The Hilbert Transform on the Two-Sphere: A Spectral Characterization

The local analysis of signals arising on the sphere is a common task in earth sciences. On the real line the analytic signal turned out to be an important representation in local one-dimensional signal processing. Its generalization to two dimensions is the monogenic signal, and the properties of the analytic and the monogenic signal in the Fourier domain are well known. A generalization to the sphere is given by the Hilbert transform on the sphere known from Clifford analysis. To obtain a spectral characterization, the transform has to be decomposed into spherical harmonic functions. In this paper, we derive the spherical harmonic coefficients of the Hilbert transform on the sphere and give a series expansion. This will show that it acts as a differential operator on the spherical harmonic basis functions of the Laplace equation solution, analogously to the Riesz transform in two dimensions. This allows an interpretation of the Hilbert transform suitable for signal processing of signals naturally arising on the two-sphere. We show that the scale space naturally arising is a Poisson scale space in the unit ball. In addition, the obtained interpretation of the Hilbert transform is used for orientation analysis of plane waves. This representation is justified as a novel signal model on the sphere which can be used to construct intensity and rotation-invariant operators for local signal analysis in a scale-space concept.     

The intraseasonal oscillation in ECHAM4 Part II: sensitivity studies

The focus is on sensitivity studies to identify factors that increase the skill of the ECHAM4 atmosphere general circulation model (GCM) in representing the intraseasonal oscillation (ISO). The ISO mode is dominated by an eastward propagating oscillation during boreal winter, also known as the Madden-Julian oscillation. A previous study compared observations and reanalysis data to uncoupled and coupled versions of the ECHAM4 GCM. The sensitivity experiments in the present study use those results to assess the importance of the following mechanisms for the simulation of the ISO. First, the vertical resolution is increased to indicate the effect of improved representation of the tropospheric stratification. Second, the horizontal resolution is increased to investigate the importance of the ratio of vertical and horizontal resolution. Third, the effects of the land-sea distribution are studied in an experiment with land points associated with the maritime continent replaced by sea points. Fourth, the ECHAM4 GCM is forced by a T42 version of the observed optimum interpolated SST (OISST) dataset as used in the ECMWF reanalysis to study the influence of the SST as a boundary condition. In addition to integrations with monthly mean SSTs, also an experiment with weekly mean SSTs is examined. The increased vertical resolution slightly slows down the propagation speed of the simulated ISO. Increasing the horizontal resolution from T42 to T106 results in a very noisy and therefore poorer simulation of the ISO. It is suggested that this is due to an inappropriate ratio of vertical and horizontal resolution. Replacing the land points associated with the maritime continent with sea points leads to a more realistic representation of convection over the maritime continent than in the standard model. A consequence is a reduction of the erroneous eastward shift of the simulated ISO activity, although the phase speed of the ISO is simultaneously increased. ECHAM4 forced by an OISST dataset interpolated to the models T42 grid leads to the strongest improvements, since the annual mean AMIP SST averaged over the maritime continent region is 0.14 K warmer than the OISST, and individual grid points can be more than 0.5 K warmer. The reason is that the AMIP SST uses only measurements over water for grid points that are partly covered by land, whereas the OISST also blends these measurements with measurements over the land portions. ECHAM4 forced by the interpolated OISST, which is in the mean only 0.04 K colder over the maritime continent than the OISST, produces a reasonable ISO with a mean period of 40 days for a forcing with monthly mean SSTs and 48 days for a forcing with weekly mean SSTs. These results illustrate the strong influence of the details of the prescribed SST on the simulation of the ISO.     

The hydrologic effects of intense groundwater pumpage in east-central Hillsborough County,Florida, U.S.A.

Well problems, water shortages, local flooding, and induced sinkholes have been periodic problems for residents in east-central Hillsborough County, Florida. This agricultural area has experienced dramatic short-term water-level declines in the Floridan aquifer from seasonal groundwater withdrawals. The sudden declines in the potentiometric surface have been caused from intense irrigation pumpage, primarily for frost and freeze protection and fruit setting. Citrus and strawberry crops are protected from occasional freezes by the application of warm groundwater to maintain minimum soil temperatures of 32°F(0°C). Local residents with inadequately constructed wells lose their source of water when the potentiometric surface is lowered to depths where their wells do not function. Some residents have lost their water supply for a week or more, and many have incurred damage to their pumps. The drawdown of the potentiometric surface in some areas has induced sinkholes causing property damage for some residents and concern for others. In addition, the high application rates for frost and freeze irrigation have created run-off problems resulting in local flooding to some residents. Fortunately, there has been no damage to resident homes from the flooding or sinkholes. This report summarizes the area's hydrogeology, and the consequences of heavy freeze irrigation. A finite-difference, numerical model is used to quantify the regional impacts to the potentiometric surface of the Floridan aquifer from estimated irrigation pumpage. Management recommendations for alleviating the problems are also discussed in the report.     

Use of a harpacticoid copepod in toxicity tests

The harpacticoid copepod Nitocra spinipes has been tested for acute toxicity of 12 metal chlorides in brackish water. Their order of toxicity, expressed as 96 h LC₅₀, was in good agreement with other investigations performed in freshwater and seawater. The 96 h LC₅₀-values were of intermediate levels compared to these two environments. The organochlorines p,p′-DDE and p,p′-DDE methyl sulphone were tested for effects on reproduction and mortality during two weeks, and it was found that p,p′-DDE was the most toxic. It is concluded from the investigation that N. spinipes is a suitable toxicity test organism in brackish water.     

Comparison of DNA damage in the early life stages of cod, Gadus morhua, originating from the Barents Sea and Baltic Sea

DNA adducts in cod embryos and larvae were analysed by ³²P-postlabeling to test the hypothesis that anthropogenic substances, which could form reactive intermediates, are involved in the reproductive failure of cod (Gadus morhua) from the Baltic Sea. A comparison with cod from the Barents Sea was performed. The mean value of DNA adducts in cod embryos/larvae from the Baltic Sea was 2.3 nmol of adducts/mol nucleotides, compared to 0.12 nmol of adducts/mol nucleotides in the embryos/larvae from the Barents Sea.     

Estimation of chlorophyll-a concentration in the Zhujiang Estuary from SeaWiFS data

The chlorophyll-a concentration is generally overestimated for the southern China coastalwaters if the default algorithm of the SeaDAS is employed. An algorithm is developed for retrieval of chlorophyll-a concentration in the Zhujiang Estuary, Guangdong Province, China, by using simulated reflectance data. The simulated reflectance is calculated corresponding to the SeaWiFS wavelength bands, via a general model by inputting measured water components, i.e. , the suspended sediment, chlorophyll-a, and yellow substance (DOC) concentration data of 130 samples. Empirical relationships of the chlorophyll-a concentration to 240 different band combinations are investigated based on the simulated reflectance data, and the band combination, R_5R_6/R_3R_4, is found to be the optimum one for the development of an algorithm valid for the Zhujiang Estuary. This algorithm is then employed to determine the chlorophyll-a concentration from SeaWiFS data. The estimated concentrations have a better accuracy than those obtai