Addition Of Metrics Research Articles

Comparison of TanDEM-X InSAR data and high-density ALS for the prediction of forest inventory attributes in plantation forests with steep terrain

Satellite interferometric synthetic aperture radar (InSAR) is emerging as a viable low-cost alternative method to airborne laser scanning (ALS) for forest inventory though little research has examined its efficacy for plantation forests located in temperate regions on steep terrain. InSAR and ALS data were collected from Geraldine Forest which is located on rolling to very steep topography in the southeast of New Zealand. These data were combined with an extensive set of plot measurements from which mean top height (H), basal area (G), stem density (N), and total stem volume (TSV) were calculated. InSAR and ALS-based Random Forest models of each variable were developed and compared.Using the ALS data as a reference, the mean RMSE of the InSAR DSM and DTM surfaces were, respectively, 4.58 and 8.09 m and these errors increased to mean values of, respectively, 6.02 and 10.17 m for slopes of 40–50°.ALS-based models were substantially more precise than those developed from InSAR for H (R2 = 0.86 vs. 0.60; RMSE% = 5.47 vs. 10.8%), G (R2 = 0.56 vs. 0.32; RMSE% = 21.5 vs. 30.4%), N (R2 = 0.47 vs. 0.09; RMSE% = 32.3 vs. 43.2%), and TSV (R2 = 0.70 vs. 0.41; RMSE% = 19.4 vs. 30.7%). The base metrics (i.e. ALS height and canopy cover variables) accounted for most of the variance in the ALS models with addition of further metrics providing ≤ 1% reduction in the RMSE%. Base metrics (i.e. InSAR observables) also accounted for most of the variation in InSAR models. Addition of metrics from a mixed Canopy Height Model (CHM), derived from InSAR Digital Surface Model (DSM) and ALS Digital Terrain Model (DTM), resulted in reductions in RMSE% of 3.1–5.4% for H, G, and TSV models with addition of textural metrics providing further reductions of 0.2–0.3% for H and G models. Addition of metrics from the radar CHM, derived from the InSAR DTM and DSM, and texture metrics reduced the RMSE% of the base model for N by 2.3% and 0.5%, respectively.The results were generated using a SAR image pair with a height of ambiguity (HOA) that was higher than ideal, which reduced the sensitivity of results to changes in terrain. Despite this limitation, and the steep slopes throughout the forest, the InSAR models described here had comparable precision to developed InSAR models for key inventory metrics from previous studies.

A class of solutions of Einstein's equations which admit a 3-parameter group of isometries

The Plebanski and Stachel and Goenner and Stachel lists of metrics which are solutions of Einstein's field equations, have two double eigenvalues and admit 3-parameter groups of isometries with 2-dimensional spacelike orbits are completed by the addition of metrics which result from the use of a more general metric form.