I Introduction

An issue of importance to the Single-Column model (SCM) investigator is that of sensitive dependence on initial conditions. As Lorenz discovered in 1963, slight differences in the basic atmospheric state used to initialize a computer model for weather prognostication can lead to divergent solutions as the model integrates forward in time. These divergent solutions are due to the non-linear nature of the mathematical equations used in the model that govern atmospheric physics and dynamics. In addition to questions regarding correct spatial atmospheric sampling and objective analysis methods, this aspect of non-linearity has obvious implications for climate modeling from the standpoint of instrument error and other dataset irregularities. This is especially true for any climate models, SCMs included, which seek to simulate weather conditions for several months or years into the future by using observational data for both initialization and prescription. Thus, since one of the motivations for driving SCMs with observational data, such as that provided by the Atmospheric Radiation Measurement (ARM) program (Stokes and Schwartz, 1994), is to compare the model's predictions against actual weather observations as a means of assessing the SCM's performance, it would be useful to learn if, and to what degree, an SCM can be sensitive to the data used for its initialization and prescription. More generally, the question can be posed as to whether it is even reasonable to expect an SCM to be able to produce atmospheric states that resemble actual weather conditions at the end of a given time period.
 

II Methods

In an attempt to shed some light on this question, two experiments have been conducted. In the first, the Colorado State University SCM was driven with ARM Southern Great Plains (SGP) data in north-central Oklahoma and south-central Kansas during the summer 1995 Intensive Observation Period (IOP). The model was run 100 times with all of the initializing and forcing data being identical in each case, save for one item: the temperature sounding used to initialize each 17-day run was perturbed slightly. These perturbed profiles were produced by adding to the objectively analyzed temperature observation provided by Lawrence Livermore National Laboratories (LLNL) (Leach et al., 1996, 1997) a series of temperature increments ranging between +0.5 and -0.5 degrees Celsius as computed by a random number generator. Errors of this magnitude are reasonable approximations of the degree of instrument error one could expect from the radiosonde arrangement used at the SGP Cloud and Radiation Testbed (CART) site. As mentioned above, the moisture and wind profiles, and surface pressure used in the initialization process were the same for each of the 100 runs, as well as the fields used to force the model at each time-step such as horizontal wind divergence, horizontal tendencies due to advection of temperature and moisture, the surface pressure tendency, surface latent and sensible heat fluxes, and profiles of u- and v-wind components.

Additionally, another set of 100 runs was executed using the same forcing and initial conditions as before, including the same set of temperature perturbations to the initial conditions, except that instead of forcing the SCM with horizontal tendencies due to advection of temperature and moisture (which is called "vertical flux forcing" in the plots below), relaxation tendencies of horizontal temperature and moisture advection based on physical properties of the data were employed (see Randall and Cripe, 1999 for a detailed discussion of these different forcing methods). Since the relaxation forcing method is designed to keep the SCM from "wandering" too far from the observed state of the atmosphere at each time-step, it was anticipated that the results from this group of 100 runs should show less disagreement over the course of the IOP than the group where no relaxation was used. The results of both groups of runs are shown in part III below.

A parallel set of runs following a similar methodology was completed in the second experiment, only this time using Global Atmospheric Research Program's (GARP) Atlantic Tropical Experiment (GATE) dataset for comparison with the SCM results based on the ARM SGP CART site data. The particular version of GATE data used  was Ooyama's (1987) scale-controlled objective analysis of the data  onto a 1x1 degree square grid box, covering an area of 9x9 degree squares within 4 - 14 N latitude and 19 - 28 W longitude. The data were collected during Phase III of GATE in the eastern Atlantic Inter-Tropical Convergence Zone by a network of ship observations and radiosonde launches (Reed et al., 1977; Thompson et al., 1979). Surface rainfall rates were estimated by means of radar observations (Hudlow and Patterson, 1979). Instead of using a random number generator to perturb the temperature sounding used to initialize the SCM, the temperature profile from each of the 81 gridpoints in the dataset produced by Ooyama's scale-controlled objective analysis were employed, with the remainder of the initialization and prescription forcing for each run coming from the center gridpoint. The range of differences between temperatures on corresponding pressure levels of each of the gridpoint soundings amounted to less than 1 C.
 

III Results from Sensitive Dependence on Initial Conditions Experiment

The results from both experiments 1 and 2 outlined above are presented by means of a slide show. Please click the "enter" button below to start.
 

It has been shown that the results of the Colorado State University SCM are sensitive to initial conditions. Although the differences in the prognostic variables among the runs over the duration of the simulation periods are not enough to completely discredit results from the model, at least for integrations over a 17-day period, the differences are still considerable and point to the role that small fluctuations in observational data can play. Additionally, the greater degree of coherence in the results between the perturbed runs and the observations when relaxation forcing was used to drive the model instead of horizontal advective forcing argues for the relaxation-type of approach when initializing and driving models with data derived from real-time observations to minimize model sensitivity.

References:

Randall, D. A. and D. G. Cripe, 1999: Alternative Methods for specification of observed forcing in single-column models and cloud system models. J. Geophys. Res., (submitted).

Reed, R. J., D. C. Norquist, and E. Recker, 1977: The structure and properties of African wave disturbances as observed during Phase III of GATE. Mon. Wea. Rev., 105, 317-333.

Stokes, G. M., and S. E. Schwartz, 1994: The Atmospheric Radiation Measurement (ARM) Program: Programmatic background and design of the Cloud and Radiation Test Bed. Bull. Amer. Meteor. Soc., 75, 1201-1221.

Thompson, R. M., S. W. Payne, E. Recker, and R. J. Reed, 1979: Structure and properties of synoptic scale wave disturbances in the Intertropical Convergence Zone of the eastern Atlantic. J. Atmos. Sci., 36, 53-72.

Douglas Cripe
Department of Atmospheric Science
Colorado State University
Fort Collins, CO 80523-1371

Office Phone: 970.491.8327
Office Fax : 970.491.8428

doug@atmos.colostate.edu