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Cut cells use regular or nearly regular polygonal cells to describe fields. For a given orography, some cells may be completely under the mountain, some completely above the mountain, and some are partially filled with air. While there are reports indicating considerably improved simulations with cut cells, inaccuracies may arise with some approximations, producing noise in fields near the surface. This behavior may depend strongly on the approximations made for the advection terms near the surface. This paper investigates the accuracy of advection for numerical schemes for a nondivergent flow near a mountain surface. The schemes use C-grid staggering with densities located at cell centers or on the corners of cells. Also, a nonconserving scheme is considered, which was used in the past with real-data cut-cell simulations. Since the cut cells near the surface create an irregular resolution, the accuracy and order of some approximations may break down near the surface. The objective of this paper is to find schemes having the same accuracy for advection near the surface as in the interior of the domain. As a test problem, uniform advection by a nondivergent velocity field is used with a 45° slope mountain (represented as a straight line) on a rectangular grid. Along the surface a sequence of triangular and pentagonal cells of quite different sizes are generated. Some schemes being discussed for cut cells lead to inaccurate and noisy solutions for this perfectly smooth mountain. A scheme using piecewise linear basis functions in a C grid with density points at the cell corners avoids these inaccuracies. [ABSTRACT FROM AUTHOR]

The adjoint-based observation impact estimation method has been providing essential information to improve data assimilation systems (DASs) in numerical weather prediction (NWP). This paper has two purposes. The first is to verify the four approximations used in the method: iterative construction of the Kalman gain adjoint operator, the tangent linear (TL) approximation of a forecast model, ignoring cross terms of observation impacts, and approximations for incremental DASs. The second is to add new information to our knowledge of observation impacts. For the verification of the adjoint-based method, we use the TL-based observation impact estimation method that can calculate the same quantity as the adjoint-based method without adjoint calculations. Results of these verifications and observation impact estimations performed on the global NWP system of the Japan Meteorological Agency are as follows. First, observation impacts calculated using the adjoint-based method agree well with those from the TL-based method, with the correlation coefficient between them exceeding 0.97. Second, estimated observation impacts are consistent with previous studies in many aspects. There are also system-dependent properties, such as relatively small impacts from GPS radio occultation data above 13 km. Furthermore, new aspects of observation impacts are found: 1) the probability density function of the observation impact agrees well with the scalar theory when giving the experimental value of the observation and the forecast error standard deviations; 2) later observations in the data assimilation window have larger positive impacts; and 3) impacts of AMSU-A in the Southern Hemisphere are more than double those in the Northern Hemisphere. [ABSTRACT FROM AUTHOR]

Several equivalent equations for the evolution of the wave-averaged current momentum have been proposed, implemented, and used. In contrast, the equation for the total momentum, which is the sum of the current and wave momenta, has not been widely used because it requires a less practical wave forcing. In an update on previous derivations, Mellor proposed a new formulation of the wave forcing for the total momentum equation. Here, the authors show that this derivation misses a leading-order term that has a zero depth-integrated value. Corrected for this omission, the wave forcing is equivalent to that in the first paper by Mellor. When this wave forcing effect on the currents is approximated it leads to an inconsistency. This study finally repeats and clarifies that the vertical integration of several various forms of the current-only momentum equations are consistent with the known depth-integrated equations for the mean flow momentum obtained by subtracting the wave momentum equation from the total momentum equation. Several other claims in prior Mellor manuscripts are discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the validity of the gradient wind balance approximation during the intensification phase of a tropical cyclone in Ooyama's three-layer model. For this purpose, the sensitivity to various model modifications is examined, given by the inclusion of (i) unbalanced dynamics in the free atmosphere, (ii) unbalanced dynamics in the slab boundary layer, (iii) a height-parameterized boundary layer model, and (iv) a rigid lid. The most rapid intensification occurs when the model employs the unbalanced slab boundary layer, while the simulation with the balanced boundary layer reveals the slowest intensification. The simulation with the realistic height-parameterized boundary layer model exhibits an intensification rate that lies in between. Intensification is induced by a convective ring in all experiments, but a distinct contraction of the radius of maximum gradient wind only takes place with unbalanced boundary layer dynamics. In all experiments the rigid lid and the balance approximation for the free atmosphere have no crucial impact on intensification, and a linear stability analysis cannot explain the found sensitivity to intensification. Most likely the nonlinear momentum advection term plays an important role in the boundary layer. It is found on the basis of a diagnostic radial mass flux equation that the source term for latent heat provides the largest contribution to intensification and contraction. Furthermore, it turns out that the position of the convective ring inside or outside of the radius of maximum gradient wind (RMGW) is of vital importance for intensification and most likely explains the large impact of boundary layer imbalance. [ABSTRACT FROM AUTHOR]

This paper presents a new data assimilation approach based on the particle filter (PF) that has potential for nonlinear/non-Gaussian applications in geoscience. Particle filters provide a Monte Carlo approximation of a system's probability density, while making no assumptions regarding the underlying error distribution. The proposed method is similar to the PF in that particles-also referred to as ensemble members-are weighted based on the likelihood of observations in order to approximate posterior probabilities of the system state. The new approach, denoted the local PF, extends the particle weights into vector quantities to reduce the influence of distant observations on the weight calculations via a localization function. While the number of particles required for standard PFs scales exponentially with the dimension of the system, the local PF provides accurate results using relatively few particles. In sensitivity experiments performed with a 40-variable dynamical system, the local PF requires only five particles to prevent filter divergence for both dense and sparse observation networks. Comparisons of the local PF and ensemble Kalman filters (EnKFs) reveal advantages of the new method in situations resembling geophysical data assimilation applications. In particular, the new filter demonstrates substantial benefits over EnKFs when observation networks consist of densely spaced measurements that relate nonlinearly to the model state-analogous to remotely sensed data used frequently in weather analyses. [ABSTRACT FROM AUTHOR]

Particle filtering methods for data assimilation may suffer from the 'curse of dimensionality,' where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of , a statistic that depends on observation-space quantities and that is related to the system dimension when the number of observations is large; for linear, Gaussian systems, the statistic can be computed from eigenvalues of an appropriately normalized covariance matrix. Tests with a low-dimensional system show that these asymptotic results remain useful when the system is nonlinear, with either the standard or optimal proposal implementation of the particle filter. This study explores approximations to the covariance matrices that facilitate computation in high-dimensional systems, as well as different methods to estimate the accumulated system noise covariance for the optimal proposal. Since may be approximated using an ensemble from a simpler data assimilation scheme, such as the ensemble Kalman filter, the asymptotic relations thus allow an estimate of the ensemble size required for a particle filter before its implementation. Finally, the improved performance of particle filters with the optimal proposal, relative to those using the standard proposal, in the same low-dimensional system is demonstrated. [ABSTRACT FROM AUTHOR]

Ensemble-variational data assimilation algorithms that can incorporate the time dimension (four-dimensional or 4D) and combine static and ensemble-derived background error covariances (hybrid) are formulated in general forms based on the extended control variable and the observation-space-perturbation approaches. The properties and relationships of these algorithms and their approximated formulations are discussed. The main algorithms discussed include the following: 1) the standard ensemble 4DVar (En4DVar) algorithm incorporating ensemble-derived background error covariance through the extended control variable approach, 2) the 4DEnVar neglecting the time propagation of the extended control variable (4DEnVar-NPC), 3) the 4D ensemble-variational algorithm based on observation space perturbation (4DEnVar), and 4) the 4DEnVar with no propagation of covariance localization (4DEnVar-NPL). Without the static background error covariance term, none of the algorithms requires the adjoint model except for En4DVar. Costly applications of the tangent linear model to localized ensemble perturbations can be avoided by making the NPC and NPL approximations. It is proven that En4DVar and 4DEnVar are mathematically equivalent, while 4DEnVar-NPC and 4DEnVar-NPL are mathematically equivalent. Such equivalences are also demonstrated by single-observation assimilation experiments with a 1D linear advection model. The effects of the non-flow-following or stationary localization approximations are also examined through the experiments. All of the above algorithms can include the static background error covariance term to establish a hybrid formulation. When the static term is included, all algorithms will require a tangent linear model and an adjoint model. The first guess at appropriate time (FGAT) approximation is proposed to avoid the tangent linear and adjoint models. Computational costs of the algorithms are also discussed. [ABSTRACT FROM AUTHOR]

One of the proposed mechanisms for energy loss in the ocean is through dissipation of internal waves, in particular above rough topography where internal lee waves are generated. Rates of dissipation and diapycnal mixing are often estimated using linear internal wave generation theory and a constant value for mixing efficiency. However, previous oceanographic measurements found that nonlinear dynamics may be important close to topography. To investigate the role of nonlinear interactions, we conduct idealized 3D direct numerical simulations (DNS) of steady flow over 1D topography and vary the topographic height, which correlates to the degree of flow nonlinearity. We analyze the spatial distribution of energy transfer rates between internal waves and the nongeostrophic portion of the time-mean flow, and of dissipation and diapycnal mixing rates. In our simulations with taller, more nonlinear topographies, energy transfer rates are similar to previously unexplained oceanographic observations near topography: internal waves gain energy from time-mean flow through horizontal straining and lose energy through vertical shearing. In the tall topography simulations, buoyancy fluxes also play a significant role, consistent with observations but contrary to linear wave theory, suggesting that quasigeostrophy-based approximations and linear theory may not hold in some regions above rough topography. Both dissipation and mixing rates increase with topographic height, but their vertical distributions differ between topographic regimes. As such, the vertical profile of mixing efficiency is different for linear and nonlinear topographic regimes, which may need to be incorporated into parameterizations of small-scale processes in models and estimates of ocean energy loss. [ABSTRACT FROM AUTHOR]

The relative roles of buoy and Argo observations in two sea surface temperature (SST) analyses are studied in the global ocean and tropical Pacific Ocean over 2000–16 using monthly Extended Reconstructed SST version 5 (ERSSTv5) and Daily Optimum Interpolation SST version 2 (DOISST). Experiments show an overall higher impact by buoys than Argo floats over the global oceans and an increasing impact by Argo floats. The impact by Argo floats is generally larger in the Southern Hemisphere than in the Northern Hemisphere. The impact on trends and anomalies of globally averaged SST by either one is small when the other is used. The warming trend over 2000–16 remains significant by including either buoys or Argo floats or both. In the tropical Pacific, the impact by buoys was large over 2000–05 when the number of Argo floats was low, and became smaller over 2010–16 when the number and area coverage of Argo floats increased. The magnitude of El Niño and La Niña events decreases when the observations from buoys, Argo floats, or both are excluded. The impact by the Tropical Atmosphere Ocean (TAO) and Triangle Trans-Ocean Buoy Network (TRITON) is small in normal years and during El Niño events. The impact by TAO/TRITON buoys on La Niña events is small when Argo floats are included in the analysis systems, and large when Argo floats are not included. The reason for the different impact on El Niño and La Niña events is that the drifting buoys are more dispersed from the equatorial Pacific region by stronger trade winds during La Niña events. [ABSTRACT FROM AUTHOR]

A framework for conceptual understanding of slow, convectively coupled disturbances is developed and applied to several canonical tropical problems, including the water vapor content of an atmosphere in radiative–convective equilibrium, the relationship between convective precipitation and column water vapor, Walker-like circulations, self-aggregation of convection, and the Madden–Julian oscillation. The framework is a synthesis of previous work that developed four key approximations: boundary layer energy quasi equilibrium, conservation of free-tropospheric moist and dry static energies, and the weak temperature gradient approximation. It is demonstrated that essential features of slow, convectively coupled processes can be understood without reference to complex turbulent and microphysical processes, even though accounting for such complexity is essential to quantitatively accurate modeling. In particular, we demonstrate that the robust relationship between column water vapor and precipitation observed over tropical oceans does not necessarily imply direct sensitivity of convection to free-tropospheric moisture. We also show that to destabilize the radiative–convective equilibrium state, feedbacks between radiation and clouds and water vapor must be sufficiently strong relative to the gross moist stability. [ABSTRACT FROM AUTHOR]

Which of two competing continuous forecasts is better? This question is often asked in forecast verification, as well as climate model evaluation. Traditional statistical tests seem to be well suited to the task of providing an answer. However, most such tests do not account for some of the special underlying circumstances that are prevalent in this domain. For example, model output is seldom independent in time, and the models being compared are geared to predicting the same state of the atmosphere, and thus they could be contemporaneously correlated with each other. These types of violations of the assumptions of independence required for most statistical tests can greatly impact the accuracy and power of these tests. Here, this effect is examined on simulated series for many common testing procedures, including two-sample and paired t and normal approximation z tests, the z test with a first-order variance inflation factor applied, and the newer Hering-Genton (HG) test, as well as several bootstrap methods. While it is known how most of these tests will behave in the face of temporal dependence, it is less clear how contemporaneous correlation will affect them. Moreover, it is worthwhile knowing just how badly the tests can fail so that if they are applied, reasonable conclusions can be drawn. It is found that the HG test is the most robust to both temporal dependence and contemporaneous correlation, as well as the specific type and strength of temporal dependence. Bootstrap procedures that account for temporal dependence stand up well to contemporaneous correlation and temporal dependence, but require large sample sizes to be accurate. [ABSTRACT FROM AUTHOR]

Visible satellite images contain high-resolution information about clouds that would be well suited for convective-scale data assimilation. This application requires a forward operator to generate synthetic images from the output of numerical weather prediction models. Only recently have 1D radiative transfer (RT) solvers become sufficiently fast for this purpose. Here computationally efficient methods are proposed to increase the accuracy and consistency of an operator based on the Method for Fast Satellite Image Synthesis (MFASIS) 1D RT. Two important problems are addressed: the 3D RT effects related to inclined cloud tops and the overlap of subgrid clouds. It is demonstrated that in a rotated frame of reference, an approximate solution for the 3D RT problem can be obtained by solving a computationally much cheaper 1D RT problem. Several deterministic and stochastic schemes that take the overlap of subgrid clouds into account are discussed. The impact of the inclination correction and the overlap schemes is evaluated for synthetic 0.6-mm SEVIRI images computed from operational forecasts of the German-focusedCOSMO(COSMO-DE) Model for a test period in May-June 2016. The cloud-top inclination correction increases the information content of the synthetic images considerably and reduces systematic errors, in particular for larger solar zenith angles. Taking subgrid cloud overlap into account is essential to avoid large systematic errors. The results obtained using several different 2D cloud overlap schemes are very similar, whereas small but significant differences are found for the most consistent 3D method, which accounts for the fact that the RT problem is solved for columns tilted toward the satellite. [ABSTRACT FROM AUTHOR]

The drift of temperature measurements by semiconductor negative temperature coefficient thermistors is a well-known problem. This study analyzes the drift characteristics of the thermistors designed and used at the Royal Netherlands Institute for Sea Research for measuring high-frequency temperature fluctuations in the ocean. These thermistors can be calibrated to high precision and accuracy (better than 1 mK) and have very low noise levels. The thermistors can measure independently for long periods of time (more than one year), and the identification and compensation of the drift are thus essential processing steps. A laboratory analysis showing that the drift is similar, in its functional form, to the drift of commercial thermistors described in the literature is presented. An effective procedure to estimate this drift from ocean observations is described and tested using three datasets from the deep Atlantic Ocean. Since the functional form of the drift rate is, with good approximation, universal among different sensors, the procedure could easily be adapted to other datasets and, the authors argue, to measurements from thermistors by other manufacturers too. [ABSTRACT FROM AUTHOR]

A comparison between anelastic and compressible convection-permitting weather forecasts for the Alpine region is presented. This involves mesoscale simulation of a typical westerly flow accompanied by a passage of frontal systems as well as intense airmass convection and orographic convection. The limited-area model employing a 2.2-km horizontal grid length is driven by time-dependent boundary conditions from a coarse-resolution model. The results obtained with the anelastic and the compressible model versions show good agreement. Validations of the 10-m wind, 2-m temperature, 2-m dewpoint temperature, total cloud cover, and surface precipitation against observations for a seven-member forecast ensemble reveal only minor differences between the two configurations. The sensitivity study demonstrates only a small impact of realistic pressure perturbations (about a reference profile) on the solutions. Overall, anelastic approximation proves remarkably accurate in simulating moist mesoscale dynamics. The study has been conducted using a newly developed hybrid limited-area nonhydrostatic version of the Consortium for Small-Scale Modeling (COSMO) model. This version facilitates the use of two alternative dynamical cores: compressible (original) and anelastic (new). The new dynamical core, which is based on the Euler-Lagrangian (EULAG) solver, aims at integrating atmospheric flow equations at resolutions higher than O(1) km for steep orography. A coupler has been developed to merge the EULAG dynamical core with the COSMO numerical weather prediction framework. [ABSTRACT FROM AUTHOR]

This work assesses the large-scale applicability of the recently proposed nonlinear ensemble transform filter (NETF) in data assimilation experiments with the NEMO ocean general circulation model. The new filter constitutes a second-order exact approximation to fully nonlinear particle filtering. Thus, it relaxes the Gaussian assumption contained in ensemble Kalman filters. The NETF applies an update step similar to the local ensemble transform Kalman filter (LETKF), which allows for efficient and simple implementation. Here, simulated observations are assimilated into a simplified ocean configuration that exhibits globally high-dimensional dynamics with a chaotic mesoscale flow. The model climatology is used to initialize an ensemble of 120 members. The number of observations in each local filter update is of the same order resulting from the use of a realistic oceanic observation scenario. Here, an importance sampling particle filter (PF) would require at least 106 members. Despite the relatively small ensemble size, the NETF remains stable and converges to the truth. In this setup, the NETF achieves at least the performance of the LETKF. However, it requires a longer spinup period because the algorithm only relies on the particle weights at the analysis time. These findings show that the NETF can successfully deal with a large-scale assimilation problem in which the local observation dimension is of the same order as the ensemble size. Thus, the second-order exact NETF does not suffer from the PF's curse of dimensionality, even in a deterministic system. [ABSTRACT FROM AUTHOR]

The cloud-to-ground (CG) lightning data being detected by the China Lightning Detection Network between 2010 and 2013 are employed to gain insight into the spatial and temporal distribution of CG lightning in China. There are clear interannual and seasonal variations of CG lightning activity. The mean total CG and positive CG (PCG) flashes in 2010-13 are approximately 6.44 million and 0.42 million, respectively, and the mean percentage of PCG (PPCG) is 6.6%. CG and PCG flashes predominately occur during summer, with August being the peak month for CG and June for PCG. PPCG in the cold season is considerably greater than in the warm season; its maximum of 56.2% is in January and the minimum value of 4.0% is found in August. The centers of maximum mean annual CG density are scattered throughout southern China, the Sichuan basin, and the south of Jiangsu Province. The CG density in the high elevations and arid regions of western China is less than that in the low elevations and coastal regions of southeastern China. In addition, daily CG density and CG lightning days in southeastern China are greater than in northwestern China, but PPCG in western China is apparently greater than that in eastern China. Areas experiencing more than 30 CG lightning days per year are primarily south of 30°N, with 10-30 lightning days per year in northern and northeastern China, and approximately 10-20 lightning days per year over the central Tibetan Plateau. [ABSTRACT FROM AUTHOR]

The day-night band (DNB) low-light-level visible sensor, mounted on the Suomi-National Polar-Orbiting Partnership ( SNPP) satellite, can measure visible radiances from the earth and atmosphere (solar/lunar reflection, and natural/anthropogenic nighttime light emissions) during both day and night and can achieve unprecedented nighttime low-light-level imaging with its accurate radiometric calibration and fine spatiotemporal resolution. Based on the good characteristics of DNB, a multichannel threshold (MCT) algorithm combining DNB with other Visible-Infrared Imager-Radiometer Suite (VIIRS) channels is proposed to monitor nighttime fog/low stratus. Through a gradual separation of the underlying surface (land, vegetation, water bodies, and city lights), snow, and high/medium clouds, a fog/low-stratus region can ultimately be extracted by the algorithm. Then, the algorithmic feasibility is verified by three typical cases of heavy fog/low stratus in China. The experimental results demonstrate that the outcomes of the MCT algorithm approximately coincide with the ground-measured results. Furthermore, the MCT algorithm shows promise for nighttime fog/low-stratus detection in some example cases with about a 0.84 average probability of detection (POD), a 0.73 average critical success index (CSI), and a 0.15 average false alarm ratio (FAR), which reveals some improvement over the conventional dual-channel difference (DCD) algorithm. [ABSTRACT FROM AUTHOR]

Many issues may challenge standard interpolation techniques to produce high-resolution gridded maps of sea surface height in the context of future missions like Surface Water and Ocean Topography (SWOT). The present study proposes a new method to address these challenges. Based on the conservation of potential vorticity, the method provides a simple dynamic approach to interpolation through temporal gaps between high spatial resolution observations. For gaps shorter than 20 days, the dynamic interpolation is extremely efficient and allows for the reconstruction of the time evolution of small mesoscale eddies (below 100 km) that would be smoothed out by conventional methods based on optimal mapping. Such a simple approach offers some perspectives for developing high-level products from high-resolution altimetry data in the future. [ABSTRACT FROM AUTHOR]

The equations of motion are reexamined with the objective of improving upon the Boussinesq approximation. The authors derive new equations that conserve energy, filter out sound waves, are more accurate than the Boussinesq set, and are computationally competitive with them. The new equations are partly enabled by exploiting a reversible exchange between internal and gravitational potential fluid energy. To improve upon these equations appears to require the inclusion of acoustics, at which point one should use full Navier-Stokes. This study recommends the new sets for testing in general circulation modeling. [ABSTRACT FROM AUTHOR]

The dynamics of modulated point vortex pairs is investigated on a rotating sphere, where modulation is chosen to reflect the conservation of angular momentum (potential vorticity). In this setting the authors point out a qualitative difference between the full spherical dynamics and the one obtained in a β-plane approximation. In particular, dipole trajectories starting at the same location evolve to completely different directions under these two treatments, despite the fact that the deviations from the initial latitude remain small. This is a strong indication for the mathematical inconsistency of the traditional β-plane approximation. At the same time, a consistently linearized set of equations of motion leads to trajectories agreeing with those obtained under the full spherical treatment. The β-plane advection patterns due to chaotic advection in the velocity field of finite-sized vortex pairs are also found to considerably deviate from those of the full spherical treatment, and quantities characterizing transport properties (e.g., the escape rate from a given region) strongly differ. [ABSTRACT FROM AUTHOR]