Determination of Frequency for Remeasuring Ground and Vegetation Cover Factor Needed for Soil Erosion Modeling

Determining a remeasurement frequency of variables over time is required in monitoring environmental systems. This article demonstrates methods based on regression modeling and spatio-temporal variability to determine the time interval to remeasure the ground and vegetation cover factor on permanent plots for monitoring a soil erosion system. The spatio-temporal variability methods include use of historical data to predict semivariograms, modeling average temporal variability, and temporal interpolation by two-step kriging. The results show that for the cover factor, the relative errors of the prediction increase with an increased length of time interval between remeasurements when using the regression and semivariogram models. Given precision or accuracy requirements, appropriate time intervals can be determined. However, the remeasurement frequency also varies depending on the prediction interval time. As an alternative method, the range parameter of a semivariogram model can be used to quantify average temporal variability that approximates the maximum time interval between remeasurements. This method is simpler than regression and semivariogram modeling, but it requires a long-term dataset based on permanent plots. In addition, the temporal interpolation by two-step kriging is also used to determine the time interval. This method is applicable when remeasurements in time are not sufficient. If spatial and temporal remeasurements are sufficient, it can be expanded and applied to design spatial and temporal sampling simultaneously.     

Relating net nitrogen input in the Mississippi River basin to nitrate flux in the lower Mississippi River: a comparison of approaches

A quantitative understanding of the relationship between terrestrial N inputs and riverine N flux can help guide conservation, policy, and adaptive management efforts aimed at preserving or restoring water quality. The objective of this study was to compare recently published approaches for relating terrestrial N inputs to the Mississippi River basin (MRB) with measured nitrate flux in the lower Mississippi River. Nitrogen inputs to and outputs from the MRB (1951 to 1996) were estimated from state-level annual agricultural production statistics and NOy (inorganic oxides of N) deposition estimates for 20 states that comprise 90% of the MRB. A model with water yield and gross N inputs accounted for 85% of the variation in observed annual nitrate flux in the lower Mississippi River, from 1960 to 1998, but tended to underestimate high nitrate flux and overestimate low nitrate flux. A model that used water yield and net anthropogenic nitrogen inputs (NANI) accounted for 95% of the variation in riverine N flux. The NANI approach accounted for N harvested in crops and assumed that crop harvest in excess of the nutritional needs of the humans and livestock in the basin would be exported from the basin. The U.S. White House Committee on Natural Resources and Environment (CENR) developed a more comprehensive N budget that included estimates of ammonia volatilization, denitrification, and exchanges with soil organic matter. The residual N in the CENR budget was weakly and negatively correlated with observed riverine nitrate flux. The CENR estimates of soil N mineralization and immobilization suggested that there were large (2000 kg N ha-1) net losses of soil organic N between 1951 and 1996. When the CENR N budget was modified by assuming that soil organic N levels have been relatively constant after 1950, and ammonia volatilization losses are redeposited within the basin, the trend of residual N closely matched temporal variation in NANI and was positively correlated with riverine nitrate flux in the lower Mississippi River. Based on results from applying these three modeling approaches, we conclude that although the NANI approach does not address several processes that influence the N cycle, it appears to focus on the terms that can be estimated with reasonable certainty and that are correlated with riverine N flux.     

Sampling and Mapping a Soil Erosion Cover Factor by Integrating Stratification,Model Updating and Cokriging with Images

Cost-efficient sample designs for collection of ground data and accurate mapping of variables are required to monitor natural resources and environmental and ecological systems. In this study, a sample design and mapping method was developed by integrating stratification, model updating, and cokriging with Landsat Thematic Mapper (TM) imagery. This method is based on the spatial autocorrelation of variables and the spatial cross-correlation among them. It can lead to sample designs with variable grid spacing, where sampling distances between plots vary depending on spatial variability of the variables from location to location. This has potential cost-efficiencies in terms of sample design and mapping. This method is also applicable for mapping in the case in which no ground data can be collected in some parts of a study area because of the high cost. The method was validated in a case study in which a ground and vegetation cover factor was sampled and mapped for monitoring soil erosion. The results showed that when the sample obtained with three strata using the developed method was used for sampling and mapping the cover factor, the sampling cost was greatly decreased, although the error of the map was slightly increased compared to that without stratification; that is, the sample cost-efficiency quantified by the product of cost and error was greatly increased. The increase of cost-efficiency was more obvious when the cover factor values of the plots within the no-significant-change stratum were updated by a model developed using the previous observations instead of remeasuring them in the field.     

Uncertainty analysis of predicted disturbance from off-road vehicular traffic in complex landscapes at fort hood

The US Army Engineering Research Development Center (ERDC) uses a modified form of the Revised Universal Soil Loss Equation (RUSLE) to estimate spatially explicit rates of soil erosion by water across military training facilities. One modification involves the RUSLE support practice factor (P factor), which is used to account for the effect of disturbance by human activities on erosion rates. Since disturbance from off-road military vehicular traffic moving through complex landscapes varies spatially, a spatially explicit nonlinear regression model (disturbance model) is used to predict the distribution of P factor values across a training facility. This research analyzes the uncertainty in this model's disturbance predictions for the Fort Hood training facility in order to determine both the spatial distribution of prediction uncertainty and the contribution of different error sources to that uncertainty. This analysis shows that a three-category vegetation map used by the disturbance model was the greatest source of prediction uncertainty, especially for the map categories shrub and tree. In areas mapped as grass, modeling error (uncertainty associated with the model parameter estimates) was the largest uncertainty source. These results indicate that the use of a high-quality vegetation map that is periodically updated to reflect current vegetation distributions, would produce the greatest reductions in disturbance prediction uncertainty.     

The effect of model structure and data in modeling land conditions in disturbed complex ecosystems

Off-road vehicles increase soil erosion by reducing vegetation cover and other types of ground cover, and by changing the structure of soil. The investigation of the relationship between disturbance from off-road vehicles and the intensity of the activities that involve use of vehicles is essential for water and soil conservation and facility management. Models have been developed in a previous study to predict disturbance caused by off-road vehicles. However, the effect of data on model quality and model performance, and the appropriate structure of models have not been previously investigated. In order to improve the quality and performance of disturbance models, this study was designed to investigate the effects of model structure and data. The experiment considered and tested: (1) two measures of disturbance based on the Vegetation Cover Factor (C Factor) of the Revised Universal Soil Loss Equation (RUSLE) and Disturbance Intensity; (2) model structure using two modeling approaches; and (3) three subsets of data. The adjusted R-square and residuals from validation data are used to represent model quality and performance, respectively. Analysis of variance (ANOVA) is used to identify factors which have significant effects on model quality and performance. The results of the ANOVA show that subsets of data have significant effects on both model quality and performance for both measures of disturbance. The ANOVA also detected that the C Factor models have higher quality and performance than the Disturbance models. Although modeling approaches are not a significant factor based on the ANOVA tests, models containing interaction terms can increase the adjusted R-squares for nearly all tested conditions and the maximum improvement can reach 31%.     

Simulating Spatial Pattern and Dynamics of Military Training Impacts for Allocation of Land Repair Using Images

The land management of US Army installations requires information on land conditions and their history for planning future military training activities and allocation of land repair. There is thus a strong need for methodology development to estimate the land conditions and cumulative military training impacts for the purpose of repair and restoration. In this study, we simulated at Fort Riley, USA, spatial patterns and temporal dynamics of military training impacts on land conditions quantified as percent ground cover using an image-aided spatial conditional co-simulation algorithm. Moreover, we estimated the historical percent ground cover as a measure of the cumulative impacts, and then calculated the allocation of land repair and restoration based on both current and historical land conditions. In addition, we developed a loss function method for allocation of land repair and restoration. The results showed: (1) this co-simulation algorithm reproduced spatial and temporal variability of percent ground cover and provided estimates of uncertainties with the correlation coefficients and root mean square errors between the simulated and observed values varying from 0.63 to 0.88 and from 23% to 78%, respectively; (2) with and without the cumulative impacts, the obtained spatial patterns of the land repair categories were similar, but their land areas differed by 5% to 40% in some years; (3) the combination of the loss function with the co-simulation made it possible to estimate and computationally propagate the uncertainties of land conditions into the uncertainties of expected cost loss for misallocation of land repair and restoration; and (4) the loss function, physical threshold, and probability threshold methods led to similar spatial patterns and temporal dynamics of the land repair categories, however, the loss function increased the land area by 5% to 30% for intense and moderate repairs and decreased the area by 5% to 30% for no repairs and light repairs for most of the years. This approach provided the potential to improve and automate the existing land rehabilitation and maintenance (LRAM) system used for the land management of the U.S. Army installations, and it can be applied to the management of other civil lands and environments. In conclusion, this study overcame the important gaps that exist in the methodological development and application for simulating land conditions and cumulative impacts due to human activities, and also in the methods for the allocation of land for repair and restoration.     

Optimal spatial resolution for collection of ground data and multi-sensor image mapping of a soil erosion cover factor

Military training activities disturb ground and vegetation cover of landscapes and increases potential soil erosion. To monitor the dynamics of soil erosion, there is an important need for an optimal sampling design in which determining the optimal spatial resolutions in terms of size of sample plots used for the collection of ground data and the size of pixels for mapping. Given a sample size, an optimal spatial resolution should be cost-efficient in both sampling costs and map accuracy. This study presents a spatial variability-based method for that purpose and compared it with the traditional methods in a study area in which a soil erosion cover factor was sampled and mapped with multiple plot sizes and multi-sensor images. The results showed that the optimal spatial resolutions obtained using the spatial variability-based method were 12 and 20m for years 1999 and 2000, respectively, and were consistent with those using the traditional methods. Moreover, the most appropriate spatial resolutions using the high-resolution images were also consistent with those using ground sample data, which provides a potential to use the high-resolution images instead of ground data to determine the optimal spatial resolutions before sampling. The most appropriate spatial resolutions above were then verified in terms of cost-efficiency which was defined as the product of sampling cost and map error using ordinary kriging without images and sequential Gaussian co-simulation with images to generate maps.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Prediction and uncertainty source analysis of the spatial and temporal disturbance from off-road vehicular traffic in a complex ecosystem

Vehicle use during military training activities results in soil disturbance and vegetation loss. The capacity of lands to sustain training is a function of the sensitivity of lands to vehicle use and the pattern of land use. The sensitivity of land to vehicle use has been extensively studied. Less well understood are the spatial patterns of vehicle disturbance. Since disturbance from off-road vehicular traffic moving through complex landscapes varies spatially, a spatially explicit nonlinear regression model (disturbance model) was used to predict the pattern of vehicle disturbance across a training facility. An uncertainty analysis of the model predictions assessed the spatial distribution of prediction uncertainty and the contribution of different error sources to that uncertainty.For the most part, this analysis showed that mapping and modeling process errors contributed more than 95% of the total uncertainty of predicted disturbance, while satellite imagery error contributed less than 5% of the uncertainty. When the total uncertainty was larger than a threshold, modeling error contributed 60% to 90% of the prediction uncertainty. Otherwise, mapping error contributed about 10% to 50% of the total uncertainty. These uncertainty sources were further partitioned spatially based on other sources of uncertainties associated with vehicle moment, landscape characterization, satellite imagery, etc.