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NASA NTRS1991

The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow

The effect of an arbitrarily oriented mean passive scalar gradient on one-point passive scalar statistics is studied in homogeneous turbulent shear flow in the limit of rapid shearing. By neglecting the nonlinear inertial transfer to small scales an analytical solution for individual Fourier modes is obtained for the case of unity Prandtl number. This solution is used to compute the development of one-point statistics for the velocity and scalar fields in the inviscid limit. Comparisons to direct numerical simulations of the full nonlinear equations for the same flow show that, in addition to describing the early time response to the imposed shear, the linear solution gives reasonable estimates of several correlation coefficients for the developed shear flow.

Rogers, Michael M.↗
NASA NTRS1992

Modeling of the reactant conversion rate in a turbulent shear flow

Results are presented of direct numerical simulations (DNS) of spatially developing shear flows under the influence of infinitely fast chemical reactions of the type A + B yields Products. The simulation results are used to construct the compositional structure of the scalar field in a statistical manner. The results of this statistical analysis indicate that the use of a Beta density for the probability density function (PDF) of an appropriate Shvab-Zeldovich mixture fraction provides a very good estimate of the limiting bounds of the reactant conversion rate within the shear layer. This provides a strong justification for the implementation of this density in practical modeling of non-homogeneous turbulent reacting flows. However, the validity of the model cannot be generalized for predictions of higher order statistical quantities. A closed form analytical expression is presented for predicting the maximum rate of reactant conversion in non-homogeneous reacting turbulence.

Frankel, S. H.↗
NASA NTRS1992

Sensors and sensor systems for guidance and navigation II; Proceedings of the Meeting, Orlando, FL, Apr. 22, 23, 1992

Topics discussed in this volume include aircraft guidance and navigation, optics for visual guidance of aircraft, spacecraft and missile guidance and navigation, lidar and ladar systems, microdevices, gyroscopes, cockpit displays, and automotive displays. Papers are presented on optical processing for range and attitude determination, aircraft collision avoidance using a statistical decision theory, a scanning laser aircraft surveillance system for carrier flight operations, star sensor simulation for astroinertial guidance and navigation, autonomous millimeter-wave radar guidance systems, and a 1.32-micron long-range solid state imaging ladar. Attention is also given to a microfabricated magnetometer using Young's modulus changes in magnetoelastic materials, an integrated microgyroscope, a pulsed diode ring laser gyroscope, self-scanned polysilicon active-matrix liquid-crystal displays, the history and development of coated contrast enhancement filters for cockpit displays, and the effect of the display configuration on the attentional sampling performance.

Welch, Sharon S.↗
NASA NTRS1993

On the apparent insignificance of the randomness of flexible joints on large space truss dynamics

Deployable periodic large space structures have been shown to exhibit high dynamic sensitivity to period-breaking imperfections and uncertainties. These can be brought on by manufacturing or assembly errors, structural imperfections, as well as nonlinear and/or nonconservative joint behavior. In addition, the necessity of precise pointing and position capability can require the consideration of these usually negligible and unknown parametric uncertainties and their effect on the overall dynamic response of large space structures. This work describes the use of a new design approach for the global dynamic solution of beam-like periodic space structures possessing parametric uncertainties. Specifically, the effect of random flexible joints on the free vibrations of simply-supported periodic large space trusses is considered. The formulation is a hybrid approach in terms of an extended Timoshenko beam continuum model, Monte Carlo simulation scheme, and first-order perturbation methods. The mean and mean-square response statistics for a variety of free random vibration problems are derived for various input random joint stiffness probability distributions. The results of this effort show that, although joint flexibility has a substantial effect on the modal dynamic response of periodic large space trusses, the effect of any reasonable uncertainty or randomness associated with these joint flexibilities is insignificant.

Koch, R. M.↗
NASA NTRS1993

Parallel runway requirement analysis study. Volume 2: Simulation manual

This document is a user manual for operating the PLAND_BLUNDER (PLB) simulation program. This simulation is based on two aircraft approaching parallel runways independently and using parallel Instrument Landing System (ILS) equipment during Instrument Meteorological Conditions (IMC). If an aircraft should deviate from its assigned localizer course toward the opposite runway, this constitutes a blunder which could endanger the aircraft on the adjacent path. The worst case scenario would be if the blundering aircraft were unable to recover and continue toward the adjacent runway. PLAND_BLUNDER is a Monte Carlo-type simulation which employs the events and aircraft positioning during such a blunder situation. The model simulates two aircraft performing parallel ILS approaches using Instrument Flight Rules (IFR) or visual procedures. PLB uses a simple movement model and control law in three dimensions (X, Y, Z). The parameters of the simulation inputs and outputs are defined in this document along with a sample of the statistical analysis. This document is the second volume of a two volume set. Volume 1 is a description of the application of the PLB to the analysis of close parallel runway operations.

Ebrahimi, Yaghoob S.↗
NASA NTRS1994

Radiative interactions in chemically reacting compressible nozzle flows using Monte Carlo simulations

The two-dimensional spatially elliptic Navier-Stokes equations have been used to investigate the radiative interactions in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The radiative heat transfer term in the energy equation is simulated using the Monte Carlo method (MCM). The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The spectral correlation has been considered in the Monte Carlo formulations. Results obtained demonstrate that the effect of radiation on the flow field is minimal but its effect on the wall heat transfer is significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and the nozzle size on the radiative and conductive wall fluxes.

Liu, J.↗
NASA NTRS1994

Statistics of pressure and pressure gradient in homogeneous isotropic turbulence

The statistics of pressure and pressure gradient in stationary isotropic turbulence are measured within direct numerical simulations at low to moderate Reynolds numbers. It is found that the one-point pdf of the pressure is highly skewed and that the pdf of the pressure gradient is of stretched exponential form. The power spectrum of the pressure P(k) is found to be larger than the corresponding spectrum P(sub G)(k) computed from a Gaussian velocity field having the same energy spectrum as that of the DNS field. The ratio P(k)/P(sub G)(k), a measure of the pressure-field intermittence, grows with wavenumber and Reynolds number as -R(sub lambda)(exp 1/2)log(k/k(sub d)) for k less than k(sub d)/2 where k(sub d) is the Kolmogorov wavenumber. The Lagrangian correlations of pressure gradient and velocity are compared and the Lagrangian time scale of the pressure gradient is observed to be much shorter than that of the velocity.

Gotoh, T.↗
NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗
NASA NTRS1997

Evolution of Structure in the Intergalactic Medium and the Nature of the LY-Alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.

Bi, Hongguang↗
NASA NTRS2001

Galaxy Cluster Gas Mass Fractions From Sunyaev-Zeldovich Effect Measurements: Constraints on Omega(M)

Using sensitive centimeter-wave receivers mounted on the Owens Valley Radio Observatory and Berkeley-Illinois-Maryland-Association millimeter arrays, we have obtained interferometric measurements of the Sunyaev-Zeldovich(SZ) effect toward massive galaxy clusters. We use the SZ data to determine the pressure distribution of the cluster gas and, in combination with published X-ray temperatures, to infer the gas mass and total gravitational mass of 18 clusters. The gas mass fraction, f(g), is calculated for each cluster and is extrapolated to the fiducial radius r(500) using the results of numerical simulations. The mean f(g) within r(500) is 0.081(+ 0.009 / - 0.011) per h(100) (statistical uncertainty at 68% confidence level, assuming Omega(M) = 0.3, Omega(Lambda) = 0.7). We discuss possible sources of systematic errors in the mean f(sub g) measurement. We derive an upper limit for Omega(M) from this sample under the assumption that the mass composition of clusters within r(500) reflects the universal mass composition: Omega(M)h is less than or equal to Omega(B)/f(g). The gas mass fractions depend on cosmology through the angular diameter distance and the r(500) correction factors. For a flat universe (Omega(Lambda) is identical with 1 - Omega(M)) and h = 0.7, we find the measured gas mass fractions are consistent with Omega(M) is less than 0.40, at 68% confidence. Including estimates of the baryons contained in galaxies and the baryons which failed to become bound during the cluster formation process, we find Omega(M) is approximately equal to 0.25.

Grego, Laura↗
NASA NTRS2001

Cloud and Radiation Studies during SAFARI 2000

Though the emphasis of the Southern Africa Regional Science Initiative 2000 (SAFARI-2000) dry season campaign was largely on emission sources and transport, the assemblage of aircraft (including the high altitude NASA ER-2 remote sensing platform and the University of Washington CV-580, UK MRF C130, and South African Weather Bureau JRA in situ aircrafts) provided a unique opportunity for cloud studies. Therefore, as part of the SAFARI initiative, investigations were undertaken to assess regional aerosol-cloud interactions and cloud remote sensing algorithms. In particular, the latter part of the experiment concentrated on marine boundary layer stratocumulus clouds off the southwest coast of Africa. Associated with cold water upwelling along the Benguela current, the Namibian stratocumulus regime has received limited attention but appears to be unique for several reasons. During the dry season, outflow of continental fires and industrial pollution over this area can be extreme. From below, upwelling provides a rich nutrient source for phytoplankton (a source of atmospheric sulphur through DMS production as well as from decay processes). The impact of these natural and anthropogenic sources on the microphysical and optical properties of the stratocumulus is unknown. Continental and Indian Ocean cloud systems of opportunity were also studied during the campaign. Aircraft flights were coordinated with NASA Terra Satellite overpasses for synergy with the Moderate Resolution Imaging Spectroradiometer (MODIS) and other Terra instruments. An operational MODIS algorithm for the retrieval of cloud optical and physical properties (including optical thickness, effective particle radius, and water path) has been developed. Pixel-level MODIS retrievals (11 km spatial resolution at nadir) and gridded statistics of clouds in th SAFARI region will be presented. In addition, the MODIS Airborne Simulator flown on the ER-2 provided high spatial resolution retrievals (50 m at nadir). These retrievals will be discussed and compared with in situ observations.

Platnick, Steven↗
NASA NTRS2002

Number Partitioning via Quantum Adiabatic Computation

We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.

Smelyanskiy, Vadim N.↗
NASA NTRS2003

Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (D(sub A)) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X-ray and/or SZ (Sunyaev-Ze'dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg(sup 2) SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Omega(sub m), can be determined within about 25%, Omega(sub lambda) within 20% and w within 16%. We show that combined dN/dz+(sub lambda) constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in D(sub lambda). We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz+ D(lambda) constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut-offs in the range 0.55 approx. less than 1. Subject headings: cosmological parameters - cosmology: theory - galaxies:clusters: general

Molnar, Sandor M.↗
NASA NTRS2007

Measurement and Simulation of the Variation in Proton-Induced Energy Deposition in Large Silicon Diode Arrays

The proton induced charge deposition in a well characterized silicon P-i-N focal plane array is analyzed with Monte Carlo based simulations. These simulations include all physical processes, together with pile up, to accurately describe the experimental data. Simulation results reveal important high energy events not easily detected through experiment due to low statistics. The effects of each physical mechanism on the device response is shown for a single proton energy as well as a full proton space flux.

Howe, Christina L.↗
NASA NTRS2009

The Transition of High-Resolution NASA MODIS Sea Surface Temperatures into the WRF Environmental Modeling System

The NASA Short-term Prediction Research and Transition (SPoRT) Center has developed a Moderate Resolution Imaging Spectroradiometer (MODIS) sea surface temperature (SST) composite at 2-km resolution that has been implemented in version 3 of the National Weather Service (NWS) Weather Research and Forecasting (WRF) Environmental Modeling System (EMS). The WRF EMS is a complete, full physics numerical weather prediction package that incorporates dynamical cores from both the Advanced Research WRF (ARW) and the Non-hydrostatic Mesoscale Model (NMM). The installation, configuration, and execution of either the ARW or NMM models is greatly simplified by the WRF EMS to encourage its use by NWS Weather Forecast Offices (WFOs) and the university community. The WRF EMS is easy to run on most Linux workstations and clusters without the need for compilers. Version 3 of the WRF EMS contains the most recent public release of the WRF-NMM and ARW modeling system (version 3 of the ARW is described in Skamarock et al. 2008), the WRF Pre-processing System (WPS) utilities, and the WRF Post-Processing program. The system is developed and maintained by the NWS National Science Operations Officer Science and Training Resource Coordinator. To initialize the WRF EMS with high-resolution MODIS SSTs, SPoRT developed the composite product consisting of MODIS SSTs over oceans and large lakes with the NCEP Real-Time Global (RTG) filling data over land points. Filling the land points is required due to minor inconsistencies between the WRF land-sea mask and that used to generate the MODIS SST composites. This methodology ensures a continuous field that adequately initializes all appropriate arrays in WRF. MODIS composites covering the Gulf of Mexico, western Atlantic Ocean and the Caribbean are generated daily at 0400, 0700, 1600, and 1900 UTC corresponding to overpass times of the NASA Aqua and Terra polar orbiting satellites. The MODIS SST product is output in gridded binary-1 (GRIB-1) data format for a seamless incorporation into WRF via the WPS utilities. The full-resolution, 1-km MODIS product is sub-sampled to 2-km grid spacing due to limitations in handling very large dimensions in the GRIB-1 data format. The GRIB-1 files are posted online at ftp://ftp.nsstc.org/sstcomp/WRF/, which is directly accessed by the WRF EMS scripts. The MODIS SST composites are also downloaded to the EMS data server, which is accessible by the WRF EMS users and NWS WFOs. The SPoRT MODIS SST composite provides the model with superior detail of the ocean gradients around Florida and surrounding waters, whereas the operational RTG SST typically depicts a relatively smooth field and is not able to capture sharp horizontal gradients in SST. Differences of 2-3 C are common over small horizontal distances, leading to enhanced SST gradients on either side of the Gulf Stream and along the edges of the cooler shelf waters. These sharper gradients can in turn produce atmospheric responses in simulated temperature and wind fields as depicted in LaCasse et al. Differences in atmospheric verification statistics over a several month study were generally small in the vicinity of south Florida; however, the validation of SSTs at specific buoy locations revealed important improvements in the biases and RMS errors, especially in the vicinity of the cooler shelf waters off the east-central Florida coast. A current weakness in the MODIS SST product is the occurrence of occasional discontinuities caused by high latency in SST coverage due to persistent cloud cover. An enhanced method developed by Jedlovec et al. (2009, GHRSST User Symposium) reduces the occurrence of these problems by adding Advanced Microwave Scanning Radiometer -- EOS (AMSR-E) SST data to the compositing process. Enhanced SST composites are produced over the ocean regions surrounding the Continental U.S. at four times each day corresponding to Terra and Aqua equator crossing times. For a given day and overpass time, both MODInd AMSR-E data from the previous seven days form a collection used in the compositing. At each MODIS pixel, cloud-free SST values from the collection are used to form a weighted average based on their latency (number of days from the current day). In this way, recent SST data are given more weight than older data. One of the primary issues involved in incorporating the AMSR-E microwave data in the composites is the tradeoff between the decreased spatial resolution of the AMSR-E data (25 km) and the increased coverage due to its near all-weather capability. Currently, the AMSR-E is given a weight of 20% compared to MODIS data, thereby preserving the spatial structure observed in the MODIS data. Day-time (night-time) AMSR-E SST data from Aqua are used with both Terra and Aqua MODIS day-time (night-time) SST data sets.

Case, Jonathan L.↗
NASA NTRS2011

Widespread Nanoflare Variability Detected with Hinode/XRT in a Solar Active Region

It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun s hot corona, but whether they are the explanation for most of the multi-million degree plasma has been a matter of ongoing debate. We here present evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on-board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multi-pixel subregions, or the entire active region. Negative fluctuations (corresponding to reduced intensity) are greater in number but weaker in amplitude, so that the median fluctuation is negative compared to a mean of zero. Using Monte Carlo simulations, we show that only part of this asymmetry can be explained by Poisson photon statistics. The remainder is explainable with a tendency for exponentially decreasing intensity, such as would be expected from a cooling plasma produced, e.g., from a nanoflare. We suggest that nanoflares are a universal heating process within active regions.

Reale, Fabio↗
NASA NTRS2012

Analysis of Fine-Mode Aerosol Retrieval Capabilities by Different Passive Remote Sensing Instrument Designs

Remote sensing of aerosol optical properties is difficult, but multi-angle, multi-spectral, polarimetric instruments have the potential to retrieve sufficient information about aerosols that they can be used to improve global climate models. However, the complexity of these instruments means that it is difficult to intuitively understand the relationship between instrument design and retrieval success. We apply a Bayesian statistical technique that relates instrument characteristics to the information contained in an observation. Using realistic simulations of fine size mode dominated spherical aerosols, we investigate three instrument designs. Two of these represent instruments currently in orbit: the Multiangle Imaging SpectroRadiometer (MISR) and the POLarization and Directionality of the Earths Reflectances (POLDER). The third is the Aerosol Polarimetry Sensor (APS), which failed to reach orbit during recent launch, but represents a viable design for future instruments. The results show fundamental differences between the three, and offer suggestions for future instrument design and the optimal retrieval strategy for current instruments. Generally, our results agree with previous validation efforts of POLDER and airborne prototypes of APS, but show that the MISR aerosol optical thickness uncertainty characterization is possibly underestimated.

Knobelspiesse, Kirk↗
NASA NTRS2016

Assimilation of Gridded Terrestrial Water Storage Observations from GRACE into a Land Surface Model

Observations of terrestrial water storage (TWS) from the Gravity Recovery and Climate Experiment (GRACE) satellite mission have a coarse resolution in time (monthly) and space (roughly 150,000 km(sup 2) at midlatitudes) and vertically integrate all water storage components over land, including soil moisture and groundwater. Data assimilation can be used to horizontally downscale and vertically partition GRACE-TWS observations. This work proposes a variant of existing ensemble-based GRACE-TWS data assimilation schemes. The new algorithm differs in how the analysis increments are computed and applied. Existing schemes correlate the uncertainty in the modeled monthly TWS estimates with errors in the soil moisture profile state variables at a single instant in the month and then apply the increment either at the end of the month or gradually throughout the month. The proposed new scheme first computes increments for each day of the month and then applies the average of those increments at the beginning of the month. The new scheme therefore better reflects submonthly variations in TWS errors. The new and existing schemes are investigated here using gridded GRACE-TWS observations. The assimilation results are validated at the monthly time scale, using in situ measurements of groundwater depth and soil moisture across the U.S. The new assimilation scheme yields improved (although not in a statistically significant sense) skill metrics for groundwater compared to the open-loop (no assimilation) simulations and compared to the existing assimilation schemes. A smaller impact is seen for surface and root-zone soil moisture, which have a shorter memory and receive smaller increments from TWS assimilation than groundwater. These results motivate future efforts to combine GRACE-TWS observations with observations that are more sensitive to surface soil moisture, such as L-band brightness temperature observations from Soil Moisture Ocean Salinity (SMOS) or Soil Moisture Active Passive (SMAP). Finally, we demonstrate that the scaling parameters that are applied to the GRACE observations prior to assimilation should be consistent with the land surface model that is used within the assimilation system.

GRACE↗