Model Initial Conditions Research Articles

Improving monthly streamflow forecasts through assimilation of observed streamflow for rainfall-dominated basins across the CONUS

Among different sources of uncertainty in hydrologic modeling (i.e., model structure, parameter estimation, input data, etc.), consecutive error reduction of model initial conditions can prevent a model from drifting away from reality and consequently improving model estimates. Most approaches that evaluated the correction of initial conditions through data assimilation (DA) have focused on improving hydrologic model simulations (i.e., under observed forcings) rather than evaluating the model performance in a forecasting context. This paper investigates the utility of Ensemble Kalman Filter (EnKF) data assimilation in which available observed streamflow is exploited to update state variables of a conceptual water balance model for forecasting monthly streamflow over 340 rainfall-dominated river basins across the contiguous United States (CONUS). Our results demonstrate that after EnKF application, streamflow simulation skill improves in terms of both Relative Root Mean Square Error (R-RMSE) and correlation coefficient (CC) for almost 90% of the selected river basins. Evaluating the model performance under different flow conditions shows that EnKF has stronger positive effect on monthly low flow predictions comparing to monthly high flows particularly during the summer season. The utility of EnKF is also assessed in the context of 1-month ahead streamflow forecasting. Due to the updated model initial conditions, streamflow forecasts are improved throughout the year even though the skill in hydrologic forecasts is predominantly dependent on the accuracy of precipitation forecasts.

Dependence on initial conditions versus model formulations for medium‐range forecast error variations

Understanding the root causes of forecast errors and occasional very poor forecasts is essential but difficult. In this paper we investigate the relative importance of initial conditions and model formulation for medium‐range errors in 500 hPa geopotential height. The question is addressed by comparing forecasts produced with ECMWF‐IFS and NCEP‐GFS forecasting systems, and with the GFDL‐fvGFS model initialized with the ECMWF and NCEP initial conditions. This gives two pairs of configurations that use the same initial conditions but different models, and one pair with the same model but different initial conditions. The first conclusion is that the initial conditions play the major role in differences between the configurations in terms of the average root‐mean‐square error for both Northern and Southern Hemispheres as well as Europe and the contiguous US (CONUS), while the model dominates the systematic errors. A similar conclusion is also found by verifying precipitation over low latitudes and the CONUS. The day‐to‐day variations of 500 hPa geopotential height scores are exemplified by one case of a forecast bust over Europe, where the error is found to be dominated by initial errors. The results are generalized by calculating correlations between errors integrated over Europe, CONUS and a region in the southeastern Pacific from the different configurations. For Europe and southeast Pacific, the correlations in the medium range are highest between the pairs that use the same initial conditions, while over CONUS they are highest for the pair with the same model. This suggests different mechanisms behind the day‐to‐day variability of the score for these regions. Over CONUS the link is made to the propagation of troughs over the Rockies, and the result suggests that the large differences in parametrizations of orographic drag between the models play a role.

Transverse momentum distribution of charged hadrons based on wounded quark model

In nucleus-nucleus collisions, new particles are produced mainly through strong interactions among the constituents of the QCD medium. The search of a unified phenomenological model to understand this production mechanism is one of the main motivation behind the heavy ion experiments. A vast variety of data coming from nucleus-nucleus collision experiments put a stringent constraint on the particle production models. A unified and proper model must satisfy the various data regarding pseudorapidity distributions, transverse energy density distributions, transverse momentum distributions with respect to control parameters in different types of collisions at various energies simultaneously. Recently we proposed a new version of wounded quark model (WQM) which actually satisfies many points of this criteria. However, these kind of static initial model conditions have problem in calculating the transverse momentum distributions of charged hadrons. In this article, we have used the important ingredients of WQM like number of wounded quarks and number of quark-quark collisions to fit the transverse momentum spectra of charged hadrons. Based on the assumption of different mechanisms at different regions, i.e. different mechanisms for soft $ p_{T}$ and hard momentum part, we have proposed a parameterization made of two functions to calculate the transverse momentum spectra in different collisions at different energies ranging from higher RHIC to LHC. We hope that this study along with our recent work on WQM will become a more suitable choice as unified model for particle production in strong interaction, instead of wounded nucleon model.

Understanding Biases in Simulating the Diurnal Cycle of Convection over the Western Coast of Sumatra: Comparison with Pre-YMC Observation Campaign

Abstract Biases in simulating the diurnal cycle of convection near the western coast of the island of Sumatra have been investigated using the data from the pilot field campaign of the Years of the Maritime Continent (pre-YMC). The campaign was carried out at a sea [Research Vessel (R/V) Mirai] and a land (Bengkulu, Sumatra) site. Simulations are performed using a tropical configuration of the Met Office model at a grid resolution of 1.5 km in a limited-area mode. The focus of this study is to understand how biases in the input conditions from ECMWF high-resolution deterministic forecast affect the diurnal cycle. Modeled precipitation is found to be delayed and weak, with cold SST bias in the model as the key contributing factor affecting convection at both sites. Colder SST causes a delay in the trigger of convection at Bengkulu by delaying the onset of the local land breeze, which in turn delays the local convergence. The cold outflow from precipitation over the adjacent mountain is also found to be delayed in the model, contributing to the total delay. This delay in the evening convection at Bengkulu is shown to directly affect the timing of nighttime convection at Mirai. Weaker convection at Bengkulu is argued to be due to lower-tropospheric dry humidity bias in the model initial condition. Convection at Mirai is shown to be caused by the convergence of the cold outflow from Bengkulu with the prevailing landward wind over the sea. Both thermodynamic and dynamic conditions near the cold outflow front are found to be less favorable for intense convection in the simulation, the reason for which is argued to be a combination of the cold SST bias and a weaker cold outflow.

Impact of airborne cloud radar reflectivity data assimilation on kilometre-scale numerical weather prediction analyses and forecasts of heavy precipitation events

Abstract. This article investigates the potential of W-band radar reflectivity to improve the quality of analyses and forecasts of heavy precipitation events in the Mediterranean area. The “1D+3DVar” assimilation method, operationally employed to assimilate ground-based precipitation radar data in the Météo-France kilometre-scale numerical weather prediction (NWP) model AROME, has been adapted to assimilate the W-band reflectivity measured by the airborne cloud radar RASTA (Radar Airborne System Tool for Atmosphere) during a 2-month period over the Mediterranean area. After applying a bias correction, vertical profiles of relative humidity are first derived via a 1-D Bayesian retrieval, and then used as relative humidity pseudo-observations in the 3DVar assimilation system of AROME. The efficiency of the 1-D Bayesian method in retrieving humidity fields is assessed using independent in-flight humidity measurements. To complement this study, the benefit brought by consistent thermodynamic and dynamic cloud conditions has been investigated by separately and jointly assimilating the W-band reflectivity and horizontal wind measurements collected by RASTA in the 3 h 3DVar assimilation system of AROME. The data assimilation experiments are conducted for a single heavy precipitation event and then also for 32 cases. Results indicate that the W-band reflectivity has a larger impact on the humidity, temperature and pressure fields in the analyses compared to the assimilation of RASTA wind data alone. Besides, the analyses get closer to independent humidity observations if the W-band reflectivity is assimilated alone or jointly with RASTA wind data. Nonetheless, the impact of the W-band reflectivity decreases more rapidly as the forecast range increases when compared to the assimilation of RASTA wind data alone. Generally, the joint assimilation of the W-band reflectivity with wind data results in the best improvement in the rainfall precipitation forecasts. Consequently, results of this study indicate that consistent thermodynamic and dynamic cloud conditions in the analysis leads to an improvement of both model initial conditions and forecasts. Even though to a lesser extent, the assimilation of the W-band reflectivity alone also results in a slight improvement of the rainfall precipitation forecasts.

Set propagation in dynamical systems with generalised polynomial algebra and its computational complexity

This paper presents an approach to propagate sets of initial conditions and model parameters through dynamical systems. It is assumed that the dynamics is dependent on a number of model parameters and that the state of the system evolves from some initial conditions. Both model parameters and initial conditions vary within a set Ω. The paper presents an approach to approximate the set Ω with a polynomial expansion and to propagate, under some regularity assumptions, the polynomial representation through the dynamical system. The approach is based on a generalised polynomial algebra that replaces algebraic operators between real numbers with operators between polynomials. The paper first introduces the concept of generalised polynomial algebra and its use to propagate sets through dynamical systems. Then it analyses, both theoretically and experimentally, its time complexity and compares it against the time complexity of a non-intrusive counterpart. Finally, the paper provides an empirical convergence analysis on two illustrative examples of linear and non-linear dynamical systems.

Predictability in process-based ensemble forecast of influenza.

Process-based models have been used to simulate and forecast a number of nonlinear dynamical systems, including influenza and other infectious diseases. In this work, we evaluate the effects of model initial condition error and stochastic fluctuation on forecast accuracy in a compartmental model of influenza transmission. These two types of errors are found to have qualitatively similar growth patterns during model integration, indicating that dynamic error growth, regardless of source, is a dominant component of forecast inaccuracy. We therefore examine the nonlinear growth of model initial error and compute the fastest growing directions using singular vector analysis. Using this information, we generate perturbations in an ensemble forecast system of influenza to obtain more optimal ensemble spread. In retrospective forecasts of historical outbreaks for 95 US cities from 2003 to 2014, this approach improves short-term forecast of incidence over the next one to four weeks.

Variational Deconvolution of Conically Scanned Passive Microwave Observations With Error Quantification

The deconvolution of potentially cloud-affected passive microwave brightness temperatures is an important step for utilization in direct data assimilation in cloud-resolving numerical weather prediction (NWP) models for the purpose of improving model initial conditions. Geophysical retrieval algorithms, such as precipitation rate retrievals, also benefit from consistent resolution across channels. In this paper, we explore how to derive the posterior error estimates that are required for ingestion into data assimilation models or end-to-end error-quantified retrieval algorithms. To this end, we present a minimum variance, best linear-unbiased estimator approach that seeks an optimal estimate of the apparent (i.e., without the effects of antenna pattern convolution) brightness temperatures by iteratively minimizing a cost function measuring the lack of fit between observations and departures from a first guess. Both the observation and first-guess departure terms are weighed by a corresponding covariance term that estimates their relative uncertainty. The first-guess uncertainty, a Bayesian prior “belief” in the spread of the first-guess error, is estimated using geophysical fields from an NWP model in a radiative transfer model plus an antenna pattern forward operator, then iteratively improved using the posterior deconvolved brightness temperatures of actual special sensor microwave imager/sounder observations. The error for the posterior distribution, subject to the initial belief, is derived. The error-quantified results are shown to increase the spatial resolution of microwave observations.

Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation

We show that two widely accepted model reduction techniques, balanced truncation (BT) and balanced singular perturbation approximation (BSPA), can be derived as limiting approximations of a carefully constructed parameterization of linear time invariant systems by employing the model boundary approximation method (MBAM) [1] . We also show that MBAM provides a novel way to interpolate between BT and BSPA, by exploring the set of approximations on the boundary of the “model manifold,” which is associated with the specific choice of model parameterization and initial condition and is embedded in a sample space of measured outputs, between the elements that correspond to the two model reduction techniques. This paper suggests similar types of approximations may be obtainable in topologically similar places (i.e., on certain boundaries) on the associated model manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted model reduction techniques to nonlinear systems. 1

Computer Research of Building Materials

A computer study of the technological processes for the production of building materials based on the use of reversible autocatalysis reactions is carried out. For the mathematical description of the process of autocatalytic reactions, mathematical models are used, described by a initial-boundary problems for the Carleman system. The considered mathematical model describes the autocatalysis reaction under the following assumptions: the rate of decrease in the density of positive ions is proportional to the square of the deviation of the density of positive ions from the equilibrium state, the rate of decrease in the density of negative ions is proportional to the square of the deviation of the density of negative ions from the equilibrium position and the law of conservation of the total charge of the system including liquid solution. This mathematical model is non-linear, therefore numerical methods are used for its study. For a numerical solution of the initial-boundary value problem for the Carleman system, a finite-difference method of the second order of accuracy is used. For the numerical investigation of the solution obtained, linear interpolation and spline interpolation are used. A numerical study is made on the dependence of the chemical reaction time from the parameters of the model and various initial conditions.

Visualization of cosmological density fluctuations with phase space analysis: case study: Brans\u2013Dicke theory

Cosmological perturbation theory is a powerful tool to understanding the large-scale structure of the Universe. However, the set of field equations describes the general linear perturbations for the cosmological models is highly nonlinear and coupled where no analytical solution can be found. It is only after some simplification and numerical computation that we obtain limited solutions. On way around is to employ the phase space analysis and investigate the asymptotic stability of the model. The advantage of using this approach is that the system of field equations become simpler to solve numerically. The algorithm also determines the stability of the system. Here, we apply this approach in Brans–Dicke cosmology and study the attractor solutions after fitting the model with the SNeIa observational data. As a result, the model confirms small fluctuations of energy density. The model also predicts current universe acceleration confirmed by observation and benefits from phase space analysis that the new dynamical variables are independent of the model initial conditions.

Radar Data Assimination in WRF Model to Forecast Heavy Rainfall at Ho Chi Minh City

Abstract: This article using high resolution WRF model simulation on a heavy rainfall in summer at Hochiminh city by using radar data to assimilation initial conditions with 3DVAR method, the WRF3Dvar running simulation with two modes: cold start and warm start combine with three cases: only Reflectivity of radar; Reflectivity and Doppler radar radial wind observations; Reflectivity, Doppler radar radial wind, and GTS data. The background error used was CV7 created from 6 months forecast in South Vietnam. Radar data before assimilation was quality control and thinned to remove noise and create the best observation. 24 station rainfall in South Vietnam using to an evaluation of WRF model simulation. Results show assimilation only reflectivity will affect to variable qcloud, qvapor and qrain on the initial condition of model and assimilation only Doppler radar radial wind improve wind. Compare each case show warm start simulation precipitation better than the cold start, assimilation both Doppler radar radial wind observations, the reflectivity of radar and GTS better than another case.
 Key words: WRFDA,RADAR

Role of Planetary Boundary Layer Processes in the Simulation of Tropical Cyclones Over the Bay of Bengal

The behaviour of planetary boundary layer (PBL) schemes initialized at different life stages of a tropical cyclone (TC) is studied by considering seven Bay of Bengal TC cases. In each TC case, the Advanced Research Weather Research and Forecasting (WRF-ARW) model is initialized at four life stages (depression to very severe cyclone storm) with National Center for Environmental Prediction (NCEP) Global analysis and integrated up to 96 h. A set of six PBL sensitivity experiments are conducted at four stages for all seven TC cases to analyse the impact of the model boundary layer in simulating the TC track and intensity parameters. The model-produced track, intensity and rainfall patterns are evaluated with the best track, intensity and gridded rainfall estimates obtained from the India Meteorological Department (IMD). The spatial and radius/height section simulated fields are evaluated with satellite retrievals. Results depict that the six PBL schemes during model initialization at different stages of a TC have produced sizable differences in the simulation of track and intensity parameters. The local and nonlocal schemes produced different results based on the TC stage at which the model is initialized. The results also suggest that if the model is initialized with a non-organized cyclonic vortex such as depression stage of the storm, PBL schemes exhibit high sensitivity and spread in terms of both track and intensity. While the spread between PBL schemes was significantly reduced and found close to the observed estimates when the model was initialized at the advanced stages of the TC. In addition, the local 1.5-order closure scheme simulated the storm parameters relatively better when the cyclone vortex was not well organized in the model's initial conditions, while the non-local and first-order closure schemes perform better with initial model conditions of a well-defined cyclonic vortex.

Uncertainty in malaria simulations in the highlands of Kenya: Relative contributions of model parameter setting, driving climate and initial condition errors.

In this study, experiments are conducted to gauge the relative importance of model, initial condition, and driving climate uncertainty for simulations of malaria transmission at a highland plantation in Kericho, Kenya. A genetic algorithm calibrates each of these three factors within their assessed prior uncertainty in turn to see which allows the best fit to a timeseries of confirmed cases. It is shown that for high altitude locations close to the threshold for transmission, the spatial representativeness uncertainty for climate, in particular temperature, dominates the uncertainty due to model parameter settings. Initial condition uncertainty plays little role after the first two years, and is thus important in the early warning system context, but negligible for decadal and climate change investigations. Thus, while reducing uncertainty in the model parameters would improve the quality of the simulations, the uncertainty in the temperature driving data is critical. It is emphasized that this result is a function of the mean climate of the location itself, and it is shown that model uncertainty would be relatively more important at warmer, lower altitude locations.

Validity of parameter optimization in improving MJO simulation and prediction using the sub-seasonal to seasonal forecast model of Beijing Climate Center

Using the sub-seasonal to seasonal forecast model of Beijing Climate Center, several key physical parameters are perturbed by the Latin hypercube sampling method to find a better configuration for representation of Madden–Julian oscillation (MJO) in the free-run simulation. We find that although model simulation is especially sensitive to some parameters, there are overall no significant linear relationships between model skill and any one of the parameters, and the optimum performance can be obtained by combined perturbations of multiple parameters. By optimization, MJO’s spectrum, intensity, spatial structure and propagation, as well as the mean state and variance, are all improved to some extent, suggesting the correspondence and interrelation of model’s performances in simulating different characteristics of MJO. Further, several sets of initialized hindcasts using the optimized parameters are conducted, and their results are compared with the hindcasts using only improved initial conditions. We show that with an optimized model, the forecast of MJO beyond 3-week lead time is not improved, and the maximum useful skill is only slightly increased, implying that a decrease of model error does not always translate into an increase of forecast skill at all lead time. However, the skill is obviously enhanced during lead times of 2–3 weeks for forecasts in most seasons and initial phases except for a few cases. Particularly, the deficiency in forecasting MJO’s propagation from the Indian Ocean to the Pacific is relieved, further highlighting the positive contribution of reducing model error compared to previous work that only reduced initial condition error. In this study, we also show benefits of multi-scheme ensemble strategy in describing uncertainties of model error and initial condition error and thus improving MJO forecast.

Application of Multivariate Sensitivity Analysis Techniques to AGCM-Simulated Tropical Cyclones

Abstract This work demonstrates the use of Sobol’s sensitivity analysis framework to examine multivariate input–output relationships in dynamical systems. The methodology allows simultaneous exploration of the effect of changes in multiple inputs, and accommodates nonlinear interaction effects among parameters in a computationally affordable way. The concept is illustrated via computation of the sensitivities of atmospheric general circulation model (AGCM)-simulated tropical cyclones to changes in model initial conditions. Specifically, Sobol’s variance-based sensitivity analysis is used to examine the response of cyclone intensity, cloud radiative forcing, cloud content, and precipitation rate to changes in initial conditions in an idealized AGCM-simulated tropical cyclone (TC). Control factors of interest include the following: initial vortex size and intensity, environmental sea surface temperature, vertical lapse rate, and midlevel relative humidity. The sensitivity analysis demonstrates systematic increases in TC intensity with increasing sea surface temperature and atmospheric temperature lapse rates, consistent with many previous studies. However, there are nonlinear interactions among control factors that affect the response of the precipitation rate, cloud content, and radiative forcing. In addition, sensitivities to control factors differ significantly when the model is run at different resolution, and coarse-resolution simulations are unable to produce a realistic TC. The results demonstrate the effectiveness of a quantitative sensitivity analysis framework for the exploration of dynamic system responses to perturbations, and have implications for the generation of ensembles.

Effects of parameter and data uncertainty on long-term projections in a model of the global forest sector

This study explored the consequences for long-term projections and impact analysis of the uncertainty in model parameters and initial conditions. Using the Global Forest Products Model, multiple replications of projections were carried out with parameters or initial condition data sampled randomly from their assumed distribution. The results showed that parameter uncertainty led to uncertainty of the projections increasing steadily with the time horizon, and more rapidly than the uncertainty stemming from initial conditions. Among the parameter uncertainties, those in the supply and demand elasticities tended to dominate the uncertainty in the other parameters describing forest growth, manufacturing activities, and trade inertia. In an application to impact analysis it was found that, due only to the uncertainty of the model parameters, and conditional on other assumptions, an assumed rise in global temperature of 2.8 °C over a century caused the forest stock in 2065 to be 2.4% to 4.0% higher in developed countries, and 2.5% to 3.9% lower in developing countries, with 68% probability, a conservative estimate of the true uncertainty given all the other factors involved in such a prediction.

Modified Hybrid Grey Model (1,1) to Forecast Cellular Subscribers

This study develops MHGM (1,1) (Modified Hybrid Grey Model) which is the combination of two models first one is improved GM (1,1), this model consists of optimization of initial and background values and other is concave EDDGM (1,1) (Dynamic Discrete Grey Model) termed, in this model equal division technique is applied to fit the concavity of cumulative sequence and after that created dynamic average value and on the basis of that dynamic average value dynamic discrete GM (1,1) model is established and by the gradual heuristics method or the dichotomy approach the initial equal division number is obtained. We have fixed equal division number ‘n’ between 0 and 1in MHGM (1,1). For forecasting of starting half years we use y(0)(m) as initial condition of model in time restored function and also multiply by a factor e-b 1 to adjust the model. This model has applied without solving by heuristics or dichotomy method. Subscribers of cellular networks increase day by day in Pakistan; cellular industry has total five networks in Pakistan. In this paper data of three cellular networks subscribers that are Mobilink, Ufone and Zong have taken as application of models and it has been proved by using mean absolute percentage error that the forecast accuracy of MHGM (1,1) is better than GM (1,1) (Grey Model) and improved grey model (1,1).

Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO

Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Var) data assimilation system was developed for an intermediate coupled model (ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer (Te), which is empirically and explicitly related to sea level (SL) variation. The strength of the thermocline effect on SST (referred to simply as “the thermocline effect”) is represented by an introduced parameter, αTe. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Var data assimilation system implemented in the ICM are also discussed.

Comparative analysis of dengue versus chikungunya outbreaks in Costa Rica

For decades, dengue virus has been a cause of major public health concern in Costa Rica, due to its landscape and climatic conditions that favor the circumstances in which the vector, Aedes aegypti, thrives. The emergence and introduction throughout tropical and subtropical countries of the chikungunya virus, as of 2014, challenged Costa Rican health authorities to provide a correct diagnosis since it is also transmitted by the same vector and infected hosts may share similar symptoms. We study the 2015–2016 dengue and chikungunya outbreaks in Costa Rica while establishing how point estimates of epidemic parameters for both diseases compare to one another. Longitudinal weekly incidence reports of these outbreaks signal likely misdiagnosis of infected individuals: underreporting of chikungunya cases, while overreporting cases of dengue. Our comparative analysis is formulated with a single-outbreak deterministic model that features an undiagnosed class. Additionally, we also used a genetic algorithm in the context of weighted least squares to calculate point estimates of key model parameters and initial conditions, while formally quantifying misdiagnosis.