An idealized 1½-layer isentropic model with convection and precipitation for satellite data assimilation research. Part I: model dynamics

2021 ◽  
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
Satellite Data ◽  
Layer Structure ◽  
Water Model ◽  
Stationary Waves ◽  
Fluid Temperature ◽  
Layer Model ◽  
Model Dynamics ◽  
Isentropic Model

Abstract An isentropic 1½-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data-assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic 2-layer model without convection and precipitation is shown in a companion paper (Part II).

scholarly journals An idealized 1½-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

2021 ◽  
Keyword(s):  
Shallow Water ◽  
Radiosonde Data ◽  
Water Model ◽  
Shallow Water Model ◽  
Layer Model ◽  
Apparent Inconsistency ◽  
Model Derivation ◽  
Two Layer Model ◽  
Isentropic Model ◽  
Mathematical Derivation

Abstract In this part II paper we present a fully consistent analytical derivation of the ‘dry’ isentropic 1½-layer shallow water model described and used in part I of this study, with no convection and precipitation. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis which is used to resolve an apparent inconsistency arising from the application of a rigid-lid approximation to an isentropic two-layer shallow water model. Real observations based on radiosonde data are used to justify the scaling assumptions used throughout the paper, as well as in part I. Eventually, a fully consistent isentropic 1½-layer model emerges from imposing fluid at rest (v1 = 0) and zero Montgomery potential (M1 = 0) in the upper layer of an isentropic two-layer model.

Balanced Ocean-Data Assimilation near the Equator

2002 ◽  
Vol 32 (9) ◽  
pp. 2509-2519 ◽  
Author(s):  
Gerrit Burgers ◽  
Magdalena A. Balmaseda ◽  
Femke C. Vossepoel ◽  
Geert Jan van Oldenborgh ◽  
Peter Jan van Leeuwen
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
General Circulation ◽  
General Circulation Models ◽  
Density Field ◽  
Water Model ◽  
Optimal Interpolation ◽  
Shallow Water Model ◽  
Ocean Data Assimilation ◽  
Zonal Velocity

Abstract The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

scholarly journals Hybrid 4DVAR with a Local Ensemble Tangent Linear Model: Application to the Shallow-Water Model

2016 ◽  
Vol 145 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Douglas R. Allen ◽  
Craig H. Bishop ◽  
Sergey Frolov ◽  
Karl W. Hoppel ◽  
David D. Kuhl ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Shallow Water ◽  
Linear Model ◽  
Bottom Topography ◽  
Grid Point ◽  
Model Error ◽  
Water Model ◽  
State Variables ◽  
Shallow Water Model

Abstract An ensemble-based tangent linear model (TLM) is described and tested in data assimilation experiments using a global shallow-water model (SWM). A hybrid variational data assimilation system was developed with a 4D variational (4DVAR) solver that could be run either with a conventional TLM or a local ensemble TLM (LETLM) that propagates analysis corrections using only ensemble statistics. An offline ensemble Kalman filter (EnKF) is used to generate and maintain the ensemble. The LETLM uses data within a local influence volume, similar to the local ensemble transform Kalman filter, to linearly propagate the state variables at the central grid point. After tuning the LETLM with offline 6-h forecasts of analysis corrections, cycling experiments were performed that assimilated randomly located SWM height observations, based on a truth run with forced bottom topography. The performance using the LETLM is similar to that of the conventional TLM, suggesting that a well-constructed LETLM could free 4D variational methods from dependence on conventional TLMs. This is a first demonstration of the LETLM application within a context of a hybrid-4DVAR system applied to a complex two-dimensional fluid dynamics problem. Sensitivity tests are included that examine LETLM dependence on several factors including length of cycling window, size of analysis correction, spread of initial ensemble perturbations, ensemble size, and model error. LETLM errors are shown to increase linearly with correction size in the linear regime, while TLM errors increase quadratically. As nonlinearity (or forecast model error) increases, the two schemes asymptote to the same solution.

scholarly journals Wind extraction potential from 4D-Var assimilation of stratospheric O<sub>3</sub>, N<sub>2</sub>O, and H<sub>2</sub>O using a global shallow water model

2014 ◽  
Vol 14 (7) ◽  
pp. 3347-3360 ◽  
Author(s):  
D. R. Allen ◽  
K. W. Hoppel ◽  
D. D. Kuhl
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
Continuity Equation ◽  
Potential Temperature ◽  
Mean Value ◽  
Water Model ◽  
Sufficient Information ◽  
Observation Error ◽  
Noise Levels ◽  
The Impact

Abstract. The wind extraction due to assimilation of stratospheric trace gas (tracer) data is examined using a 4D-Var (four-dimensional variational) data assimilation system based on the shallow water equations coupled to the tracer continuity equation. The procedure is outlined as follows. First, a nature run is created, simulating middle stratospheric winter conditions. Second, ozone (O3), nitrous oxide (N2O), and water vapor (H2O) (treated in this study as passive tracers) are initialized using Aura Microwave Limb Sounder (MLS) mixing ratios at 850 K potential temperature and are advected by the nature run winds. Third, the initial dynamical conditions are perturbed by using a 6 h offset. Fourth, simulated hourly tracer observations on the full model grid are assimilated with a 4D-Var system in which tracer and winds are coupled via the adjoint of the tracer continuity equation. Multiple assimilation experiments are performed by varying the amount of random observation error added to the simulated measurements. Finally, the wind extraction potential (WEP) is calculated as the reduction of the vector wind root mean square error (RMSE) relative to the maximum possible reduction. For a single 6 h assimilation cycle with the smallest observation error, WEP values are ~60% for all three tracers, while 10-day multi-cycle simulations result in WEP of ~90%, wind errors of ~0.3 m s−1, and height errors of ~13 m. There is therefore sufficient information in the tracer fields to almost completely constrain the dynamics, even without direct assimilation of dynamical information. When realistic observation error is added (based on MLS precisions at 10 hPa), the WEP after 10 days is 90% for O3, 87% for N2O, and 72% for H2O. O3 and N2O provide more wind information than H2O due to stronger background gradients relative to the MLS precisions. The RMSE for wind reach a minimum level of ~0.3–0.9 m s−1 for the MLS precisions, suggesting a limit to which realistic tracers could constrain the winds, given complete global cover age. With higher observation noise levels, the WEP values decrease, but the impact on the winds is still positive up to noise levels of 100% (relative to the global mean value) when compared to the case of no data assimilation.

scholarly journals A Consistent Hybrid Variational-Smoothing Data Assimilation Method: Application to a Simple Shallow-Water Model of the Turbulent Midlatitude Ocean

2011 ◽  
Vol 139 (11) ◽  
pp. 3333-3347 ◽  
Author(s):  
Monika Krysta ◽  
Eric Blayo ◽  
Emmanuel Cosme ◽  
Jacques Verron
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
Covariance Matrix ◽  
Hybrid Method ◽  
Water Model ◽  
Shallow Water Model ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Matrix

Abstract In the standard four-dimensional variational data assimilation (4D-Var) algorithm the background error covariance matrix remains static over time. It may therefore be unable to correctly take into account the information accumulated by a system into which data are gradually being assimilated. A possible method for remedying this flaw is presented and tested in this paper. A hybrid variational-smoothing algorithm is based on a reduced-rank incremental 4D-Var. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the matrix. In the analysis step, a low-dimensional error covariance matrix is updated so as to take into account the increased confidence level in the state vector it describes, once the observations have been introduced into the system. In the forecast step, the basis spanning the corresponding control subspace is propagated via the tangent linear model. The hybrid method is implemented and tested in twin experiments employing a shallow-water model. The background error covariance matrix is initialized using an EOF decomposition of a sample of model states. The quality of the analyses and the information content in the bases spanning control subspaces are also assessed. Several numerical experiments are conducted that differ with regard to the initialization of the matrix. The feasibility of the method is illustrated. Since improvement due to the hybrid method is not universal, configurations that benefit from employing it instead of the standard 4D-Var are described and an explanation of the possible reasons for this is proposed.

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