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NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗

NASA NTRS2023

Time Series of Magnetic Field Parameters Extracted from Merged Space-Weather MDI/HMI Active Region Patches as Potential Tool for Solar Flare Forecasting

Space-Weather MDI Active Region Patches (SMARPs) and Space-Weather HMI Active Region Patches (SHARPs) are two recently developed data products, which have been used for solar flare prediction studies. The present work is an effort to expand the application of SMARP and SHARP summary heliomagnetic parameters to the forecasting of solar flares. A new data product was derived by filtering, rescaling, and merging the SMARP and SHARP summary parameter data series, which were further converted into two-dimensional arrays by selecting time slices corresponding to R-value maxima, where R-value is a measure of the unsigned magnetic flux near polarity inversion lines. The resulting combined MDI-HMI time series currently span the period between April 4, 1996 and December 13, 2022, and can be extended to a more recent date, providing an opportunity to correlate and compare them with other solar activity parameters, such as the daily solar flare index, which is computed as a sum of the product of GOES X-ray flare magnitude and flare duration, for all M- and X-class flares during a day. Preliminary results demonstrate a significant overall correlation, with Pearson coefficients between 0.339 and 0.627. In addition, an oscillating pattern is seen in the daily-averaged sliding-window correlation coefficient. Time-lagged cross-correlation indicates that a leader-follower dynamic exists in some parameters, especially R-value, where they lead the flare index by at least several days, which may have potential for further application in space weather forecasting.

Heliophysics↗

NASA NTRSDate not supplied

Examination of L-Band Brightness Temperature Forecasts in the SMAP Level-4 Soil Moisture Analysis

The NASA Soil Moisture Active Passive (SMAP) mission [4] has been providing L-band (1.4 GHz) passive microwave brightness temperature (Tb) observations since April 2015. By assimilating the Tb observations into the NASA Catchment land surface model [5] using a spatially distributed ensemble Kalman filter, the NASA Global Modeling and Assimilation Office generates the SMAP Level-4 Soil Moisture (L4_SM) product, which provides global, 3-hourly, 9-km resolution estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture with ~2.5-day latency for use in research and applications [6]. The L4_SM product also includes estimates of soil temperature, land surface fluxes, and assimilation diagnostics such as the model forecast and observed Tb values [7]. The output from the L4_SM system is routinely monitored by the L4_SM team. Such monitoring provides valuable information; instances of unusually large Tb observation-minus-forecast (O-F) residuals can indicate events during which soil moisture conditions are poorly described in the land modeling system [7,8]. For example, repeated occurrences of very large Tb O-F values in central Australia were traced back to deficiencies in the gauge-based precipitation product used in the land modeling system through L4_SM Version 5; this discovery prompted the use, beginning in Version 6, of satellite- and gauge-based precipitation observations outside of North America [9]. Recently, a statistical analysis of the Tb O-F residuals revealed systematic errors in the “tau-omega” L-band radiative transfer model that converts the land-model simulated soil moisture and temperature into the forecast Tb prior to the L4_SM analysis. The L4_SM analysis is built on the ensemble Kalman filter and assumes unbiased forecast errors. The presence of systematic Tb forecast errors could thus adversely impact the quality of the analyzed soil moisture. In this paper, we examine the Tb O-F residuals of the latest Version 7 L4_SM data (Science Version ID Vv7030 and Vv7032) [10,11,12]. In the L4_SM Version 7 algorithm, key parameters of the L-band radiative transfer model, including soil roughness, scattering albedo, and a (seasonally varying) climatology of vegetation opacity, are obtained from the SMAP Level-2 Radiometer retrieval product (Version 5) [1]. Additionally, we also use ground measurements of surface soil moisture and soil temperature from the SMAP core validation sites as in situ reference of soil conditions [2,3]. As part of the L4_SM system calibration, the seasonally-varying bias between the model forecast Tb and the observed values is removed prior to the assimilation of the SMAP Tb observations [7]. That is, the L4_SM system is designed to only correct errors in synoptic-scale and interannual variations from the long-term mean seasonal cycle while maintaining the model’s (potentially erroneous) climatology. The Tb O-F residuals examined here are thus computed using SMAP Tb observations after they are rescaled to the mean seasonal cycle of Tb from the modeling system without SMAP data assimilation. Consequently, the long-term average of the Tb O-F residuals has a global mean of only 0.13 K and locally small values, ranging from -1 to 3 K. Despite the small time-average values of the Tb O-F residuals, the model forecast Tb was nevertheless found to exhibit undesirable systematic errors. At some locations, the time-average Tb O-F values strongly depend on surface soil moisture (SM). At the Yanco SMAP core validation site, for example, the Tb O-F residuals typically range from 5 to 15 K under dry soil moisture conditions (SM < 0.15 m3 m-3) yet are predominantly negative under wet soil moisture conditions (SM > 0.25 m3 m-3), with values ranging from 0 to -40 K. This results in soil moisture analysis increments that persistently make the soil drier under dry SM conditions and persistently make the soil wetter under wet SM conditions, suggesting an error in the dynamic range of the simulated Tb, soil moisture or soil temperature. In this paper, we describe the higher-order systematic Tb forecast errors in more detail, examine their impact on the L4_SM product quality, and explore potential avenues to further improve the L4_SM algorithm.

Rolf Reichle↗

NASA NTRSDate not supplied

Insights into Long-Term Global Precipitation from IMERG and GPCP

Multiple satellite-based datasets provide estimates of the long-term record of global precipitation. Each necessarily includes both the real atmospheric behavior and a collection of artifacts driven by the input data sources and design choices in the retrievals and dataset construction. For this presentation, the Integrated Multi-satellitE Retrievals for GPM (IMERG) products from the Global Precipitation Measurement (GPM) mission’s U.S. Science Team are designed as a modern High-Resolution Precipitation Product (HRPP), while the Global Precipitation Climatology Project’s (GPCP) products are designed as a modern Climate Data Record (CDR). Although they share some common input data sources, the computational process for each is rather different. Comparing the precipitation estimates from each algorithm gives us insights into likely artifacts and the natural variations that are common to both. The goal of an HRPP is to give the best estimate of precipitation at each time step in the dataset, generally meaning that “all possible available” data are used. In contrast, the CDR is intended to provide a precipitation record that has relatively homogeneous statistics, necessary for climate analysis. Each analysis strives for both goals, of course, but this means that the HRPP uses the disparate collection of satellites whose statistics don’t quite match the ideal record, while the CDR is computed from fewer satellites that provide a relatively homogeneous set of precipitation statistics. This presentation employs the current versions of the IMERG and GPCP products, V07B and V3.2, respectively. A variety of analyses have demonstrated that IMERG has more artifacts, as expected, which tend to result from changes in the source of intercalibration for the various input satellites, namely the Combined Radar-Radiometer Algorithm using TMI and PR during the TRMM era and using GMI and DPR-Ku during the GPM era. As well, a shift occurs when the altitudes of the TRMM and GPM satellites change as a result of orbit boosts. For the most part the mean precipitation shows good continuity across these boundaries, but there are noticeable changes in the respective histograms. The latter has taken on more importance in recent years due to increased scrutiny on extremes which implicitly focus on the upper end of the precipitation histograms. The GPCP product is more homogeneous, with only one major change in calibrator, transitioning from the SSMI series of satellites to the SSMIS series of satellites in 2009. The GPCP analysis does a good job of minimizing artifacts in the means at this boundary, while the histograms show a smaller, but still noticeable shift in the histograms, a result that is similar to data boundaries in IMERG. The GPCP Daily, which is a month-by-month rescaling of the daily accumulated IMERG Final product, shows more consistency than the equivalent daily IMERG, but inherits the histogram shifts from IMERG. Given this overlay of artifacts, there is enough consistency between the products to illustrate some important long-term variations, including interannual variations, not all of which are easily attributable to ENSO events, and trends that are large regionally, but comparatively small when averaged across the globe.

precipitation↗

NASA NTRS2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

Solar energetic particles↗

NASA NTRS2023

Impact of Design Factors for ESA CCI Satellite Soil Moisture Data Assimilation over Europe

In this study, soil moisture retrievals of the combined active–passive ESA Climate Change Initiative (CCI) soil moisture product are assimilated into the Noah-MP land surface model over Europe using a one-dimensional ensemble Kalman filter and an 18-yr study period. The performance of the data assimilation (DA) system is evaluated by comparing it with a model-only experiment (at in situ sites) and by assessing statistics of innovations and increments as DA diagnostics (over the entire domain). For both assessments, we explore the impact of three design choices, resulting in the following insights. 1) The magnitude of the assumed observation errors strongly affects the skill improvements evaluated against in situ stations and internal diagnostics. 2) Choosing between climatological or monthly cumulative distribution function matching as the observation bias correction method only has a marginal effect on the in situ skill of the DA system. However, the internal diagnostics suggest a more robust system parameterization if the observations are rescaled monthly. 3) The choice of atmospheric reanalysis dataset to force the land surface model affects the model-only skill and the DA skill improvements. The model-only skill is higher with input from the MERRA-2 than with input from the ERA5 reanalysis, resulting in larger DA skill improvements for the latter. Additionally, we show that the added value of the DA strongly depends on the quality of the satellite retrievals and land cover, with the most substantial soil moisture skill improvements occurring over croplands and skill degradation occurring over densely forested areas.

Soil moisture↗