A methodology for merging multisensor precipitation estimates based on expectation‐maximization and scale‐recursive estimation

Abstract

[1] Scale-recursive estimation (SRE) is a Kalman-filter-based methodology, which can be used to produce optimal (in terms of bias and minimum variance) estimates of a field at any desired scale given uncertain and sparse observations at different scales. SRE requires the specification of the state equation, which describes the variability of the precipitation process across scales, and the observation equation, which relates the observations to the state. Typical models for describing the multiscale rainfall variability are the multiplicative cascade models. However, in order to convert them into the additive form needed by SRE, one needs to work in the log space, thus creating a problem in handling zero-intermittency in a satisfactory way. In this paper, we propose an alternative approach, based on a data-driven identification methodology, which operates directly on the data and does not require a prespecified multiscale model structure. Rather, system identification and estimation are performed simultaneously via a likelihood-based expectation-maximization (EM) procedure. The merits of the proposed approach versus approaches based on multiplicative cascade models are explored via several examples of synthetic and real precipitation fields. For practical application the proposed approach will need to be extended to include the temporal evolution of storms. This extension presents theoretical challenges, and until these are addressed, a simple alternative is explored of coupling the EM-SRE approach with a spatial downscaling methodology to merge precipitation observations available at different spatial and temporal scales. An example application is presented motivated by its relevance to the Global Precipitation Measuring (GPM) mission.Citation: Gupta, R., V. Venugopal, and E. Foufoula-Georgiou (2006), A methodology for merging multisensor precipitation estimates based on expectation-maximization and scale-recursive estimation,

Use of Scale Recursive Estimation for assimilation of precipitation data from TRMM (PR and TMI) and NEXRAD

“…In recent contributions (e.g. [64,80,34]) the issue of intermittence was bypassed using ad hoc approaches, either by neglecting the null values (e.g. by withholding of the relative nodes, suitable when negligible intermittence is seen) or by inserting ''small values'' of precipitation.…”

“…Tustison et al [80] presented a preliminary framework based on SRE for verification of quantitative precipitation forecast (henceforth, QPF), modeling rainfall as either a lognormal cascade (henceforth, LN) or a Bounded lognormal cascade (henceforth, BLN). Gupta et al [34] showed the use of Maximum Likelihood Estimation (henceforth, MLE), using an estimation maximization (henceforth, EM) approach (e.g. [40]) for system identification.…”

Evaluation of future hydrological cycle under climate change scenarios in a mesoscale Alpine watershed of Italy

“…Calibration of the model is carried out using the approach of Scale Recursive Estimation (SRE) coupled with maximum likelihood estimation, by the Expectation Maximization algorithm, EM (see e.g. Gupta et al, 2006).…”

Precipitation downscaling using random cascades: a case study in Italy

“…in Tustison et al, 2003). Gupta et al (2006), andBocchiola (2007) demonstrated that so doing better process noise estimates (i.e. σ 2 ws ), are obtained.…”

“…Groppelli (bibiana.groppelli@polimi.it) statistical downscaling via Stochastic Space Random Cascades (SSRC) (Tessier et al, 1993;Gupta, 1994, 1996;Langousis, 2005, 2009;Veneziano et al, 2006). A considerable effort has been recently devoted towards multi scale data assimilation schemes using scale recursive estimation SRE based upon the SSRC theory (Primus et al, 2001;Tustison et al, 2003;Bocchiola and Rosso, 2006;Gupta et al, 2006;Bocchiola, 2007).…”