[version 1; peer review: 2 approved, 1 approved with reservations]
No competing interests were disclosed.
Traditional sample designs for household surveys are contingent upon the availability of a representative primary sampling frame. This is defined using enumeration units and population counts retrieved from decennial national censuses that can become rapidly inaccurate in highly dynamic demographic settings. To tackle the need for representative sampling frames, we propose an original gridbased sample design framework introducing essential concepts of spatial sampling in household surveys. In this framework, the sampling frame is defined based on gridded population estimates and formalized as a bidimensional random field, characterized by spatial trends, spatial autocorrelation, and stratification. The sampling design reflects the characteristics of the random field by combining contextual stratification and proportional to population size sampling. A nonparametric estimator is applied to evaluate the sampling design and inform sample size estimation. We demonstrate an application of the proposed framework through a case study developed in two provinces located in the western part of the Democratic Republic of the Congo. We define a sampling frame consisting of settled cells with associated population estimates. We then perform a contextual stratification by applying a principal component analysis (PCA) and
Research and policymaking often require demographic data, such as population enumerations and age and sex structures. While these data have been historically derived from national censuses ^{ 1 }, the past 40 years have witnessed an increasing interest in the use of household surveys for demographic estimations ^{ 2 }. Starting from 2000, for instance, the US Census adopted the dual system estimation that complements the national census with a richer set of demographic and socioeconomic characteristics captured using household surveys ^{ 3 }. This kind of survey provides a costeffective way to access an extensive range of attributes that can be ultimately generalized to a larger population of interest ^{ 4 }. Generalization is especially valuable in low and middleincome countries with outdated, inaccurate or incomplete censuses, where a sample of representative households can be used to estimate demographic data ^{ 5 }.
Traditional sample designs for household surveys build on three pillars — the sampling frame, sampling design, and estimator ^{ 6 }. The sampling frame consists of a list of all potential sampling units ^{ 7 }, the sample design defines the probability of any given unit to be sampled ^{ 8 }, and the estimator determines the rule to generalize the estimate (for example, recovering the mean characteristics of the population of interest using the mean characteristics of the sampled households) ^{ 6 }. In low and middleincome countries, these sample designs are generally set up in two stages because of logistical and financial considerations ^{ 9 }. This form of multistage design involves the initial sampling from the primary frame, which is composed of nonoverlapping enumeration units. Following the definition of a secondary frame resulting from the enumeration of all households in the sampled enumeration units, households are finally sampled ^{ 9 }.
The primary frame is an essential aspect of twostage sampling designs because it is meant to provide an accurate, complete, and uptodate representation of the distribution of the population of interest ^{ 7 }. This is defined using enumeration units and population counts retrieved from the most recent national census, an exercise that, in the bestcase scenario, is carried out on a decadal basis ^{ 10 }. Census data become rapidly outdated because a maximum timespan of two years should typically occur between the definition of the sampling frame and the sample design implementation ^{ 7 }. As a consequence, sample designs for household surveys are increasingly relying on alternative sampling frames, typically derived from gridded population estimates ^{ 10 }. These estimates are produced through topdown spatial disaggregation of national census data ^{ 11 } or bottomup spatial interpolation based on household survey data collected within small geographic areas ^{ 12 }.
Adopting a gridded sampling frame requires adjusting the three pillars of household sample design conceived for onedimensional listings to a bidimensional geographic space ^{ 4 }. This adjustment can be achieved by considering the three core concepts of spatial sampling — the random field, the design, and the estimator ^{ 13 }. The notion of random field formalizes the population of interest through a bidimensional random process characterized by errors, trends, autocorrelation, and stratification ^{ 14 }; the design reflects the specificities of the random field in the selection of sampling units; and the estimator defines the generalization of the estimate retrieved from the sampling units to the entire sampling frame ^{ 15 }. Despite the need for bridging sample designs for household surveys and spatial sampling, explicit joint methodological frameworks are currently still rare ^{ 10 }.
To fill this knowledge gap, we propose a gridbased sample design for household surveys that embeds the three core concepts of spatial sampling ^{ 13 }. In doing so, the gridded sampling frame is formalized as a bidimensional random field ^{ 13 }; the design considers spatial trends, spatial autocorrelation, and stratification through a contextually stratified ^{ 16 } proportional to population size sampling ^{ 5 }; a nonparametric estimator is used to assess the sampling design and inform sample size estimation ^{ 17 }. We demonstrate the application of this sample design framework with a case study developed in two provinces located in the western part of the Democratic Republic of Congo. This country had its last census over 30 years ago, and sampling frames for household surveys are still based on these extremely outdated population figures ^{ 18 }. The results of the case study provide valuable insights into the implementation of the proposed framework and foster further research into gridbased sample designs.
The key elements of this framework are the sampling frame (
The notion of sampling frame is at the core of household sample design because it ensures that every household has a known probability of being surveyed ^{ 7 }. This concept, however, is not frequently adopted in other disciplines, such as environmental sciences, because full listings are considered impractical or even impossible ^{ 13 }. To overcome this issue, in the domain of geostatistics, the complete listing of the population of interest is replaced by the listing of the geographical location where it can be found ^{ 16 }. For this purpose, a regular geometric grid with square or hexagonal patterns is overlaid on the study area to enable equal sampling probability ^{ 25 }. Given the heterogeneous geographic distribution of the human population, in the past, the use of gridded sampling frames has been discouraged for household surveys ^{ 16 }. However, other spatially explicit sampling frames, for instance, based on parcel boundaries ^{ 26 } or air pollution levels ^{ 16 }, have already been adopted in the past for household sampling.
Gridded population sampling frames are being increasingly adopted in household sampling carried out in low and middleincome countries with outdated census frames ^{ 10 }. This is because, in some instances, traditional sampling frames lack complete geographic coverage, welldefined geographic boundaries and uptodate population data ^{ 9 }. Conversely, a gridded sampling frame provides comprehensive coverage of welldefined regular sampling units — the grid cell ^{ 5 }. The increasing availability of highresolution gridded population estimates, with cells measuring between 30 ^{ 27 } and 250 meters ^{ 28 }, also enables deriving sampling frames of relatively fine spatial resolution. Whether gridded population estimates have known inaccuracies connected with the quality of the input datasets ^{ 5 } and selected spatial disaggregation techniques ^{ 11 }, they are generally considered to provide a more accurate approximation of the geographical distribution of population counts than outdated census enumerations ^{ 5, 11 }.
While most gridded population estimates are constrained to settled areas
^{
11
}, WorldPop topdown estimates provide a continuous populationcount value across all land masses to ensure that sparselypopulated areas are not omitted
^{
29
}. This dataset also offers the advantage of a systematic global coverage and an accuracy assessment
^{
29
}. Furthermore, a gridded sampling frame derived from WorldPop topdown estimates can be refined using global settlement datasets such as the Global Urban Footprint (GUF)
^{
30
} and the Global Human Settlement Layer (GHSL)
^{
28
} using the settled area as a limiting ancillary variable
^{
31
}. The sampling frame, defined based on the population counts within settled cells, can be formalized as a random field (ℜ), where the population count in a settled cell (
Equation 1
The population count within a settled cell (
Opposite to geostatistics, household surveys adopt designbased sampling strategies because the population of interest is considered unknown but fixed and entirely measurable ^{ 4 }. Within different design strategies, household surveys in low and mediumincome countries are often based on twostage sampling designs ^{ 9 }. This design involves drawing enumeration units from a primary sampling frame with probability proportional to population size, in which a number of households are subsequently randomly surveyed ^{ 7 }. Firststage sampling is crucial to improve sampling efficiency because it can incorporate characteristics of the random field ^{ 6 }. For example, enumeration areas may be selected with probabilities proportional to their population sizes to better account for spatial heterogeneity and to include densely populated areas that would likely be excluded from a random sample. However, the scarce accuracy of the population enumerations retrieved from the last census and the definition of coarse strata can limit the efficiency of proportional to population size sampling for household surveys ^{ 36 }.
Stratified sampling assumes that the population of interest can be partitioned into more homogeneous subpopulations, or strata ^{ 13 }. This is to capture the spatial heterogeneity in the population of interest globally, and, consequently, to reduce the insample spatial autocorrelation ^{ 6 }. Stratification can be based on prior knowledge, presampling, or proxy variables ^{ 37 }. In household sampling, strata often consist of a proxy reflecting the urban/rural divide ^{ 8 }, a strategy that is reproduced in existing gridbased sampling designs to provide independent estimates for planning and decisionmaking ^{ 5 }. The use of bidimensional gridded sampling frames enables finer contextual stratification by incorporating information on geographic phenomena influencing the distribution of the population of interest ^{ 16 }. This can be achieved by accessing ancillary gridded datasets related to socioeconomic (e.g., distance to major roads and urban centres) or physical characteristics (e.g., terrain and climate) that are embedded in topdown population models ^{ 38 }.
For each ancillary dataset, the cell values intersecting the settled cells define a highdimensional space describing geographical context. This approach enables to define contextual strata by combining two popular methods for dimensionality reduction
^{
39
} — principal component analysis (PCA)
^{
40
} and
Within each stratum, proportional to population size sampling has a straightforward implementation in gridded sampling designs, through dedicated software packages
^{
5
} and web platforms (e.g.
The probability scheme resulting from stratified proportional to population size sampling
Equation 2
The probability of selecting a specific cell
Equation 3
The probability of selecting a specific cell
Equation 4
Based on the probability scheme specified above, it is possible to produce an unbiased estimator that can be used to evaluate the sampling design and inform sample size estimation.
In household sampling design, the estimand is a parameter summarizing the random variable of interest, such as the mean, variance, or total
^{
8
}. Typical examples are the mean proportion of children under five years old or the number of women of childbearing age. In this setting, the estimator is built using a parametric attribute of the random variable of interest
^{
47
}. However, the use of nonparametric estimators enables to retrieve the characteristics of the entire random variable
^{
48,
49
}. In the case of sample design for household surveys, the random variable consists of the population count across settled cells, where a large number of cells have mediumtolow population counts and only a few have high population counts. To capture the characteristics of the entire population of interest, the estimand becomes the full probability distribution of the random variable through its CDF
^{
50
}. The CDF (
Equation 5
Given that the proposed sample design is not random but probabilistic, the estimator needs to be weighted for the respective probability scheme
^{
51
}. Typical parametric estimators, such as the mean or total, can be weighted using the HorvitzThompson estimator, by implementing the inverse of the probability scheme
^{
47
}. This concept can be extended to nonparametric estimators, by weighting the ECDF using the inverse of the probability scheme, and producing a weighted empirical cumulative distribution function (WECDF)
Equation 6
In household surveys, the sample size is typically determined using a power analysis applied to the parametric estimator, which is assumed to be normally distributed for large sample sizes
^{
8
}. For nonparametric estimators, such as the WECDF, a simulation study can enable evaluation of the sample size required to provide an accurate representation of the population of interest across the different strata
^{
17
}. For this purpose, the same gridded population data used in proportional to population size sampling can serve as a proxy for the entire population of interest. The population counts across sampling frame cells are used to derive the ECDF for the entire population of interest and the WECDF for different sample sizes, and compare the two distributions using a nonparametric statistic — the KolmogorovSmirnov distance (
Equation 7
We demonstrate an application of the proposed gridbased sample design framework in two provinces in the western part of the DRC. This country is the secondlargest by area and the fourthmostpopulous in Africa. However, official population figures are currently lacking because the last census was carried out over thirty years ago, in 1984. Attempts to produce demographic data are routinely being carried out using population estimates and projections (e.g.,
The study area covers the KongoCentral and Kinshasa provinces, in the Democratic Republic of the Congo. Together, these provinces constitute the most dynamic socioeconomic region of the country. In this region, approximately 80% of the population lives in urban areas — in the capital city of Kinshasa, the cities of Boma and Matadi, and a number of smaller cities and towns
^{
53
}.
Cities and towns develop mostly across the Congo river basin, while smaller towns can be found in the sparselypopulated plateau at the NorthWest and SouthEast of the study area. At elevated locations, the vegetation is prominent with the rain forest at the NorthWest and the savannah at the SouthEast.
We accessed a settlement layer produced by the Oak Ridge National Laboratory using feature extraction from highresolution imagery for population modelling work undertaken in the Kinshasa and KongoCentral provinces. The settlement layer consists of settlement polygons of approximately 7 meters resolution that were subsequently subset to the official province boundaries provided by the Central Bureau of Census (BCR) of the Democratic Republic of the Congo. Comprehensive metadata are provided in
The column “Type” indicates the characteristics addressed. The column “Format” describes the type of input data. The column “Type” defines the type of variable. The column “Source” reports the links to the datasets used in the case study.
Type  Name  Provider  Year  Format  Variable  Source 

SE  Distance to

Armed Conflict

2016  VECT  CONT 

SE  Travel distance

Malaria Atlas

2015  RAST  CONT 

INF  Distance to

OSM/WorldPop  2016  RAST  CONT 

INF  Light intensity at

VIIRS/WorldPop  2016  RAST  CONT 

ENV  Degree of

GHSSMOD  2015  RAST  CAT 

ENV  Land cover  ESACCI  2015  RAST  CAT 

PHY  Elevation  SRTM/WorldPop  2000  RAST  CONT 

PHY  Slope  SRTM/WorldPop  2000  RAST  CONT 

CLIM  Rainfall  WorldClim  1960–2000  RAST  CONT 

CLIM  Temperature  WorldClim  1960–2000  RAST  CONT 

—  Population

WorldPop  2016  RAST  CONT 

—  Settlement layer  ORNL/WorldPop  2016  VECT  CAT 

—  Administrative

Central Bureau

2018  VECT  CAT 

*Datasets not publicly available.
SE, socioeconomic; INF, infrastructural; ENV, environmental; PHY, physical; CLIM, climatic; VECT, vector; RAST, raster; CONT, continuous; CAT, categorical.
The gaps between settlement layer and the settled cells tend to vary considerably across the urban area of Boma (A), the suburban areas at the outskirts of Kinshasa (C), the town of Mbankana (D), and the rural area north of the town of Kimpese (B).
We retrieved ten gridded datasets describing the socioeconomic (i.e., distance to conflict points and light intensity at night), infrastructure (i.e., distance to major roads and travel distance to cities), environmental (i.e., land cover and degree of urbanization), physical (i.e., elevation and slope), and climatic (i.e., temperature and rainfall) characteristics of the study area. These datasets have been selected because they represent key geospatial covariates in topdown population models developed by WorldPop
^{
38
}. Comprehensive metadata are provided in
Three, five, and eight clusters are the best scenarios, according to the “elbow” method, for capturing the variance in the nine principal components derived from the gridded data attributes.
The legends show the ratio of settled cells allocated to the different clusters. Overall, the spatial patterns resulting from the three scenarios produce comparable outputs, with a clear distinction between the urban (Boma — A) and suburban (outskirts of Kinshasa — C) areas versus the town (Mbankana — D) and rural area (North of Kimpese — B).
We accessed highresolution gridded population estimates for 2016 from WorldPop and allocated population figures to the corresponding settled cells. Comprehensive metadata are provided in
The large horizontal black lines show the median, the boxes the interquartile range, the whiskers the minimum and maximum, and the dots the outliers.
We sampled settled cells from each contextual stratum proportionally to the respective population counts.
The ECDFs are depicted as black lines and the ECDFs as coloured lines. Sample sizes for the ECDFs span between 1 and 1000. The settled cells are selected using proportional to population size sampling for each contextual stratum (high, medium, and low urban status), independently.
We computed the KolmogorovSmirnov distance between the baseline ECDF and the WECDF for sample sizes spanning between 1 and 1000 across the different strata. We replicated this procedure 1000 times for the different sample sizes and averaged the distance metrics to provide a robust assessment of the distance between the two functions.
For sample sizes spanning between 1 and 1000, 1000 repetitions have been carried out and then averaged to produce a more robust assessment. The box highlights sample sizes resulting in reasonable distance metrics. The circles show the sample sizes resulting in a distance of 0.15.
To obtain similar sampling performances, we sampled 139, 171 and 83 settled cells from the strata with high, medium, and low urban status, respectively, proportionally to population size.
The resulting sampling weights vary considerably across strata. Higher weights can be observed in areas of lower population counts per settled cell within the medium urban status stratum, while lower weights can be found in the sparsely populated low urban status stratum.
In low and middleincome countries, sample designs for household surveys are traditionally set up in two stages for logistical and financial considerations
^{
9
}. This form of multistage sampling involves an initial sampling from the primary frame, which consists of nonoverlapping enumeration units defined proportionally to population size
^{
7
}. These enumeration units are typically derived from the last national census, which is usually carried out on a decadal basis
^{
54
}. In reality, the timespans between censuses can be even larger as, according to the United Nations’ Department of Economic and Social Affairs,
The uncertainty associated with nonrepresentative sampling frames propagates through the sampling design to the estimator ^{ 8 }. As a consequence, the resulting household surveys can limit the accuracy of the derived demographic data ^{ 18 }. To tackle this issue, research in the domain of household sample design recently started to focus on the use of gridded population data to produce actionable sampling frames ^{ 10 }. Given the geographically explicit nature of gridded sampling frames, sample designs for household surveys can arguably benefit from spatial sampling techniques traditionally applied in natural sciences ^{ 13 }. To date, only a limited number of sample designs for household surveys have explicitly considered concepts of spatial sampling through the concepts of random field, sampling design and estimator. Two such studies reflect the characteristics of the random field in sample design using parcel boundaries ^{ 26 } and air pollution levels ^{ 16 }. However, none of these studies explicitly considered the geographic distribution of the reference population in their sample design.
To tackle the limits of traditional sample designs, we proposed an innovative gridbased sample design framework for household surveys. This framework is centred around the concept of gridded sampling frame, a concept that is traditionally being adopted in natural sciences ^{ 8 } and, more recently, in sampling for household surveys ^{ 10 }. The use of geographically explicit sampling units enabled us to revise the three pillars of traditional sample design — sampling frame, sampling design, and estimator — through the elements of the core components of spatial sampling ^{ 13 }. A key element of the proposed framework is formalizing the population distribution as a random field, and tackle spatial trends, spatial autocorrelation, and stratification of the reference population. These considerations are embedded in the sampling design, where contextual stratification ^{ 8 } and populationweighted sampling ^{ 36 } are used jointly to improve sampling efficiency. Both the sampling design and the sample size are assessed based on a nonparametric estimator to assess generalization to the entire reference population ^{ 48, 49 }.
We demonstrated an application of our proposed sample design framework with a case study developed in two provinces in the western part of DRC. In this country, existing sampling frames are typically developed based on outdated census figures dating from 1984. As a result, much demographic information produced through the six national surveys carried out since 2004 is highly uncertain
^{
18
}. We built a gridded sampling frame for the study area consisting of settled cells of approximatively 90 meters spatial resolution. We then defined the two essential elements of our sampling design, namely the contextual strata based on a combination of PCA and
The case study underscores some challenges of the proposed gridbased sample design. First, the spatial accuracy of a gridded sampling frame is contingent upon the quality of the input settlement layer. The case study showed that the settlement layer enables to detect settlement patterns at high spatial resolution across urban and rural locations. The use of settlement data of lower spatial resolutions would reduce the accuracy of the sampling frame, especially in regions where the builtup area is more scattered. Second, the dimensionality reduction techniques employed to define contextual strata suffer inherent limitations in detecting complex dimensionality structures. Alternative unsupervised classification methods should be tested ^{ 55 }. The sampling design can also be affected by the quality of the gridded population data used to define the probability scheme. Even if these gridded data are argued to be more accurate than the related administrative counts ^{ 21 }, their fitness for use is contingent upon a number of criteria listed elsewhere ^{ 11 }. The use of a nonparametric estimator to assess sampling efficiency also demonstrated systematic oversampling of settled cells with higher population counts when sampling proportional to population size. This involves that larger sample sizes are required within heterogeneous strata.
The proposed gridsampling design inspired the selection of household survey locations in the KongoCentral and Kinshasa provinces in 2018 as part of the
Most of the data used in our case study are freely available and can be accessed following the references presented in
This work is part of the GRID3 project (GeoReferenced Infrastructure and Demographic Data for Development) funded by the Bill and Melinda Gates Foundation and the United Kingdom Department of International Development (DFID) [OPP1182408]. The project is a collaboration between WorldPop at the University of Southampton, the Flowminder Foundation, the United Nations Population Fund (UNFPA), and the Center for International Earth Science Information Network (CIESIN) within the Earth Institute at Columbia University. We thank the UCLADRC Health Research and Training Program, the Kinshasa School of Public Health (KSPH), and the DRC Bureau Central du Recensement (BCR) for coordinating and conducting the microcensus survey in KongoCentral and Kinshasa provinces, for which this sample design framework was developed. We also acknowledge the help of Douglas R. Leasure, Maksym Bondarenko, Warren C. Jochem, and Heather R. Chamberlain at WorldPop, and Eric M. Weber at Oak Ridge National Laboratory.
The paper presents an innovative way to provide for an alternative to "bottomup" sampling for household surveys, by proposing a twostage "topdown" sampling technique that makes use of all the available geodatasets and that duly corrects as much as possible for possible errors.
I find the exercise generally very convincing and also welcome, especially in cases like the DRC where bottomup data are virtually absent.
I also find the paper particularly well developed, it also very clearly indicates the original data sources, allowing and almost inviting readers to engage in further inquiry or replication.
The only element I found lacking perhaps is a performance test of the new method compared to the sampling used in one or more existing surveys: would the "newly sampled" results, in the end, significantly differ from the results derived from the usual method? Such an exercise might give a good indication of the value/usefulness of this new sampling method.
Is the rationale for developing the new method (or application) clearly explained?
Yes
Is the description of the method technically sound?
Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?
Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?
Partly
Are sufficient details provided to allow replication of the method development and its use by others?
Yes
Reviewer Expertise:
economics, experience in analysing household surveys, particularly in the DRC.
I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.
This wellillustrated paper is proposing a gridbased sample design framework where contextual stratification and proportional to population size sampling are combined to achieve representative sampling for household surveys. This framework is targeted to low and middleincome countries and is illustrated with case study developed in two provinces located in the western part of the Democratic Republic of Congo.
I only have a few suggestions to improve the paper:
The spatial nature of the data could be incorporated into the classification algorithm using any type of spatiallyconstrained clustering; either by incorporating a measure of geographical proximity directly into the computation of the dissimilarity matrix (e.g., Oliver and Webster, 1989 ^{ 1 }) or the application of contiguityconstrained hierarchical agglomerative clustering approach (e.g., Recchia, 2010 ^{ 2 }). This should reduce the saltandpepper effect observed by the authors.
It might be worth exploring the imposition of a minimum separation distance between sampling units in order to ensure a spatially representative sample while satisfying the other constraints (contextual stratification, proportional to population size sampling).
The caption of Fig. 7 should be modified as follows: “the
Is the rationale for developing the new method (or application) clearly explained?
Yes
Is the description of the method technically sound?
Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?
Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?
Yes
Are sufficient details provided to allow replication of the method development and its use by others?
Yes
Reviewer Expertise:
geostatistics
I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.
A review of ‘A gridbased sample design framework for household surveys’, by Gianluca Boo et al.
The paper describes the set up and implementation of a household survey carried out in the western Kongo. It is a study of clear interest and relevance, although relatively simple in its different aspects. In fact, the introduction is promising much more than what is delivered in the paper. For instance, the role of geostatistics (hence of spatial dependencies) disappears shortly after equation 1. But what comes out of it in the end, i.e. the implementation, can certainly serve as a ‘framework’. Also the case study has its merits, and in particular figure 7 is convincing. The following changes should be made to make the manuscript acceptable for indexing:
Adjust the introduction such that it becomes more realistic and in line with the framework as presented.
The terms ‘frame’ and ‘framework’ need a definition.
Figure 8, at the left side, has a strange red line, increasing from about 0.18 until 0.35. This artifact of the software should be removed.
In the discussion section there is a mentioning of representative and nonrepresentative samples. This should be further considered, as so far the sampling is done mainly in a design based frame. There is literature, notably by Brus et al. that integrate designbased sampling with modelbased sampling. I would appreciate it if the authors could add a paragraph on this frame in the discussion section.
Also: much is
Is the rationale for developing the new method (or application) clearly explained?
Partly
Is the description of the method technically sound?
Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?
Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?
Yes
Are sufficient details provided to allow replication of the method development and its use by others?
Partly
Reviewer Expertise:
Spatial statistics, spatial sampling
I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.