Schedule for: 17w5061 - Nonlinear and Stochastic Problems in Atmospheric and Oceanic Prediction

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Recent studies have questioned the degree to which interactive ocean circulations are important for making useful predictions of the next decade. We investigate this question by identifying the most predictable patterns of global sea surface temperature in coupled atmosphere-ocean models. Remarkably, the most predictable patterns in models that include interactive ocean circulation are very similar to predictable patterns in models without interactive ocean circulations (i.e., models whose ocean is represented by a 50m-deep slab ocean mixed layer with no interactive currents). In addition, these patterns can be skillfully predicted in observational data using empirical models trained on simulations from either type of climate model. These results suggest that interactive ocean circulation is not essential for the spatial structure of multi-year predictability previously identified in coupled models and observations. However, the time scale of predictability, and the relation of these predictable patterns to other climate variables, is sensitive to whether the model supports interactive ocean circulations or not, especially over the North Atlantic. To understand this sensitivity, a hierarchy of ocean models coupled to stochastic atmospheric models are examined, ranging from slab mixed-layer models to a stochastically forced Stommel box model. The box model is able to reproduce many statistical characteristics of sea surface temperatures that are relevant to predictability. This model is then used to suggest hypotheses that can be tested about the role of ocean dynamics in multi-year predictability.

The atmosphere and ocean of the North Atlantic have undergone significant changes in the past century. To understand these changes, their mechanisms, and their regional implications requires a quantitative understanding of processes in the coupled ocean and atmosphere system. Central to this understanding is the role played by the dominant patterns of ocean and atmospheric variability which define coherent variations in physical characteristics over large areas. Four dominant subseasonal weather regimes are defined using Bayesian Gaussian mixture models. All correlation patterns of the Sea Level Pressure (SLP) anomalies with the membership probability timeseries for the weather regimes show similarities with the dipole structure typical for the North Atlantic Oscillation (NAO). The SLP patterns of two of the regimes represent the opposite phases NAO+ and NAO-. The two other weather regimes, the Atlantic Ridge (AR) and Scandinavian-Greenland dipole (SG), have dipole spatial structures with the northern and southern centres of action shifted with respect to the NAO pattern. These two patterns define blocking structures over Scandinavia and near the southern tip of Greenland, respectively. The storm tracks typical for the four regimes resemble the well known paths for positive/negative phases of NAO for the NAO+/NAO- weather regimes, and paths influenced by blocking off the south Greenland tip for AR and over Scandinavia for SG. The correlation patterns of momentum and heat fluxes to the ocean for the four regimes have tripole structures with positive (warm) downward heat flux anomalies over the Subpolar North Atlantic (SPNA) for the NAO- and the AR and negative heat flux anomalies over the SPNA for the NAO+. The downward heat flux anomalies associated with the SG are negative over the Labrador Sea and positive over the eastern SPNA. The long-term impact of the weather regimes on the regional climate is characterized by their distribution; i.e. the frequency of occurrence and persistence in time of each of them. Four typical distributions of the weather regimes are identified in this study which are associated with four dominant spatial interannual patterns representing the phases of two asymmetrical ``modes''. The first two patterns have the spatial structures of positive and negative phases of the North Atlantic Oscillation (NAO). The third and fourth patterns, here referred to as G+ and G-, define the opposite phases of a mode, that has a spatial structure defined by three centers found over Florida, south of Greenland and over Scandinavia. The NAO+ interannual patterns are associated with negative anomalies of the surface downward heat flux and ocean heat content over the SPNA. The NAO- and G+ are associated with positive anomalies of heat flux and ocean heat content. In the 1960s the dominant NAO- and G+ interannual patterns favored warmer than normal atmospheric and ocean temperatures over the SPNA. The winters in the late 1980s and early 1990s over the SPNA were colder than normal. This decadal shift in the atmospheric state between the 1970s and 1980s was associated with a change in the dominant interannual patterns towards NAO+~and~G- in the late 1980s and early 1990s. The recent warming of the SPNA since the mid-1990s was related to the dominance of the G+/G- interannual patterns in the distribution of interannual patterns probability membership. Our analysis suggests that this decadal variability was associated with a long-term shifts in atmospheric behavior over the SPNA that can be described by a change in the 1980s of the distribution of membership probabilities for interannual patterns. In the phase space of the interannual patterns, this transition is characterized with a shift from the NAO-/G+/G- subspace subspace in the 1950 and 1960s, towards NAO+/G+/G- since the mid 1980s.. Based on this analysis we developed a a computationally efficient stochastic weather generator for analysis and prediction of the Subpolar North Atlantic amospheric decadal variability. The method is tested by the stochastic simulation of sea level pressure over the sub-polar North Atlantic. The weather generator includes a hidden Markov model, which propagates regional circulation patterns identified by a self organising map analysis, conditioned on the state of large-scale interannual patterns. The remaining residual effects are propagated by a regression model with added noise components. The regression step is performed by one of two methods, a linear model or artificial neural networks and the performance of these two methods is assessed and compared.

In many locations, sea surface wind components (particularly the zonal) display a pronounced skewness such that where the mean component is positive the skewness is negative (and vice versa). Several years ago, I proposed an idealized model for this behaviour in which the skewness arises because of the nonlinear dependence of surface momentum fluxes on near-surface wind speed. A recent study (Proistoescu et al., GRL, 2016) considered the skewness of tropospheric temperature measurements from radiosondes, and showed that the skewness of the time series is generally reduced by digital filtering. They put forward a geometrical argument for the general nature of this result, through consideration of the bispectrum of the process. This argument, however, assumes that the time series are serially independent. They then used simulations to show that serially-dependent Correlated Multiplicative-Additive (CAM) noise also shows this behaviour. In such processes, which have been suggested as generic models for non-Gaussian variability in the atmosphere and ocean, the skewness arises because of the presence of multiplicative noise. In this talk, I will show that lowpass filtering of sea surface wind actually enhances the skewness if the cutoff frequency is not too low. Extrema of skewness are found when the cutoff frequency corresponds to the synoptic timescale in the midlatitudes, and for timescales associated with subseasonal to seasonal variability in the equatorial band. I will show that this behaviour is captured by an idealized stochastic model of sea surface winds, such that the optimal lowpass cutoff frequency is set by a nonlinear dynamical timescale. These results suggest an approach to determining if non-Gaussianity results from dynamical nonlinearity or multiplicative noise, and indicate in particular that for sea-surface winds it is the former rather than the latter.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Ensemble integrations using a primitive equation atmospheric model were performed to investigate the atmospheric transient response to tropical thermal forcings that resemble El Nino and La Nina. The response develops in the North Pacific within one week after the integration. The signal in the North Atlantic and Europe is established by the end of the second week. Significant asymmetry was found between the responses in the El Nino and the La Nina that is similar to the observations, i.e., one feature is that the 500 hPa positive height response in the North Pacific of the La Nina run is located about 30 degrees west of the negative response of the El Nino run; and another feature is that the responses in the North Atlantic and Europe for the La Nina and El Nino cases have similar patterns with the same polarity. Numerical experiments are also performed with anomalous tropical thermal forcings that resemble positive MJO (a dipole tropical diabatic heating similar to phase 2) and negative MJO (similar to phase 6). The response in the first week is largely linear. After that, significant asymmetry is found between the response in positive MJO and negative MJO. This simulated nonlinearity is in agreement with the observations. Several factors contribute to this nonlinearity of the response. In the Tropics, the shape of the Rossby wave response and the zonal extent of the Kelvin wave are not symmetric in the positive and negative forcing experiments, which is associated with the dependence of the wave property on the modified zonal mean flow. This is especially important in the equatorial region to the west of the forcing, which is likely responsible for the phase shift of the major extratropical response in the North Pacific. The transient eddy activity in the extratropics feeds back to the response and helps to maintain the nonlinearity.

I will present an overview of dynamic transition theory and its applications to various geophysical fluid flows.

A prominent feature of geophysical flows is the formation of large scale structures such as vortices and jets. Understanding the dynamics of these structures (e.g. fluctuations of the Jet Stream, abrupt transitions between different flow regimes,...) is a crucial point for weather and climate. Unlike other turbulent flows, geophysical flows may also exhibit a clear timescale separation between the large-scale structures and the small-scale turbulent fluctuations. I will discuss how this property can be used to construct a perturbative theory which describes the large-scale flow, relying on a technique known as stochastic averaging. Using direct numerical simulations in an idealized situation (vortices on a plane), I will study the validity and limitations of this approach by testing analytical predictions for the structure of the large-scale flow, such as the velocity profile or the eddy momentum flux profile. Finally, I will discuss the long term dynamics of large-scale geophysical flows and the abrupt transitions they undergo, using tools from large deviation theory.

Kinetic energy in the atmospheric mesoscale closely follows a -5/3 power law. Most theories addressing this assume unbalanced dynamics but ignore the tropopause (where the bulk of the data was collected). Instead, the debate centers around the extent to which the mesoscale spectrum might be thought of as quasi-linear waves versus fully nonlinear turbulence. Conversely, it has also been proposed that the shallow spectrum is related to tropopause-induced modificatons of quasigeostrophic dynamics. Here we consider these various points of view by examining simulations of freely decaying turbulence in a non-hydrostatic Boussinesq model for which the base state stratification contains a tropopause. For weak flow, results are consistent with quasigeostrophic dynamics: the flow is characterized by secondary roll-ups of filaments near the tropopause, but not elsewhere. For flow strengths more typical of the atmosphere, the shallow part of the spectrum is unbalanced. Similar to previous results ignoring the tropopause, the transition to an approximate -5/3 power law can be thought of as the crossing point of a shallow spectrum of unbalanced energy with a steeper spectrum of (geostrophically) balanced energy. Various diagnostics suggest that, although results are consistent with weakly nonlinear theories at large (synoptic) scales, the (model) mesoscale itself is turbulent. Implications and limitations of these findings are discussed, including implications for stimulated loss of balance, or SLOB.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

To implement Bayes’ Theorem for data assimilation, an ensemble Kalman filter (EnKF) uses a set of model integrations to simulate the temporally-varying background probability distribution function. Due to the merit of derived data assimilation solution coherently combining model and observational information, EnKF has risen as a widely-promising data assimilation algorithm in weather and climate studies. However, its huge computational resource demanding for ensemble model integrations sets a significant limitation on applications in high resolution coupled earth systems. Given that the background error statistics consist of stationary, slow-varying and fast varying parts, a high efficiency approximate EnKF (Hea-EnKF) is designed to dramatically enhance the computational efficiency. The Hea-EnKF is a combination of stationary, slow-varying and fast-varying filters, implemented in regressions sampled from large size single model solution data and updated with the model integrations. Validation shows that due to improved representation on stationary and slow-varying background statistics, the Hea-EnKF while only requiring a small fraction of computer resources can be better than the standard EnKF that uses finite ensemble statistics. The new algorithm makes practical to assimilate multi-source observations into any high-resolution coupled model intractable with current super-computing power for weather-climate analysis and predictions.

We introduce a conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows a practical information barrier that requires an exponential increase of the number of tracers. A suite of reduced filters are designed and compared in filtering different dynamical features, where an information-theoretic framework is adopted to assess the model error. In the last part of the talk, a brief discussion of applying conditional Gaussian filters to solve high-dimensional Fokker-Planck equation will be included. This method is able to beat the curse of dimensions in traditional particle methods. It has a potential in understanding parameterization and causality in turbulent flows.

In weather and climate prediction, data assimilation combines data with dynamical models to make prediction, using ensemble of solutions to represent the uncertainty. Due to limited computational resources, reduced models are needed and coarse-grid models are often used, and the effects of the subgrid scales are left to be taken into account. A major challenge is to account for the memory effects due to coarse graining while capturing the key statistical-dynamical properties. We propose a stochastic parametrization method which accounts for the memory effects by nonlinear autoregression moving average (NARMA) type models, and demonstrate by examples that the resulting NARMA type stochastic reduced models can capture the key statistical and dynamical properties and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

The sea surface temperature (SST) is a key variable in computing surface heat fluxes and plays a central role in ocean forecast and analysis. SST observations from satellites are derived using infrared and microwave sensors, which measure the skin (~10 mm depth) and sub-skin (~1 mm depth) temperatures. Diurnal variability in SST, at these depths, has nonlinear sensitivity to atmospheric forcing. For example, in low wind and/or high insolation conditions significant near-surface diurnal warming can occur. Most ocean general circulation models lack sufficient vertical resolution to adequately resolve the near-surface thermo-dynamical processes needed for accurately simulating diurnal variability. This presents a significant challenge in the assimilation of satellite SST observations. I will present progress on work towards a dynamically-based observation operator for the assimilation of SST observations that can account for near-surface thermo-dynamical processes. A method is presented that aims at diagnosing the diurnal cycle amplitude of skin and sub-skin SST, given the oceanic and the atmospheric states, mostly for assimilation purposes. Statistical relationships between the skin or sub-skin SST and the water temperature at depth are derived by means of a high-resolution one-dimensional column model. The main modes of correlations are extracted through canonical correlation analysis from these outputs, conditioned to the atmospheric state. In this manner, an observation operator that projects an ocean general circulation model temperature profile onto skin and sub-skin SST equivalents is built. This new operator is currently being tested in operational configurations of analysis and forecasting models in the Mediterranean Sea.

In this talk, we will present some progresses in improving seasonal climate predictions by using more advanced mathematical methods. The first example is to rely on the basic properties of stochastic theory to develop an efficient technique for the extraction of climatically relevant singular vectors (CSV) in the presence of weather noise. Emphasis is placed on the applications of the CSV in seasonal climate predictions and to construct optimal ensemble climate predictions. The results indicates that the CSVs can well characterize the optimal error growth of the climate predictions and lead to better ensemble predictions than traditional time lag (TLE) method. The second example is about our recent progress in the state estimate of state-space models with applications of Bayesian-based algorithms. A simplified algorithm of Sigma-point Kalman filter is develop to deal with the state estimation of high-dimensional systems like atmospheric and oceanic general circulation models.

Particle filters (PF) are sequential Monte Carlo methods based on particle representation of probability density functions (PDFs), which can be applied to any state-space model with no Gaussian assumption. A challenge of PF is to avoid the filter degeneracy - a situation in which almost every particle has negligible weight and contributes little to representing the PDFs - with limited computational resources, that is still an open question. We have tried several strategies to overcome this filter degeneracy problem, include using a hybrid scheme of PF and EnKF with a tunable parameter, and using vector weights to achieve localization. The results show great potentials to develop the feasible PF for large geophysical model systems with nonlinear/non-Gaussian observational systems.

Designing an efficient seasonal forecasting system is ensuring that the uncertainty in the initial conditions is sampled optimally. Perturbation in the initial condition and the methodology used for sampling perturbation optimally plays a key role in the improvement of the current seasonal climate forecast. In this study the error growth properties of initial perturbation are investigated using climatically relevant singular vectors (CSVs). The Community Climate System Model version 4 (CCSM4) is used as a simulation tool to examine the growth of optimal perturbations with different lead times over the South Asian Monsoon region. It is found that reliable set of CSVs can be estimated by running an ensemble of model forecasts. Amplification of the optimal perturbations occurs for more than 1 month and possibly up to 6 months. The results show the growth rates of the singular vectors are very sensitive to the variable of perturbation, number of perturbations and the error norm. When the SV is used as an initial perturbation, the forecast skill of key atmospheric variables over South Asian Monsoon region is significantly improved. Further, it is demonstrated that the predictions with the singular vector have a more reliable ensemble spread, suggesting a potential merit for a probabilistic forecast. The promising results reported here should hopefully encourage further investigation of the methodology at different timescales.

In this joint work with Ming-Cheng Shiue, a semi-discretized Euler scheme to solve three dimensional primitive equations is studied. With suitable assumptions on the initial data, the long time stability of the proposed scheme is shown by proving that the H1 norm (in space variables) is bounded.

We discuss numerical algorithms that are able to capture the long-time statisitcal properties, i.e., the climate, of large dissipative turbulent systems. The key ingredients are similar to those embodied in the classical Lax criteria on convergence of numerical schemes for linear PDEs: consistency and stability in some appropriate sense. Both deterministic and stochastic systems will be discussed. Applications to certain prototype GFD models will be presented.

This paper presents a review of progresses in the study of the nonlinear Local Lyapunov exponent (NLLE) and attractor radius as well as their applications to predictability study and ensemble predictions. The basic theory of the NLLE, local attractor radius and global attractor radius of nonlinear systems is firstly introduced. Then, the definition of NLLE is extended in the high-dimensional situation, and the NLLE spectrum (NLLEs) is introduced to estimate the predictability of multidimensional chaotic system, which realistically characterizes the error growth rates in different growing directions of system. Their applications are discussed from the following major aspects: (1) Quantifying spatial-temporal distributions of the predictability limits of weather and climate from daily to decadal time scale (e.g., quasi-biweekly oscillation (QBWO), Madden–Julian Oscillation (MJO), East Asian Summer Monsoon (EASM), Tropical cyclone (TC), seasonal, interannual and decadal as well). These applications provide a new perspective to promote the understanding of the predictability limits of weather and climate, which could be used as a baseline for improving the prediction. (2) Attribution of predictability (effects of different forcings, predictability barrier, the role of fast and slow variables in coupled systems, etc.). These findings reveal the possible existence of an intrinsic finite limit of predictability in a coupled system that possesses many scales of time or motion. (3) Applications to numerical prediction (predication of predictability, ensemble predictions, target observation, and etc.) The Nonlinear local Lyapunov vectors (NLLVs) are developed to indicate orthogonal directions in phase space with different perturbation growth rates. The NLLV method is used to generate initial perturbations and implement ensemble forecasts in numerical models.

The predictability of large-scale atmospheric flow is characterised by finite-time Lyapunov exponents and covariant Lyapunov vectors. The fluctuations of the Lyapunov exponents and the Kolmogorov-Sinai entropy as a function of prediction time are discussed. Extreme value theory is used to study the tail behaviour of the distributions. Also a large deviation principle for the Lyapunov exponents is established and a multivariate fluctuation analysis is performed. Then predictability is investigated conditional on large-scale weather regimes. A cluster algorithm is used to identify flow patterns associated with particularly low and high predictability. The study is performed in a three-level quasigeostrophic atmospheric model with realistic mean state and variability.

Weather has long been known to possess a limited predictability of ~ 2 weeks due to the inherent chaotic nature of the atmosphere. Because of the strong dependence of predictability on underlying dynamics, a natural question is how far in advance can we predict hurricane intensity, given that the hurricane rotational dynamics is highly axisymmetric at the meso scale? In this study, we will examine TC development in a phase space of hurricane scales and demonstrate the existence of an intensity attractor at the maximum potential intensity (MPI) limit. Estimation of the local leading Lyapunov exponent inside this attractor shows that the MPI attractor is not only an attracting set but also chaotic in nature. This finding of the chaotic MPI attractor suggests an upper bound on the predictability limit of the TC intensity, which prevents us from improving the accuracy of hurricane intensity forecasts beyond a certain threshold.

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño–Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism. Moreover, reasonable considerations of the model-error perturbations during the ensemble forecast process can alleviate the barrier caused by initial uncertainties through coordinately simulating the seasonal variations of the forecast uncertainty in order to significantly improve the probabilistic prediction skills and then to disorder the seasonal predictability related to the spring prediction barrier.

Several important issues of El Niño-Southern Oscillation (ENSO) predictability were studied using the latest version of the Zebiak-Cane model. A fully physically-based tangent linear model was constructed for the Zebiak-Cane model and a singular vector (SV) analysis for the 161 year (1856-2016) was performed. It was found that the leading SVs are less sensitive to initial conditions while singular values and final perturbation patterns exhibit a strong sensitivity to initial conditions. The dynamical diagnosis shows that the total linear and nonlinear heating terms play opposite roles in controlling the optimal perturbation growth. At decadal/interdecadal time scales, an inverse relationship exists between the leading singular value (S1) and correlation-based skill measures whereas an in-phase relationship exists between the S1 and MSE-based skill measures. However, S1 is not a good predictor of prediction skill at shorter time scales and for individual predictions. An offsetting effect was found between linear and nonlinear perturbation growth rates, which have opposite contributions to the S1. Ensemble and probabilistic ENSO predictions were performed for the 161 yrs. Results suggest that “reliability” is more sensitive to choice of ensemble construction strategy than “resolution”. The strategy produces the most reliable and skillful ENSO probabilistic prediction, benefiting from the contribution of the stochastic optimal winds and singular vector of SSTA.

Stochastic schemes to represent model uncertainty in the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system has helped improve its probabilistic forecast skill over the past decade by both improving its reliability and reducing the ensemble mean error. The largest uncertainties in the model arise from the model physics parameterizations. In the tropics, the parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate. Super-parameterisation is a promising recent alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud-resolving model (CRM) embedded within a global climate model (GCM). These two approaches (stochastic and super-parameterization) in convection parameterization have emerged as new paths forward and complement the conventional approaches rather than replace them. We study the impact of these two approaches and a combination of the two on forecasts from weather to sub-seasonal and climate timescales. Results from the evaluation of model forecast skill and fidelity in the Tropics and for organized convective systems such as the MJO will be presented. We show that the combination of the two approaches helps improve the reliability of forecasts of certain tropical phenomena, especially in regions that are affected by deep convective systems. This has implications for improving conventional convection parameterization using hybrid approaches for probabilistic earth system forecasting as we await the exascale computing systems of the future to resolve convective processes in climate models.

Nonlinear local Lyapunov vectors (NLLVs), theoretically inherited from the linear Lyapunov vectors (LVs) in a nonlinear framework, are developed to indicate orthogonal directions in phase space with different perturbation growth rates. Practically NLLVs generates flow dependent perturbations with full nonlinear models as in the breeding method, but regularly conducts the Gram–Schmidt reorthonormalization processes on the perturbations. The advantages of the sampling of the unstable subspace with the mutually orthogonal NLLVs instead of the most unstable direction with the dependent bred vectors (BVs) are clarified by using their respective unstable mode to predict the structure of forecast error growth. Additionally, the NLLVs have overall higher but correlated local dimensions compared to the BVs which may be beneficial for the former to increase the ensemble spread and capture the instabilities as well. The NLLV method is used to generate initial perturbations and implement ensemble forecasts in nonlinear models (the Lorenz63 model, Lorenz96 model, a barotropic quasi-geostrophic model and the Zebiak-Cane model) to explore the validity of the NLLV method. The performance of the NLLV method is compared comprehensively and systematically with other methods such as the ensemble transform Kalman filter (ETKF) method, the BV and the random perturbation (Monte Carlo) methods. Overall, the ensemble spread of NLLVs is more consistent with the errors of the ensemble mean, which indicates the better performance of NLLVs in simulating the evolution of analysis errors. In addition, the NLLVs perform significantly better than the BVs in terms of reliability and the random perturbations in resolution. The NLLV scheme has slightly higher ensemble forecast skill than the ETKF scheme. The NLLV scheme has significantly simpler algorithm and less computation time than the ETKF.

Before Numerical Weather Prediction (NWP), some forecasts were based on largescale similarities between the most recent synoptic chart and charts from archives, presuming that two similar atmospheric states would remain similar for a period of time. In 1969, Edward Lorenz showed that small differences between two resembling atmospheric states grow rapidly, and the likelihood of encountering any truly good upper-level analog is small. Today, analog forecasts are applied to predict model errors rather than the atmosphere’s future state. Analog ensembles are especially valuable when computational resources are not available to produce NWP ensembles. The method’s skill is attained when analogs are used to post-process deterministic NWP forecasts, by correcting local and flow-dependent errors, which originate mainly from imperfect parameterizations and inaccurate topography. This talk is intended to motivate a discussion about analog ensembles, which for the past decade have been consistently producing skillful statistical forecasts.

Soil moisture plays a significant role in the energy and water balances in land-atmosphere exchange. The model errors are an important factor causing the uncertainty in simulated soil moisture. This study addresses three questions. First, what is the extent of uncertainty in simulated soil moisture due to model parameters errors? Second, can we find out the important and key parameters combination leading to the uncertainty in simulated soil moisture among all physical parameters? To answer the above two questions, in four regions of China, the approach of conditional nonlinear optimal perturbation related to parameters (CNOP-P) and a sophisticated land surface model (the Common Land Model, CoLM) are employed. The model parameters errors that cause the largest uncertainties in simulated soil moisture are determined using the CNOP-P approach, which could calculate the upper bound of uncertainties due to the parameters errors and investigate the nonlinear effect of parameters combination on the uncertainties of simulation and prediction. The range of uncertainty for the simulated soil moisture is from 0.04 to 0.58 m3 m-3. Among 28 parameters, four important parameters (upper porosity, upper and lower Clapp and Hornberger “b” parameters, and the temperature coefficient of the conductance-photosynthesis model) could cause the large uncertainties in simulated soil moisture and are regarded as the relatively sensitive parameters combination. Finally, can the uncertainty in simulated soil moisture be lessened by reducing the errors of important and key physical parameters? The results show that the simulation ability of soil moisture could be improved if the errors in these important parameters combination are cut down. The improvement extent (61.6%) in simulated soil moisture using the CNOP-P approach is larger than that (53.4%) using the one-at-a-time (OAT) approach in China. These results indicate that the nonlinear effect of important physical parameters combination is beneficial to improve the simulation ability and prediction skill of the soil moisture. And, the CNOP-P approach is an effective method to discern the nonlinear effect of important physical parameters combination on the numerical simulation and prediction.

Predictive anisotropy is a phenomenon referring to unequal predictability of surface wind components in different directions. This study addresses the question whether predictive anisotropy resulting from statistical prediction is influenced by physical factors or by types of regression methods (linear vs nonlinear) used to construct the statistical prediction. A systematic study of statistical predictability of surface wind components at 2109 land stations across the globe is carried out. The results show that predictive anisotropy is a common characteristic for both linear and nonlinear statistical prediction, which suggests that type of regression methods is not a major influential factor. Strong predictive anisotropy and poor predictability are more likely to be associated with wind components characterized by relatively weak and non-Gaussian variability and in areas characterized by surface heterogeneity. An idealized mathematical model is developed separating predictive signal and noise between large-scale (predictable) and local (unpredictable) contribution to the variability of surface wind, such that small signal to noise ratio (SNR) corresponds to low and anisotropic predictability associated with non-Gaussian local variability. The comparison of observed and simulated statistical predictability by Regional Climate models (RCM) and reanalysis in the Northern Hemisphere indicates that small-scale processes which cannot be captured well by RCMs contribute to poor predictability and strong predictive anisotropy in observations. A second idealized mathematical model shows that spatial variability in specifically the minimum directional predictability, resulting from local processes, is the major contributor to predictive anisotropy. Overall, the results suggest that changes in statistical predictability which vary with the SNR are likely to be attributed to local processes.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.