1. Introduction

In order to understand how continental soil moisture is used in a constructed analogue one needs to know first how soil moisture data are obtained.

Soil moisture is not measured at enough places for a long enough time to base a monitoring system for the United States on true observations. Rather, soil moisture data are generated by models in which observations play a role, but much else is generated by smart physics. Symbolically a soil moisture model can be represented by dw/dt = P - E - R + other, where w is soil moisture, P is precipitation, E is evaporation, and R is surface runoff. The w data set we will use here has been described in Huang et al(1996), where a simple hydrological model was presented. About 5 parameters are fitted to reproduce observed runoff in Oklahoma, given observed P. The E (based on Thornwhaite's expression for potential evaporation, requiring T as input) and w are important 'data' coming out of this procedure, and will be treated as proxy-observations below. Using the Oklahoma fitted parameters elsewhere, a data set for the period 1932-present has been generated at 344 Climate Divisions in the US. {As an aside: Global gridded data for a coarse resolution 1979-1998 is available also}.

One particularly important consideration is that the interannual variability in P is 2 to 3 times larger than that in E. This places an enormous burden on having accurate P - in fact everything else is secondary. This is precisely the reason why we cannot (as yet) use soil moisture produced by such comprehensive approaches as CDAS/Reanalysis (Kalnay et al 1996), because even though NCEP's Medium Range Forecast (MRF) has a better land surface model than was used in Huang et al (1996), the MRF does not assimilate observed P, but rather generates its own precipitation in the 6 hours leading up to making the next guess field - these P estimates are unsatisfactory. We thus resort to a stand alone off line model integration of a soil model requiring only P and T as input. The GCIP Land Data Assimilation Project (LDAS) is based on much the same considerations, using however the ETA land surface model. {We do consider to use the state of the art ETA land surface model (replacing Huang et al 1996) at a future time.}

2. Constructed Analogue

We construct here an analogue in terms of just the soil moisture over the contiguous United States. Suppose w^base(x,y) is a (any) soil moisture anomaly field to which we desire an analogue. I.e. we want to minimize

Q = { w^base(x,y) - w^con(x,y)}² where

w^con(x,y) = sum ( a _j w_j(x,y)) (1)

where, w_j is the soil moisture anomaly observed in year j (j=1 to 66, corresponding to 1932 to 1997), x and y are spatial coordinates, and _j are the weights assigned to each historical year, such that the l.h.s. matches the field we seek to reproduce. The method of finding a_j is given in Van den Dool (1994). In order to reproduce the soil moisture at the end of March 1998, for example, the following list of weights was obtained: