MultiscaleDTM: An open-source R package for multiscale geomorphometric analysis

Digital terrain models (DTMs) are datasets containing altitude values above or below a reference level, such as a reference ellipsoid or a tidal datum over geographic space, often in the form of a regularly gridded raster. They can be used to calculate terrain attributes that describe the shape and characteristics of topographic surfaces. Calculating these terrain attributes often requires multiple software packages that can be expensive and specialized. We have created a free, open-source R package, MultiscaleDTM , that allows for the calculation of members from each of the five major thematic groups of terrain attributes: slope, aspect, curvature, relative position, and roughness, from a regularly gridded DTM. Furthermore, these attributes can be calculated at multiple spatial scales of analysis, a key feature that is missing from many other packages. Here, we demonstrate the functionality of the package and provide a simulation exploring the relationship between slope and roughness. When roughness measures do not account for slope, these attributes exhibit a strong positive correlation. To minimize this correlation, we propose a new roughness measure called adjusted standard deviation. In most scenarios tested, this measure produced the lowest rank correlation with slope out of all the roughness measures tested. Lastly, the simulation shows that some existing roughness measures from the literature that are supposed to be independent of slope can actually exhibit a strong inverse relationship with the slope in some cases.     

Kernel distributed residual function in a revised multiple order autoregressive model and its applications in hydrology

ABSTRACT

This paper describes a new approach to fill missing data in hydrologic series. Based on a multiple-order autoregressive model, our algorithm represents the random term with an empirical distribution function that includes different parameters for the low, medium and high ranges of the modelled hydrologic variable. The algorithm involves a corrective mechanism that preserves the original statistical distribution of the series that are filled, while also eliminating the possibility of obtaining negative values for low flows. The algorithm requires multiple correlated hydrologic time series with sufficient data to permit accurate calculation of their statistical properties. It ensures that both the original statistical dependence among the data series and the statistical distribution functions will be preserved after the missing data had been filled. The model has been tested using 15 streamflow series in the Upper Bow River watershed in Alberta, Canada.     

A simple method for effective multi-site generation of stochastic hydrologic time series

This paper presents an algorithm for generating stationary stochastic hydrologic time series at multiple sites. The ideas in this paper constitute a radical departure from commonly accepted methodologies. The approach relies on the recent advances in statistical science for simulating random variables with arbitrary marginal distributions and a given covariance structure, and on an algorithm for re-ordering the generated sub-sets of each synthetic year of data such that the annual auto-correlation of desired lag is maintained, along with the autocorrelations between the end of the preceding year and the beginning of the current year. The main features of the proposed algorithm are simplicity and ease of implementation. A numerical test is presented containing the generation of 1000 years of weekly stochastic series for four sites based on the 84 years of historical natural weekly flows from Southern Alberta in Canada.