A. Mary Selvam

Universal quantification for deterministic chaos in dynamical systems

Abstract A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth, i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1/τ2 ( = 0.382) where τ is the golden mean. k being less than half accounts for the fractal (broken) Euclidean geometry of the strange attractor. (c) The Feigenbaums universal constantsa and d are functions of k and, further, the expression 2a2 = πd quantifies the steady-state ordered emergence of the fractal geometry of the strange attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statistical normal distribution. The model prediction of (d) is verified for the Lorenz attractor and for the computable chaotic orbits of Bernoulli shifts, pseudorandom number generators, and cat maps.

Characteristics of Raindrop Charge and Associated Electric Field in Different Types of Rain

Abstract Simultaneous measurements of raindrop charge, atmospheric electric field and rain intensity were made at Poona using fast response, continuous recording surface instruments during four types of rain: pre-monsoon (thunderstorm rain), monsoon rain type I (tight intermittent rain), monsoon rain type II (heavy continuous rain) and post-monsoon (thunderstorm rain). Measurements were also made of the conductivity of rainwater samples collected during the monsoon season. On some days of this period data on cloud thickness as obtained from the aircraft flights in the region were also available. The electric field associated with negatively charged raindrops was less negative than that associated with positively charged drops. The raindrop charge spectrum showed different characteristics during the four types of rain studied. It was broadest during the pre-monsoon rain when the convective activity was a maximum. It followed a log-normal distribution during the monsoon rain type I and it was peaked and ske...

Some thermodynamical and microphysical aspects of monsoon clouds

The thermodynamical and microphysical characteristics of monsoon clouds in the Poona, Bombay and Rihand regions were investigated using extensive aircraft in-cloud observations. The number of clouds sampled at Poona, Bombay and Rihand is 2199, 169 and 104 respectively.The temperatures inside the cloud are colder than its environment at Poona and Rihand. The maximum difference is about 3°C at the cloud base level and the difference decreased with height. At Bombay the difference is less than 1°C and at some levels the temperatures inside the cloud are warmer than its environment.The lapse rates of temperatures inside the cloud are slightly less than those in the immediate environment of the cloud. The environmental lapse rates are nearly equal to the saturated adiabatic value.The positive increments in liquid water content (LWC) are associated with the increments in temperature inside the cloud. Similarly positive increments in temperatures inside the cloud are associated with the increments in temperature of its immediate environment at the same level or the layer immediately above.The maximum cloud lengths observed at Poona and Bombay respectively are 14 and 3 km. The horizontal cross-section of LWC showed a maximum number of 13 peaks in clouds at Poona while only 7 peaks were observed at Bombay. The location of maximum LWC in the horizontal cross-section is more or less at the centre of the cloud. The LWC profile showed an increase with height from the base of the cloud at Poona and Bombay. There is no marked variation of LWC with height at Rihand.The total droplet concentration at different altitudes at Poona and Bombay is in the range 28–82 cm−3. The size distribution of cloud droplets experienced a broadening effect with increase in height from the cloud base at Poona. The broadening effect at Bombay is not as marked as that at Poona.

The dynamics of non‐linear ionospheric rf wave processes

High power narrow band rf pulses used in ionospheric heating experiments undergo spectral broadening in the ionosphere. In this paper it is shown that the universal period doubling route to chaos is the mechanism by which the incident rf pump energy generates larger eddies in the ionospheric plasma analogous to triggering of chaos in a non‐linear optical medium by a laser energy pump. In summary, the physics of the universal period doubling route to chaos implies growth of self similar large eddy continuum circulations from space time integrated mean of inherent smaller scale perturbations at incremental length steps equal to the turbulence scale length. The ionosphere‐troposphere coupling mechanism which can possibly trigger inadvertant weather/climate change by the ionospheric heating experiments is discussed.

Some physical aspects of summer monsoon clouds-comparison of cloud model results with observations

The physical characteristics of the summer monsoon clouds were investigated. The results of a simple cloud model were compared with the aircraft cloud physical observations collected during the summer monsoon seasons of 1973, 1974, 1976 and 1981 in the Deccan Plateau region.The model predicted profiles of cloud liquid water content (LWC) are in agreement with the observed profiles. There is reasonable agreement between the model predicted cloud vertical thickness and observed rainfall.The observed cloud-drop spectra were found to be narrow and the concentration of drops with diameter > 20μn is either low or absent on many occasions. In such clouds the rain-formation cannot take place under natural atmospheric conditions due to the absence of collision-coalescence process. A comparison of the model predicted and observed rainfall suggested that the precipitation efficiency in cumulus clouds of small vertical thickness could be as low as 20 per cent.The clouds forming in the Deccan Plateau region during the summer monsoon are, by and large, cumulus and strato-cumulus type. The vertical thickness of the cumulus clouds is in the range of 1.0-2.0 km. The LWC is found to be more in the region between 1.6-1.9 km A. S. L., which corresponds to the level at almost 3 / 4 th of the total vertical thickness of the cloud and thereafter the LWC sharply decreased. Nearly 98 percent of the tops of the low clouds in the region are below freezing level and the most frequent range of occurrence of these cloud—tops is in the range of 2.0-3.0 km A. S. L. The dominant physical mechanism of rain-formation in these summer monsoon clouds is the collision-coalescence process.

Some unique characteristics of atmospheric interannual variability in rainfall time series over India and the United Kingdom

Continuous periodogram analyses of two 50-years (1871–1920 and 1936–1985) of summer monsoon rainfall over the Indian region and one 84-years set (1893–1976) of winter half-year rainfall over England and Wales show that the power spectra of disparate rainfall regimes follow the universal and unique inverse power law form of the statistical normal distribution with the percentage contribution to total variance representating the eddy probability corresponding to the normalized standard deviation equal to [(log L/logT50)−1] whereL is the period in years andT50 the period up to which the cumulative percentage contribution to total variance is equal to 50. The above results are consistent with a recently developed non-deterministic cell dynamical system model for atmospheric flows. The implications of the above results for prediction of interannual variability of rainfall is discussed.

Diurnal and seasonal variations of space charge, electric field and cloud condensation nuclei in the lowest layer of the atmosphere

Diurnal and seasonal variations of space charge, vertical electric field and cloud condensation nuclei in the lowest layers of the atmosphere during winter, pre-monsoon, monsoon and post-monsoon seasons were studied. The curve showing the diurnal variation of space charge exhibited a double oscillation corresponding to that of the electric field during winter and pre-monsoon seasons. Similar features are absent during monsoon and post-monsoon seasons. During pre-monsoon the semi-diurnal components of space charge and electric field are in phase while in winter the semi-diurnal component of space charge occurs 1 h ahead of the electric field component. The mean values and diurnal ranges of both space charge and electric field are high during winter/pre-monsoon and are low during monsoon/post-monsoon seasons. The diurnal range of temperature and concentration of cloud condensation nuclei are positively correlated with space charge and the electric field. The pre-sunrise minimum in the electric field is associated with the characteristics of the F-region of the ionosphere rather than with the ground sunrise time. The variations in the F, layer critical frequency (foFJ are reflected in the diurnal and ter-diurnal components of the surface electric field. The results of the present study support the hypothesis that the increase in the electrosphere potential could be the source of the atmospheric electric sunrise effect (Muir, 1975).

A Universal Spectrum for Interannual Variability of Monsoon Rainfall over India

Continuous periodogram analyses of 115 years (1871–1985) summer monsoon rainfall over the Indian region show that the power spectra follow the universal and unique inverse power law form of the statistical normal distribution with the percentage contribution to total variance representing the eddy probability corresponding to the normalized standard deviation equal to [(logL / logT50)-1] whereL is the period length in years andT50 the period up to which the cumulative percentage contribution to total variance is equal to 50. The above results are consistent with a recently developed non-deterministic cell dynamical model foratmospheric flows. The implications of the above result for prediction of interannual variability of rainfall is discussed.

Variations of Thermodynamical Parameters in the Atmospheric Boundary Layer over the Deccan Plateau Region, India

The thermodynamical structure of the atmospheric boundary layer over the Deccan plateau region has been studied with aerological data for 1980 and 1981.The temperatures in the sub-cloud layer were lower on active monsoon days than dose on weak monsoon days. An opposite trend was noticed in the layer above the 900 mbar level. The moisture content on active monsoon days was higher than that on weak monsoon days. The profile of relative humidity above the 850 mbar level showed large deviations between the active and weak monsoon conditions. On active monsoon days the values of dry static stability were higher than those on weak monsoon days. An opposite trend was noticed in the case of moist static stability. On active monsoon days the magnitudes of thev components of wind were small compared with those of theu components, and the latter showed a gradual decrease with height.

A study of the gaseous and particulate pollutants in the environment of a thermal power plant project area

Observations on gaseous and particulate pollutants were undertaken at four locations in the region of a thermal power plant (TPP), which is under construction at Tuticorin, south India. The predicted concentrations Of SO2 due to the emissions from the TPP and its possible impact on the inhabitants and climate in the downwind region were evaluated. Also, the predicted concentrations downwind of a Petrochemical Industrial Complex (PIC) located in the vicinity of the TPP were computed and compared with the measured concentrations.The predicted maximum concentration of SO2 at 6 km downwind of TPP is about 530 μg m−3 under most favourable wind conditions. The anticipated increase in SO2 due to the thermal power plant under construction may therefore be substantial.The predicted concentrations Of SO2, at a distance of 1.8 km downwind of the PIC, varied between 34 and 216 μg m−3 for wind directions ranging from 70 to 90° and for Pasquill stability category C. The plume would be over the observational site when the wind direction is 80°. The maximum measured concentration was 23 ug m−3. The discrepancy was due to the rapid fluctuations in the wind direction during the observational period over a wide range from 20 to 90°.