A simplified cloud model adjoint

Adjoint of a parameterized moisture convection model

Robert G. Fovell
Meteorology and Atmospheric Physics   (in press)

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Abstract

Adjoint models have found use as "dynamical tracers", helping to track a feature or phenomenon back to its origin. Their application to the study of atmospheric convection, however, is challenged by the complexity and nonlinearity of diabatic processes. Herein, the adjoint of a significantly simpler parameterized moisture (PM) model is described and tested. The PM model eliminates explicit moisture by making latent heating conditionally proportional to updraft velocity and providing a lower tropospheric heat sink mimicking rainwater evaporation.

The PM adjoint, of course, is useful only if the parameterization can produce realistic results. Earlier work suggested that the PM framework possessed a fundamental flaw that made its storms have an excessive impact on their upstream environments. In fact, the adjoint was used to identify the origin of the discrepancies between PM and traditional cloud model storms, thereby leading to the parameterization improvements and dynamical insights recently discussed in Fovell (2002). The present paper is a companion to that study, describing how the adjoint model was constructed, tested and utilized. In addition, an even more realistic adjoint framework is described.

Paper

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Figures (including color versions) and captions

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Figure 1 - Schematic model illustrating PM model design. Fovell and Tan's (2000) low CAPE sounding is depicted at right.

Figure 1

Figure 2 - Perturbation fields of potential temperature θ' (shaded; K) and horizontal velocity u' (3 m s-1 contours) for the control run. The zero contour is suppressed. Only a portion of the domain is shown.

Figure 2

Figure 3 - As in Fig. 2, but for perturbation pressure p' (shaded; hPa) and vertical velocity w (3 m s-1 contours). Additionally, the -1 m s-1 vertical velocity contour has been included.

Figure 3

Figure 4 - Control (shaded) and adjoint sensitivity (contoured) fields at 4000 sec: (a) perturbation potential temperature field θ-hat (.05 m s-1 K-1 contours); (b) horizontal velocity field u-hat (.0075 [nondimensional] contours). Control field is full, storm-relative u rather than u'. Shown in panel (a) is the circulatory tendency implied by the adjoint sensitivity field.

Figure 4

Figure 5 - As in Fig. 4, but showing: (a) vertical velocity sensitivity field w-hat (.001 [nondimensional] contours); (b) perturbation pressure sensitivity field p-hat (.002 m s-1 hPa-1 contours).

Figure 5

Figure 6 - As in Fig. 4, but at 3000 sec. Temperature sensitivity contour interval is .025 m s-1 K-1; for the horizontal velocity sensitivity it is .005 (nondimensional).

Figure 6

Figure 7 - As in Fig. 5, but at 3000 sec. Vertical velocity sensitivity contoured at .002 (nondimensional) intervals; for the pressure sensitivity it is .001 m s-1 hPa-1.

Figure 7

Figure 8 - As in Fig. 6, but for the diabatic adjoint run. Temperature sensitivity contour interval is .03 m s-1 K-1; for the horizontal velocity sensitivity it is .005 (nondimensional).

Figure 8

Figure 9 - As in Fig. 7, but for the diabatic adjoint run. Vertical velocity sensitivity contour interval is .003 (nondimensional); for the pressure sensitivity it is .0015 m s-1 hPa-1).

Figure 9

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