Meteorological Equations Research Articles

Orbital forcing of tropical climate dynamics in the Early Cambrian

According to modern atmospheric circulation models, the Intertropical Convergence Zone (ITCZ), as the Earth's meteorological equator, plays an essential role in the low-latitude hydrologic cycles. The limited availability of high-resolution tropical climate archives, especially from the Early Paleozoic Era, severely limits our understanding of ITCZ migration dynamics in deep time. Here we present high-resolution climate-proxy records (i.e., magnetic susceptibility (MS) and Zirconium/Aluminum (Zr/Al)) from tropical marine sediments of the ~526-million-year-old Qiongzhusi Formation in South China to investigate the link between orbitally forced insolation changes, ITCZ migration dynamics, and low-latitude climate processes. These orbital-scale variations in MS and Zr/Al series are interpreted as alternations between wet and dry cycles, controlled by monsoon intensity under the orbitally forced ITCZ-related paleo-Hadley Cell dynamics. Our results show that combined precession and obliquity orbital cycles had an impact on the Early Cambrian ITCZ migration. Specifically, the precession and obliquity forcing shift the mean position of the ITCZ latitudinally by changing the interhemispheric pressure contrasts, thus affecting the low latitude hydroclimate cycle. We report semi-precession cycles of 8.3–7.9 kyr, which were probably associated with the twice-annual passage of the ITCZ across the intertropical zone, consistent with the paleogeographical location of South China near the equator during the Early Cambrian. Observed ~1.1 – ~1.5 Myr eccentricity amplitude modulation (AM) cycles and ~ 1.0 – ~1.2 Myr obliquity AM cycles may provide geological evidence for the chaotic motion between Earth and Mars in the Early Cambrian. • Combined precession and obliquity cycles regulated the Early Cambrian ITCZ migration. • We report the semi-precession cycles of 7.9–8.3 kyr in the Early Cambrian. • Our study provides geological evidence for the chaotic Solar System in the Early Cambrian.

Instabilities in the Shallow-Water System with a Semi-Lagrangian, Time-Centered Discretization

Abstract Conventional wisdom suggests that the combination of semi-Lagrangian advection and an implicit treatment of gravity wave terms should result in a combined scheme for the shallow-water equations stable for high Courant numbers. This wisdom is well justified by linear analysis of the system about a uniform reference state with constant fluid depth and velocity, but it is only assumed to hold true in more complex scenarios. This work finds that this conventional wisdom no longer holds in more complicated flow regimes, in particular when the background state is given by steady-state flow past topography. Instead, this background state admits a wide range of instabilities that can lead to noise in atmospheric forecasts. Significance Statement This work shows that solutions to the shallow-water equations with a semi-Lagrangian treatment of advection and an implicit, time-centered treatment of gravity wave terms can be unstable when there is a background state of flow over topography. This basic algorithm is used by many operational weather-forecasting models to simulate the meteorological equations, and showing an instability in the simplified, shallow-water system suggests that a similar mechanism may be responsible for “noise” in operational weather forecasts under some circumstances. If this problem can be addressed, it could allow numerical weather models to operate with less dissipation, improving forecast quality.

Rainfall Variability and Trend Analysis of Rainfall in West Africa (Senegal, Mauritania, Burkina Faso)

This study concerns the West African Sahel. The Sahelian climate is characterized by a long dry season and a rainy season which starts in June and ends in September–October. This latter season is associated with the process of oceanic moisture transfer to the mainland (the West African Monsoon). This movement is governed by an overall moving of the meteorological equator and its low-pressure corridor (Intertropical Convergence Zone, ITCZ) towards the north, under the effect of the attraction of the Saharan thermal depressions and a greater vigor of the anticyclonic nuclei. This study was conducted on 27 Sahelian climatic stations in three countries (Burkina Faso, Mauritania, and Senegal). The method used to determine the modes of this variability and the trends of rainfall is the chronological graphic method of information processing (MGCTI) of the “Bertin Matrix” and continuous wavelets transform (CWT). Results show a rain resumption observed in the recent years over the Sahelian region and a convincing link with the surface temperature of the Atlantic Ocean.

Circumventing the pole problem of reduced lat–lon grids with local schemes. Part I: Analysis and model formulation

This paper describes a possible strategy for numerically integrating global meteorological equations cast in spherical coordinates with local/scalable algorithms on a reduced latitude–longitude grid. This approach is designed to address a major obstacle known as the “pole problem” in the literature. The nature of the problem is carefully examined in order to determine the conditions for its appearance (or disappearance). A class of discretization schemes avoiding the problem while being based on local algorithms of various accuracy orders is then proposed for non‐staggered grids. A numerical model for solving shallow‐water equations on the sphere with these discrete schemes (GRASS) has been developed and its ability to circumvent the pole problem is demonstrated through basic validations. Further validations on standard test‐cases are presented in Part II.

Accuracy of radar-based precipitation measurement: An analysis of the influence of multiple scattering and non-spherical particle shape

Two assumptions are typically made when radar echo signals from precipitation are analyzed to determine the micro-physical parameters of raindrops: (1) the raindrops are assumed to be spherical; (2) multiple scattering effects are ignored. Radar cross sections (RCS) are usually calculated using Rayleigh's scattering equation with the simple addition method in the radar meteorological equation. We investigate the extent to which consideration of the effects of multiple scattering and of the non-spherical shapes within actual raindrop swarms would result in RCS values significantly different from those obtained by conventional analytical methods. First, we establish spherical and non-spherical raindrop models, with Gamma, JD, JT, and MP size distributions, respectively. We then use XFDTD software to calculate the radar cross sections of the above raindrop models at the S, C, X and Ku radar bands. Our XFDTD results are then compared to RCS values calculated by the Rayleigh approximation with simple addition methods. We find that: (1) RCS values calculated using multiple scattering XFDTD software differ significantly from those calculated by the simple addition method at the same band for the same model. In particular, for the spherical raindrop models, the relative differences in RCS values between the methods range from a maximum of 89.649% to a minimum of 43.701%; for the non-spherical raindrop models, the relative differences range from a maximum of 85.868% to a minimum of 11.875%. (2) Our multiple scattering XFDTD results, compared to those obtained from the Rayleigh formula, again differ at all four size distributions, by relative errors of 169.522%, 37.176%, 216.455%, and 63.428%, respectively. When nonspherical effects are considered, differences in RCS values between our XFDTD calculations and Rayleigh calculations are smaller; at the above four size distributions the relative errors are 0.213%, 0.171%, 7.683%, and 44.514%, respectively. RCS values computed by considering multiple scattering and non-spherical particle shapes are larger than Rayleigh RCS results, at all of the above four size distributions; the relative errors between the two methods are 220.673%, 129.320%, 387.240%, and 186.613%, respectively. After changing the arrangement of particles at four size distributions in the case of multiple scattering effect and non-spherical effect, the RCS values of Arrangement 2 are smaller than those of Arrangement 1; the relative errors for Arrangement 2, compared to Rayleigh, are 60.558%, 76.263%, 85.941%, 64.852%, respectively. We have demonstrated that multiple scattering, non-spherical particle shapes, and the arrangement within particle swarms all affect the calculation of RCS values. The largest influence appears to be that of the multiple scattering effect. Consideration of particle shapes appears to have the least influence on computed RCS values. We conclude that multiple scattering effects must be considered in practical meteorological detection.

Introduction: The Ethiopic Ocean - History and Historiography, 1600-1975

ABSTRACT: Atlantic history is generally surveyed through the prism of the North Atlantic. Yet the South Atlantic had a distinct historical pattern through the Sailing Age. Eighteenth- and nineteenth-century maps and nautical guides, taking into account the system of currents and winds under the meteorological equator, which is on the north side of the geometrical equator, called the southern part of the Atlantic the “Ethiopic Ocean.” This term helps to emphasize the singularity, the boundaries, and the periodization of South Atlantic history. Indeed, generations of missiologist, colonial, and self-taught authors, as well as great and less great historians, researched such subjects. Their works depict a genealogy of the South Atlantic World that leads to a more diversified and perhaps more conclusive Atlantic history. KEYWORDS: Atlantic history, South Atlantic historiography, Ethiopic Ocean, slave trade

A Semi-Implicit Modification to the Lorenz N-Cycle Scheme and Its Application for Integration of Meteorological Equations

Abstract The Lorenz N-cycle is an economical time integration scheme that requires only one function evaluation per time step and a minimal memory footprint, but yet possesses a high order of accuracy. Despite these advantages, it has remained less commonly used in meteorological applications, partly because of its lack of semi-implicit formulation. In this paper, a novel semi-implicit modification to the Lorenz N-cycle is proposed. The advantage of the proposed new scheme is that it preserves the economical memory use of the original explicit scheme. Unlike the traditional Robert–Asselin (RA) filtered semi-implicit leapfrog scheme whose formal accuracy is only of first order, the new scheme has second-order accuracy if it adopts the Crank–Nicolson scheme for the implicit part. A linear stability analysis based on a univariate split-frequency oscillation equation suggests that the 4-cycle is more stable than other choices of N. Numerical experiments performed using the dynamical core of the Simplified Parameterizations Primitive Equation Dynamics (SPEEDY) atmospheric general circulation model under the framework of the Jablonowski–Williamson baroclinic wave test case confirms that the new scheme in fact has second-order accuracy and is more accurate than the traditional RA-filtered leapfrog scheme. The experiments also give evidence for Lorenz’s claim that the explicit 4-cycle scheme can be improved by running its two “isomeric” versions in alternating sequences. Unlike the explicit scheme, however, the proposed semi-implicit scheme is not improved by alternation of the two versions.

THE FORMATION OF LARGE-AMPLITUDE FINGERS IN ATMOSPHERIC VORTICES

Large-scale low-pressure systems in the atmosphere are occasionally observed to possess Kelvin–Helmholtz fingers, and an example is shown in this paper. However, these structures are hundreds of kilometres long, so that they are necessarily affected strongly by nonlinearity. They are evidently unstable and are observed to dissipate after a few days.A model for this phenomenon is presented here, based on the usual $f$-plane equations of meteorology, assuming an atmosphere governed by the ideal gas law. Large-amplitude perturbations are accounted for, by retaining the equations in their nonlinear forms, and these are then solved numerically using a spectral method. Finger formation is modelled as an initial perturbation to the $n$th Fourier mode, and the numerical results show that the fingers grow in time, developing structures that depend on the particular mode. Results are presented and discussed, and are also compared with the predictions of the ${\it\beta}$-plane theory, in which changes of the Coriolis acceleration with latitude are included. An idealized vortex in the northern hemisphere is considered, but the results are at least in qualitative agreement with an observation of such systems in the southern hemisphere.

Monitoring Climate Changes on Small Scale Networks Using Ground Based GPS and Meteorological Data

Abstract The total zenith tropospheric delay (ZTD) and its components, hydrostatic and wet parts are important parameters of the atmosphere and directly or indirectly reflect climate processes. This possibility can be more adaptive when meteorological data are combined to co-located meteorological sensors with GPS stations. In this paper eighteen months with one hour time interval ZTD estimates of a permanent GPS station are analyzed with the associated atmospheric parameters provided from a co-located meteorological sensor. The mathematical relationship through the multiple stepwise regression analysis reflects the plausible physical link of temperature and relative humidity values with ZTD’s. This regression equation is assessed by a second data set performed by a small GPS baseline few months later for the same study area. It was found that mainly due to the zenith wet delay variations and with the help of fundamental meteorological equations the behavior of water vapor pressure can be monitored and estimated. This is possible when an appropriate setup of GPS stations and a co-located meteorological sensor exist and if the GPS stations sound the same part of atmosphere. Therefore, the GPS tropospheric products are good indicators for a climate monitoring tool and can help address the physics of a climate model.

Climate change and marine ecosystems

One of the most pressing questions of the day is how natural systems will respond to future changes in climate. By looking to the past we know that climate-driven phenomena have resulted in large changes to marine ecosystems; dramatic shifts in the abundance of fish off the coast of Peru occurred at the end of the Little Ice Age (LIA) (1). These shifts were linked to a southward migration in the mean position of the InterTropical Convergence Zone (ITCZ). Frequent flyers know the ITCZ as a region of increased turbulence found between the northern and southern hemispheres; it is a region of low atmospheric pressure that rings the globe and is often referred to as the meteorological equator, albeit mostly north of it. As the polar ice caps expanded during the LIA, the mean position of the ITCZ was pushed southward of its present location (1, 2), shutting down the Walker circulation in the Pacific, one of the drivers of increased productivity off the coast of Peru. The abundant concentrations of small pelagic fish that in the present day make Peru the most productive region in the world in terms of fish (3) were hardly evident in sediment cores during the LIA but returned dramatically when conditions warmed (1). A similar migration of the ITCZ occurs seasonally when during the boreal winter the mean position is found 5–10° farther south than during boreal summer. The opposite northward migration is predicted during a warmer world (2). In PNAS, Taylor et al. (4) describe the response of a marine ecosystem in the marginal southern Caribbean Sea to present-day northward migrations of the ITCZ (Fig. 1). Using 15 y of repeated measurements, they show how the upwelling-favorable trade winds have diminished by the northward migration of the ITCZ, warming the ocean and decreasing primary productivity with effects cascading through the local ecosystem.

THREE-DIMENSIONAL MODELING OF HOT JUPITER ATMOSPHERIC FLOWS

We present a three dimensional hot Jupiter model, extending from 200 bar to 1 mbar, using the Intermediate General Circulation Model from the University of Reading. Our horizontal spectral resolution is T31 (equivalent to a grid of 48x96), with 33 logarithmically spaced vertical levels. A simplified (Newtonian) scheme is employed for the radiative forcing. We adopt a physical set up nearly identical to the model of HD 209458b by Cooper & Showman (2005,2006) to facilitate a direct model inter-comparison. Our results are broadly consistent with theirs but significant differences also emerge. The atmospheric flow is characterized by a super-rotating equatorial jet, transonic wind speeds, and eastward advection of heat away from the dayside. We identify a dynamically-induced temperature inversion ("stratosphere") on the planetary dayside and find that temperatures at the planetary limb differ systematically from local radiative equilibrium values, a potential source of bias for transit spectroscopic interpretations. While our model atmosphere is quasi-identical to that of Cooper & Showman (2005,2006) and we solve the same meteorological equations, we use different algorithmic methods, spectral-implicit vs. grid-explicit, which are known to yield fully consistent results in the Earth modeling context. The model discrepancies identified here indicate that one or both numerical methods do not faithfully capture all of the atmospheric dynamics at work in the hot Jupiter context. We highlight the emergence of a shock-like feature in our model, much like that reported recently by Showman et al. (2009), and suggest that improved representations of energy conservation may be needed in hot Jupiter atmospheric models, as emphasized by Goodman (2009).

ATMOSPHERIC CIRCULATION OF HOT JUPITERS: A SHALLOW THREE-DIMENSIONAL MODEL

Remote observing of exoplanetary atmospheres is now possible, offering us access to circulation regimes unlike any of the familiar solar system cases. Atmospheric circulation models are being developed to study these new regimes but model validations and intercomparisons are needed to establish their consistency and accuracy. To this end, we present a simple Earth-like validation of the pseudospectral solver of meteorological equations called Intermediate General Circulation Model (IGCM), based on Newtonian relaxation to a prescribed latitudinal profile of equilibrium temperatures. We then describe a straightforward and idealized model extension to the atmospheric flow on a hot Jupiter with the same IGCM solver. This shallow, three-dimensional hot Jupiter model is based on Newtonian relaxation to a permanent day–night pattern of equilibrium temperatures and the absence of surface drag. The baroclinic regime1 of the Earth's lower atmosphere is contrasted with the more barotropic regime of the simulated hot Jupiter flow. For plausible conditions at the 0.1–1 bar pressure level on HD 209458b, the simulated flow is characterized by unsteadiness, subsonic wind speeds, a zonally perturbed superrotating equatorial jet and large-scale polar vortices. Violation of the Rayleigh–Kuo inflexion point criterion on the flanks of the accelerating equatorial jet indicates that barotropic (horizontal shear) instabilities may be important dynamical features of the simulated flow. Similarities and differences with previously published simulated hot Jupiter flows are briefly noted.

WATER USE EFFICIENCY OF WHEAT UNDER DRIP IRRIGATION SYSTEMS AT AL – MAGHARA AREA, NORTH SINAI, EGYPT.

A field experiment was conducted during 2004/2005 season in El – Maghara Research Station, about 90 Km South El-Arish city, North Sinai Governorate, Egypt to study water use efficiency of three wheat varieties (i.e. Sakha 8 , Giza 7 and Giza 69) as affected by four irrigation applied rates by means of adding 4 L/h – 8 L/h on one line and on two lines. Statistically Split – Split plot design was used. The results revealed that grain and straw yields of wheat were increased by irrigating with drip irrigation on the two lines of laterals GR with 4 L/h application rate. Meanwhile, the variety Giza 7 was superior in grain and straw yields compared with the other two varieties. Seasonal amount of water applied for wheat crop was about 2087 m3/fed, as calculated by Penman – Montieth meteorological equation. Moreover, the highest grain yields were 2145, 2120 and 2085 Kg/fed. for Giza 7, Sakha 8 and Giza 69, respectively with the two lines of 4 L/h application rate. Water use efficiency for the three varieties expressed as Kg/m3 of water consumed was increased using (S3 = 4 L/h on 2 lines) treatment and the highest WUE values were 1.20, 1.17 & 1.13 Kg/m3 for Giza 7, Sakha 8 and Giza 69, respectively.

Assimilating concentration observations for transport and dispersion modeling in a meandering wind field

Assimilating concentration data into an atmospheric transport and dispersion model can provide information to improve downwind concentration forecasts. The forecast model is typically a one-way coupled set of equations: the meteorological equations impact the concentration, but the concentration does not generally affect the meteorological field. Thus, indirect methods of using concentration data to influence the meteorological variables are required. The problem studied here involves a simple wind field forcing Gaussian dispersion. Two methods of assimilating concentration data to infer the wind direction are demonstrated. The first method is Lagrangian in nature and treats the puff as an entity using feature extraction coupled with nudging. The second method is an Eulerian field approach akin to traditional variational approaches, but minimizes the error by using a genetic algorithm (GA) to directly optimize the match between observations and predictions. Both methods show success at inferring the wind field. The GA-variational method, however, is more accurate but requires more computational time. Dynamic assimilation of a continuous release modeled by a Gaussian plume is also demonstrated using the genetic algorithm approach.

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

Abrupt resumption of the African Monsoon at the Younger Dryas—Holocene climatic transition

A high-resolution sedimentary record from Lake Masoko (Tanzania), based on pollen assemblages and magnetic susceptibility, shows that the most prominent environmental change of the last 45 000 years occurred ca 11.7 cal. ka BP, near the end of the Younger Dryas event. During this climatic transition, the Masoko catchment vegetation changed from being intolerant to a long/severe dry season to being tolerant, while the inferred lake-dynamics indicates strengthened seasonal fluctuations and/or lower levels than before. Comparison of the Masoko record with other regional palaeoclimatic data shows that evidence of this climatic transition is widespread in tropical Africa. The proposed failure of the African Monsoon during the Younger Dryas, associated with a southward position/migration of the meteorological equator in East Africa, was followed by an abrupt and lasting resumption of monsoon activity, and more pronounced migration of the Intertropical Convergence Zone (ITCZ) over the African continent. Such a reorganisation of the atmospheric circulation, equally observed across the whole tropical region (South America, East and West Asia, and Africa), could have been a strong amplifier of northern high latitude changes in temperature and precipitation across this major climatic transition.

Multiple spatial scales in engineering and atmospheric low Mach number flows

The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of this theory to a single spatial scale reproduce automatically the zero Mach number variable density flow equations for the small scales, and the linear acoustic equations with spatially varying speed of sound for the large scales. Following the same line of thought we show how a large number of well-known simplified equations of theoretical meteorology can be derived in a unified fashion directly from the three-dimensional compressible flow equations through systematic (low Mach number) asymptotics. Atmospheric flows are. however, characterized by several singular perturbation parameters that appear in addition to the Mach number; and that are defined independently of any particular length or time scale associated with some specific flow phenomenon. These are the ratio of the centripetal acceleration due to the earth's rotation vs. the acceleration of gravity, and the ratio of the sound speed vs. the rotational velocity of points on the equator. To systematically incorporate these parameters in an asymptotic approach, we couple them with the square root of the Mach number in a particular distinguished so that we are left with a single small asymptotic expansion parameter, e. Of course, more familiar parameters, such as the Rossby and Froude numbers may then be expressed in terms of £ as well. Next we consider a very general asymptotic ansatz involving multiple horizontal and vertical as well as multiple time scales. Various restrictions of the general ansatz to only one horizontal, one vertical. and one time scale lead directly to the family of simplified model equations mentioned above. Of course, the main purpose of the general multiple scales ansatz is to provide the means to derive true multiscale models which describe interactions between the various phenomena described by the members of the simplified model family. In this context we will summarize a recent systematic development of multiscale models for the tropics (with Majda).

A 10-Yr Climatology of Oceanic Water Vapor Derived from the TOPEX Microwave Radiometer

Abstract Using the newly available TOPEX Microwave Radiometer (TMR) data spanning 1993 through 2002, a 10-yr climatology of oceanic water vapor (OWV) is constructed, of which the distribution and variation at various spatial–temporal scales are investigated. The new dataset confirms most of the well-known OWV features, and yields a number of interesting findings, due to its high quality, long duration, and unique orbit. 1) The TMR-derived climatology compares well, in both overall pattern and general statistics, with similar results based on radiosondes and other satellites. Climatological comparisons with sea surface temperature and oceanic precipitation suggest that the western Pacific warm pool is “mirrored” in the atmosphere as a “wet pool,” whereas the meteorological equator is reflected in OWV as a transocean equatorial wet belt. 2) It is found that El Nino (La Nina) events are accompanied by a significant increase (decrease) in the amount of OWV between 10°S and 10°N with a somewhat unexpected Sout...

On the Use of a Wider Class of Linear Systems for the Design of Constant-Coefficients Semi-Implicit Time Schemes in NWP

The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach which may be detrimental in terms of stability. It is shown theoretically that an increased robustness can sometimes be obtained by choosing the reference linear system in a wider set of possibilities. The potential benefits of this new approach are illustrated in two simple examples. The advantage in robustness is not obtained at the price of an increased error or complexity.

Open Boundary Conditions for the Primitive and Boussinesq Equations

It was shown by Oliger and Sundstrom, in 1978, that the initial boundary value problems for the hydrostatic primitive equations of meteorology and oceanography are ill posed if the boundaries are open and fixed in space. In this article it is shown, with theory and computation, that the same problems are well posed for a suitable set of local (pointwise applied) boundary conditions, if a mild vertical viscosity is added to the hydrostatic equation. Some indications on the behavior of the solutions, as the vertical viscosity parameter goes to zero, are also given. The Boussinesq equations are shown to be well posed in the same context of boundaries open and fixed in space. Finally, numerical simulations supporting the analysis are included.