
|Mountains|20 million|168 thousand|

# 3.2. Roads vs. road sequences

Roads do not exist in isolation, but as part of networks. As such, proposed roads may implicitly depend on the construction of other roads linking them to the existing road network. We reviewed the proposed roads and grouped them into combination sets with internal hierarchies (tiers) reflecting these spatial dependencies. Thus a tier 2 road enables a tier 3 road to be built but depends in turn on a tier 1 road being built. Applying these hierarchical concepts to generate all plausible combinations of road tiers expands the number of candidates from 92 roads to 261 combinations – called sequences – and corresponding GIS files were created from visually observable hierarchies. In a real-world scenario, such hierarchies would be identified by experts in road construction and regional accessibility; the priority here was to illustrate our process and its accommodation of such hierarchies. The accessibility improvement modeling process was then run for these sequences as well. The notion of such tiers that form part of the sequences identification process is illustrated in Figure 5 for a number of connecting roads ranked into three tiers. For narrative simplicity, in the remainder of this paper all potential additions to a candidate layout are referred to as a road sequence – whether a standalone road or a combination of roads.

# 3.3. Geospatial cost-time analyses

A recently released geospatial model of Nepal representing distances in units of time offers a scalable, replicable solution to the problem of modeling travel in Karnali (Banick and Kawasoe, 2019).<sup>2</sup> The model calculates the minimum travel time to cross every 30 m<sup>2</sup> of Nepal’s two dimensional surface based on the underlying terrain, landcover, altitude, roads, and road conditions; an accompanying monsoon model adjusts these factors and resulting travel times for monsoon conditions. The two dimensional output is packaged into a 30 m<sup>2</sup> gridded (“raster”) friction surface that can be used to calculate accessibility to various services from any place on the grid. These accessibility rasters can be aggregated into descriptive statistics at almost any useful level of analysis – administrative areas, catchments for specific markets or hospitals, or catchments for individual roads.

Applying the friction surface to services of interest allowed us to specify the precise accessibility gains associated with each planned road or sequence of roads in Karnali province. We measured the increase in accessibility associated with specific proposed roads by generating a friction surface for every proposed road incorporating its projected travel time improvements, then using said model to calculate accessibility to selected nearby services. Comparing these to similar measures from a reference data set based on the existing road network yielded the accessibility improvement associated with an individual road.

> 2Readers with a deeper interest in the process of cost-time modeling and subsequent accessibility analysis in Nepal are encouraged to refer to Banick and Kawasoe (2019), where the modeling process and parameters are discussed at length.

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