the constraints given in table 2. The aim of the merging process is to obtain regions as close to the target as possible and with population below threshold (e.g. 750) and area within a specified range (e.g. 0.1 to 9km<sup>2</sup> ) while ensuring that merged areas do not cut across obstacles or administrative borders. With a lower priority, the process also tends to produce shapes that are as compact as possible. By construction, the boundaries of the EAs resulting from the merging process will also follow geo-referenced features (or square sides, if quadtree squares are needed).

The merging process takes as inputs: 1/ the PU features defined in the split process, 2/ ranges of target population and area values for EAs (table 2), 3/ the gridded population density dataset to compute the population for re-merged region at each step, and 4/ a set of specified boundaries across which regions should not be merged (e.g. large rivers, delineation of urban and rural strata, administrative boundaries). Since this is a computationally intensive process, the method was applied to every 18 pre-war regions separately.

To complete the merging step, we used the Automated Zone-design Tool (AZTool) since it is publicly available, most compatible compare to the other tools for the purpose of this study and user-friendly. AZTool was developed by Martin et. (2002) and is based on Openshaw’s (1977) Automated Zoning Procedure (AZP). The AZP methodology was developed by the Office for National Statistics (ONS) for the 2001 census in England and Wales (Cocking et al 2011) and to revise census geography in New Zealand (Martin and Lyndon 2009). AZTool iteratively combines and recombines sets of geographic building blocks to generate larger zones optimized to meet a set of pre-defined user-specified constraints. Such specified constraints include population threshold (Min, Max and target) and compactness of the shape. Criteria and constraints used in the current study are reported in table 2. Compactness is a minor constraint used so that shapes ‘tend’ to be compact and avoid difficult shapes such as snake-like shapes. Donut is one output area surrounding another. The Area constraint was not originally included as a constraint in AZTool, however, we modified the .xml file to include the area constraint for the purpose of this study.

Table 2. Illustrates the criteria were set in AZTool to generate sensible EAs in Somalia rural area.

|**Criteria**|**Hard Constraint**|**Soft Constraint**|**On or off**|
|---|---|---|---|
|Shape compactness||Yes|on|
|Population|Min=0 and Max=750|Target=650|on|
|Area|Min=0.1 km<sup>2</sup>and Max=9 km<sup>2</sup>|Target=8.8 km<sup>2</sup>|on|
|Donuts|Yes||on|

# **2.6 Computation of EA probability of selection**

The split and merge algorithm results in a partition of the country into regions that satisfy the definition of an EA. We calculate the population of each EA using the population density map and compute the probability of selection. The probability of sampling for each EA was defined according to the expected population within each EA divided by the total population in the regional stratum, recalling that the country was divided into 18 pre-war regions and further subdivided into urban/rural strata.

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