The structure of the background errors in a global wave model.

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. For example, the current operational wave data assimilation system at the Australian Bureau of Meteorology (BoM) prescribes globally uniform background error correlations of Gaussian shape with a length scale of 300 km and the error variance of both the background and observation errors is defined to be 0.25 m². This thesis describes an investigation into the determination of the background errors in a global wave model. There are two methods that are commonly used to determine background errors: the observational method and the 'NMC method'. The observational method is the main tool used in this thesis, although the 'NMC method' is considered also. The observational method considers correlations of the differences between observations and the background, in this case, the modelled Significant Wave Height (SWH) field. The observations used are satellite altimter estimates of SWH. Before applying the method, the effect of the irregular satellite sampling pattern is examined. This is achieved by constructing a set of anomaly correlations from modelled wave fields. The modelled wave fields are then sampled at the locations of the altimeter observations and the anomaly correlations are recalculated from the simulated altimeter data. The results are compared to the original anomaly correlations. It is found that in general, the altimeter sampling pattern underpredicts the spatial scale of the anomaly correlation. Observations of SWH from the ERS-2 altimeter are used in this thesis. To ensure that the observations used are of the highest quality possible, a validation of the European Remote Sensing Satellite 2 (ERS-2) SWH observations is performed. The altimeter data are compared to waverider buoy observations over a time period of approximately 4.5 years. With a set of 2823 co-located SWH estimates, it is found that in general, the altimeter overestimates low SWH and underestimates high SWH. A two-branched linear correction to the altimeter data is found, which reduces the overall rms error in SWH to approximately 0.2 m. Results from the previous sections are then used to calculate the background error correlations. Specifically, correlations of the differences between modelled SWH and the bias-corrected ERS-2 data are calculated. The irregular sampling pattern of the altimeter is accounted for by adjusting the correlation length scales according to latitude and the calculated length scale. The results show that the length scale of the background errors varies significantly over the globe, with the largest scales at low latitudes and shortest scales at high latitudes. Very little seasonal or year-to-year variability is detected. Conversely, the magnitude of the background error variance is found to have considerable seasonal and year-to-year variability. By separating the altimeter ground tracks into ascending and descending tracks, it is possible to examine, to a limited extent, whether any anisotropy exists in the background errors. Some of the areas on the globe that exhibit the most anisotropy are the Great Australian Bight and the North Atlantic Ocean. The background error correlations are also briefly examined via the 'NMC method', i.e., by considering differences between SWH forecasts of different ranges valid at the same time. It is found that the global distribution of the length scale of the error correlation is similar to that found using the observational method. It is also shown that the size of the correlation length scale increases as the forecast period increases. The new background error structure that has been developed is incorporated into a data assimilation system and evaluated over two month-long time periods. Compared to the current operational system at the BoM, it is found that this new structure improves the skill of the wave model by approximately 10%, with considerable geographical variability in the amount of improvement.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 200

The Midlatitude Resolution Capability of Sea Level Fields Constructed from Single and Multiple Satellite Altimeter Datasets

A formalism recently developed for determining the effects of sampling errors on objectively smoothed fields constructed from an irregularly sampled dataset is applied to investigate the relative merits of single and multiple satellite altimeter missions. For small smoothing parameters, the expected squared error of smoothed fields of sea surface height (SSH) varies geographically at any particular time and temporally at any particular location. The philosophy proposed here for determining the resolution capability of SSH fields constructed from altimeter data is to identify smoothing parameters that are sufficiently large to satisfy two criteria: 1) the expected squared errors of the estimates of smoothed SSH over the space–time estimation grid must be either spatially and temporally homogeneous to within some a priori specified degree of tolerance or smaller than some a priori specified threshold, and 2) the space–time estimation grid on which smoothed SSH estimates are constructed must satisfy the Nyquist criteria for the wavenumbers and frequencies included in the smoothed fields. The method is illustrated here by adopting a specified tolerance of 10% variability and a nominal expected squared error threshold of 1 cm² to determine the resolution capabilities of SSH fields constructed from 10 single and multiple combinations of altimeter measurements by TOPEX/Poseidon, the ERS Earth Resource Satellites, and Geosat. Because of the lack of coordination of the orbit configurations of these satellites (different repeat periods and different orbit inclinations), the mapping resolution capabilities of the combined datasets are not significantly better than those of fields constructed from TOPEX/Poseidon data alone. The benefits of coordinated multiple missions are demonstrated by consideration of several multiple combinations of 10-, 17-, and 35-day orbit configurations

The Impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the observational method of Hollingsworth and Lönnberg. The observational method considers correlations of the differences between observations and the background. For the case of significant wave height (SWH), potential observations come from satellite altimeters. In this work, the effect of the irregular sampling pattern of the satellite on estimates of background errors is examined. This is achieved by using anomalies from a 3-month mean as a proxy for model errors. A set of anomaly correlations is constructed from modeled wave fields. The isotropic length scales of the anomaly correlations are found to vary considerably over the globe. In addition, the anomaly correlations are found to be significantly anisotropic. The modeled wave fields are then sampled at simulated altimeter observation locations, and the anomaly correlations are recalculated from the simulated altimeter data. The results are compared to the original anomaly correlations. It is found that, in general, the simulated altimeter data can capture most of the geographic and seasonal variability in the isotropic anomaly correlation length scale. The best estimates of the isotropic length scales come from a method in which correlations are calculated between pairs of observations from prior and subsequent ground tracks, in addition to along-track pairs of observations. This method was found to underestimate the isotropic anomaly correlation length scale by approximately 10%. The simulated altimeter data were not so successful in producing realistic anisotropic correlation functions. This is because of the lack of information in the zonal direction in the simulated altimeter data. However, examination of correlations along ascending and descending ground tracks separately can provide some indication of the areas on the globe for which the anomaly correlations are more anisotropic than others

Forecast Divergences of a Global Wave Model

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the "NMC method." This method examines the forecast divergence component of the background error growth by considering differences between forecasts of different ranges valid at the same time. In this paper, the NMC method is applied to global forecasts of significant wave height (SWH) and surface wind speed (U10). It is found that the isotropic correlation length scale of the SWH forecast divergence (LSWH) has considerable geographical variability, with the longest scales just to the south of the equator in the eastern Pacific Ocean, and the shortest scales at high latitudes. The isotropic correlation length scale of the U10 forecast divergence (LU10) has a similar distribution with a stronger latitudinal dependence. It is found that both LSWH and LU10 increase as the forecast period increases. The increase in LSWH is partly due to LU10 also increasing. Another explanation is that errors in the analysis or the short-range SWH forecast propagate forward in time and disperse and their scale becomes larger. It is shown that the forecast divergence component of the background error is strongly anisotropic with the longest scales perpendicular to the likely direction of propagation of swell. In addition, in regions where the swell propagation is seasonal, the forecast divergence component of the background error shows a similar strong seasonal signal. It is suggested that the results of this study provide a lower bound to the description of the total background error in global wave models

The impact of inhomogenous background errors on a global wave data assimilation system

One of the main limitations in current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. In this work, models for the observational error variance, background error variance and backgroun

Background errors in a global wave model determined from altimeter data

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the observational method of Hollingsworth and Lönnberg [1986] . This method considers correlations of the differences between observations and the background. For the case of Significant Wave Height (SWH), potential observations come from satellite altimeters. In this paper, correlations of the differences between modeled SWH and bias-corrected ERS-2 data are calculated. The irregular sampling pattern of the altimeter is accounted for by adjusting the correlation length scales according to latitude and the calculated length scale. The results show that the length scale of the background errors varies significantly over the globe, with the largest scales at low latitudes and shortest scales at high latitudes. Very little seasonal or year-to-year variability in the correlation length scales is detected. Conversely, the magnitude of the background error variance is found to have considerable seasonal and year-to-year variability. By separating the altimeter ground tracks into ascending and descending tracks, it is possible to examine, to a limited extent, whether any anisotropy exists in the background errors

Forecast divergences of a global wave model

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the “NMC method.” This method examines the forecast divergence component of the background error growth by considering differences between forecasts of different ranges valid at the same time. In this paper, the NMC method is applied to global forecasts of significant wave height (SWH) and surface wind speed (U10). It is found that the isotropic correlation length scale of the SWH forecast divergence (LSWH) has considerable geographical variability, with the longest scales just to the south of the equator in the eastern Pacific Ocean, and the shortest scales at high latitudes. The isotropic correlation length scale of the U10 forecast divergence (LU10) has a similar distribution with a stronger latitudinal dependence. It is found that both LSWH and LU10 increase as the forecast period increases. The increase in LSWH is partly due to LU10 also increasing. Another explanation is that errors in the analysis or the short-range SWH forecast propagate forward in time and disperse and their scale becomes larger. It is shown that the forecast divergence component of the background error is strongly anisotropic with the longest scales perpendicular to the likely direction of propagation of swell. In addition, in regions where the swell propagation is seasonal, the forecast divergence component of the background error shows a similar strong seasonal signal. It is suggested that the results of this study provide a lower bound to the description of the total background error in global wave models