Improvements in the estimation of daily minimum air temperature in peninsular Spain using MODIS land surface temperature

Air temperature (T_a) is a key variable in many environmental risk models and plays a very important role in climate change research. In previous studies we developed models for estimating the daily maximum (T_max), mean (T_mean), and minimum air temperature (T_min) in peninsular Spain over cloud-free land areas using Moderate Resolution Imaging Spectroradiometer (MODIS) data. Those models were obtained empirically through linear regressions between daily T_a and daytime Terra-MODIS land surface temperature (LST), and then optimized by including spatio-temporal variables. The best T_mean and T_max models were satisfactory (coefficient of determination (R²) of 0.91–0.93; and residual standard error (RSE) of 1.88–2.25 K), but not the T_min models (R² = 0.80–0.81 and RSE = 2.83–3.00 K). In this article T_min models are improved using night-time Aqua LST instead of daytime Terra LST, and then refined including total precipitable water (W) retrieved from daytime Terra-MODIS data and the spatio-temporal variables curvature (c), longitude (λ), Julian day of the year (JD) and elevation (h). The best T_min models are based on the National Aeronautics and Space Administration (NASA) standard product MYD11 LST; and on the direct broadcast version of this product, the International MODIS/AIRS Processing Package (IMAPP) LST product. Models based on Sobrino’s LST1 algorithm were also tested, with worse results. The improved T_min models yield R² = 0.91–0.92 and RSE = 1.75 K and model validations obtain similar R² and RSE values, root mean square error of the differences (RMSD) of 1.87–1.88 K and bias = 0.11 K. The main advantage of the T_min models based on the IMAPP LST product is that they can be generated in nearly real-time using the MODIS direct broadcast system at the University of Oviedo.     

The effect of aerodynamic handlebars on oxygen consumption while cycling at a constant speed

Abstract

In this study, the oxygen consumption ([Vdot]O₂) of bicycling was measured at a fixed speed (40 km·h^?1on level terrain, with normal and aerodynamic handlebars using a Douglas bag collection system. Eleven elite (USCF category I or 2) men cyclists age 24 to 40 years (X¯=28·5, SD±4·6) performed four consecutive (two with each bar in alternating order) steady state rides at 40 km· h^?1over a 4 km flat course (same direction each trial). Expired gases were collected in a 1501 Douglas bag attached to a following vehicle during the last 45 s (approx. 0·5 km) of each trial. A repeated measures analysis of variance revealed a significant (p<0·02) handlebar effect. Specifically, [Vdot]O₂was 2% lower under the aerodynamic handlebar treatment (X¯=4·26, SD±0·36 1 min^?1when compared with that of the normal handlebar treatment (X¯=4·34, SD±0·35 1 min^?1The results of this study demonstrate that the reported aerodynamic advantage of the aerodynamic handlebars produces a small but significant reduction in the [Vdot]O₂of bicycling at 40 km·h^?1     

Estimating daily maximum air temperature from MODIS in British Columbia,Canada

Air temperature (T_a) is an important climatological variable for forest research and management. Due to the low density and uneven distribution of weather stations, traditional ground-based observations cannot accurately capture the spatial distribution of T_a, especially in mountainous areas with complex terrain and high local variability. In this paper, the daily maximum T_a in British Columbia, Canada was estimated by satellite remote sensing. Aqua MODIS (Moderate Resolution Imaging Spectroradiometer) data and meteorological data for the summer period (June to August) from 2003 to 2012 were collected to estimate T_a. Nine environmental variables (land surface temperature (LST), normalized difference vegetation index (NDVI), modified normalized difference water index (MNDWI), latitude, longitude, distance to ocean, altitude, albedo, and solar radiation) were selected as predictors. Analysis of the relationship between observed T_a and spatially averaged remotely sensed LST indicated that 7 × 7 pixel size was the optimal window size for statistical models estimating T_a from MODIS data. Two statistical methods (linear regression and random forest) were used to estimate maximum T_a, and their performances were validated with station-by-station cross-validation. Results indicated that the random forest model achieved better accuracy (mean absolute error, MAE = 2.02°C, R² = 0.74) than the linear regression model (MAE = 2.41°C, R² = 0.64). Based on the random forest model at 7 × 7 pixel size, daily maximum T_a at a resolution of 1 km in British Columbia in the summer of 2003–2012 was derived, and the spatial distribution of summer T_a in this area was discussed. The satisfactory results suggest that this modelling approach is appropriate for estimating air temperature in mountainous regions with complex terrain.     

Root-locus Equations of the Fourth Degree†

The paper is a study of the geometrical properties of root-loci for higher-order systems. Properties of general higher-plane algebraic curves are invoked to provide the broad framework of reference for systematic investigation of root-locus properties. Such an approach affords better integrated and more comprehensive understanding of the nature of the root-paths for higher-order systems.

The discussion is a composite one, encompassing all T(N,M) systems of the order N + M Δ h = 5 and 6, whose equations involve fourth-degree powers in ω: N and M denote the number of poles and zeros, respectively, of the open-loop function G(S) where, S = σ + jω.

The examples cited are illustrative of all significant features of higher-plane algebraic curves as manifest in root-locus shapes. Conditions for existence of such features in root-loci are examined and procedures for their identification and location established.     

Empirical models for estimating daily surface water vapour pressure,air temperature,and humidity using MODIS and spatiotemporal variables. Applications to peninsular Spain

In this article, we present empirical models for estimating daily surface water vapour pressure (e₀), air temperature (T_a), and relative humidity (RH) over cloud-free land areas in peninsular Spain using Moderate Resolution Imaging Spectroradiometer (MODIS) and spatiotemporal variables. The models were obtained and validated using daily mean, maximum, and minimum e₀, T_a, and RH data (year 2010) from 331 ground-level meteorological stations and the diurnal Terra-MODIS data in peninsular Spain, but the methodology can easily be extrapolated and used to obtain algorithms for other regions around the world. The best e₀ models are based on total precipitable water (W) estimations obtained by MOD05 or IMAPP WVNIR products and the spatiotemporal variables of longitude (λ), distance to the coast (d_coast), and Julian day (JD). Other models based on Sobrino’s W algorithm or on Recondo’s e₀ algorithm for Asturias (in northern Spain) were also tested. The best T_a models are based on land surface temperature (LST) obtained by the MOD11 LST or IMAPP LST products and on other remote-sensing variables, such as W and the normalized difference vegetation index (NDVI), and the spatiotemporal variables λ, JD, and height (h). Models based on Sobrino’s LST algorithms were also tested. RH can be derived directly from e₀ and T_a or from models similar to those used to obtain e₀ and T_a. Models based on the NASA standard products MOD05 and MOD11 LST are slightly better than those based on IMAPP products, but the advantage of IMAPP products for our purposes is that they can be generated in almost real time from the data obtained by the MODIS antenna at the University of Oviedo. IMAPP models obtain the following: R² = 0.83-0.79-0.70 and RSE = 1.62-1.59-1.76 hPa for e_0mean, e_0max, and e_0min; and R² = 0.91-0.91-0.80 and RSE = 1.96-2.25-3.00 K for T_mean, T_max, and T_min. Worse results are obtained for RH: R² = 0.49-0.39 and RSE = 7.21-9.75% for RH_min and RH_mean, with no correlation found for RH_max. Model validations yield R² and RSE values similar to those obtained in the models, with an RMSD = 1.86-1.99-2.21 hPa for e_0mean, e_0max, and e_0min; an RMSD = 2.05-2.40-2.95 K for T_mean, T_max, and T_min; and RMSD = 8-11% for RH_min and RH_mean. The bias is small in all cases: <0.2 hPa for e₀, ≤0.1 K for T_a, and ≤ |1|% for RH. From the results of this article, we propose substituting the traditionally used RH variable with the e₀ variable to be used as meteorological variable in environmental risk models such as, for example, fire risk models.     

Optimum Control of a Certain Class of Servomechanism†

Linear control systems governed by the vector matrix differential equation x = A x + B u have been considered. It has been shown how to find the optimum control u so that the system, starting from an initial position x(0), is steered to a state specifying the first p coordinates of the system in time t _o fixed in advance, the values attained by the (n—p) coordinates being immaterial, where n is the dimension of the system. The optimization considered here is with regard to the norm of u supposed to belong to L _m E _r space.     

Regulator problem for linear discrete-time systems with non-symmetrical constrained control

The regulator problem is studied for linear discrete-time systems with non-symmetrical constrained control, i.e. systems described by the state equation x _k+1 = Ax _k + Bu _k, where u _k ? Ω, and u _k = Fx _k. Necessary and sufficient conditions allowing us to obtain the largest non-symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established. The case of symmetrically constrained control is obtained as a particular case.     

Positional solutions of Hamilton-Jacobi equations in control problems for discrete-continuous systems

We develop a canonical global optimality theory based on operating with the set of solutions for the Hamilton-Jacobi inequalities that parametrically depend on the initial (or final) position. These solutions, called positional L-functions (of Lyapunov type), naturally arise in the studies of control problems for discrete-continuous (hybrid, impulse) systems; an important prototype of such problems are classical optimal control problems with general end constraints on the trajectory. We analyze sufficient optimality conditions with this new class of L-functions and invert the maximum principle into a sufficient condition for nonlinear problems of optimal impulse control.     

A multiprocessor based heuristic for multi-dimensional multiple-choice knapsack problem

This paper presents a multiprocessor based heuristic algorithm for the Multi-dimensional Multiple Choice Knapsack Problem (MMKP). MMKP is a variant of the classical 0–1 knapsack problem, where items having a value and a number of resource requirements are divided into groups. Exactly one item has to be picked up from each group to achieve a maximum total value without exceeding the resource constraint of each type. MMKP has many real world applications including admission control in adaptive multimedia server system. Exact solution to this problem is NP-Hard, and hence is not feasible for real time applications like admission control. Therefore, heuristic solutions have been developed to solve the MMKP. M-HEU is one such heuristic, which solves the MMKP achieving a reasonable percentage of optimality. In this paper, we present a multiprocessor algorithm based on M-HEU, which runs in O(T/p+s(p)) time, where T is the time required by the algorithm using single processor, p is the number of processors and s(p), a function of p, is the synchronization overhead. We also present the worst-case analysis of our algorithm, the computation of the optimal number of processors as well as the lower bound of the total value that can be achieved by the heuristic.     

The reliability of the Extra Load Index as a measure of relative load carriage economy

Abstract

The aim of this study was to measure the reliability of the extra load index (ELI) as a method for assessing relative load carriage economy. Seventeen volunteers (12 males, 5 females) performed walking trials at 3 km·h^?1, 6 km·h^?1 and a self-selected speed. Trial conditions were repeated 7 days later to assess test–retest reliability. Trials involved four 4-minute periods of walking, each separated by 5 min of rest. The initial stage was performed unloaded followed in a randomised order by a second unloaded period and walking with backpacks of 7 and 20 kg. Results show ELI values did not differ significantly between trials for any of the speeds (p = 0.46) with either of the additional loads (p = 0.297). The systematic bias, limits of agreement and coefficients of variation were small in all trial conditions. We conclude the ELI appears to be a reliable measure of relative load carriage economy.

Practitioner Summary: This paper demonstrates that the ELI is a reliable measure of load carriage economy at a range of walking speeds with both a light and heavy load. The ELI, therefore, represents a useful tool for comparing the relative economy associated with different load carriage systems.     

An important property of non-minimum-phase multiple-input-multiple-output feedback systems

The non-minimum-phase (NMP( property is easily determined from the requirement that the plant input is bounded. In the single-input-single-output (SISO) system, a right-half-plane (RHP) plant zero at s = b constrains the system transfer function to have a zero at b. Also, the available feedback benefits are significantly restricted. The n × n multiple-input-multiple-output (MIMO) system is NMP if the plant determinant δhas any RHP zeros, say at plant transfer matrix and T = [t_ij is the closed-loop system transfer matrix. It has been thought that all n²t_ij (and the n₂ plant disturbance response function rfj), must suffer from the NMP liability in their feedback properties. It is shown that only one row of need so suffer, with a any fixed integer in [1, n].The remaining n(n — 1) elements can be completely free of the NMP liability. A mathematically rigorous synthesis technique previously developed for MP systems is shown to be well suited for precise numerical design for such NMP MIMO plants with significant uncertainties. In this technique, the MIMO design problem is converted into a number of equivalent SISO problems. An example involving disturbance attenuation in a highly uncertain 2×2 NMP plant is included.     

Fliess operators on Lp spaces: convergence and continuity

Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coefficients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some fixed upperbound. In some emerging applications, however, it is more natural to consider other classes of inputs. In this paper, L_p function spaces are considered. In particular, it is shown that the classic growth conditions also provide sufficient conditions for convergence and continuity when the admissible inputs are from a ball in L_p[t₀,t₀+T], where T is bounded and p1. In addition, stronger global growth conditions are given that apply even for the case where T is unbounded. When the coefficients of a Fliess operator have a state space representation, it is shown that the state space model will always locally realize the corresponding input–output map on L_p[t₀,t₀+T] for sufficiently small T>0. If certain well-posedness conditions are satisfied then the state space model will globally realized the input–output mapping for unbounded T when the coefficients satisfy the global growth condition.     

Optimal control of the behavior of solutions of an initial boundary value problem simulating rotation of a solid with an elastic rod

The paper discusses an initial boundary value problem simulating the rotation of a discretecontinuum mechanical system, which consists of a solid and rigidly connected elastic rod. For the initial boundary problem, the concept of the solution is determined and its existence, uniqueness, and continuous dependence on the initial conditions and parameters of the boundary problem are determined. The following control problems are solved: the problem of conversion of the solution from the initial phase state to the final one at a given time with the minimum of the norm of the control function in space L _∞(0, T) and the problem of the response rate under limitation of the norm of the control function in the specified space. The maximum principle is formulated, and an algorithm for optimal control of the simulation is proposed. The problem of moments is used as the investigation method.     

Lifting of trajectories of control systems related by smooth mappings

Given a pair of control systems and whose state spaces are differentiable manifolds M and N, respectively, we focus on situations where there exists a mapping that induces some type of correspondence between the trajectories of the systems. An important instance of this situation occurs when f is a complex system (for example, one having many states), h is a subsystem of f (presumably, with fewer states and a simpler structure than f), and Φ is a mapping from the full state space M to a reduced state space N. Some recent research has concentrated on the concept of Φ-related systems, where it is required that Φ send trajectories of f onto trajectories of h. Here we approach the problem from a different direction and ask under what conditions trajectories of the subsystem h can be lifted to trajectories of the full system f. We provide computable sufficient conditions for the local and global lifting of trajectories from N to M. Connections between the lifting problem and the problem of global (f,g)-invariance are also discussed briefly.     

The energy demands of portable gas analysis system carriage during walking and running

The aim of this study was to evaluate the carriage of a portable gas analyser during prolonged treadmill exercise at a variety of speeds. Ten male participants completed six trials at different speeds (4, 8 and 12 km h^? 1) for 40 min whilst wearing the analyser (P) or where the analyser was externally supported (L). Throughout each trial, respiratory gases, heart rate (HR), perceptions of effort and energy expenditure (EE) were measured. Significantly higher EE occurred during P12 (p = 0.01) than during L12 (855.3 ± 104.3; CI = 780.7–930.0 and 801.5 ± 82.2 kcal; CI = 742.7–860.3 kcal, respectively), but not at the other speeds; despite this, perceptions of effort and HR responses were unaffected. This additional EE is likely caused by alterations to posture which increase oxygen demand. The use of such systems is unlikely to affect low-intensity tasks, but researchers should use caution when interpreting data, particularly when exercise duration exceeds 30 min and laboratory-based analysers should be used where possible.     

Sub-pixel evaluation of sea ice roughness using AMSR-E data

The rapidly changing sea ice regime in the Arctic has necessitated an evaluation of sea ice roughness at smaller scales than those provided by satellites. In this article, we evaluate sub-pixel (<5.4 km) sea ice roughness using AMSR-E brightness temperature (T_b) 89 GHz data and in situ physical roughness data acquired using a helicopter-based laser system in the southern Beaufort Sea during April–June of 2008. The analysis shows a statistically significant correlation (r² = 0.61, P-value < 0.05, regression line slope = –79.93) of T_b at horizontal polarization (H-pol) decreasing with increasing root mean square (RMS) heights. These results suggest that 89 H-pol is more sensitive (than vertical polarization (V-pol)) to the changes in physical roughness. The temporal evolution in AMSR-E T_b values at 89 H-pol and 89 V-pol shows a decrease from April to June. We conclude that solely the AMSR-E T_b at 5.4 km is insufficient to fully account for the changes occurring in the dielectric properties and surface roughness of sea ice at sub-pixel level of 1–4 km during April–June.     

Estimation of air temperature and reference evapotranspiration using MODIS land surface temperature over Greece

Moderate Resolution Imaging Spectroradiometer (MODIS), land surface temperature data, during daytime (LST_day) or night-time (LST_night), were employed for predicting maximum (T_max) or minimum (T_min) air temperature measured at ground stations, respectively, in order to be used as alternative inputs in minimum data-based reference evapotranspiration (ET) models in 28 stations in Greece during the growing season (May–October). The deviations between daily LST_night and T_min were found to be small, but they were greater between LST_day and T_max. Furthermore, the temperature vegetation index (TVX) method was employed for achieving more accurate T_max values from LST_day, after determining the normalized difference vegetation index of a full canopy (NDVI_max). The TVX method was validated on ‘temporal’ basis, but when the method was tested spatially, the improvement on the T_max estimates from LST_day was not encouraging, for being used operationally over Greece. Thus, LST_day or LST_night MODIS data were used as inputs in three ET models [Hargreaves–Samani, Droogers–Allen, and Reference Evapotranspiration Model for Complex Terrains (REMCT)] and their estimations, as compared with ground-based Penman–Monteith estimates, indicated that the REMCT model achieved the most accurate ET predictions (r = 0.93, mean bias error = 0.44 mm day^–1 and root mean square error = 0.74 mm day^–1), which can allow the spatial analysis of ET at higher spatial resolutions in areas with lack of ground temperature data.     

Modelling above-ground live trees biomass and carbon stock estimation of tropical lowland Dipterocarp forest: integration of field-based and remotely sensed estimates

Carbon exists as carbon dioxide (CO₂) which is one of the greenhouse gases (GHG) in the atmosphere that has an enormous influence on the impact of climate change. Therefore, the forest plays an undeniably pivotal role as a carbon sink, which absorbs carbon dioxide from the atmosphere. This research aims to develop allometric equation for above-ground live tree biomass (AGB) by combining field-based, combination of field data observation and technology (WV-3 and light detection and ranging (lidar)) and by using only technology derivation. The independent predictor was induced based on the literature review and theories, and an ordinary least square (OLS) estimator will be used to develop multiple linear regression models. During model selection, the best model fit was selected by calculating statistical parameters such as residual of the coefficient of determination (R²) selection methods, adjusted coefficient of determination (R²_adj), root mean square error, graphical analysis of the residuals, standard error (S_yx), and Akaike information criterion. An allometric equation of this research was developed using carbon stocks as dependent variables, and four of the predictor’s variables: diameter at breast height (DBH); total height observed at field (h_F); total height derived from airborne lidar (h_L); and morphometric variables of the crown projection area (CPA). Based on the statistic indicators, the most suitable model is Model 1, ln (S_c) = – β₀ + β₁ ln (h_L) + β₂ ln (DBH) + β₃ ln (CPA) for the combination of remote sensing and field observation; ln (S_c) = – β₀ + β₁ ln (h_F) + β₂ ln (DBH) for field inventory only; and ln (S_c) = – β₀ + β₁ ln (h_L) + β₂ ln (CPA) for remote sensing only. This model is reliable in forest management to estimate the AGB and carbon stock estimation using a selection of variable sources.     

Mappings of linear vector spaces induced by a transformation matrix and its applications†

The projections of a vector Ax along a certain orthonormal basis are chosen as the n components of a vector ρ. As the vector x sweeps the n–dimensional space, the locus of the point vector ρ is a closed surface, called the ρ locus. Some of the properties of the ρ locus are similar to those of the eigenvalues of the A matrix. These properties are exploited in the analysis of the unforced, linear time-invariant, dynamical system given by [xdot] = Ax and for the forced systems of the [xdot] = Ax + Bu, where u represents an impulse, step, ramp or sinusoidal input.