The development of general circulation models (GCMs) is an important task among the current efforts to understand and predict the climate. A key element of atmospheric GCMs is the so-called "dynamical core", the component of a GCM that deals with the numerical solution of the dry, adiabatic primitive equations. In order to build reliable dynamical cores, it is important to test them against known solutions.

At present, the only widely used test case for dry dynamical cores is the one proposed by Held & Suarez (1994), in which simply defined parametrizations of two key physical processes (thermal relaxation and surface drag) are added to the dynamical core. The model behavior is then tested by performing a 1,000-day integration and comparing the time-averaged fields to those in the Held & Suarez test case. One major drawback of this test case, however, is that a large amount of averaging needs to be performed before the results of a given model can be compared to those of the test case. It is conceivable that subtle coding errors or noisy features may not reveal themselves owing to the averaging. A second drawback is that numerical convergence was not demonstrated by the authors. A final, though minor drawback, is that new parameterizations need to be added to the dynamical core itself.

We here propose a new test case, meant to address the shortcomings of the Held & Suarez test case, and serve as a complementary tool for testing dynamical cores. Our new test case is an initial-value problem, with the zonal winds specified to be those of a baroclinically unstable, midlatitude zonal jet, analytically specified to be very close to the LC1 paradigm described by Thorncroft et al (1993). This zonal jet is slightly perturbed, and its evolution is integrated for 10 days. We present snapshots of the fields at various time intervals (e.g. the vorticity near the surface) as the baroclinic instability develops. We also show the time evolution of several diagnostic quantities over the 10 days of integration, and provide tables of these to serve as numerical benchmarks against which new dynamical cores can be precisely and quantitatively compared.

Unlike the Held & Suarez test case, our test case involves the addition of no additional parametrizations to the dynamical core, and requires a much shorter integration time. Also, the instantaneous fields computed with a new dynamical core can be compared directly to those of the benchmark, without the need for temporal or spatial averaging. Finally, by demonstrating numerical convergence, our new test case de facto provides a new, non-trivial, exact -- albeit numerically derived -- solution to the time-dependent primitive equations in spherical coordinates.