## 1. Introduction

[2] Agricultural drought is commonly defined as the presence of insufficient soil water available for adequate crop and forage production. As a result, agricultural drought is typically monitored using soil moisture anomaly products generated during the growing season at weekly or monthly time scales [*Anderson et al.*, 2011]. Consistent estimates of soil moisture for drought monitoring can be obtained in various ways; for example through remote sensing or through modeling of the land-surface water budget. However, these estimates are not perfect and each method has characteristic uncertainties [*Koster et al.*, 2009; *Jackson et al.*, 2010]. Therefore, it is frequently desirable to merge independent realizations to obtain a more accurate unified estimate. Theoretically, the more independent data that are merged, the larger the reduction in the noise of the merged product and past work, in a variety of fields, has demonstrated the benefits of combining geophysical estimates obtaining from a range of observational and modeling resources into a single hybrid estimate (see, e.g., *Ebert* [2001] or *Xie and Arkin* [1996]). However, it is important to weigh the products based on their relative accuracies in order to minimize errors.

[3] Data assimilation using Kalman filter-based methodologies is one of the most commonly used approaches for merging different products while taking into account their relative uncertainties. Kalman filter theory can be shown to be a recursive solution of the least squares problem [*Sorenson*, 1970] for an appropriate time frame. The solution of *Kalman* [1960]enables propagation of the best estimate and its errors in time, whereas in ordinary least squares the solution is assumed constant in time. The goal for both solutions is obtaining an estimate with minimized error variance. However, both solutions also require prior knowledge of product uncertainties to obtain an optimal analysis. In land data assimilation studies, Kalman filter-based methodologies often rely on ad-hoc statistical descriptions of errors in assimilated observations, model parameters, or model forcings. As a result, the relative weighting applied to modeled and observed soil moisture information by a land data assimilation is arguably subjective and does not necessarily reflect an optimized integration of independent data sources [*Crow and Van Loon*, 2006; *Reichle et al.*, 2008]. Therefore, our goal here is the development of an objective merging that is less dependent on uncertain, user-defined error assumptions.

[4] Triple collocation is a method that objectively obtains error estimates for three or more independent products. This method was originally introduced by *Stoffelen* [1998] and *Caires and Sterl* [2003]to estimate near-surface wind speed errors, and later applied in many hydrological applications. In particular*Scipal et al.* [2008]estimated the errors in passive microwave-, active microwave-, and model-based soil moisture products.*Miralles et al.* [2010]estimated errors in passive microwave-, station-, and model-based soil moisture products and validated the error estimates using watershed scale station-based data.*Dorigo et al.* [2010]evaluated the uncertainties of global passive microwave-, active microwave-, and model-based soil moisture products.*Hain et al.* [2011]estimated errors in passive microwave-, thermal infrared-, and model-based soil moisture realizations and found passive microwave- and thermal infrared-based soil moisture products yield complementary soil moisture information.*Parinussa et al.* [2011b]estimated errors in passive microwave-, active microwave-, and antecedent precipitation index-based soil moisture products, then compared the triple collocation-based errors with data assimilation-based error estimates [*Crow*, 2007], and found very high correlation between the error estimates of these two techniques.

[5] It is relatively straight forward to use triple collocation as a means to estimate observation error covariance parameters required by land data assimilation systems [*Crow and van den Berg*, 2010]. However, applying triple collocation to the parameterization of modeling error within a Kalman filter is more difficult, and—to our knowledge—has not yet been attempted. In particular, a Kalman filter requires covariance information regarding background errors that vary in time according to flow conditions and/or the frequency of assimilated observations. In contrast, triple collocation provides only a temporally constant value of error representing a continuous, nonupdated integration of the forecast model. Likewise, triple collocation provides only information about the magnitude of modeling errors and not their source and/or impact on the full model forecast covariance matrix. Such information is often important in land data assimilation applications [*Crow and Van Loon*, 2006]. While potentially resolvable, these challenges suggest that the initial use of triple collocation-based modeling errors should be based on a relatively simple least square framework as opposed to a full data assimilation approach.

[6] Here we propose an objective methodology that does not require any user-defined error parameters as input. In this approach, different anomaly soil moisture products are merged in a least squares framework that relies on product error estimates obtained from triple collocation. Specifically, we have merged weekly, growing-season soil moisture anomaly products obtained from thermal remote sensing via the atmosphere land exchange inversion (ALEXI [*Anderson et al.*, 2007a]) model, microwave remote sensing via the land parameter retrieval model (LPRM [*Owe et al.*, 2008]), and the Noah [*Ek et al.*, 2003] land surface model. The least squares framework is also able to provide estimates of uncertainty in the merged product, which could be used to augment existing drought products. It should be stressed that the presented approach is particularly well suited for agricultural drought applications commonly based on the detection of growing-season soil moisture anomalies at weekly to monthly time scales. The proposed methodology can also potentially add value to soil moisture products derived from current and future soil moisture satellite missions (i.e., SMOS (soil moisture and ocean salinity); SMAP (soil moisture active passive)) by optimally merging them with various independent soil moisture estimates.

[7] The general least squares solution is briefly reviewed in section 2. Section 3 reviews the triple collocation equations, section 4 introduces the input data, section 5 presents the results, and section 6 summarizes our conclusions.