A simple model of a building cumulus cloud

Summary A model of a building cumulus structure is described. The one-stage model published in[1] was used to describe ascent of two cloudy parcels that a cloud is supposed to be formed of. The other ascent is assumed to take place after the first cloud element sinks back as a result of evaporative cooling. The numerical results and their evaluation are given for various rates of mixing at the cloud top level of the first cloud volume.     

A steady-state model of a cumulus cloud

nua u mam n ma aa ¶rt;mn ¶rt;u aa, ma a n¶rt;a [1]. mma m ¶rt;u aa a ¶rt;auu nauMi (uuuu n) uMa (¶rt;uauu anm), m amm u nu [2–5]. u¶rt;m mam u nu ¶rt;u ¶rt; u¶rt; mu ¶rt; u a ¶rt; ¶rt;a. mu a aa, n¶rt;ua m a aa, nua a¶rt; u u _i uu a a¶rt; z_i nu nu aa ¶rt; ¶rt;a, m ¶rt;um mua m, a¶rt;u ¶rt; a, ¶rt;m, mnam, anu ¶rt; naa, nm a an u nu. a ¶rt;mn ¶rt;u m n a nu u ¶rt;mn ¶rt;u, ma a ma n¶rt;a [1].     

A simple formula for the second derivative method of interpretation

Summary Second derivative coefficients for various grid systems are derived followingPeters' andElkins' approaches. Two simple formulae, one for three dimensional bodies and the other for two dimensional bodies are also suggested. These utilise the average of the anomalies around a single circle and the anomaly at the central point.All the coefficient sets and the proposed simple formulae are applied to gravity fields of spheres and cylinders. Coefficients ofElkins' type derived with a weightage of 1/r ⁴ to all the circles gave excellent results in both the cases of spheres and cylinders, whereasPeters' coefficients without any weightage to the circles gave reliable results in case of cylinders only. The simple formulae suggested gave more accurate results than any of the above coefficient sets.     

A parameterization scheme for upward lightning in the cloud model and a discussion of the initial favorable environmental characteristics in the cloud

The upward lightning (UL) initiated from the top of tall buildings (at least above 100 m) is a type of atmospheric discharge. Currently, we understand the nature of the UL from ground observations, but the corresponding theoretical research is lacking. Based on an existing bidirectional leader stochastic model, a stochastic parameterization scheme for the UL has been built and embedded in an existing two-dimensional thundercloud charge/discharge model. The ULs simulated from the experiments with two-dimensional high resolution agree generally with the observation results. By analyzing the charge structure of thunderstorm clouds, we determined the in-cloud environmental characteristics that favor the initiation of conventional cloud-to-ground (CG) flashes and analyzed the differences and similarities of some characteristics of the positive and the negative UL. Simulation results indicate that the positive ULs are typically other-lightning-triggered ULs (OLTUL) and are usually a discharge phenomenon between the ground and the lower positive charge region appearing below the main middle negative charge region. The effect of the previous in-cloud lightning (IC) process of space electrical field provides favorable conditions for the initiation of a positive UL. Its entire discharge process is limited, and the branches of the leader are fewer in number as its discharge is not sufficient. A negative UL is generally a discharge phenomenon of the dipole charge structure between the ground and the main negative charge region. The lower temperature stratification and the sinking of the hydrometeors typically initiate a negative UL. Negative ULs develop strongly and have more branches. The OLTUL is initiated mainly during the development stage of a thunderstorm, while the self-triggered UL (STUL) is initiated mainly during the dissipation stage of a thunderstorm.     

A comparison of total precipitation values estimated from measurements and a 1D cloud model

The purpose of this study is to establish a relation between observed total precipitation values and estimations from a one-dimensional diagnostic cloud model. Total precipitation values estimated from maximum liquid water content, maximum vertical velocity, cloud top height, and temperature excess are also used to provide an equation for the total precipitation prediction. Data for this study were collected in Istanbul during the autumns of 1987 and 1988. The statistical models are developed with multiple regression technique and then comparatively verified with independent data for 1990. The multiple regression coefficients are in the range of 75% to 80% in the statistical models. Results of the test showed that total precipitation values estimated from the above techniques are in good agreement, with correlation coefficient between 40% and 46% based on test data for 1990.     

Parameterizations of cloud feedback in a radiative-convective model

The effect of cloud feedback on the response of a radiative-convective model to a change in cloud model parameters, atmospheric CO₂ concentration, and solar constant has been studied using two different parameterization schemes. The method for simulating the vertical distribution of both cloud cover and cloud optical thickness, which depends on the relative humidity and on the saturation mixing ratio of water vapor, respectively, is the same in both approaches, but the schemes differ with respect to modeling the water vapor profile. In scheme I atmospheric water vapor is coupled to surface parameters, while in scheme II an explicit balance equation for water vapor in the individual atmospheric layers is used. For both models the combined effect of feedbacks due to variations in lapse rate, cloud cover, and cloud optical thickness results in different relationships between changes in surface temperature, planetary temperature, and cloud cover. Specifically, for a CO₂ doubling and a 2% increase in solar constant, in both models the surface warming is reduced by cloud feedback, in contrast to no feedback, with the greater reduction in scheme I as compared to that of scheme II.     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

On the interpretation of recharge estimates from steady-state model calibrations

Ground water recharge is often estimated through the calibration of ground water flow models. We examine the nature of calibration errors by considering some simple mathematical and numerical calculations. From these calculations, we conclude that calibrating a steady-state ground water flow model to water level extremes yields estimates of recharge that have the same value as the time-varying recharge at the time the water levels are measured. These recharge values, however, are a subdued version of the actual transient recharge signal. In addition, calibrating a steady-state ground water flow model to data collected during periods of rising water levels will produce recharge values that underestimate the actual transient recharge. Similarly, calibrating during periods of falling water levels will overestimate the actual transient recharge. We also demonstrate that average water levels can be used to estimate the actual average recharge rate provided that water level data have been collected for a sufficient amount of time.     

瞬变电磁快速成像解释系统研究

为了提高瞬变电磁测深法对地探测的垂向分辨能力,文中研究了磁偶源瞬变电磁法快速成像的方法.详细讨论了电磁波与地震波在介质中的传播规律,分析了磁偶源瞬变电磁场在远区的响应特性.根据磁偶源瞬变电磁场与反射地震波的传播规律的相似性,提出了TEM资料拟地震快速成像解释的思路.理论模型正、反演计算结果表明方法理论是可行的,野外实测资料处理结果进一步说明了该方法是有效的.     

A theoretical model of water and trade

Water is an essential input for agricultural production. Agriculture, in turn, is globalized through the trade of agricultural commodities. In this paper, we develop a theoretical model that emphasizes four tradeoffs involving water-use decision-making that are important yet not always considered in a consistent framework. One tradeoff focuses on competition for water among different economic sectors. A second tradeoff examines the possibility that certain types of agricultural investments can offset water use. A third tradeoff explores the possibility that the rest of the world can be a source of supply or demand for a country’s water-using commodities. The fourth tradeoff concerns how variability in water supplies influences farmer decision-making. We show conditions under which trade liberalization affect water use. Two policy scenarios to reduce water use are evaluated. First, we derive a target tax that reduces water use without offsetting the gains from trade liberalization, although important tradeoffs exist between economic performance and resource use. Second, we show how subsidization of water-saving technologies can allow producers to use less water without reducing agricultural production, making such subsidization an indirect means of influencing water use decision-making. Finally, we outline conditions under which riskiness of water availability affects water use. These theoretical model results generate hypotheses that can be tested empirically in future work.     

一个中纬电离层E层理论模式

本文建立了一个中纬电离层E层理论模式. 该模式从NO+,O２＋,O+和N２＋这四种主要离子的连续性方程出发,通过数值模拟得到中纬电离层E层电子和各种离子密度随时间和高度的变化情况. 计算结果能较好地反映出E层电子密度峰值（NmE）或E层临界频率（foE）的日变化、季节变化以及随太阳活动的变化趋势. 将模式的计算结果与武汉地区测高仪的观测数据进行比较,结果证明模式能够较为客观地反映中纬电离层E层的实际形态. 针对以往电离层E层理论模式存在的主要问题,本文还进一步讨论了几种重要因素,包括二次离化源,λ<150?谱段的辐射通量,吸收截面以及NO分布对于模式计算结果的影响.     

Geomagnetic reversals in a simple geodynamo model

A simple finite-dimensional geodynamo model, obtained from the equations of the mean field electrodynamics and reproducing the phenomenon of geomagnetic reversals, is proposed. It has been indicated that the reversal scale obtained in the scope of this model is rather close to the observed scale in its properties. The reversal mechanism is related to the α-effect fluctuations. It is not necessary to substantially change the hydrodynamic parameters of the problem so that a reversal originates in the scope of such a model, but it is only sufficient to take the α-effect fluctuations into account. If the rms deviation of fluctuations accounts for 10% of the average α value, a fluctuation of two-three standard deviations is sufficient for the origination of a reversal, which quite agrees with the concept that reversals are rather rare phenomena. Another factor resulting in the regime with reversals is that the model can generate magnetic fields with different behaviors in different regions of the parametric space in linear mode: monotonically increasing fields and fields increasing with oscillations.     

A simple model to estimate monthly forest evapotranspiration in Japan from monthly temperature

The estimation of evapotranspiration (E) in forested areas is required for various practical purposes (e.g. evaluation of drought risks) in Japan. This study developed a model that estimates monthly forest E in Japan with the input of monthly temperature (T). The model is based on the assumptions that E equals the equilibrium evaporation rate (E_eq) and that E_eq is approximated by a function of T. The model formulates E as E (mm month⁻¹) = 3·48 T ( °C) + 32·3. The accuracy of the model was examined using monthly E data derived using short‐term water balance (WB) and micrometeorological (M) methods for 15 forest sites in Japan. The model estimated monthly E more accurately than did the Thornthwaite and Hamon equations according to regression analysis of the estimated E and E derived using the WB and M methods. Although the model tended to overestimate monthly E, the overestimation could be reduced by considering the effect of precipitation on E. As T data are commonly available all over Japan, the model would be a useful tool to estimate forest E in Japan. Copyright © 2010 John Wiley & Sons, Ltd.     

The use of the simple 1D steady-state convective cloud model in the decision tree for determining the probability of thunderstorm occurrence

Summary The algorithm of a binary decision tree [1–3] determining the probability of thunderstorm occurrence was applied to a set of predictors including the instability indices and results of the 1D steady-state convective cloud model. Predictants A, B, C, D=1/0 correspond to various temporal and spatial limits for thunderstorm occurrence recorded at synoptic stations in an area 100km around Prague. The predictors were found on the basis of TEMP 12.00 GMT data from the Prague Libuš station for the months V–VIII in the years 1981–1985. The first tests were carried out to compare the decision quality for various types of predictants and for sets of predictors consisting only of the instability indices, only of model predictors and of both quantities. The best results were obtained using a decision tree constructed on the basis of sets of all the predictors, where the model predictors were employed primarily in the unstable branch of the tree. The best decision quality was obtained for predictant B, in agreement with the concept of the strongest connection between the thermodynamic state of the atmosphere and the area of the extent of thunderstorm occurrence.

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Резюме К нaбору nре?rt;uкmоров, включaющему uн?rt;ексы неусmоŭчuвосmu u резульmamы о?rt;номерноŭ сmaцuонaрноŭ мо?rt;елu кучево?rt;о облaкa, был nрuменен aл?rt;орumм ?rt;воuчно?rt;о рaзрешaюще?rt;о ?rt;еревa [1–3], оnре?rt;еляющuŭ верояmносmь nоявленuя ?rt;розы. Пре?rt;uкmaнmы А, В, С, D=1/0 сооmвеmсmвуюm рaзному временному u nросmрaнсmвенному оnре?rt;еленuю nоявленuя ?rt;розы, зaре?rt;uсmрuровaнному сuноnmuческuмu сmaнцuямu в 100-кuломеmровоŭ окресmносmu Прa?rt;u. Пре?rt;uкmоры былu оnре?rt;елены нa основе ?rt;aнных ТЕМР 12.00 ГМТ с сmaнцuu Прa?rt;a Лuбущ ?rt;ля месяцев V–VIII 1981–1985. Первые mесmы нanрaвлены нa срaвненuе кaчесmвa рaзрешенuя ?rt;ля рaзных munов nре?rt;uкmaнmов u ?rt;ля нaборов nре?rt;uкmоров, сосmоящuх mолько uз uн?rt;ексов неусmоŭчuвосmu, mолько uз мо?rt;ельных nре?rt;uкmоров u uз велuчuн о?rt;оuх munов. Нauлучшuе резульmamы uмеюm рaзрешaющuе ?rt;еревья, nосmроенные нa нaборaх всех nре?rt;uкmоров, nрuчем мо?rt;ельные nре?rt;uкmоры ?rt;еŭсmвуюm nреж?rt;е все?rt;о в неусmоŭчuвоŭ веmвu ?rt;еревьев. Нauвысше?rt;о кaчесmвa рaзрешенuя было ?rt;осmu?rt;нуmо ?rt;ля nре?rt;uкmaнma В, чmо нaхо?rt;umся в со?rt;лaсuu с nоняmuем о сaмоŭ сuльноŭ связu меж?rt;у mермо?rt;uнaмuческuм сосmоянuем amмосферы u nоверхносmью, нa коmороŭ uмееm шuрокое nоявленuе ?rt;роз.