scholarly journals Numerical issues associated with compensating and competing processes in climate models: an example from ECHAM-HAM

2013 ◽  
Vol 6 (3) ◽  
pp. 861-874 ◽  
Author(s):  
H. Wan ◽  
P. J. Rasch ◽  
K. Zhang ◽  
J. Kazil ◽  
L. R. Leung
Keyword(s):  
Nucleation Rate ◽  
Climate Models ◽  
Cloud Condensation Nuclei ◽  
Operator Splitting ◽  
Time Integration ◽  
Lower Troposphere ◽  
Lessons Learned ◽  
Time Step ◽  
Simulated Concentration ◽  
Long Time

Abstract. The purpose of this paper is to draw attention to the need for appropriate numerical techniques to represent process interactions in climate models. In two versions of the ECHAM-HAM model, different time integration methods are used to solve the sulfuric acid (H2SO4) gas evolution equation, which lead to substantially different results in the H2SO4 gas concentration and the aerosol nucleation rate. Using convergence tests and sensitivity simulations performed with various time stepping schemes, it is confirmed that numerical errors in the second model version are significantly smaller than those in version one. The use of sequential operator splitting in combination with a long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors of nucleation rate in version two, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei (CCN) in the lower troposphere. These errors can be significantly reduced by employing solvers that handle production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-timescale problems involving compensating and competing processes, a common occurrence in current climate models.

scholarly journals Numerical issues associated with compensating and competing processes in climate models: an example from ECHAM-HAM

2013 ◽  
Vol 6 (1) ◽  
pp. 685-720
Author(s):  
H. Wan ◽  
P. J. Rasch ◽  
K. Zhang ◽  
J. Kazil ◽  
L. R. Leung
Keyword(s):  
Nucleation Rate ◽  
Climate Models ◽  
Cloud Condensation Nuclei ◽  
Operator Splitting ◽  
Time Integration ◽  
Lower Troposphere ◽  
Lessons Learned ◽  
Time Step ◽  
Simulated Concentration ◽  
Long Time

Abstract. The purpose of this paper is to draw attention to the need for appropriate numerical techniques to represent process interactions in climate models. In two versions of the ECHAM-HAM model, different time integration methods are used to solve the sulfuric acid (H2SO4) gas evolution equation, which lead to substantially different results in the H2SO4 gas concentration and the aerosol nucleation rate. Using convergence tests and sensitivity simulations performed with various time stepping schemes, it is confirmed that numerical errors in the second model version are significantly smaller than those in version one. The use of sequential operator splitting in combination with long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors of nucleation rate in version two, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei (CCN) in the lower troposphere. These errors can be significantly reduced by employing an implicit solver that handles production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-time-scale problems involving compensating and competing processes, a common occurrence in current climate models.

scholarly journals Quantifying and attributing time step sensitivities in present-day climate simulations conducted with EAMv1

2021 ◽  
Vol 14 (4) ◽  
pp. 1921-1948
Author(s):  
Hui Wan ◽  
Shixuan Zhang ◽  
Philip J. Rasch ◽  
Vincent E. Larson ◽  
Xubin Zeng ◽  
...  
Keyword(s):  
Time Integration ◽  
Lower Troposphere ◽  
Cloud Fraction ◽  
Coarse Grained ◽  
Step Size ◽  
Time Step ◽  
Upper Troposphere ◽  
Truncation Errors ◽  
Integration Error ◽  
Climate Simulations

Abstract. This study assesses the relative importance of time integration error in present-day climate simulations conducted with the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) at 1∘ horizontal resolution. We show that a factor-of-6 reduction of time step size in all major parts of the model leads to significant changes in the long-term mean climate. Examples of changes in 10-year mean zonal averages include the following: up to 0.5 K of warming in the lower troposphere and cooling in the tropical and subtropical upper troposphere, 1 %–10 % decreases in relative humidity throughout the troposphere, and 10 %–20 % decreases in cloud fraction in the upper troposphere and decreases exceeding 20 % in the subtropical lower troposphere. In terms of the 10-year mean geographical distribution, systematic decreases of 20 %–50 % are seen in total cloud cover and cloud radiative effects in the subtropics. These changes imply that the reduction of temporal truncation errors leads to a notable although unsurprising degradation of agreement between the simulated and observed present-day climate; to regain optimal climate fidelity in the absence of those truncation errors, the model would require retuning. A coarse-grained attribution of the time step sensitivities is carried out by shortening time steps used in various components of EAM or by revising the numerical coupling between some processes. Our analysis leads to the finding that the marked decreases in the subtropical low-cloud fraction and total cloud radiative effect are caused not by the step size used for the collectively subcycled turbulence, shallow convection, and stratiform cloud macrophysics and microphysics parameterizations but rather by the step sizes used outside those subcycles. Further analysis suggests that the coupling frequency between the subcycles and the rest of EAM significantly affects the subtropical marine stratocumulus decks, while deep convection has significant impacts on trade cumulus. The step size of the cloud macrophysics and microphysics subcycle itself appears to have a primary impact on cloud fraction in the upper troposphere and also in the midlatitude near-surface layers. Impacts of step sizes used by the dynamical core and the radiation parameterization appear to be relatively small. These results provide useful clues for future studies aiming at understanding and addressing the root causes of sensitivities to time step sizes and process coupling frequencies in EAM. While this study focuses on EAMv1 and the conclusions are likely model-specific, the presented experimentation strategy has general value for weather and climate model development, as the methodology can help researchers identify and understand sources of time integration error in sophisticated multi-component models.

scholarly journals Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs

2021 ◽  
Vol 88 (2) ◽  
Author(s):  
Alec Dektor ◽  
Abram Rodgers ◽  
Daniele Venturi
Keyword(s):  
Operator Splitting ◽  
Time Integration ◽  
Planck Equation ◽  
Two Dimensions ◽  
Low Rank ◽  
Nonlinear Pdes ◽  
High Dimensional ◽  
Time Step ◽  
Tensor Methods ◽  
Modeling Errors

AbstractWe present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new rank-adaptive algorithm based on a thresholding criterion that limits the component of the PDE velocity vector normal to the FTT tensor manifold. This yields a scheme that can add or remove tensor modes adaptively from the PDE solution as time integration proceeds. The new method is designed to improve computational efficiency, accuracy and robustness in numerical integration of high-dimensional problems. In particular, it overcomes well-known computational challenges associated with dynamic tensor integration, including low-rank modeling errors and the need to invert covariance matrices of tensor cores at each time step. Numerical applications are presented and discussed for linear and nonlinear advection problems in two dimensions, and for a four-dimensional Fokker–Planck equation.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals Clutter Cancellation and Long Time Integration for GNSS-Based Passive Bistatic Radar

2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Author(s):  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
Time Integration ◽  
Detection Performance ◽  
Bistatic Radar ◽  
Detection Range ◽  
Robust Detection ◽  
Coherent Integration ◽  
Long Time ◽  
Long Time Integration

Clutter cancellation and long time integration are two vital steps for global navigation satellite system (GNSS)-based bistatic radar target detection. The former eliminates the influence of direct and multipath signals on the target detection performance, and the latter improves the radar detection range. In this paper, the extensive cancellation algorithm (ECA), which projects the surveillance channel signal in the subspace orthogonal to the clutter subspace, is first applied in GNSS-based bistatic radar. As a result, the clutter has been removed from the surveillance channel effectively. For long time integration, a modified version of the Fourier transform (FT), called long-time integration Fourier transform (LIFT), is proposed to obtain a high coherent processing gain. Relative acceleration (RA) is defined to describe the Doppler variation results from the motion of the target and long integration time. With the estimated RA, the Doppler frequency shift compensation is carried out in the LIFT. This method achieves a better and robust detection performance when comparing with the traditional coherent integration method. The simulation results demonstrate the effectiveness and advantages of the proposed processing method.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

scholarly journals The effects of aerosols on precipitation and dimensions of subtropical clouds: a sensitivity study using a numerical cloud model

2006 ◽  
Vol 6 (1) ◽  
pp. 67-80 ◽  
Author(s):  
A. Teller ◽  
Z. Levin
Keyword(s):  
Water Vapor ◽  
Climate Models ◽  
Cloud Model ◽  
Cloud Condensation Nuclei ◽  
Sensitivity Study ◽  
Meteorological Conditions ◽  
Dust Particles ◽  
Noticeable Effect ◽  
Convective Clouds ◽  
Ice Nuclei

Abstract. Numerical experiments were carried out using the Tel-Aviv University 2-D cloud model to investigate the effects of increased concentrations of Cloud Condensation Nuclei (CCN), giant CCN (GCCN) and Ice Nuclei (IN) on the development of precipitation and cloud structure in mixed-phase sub-tropical convective clouds. In order to differentiate between the contribution of the aerosols and the meteorology, all simulations were conducted with the same meteorological conditions. The results show that under the same meteorological conditions, polluted clouds (with high CCN concentrations) produce less precipitation than clean clouds (with low CCN concentrations), the initiation of precipitation is delayed and the lifetimes of the clouds are longer. GCCN enhance the total precipitation on the ground in polluted clouds but they have no noticeable effect on cleaner clouds. The increased rainfall due to GCCN is mainly a result of the increased graupel mass in the cloud, but it only partially offsets the decrease in rainfall due to pollution (increased CCN). The addition of more effective IN, such as mineral dust particles, reduces the total amount of precipitation on the ground. This reduction is more pronounced in clean clouds than in polluted ones. Polluted clouds reach higher altitudes and are wider than clean clouds and both produce wider clouds (anvils) when more IN are introduced. Since under the same vertical sounding the polluted clouds produce less rain, more water vapor is left aloft after the rain stops. In our simulations about 3.5 times more water evaporates after the rain stops from the polluted cloud as compared to the clean cloud. The implication is that much more water vapor is transported from lower levels to the mid troposphere under polluted conditions, something that should be considered in climate models.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

Impact of climate change on water availability in Tropical Andean catchments: a case study in the Vilcanota catchment, Peru

2021 ◽  
Author(s):  
Selina Meier ◽  
Randy Munoz ◽  
Christian Huggel
Keyword(s):  
Climate Change ◽  
Water Management ◽  
Water Demand ◽  
Climate Models ◽  
Local Population ◽  
Time Step ◽  
Glacier Surface ◽  
Hydrological Simulation ◽  
Sustainable Water Management ◽  
Monthly Runoff

<p>Water scarcity is increasingly becoming a problem in many regions of the world. On the one hand, this can be attributed to changes in precipitation conditions due to climate change. On the other hand, this is also due to population growth and changes in consumer behaviour. In this study, an analysis is carried out for the highly glaciated Vilcanota River catchment (9808 km<sup>2</sup> – 1.2% glacier area) in the Cusco region (Peru). Possible climatic and socioeconomic scenarios up to 2050 were developed including the interests from different water sectors, i.e. agriculture, domestic and energy.</p><p>The analysis consists of the hydrological simulation at a monthly time step from September 2043 to August 2050 using a simple glacio-hydrological model. For historic conditions (1990 to 2006) a combination of gridded data (PISCO precipitation) and weather stations was used. Future scenario simulations were based on three different climate models for both RCP 2.6 and 8.5. Different glacier outlines were used to simulate changes in glacier surface through the time for both historic (from satellite data) and future (from existing literature) scenarios. Furthermore, future water demand simulations were based on the SSP1 and SSP3 scenarios.</p><p>Results from all scenarios suggest an average monthly runoff of about 130 m<sup>3</sup>/s for the Vilcanota catchment between 2043 and 2050. This represents a change of about +5% compared to the historical monthly runoff of about 123 m<sup>3</sup>/s. The reason for the increase in runoff is related to the precipitation data from the selected climate models. However, an average monthly deficit of up to 50 m<sup>3</sup>/s was estimated between April and November with a peak in September. The seasonal deficit is related to the seasonal change in precipitation, while the water demand seems to have a less important influence.</p><p>Due to the great uncertainty of the modelling and changes in the socioeconomic situation, the data should be continuously updated. In order to construct a locally sustainable water management system, the modelling needs to be further downscaled to the different subcatchments in the Vilcanota catchment. To address the projected water deficit, a new dam could partially compensate for the decreasing storage capacity of the melting glaciers. However, the construction of the dam could meet resistance from the local population if they cannot be promised and communicated multiple uses of the new dam. Sustainable water management requires the cooperation of all stakeholders and all stakeholders should be able to benefit from it so that they will support future projects.</p>

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