Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.

The frontal eye field sends predictively remapped visual signals to the superior colliculus

We perceive a stable visual world even though saccades often move our retinas. One way the brain may achieve a stable visual percept is through predictive remapping of visual receptive fields: just before a saccade, the receptive field of many neurons moves from its current location ("current receptive field") to the location it is expected to occupy after the saccade ("future receptive field"). Goldberg and colleagues found such remapping in cortical areas, e.g. in the frontal eye field (FEF), as well as in the intermediate layers of the superior colliculus (SC). In the present study we investigated the source of the SC's remapped visual signals. Do some of them come from the FEF? We identified FEF neurons that project to the SC using antidromic stimulation. For neurons with a visual response, we tested whether the receptive field shifted just prior to making a saccade. Saccadic amplitudes were chosen to be as small as possible while clearly separating the current and future receptive fields; they ranged from 5-30 deg. in amplitude and were directed contraversively. The saccadic target was a small red spot. We probed visual responsiveness at the current and future receptive field locations using a white spot flashed at various times before or after the saccade. Predictive remapping was indicated by a visual response to a probe flashed in the future receptive field just before the saccade began. We found that many FEF neurons projecting to the SC exhibited predictive remapping. Moreover, the remapping was as fast and strong as any previously reported for FEF or SC. It is clear, therefore, that remapped visual signals are sent from FEF to SC, providing direct evidence that the FEF is one source of the SC's remapped visual signals. Because remapping requires information about an imminent saccade, we hypothesize that remapping in FEF depends on corollary discharge signals such as those ascending from the SC through MD thalamus (Sommer and Wurtz 2002).

Reversible inactivation of macaque frontal eye field.

The macaque frontal eye field (FEF) is involved in the generation of saccadic eye movements and fixations. To better understand the role of the FEF, we reversibly inactivated a portion of it while a monkey made saccades and fixations in response to visual stimuli. Lidocaine was infused into a FEF and neural inactivation was monitored with a nearby microelectrode. We used two saccadic tasks. In the delay task, a target was presented and then extinguished, but the monkey was not allowed to make a saccade to its location until a cue to move was given. In the step task, the monkey was allowed to look at a target as soon as it appeared. During FEF inactivation, monkeys were severely impaired at making saccades to locations of extinguished contralateral targets in the delay task. They were similarly impaired at making saccades to locations of contralateral targets in the step task if the target was flashed for < or =100 ms, such that it was gone before the saccade was initiated. Deficits included increases in saccadic latency, increases in saccadic error, and increases in the frequency of trials in which a saccade was not made. We varied the initial fixation location and found that the impairment specifically affected contraversive saccades rather than affecting all saccades made into head-centered contralateral space. Monkeys were impaired only slightly at making saccades to contralateral targets in the step task if the target duration was 1000 ms, such that the target was present during the saccade: latency increased, but increases in saccadic error were mild and increases in the frequency of trials in which a saccade was not made were insignificant. During FEF inactivation there usually was a direct correlation between the latency and the error of saccades made in response to contralateral targets. In the delay task, FEF inactivation increased the frequency of making premature saccades to ipsilateral targets. FEF inactivation had inconsistent and mild effects on saccadic peak velocity. FEF inactivation caused impairments in the ability to fixate lights steadily in contralateral space. FEF inactivation always caused an ipsiversive deviation of the eyes in darkness. In summary, our results suggest that the FEF plays major roles in (1) generating contraversive saccades to locations of extinguished or flashed targets, (2) maintaining contralateral fixations, and (3) suppressing inappropriate ipsiversive saccades.

Grabbing Your Attention: The Impact of Finding a First Target in Multiple-Target Search

For over 50 years, the Satisfaction of Search effect, and more recently known as the Subsequent Search Miss (SSM) effect, has plagued the field of radiology. Defined as a decrease in additional target accuracy after detecting a prior target in a visual search, SSM errors are known to underlie both real-world search errors (e.g., a radiologist is more likely to miss a tumor if a different tumor was previously detected) and more simplified, lab-based search errors (e.g., an observer is more likely to miss a target ‘T’ if a different target ‘T’ was previously detected). Unfortunately, little was known about this phenomenon’s cognitive underpinnings and SSM errors have proven difficult to eliminate. However, more recently, experimental research has provided evidence for three different theories of SSM errors: the Satisfaction account, the Perceptual Set account, and the Resource Depletion account. A series of studies examined performance in a multiple-target visual search and aimed to provide support for the Resource Depletion account—a first target consumes cognitive resources leaving less available to process additional targets.

To assess a potential mechanism underlying SSM errors, eye movements were recorded in a multiple-target visual search and were used to explore whether a first target may result in an immediate decrease in second-target accuracy, which is known as an attentional blink. To determine whether other known attentional distractions amplified the effects of finding a first target has on second-target detection, distractors within the immediate vicinity of the targets (i.e., clutter) were measured and compared to accuracy for a second target. To better understand which characteristics of attention were impacted by detecting a first target, individual differences within four characteristics of attention were compared to second-target misses in a multiple-target visual search.

The results demonstrated that an attentional blink underlies SSM errors with a decrease in second-target accuracy from 135ms-405ms after detection or re-fixating a first target. The effects of clutter were exacerbated after finding a first target causing a greater decrease in second-target accuracy as clutter increased around a second-target. The attentional characteristics of modulation and vigilance were correlated with second- target misses and suggest that worse attentional modulation and vigilance are predictive of more second-target misses. Taken together, these result are used as the foundation to support a new theory of SSM errors, the Flux Capacitor theory. The Flux Capacitor theory predicts that once a target is found, it is maintained as an attentional template in working memory, which consumes attentional resources that could otherwise be used to detect additional targets. This theory not only proposes why attentional resources are consumed by a first target, but encompasses the research in support of all three SSM theories in an effort to establish a grand, unified theory of SSM errors.

Sensor Planning for Bayesian Nonparametric Target Modeling

Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.

Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.

Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with

little or no prior knowledge