Melt Pond Scheme Parameter Estimation Using an Adjoint Model

Melt ponds significantly affect Arctic sea ice thermodynamic processes.The melt pond parameterization scheme in the Los Alamos sea ice model(CICE6.0) can predict the volume,area fraction(the ratio between melt pond area to sea ice area in a model grid),and depth of melt ponds.However,this scheme has some uncertain parameters that affect melt pond simulations.These parameters could be determined through a conventional parameter estimation method,which requires a large number of sensitivity simulations.The adjoint model can calculate the parameter sensitivity efficiently.In the present research,an adjoint model was developed for the CESM(Community Earth System Model) melt pond scheme.A melt pond parameter estimation algorithm was then developed based on the CICE6.0 sea ice model,melt pond adjoint model,and L-BFGS(Limited-memory Broyden-Fletcher-Goldfard-Shanno) minimization algorithm.The parameter estimation algorithm was verified under idealized conditions.By using MODIS(Moderate Resolution Imaging Spectroradiometer)melt pond fraction observation as a constraint and the developed parameter estimation algorithm,the melt pond aspect ratio parameter in CESM scheme,which is defined as the ratio between pond depth and pond area fraction,was estimated every eight days during summertime for two different regions in the Arctic.One region was covered by multi-year ice(MYI) and the other by first-year ice(FYI).The estimated parameter was then used in simulations and the results show that:(1) the estimated parameter varies over time and is quite different for MYI and FYI;(2) the estimated parameter improved the simulation of the melt pond fraction.

Theoretical Aspect of Suitable Spatial Boundary Condition Specified for Adjoint Model on Limited Area

Theoretical argumentation for so-called suitable spatial condition is conducted by the aid of homotopy framework to demonstrate that the proposed boundary condition does guarantee that the over-specification boundary condition resulting from an adjoint model on a limited-area is no longer an issue, and yet preserve its well-poseness and optimal character in the boundary setting. The ill-poseness of over-specified spatial boundary condition is in a sense, inevitable from an adjoint model since data assimilation processes have to adapt prescribed observations that used to be over-specified at the spatial boundaries of the modeling domain. In the view of pragmatic implement, the theoretical framework of our proposed condition for spatial boundaries indeed can be reduced to the hybrid formulation of nudging filter, radiation condition taking account of ambient forcing, together with Dirichlet kind of compatible boundary condition to the observations prescribed in data assimilation procedure. All of these treatments, no doubt, are very familiar to mesoscale modelers. Key words Variational data assimilation - Adjoint model - Over-specified partial boundary condition This research work is sponsored by the National Key Programme for Developing Basic Sciences (G1998040907), the Project of Natural Science Foundation of Jiangsu Province (BK99020), the President Foundation of Nanjing University (985) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

The Improvement Made by a Modified TLM in 4DVAR with a Geophysical Boundary Layer Model

The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.

Sensitivity Experiments of an Eastward-Moving Southwest Vortex to Initial Perturbations

Whether the initial conditions contain pronounced mesoscale signals is important to the simulation of the southwest vortex. An eastward-moving southwest vortex is simulated using the PSU/NCAR MM5. A modest degree of success is achieved, but the most serious failure is that the formation and displacement of the simulated vortex in its early phase are about fourteen hours later than the observed vortex. Considering the relatively sparse data on the mesoscale vortex and in an attempt to understand the cause of the forecast failure, an adjoint model is used to examine the sensitivity of the southwest vortex to perturbations of initial conditions. The adjoint sensitivity indicates how small perturbations of model variables at the initial time in the model domain can influence the vortex. A large sensitivity for zonal wind is located under 400 hPa, a large sensitivity for meridional wind is located under 500 hPa, a large sensitivity for temperature is located between 500 and 900 hPa, and almost all of the large sensitivity areas are located in the southwestern area. Based on the adjoint sensitivity results, perturbations are added to initial conditions to improve the simulation of the southwest vortex. The results show that the initial conditions with perturbations can successfully simulate the formation and displacement of the vortex; the wind perturbations added to the initial conditions appear to be a cyclone circulation under the middle level of the atmosphere in the southwestern area with an anticyclone circulation to its southwest; a water vapor perturbation added to initial conditions can strengthen the vortex and the speed of its displacement.

Application and Characteristic Analysis of the Moist Singular Vector in GRAPES-GEPS

The singular vector(SV)initial perturbation method can capture the fastest-growing initial perturbation in a tangent linear model(TLM).Based on the global tangent linear and adjoint model of GRAPES-GEPS(Global/Regional Assimilation and Prediction System-Global Ensemble Prediction System),some experiments were carried out to analyze the structure of the moist SVs from the perspectives of the energy norm,energy spectrum,and vertical structure.The conclusions are as follows:The evolution of the SVs is synchronous with that of the atmospheric circulation,which is flowdependent.The moist and dry SVs are located in unstable regions at mid-to-high latitudes,but the moist SVs are wider,can contain more small-and medium-scale information,and have more energy than the dry SVs.From the energy spectrum analysis,the energy growth caused by the moist SVs is reflected in the relatively small-scale weather system.In addition,moist SVs can generate perturbations associated with large-scale condensation and precipitation,which is not true for dry SVs.For the ensemble forecasts,the average anomaly correlation coefficient of large-scale circulation is better for the forecast based on moist SVs in the Northern Hemisphere,and the low-level variables forecasted by the moist SVs are also improved,especially in the first 72 h.In addition,the moist SVs respond better to short-term precipitation according to statistical precipitation scores based on 10 cases.The inclusion of the large-scale condensation process in the calculation of SVs can improve the short-term weather prediction effectively.

Characteristics and Nonlinear Growth of the Singular Vector Related to a Heavy Rainfall Case over the Korean Peninsula

In this study, singular vectors related to a heavy rainfall case over the Korean Peninsula were calculated using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model （MM5） adjoint modeling system. Tangent linear and adjoint models include moist physical processes, and a moist basic state and a moist total energy norm were used for the singular-vector calculations. The characteristics and nonlinear growth of the first singular vector were analyzed, focusing on the relationship between the basic state and the singular vector. The horizontal distribution of the initial singular vector was closely related to the baroclinicity index and the moisture availability of the basic state. The temperature-component energy at a lower level was dominant at the initial time, and the kinetic energy at upper levels became dominant at the final time in the energy profile of the singular vector. The nonlinear growth of the singular vector appropriately reflects the temporal variations in the basic state. The moisture-component energy at lower levels was dominant at earlier times, indicating continuous moisture transport in the basic state. There were a large amount of precipitation and corresponding latent heat release after that period because the continuous moisture transport created favorable conditions for both convective and nonconvective precipitation. The vertical propagation of the singular-vector energy was caused by precipitation and the corresponding latent heating in the basic state.

Variational Data Assimilation Experiments of Mei-Yu Front Rainstorms in China

The numerical forecasts of mei-yu front rainstorms in China has been an important issue. The intensity and pattern of the frontal rainfall are greatly influenced by the initial fields of the numerical model. The 4-dimensional variational data assimilation technology (4DVAR) can effectively assimilate all kinds of observed data, including rainfall data at the observed stations, so that the initial fields and the precipitation forecast can both be greatly improved. The non-hydrostatic meso-scale model (MM5) and its adjoint model are used to study the development of the mei-yu front rainstorm from 1200 UTC 25 June to 0600 UTC 26 June 1999. By numerical simulation experiments and assimilation experiments, the T106 data and the observed 6-hour rainfall data are assimilated. The influences of many factors, such as the choice of the assimilated variables and the weighting coefficient, on the precipitation forecast results are studied. The numerical results show that 4DVAR is valuable and important to mei-yu front rainfall prediction.

Water flooding optimization with adjoint model under control constraints

The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conven-tional solving method of the maximum principle requires two solutions of time series： the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelera-tes the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.

Machine learning for adjoint vector in aerodynamic shape optimization

Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for it to obtain the gradients of all design variables. However, the computational cost of adjoint vector is approximately equal to that of flow computation. In order to accelerate the solution of adjoint vector and improve the efficiency of adjoint-based optimization, machine learning for adjoint vector modeling is presented. Deep neural network (DNN) is employed to construct the mapping between the adjoint vector and the local flow variables. DNN can efficiently predict adjoint vector and its generalization is examined by a transonic drag reduction of NACA0012 airfoil. The results indicate that with negligible computational cost of the adjoint vector, the proposed DNN-based adjoint method can achieve the same optimization results as the traditional adjoint method.

Model adjointization and its cost

In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also, two constants of fundamental importance in AD, s and m, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.

Tracking a Severe Pollution Event in Beijing in December 2016 with the GRAPES–CUACE Adjoint Model

We traced the adjoint sensitivity of a severe pollution event in December 2016 in Beijing using the adjoint model of the GRAPES–CUACE（Global/Regional Assimilation and Prediction System coupled with the China Meteorological Administration Unified Atmospheric Chemistry Environmental Forecasting System）. The key emission sources and periods affecting this severe pollution event are analyzed. For comaprison, we define 2000 Beijing Time 3 December 2016 as the objective time when PM2.5 reached the maximum concentration in Beijing. It is found that the local hourly sensitivity coefficient amounts to a peak of 9.31 μg m^–3 just 1 h before the objective time, suggesting that PM2.5 concentration responds rapidly to local emissions. The accumulated sensitivity coefficient in Beijing is large during the 20-h period prior to the objective time, showing that local emissions are the most important in this period.The accumulated contribution rates of emissions from Beijing, Tianjin, Hebei, and Shanxi are 34.2%, 3.0%, 49.4%,and 13.4%, respectively, in the 72-h period before the objective time. The evolution of hourly sensitivity coefficient shows that the main contribution from the Tianjin source occurs 1–26 h before the objective time and its peak hourly contribution is 0.59 μg m^-3 at 4 h before the objective time. The main contributions of the Hebei and Shanxi emission sources occur 1–54 and 14–53 h, respectively, before the objective time and their hourly sensitivity coefficients both show periodic fluctuations. The Hebei source shows three sensitivity coefficient peaks of 3.45, 4.27, and 0.71 μg m^–3 at 4, 16, and 38 h before the objective time, respectively. The sensitivity coefficient of the Shanxi source peaks twice, with values of 1.41 and 0.64 μg m^–3 at 24 and 45 h before the objective time, respectively. Overall, the adjoint model is effective in tracking the crucial sources and key periods of emissions for the severe pollution event.

Adjoint code generator

The adjoint code generator （ADG） is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables.Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques.In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG.In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization.Some experimental results in several applications are presented at the end.

Numeric modelling and risk assessment of pollutions in the Chinese Bohai Sea

To simulate the dynamic process of total nitrogen(TN) in seas, numerical modelling combined with the adjoint method is implemented in this study. Because nonpoint source terms(ST) and initial values(IV) of TN are essential but difficult to determine, the adjoint method was applied to a numerical model, and the ST and IV terms of TN were inverted via routine monitoring data in the Bohai Sea. In twin experiments, the adjoint method was capable of inverting the prescribed spatio-temporally distributed ST and the spatial distributed IV. In practical experiments, the results demonstrated that the simulation precision with ST inversion was higher than that with IV inversion and was accurate with joint initial values and source term(IST) inversion. This result indicates that nonpoint source TN is essential for the simulation of TN concentration. Furthermore, the simulated results indicate that the pollution in three bays of the Bohai Sea is rather severe. The model in this study is not specific to the Bohai Sea and can be generalized to other areas, such as the Beibu Gulf. These findings may assist in the development of cost-effective controls for accidental or planned industrial pollutant releases into coastal waters.

Air quality short-term control in an industrial region under adverse weather conditions

A new short-term optimal control of air quality in an industrial region during atmospheric inversions is proposed.lts goal is to prevent violation of health standard of air quality in a few monitored zones.The control establishes restrictions on the emission rates of industrial sources and includes the identification of the industrial sources violating(exceeding)the emission rates set by the control.Both control and identification are based on using solutions to an adjoint dispersion model.Conditions that show the convergence of the emission rates,prescribed by the control,to the original emission rates of the industrial sources are given(Theorems 4 and 5).These results ensure that the new emission rates of industrial sources(established by the control)will be as close as possible to the original emission rates throughout the entire period of application of the control.This creates the minimum possible restrictions on the functioning of industrial enterprises.The highlight of the new control is the possibility of selecting special weights for each pollution source in the goal function that is minimized.These weights are mainly aimed at reducing the intensity of emissions of the main sources of pollution.An example demonstrates the ability of the new method.A similar approach can also be used to develop methods for cleaning water zones polluted by oil(the problem of bioremediation),and to prevent excessive pollution of urban areas with automobile emissions.