Atmospheric radiative equilibria in a simple column model

 An analytic radiative-equilibrium model is formulated where both short- and longwave radiation are treated as two-stream (down- and upward) fluxes. An equilibrium state is defined in the model by the vertical temperature profile. The sensitivity of any such state to the model atmosphere’s optical properties is formulated analytically. As an example, this general formulation is applied to a single-column 11-layer model, and the model’s optical parameters are obtained from a detailed radiative parametrization of a general circulation model. The resulting simple column model is then used to study changes in the Earth-atmosphere system’s radiative equilibrium and, in particular, to infer the role of greenhouse trace gases, water vapor and aerosols in modifying the vertical temperature profile. Multiple equilibria appear when a positive surface-albedo feedback is introduced, and their stability is studied. The vertical structure of the radiative fluxes (both short- and longwave) is substantially modified as the temperature profile changes from one equilibrium to another. These equilibria and their stability are compared to those that appear in energy-balance models, which heretofore have ignored the details of the vertical temperature and radiation profiles. Received: 22 December 1995/Accepted: 17 January 1997     

Self-generated aperiodic behaviour in a simple climate model

Climatic variability arising from the coupling between ocean temperature and sea-ice extent is studied in a spatially distributed system. A spatial degree of freedom is crudely introduced by the coupling, through energy transfer, of two box models each of which describes a different space region. The evolution equations are cast into a normal form and some qualitative features of this general class of models are predicted. It is shown, both analytically and numerically, that internally generated complexity in the form of aperiodic behaviour can be a natural consequence of spatially distributed systems.     

A simple quasi-geostrophic coupled ocean-atmosphere model

The quasi-geostrophic atmospheric and oceanic equations of momentum and thermodynamics with dissipation factors are used to create a simple coupled ocean-atmosphere model describing the large-scale shallow-water mo-tion. We discuss the ocean-atmosphere coupling effect in mid-high and low latitudes separately and analyze charac-teristics of which the oscillatory periods of coupled low-frequency modes (ocean mode) vary with the coupling fre-quency and latitudinal number. This can interpret the correlation between low-frequency oscillation and ocean-at-mosphere interaction. Then from the dispersion curves of atmosphere and ocean, we reveal effect of the coupling strength on the propagation of Rossby waves. The convection mechanism between the two modes is also discussed in view of the slowly varying wave train.The results show that Newtonian cooling and Rayleigh friction play a stable rule in oceanic Rossby waves, the period of coupled low-frequency mode grows with the increment of the coupling frequency. The larger the latitudinal number is, the more rapidly it grows. When the coupling frequency tends to critical value, the oceanic Rossby waves become static. When the ocean-atmosphere coupling strength grows to some degree, the propagation of oceanic Rossby waves will become opposite to its original direction. One part of the oceanic Rossby waves is converted into atmospheric Rossby waves, the energy conversion coefficient is also solved out.     

A simple model of drainage flow in a valley

A model of the drainage flow in a valley under calm conditions has been developed on the basis of the conservation laws of mass, momentum, and heat. The inflow of mass and heat from side-slopes is incorporated, and the momentum and sensible heat exchanges between valley drainage flow and valley floor are parameterized.The characteristic velocity of valley drainage flow is expressed in terms of the following parameters: three potential temperature differences representing the temperature field in the valey; topographic parameters of the valley; mean bulk coefficients representing the aerodynamic conditions of the valley floor; and the stability of the ambient atmosphere. The characteristic thickness includes additional parameters of side-slope flow.That the model satisfactorily predicts the characteristic thickness and velocity is shown from comparison with observations from valleys several hundred meters to a few hundred kilometers long.     

A simple model for large-scale thermohaline convection

Large-scale thermohaline circulation cells in the world oceans exist due to horizontal density gradients. Owing to differential heating between equator and pole a north-south density gradient is present at the ocean surface. An additional mechanism for producing north-south density gradients is the heat and salinity transport by boundary currents in the upper parts of the world oceans. In the North Atlantic, high density sinking water is produced by a convergence of salt water from the south and cold water from the north.We have investigated large-scale thermohaline convection cells by time integrating a two-dimensional Boussinesq model. The flow is driven by an imposed density gradient at the upper boundary (mixed layer) and an externally prescribed, meridionally varying density flux in the interior of the model domain. We perform numerical simulations and through time integrations we determine equilibrium states of the model. By changing the forcing parameters slowly during the course of a time integration, we have identified regions in parameter space where a hysteretic behaviour may be found. For a given set of the forcing parameters the model has two stable equilibrium states which differ in the direction of the circulation.We have thus found that due to the nonlinear nature of the balance between advection, internal mixing and forcing more than one stable equilibrium circulation pattern can be found under a given set of external forcing parameters. This result may offer a potential explanation for the existing asymmetries between the thermohaline circulation patterns in the Atlantic and Pacific Oceans as well as possible implications for the climatic state of the oceans under changing external conditions.     

A simple mathematical model of airflow in waving plant canopies

A simple mathematical model is proposed, which combines the effects of mean wind speed, plant spacing and the drag coefficients of individual plants to calculate the fluctuating airflow within a waving crop canopy. The model is non-linear and is only amenable to analytical treatment when linearized; however, the full non-linear version can be solved on an analogue computer.The linear and non-linear results show unexpectedly good agreement, and the success of the linearization allows clear conclusions to be drawn about the relationship between the elasticity, geometry and mean wind speed through a stand of plants and the fluctuating components of airflow and stalk motion.Finally, the analytical results are in qualitative agreement with wind-tunnel results from two model canopies with different characteristics.     

A simple model for potential dewfall in an arid region

It is not always easy to know, post-facto, whether both dewfall and fog may have occurred over a given evening period. Instrumentation limitations make it difficult to quantify dew deposition since they rely on artificial sensing surfaces that are either visually examined on a daily basis or recorded. In arid to Mediterranean regions, both dew and fog can play significant ecological roles as suppliers of moisture. Long-term observation records of dew and fog in such regions tend to be limited, however, due partly to a lack of interest and limited distribution of well-instrumented meteorological stations. Simple meteorological criteria are suggested here to calculate potential dewfall and to indicate whether fog was likely to have occurred over a given evening. A field campaign was carried out in the NW Negev desert, Israel, in September and October 1997, to collect meteorological data and carry out dewfall measurements.     

输电线路运行安全影响因素分析及防治措施

以浙江省为例,进行省域冰区图绘制和杆塔尺度的输电线路评估。首先,利用覆冰生成数值模式,针对2005— 2014年覆冰灾害进行了逐小时0.01°× 0.01°分辨率的覆冰过程反演,结合Gumbel极值分布刻画各栅格超越概率分布并绘制浙江省冰区图;其次,通过多因素比较分析,建立基于高程要素的杆塔覆冰降尺度方案;最后,基于区域灾害风险评估方法,选取易损性评估模型,对浙江省输电线路覆冰灾害下的杆塔失效率给出了定量评估。结果显示,浙江省冰区呈北、中、南带状分布,且中部覆冰带可能强度最大;在当前气候背景条件下,忽略人为抗冰、融冰等作用,浙江省中部及北部的输电线路覆冰风险相对较高。

     

The development and structure of nocturnal slope winds in a simple valley

The results of an observational and modeling study of the nocturnal slope winds in a simple valley are presented. The valley was approximately 225 m deep in the region of the measurements, and featured a uniform slope angle of approximately 23 ° on one of its sidewalls. The wind and temperature structure of the katabatic flows on the valley sidewalls were measured with tower-mounted instruments, and a Doppler sodar and instruments on a tethered balloon and a 61-m tower were used to determine the atmospheric conditions near the center of the valley. The temperature structure of the slope flows was summarized by characteristic scale parameters h and T for the inversion depth and strength, respectively. On the sidewalls 50 m above the valley floor, the inversion depths were generally smaller and the inversion strengths were weaker than they were on the sidewalls 100 m higher. These results differ significantly from those obtained over a simple slope of an isolated mountain or ridge. The down-valley winds are shown to be important in limiting the strength of the sidewall inversions. The formation of an inversion in the valley also has a pronounced effect on the structure of the slope flows. Numerical simulations suggest that the presence of adiabatic layers in the valley atmosphere is associated with decreases in the slope-flow inversion depth with increasing downslope distance. The simulations also indicate that the length scales that characterize the momentum and inversion depths behave similarly in flows down simple slopes but not in flows down the sidewalls of a valley.Work supported by the U.S. Army Research Office under Contract DA-AG29-K-0231 and the U.S. Department of Energy under Contract DE-AC06-76RLO 1830.     

Convective momentum transport in a simple multicloud model for organized convection

从多层原始方程组出发,分析了不同尺度天气系统各层的动能水平梯度与该层地转偏差之间的关系,并对南京2010年7月22日暴雨过程的动能水平梯度模进行了诊断。结果表明：在天气尺度和α中尺度系统中,各层动能水平梯度模与该层地转偏差的模大致成正比。对天气尺度系统,该比例系数为地转参数,与该系统本身无关。对α中尺度系统,该比例系数与该系统本身有关。在β中尺度系统中,各层动能水平梯度模小于等于两项之和,而这两项中第一项与地转偏差的模成正比,另一项则为地转偏差时间导数的模。动能水平梯度大值区运动的非平衡性和爆发性强。在暴雨落区和飑线上,各层动能水平梯度的模均较大。通过对动能水平梯度模的诊断,能够从风场角度来分析各尺度系统,这对中尺度系统的诊断分析尤为重要。

     

Behaviour of Coupled Modes in a Simple Nonlinear Air-Sea Interaction Model

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Continuous versus discontinuous albedo representations in a simple diffusive climate model

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.     

A simple model of drainage flow on a slope

The concept of a cold air ‘Parcel’ is introduced for describing the bulk properties of drainage flow. By means of a model based on the momentum and sensible heat transports under calm conditions, the thickness h and velocity u of the Parcel are derived in simple forms. It is shown that h and u correspond to the inversion height and maximum velocity of actual drainage flow. The governing parameters for h and u are the length and vertical drop of the slope, potential temperature difference between the ambient atmosphere and the Parcel, aerodynamic condition of the slope surface expressed by the mean bulk coefficients, and ambient stability. The mean bulk coefficients depend on the roughness lengths for the velocity and potential temperature profiles and are decreasing functions of the slope length. The Parcel Model agrees qualitatively with Manins and Sawford's (1979) model under neutral ambient stratification. But agreement is not so good under stable conditions. The thickness and velocity of drainage flow predicted by the Parcel Model agree with observations on slopes several tens of meters to several hundred kilometers long.     

A simple model of blocking action over a hemisphere

Theoretical and Applied Climatology - A two-zone model of the atmospheric circulation over a hemisphere is considered. The latitude φ of the boundary between the zone of the Rossby circulation...     

Flux correction: tests with a simple ocean-atmosphere model

 Flux correction schemes are used in order to suppress the drift of coupled ocean atmosphere models. This technique is tested for a simple box model of the climate system. Two “perfect” models of the ocean and the atmosphere are available. These are coupled to form an ocean-atmosphere model representing the true climate system. This climate system is simulated by a climate model which is also constructed by coupling those two perfect models. This time, however, both models are run first separately as models of the atmosphere and the ocean. In that case, “observations” from the climate system are prescribed at the ocean surface in the uncoupled models. It is assumed that these observations are imperfect. A drift results, when these models are coupled to form an ocean-atmosphere stimulation model. A flux adjustment scheme is implemented to remove this drift. It is argued that the merits and shortcomings of the flux correction technique can be assessed more clearly this way than by coupling imperfect models as is done normally. Sensitivity tests are performed where either radiation parameters are changed or a salt anomaly is implanted. Model parameters are chosen such that the ocean has a thermally direct circulation in the unperturbed climate state. It is found that the flux correction technique is performing satisfactorily as long as the imposed perturbations are small enough so that the ocean circulation does not change its sense. If, however, the model climate is close to the transition to an indirect circulation, then the flux correction technique is unreliable. The predictions of the coupled model with flux correction may deviate substantially from the response of the climate system in that case. Received: 4 December 1995/Accepted: 15 October 1996     

A coupled simple climate model and its global analysis

Summary An atmosphere-land coupled simple climate model is constructed and its climatic properties are analyzed by introducing a global analysis method, cell mapping. The simple model is a nonlinear six order simplified climate model featured with chaotic dynamics, dissipation, and forcing source, which are the main features of the real climate system. The cell mapping method is applied with this coupled system. Numerical experiments are carried out for investigating the interactions between the fast-changing atmospheric variables and slow-changing underlying surface variables. The predictability of the system is also investigated via the global analysis, with which the evolution of the system is translated to the evolution of probability transition on a Markov Chain. An effective scheme is proposed for computing the probability transition matrix for the coupled system. Predictions can be made based on the combination of dynamics and statistics. The importance of constructing the coupled model is shown by globally analyzing the predictability of the coupled system. The coupling mechanism prolongs the memorization of initial information, and then the predictability as well.