Prediction Error Growth in a more Realistic Atmospheric Toy Model with Three Spatiotemporal Scales

This article studies the growth of the prediction error over lead time in a schematic model of atmospheric transport. Inspired by the Lorenz (2005) system, we mimic an atmospheric variable in 1 dimension, which can be decomposed into three spatiotemporal scales. We identify parameter values that provide spatiotemporal scaling and chaotic behavior. Instead of exponential growth of the forecast error over time, we observe a more complex behavior. We test a power law and the quadratic hypothesis for the scale dependent error growth. The power law is valid for the first days of the growth, and with an included saturation effect, we extend its validity to the entire period of growth. The theory explaining the parameters of the power law is confirmed. Although the quadratic hypothesis cannot be completely rejected and could serve as a first guess, the hypothesis’s parameters are not theoretically justifiable. In addition, we study the initial error growth for the ECMWF forecast system (500 hPa geopotential height) over the 1986 to 2011 period. For these data, it is impossible to assess which of the error growth descriptions is more appropriate, but the extended power law, which is theoretically substantiated and valid for the Lorenz system, provides an excellent fit to the average initial error growth of the ECMWF forecast system. Fitting the parameters, we conclude that there is an intrinsic limit of predictability after 22 days.

Optimally growing initial errors of El Niño events in the CESM

The optimally growing initial errors (OGEs) of El Niño events are found in the Community Earth System Model (CESM) by the conditional nonlinear optimal perturbation (CNOP) method. Based on the characteristics of low-dimensional attractors for ENSO (El Niño Southern Oscillation) systems, we apply singular vector decomposition (SVD) to reduce the dimensions of optimization problems and calculate the CNOP in a truncated phase space by the differential evolution (DE) algorithm. In the CESM, we obtain three types of OGEs of El Niño events with different intensities and diversities and call them type-1, type-2 and type-3 initial errors. Among them, the type-1 initial error is characterized by negative SSTA errors in the equatorial Pacific accompanied by a negative west–east slope of subsurface temperature from the subsurface to the surface in the equatorial central-eastern Pacific. The type-2 initial error is similar to the type-1 initial error but with the opposite sign. The type-3 initial error behaves as a basin-wide dipolar pattern of tropical sea temperature errors from the sea surface to the subsurface, with positive errors in the upper layers of the equatorial eastern Pacific and negative errors in the lower layers of the equatorial western Pacific. For the type-1 (type-2) initial error, the negative (positive) temperature errors in the eastern equatorial Pacific develop locally into a mature La Niña (El Niño)-like mode. For the type-3 initial error, the negative errors in the lower layers of the western equatorial Pacific propagate eastward with Kelvin waves and are intensified in the eastern equatorial Pacific. Although the type-1 and type-3 initial errors have different spatial patterns and dynamic growing mechanisms, both cause El Niño events to be underpredicted as neutral states or La Niña events. However, the type-2 initial error makes a moderate El Niño event to be predicted as an extremely strong event.

An empirical analysis of residential meter degradation in Gauteng Province, South Africa

Understanding the degradation rates of water meters assists utilities in making informed management decisions regarding meter replacement programmes and meter technology selection. This research evaluated the performance of 200 residential meters of two different technologies commonly used in Gauteng, South Africa, namely velocity meters and volumetric meters. This was done by conducting empirical meter testing in a verification laboratory and evaluating the degradation accuracy of each meter technology based on age and volume. Results indicate that velocity meters experience an accuracy degradation rate of approximately −1.13% per 1 000 kL of volume passed through the meter and an inferred initial error of −10.80%. Meter accuracy was not strongly related to age of the velocity meters tested. Volumetric meters did not exhibit a strong link with either age or accumulated volume, indicated by a loose grouping of results. These results indicate that accumulated volume of a velocity meter is a more reliable predictor of accuracy than age, and should be used when planning replacement strategies for velocity meters. Additionally, the lack of predictable degradation rates related to either age or accumulated volume for volumetric meters indicates that the accuracy of volumetric meters is primarily affected by other external factors, such as particulates or entrained air in the water network. These findings will assist utility managers in predicting the accuracy of their meter fleet and in making informed decisions regarding meter replacement.

Effect of East Gyro Drift and Initial Azimuth Error on the Compass Azimuth Alignment Convergence Time

The effect of gyro constant drift and initial azimuth error on the convergence time of compass azimuth is analyzed in this article. Using our designed compass azimuth alignment system, we obtain the responses of gyro constant drift and initial azimuth error in the frequency domain. The corresponding response function in the time domain is derived using the inverse Laplace transform, and its convergence time is then analyzed. The analysis results demonstrate that the convergence time of compass azimuth alignment is related to the second-order damping oscillation period, the gyro constant drift, and the initial azimuth error. In this study, the error band is set to 0.01° to determine convergence. When the gyro drift is less than 0.05°/h, compass azimuth alignment can converge within 0.9 damping oscillation periods. When the initial azimuth error is less than 5°, compass azimuth alignment can converge within 1.4 damping oscillation periods. When both conditions are met, the initial error plays a major role in convergence, while gyro drift has a smaller effect on convergence time. Finally, the validity of our method is verified using simulations.