Soil sampling design and sampling techniques for soil properties monitoring – common difficulties related to forest soils

Mathematical models and statistical analysis are key instruments in soil science scientific research as they can describe and/or predict the current state of a soil system. These tools allow us to explore the behavior of soil related processes and properties as well as to generate new hypotheses for future experimentation. A good model and analysis of soil properties variations, that permit us to extract suitable conclusions and estimating spatially correlated variables at unsampled locations, is clearly dependent on the amount and quality of data and of the robustness techniques and estimators. On the other hand, the quality of data is obviously dependent from a competent data collection procedure and from a capable laboratory analytical work. Following the standard soil sampling protocols available, soil samples should be collected according to key points such as a convenient spatial scale, landscape homogeneity (or non-homogeneity), land color, soil texture, land slope, land solar exposition. Obtaining good quality data from forest soils is predictably expensive as it is labor intensive and demands many manpower and equipment both in field work and in laboratory analysis. Also, the sampling collection scheme that should be used on a data collection procedure in forest field is not simple to design as the sampling strategies chosen are strongly dependent on soil taxonomy. In fact, a sampling grid will not be able to be followed if rocks at the predicted collecting depth are found, or no soil at all is found, or large trees bar the soil collection. Considering this, a proficient design of a soil data sampling campaign in forest field is not always a simple process and sometimes represents a truly huge challenge. In this work, we present some difficulties that have occurred during two experiments on forest soil that were conducted in order to study the spatial variation of some soil physical-chemical properties. Two different sampling protocols were considered for monitoring two types of forest soils located in NW Portugal: umbric regosol and lithosol. Two different equipments for sampling collection were also used: a manual auger and a shovel. Both scenarios were analyzed and the results achieved have allowed us to consider that monitoring forest soil in order to do some mathematical and statistical investigations needs a sampling procedure to data collection compatible to established protocols but a pre-defined grid assumption often fail when the variability of the soil property is not uniform in space. In this case, sampling grid should be conveniently adapted from one part of the landscape to another and this fact should be taken into consideration of a mathematical procedure.

Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.