Application of a mixed-layer model to bare soil surfaces

A model that couples the surface energy balance equation, a surface hydraulic resistance equation, and the force-restore soil temperature model to a mixed-layer model of the planetary boundary layer is described. The mixed layer is separated from the soil by a relatively thin surface layer and is overlain by a stable free atmosphere with prescribed profiles of potential temperature and water vapour density. The model is in reasonably good agreement with daytime micrometeorological measurements made at a wet bare site at Agassiz, British Columbia, and a desert site at Pampa de La Joya, Peru. The sensitivity of the mixed-layer model to conditions in the free atmosphere, to the parameters describing the growth of the mixed layer, and to surface roughness lengths, surface hydraulic resistance, and windspeed is examined.     

A mixed-layer model for regional evaporation

A simple mixed-layer model is developed to describe evaporation into a convective planetary boundary layer (PBL). The model comprises volume budget equations for temperature and humidity, equations to describe transport through the surface layer which is treated as part of the lower boundary, and equations to describe entrainment at the top of the PBL. The ground surface is modelled as a canopy resistance. The model was integrated with canopy resistance, surface-layer resistance and available energy, (R _n – G), input as given functions of time, and the simulated PBL was allowed to grow into an atmosphere with known temperature and humidity profiles.Two variants of the mixed-layer model were tested using data from the KNMI tower site at Cabauw in the Netherlands. These variants differed only in the formulation of entrainment: one used a formulation developed by Driedonks (1982) while the other was a simpler formulation. Simulated evaporation agreed very well with observations irrespective of which entrainment formulation was used, despite discrepancies between simulated and observed PBL height growth which were sometimes quite large for the simpler formulation. Sensitivity analysis of the model confirms that good PBL height-growth predictions are not always a prerequisite for good evaporation predictions.     

The behaviour of a mixed-layer model of the convective boundary layer coupled to a big leaf model of surface energy partitioning

Daily mean values of the Priestley-Taylor coefficient, ¯, are derived from a simple model of the daily growth of a convective boundary layer. For a particular control set of driving environmental variables, ¯ is related to the prescribed bulk surface resistance, r_S by 1/¯ = 1/₀ + mr_S for parameters ₀ and m. The dependence of the parameters ₀ and m on weather is explored and a potential use of this linear relation to provide information about regional values of r_S is indicated.     

Dynamics of sea-surface temperature anomalies in the Southern Ocean diagnosed from a 2D mixed-layer model

We analyze the processes responsible for the generation and evolution of sea-surface temperature anomalies observed in the Southern Ocean during a decade based on a 2D diagnostic mixed-layer model in which geostrophic advection is prescribed from altimetry. Anomalous air–sea heat flux is the dominant term of the heat budget over most of the domain, while anomalous Ekman heat fluxes account for 20–40% of the variance in the latitude band 40°?60°S. In the ACC pathway, lateral fluxes of heat associated with anomalous geostrophic currents are a major contributor, dominating downstream of several topographic features, reflecting the influence of eddies and frontal migrations. A significant fraction of the variability of large-scale SST anomalies is correlated with either ENSO or the SAM, each mode contributing roughly equally. The relation between the heat budget terms and these climate modes is investigated, showing in particular that anomalous Ekman and air–sea heat fluxes have a co-operating effect (with regional exceptions), hence the large SST response associated with each mode. It is further shown that ENSO- or SAM-locked anomalous geostrophic currents generate substantial heat fluxes in all three basins with magnitude comparable with that of atmospheric forcings for ENSO, and smaller for the SAM except for limited areas. ENSO-locked forcings generate SST anomalies along the ACC pathway, and advection by mean flows is found to be a non-negligible contribution to the heat budget, exhibiting a wavenumber two zonal structure, characteristic of the Antarctic Circumpolar Wave. By contrast SAM-related forcings are predominantly zonally uniform along the ACC, hence smaller zonal SST gradients and a lesser role of mean advection, except in the SouthWest Atlantic. While modeled SST anomalies are significantly correlated with observations over most of the Southern Ocean, the analysis of the data-model discrepancies suggests that vertical ocean physics may play a significant role in the nonseasonal heat budget, especially in some key regions for mode water formation.     

CO2 climate sensitivity and snow-sea-ice albedo parameterization in an atmospheric GCM coupled to a mixed-layer ocean model

The snow-sea-ice albedo parameterization in an atmospheric general circulation model (GCM), coupled to a simple mixed-layer ocean and run with an annual cycle of solar forcing, is altered from a version of the same model described by Washington and Meehl (1984). The model with the revised formulation is run to equilibrium for 1 × CO₂ and 2 × CO₂ experiments. The 1 ×CO₂ (control) simulation produces a global mean climate about 1° warmer than the original version, and sea-ice extent is reduced. The model with the altered parameterization displays heightened sensitivity in the global means, but the geographical patterns of climate change due to increased carbon dioxide (CO₂) are qualitatively similar. The magnitude of the climate change is affected, not only in areas directly influenced by snow and ice changes but also in other regions of the globe, including the tropics where sea-surface temperature, evaporation, and precipitation over the oceans are greater. With the less-sensitive formulation, the global mean surface air temperature increase is 3.5 °C, and the increase of global mean precipitation is 7.12%. The revised formulation produces a globally averaged surface air temperature increase of 4.04 °C and a precipitation increase of 7.25%, as well as greater warming of the upper tropical troposphere. Sensitivity of surface hydrology is qualitatively similar between the two cases with the larger-magnitude changes in the revised snow and ice-albedo scheme experiment. Variability of surface air temperature in the model is comparable to observations in most areas except at high latitudes during winter. In those regions, temporal variation of the sea-ice margin and fluctuations of snow cover dependent on the snow-ice-albedo formulation contribute to larger-than-observed temperature variability. This study highlights an uncertainty associated with results from current climate GCMs that use highly parameterized snow-sea-ice albedo schemes with simple mixed-layer ocean models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

An advective mixed-layer model for heat and moisture incorporating an analytic expression for moisture entrainment

A slab mixed-layer model with zero-order entrainment for both temperature and humidity is developed in order to examine the relative magnitude of advective and turbulence flux convergence effects. The model formulation provides an analytic function for the ratio of surface-layer to entrainment-layer humidity flux. Model results are compared with measured mixed-layer properties over one day at a coastal location. It is concluded that the model is highly successful at simulating the mixed-layer depth, and mean mixed-layer humidity. It is suggested that a first-order model may be more appropriate for the latter half of the day when the mixed-layer depth is decreasing due to the dominance of advection over vertical turbulence flux convergence.     

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 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 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...     

A simple model of dry convective helical vortices (with applications to the atmospheric dust devil)

An asymptotic solution of inviscid Boussinesq equations for a ‘dry convective Rankine vortex’ with prescribed buoyant forcing is given. The obtained vortex solution demonstrates monotonic growth with height of the vortex core radius, which becomes infinite at a certain critical altitude, and the corresponding attenuation of the vertical vorticity. This idealized vortex is then embedded in a convectively unstable boundary layer; the resulting approximate vortex solution has been applied to determine the maximum rotational wind speed and diameter of dry convective dust-devil-like vortices.     

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     

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

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On a simple dynamics model of interaction between oasis and climate

This paper constructs a coupled system of oasis and atmosphere based on an oasis evolvement model by adding atmospheric motion to discuss the problem of oasis evolvement and its effects on regional climate.The results indicate that the range and scope of the negative temperature anomalies become larger when the oasis cover fraction increases. Correspondingly, the positive temperature anomalies becomes smaller in the desert no matter in summer or spring. And the variability is more obvious in summer than in spring.So it may be concluded that the oasis not only maintains and develops itself but also develops partial air over the desert into an oasis climate.     

Implementation of a one-dimensional enthalpy sea-ice model in a simple pycnocline prediction model for sea-ice data assimilation studies

To further explore enthalpy-based sea-ice assimilation, a one-dimensional(1D) enthalpy sea-ice model is implemented into a simple pycnocline prediction model. The 1D enthalpy sea-ice model includes the physical processes such as brine expulsion, flushing, and salt diffusion. After being coupled with the atmosphere and ocean components, the enthalpy sea-ice model can be integrated stably and serves as an important modulator of model variability. Results from a twin experiment show that the sea-ice data assimilation in the enthalpy space can produce smaller root-mean-square errors of model variables than the traditional scheme that assimilates the observations of ice concentration, especially for slow-varying states. This study provides some insights into the improvement of sea-ice data assimilation in a coupled general circulation model.     

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。

     

Chaos in a simple model of the three-dimensional, salt-dominated ocean circulation

 A simple moments model used in studying the large-scale thermally driven ocean circulation, in one hemisphere, is extended with a set of evolution equations for the basin-averaged salinity gradients. Natural formulations of the boundary conditions for the heat flux and the (virtual) salt flux are given, the latter based on the SST-evaporation feedback. Stommel’s box model result, a coexisting thermal and saline solution, is retrieved in the limit of no rotation. Including rotation in a salt-dominated setting, a steady circulation is found which bifurcates for higher Rayleigh numbers in a periodic solution which becomes chaotic through a cascade of subharmonic bifurcations. Periodic motion results from two different mechanisms. First, the stable stationary state bifurcates into a periodic solution where anomalously saline water is advected by the overturning circulation. Second, this periodic solution bifurcates into a state which is dominated, during the larger part of the cycle, by diffusion and inertia, characterized by a decreasing overturning rate, and, during the subsequent shorter part of the cycle, by rapid advection and restratification of the entire basin. The basin-averaged vertical density field is stably stratified in the steady and the periodic regimes and remains statically stable in the chaotic regime. Received: 16 July 1996 / Accepted: 29 December 1997     

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.