## 1. Introduction

[2] Accurate methods to characterize the states of hydrologic reservoirs have become more important as the reliability of historically dependable water supply has become increasingly suspect because of changing temperature and precipitation trends [e.g., *Service*, 2004; *Mote et al.*, 2005]. Temporal variability in seasonal water fluxes between major reservoirs is often poorly understood and may be affected by future climate change [*Oki and Kanae*, 2006]. On the other hand, the amount of information for characterizing hydrologic reservoirs has increased as more and more satellites provide global remote sensing measurements of the land surface at a range of spatial scales, spectral wavelengths, and temporal frequencies [*Beven and Fisher*, 1996]. Furthermore, increasingly sophisticated land surface model (LSM) schemes provide physical process models for predicting the dynamics of hydrologic reservoirs. Remote sensing measurements and LSM estimates of hydrologic states have important drawbacks, however; it is not trivial to directly invert the remotely sensed signals, and LSM accuracy is necessarily limited to the accuracy of the inputs used to force and/or parameterize the models.

[3] Data assimilation (DA) methodologies may be used to merge any number of independent estimates of hydrologic states (or other quantities of interest) at different scales, allowing for better use of the voluminous data streams, and thus show great promise for characterization of land surface states. In order to weigh the uncertainty of the various sources of information, DA methods require specification of the joint probability distribution function of all uncertain inputs. In practice, hydrologists often assume that inputs follow normal or lognormal distributions, which are completely defined by the first two statistical moments (i.e., the mean and the uncertainty). Although the effects of the magnitude and the accuracy of the input uncertainty on DA schemes can be quite significant, these uncertainty estimates are generally unknown. By “uncertainty accuracy,” we refer to how accurately the estimate of the uncertainty of each DA input represents the true uncertainty. Indeed, *Dee* [1995] argues that the characterization of input uncertainty forms the primary crux of the DA scheme. However, the sensitivity of assimilation schemes to uncertainty estimates is not often investigated.

[4] This paper explores the effects of input uncertainty magnitude and accuracy in a multiscale ensemble Kalman filter (EnKF) [*Evensen*, 2003] DA scheme designed to merge radiometric remote sensing measurements with a physically based snow scheme (in an LSM) in order to characterize snow water equivalent (SWE) and grain size. We also investigate the misspecification of input uncertainty and its propagation to certain metrics of filter performance as evidence to suggest that adaptive filtering, where the uncertainty of the state (or measurements) is simultaneously estimated along with the states, may be feasible in the context of this multiscale DA environment. This paper does not investigate the application of an adaptive filtering scheme, however. Instead, we attempt to address several crucial questions in the context of this synthetic test. First, assuming that the uncertainty is known, how sensitive are the filter results to input uncertainty? Second, relaxing the assumption that the uncertainty is known, how sensitive are the filter results to misspecification of the input uncertainty? Third, does the potential exist for application of an adaptive filtering scheme to correct misspecified uncertainty?

[5] Section 2 reviews recent work done to characterize snowpack on the one hand, and to estimate uncertainty in adaptive filtering schemes on the other. In section 3, the models and measurements utilized in this study are described. In section 4, results are presented to demonstrate the central role of input uncertainty magnitude and accuracy in this DA study and to investigate the potential to diagnose input uncertainty misspecification using several metrics of filter performance.