A Space–Time Multiscale Analysis System: A Sequential Variational Analysis Approach

Abstract

As new observation systems are developed and deployed, new and presumably more precise information is becoming available for weather forecasting and climate monitoring. To take advantage of these new observations, it is desirable to have schemes to accurately retrieve the information before statistical analyses are performed so that statistical computation can be more effectively used where it is needed most. The authors propose a sequential variational approach that possesses advantages of both a standard statistical analysis [such as with a three-dimensional variational data assimilation (3DVAR) or Kalman filter] and a traditional objective analysis (such as the Barnes analysis). The sequential variational analysis is multiscale, inhomogeneous, anisotropic, and temporally consistent, as shown by an idealized test case and observational datasets in this study. The real data cases include applications in two-dimensional and three-dimensional space and time for storm outflow boundary detection (surface application) and hurricane data assimilation (three-dimensional space application). Implemented using a multigrid technique, this sequential variational approach is a very efficient data assimilation method.

Formulations for Estimating Spatial Variations of Analysis Error Variance to Improve Multiscale and Multistep Variational Data Assimilation

“…In this case, as explained for the one-dimensional case in Section 2.2, the error variance reduction produced by each observation can be considered as an additional reduction to the reduction produced by its neighboring observations. This additional reduction is smaller than the reduction produced by a single observation, so the error variance reduction produced by analyzing the coarse-resolution observations is bounded above by ∑ Δ 2 (x), which is similar to that for the onedimensional case in (4). For the same reason as explained for the one-dimensional case in (4), this implies that the domain-averaged value of ∑ Δ 2 (x) is larger than the true averaged reduction estimated by Δ 2 ≡ 2 − 2 , where 2 is the domain-averaged analysis error variance estimated by the spectral formulation for two-dimensional cases in Section 2.3 of Xu et al [8].…”

“…The equality in (4) is for the limiting case of Δ co / → ∞ only. The inequality in (4) implies that the domainaveraged value of ∑ Δ 2 ( ) is larger than the true averaged reduction estimated by Δ 2 ≡ 2 − 2 , where 2 is the domain-averaged analysis error variance estimated by the spectral formulation for one-dimensional cases in Section 2.2 of Xu et al [8].…”

“…This problem is common for the widely adopted singlestep approach in operational variational data assimilation, especially when patchy high-resolution observations, such as those remotely sensed from radars and satellites, are assimilated together with coarse-resolution observations into a high-resolution model. To solve this problem, multiscale and multistep approaches were explored and proposed by several authors (Xie et al [4], Gao et al [5], Li et al [6], and Xu et al [7,8]). For a two-step approach (or the first two steps of a multistep approach) in which broadly distributed coarse-resolution observations are analyzed first and then locally distributed high-resolution observations are analyzed in the second step, an important issue is how to objectively estimate or efficiently compute the analysis error covariance for the analyzed field that is obtained in the first step and used to update the background field in the second step.…”

Estimating High Resolution Daily Air Temperature Based on Remote Sensing Products and Climate Reanalysis Datasets over Glacierized Basins: A Case Study in the Langtang Valley, Nepal

“…Through fusing multi-source data from ground measurements, satellite observations and numerical model products, the CLDAS provides high-quality gridded hourly Ta, air pressure, humidity, wind speed, precipitation and surface shortwave radiation. The fusion of temperature, air pressure, humidity and wind speed is mainly achieved by the Space-Time Multiscale Analysis System (STMAS), which is an upgraded version of Local Analysis and Prediction System (LAPS) of the National Oceanic and Atmospheric Administration (NOAA) [50,51] using the multi-grid sequential variational method. Validation study of this product showed the bias and root mean square error (RMSE) of Ta are less than 1 K and 1.5 K, respectively, benchmarked with national automatic ground station observed air temperature in China [52].…”

Development of fine‐resolution analyses and expanded large‐scale forcing properties: 1. Methodology and evaluation

“…When data assimilation is applied to a fine-resolution model, small-scale structures are subjected to strong filtering effects [Daley, 1991]. A few studies have demonstrated that a set of data assimilation should be applied for a sequence of reduced decorrelation length scales [e.g., Xie et al, 2011;Zhang et al, 2011]. In the MS-DA algorithm, the cost function is decomposed for distinct spatial scales.…”