Air temperature equation derived from sonic temperature and water vapor mixing ratio for turbulent airflow sampled through closed-path eddy-covariance flux systems

Air temperature (T) plays a fundamental role in many aspects of the flux exchanges between the atmosphere and ecosystems. Additionally, knowing where (in relation to other essential measurements) and at what frequency T must be measured is critical to accurately describing such exchanges. In closed-path eddy-covariance (CPEC) flux systems, T can be computed from the sonic temperature (Ts) and water vapor mixing ratio that are measured by the fast-response sensors of a three-dimensional sonic anemometer and infrared CO2–H2O analyzer, respectively. T is then computed by use of either T=Ts1+0.51q-1, where q is specific humidity, or T=Ts1+0.32e/P-1, where e is water vapor pressure and P is atmospheric pressure. Converting q and e/P into the same water vapor mixing ratio analytically reveals the difference between these two equations. This difference in a CPEC system could reach ±0.18 K, bringing an uncertainty into the accuracy of T from both equations and raising the question of which equation is better. To clarify the uncertainty and to answer this question, the derivation of T equations in terms of Ts and H2O-related variables is thoroughly studied. The two equations above were developed with approximations; therefore, neither of their accuracies was evaluated, nor was the question answered. Based on first principles, this study derives the T equation in terms of Ts and the water vapor molar mixing ratio (χH2O) without any assumption and approximation. Thus, this equation inherently lacks error, and the accuracy in T from this equation (equation-computed T) depends solely on the measurement accuracies of Ts and χH2O. Based on current specifications for Ts and χH2O in the CPEC300 series, and given their maximized measurement uncertainties, the accuracy in equation-computed T is specified within ±1.01 K. This accuracy uncertainty is propagated mainly (±1.00 K) from the uncertainty in Ts measurements and a little (±0.02 K) from the uncertainty in χH2O measurements. An improvement in measurement technologies, particularly for Ts, would be a key to narrowing this accuracy range. Under normal sensor and weather conditions, the specified accuracy range is overestimated, and actual accuracy is better. Equation-computed T has a frequency response equivalent to high-frequency Ts and is insensitive to solar contamination during measurements. Synchronized at a temporal scale of the measurement frequency and matched at a spatial scale of measurement volume with all aerodynamic and thermodynamic variables, this T has advanced merits in boundary-layer meteorology and applied meteorology.

Primality of closed path polyominoes

In this paper, we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walks, we classify all closed paths which do not contain zig-zag walks, and we give opportune toric representations of the associated ideals. To support the conjecture, we prove that having no zig-zag walks is a necessary and sufficient condition for the primality of the associated ideal of a closed path. Finally, we present some classes of prime polyominoes viewed as generalizations of closed paths.

Color2Hatch: conversion of color to hatching for low-cost printing

In this paper, we propose Color2Hatch, a decolorization method for business/presentation graphics. In Color2Hatch, each region represented as a closed path and uniformly colored in scalable vector graphics (SVG) is converted to a region hatched in black and white. From the characteristics of business graphics, the hatching patterns are designed to represent mainly the hue in the region; additionally, lightness and saturation can also be reflected. To discriminate subtle differences between colors, attached short line segments, zigzag lines, and wave lines are used in hatching by analogy to a clock. Compared with the existing decolorization methods, for example, grayscale conversion and texturing, our method is superior in the discrimination of regions, suitable for low-cost black and white printing that meets real-world needs.

Number of Distinct Homomorphic Images in Coset Diagrams

The representation of the action of PGL 2 , Z on F t ∪ ∞ in a graphical format is labeled as coset diagram. These finite graphs are acquired by the contraction of the circuits in infinite coset diagrams. A circuit in a coset diagram is a closed path of edges and triangles. If one vertex of the circuit is fixed by p q Δ 1 p q − 1 Δ 2 p q Δ 3 … p q − 1 Δ m ∈ PSL 2 , Z , then this circuit is titled to be a length- m circuit, denoted by Δ 1 , Δ 2 , Δ 3 , … , Δ m . In this manuscript, we consider a circuit Δ of length 6 as Δ 1 , Δ 2 , Δ 3 , Δ 4 , Δ 5 , Δ 6 with vertical axis of symmetry, that is, Δ 2 = Δ 6 , Δ 3 = Δ 5 . Let Γ 1 and Γ 2 be the homomorphic images of Δ acquired by contracting the vertices a , u and b , v , respectively, then it is not necessary that Γ 1 and Γ 2 are different. In this study, we will find the total number of distinct homomorphic images of Δ by contracting its all pairs of vertices with the condition Δ 1 > Δ 2 > Δ 3 > Δ 4 . The homomorphic images are obtained in this way having versatile applications in coding theory and cryptography. One can attain maximum nonlinearity factor using this in the encryption process.

The high-frequency response correction of eddy covariance fluxes – Part 2: An experimental approach for analysing noisy measurements of small fluxes

Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem–atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical or experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by Ibrom et al. (2007a) (PSAI07), in which the noise and H are fitted in different frequency ranges, and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA21). For CSA, we use a method utilizing the square root of the H with shifted vertical wind velocity time series via cross-covariance maximization (CSAH,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA21 and CSAH,sync successfully estimate the expected time constant regardless of the degree of attenuation and SNR. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias between 0.1 % and 1.4 %. PSAA21 showed almost no bias, while CSAH,sync showed bias of ±0.4 %. The accuracies of both PSA and CSA methods were not significantly affected by SNR level, instilling confidence in EC flux measurements and data processing in set-ups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA21 outperforms PSAI07, while when using cospectra the CSAH,sync approach provides accurate results. These findings are independent of the SNR value and attenuation level.

Air temperature equation derived from sonic temperature and water vapor mixing ratio for air flow sampled through closed-path eddy-covariance flux systems

Air temperar (T) plays a fundamental role in many aspects of the flux exchanges between the atmosphere and ecosystems. Additionally, it is critical to know where (in relation to other essential measurements) and at what frequency T must be measured to accurately describe such exchanges. In closed-path eddy-covariance (CPEC) flux systems, T can be computed from the sonic temperature (Ts) and water vapor mixing ratio that are measured by the fast-response senosrs of three-dimensional sonic anemometer and infrared gas analyzer, respectively. T then is computed by use of either T = Ts (1 + 0.51q)−1, where q is specific humidity, or T = Ts (1 + 0.32e / P)−1, where e is water vapor pressure and P is atmospheric pressure. Converting q and e / P into the same water vapor mixing ratio analytically reveals the difference between these two equations. This difference in a CPEC system could reach ±0.18 K, bringing an uncertainty into the accuracy of T from both equations and raises the question of which equation is better. To clarify the uncertainty and to answer this question, the derivation of T equations in terms of Ts and H2O-related variables is thoroughly studied. The two equations above were developed with approximations. Therefore, neither of their accuracies were evaluated, nor was the question answered. Based on the first principles, this study derives the T equation in terms of Ts and water vapor molar mixing ratio (χH2O) without any assumption and approximation. Thus, this equation itself does not have any error and the accuracy in T from this equation (equation-computed T) depends solely on the measurement accuracies of Ts and χH2O. Based on current specifications for Ts and χH2O in the CPEC300 series and given their maximized measurement uncertainties, the accuracy in equation-computed T is specified within ±1.01 K. This accuracy uncertainty is propagated mainly (±1.00 K) from the uncertainty in Ts measurements and little (±0.03 K) from the uncertainty in χH2O measurements. Apparently, the improvement on measurement technologies particularly for Ts would be a key to narrow this accuracy range. Under normal sensor and weather conditions, the specified accuracy is overestimated and actual accuracy is better. Equation-computed T has frequency response equivalent to high-frequency Ts and is insensitive to solar contamination during measurements. As synchronized at a temporal scale of measurement frequency and matched at a spatial scale of measurement volume with all aerodynamic and thermodynamic variables, this T has its advanced merits in boundary-layer meteorology and applied meteorology.

Revising the high frequency response correction of scalar fluxes measured by closed-path eddy covariance systems

<p>Eddy covariance (EC) scalar flux loss at high frequency is due to the incapability of the measurement system to detect small-scale variation of atmospheric turbulent signals. This systematic bias is particularly important for closed-path systems, and it is mainly related to inadequate sensor frequency response, sensor separation and the air sampling trough tubes and filters. Here, we investigate the limitations of current approaches, based on measured power spectra (PSA) or cospectra (CSA), to empirically estimated the spectral transfer function of the EC system needed for the frequency response correction of measured fluxes. We performed a systematic analysis by using EC data from a wetland and forest site for a wide range of attenuation levels and signal-to-noise ratio. We proposed a novel approach for PSA that uses simultaneously the noise and the turbulent signals present in the power spectrum, providing robust estimates of spectral transfer function for all conditions. We further theoretically derived a new transfer function to be used in the CSA approach which specifically accounts for the interaction between the low-pass filtering induced phase shift and the high frequency attenuation. We show that current CSA approaches neglect such effect, giving a non-negligible systematic bias to the estimated scalar fluxes from the studied sites. Based on these findings, we recommend that spectral correction methods, implemented in EC data processing algorithms, are revised accordingly.</p>

Improved eddy covariance flux based transpiration estimates at high relative humidity and comparison to sap flux

<p>Eddy covariance (EC) directly measures evapotranspiration (ET), which consists of transpiration and evaporation (E) from the soil and other surfaces. For process understanding it is pivotal to separate ET into its components. Yet, its computation is highly sensitive to the methodology used to estimate T. Among the multiple methods proposed in recent years, T has been estimated from EC via the Transpiration Estimation Algorithm (TEA, Nelson et al., 2020), and from the sap flux measurement network SAPFLUXNET (Poyatos et al., 2020). These methods are applicable to a large number of measurement sites worldwide, and can help constrain the global estimates of the ratio of T to ET, T/ET. While EC measures water and carbon fluxes across ecosystems globally, water vapor flux measurements can be underestimated at high relative humidity (Ibrom et al., 2007; Mammarella et al., 2009) causing errors in the measured ET and propagating into the predicted T.</p><p>Here we report a method to detect and correct the high relative humidity error caused by attenuation of high frequency in water vapor measurements of a closed-path EC system. Our results of the comparison between present water use efficiency (WUE) with previous TEA-based WUE show that the corrected WUE is lower at high relative humidity than that derived from previous TEA at the sub-daily scale. Besides, we compare the corrected T estimates from EC to concurrent SAPFLUXNET sites to show an improved relationship between sap flux and EC based T, T/ET, and WUE. Finally, we explore the main abiotic factors, such as vapor pressure deficit, air temperature, and precipitation, influencing WUE estimated from different T estimation methodologies. These results provide an improved data-driven approach to the ongoing research on ET partitioning and the factors influencing the WUE across ecosystems globally.</p><p> </p><p>Ibrom, A. et al. (2007) ‘Strong low-pass filtering effects on water vapour flux measurements with closed-path eddy correlation systems’, Agricultural and Forest Meteorology. doi.org/10.1016/j.agrformet.2007.07.007.</p><p>Mammarella, I. et al. (2009) ‘Relative humidity effect on the high-frequency attenuation of water vapor flux measured by a closed-path eddy covariance system’, Journal of Atmospheric and Oceanic Technology. doi.org/10.1175/2009JTECHA1179.1.</p><p>Nelson, J. A. et al. (2020) ‘Ecosystem transpiration and evaporation: Insights from three water flux partitioning methods across FLUXNET sites’, Global Change Biology. doi: 10.1111/gcb.15314.</p><p>Poyatos, R. et al. (2020) ‘Global transpiration data from sap flow measurements: the SAPFLUXNET database’, Earth System Science Data. doi:10.5194/essd-2020-227.</p>