You can see that the LHS chart is a much smoother curve (and better represents the classic S-curve of the normal distribution). The chart on the right uses Latin Hypercube Sampling. The chart on the left uses standard random number generation. Both include 100 samples (to start with). The simultaneous influence of several random quantities can be studied by the Latin hypercube sampling method (LHS). The charts below are sampling from a normal distribution. For complex models with many random variables, this means you can generate results in less time. In practice, this can be used to generate “better” simulation results, with lower standard error levels, with fewer trials. For two samples, it will divide the sample space in two, and generate one sample from each side. LHS will always return one sample less than 0 and one sample greater than 0. Although the probability of being positive or negative is equal, a true random number generator might return two samples less than 0, or two samples greater than 0. Latin Hypercube Sampling (LHS) is a method of sampling random numbers that attempts to distribute samples evenly over the sample space.Ī simple example: imagine you are generating exactly two samples from a normal distribution, with a mean of 0. ![]() To further the approach, a road network geospatial dataset can be included within spatial Geographic Information Systems (GIS) applications to access already produced points using a shortest-distance network method.Latin Hypercube Sampling How Latin Hypercube compares to standard random sampling By removing all locations in the initial instance from the DEM, the LHS model can be restricted to locations only with access from the adjacent road or trail. The ability to assist with the ease of access to sampling points will be in the future a contribution to the Latin Hypercube Sampling (LHS) approach. This seems a simple yet continuous issue to overcome for the scientific community and in particular, soils professionals. The lack of access can be a result of poor road access and/or difficult geographical conditions to navigate for field work individuals. Access to agricultural fields and adjacent land uses is often "pinned" as the greatest deterrent to performing soil sampling for both soil survey and soil attribute validation work. When working within the same spatial resolution for covariates, however only modifying the desired number of sampling points produced, the change of point location portrayed a strong geospatial relationship when using continuous data. This is sampling utility implementing Latin hypercube sampling from multivariate normal, uniform & empirical distribution. 1000 iterations was consistently a reasonable value used to produce sampling points that provided a good spatial representation of the environmental attributes. Some initial results of the work include using a 1000 iteration variable within the LHS model. Also, additional covariates were included in the Latin Hypercube Sampling approach which is categorical in nature such as external Surficial Geology data. The iterations within the LHS sampling were run at an optimal level so the LHS model provided a good spatial representation of the environmental attributes within the watershed. The spatial resolution of covariates included within the work ranged from 5 - 30 m. The range of specific points created in LHS included 50 - 200 depending on the size of the watershed and more importantly the number of soil types found within. These additional covariates often include but are not limited to Topographic Wetness Index (TWI), Length-Slope (LS) Factor, and Slope which are continuous data. These include a required Digital Elevation Model (DEM) and subsequent covariate datasets produced as a result of a Digital Terrain Analysis performed on the DEM. Secondary soil and environmental attributes are critical inputs that are required in the development of sampling points by LHS. This allowed for specific sets of LHS points to be produced to fulfil the needs of various partners from multiple projects working in the Ontario and Prince Edward Island provinces of Canada. The Latin Hypercube Sampling (LHS) approach to assist with Digital Soil Mapping has been developed for some time now, however the purpose of this work was to complement LHS with use of multiple spatial resolutions of covariate datasets and variability in the range of sampling points produced. AAFC - Agriculture and Agr-Food Canada, Ottawa, Canada. ![]() Sampsa Hamalainen, Xiaoyuan Geng, and Juanxia, He. Latin Hypercube Sampling (LHS) at variable resolutions for enhanced watershed scale Soil Sampling and Digital Soil Mapping.
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