Reduced-Rank Sigma-Point Kalman Filter and Its Application in ENSO Model

The main goal of my research was to develop a practical scheme for the sigma-point Kalman filter (SPKF) for its application in a realistic climate model. Large computational expense has been an obstacle to applying the SPKF to a high-dimensional system. I addressed this issue by developing an advanced SPKF data-assimilation system. My work also addressed several other factors related to the practical implementation of SPKF. The main objectives of this research were to: (i) investigate two methods to construct a reduced-rank sigma-point unscented Kalman filers (RRSPUKF) (ii) propose a localization scheme for the SPKF and (iii) implement RRSPUKF in a realistic climate model. I present two methods to approximate the error covariance by a reduced-rank approximation. In the first method, truncated singular-value decomposition (TSVD) is applied on the error-covariance matrix calculated in the data space (RRSPUKF(D)) while in the second method TSVD is applied on the error-covariance matrix calculated in the ensemble space (RRSPUKF(E)). The new algorithms are first tested on the Lorenz-96 model, a one-dimensional atmospheric '~toy' model. The performance of both rank-reduction methods are close to that of the full-rank SPKF. I propose a localization method for RRSPUKF(E). The results from numerical experiments on the Lorenz-96 model showed that when the localization and inflation were implemented, the optimal estimate was achieved with a finite number of sigma points. The realistic model I used in this study was the Zebiak-Cane (ZC) model, an intermediate complexity coupled El Niño Southern Oscillation (ENSO) prediction model. The RRSPUKFs are implemented for the ZC model with the assimilation of sea surface temperature anomalies. The results showed that both RRSPUKF(D and E) were able to correctly analyze the phase and intensity of all major ENSO events during the study period with relatively similar estimation accuracy. Furthermore, the RRSPUKF was compared against ensemble square-root filter (EnSR

This paper considers implications of different forms of the ensemble transformation in the ensemble square root filters (ESRFs) for the performance of ESRF-based data assimilation systems. It highlights the importance of using mean-preserving solutions for the ensemble transform matrix (ETM). The paper shows that an arbitrary mean-preserving ETM can be represented as a product of the symmetric solution and an orthonormal mean-preserving matrix. The paper also introduces a new flavor of ESRF, referred to as ESRF with mean-preserving random rotations. To investigate the performance of different solutions for the ETM in ESRFs, experiments with two small models are conducted. In these experiments, the performances of two mean-preserving solutions, two non-mean-preserving solutions, and a traditional ensemble Kalman filter with perturbed observations are compared. The experiments show a significantly better performance of the mean-preserving solutions for the ETM in ESRFs compared to non-mean-preserving solutions. They also show that applying the mean-preserving random rotations prevents the buildup of ensemble outliers in ESRF-based data assimilation systems.

Using radar observations, the performances of the ensemble square root filter (EnSRF) and an indirect three-dimensional variational (3DVar) data assimilation method were compared for a mesoscale convective system (MCS) that occurred in the Front Range of the Rocky Mountains, Colorado (USA). The results showed that the root mean square innovations (RMSIs) of EnSRF were lower than 3DVar for radar reflectivity and radial velocity and that the spread of EnSRF was generally consistent with its RMSIs. EnSRF substantially improved the analysis of the MCS compared with an experiment without radar data assimilation, and it produced a slight but noticeable improvement over 3DVar in terms of both coverage and intensity. Forecast results initiated from the final analysis revealed that EnSRF generally produced the best prediction of the MCS, with improved quantitative reflectivity and precipitation forecast skills. EnSRF also demonstrated better performance than 3DVar in the prediction of neighborhood probability for reflectivity at thresholds of 20 and 35 dBZ, which better matched the observed radar reflectivity in terms of both shape and extension. Additionally, the humidity, temperature, and wind fields were also improved by EnSRF; the largest error reduction was found in the water vapor field near the surface and at upper levels.

A hybrid parallel scheme for the ensemble square root filter (EnSRF) suitable for parallel assimilation of multiscale observations, including those from dense observational networks such as those of radar, is developed based on the domain decomposition strategy. The scheme handles internode communication through a message passing interface (MPI) and the communication within shared-memory nodes via Open Multiprocessing (OpenMP) threads. It also supports pure MPI and pure OpenMP modes. The parallel framework can accommodate high-volume remote-sensed radar (or satellite) observations as well as conventional observations that usually have larger covariance localization radii. The performance of the parallel algorithm has been tested with simulated and real radar data. The parallel program shows good scalability in pure MPI and hybrid MPI–OpenMP modes, while pure OpenMP runs exhibit limited scalability on a symmetric shared-memory system. It is found that in MPI mode, better parallel performance is achieved with domain decomposition configurations in which the leading dimension of the state variable arrays is larger, because this configuration allows for more efficient memory access. Given a fixed amount of computing resources, the hybrid parallel mode is preferred to pure MPI mode on supercomputers with nodes containing shared-memory cores. The overall performance is also affected by factors such as the cache size, memory bandwidth, and the networking topology. Tests with a real data case with a large number of radars confirm that the parallel data assimilation can be done on a multicore supercomputer with a significant speedup compared to the serial data assimilation algorithm.

While significant improvements have been made in understanding how the El Nino–Southern Oscillation (ENSO) impacts both North American and Asian climate, its relationship with the North Atlantic Oscillation (NAO) remains less clear. Observations indicate that ENSO exhibits a highly complex relationship with the NAO-associated atmospheric circulation. One critical contribution to this ambiguous ENSO/NAO relationship originates from ENSO’s diversity in its spatial structure. In general, both eastern (EP) and central Pacific (CP) El Nino events tend to be accompanied by a negative NAO-like atmospheric response. However, for two different types of La Nina the NAO response is almost opposite. Thus, the NAO responses for the CP ENSO are mostly linear, while nonlinear NAO responses dominate for the EP ENSO. These contrasting extra-tropical atmospheric responses are mainly attributed to nonlinear air-sea interactions in the tropical eastern Pacific. The local atmospheric response to the CP ENSO sea surface temperature (SST) anomalies is highly linear since the air-sea action center is located within the Pacific warm pool, characterized by relatively high climatological SSTs. In contrast, the EP ENSO SST anomalies are located in an area of relatively low climatological SSTs in the eastern equatorial Pacific. Here only sufficiently high positive SST anomalies during EP El Nino events are able to overcome the SST threshold for deep convection, while hardly any anomalous convection is associated with EP La Nina SSTs that are below this threshold. This ENSO/NAO relationship has important implications for NAO seasonal prediction and places a higher requirement on models in reproducing the full diversity of ENSO.

Sea surface temperature and rainfall anomaly over the Bay of Bengal during the El Niño-Southern Oscillation and the extreme Indian Ocean Dipole events between 2002 and 2016

In this study, a deterministic algorithm named Ensemble Square Root Filter (EnSRF), an algorithm significantly improved from the Ensemble Kalman Filter (EnKF), was used to integrate remotely sensed information (ASD spectral data, HJ-1 A/B CCD and Landsat-5 TM data) with a wheat (Triticum aestivum L.) growth model (WheatGrow). The analyzed values of model variables, leaf area index (LAI) and leaf nitrogen accumulation (LNA), were calculated based on EnSRF without perturbed measurements. Independent datasets were used to test EnSRF and the root mean square error (RMSE) values were 0.81 and 0.82 g m-2, with relative error (RE) values of 0.15 and 0.13, for LAI and LNA, respectively. RMSE values for LAI and LNA were 1.39 and 1.70 g m-2, respectively (RE, 0.28 and 0.34) based on EnKF, 1.17 and 1.80 g m-2 (RE, 0.24 and 0.35), respectively, based on the WheatGrow model alone, and 0.97 and 1.25 g m-2 (RE, 0.21 and 0.24), respectively, based on the remote sensing models. These results indicated that the LAI and LNA values based on EnSRF matched the measured values well compared with the EnKF, WheatGrow and remote sensing models. In addition, the predicted results are consistent with the temporal and spatial distribution of winter wheat growth status and grain yields in the study area, with RE values of less than 0.2 and 0.1 for LAI and LNA, respectively. These results provide an important approach for simulating winter wheat growth status based on combining remote sensing and crop growth models.

Remote sensing data play a critical role in improving numerical weather prediction (NWP). However, the physical principles of radiation dictate that data voids frequently exist in physical space (e.g., subcloud area for satellite infrared radiance or no-precipitation region for radar reflectivity). Such data gaps impair the accuracy of initial conditions derived from data assimilation (DA), which has a negative impact on NWP. We use the barotropic vorticity equation to demonstrate the potential of deep learning augmented data assimilation (DDA), which involves reconstructing spatially complete pseudo-observation fields from incomplete observations and using them for DA. By training a convolutional autoencoder (CAE) with a long simulation at a coarse “forecast” resolution (T63), we obtained a deep learning approximation of the “reconstruction operator,” which maps spatially incomplete observations to a model state with full spatial coverage and resolution. The CAE was applied to an incomplete streamfunction observation (∼30% missing) from a high-resolution benchmark simulation and demonstrated satisfactory reconstruction performance, even when only very sparse (1/16 of T63 grid density) observations were used as input. When only spatially incomplete observations are used, the analysis fields obtained from ensemble square root filter (EnSRF) assimilation exhibit significant error. However, in DDA, when EnSRF takes in the combined data from the incomplete observations and CAE reconstruction, analysis error reduces significantly. Such gains are more pronounced with sparse observation and small ensemble size because the DDA analysis is much less sensitive to observation density and ensemble size than the conventional DA analysis, which is based solely on incomplete observations. Significance Statement Data assimilation plays a critical role in improving the skills of modern numerical weather prediction by establishing accurate initial conditions. However, unobservable regions are common in observation data, particularly those derived from remote sensing. The nonlinear relationship between data from observable regions and the physical state of unobservable regions may impede DA efficiency. As a result, we propose that deep learning be used to improve data assimilation in such cases by reconstructing a spatially complete first guess of the physical state with deep learning and then applying data assimilation to the reconstructed field. Such deep learning augmentation is found effective in improving the accuracy of data assimilation, especially for sparse observation and small ensemble size.

Anomalous seasonal patterns of precipitation variability over South America (SA) associated with El Niño‐Southern Oscillation (ENSO) and non‐ENSO (residual) conditions were assessed during 1951–2016. Patterns were obtained from empirical orthogonal functions analysis of total and residual precipitation seasonal anomalies. In austral spring and summer, precipitation variability is dominated by a dipolar anomaly mode with a centre extending from northwestern to northeastern SA and another in central‐eastern Brazil and part of southeastern SA (SESA) during spring, and a centre in northwestern SA and another extending from northeastern SA to central and eastern Brazil and central SESA, during summer. These modes are associated with ENSO to a greater extent during spring than summer. In summer, there is a strong association of the dipolar precipitation pattern with sea surface temperature (SST) anomalies on the east coast of Brazil, which indicates local influence. In austral fall, SST anomalies in the tropical South Atlantic relate to precipitation anomalies in northeast SA, and those in the tropical north Atlantic (TNA) to precipitation anomalies in northwestern SA, through the intertropical convergence zone anomalous position modulated by SST anomalies. In this same condition, the ENSO acts only to intensify or weaken the dominant precipitation pattern, depending on its phase, mainly over SESA. In contrast, the second variability mode in fall is characterized by positive SST anomalies in the Indian Ocean and equatorial and southern Atlantic Ocean and negative in the TNA. The importance of ENSO and the Indian Ocean in the characterization of the SST dipole in the tropical Atlantic explains the main changes in precipitation patterns over northeastern Brazil not been discussed in previous studies.

El Niño Southern Oscillation (ENSO) impacts the supply of and, to some extent, the demand for primary commodities. But what are the consequences of ENSO shocks for these commodity price dynamics? I consider monthly series of 43 primary commodity prices and sea surface temperature (SST) anomalies in the Niño3.4 region from January 1980 to December 2016. The SST anomalies serve as a proxy for ENSO, as persistent positive (negative) SST deviations from their historical mean are associated with El Niño (La Niña) events. I apply a time‐varying smooth transition autoregressive modeling framework to account for potentially complex dynamic relationships between SST anomalies and prices. The estimated models reveal more amplified price responses during El Niño events, and at the onset of the ENSO cycle. I find statistically significant linkages between SST anomalies and a subset of agricultural commodity prices, which manifests in a better price forecasting for the commodities produced in the tropics. While I also find some in‐sample evidence for prices of selected nonagricultural commodities, for example, timber and metals, the ability of SST anomalies to predict these commodity prices in an out‐of‐sample setting is lacking. These findings carry important welfare implications, especially for developing economies that have been historically linked to the behavior of primary commodity prices, and offer valuable insights to policy makers working in areas related to economic growth and foreign aid programs, as well as those concerned with issues of farm income and rural poverty.

The coupling between sea surface temperature (SST) anomalies and rainfall is an important driver of tropical climate variability. Observations however reveal inconsistencies, such as decreased convective rainfall in regions with positive SST anomalies in the tropical Indian and Atlantic Oceans during and after El Niño–Southern Oscillation (ENSO) events. The upper troposphere warms during El Niño events, stabilizing the atmosphere. SST anomalies only account for the influence of the surface. Using theoretical arguments, we show that relative SST (RSST; defined as SST minus its tropical mean) anomalies, by also accounting for the influence of upper tropospheric temperature anomalies on gross moist stability, explain tropical convection interannual variations better than SST anomalies in observations and climate models. This relation further improves when RSST anomalies are weighted by the precipitation climatology to account for low and high‐precipitation regimes. Using RSST is thus essential to understand El Niño–Southern Oscillation teleconnections and interactions between modes of tropical climate variability.

Effects of the ENSO on rainfall erosivity in the Fujian Province of southeast China

The response of both the time of onset, and the strength of the Asian summer monsoon, to regional aspects of the sea surface temperature (SST) anomalies in the tropical Pacific Ocean associated with El Niño/Southern Oscillation (ENSO) has been investigated through a series of sensitivity experiments with the Universities Global Atmospheric Modelling Programme (UGAMP) General Circulation Model (UGCM). This paper builds on the work of Ju and Slingo (1995) and on their hypothesis that the relationship between the Asian summer monsoon and ENSO involved the latitudinal position and strength of the tropical convective maximum (TCM) over Indonesia and the west Pacific in the preceding spring. the inference from their results was that the modulation of the TCM might be associated either with changes in the Walker circulation through the influence of the east Pacific SST anomalies, or with changes in the local Hadley circulation associated with the in situ SST anomalies in the west Pacific. the investigation has focused on the particular contrasting years of 1983 and 1984. the experiments described in this paper are designed to isolate the effects of the principal SST anomalies in the east and central Pacific, associated with El Niño/La Niño, from those of opposite sign which develop in the west Pacific as a complementary pattern during the mature phase of El Niño/La Niño.The results of the experimentation suggest that, at least for the test cases of 1983 and 1984, the modulation of the Walker circulation, with implied additional subsidence over the eastern hemisphere, is the dominant mechanism whereby the Asian summer monsoon is weakened during El Niñño years. However, the late onset during El Niño years may also be associated with the complementary cold SST anomalies in the west Pacific which delay the northwards transition of the TCM. During La Niño, the modulation of the Walker circulation appears not to be the controlling factor which determines the stronger monsoons. the UGCM results suggest that the complementary warm SST anomalies in the west Pacific enhance the TCM, and it is this in situ response by the TCM that leads to an early onset and stronger monsoon. the importance of warm anomalies in the west Pacific in the development of a strong monsoon has been investigated further through a case‐study of the 1994 season. the year 1994 was an El Niño year in which the monsoon was unexpectedly active, but which was also marked by warmer than normal SSTs in the west Pacific.The sensitivity experiments have also elucidated the role of El Niño in influencing the precursory signature of stronger subtropical westerlies over India and south‐east Asia during the winter and spring preceding weak monsoons. the results suggested that the equatorwards shift of the subtropical jet is a remote response to the warm SST anomalies in the central and east Pacific associated with El Niño.

The response of both the time of onset, and the strength of the Asian summer monsoon, to regional aspects of the sea surface temperature (SST) anomalies in the tropical Pacific Ocean associated with El Niño/Southern Oscillation (ENSO) has been investigated through a series of sensitivity experiments with the Universities Global Atmospheric Modelling Programme (UGAMP) General Circulation Model (UGCM). This paper builds on the work of Ju and Slingo (1995) and on their hypothesis that the relationship between the Asian summer monsoon and ENSO involved the latitudinal position and strength of the tropical convective maximum (TCM) over Indonesia and the west Pacific in the preceding spring. the inference from their results was that the modulation of the TCM might be associated either with changes in the Walker circulation through the influence of the east Pacific SST anomalies, or with changes in the local Hadley circulation associated with the in situ SST anomalies in the west Pacific. the investigation has focused on the particular contrasting years of 1983 and 1984. the experiments described in this paper are designed to isolate the effects of the principal SST anomalies in the east and central Pacific, associated with El Niño/La Niño, from those of opposite sign which develop in the west Pacific as a complementary pattern during the mature phase of El Niño/La Niño. The results of the experimentation suggest that, at least for the test cases of 1983 and 1984, the modulation of the Walker circulation, with implied additional subsidence over the eastern hemisphere, is the dominant mechanism whereby the Asian summer monsoon is weakened during El Niñño years. However, the late onset during El Niño years may also be associated with the complementary cold SST anomalies in the west Pacific which delay the northwards transition of the TCM. During La Niño, the modulation of the Walker circulation appears not to be the controlling factor which determines the stronger monsoons. the UGCM results suggest that the complementary warm SST anomalies in the west Pacific enhance the TCM, and it is this in situ response by the TCM that leads to an early onset and stronger monsoon. the importance of warm anomalies in the west Pacific in the development of a strong monsoon has been investigated further through a case-study of the 1994 season. the year 1994 was an El Niño year in which the monsoon was unexpectedly active, but which was also marked by warmer than normal SSTs in the west Pacific. The sensitivity experiments have also elucidated the role of El Niño in influencing the precursory signature of stronger subtropical westerlies over India and south-east Asia during the winter and spring preceding weak monsoons. the results suggested that the equatorwards shift of the subtropical jet is a remote response to the warm SST anomalies in the central and east Pacific associated with El Niño.

Recent studies arising from both statistical analysis and dynamical disease models indicate that there is a link between the incidence of cholera, a paradigmatic waterborne bacterial illness endemic to Bangladesh, and the El Niño–Southern Oscillation (ENSO). Cholera incidence typically increases following boreal winter El Niño events for the period 1973–2001. Observational and model analyses find that Bangladesh summer rainfall is enhanced following winter El Niño events, providing a plausible physical link between El Niño and cholera incidence. However, rainfall and cholera incidence do not increase following every winter El Niño event. Substantial variations in Bangladesh precipitation also occur in simulations in which identical sea surface temperature (SST) anomalies are prescribed in the central and eastern tropical Pacific. Bangladesh summer precipitation is thus not uniquely determined by forcing from the tropical Pacific, with significant implications for predictions of cholera risk. Nonparametric statistical analysis is used to identify regions of SST anomalies associated with variations in Bangladesh rainfall in an ensemble of pacemaker simulations. The authors find that differences in the response of Bangladesh summer precipitation to winter El Niño events are strongly associated with the persistence of warm SST anomalies in the central Pacific. Also there are significant differences in the SST patterns associated with positive and negative Bangladesh rainfall anomalies, indicating that the response is not fully linear. SST anomalies in the Indian Ocean also modulate the influence of the tropical Pacific, with colder Indian Ocean SST tending to enhance Bangladesh precipitation relative to warm Indian Ocean SST for identical conditions in the central and eastern tropical Pacific. This influence is not fully linear. Forecasts of Bangladesh rainfall and cholera risk may thus be improved by considering the Niño-3 and Niño-4 indices separately, rather than the Niño-3.4 index alone. Additional skill may also be gained by incorporating information on the southeast Indian Ocean and by updating the forecast with information on the evolution of the SST anomalies into spring.