Stochastic and Statistical Methods in Climate, Atmosphere, and Ocean Science

Introduction The behavior of the atmosphere, oceans, and climate is intrinsically uncertain. The basic physical principles that govern atmospheric and oceanic flows are well known, for example, the Navier-Stokes equations for fluid flow, thermodynamic properties of moist air, and the effects of density stratification and Coriolis force. Notwithstanding, there are major sources of randomness and uncertainty that prevent perfect prediction and complete understanding of these flows. The climate system involves a wide spectrum of space and time scales due to processes occurring on the order of microns and milliseconds such as the formation of cloud and rain droplets to global phenomena involving annual and decadal oscillations such as the EL Nio-Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) [5]. Moreover, climate records display a spectral variability ranging from 1 cycle per month to 1 cycle per 100, 000 years [23]. The complexity of the climate system stems in large part from the inherent nonlinearities of fluid mechanics and the phase changes of water substances. The atmosphere and oceans are turbulent, nonlinear systems that display chaotic behavior (e.g., [39]). The time evolutions of the same chaotic system starting from two slightly different initial states diverge exponentially fast, so that chaotic systems are marked by limited predictability. Beyond the so-called predictability horizon (on the order of 10 days for the atmosphere), initial state uncertainties (e.g., due to imperfect observations) have grown to the point that straightforward forecasts are no longer useful. Another major source of uncertainty stems from the fact that numerical models for atmospheric and oceanic flows cannot describe all relevant physical processes at once. These models are in essence discretized partial differential equations (PDEs), and the derivation of suitable PDEs (e.g., the so-called primitive equations) from more general ones that are less convenient for computation (e.g., the full Navier-Stokes equations) involves approximations and simplifications that introduce errors in the equations. Furthermore, as a result of spatial discretization of the PDEs, numerical models have finite resolution so that small-scale processes with length scales below the model grid scale are not resolved. These limitations are unavoidable, leading to model error and uncertainty. The uncertainties due to chaotic behavior and unresolved processes motivate the use of stochastic and statistical methods for modeling and understanding climate, atmosphere, and oceans. Models can be augmented with random elements in order to represent time-evolving uncertainties, leading to stochastic models. Weather forecasts and climate predictions are increasingly expressed in probabilistic terms, making explicit the margins of uncertainty inherent to any prediction

Étude corrélative des paramètres physico-chimiques et des données satellites IRS1C pour caractériser la pollution aquatique. Application à la baie d’Oran, Algérie

Le contrôle de la qualité de l'eau est fondé naturellement et traditionnellement sur des mesures et des prélèvements in situ. Des images satellites étalonnées à partir des données mesurées in situ fournissent une information quantitative et continue sur le milieu aquatique et peuvent être employées pour estimer, avec une approximation raisonnable, les facteurs affectant la qualité de l’eauL’objectif de cet article consiste à établir des corrélations entre les propriétés optiques de l’eau de mer et les paramètres physico-chimiques. Nous présentons des relations exprimant les variables indicatrices de la qualité des eaux du littoral d’Oran et la réflectance calculée de chaque pixel à partir d’un modèle physique de correction radiométrique. Les mesures in- situ sont effectuées pour des zones de différentes qualités d’eaux et leurs réflectances sont calculées à partir d’une image satellite à haute résolution IRS1-C.Les meilleures corrélations sont obtenues sur le deuxième et le troisième canal visible. Pour la demande chimique en oxygène, le coefficient de corrélation atteint 0.84, pour les matières en suspension r2 = 0.88, pour la demande biochimique de l’oxygène pendant cinq jours r2 = 0.62, pour l’oxygène dissous r2 = 0.77 et pour la turbidité r2 = 0.90.Finalement, des relations linéaires sont établies avec les réflectances. L’inversion de ces relations permet d’obtenir des images transformées à partir du logiciel de traitement d’image afin d’estimer pour chaque pixel le degré de pollution du milieu.Population growth in developing countries has led to a rapid expansion of primary urban areas. Solid and liquid wastes coming from domestic consumption and industrial activities are discharged into potential water sources such as seas, lakes and other natural areas. In order to protect these areas and to control the pollution caused by such waste, it is necessary to continuously monitor these zones. Satellite imagery, such as that obtained with the IRS1C satellite, can be used to estimate, with reasonable accuracy, the factors affecting water quality. This technique allows for the necessary continuous monitoring of impacted areas and affords an overall analysis of their degree of pollution.Waste disposal affects and alters the chemical and physical characteristics of water. Moreover, water quality could be altered by the decay products of extracellular release and death of aquatic organisms. In turn, these changes can cause an alteration in the appearance of water. It is therefore reasonable to look for relations linking variations in chemical and physical properties to variations in the spectral properties of water, or more precisely, to its reflecting power. The aim of the present study was to:1. relate the reflectance of polluted water to its physico-chemical parameters;2. show the significance of such relationships.Water samples were collected from different sites:1. two outlets where sewage of Oran City is being emptied into the sea;2. far from these outlets;3. far from the port;4. far from two sites in a lake known to be subjected to both urban and industrial waste.From each site, water samples were taken at the source and from different places far from the coast. The following water quality parameters were analyzed: temperature, acidity, turbidity, suspended material, dissolved oxygen, electrical conductivity, chemical oxygen demand and 5-day biological oxygen demand. The reflectance coefficient of water in each of the studied areas was calculated using the IRS1C image at four bands. The satellite observes the earth in four spectral channels: C1 (0.45- 0.52 m); C2 (0.52 - 0.59 m); C3 (0.62 - 0.68 m) and C4 (0.77 - 0.86 m) with a spatial resolution of 6 m. The radiance measured by the satellite sensor results from solar radiation affected by several processes including absorption and diffusion on both downward and upward paths by the atmospheric components, and reflection at the ground surface.We first simulated the measurement achieved by the captor of our reference water (from the sea far from any pollution). Secondly, we used imagery treatment to determine the real value evaluated by the satellite for deep-sea water. We used both a simulated value and the real value to calculate the calibration factor for each channel. We took the image and transformed the digital account into radiance by linear relationships. For each channel, we use the reverse model to calculate the reflectance for each pixel. The substances that determine the optical properties of water surfaces, and thus influence their reflectivity, may be classified into three categories:1. living phytoplankton and the associated detritus;2. suspended particles;3. dissolved organic matter.The phytoplankton and the associated biogenic detritus generally have the same colour. In most oceanic waters, and in some coastal waters where terrigenous supplies are unimportant, the influence of phytoplankton is dominant. In natural conditions, it is very difficult to dissociate the influences of phytoplankton and those of biogenic detritus on the coefficient of absorption, for which only global estimations are made. The phytoplankton cells and the particles corresponding to biogenic detritus cause a Mie diffusion of light, which is relatively independent of the wavelength. Therefore, the colour of water gradually turns green with increasing phytoplankton concentration.As expected, our results demonstrated that for polluted waters there was a good correlation between turbidity and concentrations of suspended material. Turbidity and suspended solids have a common effect in reducing light penetration, thereby suppressing primary production in the form of algae and macrophytes. This decrease, in turn, affects the available dissolved oxygen. Our results confirmed this situation by showing a highly negative correlation between turbidity and dissolved oxygen. The oxygen needed for chemical oxidation of organic matter and the accompanied minerals is expressed as COD. Therefore, higher values of this parameter means more organic pollution. BOD5 estimates the oxygen needed for biological oxidation of organic and inorganic matter by organisms that are actually present in the polluted water. Therefore, the DCO/DBO5 ratio refers to the capacity of organisms found in the water to oxidize the organic matter found in the medium. Our results showed that this ratio increased with increasing pollution and with reflectance in the different channels. For easier water quality monitoring we could use the satellite imagery to estimate, with excellent validity, the capability of the water to reduce organic pollution resulting from urban discharge. Moreover, biological parameters could be calculated from each other since there was a high correlation found among them.The correlation between reflectance and the biochemical parameters was higher for channels C2 and C3 than for the other two channels. The following correlations between reflectance and the measured parameters chemical were obtained: oxygen demand, r = 0.84; suspended matter, r = 0.88; 5-day biological oxygen demand, r = 0.62; dissolved oxygen, r = 0.77; turbidity, r = 0.90. Finally, linear relationships were established between physico-chemical parameters and reflectance values. The inversion of these relationships offered the possibility to estimate for each pixel the degree of water quality. Figures showed clearly different distinct colour sub-areas in each of the studied areas. Each colour indicated a different degree of water quality or pollution. With this technique it was possible to construct, relatively rapidly, a global picture describing the degree of unknown pollution spread over a wide water surface

Coastal Tropical Convection in a Stochastic Modeling Framework

Recent research has suggested that the overall dependence of convection near coasts on large-scale atmospheric conditions is weaker than over the open ocean or inland areas. This is due to the fact that in coastal regions convection is often supported by meso-scale land-sea interactions and the topography of coastal areas. As these effects are not resolved and not included in standard cumulus parametrization schemes, coastal convection is among the most poorly simulated phenomena in global models. To outline a possible parametrization framework for coastal convection we develop an idealized modeling approach and test its ability to capture the main characteristics of coastal convection. The new approach first develops a decision algorithm, or trigger function, for the existence of coastal convection. The function is then applied in a stochastic cloud model to increase the occurrence probability of deep convection when land-sea interactions are diagnosed to be important. The results suggest that the combination of the trigger function with a stochastic model is able to capture the occurrence of deep convection in atmospheric conditions often found for coastal convection. When coastal effects are deemed to be present the spatial and temporal organization of clouds that has been documented form observations is well captured by the model. The presented modeling approach has therefore potential to improve the representation of clouds and convection in global numerical weather forecasting and climate models.Comment: Manuscript submitted for publication in Journal of Advances in Modeling Earth System

The Impact of Population Growth on Economic Growth in Algeria - An Econometric Study

تهدف الدراسة إلى اختبار تأثير مؤشرات النمو السكاني على النمو الاقتصادي ممثلا بنصيب الفرد من الناتج المحلي الإجمالي للفرد الجزائري خلال الفترة 1962-2013، بتطبيق النموذج المقترح من طرف Gideon Kiguru Thuku ، Gachanja Paul و Obere Almadi، حيث خلصت الدراسة إلى التأثير العكسي لكل من معدل نمو عدد السكان الإجمالي وعدد السكان في المناطق الحضرية، إضافة إلى معدل الخصوبة وعدد المواليد وحصة عدد الأطفال من عدد السكان في سن العمل على نصيب الفرد من الناتج المحلي الإجمالي، حيث يقدر هذا التأثير بدرجة تتراوح بين 51.15% إلى 60.33%.The study aims to test the impact of population growth indicators on economic growth represented by per capita gross domestic product per capita of Algeria during the period of 1962-2013, by implicating the proposed model by Gideon Kiguru Thuku, Gachanja Paul and Obere Almadi, where the study concluded that the adverse impact of both of the rate of the growth of total population and the population in urban areas, as well as the fertility rate and the number of births and the share of the number of children per the population in the age of work on the per capita gross domestic product, with an estimated impact of this degree, ranging from 51.15%  to 60.33%

Multiple Equilibria in a Single-Column Model of the Tropical Atmosphere

A single-column model run under the weak temperature gradient approximation, a parameterization of large-scale dynamics appropriate for the tropical atmosphere, is shown to have multiple stable equilibria. Under conditions permitting persistent deep convection, the model has a statistically steady state in which such convection occurs, as well as an extremely dry state in which convection does not occur. Which state is reached depends on the initial moisture profile.Comment: Submitted to Geophysical Research Letter

Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523