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Linearization of a Simple Moist Convection Scheme for Large-Scale NWP Models

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  • 1 MRB/RPN, Meteorological Service of Canada, Dorval, Quebec, Canada
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Abstract

A simple Kuo-type convection scheme with an improved closure based on moist enthalpy accession (Kuo symmetric) has been linearized for the tangent-linear (TL) and adjoint (AD) versions of the Global Environmental Multiscale (GEM) model. The nonlinear scheme exhibits a reasonable behavior in terms of heating and moistening rates when evaluated in stand-alone mode over a set of deep convective profiles. A preliminary evaluation of a straightforward linearization in the global TL model has revealed the existence of noise that leads to an unacceptable solution after 12 h of integration. By neglecting several terms in the linearization (detrainment rate and cloud properties), the temporal evolution of humidity analysis increments is improved by including this simplified linearized convection scheme in the TL model. The behavior of the linearized scheme has also been compared favorably to the linearized version of the European Centre for Medium-Range Weather Forecasts (ECMWF) mass-flux convection scheme. When examining the validity of the TL approximation for surface precipitation, it appears that linearization errors are large for both stratiform and convective rainfall (rms errors are about twice the mean absolute perturbed precipitation). These errors are not reduced when considering accumulated rain rates instead of instantaneous quantities. However, the occurrence of “on–off” processes is reduced by a temporal integration of rain. This could make the variational assimilation of accumulated precipitation rates easier. Finally, errors coming from internal nonlinearities are slightly larger than those produced by discontinuities. This confirms the interest for improving the linearity of nonlinear convection schemes for applications in variational contexts.

Corresponding author address: Jean-François Mahfouf, MRB/RPN, Meteorological Service of Canada, 2121 Transcanada Highway, Dorval, QC, H9P 1J3, Canada. Email: jean-francois.mahfouf@ec.gc.ca

Abstract

A simple Kuo-type convection scheme with an improved closure based on moist enthalpy accession (Kuo symmetric) has been linearized for the tangent-linear (TL) and adjoint (AD) versions of the Global Environmental Multiscale (GEM) model. The nonlinear scheme exhibits a reasonable behavior in terms of heating and moistening rates when evaluated in stand-alone mode over a set of deep convective profiles. A preliminary evaluation of a straightforward linearization in the global TL model has revealed the existence of noise that leads to an unacceptable solution after 12 h of integration. By neglecting several terms in the linearization (detrainment rate and cloud properties), the temporal evolution of humidity analysis increments is improved by including this simplified linearized convection scheme in the TL model. The behavior of the linearized scheme has also been compared favorably to the linearized version of the European Centre for Medium-Range Weather Forecasts (ECMWF) mass-flux convection scheme. When examining the validity of the TL approximation for surface precipitation, it appears that linearization errors are large for both stratiform and convective rainfall (rms errors are about twice the mean absolute perturbed precipitation). These errors are not reduced when considering accumulated rain rates instead of instantaneous quantities. However, the occurrence of “on–off” processes is reduced by a temporal integration of rain. This could make the variational assimilation of accumulated precipitation rates easier. Finally, errors coming from internal nonlinearities are slightly larger than those produced by discontinuities. This confirms the interest for improving the linearity of nonlinear convection schemes for applications in variational contexts.

Corresponding author address: Jean-François Mahfouf, MRB/RPN, Meteorological Service of Canada, 2121 Transcanada Highway, Dorval, QC, H9P 1J3, Canada. Email: jean-francois.mahfouf@ec.gc.ca

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