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  • Errico, R. M., and et al. , 2017: Description of the GMAO OSSE for weather analysis software package: Version 3. NASA Tech. Memo. NASA/TM-2017-104606, Vol. 48, 156 pp., https://gmao.gsfc.nasa.gov/pubs/docs/Errico987.pdf.

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  • View in gallery

    Numbers of locations of assimilated real observations within half-hourly temporal bins centered at the indicated times (UTC) during 1 Jul 2015 produced from IR images provided by (a) Himawari-7, (b) Meteosat-7, and (c) GOES-15, and by (d) MODIS on polar orbiters.

  • View in gallery

    As in Fig. 1, but for observations simulated from the corresponding NR date for 2006.

  • View in gallery

    Himawari-7 observation locations (red dots) created for the NR time of 2230 UTC 30 Jun 2006 at levels 100 < p < 300 hPa superimposed on the field of high-level cloud fractions at that same time (blue for 0% to white for 100%).

  • View in gallery

    Locations of real MODIS AMVs assimilated within the 6-h period centered on 0000 UTC 1 Jul 2015. Colors indicate observation times at hours −1.17 (dark blue), −0.78 (blue), −0.35 (light blue), 0.47 (green), and 1.62 (red) with respect to the central time.

  • View in gallery

    As in Fig. 4, but for observations simulated for the hours −1.5 (dark blue), −1. (blue), −0.5 (light blue), 0. (green), and 1.5 (red) with respect to the NR time of 0000 UTC 1 Jul 2006.

  • View in gallery

    Locations of real AMVs assimilated within the 6-h period centered on 0000 UTC 1 Jul 2015 obtained from (a) Himawari-7 VIS/IR, (b) Meteosat VIS/IR, (c) GOES IR, and (d) GOES WV images.

  • View in gallery

    As in Fig. 6, but for observations simulated from the corresponding NR date for 2006.

  • View in gallery

    Spacing of assimilated real AMVs obtained from images provided by (a) Himawari-7 VIS/IR views near Australia, (b) Meteosat-10 VIS/IR and (c) GEOS-13 IR over portions of Brazil and the South Atlantic, and (d) MODIS IR over the Arctic. These are for observations specified within the 30-min periods centered on 0000 UTC 1 Jul 2015 and 2230, 2230, and 2300 UTC 30 Jun 2015, respectively. Latitudes and longitudes are displayed for each panel.

  • View in gallery

    As in Fig. 8, but for observations simulated from the corresponding NR date for 2006.

  • View in gallery

    Histograms of numbers of cloud fraction values falling within each of 21 bins, presented as fractions of the total number of locations considered over water or ice for (a) GOES-15 in the band 0°–30°N and (b) MODIS north of 60°N for three separate pressure ranges: 143–286 (solid), 429–572 (dashed), and 856–1000 hPa (dotted).

  • View in gallery

    Histograms of numbers of values of swΔw falling within 21 bins, presented as fractions of the total number of locations considered over water in the band 30°S–0° for (a) Himawari-7 and (b) Meteosat-10 for the two separate pressure ranges: 143–286 (solid) and 286–429 hPa (dashed).

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Simulation of Atmospheric Motion Vectors for an Observing System Simulation Experiment

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  • 1 Goddard Earth Sciences Technology and Research Center, Morgan State University, Baltimore, and National Aeronautics and Space Administration Global Modeling and Assimilation Office, Greenbelt, Maryland
  • | 2 Goddard Earth Sciences Technology and Research Center, Universities Space Research Association, Columbia, and National Aeronautics and Space Administration Global Modeling and Assimilation Office, Greenbelt, Maryland
  • | 3 Goddard Earth Sciences Technology and Research Center, Morgan State University, Baltimore, and National Aeronautics and Space Administration Global Modeling and Assimilation Office, Greenbelt, Maryland
  • | 4 Science Systems and Applications, Inc., Lanham, and National Aeronautics and Space Administration Global Modeling and Assimilation Office, Greenbelt, Maryland
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Abstract

An algorithm to simulate locations of atmospheric motion vectors for use in observing system simulation experiments is described and demonstrated. It is intended to obviate likely deficiencies in nature run data if used to produce images for feature tracking. The algorithm employs probabilistic functions that are tuned based on distributions of real observations and histograms of nature run fields. For distinct observation types, the algorithm produces geographical and vertical distributions, time-mean counts, and typical spacings of simulated locations that are, at least qualitatively, similar to those of real observations and are associated with nature run cloud and water vapor fields. It thus appears suitable for generating realistic atmospheric motion vectors for use in observing system simulation experiments.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ronald M. Errico, rmerrico@verizon.net

Abstract

An algorithm to simulate locations of atmospheric motion vectors for use in observing system simulation experiments is described and demonstrated. It is intended to obviate likely deficiencies in nature run data if used to produce images for feature tracking. The algorithm employs probabilistic functions that are tuned based on distributions of real observations and histograms of nature run fields. For distinct observation types, the algorithm produces geographical and vertical distributions, time-mean counts, and typical spacings of simulated locations that are, at least qualitatively, similar to those of real observations and are associated with nature run cloud and water vapor fields. It thus appears suitable for generating realistic atmospheric motion vectors for use in observing system simulation experiments.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ronald M. Errico, rmerrico@verizon.net

1. Introduction

Atmospheric observing system simulation experiments (OSSEs) are conducted to estimate how analysis and forecast systems will respond to either new observation types or new data assimilation algorithms (Errico and Privé 2018). They generally use a data assimilation system (DAS) to ingest simulated observations with a forecast system subsequently used to evaluate their impacts. These observations are drawn from a simulation of nature, termed a “nature run” (NR). The latter is generally produced as a long-term run of a high-resolution numerical weather prediction or climate model (e.g., Putman et al. 2014). Simulated errors are added to these observations to render them imperfect, like real observations. As simulations, OSSEs are not confined to using real observations and they provide a defined truth (i.e., the NR) so that accuracy can be measured without employing often unwarranted assumptions.

Currently available or planned NRs do not describe the atmosphere with sufficient realism to directly simulate how some types of real observations are produced. Among those problem types are atmospheric motion vectors (AMVs) that are determined from examining sequences of high-resolution images of clouds or water vapor structures (Velden et al. 2005). Temporal availability of NR datasets, the effective spatial resolution of their fields (given the many kinds of smoothing employed in the NR models) and the structures of their cloud fields typically have insufficient realism to apply current image processing algorithms without substantial modification [e.g., see Lean et al. (2015) for an example that uses a model greatly exceeding the resolution of present global NRs yet still obtains only 50% of a real count of AMVs].

Fortunately, unless the intent is to specifically examine the algorithms employed in producing AMVs from images, it is unnecessary that the NR cloud and water vapor fields serve as realistic images. In particular, for creating realistic impacts of AMV observations in an OSSE context it is sufficient that a limited set of critical characteristics of such observations be simulated (Errico and Privé 2018). These include distributions (temporal counts and spatial densities) of geographic and vertical locations, and relationships between those locations and some atmospheric weather aspects. The latter include considerations that identifiable clouds or discernible water vapor gradients primarily occur where significant “weather” may be happening.

An algorithm that met many of the above requirements for simulating AMVs from an NR was developed at NASA’s Global Modeling and Assimilation Office (GMAO; Errico et al. 2017). It used NR cloud fraction and integrated precipitable water vapor (IPW) fields to define probabilities of AMV observations occurring at subsets of NR grid points. Parameters defining the probability functions were determined by a manual, sometimes painstaking, trial-and-error method with varying degrees of success. The new algorithm reported here replaces that one. It is almost entirely automated and more faithfully simulates most characteristics of present AMV observation distributions.

2. Goal of algorithm

When observations are simulated for an OSSE, there are no real instruments and only available are the NR fields. It is not the actual instruments, but rather the observations produced by them, that need to be simulated. This requires consideration of instrument characteristics that determine observation locations and qualities, but also of characteristics of observation error due to imperfections of either the instruments or DAS forward operators. The critical issue is whether the simulated datasets realistically incorporate such important characteristics of the real observations, but the means by which those characteristics are introduced by a simulation algorithm is less important: just as a real analysis only sees the observations provided, not the instruments themselves, an OSSE analysis only sees the simulated observations provided, not the algorithms that create them.

The last consideration particularly applies to AMVs, since the observations provided are wind vectors rather than the images used to create them. For this reason, the algorithm described here for simulating AMVs from an NR is designed to produce AMV datasets with the required properties rather than to create simulated satellite images that can be ingested by image processing algorithms currently employed by satellite data processing centers. In particular, the algorithm is designed to create simulated AMV observations with realistic counts, locations, and separation distances. These are characteristics that are expected to strongly affect observation impacts on analyses, particularly as the data assimilation performs spatial averaging of observation innovations based on assumed background error correlations. The simulation algorithm also considers NR cloud and IPW fields since real locations depend on such fields. It does not attempt to produce realistic observation errors, however, since in the OSSE framework developed at NASA’s GMAO, such errors are added to the simulated observations in a subsequent step as described in Errico et al. (2013) and more completely in Errico et al. (2017).

Specifically, the simulation algorithm described here is intended to produce simulated data locations that closely match characteristics of only the subset of real data actually used by the intended DAS, that is, excluding data rejected by quality-control and data thinning employed by that system. Otherwise the required task becomes complicated by the need to simulate gross, non-Gaussian observation errors and additional observations with additional information required by the observation thinning algorithms, such as data quality indicators. Yet much of this additional effort will only result in data that will be discarded by the DAS employed. Of course, by including these additional observations it may be possible to also apply them to a data assimilation with different quality-control and thinning procedures, but this is not certain until such a specific system is identified and tested. Extension of our algorithm for such more general use is therefore deferred until a later date.

One set of characteristics that we attempt to closely match especially concern mean observation counts. This does not refer simply to time-mean global counts over assimilation periods, but counts within specified latitude bands, pressure layers, time intervals within assimilation periods, and surface types (over land vs otherwise). It also includes some characteristics of the intermittency of some observation types, for example, the apparent intermittent absence of some observation types within some time intervals within different assimilation periods or temporal variations of the longitudinal extents of AMV observations produced from images by polar orbiters. These absences can occur for a variety of reasons, including instrument viewing geometry, communication delays between data providers and users, and image processing priorities. If data are absent frequently enough, the average counts of observations, and therefore their average impacts, will be affected. Examples of some of these characteristics of real AMVs are provided in section 4.

The algorithm is also intended to be sufficiently flexible to automatically adjust to account for some degree of unrealism in the NR fields or climatology. So if the IPW fields in the NR are too smooth or the mean cloud cover is too great or too small at particular pressure levels, the algorithm should be sufficiently malleable to create AMV distributions that are nonetheless realistic. Some reported OSSEs accomplish this by very simply defining AMV locations specifically where real observations were assimilated at a corresponding real time, but this will denote some locations where there clearly would be no trackable features in the NR, such as in the middle of a clear-sky high pressure layer, and will miss some locations where there should be such NR features, such as near tropical storms. This lack of correspondence is due to the chaotic nature of weather: although a good long-term NR model will produce states having realistic atmospheric statistics, it is extremely unlikely that over a long period it will generate a sequence of global weather that is identical to any such sequence seen in reality.

For demonstration of the AMV simulation algorithm here, it is applied to the NASA GMAO OSSE for Weather Analysis Software Package, version 3 (GOWASP-3; Errico et al. 2017). This version currently considers all AMV types that were assimilated operationally at the GMAO during the summer of 2015. These include observations from visible (VIS), infrared (IR), and water vapor (WV) imagers on the geostationary satellites Himawari-7 (and later Himawari-8), GOES-13, GOES-15, Meteosat-7, and Meteosat-10. It also includes those from IR images provided by AVHRR instruments on NOAA and MetOp polar orbiters and IR and WV images provided by MODIS instruments on NASA’s Terra and Aqua polar orbiters.

The NR from which observations are drawn is that produced at the GMAO in 2014 described by Putman et al. (2014). It has a horizontal grid spacing of approximately 7 km, with a vertical grid of 72 levels in addition to the surface. Only half of those levels are in the troposphere. Output is every half hour with a duration of 2 years starting in May 2005. The only connections to real dates, however, are the dates of real sea surface temperature and sea ice data used as prescribed boundary conditions. Since these boundary conditions are insufficient to totally constrain the model’s chaotic atmospheric dynamics, after a short initial period its sequence of weather differs from the sequence of real weather for those same dates. The OSSE simulation dates are, nonetheless, prescribed as those of the NR. So, although the samples of simulated results presented in later sections are described as for 2006, these may be compared with real data results for any year.

The GMAO NR has insufficient resolution to create simulated cloud and water vapor images with enough detail to perform realistic feature tracking without major modifications to either those images or tracking algorithms. Both temporal and spatial resolutions cause difficulties. Other earlier, present, or planned NRs have worse or similar deficiencies. The presented algorithm therefore intentionally circumvents simulating images and feature tracking by instead attempting to directly simulate only the results of such procedures, that is, sets of simulated AMV locations that appear realistic.

3. Simulation algorithm

The simulation algorithm is applied in three steps. The first step determines “target” counts as functions of space and time based on real observations that the simulation is to mimic. The second step determines parameters for probability functions that will be used to determine whether simulated observations are present at each location based on values of some NR fields. The last step applies those functions along with other criteria to create datasets of simulated observations.

The algorithm itself has several features that must be considered or specified. For each AMV type, this includes the consideration of the times and regions observed, the typical spatial separations between observations, the choice of an NR field used to compute a probability that an observation can be discerned, the selection of a probability function, and the specification of the function’s parameters. Each of these considerations is described in a distinct subsection within this section.

a. Consideration of times and regions

Locations of AMV observations of each type vary in space and time not simply because cloud or water vapor features do but also because viewing locations vary for polar orbiters or processing algorithms and scanning procedures vary for geostationary satellites. The frequencies of observations ingested by the GMAO DAS, for example, vary from an average of 16 times per day for Meteosat and Himawari-7 to more than 48 times per day for GOES. For Meteosat, clouds within a 60° viewing angle from nadir in any direction are considered, but for Himawari the acceptable viewing angles vary with direction. Furthermore, for Himawari, there are few observations for pressure p > 700 hPa provided over land (Otsuka et al. 2015), and for GOES, some regions in the Southern Hemisphere are omitted entirely during some observation periods (Velden et al. 2005). For some analysis periods, an observation type may be missing entirely due to processing problems or communication delays. Some examples of such intermittent behaviors are presented in section 4.

Given the variability of viewing locations and image processing algorithms employed for different AMV types, and to keep the simulation algorithm realistic but also simple and flexible (e.g., to automatically adjust to changes in viewing or processing characteristics), the AMV simulator relies on a combination of some geometry and the consideration of distributions of corresponding real observations. The geometric conditions are that observations from geostationary satellites are confined to 60° from nadir. The latitudinal extents of each type of real observation are determined and used to further restrict the corresponding simulated locations. The longitudinal extents, independent of latitude, are also determined and utilized.

Two sets of counts are determined for each AMV type. These differ in their purposes and spatial subdivisions. One set (S1) is only intended to obtain a realistic presence or absence of simulated observation at each time and longitude range considered. The second set (S2) is used to define the desired counts of observations that will be used to tune probability functions that will be employed to determine where simulations will occur. When computing either of these sets, only those real AMVs actually used by the DAS are considered, that is, only those accepted by the DAS quality-control and thinning procedures. For both sets, distinct counts are determined for AMVs obtained from distinct image-processing algorithms, imaging instruments, or satellite platforms. Hereafter, each such distinction is called an AMV “type.” Note, however, that the present algorithm considers all AMVs derived from the MODIS viewing instrument as composing a single AMV type, irrespective of its polar-orbiting satellite platform.

For S1, real observations are counted for distinct AMV types falling in distinct time periods, longitude sectors, and, separately, Northern and Southern Hemispheres (this latter distinction is particularly relevant for the polar orbiters). A region may be unpopulated because either a satellite did not view there or no trackable features were in images there. In the latter case, however, it is appropriate to allow simulated observations to be present since the NR weather may warrant such features. A region is therefore reconsidered as populated if both longitudinally adjacent sectors at that time are populated by real observations; that is, small viewing gaps are treated as populated. Observations are only simulated for those sectors and time periods that are labeled as populated by this procedure.

For S1 in the example presented in the next section, the distinct time periods considered are each 30 min long. These begin at times of consecutively archived, half-hourly, GEOS-5 NR datasets. For AMVs determined from polar orbiters or geostationary satellites, the widths of the distinct longitudinal sectors are 10° and 3.33°, respectively. The former is sufficient to characterize temporal variations of the polar orbit views and the latter captures some of the apparent viewing or processing limitations associated with some geostationary satellites. The set S1 are determined over a 14-day period for each season. Results for the same 14 days are applied over an entire 3-month season by considering that the 14-day sequence repeats itself periodically.

The set S2 is used to determine the desired mean counts of observations per analysis period (e.g., 6 h in GEOS-5), where the averaging is performed over many such periods (e.g., the same total period over which S1 is determined). This mean is called the “target” count. For each AMV type, the distinct regions considered are defined by an observation pressure range, latitude band, and views above land versus otherwise. As applied here, there are seven equally spaced pressure ranges between 0 and 1000 hPa and six equally spaced latitude bands covering pole to pole. Views for some AMV types never occur in some of these regions (e.g., there are no MODIS AMVs in the latitude bands between 60°S and 60°N and no AMVs from geostationary satellites poleward of 60°S/N).

b. Spacing of simulated observations

In addition to resolution of the viewing instrument and image-processing algorithm, DAS data thinning and quality control determine the typical horizontal separation distances Δx of nearby observations actually analyzed. These especially vary with AMV type. Also, for some types, the patterns of real assimilated observation locations appear to lie on some kind of regular grid (e.g., only along particular meridians or parallels) while for other types, the locations appear more random. Such patterns can occur due to either image processing algorithms or DAS observation thinning. It is critical that not only observation counts but also typical separation distances be well simulated, since the latter will affect considerations of correlations of observation innovations within a DAS. For realism, it is also desirable that regularity or irregularity of observation locations be simulated, although the importance of this is not as obvious.

c. Choosing fields to determine observing probabilities

For the AMV simulation algorithm here, whether or not a simulated observation is specified to exist at a particular location is properly determined by several criteria. Some are deterministic: a location must be in a viewed location at a given time (as indicated by S1) for a given AMV type, and, for a type that is based solely on visible images, a location must have a solar zenith angle that is sufficiently large that solar reflection would be viewable. Additionally, once the pressure levels of the possible observations are determined, as will be explained later in this section, the wind speeds must be greater than a minimum value of 3 m s−1 and the level must not be obscured by clouds above. The other criteria are probabilistic, based on tuned probability functions of fields derived from NR data that are selected according to the type of AMV observation and adjusted to yield desired mean counts of observations. The use of such functions creates the appearance of both order and randomness in the simulated locations, as seen for real observations.

If the observations are designed to be on a regular grid, then only grid points along particular parallels and meridians are considered. If instead the observations appear more randomly distributed, then the locations considered are the desired distance apart, but the starting longitudes or latitudes defining sequences of those locations are defined randomly. So, in general, sets of grid points with latitudinal or meridional indexes in = i0 + nΔi are specified, where i0 is either a specified or randomly chosen initial index and the value
Δi=NiΔx(2πRcosθ)1
is truncated to the nearest integer, where R is Earth’s radius and Ni is the number of longitude grid points at latitude θ.

For simulated AMVs based on cloud observations, it is appropriate to consider both NR cloud densities and cloud fractional coverage, both at locations being considered and at adjacent ones: not only must a cloud be dense enough to be noticeable but also its environment must be sufficiently inhomogeneous to render it distinguishable. Since gridded values of both of these NR fields are determined using related parameterization schemes, they are generally not entirely independent. For simplicity, therefore, GOWASP-3 only considers NR cloud fraction (c) fields when determining observing probabilities.

At any NR grid location being considered for an observation, cloud layers are determined using a maximum random overlap assumption. Any contiguous NR data levels with c > 0.02 are therefore considered to be within a single cloud layer, with distinct cloud layers separated by one or more NR data levels with c ≤ 0.02. The cloud fraction cn associated with the nth cloud layer is determined as the maximum value of c for any of the NR data levels within that layer.

For most simulated AMVs, the level for a wind observation within any cloud layer is specified as the top NR level for that layer. For observations of clouds whose tops are below a prescribed level (700 hPa here), the observation level is instead specified as that of the lowest NR data level in that cloud layer, following remarks in Forsyth (2007). The observed winds and their pressure assignments are determined from the NR fields provided at those levels.

Cloud layers that are specified as obscured by those above are not observed. For random overlap of layers, a cloud layer N is considered as obscured by those above if
1n=1N1(1cn)>c˜,
where n denotes a cloud layer index, ordered from the highest to lowest clouds, and c˜=0.60 is a threshold used to define obscurity.
For AMVs based on views of water vapor images, IPW
wn=1gpn,1pn,2qdp
is computed through each of two layers (denoted by index n) pn,1ppn,2, where g is the acceleration of gravity and q is the specific humidity. The calculation is determined from the NR fields by assuming that q is constant throughout each model layer. Values of wn are determined at each NR horizontal grid point. For each AMV data type determined from water vapor images, a range of values Δwn = wn(max) − wn(min) is then determined where all values of wn within a trapezoid, centered on the considered location, with sides Δx are examined to determine the two extremes. This is the same Δx as specified for the minimum observation spacing for this AMV type.

For the results to be presented here, the two IPW layers considered are layer 1 with p1,1 = 200 hPa and p1,2 = 600 hPa and layer 2 with p2,1 = 100 hPa and p2,2 = 300 hPa. The first approximately corresponds to the vertical extent measured by the radiance channels used to create water vapor images for real AMV determinations. The second is used to create more realistic numbers of observations at high altitudes than would otherwise be produced by the algorithm using the first layer alone.

Observation levels for simulated AMVs based on Δwn are specified by searching through the integrated layer, starting from its top (i.e., pn,1) to find the first NR level at which q>q˜n, with the minimum value q˜n specified independently for each relevant AMV type. The observation wind components and pressure at this NR level are used as the observation (before any explicit, simulated observation error is added).

d. Specifying probability functions

The relationships between observation locations and NR cloud or water vapor fields can be specified as simply as declaring that an observation is present whenever some threshold field values are exceeded. This will likely tend to unrealistically cluster the observations since it does not account for subgrid variability. This motivates the use of probability functions that, although associated with NR field values, do not necessarily exclude observations from regions where probabilities of observing may be small but nonzero.

Three families of conditional probability functions P(f) are currently used by GOWASP-3, where f is some function of either the previously determined cn or Δwn. Conditioned on a value of this function at each location and pressure level considered, an observation is specified as present if, based on a draw of a random number 0 ≤ r ≤ 1 from a uniform distribution, rP(f). For AMVs based on clouds, f = cn. For AMVs based on water vapor, f = min(snΔwn, 1), where sn is a tuned scaling factor such that the histogram of f is somewhat adequately populated throughout its range between 0 and 1.

The three families of probability functions considered are
P1(f)=α(1|f12|)m,
P2(f)=αfm,
P3(f)={1iff1ff2,0otherwise.
The tuned parameters α, m, f1, and f2 vary with AMV type, pressure layer, geographical region, and surface characterization. The P1 family is only used for AMVs that rely on clouds, P2 only for those that rely on water vapor, and P3 when P1 or P2 cannot be appropriately tuned to yield the desired (target) observation counts. The tuning procedure is described in the next section.

The function P1 is designed to maximize the probability of an observation being simulated when f = 1/2. This is intended when clouds are being considered, for which small values of f imply that only few or small clouds are present and for which large values imply that viewed features may have indiscernible, and therefore untrackable, boundaries. The function P2 is largest when f = 1, for which Δwn within a view is large, with features therefore more discernible. Larger values of the parameter m accentuate the differences in P for different values of f. In contrast, the function P3 implies that any location with f within some range is observed but outside that range, unobserved. All these functions are rather crude, but simple, satisfying the goal of the algorithm.

e. Tuning of probability functions

Before Pj(f) can be applied to determine where observations are to be located, their parameters must be specified. This requires that Pj satisfy the conditions that 1) the expected mean count of simulated observations is the “target” count Ct determined for real observations for each of the sets S2 and 2) 0 ≤ Pj(f) ≤ 1 for all f as required for a function to be a valid probability. The process of determining appropriate parameters is called tuning the probability functions. It is performed for each combination of AMV type, latitude band, surface condition, and p layer.

Given the probabilistic approach, the expected mean count E of observations for any observation subset is
E=fPj(f)h(f)df,
where h(f) is the density function describing the distribution of values of f:
Hi=fifi+1h(f)df,
with Hi denoting a histogram of binned values of f encountered for considered sets of possible observation locations for each observation subset. The first requirement, expressed in terms of such discrete histograms for computational purposes, is therefore satisfied when
Ct=iPj,iHi,
where Pj,i is an abbreviated notation for Pj[(1/2)(fi + fi+1)].
The tuning procedure first requires that the histograms of f be determined by counting the number of values Hi of f that fall within “bins” (i.e., ranges) fiffi+1. The bin demarcations are defined by
fi={0fori=0,1If1(i12)fori=1,,If1,1fori=If,
where If is some integer large enough to distinguish values of f but small enough that the histogram appears well populated in almost all bins. For the results to be presented later, If = 21.
Once each histogram is determined, the tuning of the probability functions is performed. It begins with considering either P = P1 or P = P2 depending on the AMV type, with the parameters α = 1 and m = 5 or m = 3 when f is cloud cover or scaled IPW gradient, respectively, examined as a first guess. Then, α is estimated as
α=CtiPj,iαHi,
where Pj,i/α specifically means the function Pj,i without the coefficient α. Once α is determined by (11), each Pj,i is then examined to ensure that it is bounded by 1. If not, then the procedure is repeated, including determination of a new α, for successively smaller integral values of m down to m = 1.
If the bounding criteria on P do not hold for all histogram bins for any m > 0, then the family P3 is considered. For AMV types that depend on water vapor, the maximum value of i˜ for which
Ct<i=i˜IfHi
is determined. Then
P3(f)={1forf>fi˜,0otherwise.

For AMV types that depend on clouds, the consideration of the ranges of f to consider instead begin with the range of the center histogram bin, followed by augmentations by the ranges of bins that are alternately on one side and then the other side of the center bin, progressing further from the center until the condition analogous to (12) is found. This distinction for the two AMV types preserves the basic goal of favoring locations where values of f are associated with higher probabilities.

Since the DAS quality control will reject a portion of the simulated observations, for some AMV types it is necessary to inflate the tuned α by as much as 35% so that the accepted counts match the target numbers. For others, however, no inflation is required. It remains unclear how to automate this since the QC rejections will depend on statistics of the simulated observation errors to be added before the simulated data are supplied to the DAS. This inflation is therefore performed manually by ingesting the simulated observations, with their simulated errors, in an OSSE for a few days and noting what fraction of observations are rejected by the DAS for each AMV type. The target count is then inflated so that additional observations will be created such that the actual QC-accepted count will match the original desired target count.

4. Results

A sample of results of applying the algorithm for tuning the simulation of AMV locations is described here. This includes examples illustrating several characteristics of real data that the procedure considers. It also includes a sample of results produced by some steps of the algorithm to illustrate how these perform individually.

The sets of real AMV data used for demonstration and training purposes here are those assimilated operationally during the period 1–14 July 2015 by the GEOS-5 data assimilation system employed by the GMAO. It uses a 3DVAR GSI scheme (Rienecker et al. 2008) with 6-hourly cycles. Each analysis period is centered on 0000, 0600, 1200, or 1800 UTC. Data from Meteosat images were thinned by GEOS-5, allowing only one vector wind observation in volumes with sides of 200 km and depths of 100 hPa. The sets of real or simulated observations exclude any that were rejected by the rather strict quality-control criteria employed in the GEOS-5 DAS that allows observation innovations only within a factor b of its prescribed standard deviation of observational error, with 2.5 ≥ b ≥ 1.0 varying with AMV type.

a. Counts of observations

One of the first metrics examined when validating an OSSE based on existing real observations is the set of observation counts. As an example, combined counts of locations of GOES-13 and GOES-15 IR cloud tracking observations for indicated latitudinal bands, surface types, and p layers appear in Table 1 for both real and simulated observations that are assimilated. All the counts are averages per 6-h period, with the means computed over 14 days.

Table 1.

Means of sums of counts of locations of GOES-13 and GOES-15 IR cloud tracking observations for indicated latitudinal bands, surface types, and pressure layers (only the bottom p for each layer is listed) per 6-h assimilation period during 1–14 Jul. The first set is for assimilated real observations during 2015 and the second set is for assimilated simulated observations during a 2006 OSSE.

Table 1.

Almost all of the differences of corresponding values are well within 10% of the target counts. The exceptions occur when the target counts either are extremely small or are associated with midlevel (300–700 hPa) cloudiness. For the latter exceptions, the differences are all within 20% of their target values.

b. Temporal distributions of observations

It is not simply time mean counts that must validate, but their variations in time also. This is especially important when the DAS is a 4D scheme intended to exploit such information in time. It is not necessary that actual temporal sequences of counts match precisely since there are many factors that influence variations, including adjustments in some satellite scanning positions, solar zenith angles (for images based on visible reflections), and locations of cloudy regions. Rather, it should be sufficient to achieve a qualitative resemblance to real variations.

For use with the GEOS-5 NR, the examination here tallies the real observations in temporal bins of Δt = 0.5 h. For bin n, it counts observations occurring within the period nΔtt < (n + 1)Δt. Global counts for real assimilated observations as functions of nΔt for a particular 24-h period appear in Fig. 1 for each of four AMV types: those observations derived from VIS or IR images provided by sensors on Himawari-7, Meteosat-7, GOES-15, and by MODIS on polar orbiters.

Fig. 1.
Fig. 1.

Numbers of locations of assimilated real observations within half-hourly temporal bins centered at the indicated times (UTC) during 1 Jul 2015 produced from IR images provided by (a) Himawari-7, (b) Meteosat-7, and (c) GOES-15, and by (d) MODIS on polar orbiters.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

Temporal variations of counts vary dramatically between the different types shown. The set for GOES-15 has the greatest frequency, with observations absent from only one temporal bin, although with counts that are alternatively small and then large, with ratios of approximately 4. During each 6-h assimilation period, Himawari-7 observations only fall within four temporal bins. For Meteosat-7, the occurrence is approximately every 1.5 h. For MODIS, they are more intermittent.

Counts of simulated observations corresponding to those in Fig. 1 appear in Fig. 2. All the patterns of temporal counts shown appear qualitatively similar to the real ones. As intended, the times of populated bins are the same since they are determined using the real observations as a template. (This agreement would not necessarily occur at all times if the real dataset that was used for training was applied to different simulation periods.) The simulated GOES-15 counts alternate between larger and smaller values, but differing by a factor of 2 rather than 4 as seen for the real observations. These variations occur due to processing or scanning differences during the alternating time periods for the real observations, which are only partially considered by the present algorithm. Even for this sample of only 1 day, the time means are quantitatively similar for corresponding real and simulated observations (within 1% except for Meteosat-7).

Fig. 2.
Fig. 2.

As in Fig. 1, but for observations simulated from the corresponding NR date for 2006.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

c. Association with clouds

As an example of how the simulation algorithm associates observation locations with clouds, Himawari-7 locations created for the NR time of 2230 UTC 30 June 2006 at levels 100 < p < 300 hPa are superimposed on the field of high-level cloud fractions at that time in Fig. 3. The latter field is a standard diagnostic field output by this NR. It can be seen that most, but not all, locations are along cloud edges or otherwise where clouds are broken or scattered. Only a few are in regions of extensive, apparently unbroken, clouds. Observations are not along all cloud edges. In particular, they are excluded from regions not viewed by the satellite as shown in following figures.

Fig. 3.
Fig. 3.

Himawari-7 observation locations (red dots) created for the NR time of 2230 UTC 30 Jun 2006 at levels 100 < p < 300 hPa superimposed on the field of high-level cloud fractions at that same time (blue for 0% to white for 100%).

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

d. Viewing locations

The locations of real AMV observations determined from IR MODIS images during the 6-h assimilation window centered at 0000 UTC 1 July 2015 appear in Fig. 4. Note that observations are present at five times: −1.17, −0.78, −0.35, 0.47, and 1.62 h with respect to the central time. At each time, the locations cover longitudinal ranges not exceeding approximately 180°. Note that when successive viewing times occur alternatively in Northern and Southern Hemispheres, the extents of longitudes viewed shift since Earth has rotated under the satellite orbits. For each apparent longitudinal range, there are sizeable gaps that may be due to either inadequate viewing by available satellites or unavailability of trackable features.

Fig. 4.
Fig. 4.

Locations of real MODIS AMVs assimilated within the 6-h period centered on 0000 UTC 1 Jul 2015. Colors indicate observation times at hours −1.17 (dark blue), −0.78 (blue), −0.35 (light blue), 0.47 (green), and 1.62 (red) with respect to the central time.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

Locations of simulated observations corresponding to those in Fig. 4 appear in Fig. 5. These are determined from the NR for the assimilation period centered on 1 July 2006 for the five times of −1.5, −1.0, −0.5, 0, and 1.5 h. Notice they occupy similar longitude bands at times within each corresponding 30-min window. The simulated locations extend as far equatorward as 60°, which is the same extent as seen for real observations during the entire training period, although for the particular period shown it is 5° further equatorward than any real observations.

Fig. 5.
Fig. 5.

As in Fig. 4, but for observations simulated for the hours −1.5 (dark blue), −1. (blue), −0.5 (light blue), 0. (green), and 1.5 (red) with respect to the NR time of 0000 UTC 1 Jul 2006.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

Locations of real AMVs by some geostationary satellites for the same analysis period appear in Fig. 6. These are for assimilated real observations produced from IR or VIS images provided by Himawari-7 (Fig. 6a) and Meteosat-7 or Meteosat-10 (Fig. 6b), from IR images provided by GOES-13 and GOES-15 (Fig. 6c), and from WV images provided by GOES-13 and GOES-15 (Fig. 6d). The pairs of GOES and Meteosat satellites each have nadir views that are separated by approximately 60° of longitude.

Fig. 6.
Fig. 6.

Locations of real AMVs assimilated within the 6-h period centered on 0000 UTC 1 Jul 2015 obtained from (a) Himawari-7 VIS/IR, (b) Meteosat VIS/IR, (c) GOES IR, and (d) GOES WV images.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

Note first the slightly different geometries of the apparent discs viewed by the geostationary satellites. For Meteosat, they appear circular, within 60° of nadir of each satellite. For Himawari-7, the 60° circle appears truncated longitudinally so as to confine observations to lie between 90°E and 170°W. For GOES IR, the viewing disc considered is also not circular, omitting portions south of approximately 45°S at all longitudes and portions near the equator east of 30°W and west of 180°. This appearance results from the GOES views being divided into geographic sectors with scanning provided by either a “routine” or “rapid scan” mode that may occasionally exclude some sectors from consideration (Velden et al. 2005). For GOES WV, a large portion of the potential disc for this analysis period appears eliminated south of approximately 10°S and east of 100°W. For each of the respective AMV types, similar disc omissions are apparent during other analysis periods, but not all. The present OSSE algorithm does not attempt to incorporate such intermittency, however, primarily because from simply looking at provided real observation datasets it is difficult to discern whether particular intermittent spatial gaps are caused by observation characteristics that should be simulated if practicable (such as those associated with satellite viewing, image processing, data communication, or data selection and quality control) or by a weather-dependent absence of trackable features that should be permitted to differ between the simulated and real observations (given the general lack of correspondence between the NR and real weather).

Another notable viewing difference concerns where observations are produced over land, in contrast to over water, with the latter including oceans, seas, lakes, and sea ice. Himawari-7 VIS/IR excludes most land over Asia and some over Australia. GOES IR excludes most land over North America (but not including, for example, the Great Lakes). The same exclusion does not occur for GOES WV observations. These land-versus-water differences also occur during other analysis periods for these observation types. They are a consequence of the uncertainty of either low-level cloud tracks over land (e.g., due to neglected topographic effects on the motion; Otsuka et al. 2015) or of assigned heights in those regions (e.g., where inversions may be common). Consequently, in such regions AMVs either may not be produced by a data provider or they may be discarded by a quality-control procedure employed by a data user. The present algorithm does not distinguish between the causes since it is only the end result that needs to be simulated.

Assimilated simulated observation locations for the 6-h period corresponding to those of the real data in Fig. 6 appear in Fig. 7. Note that the latitudinal and longitudinal extents of the locations match those of the real ones, as designed, although for the two GOES views, the simulated longitudinal extents are more independent of latitude. The simulated GOES IR locations also include regions farther north over land compared to real ones because its tuning distinguishes counts within latitude zones of 30° whereas the real observations over land are excluded north of approximately 20°N. An additional exclusion condition can be easily imposed to remove this minor disagreement, but perhaps at the expense of rendering the algorithm less adaptable to future processing and scanning changes.

Fig. 7.
Fig. 7.

As in Fig. 6, but for observations simulated from the corresponding NR date for 2006.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

e. Spacing of assimilated observations

The typical horizontal spacings of different AMV types vary because viewing instruments may have different resolutions, feature tracking algorithms may differ, and the DAS may apply different data thinning. Indeed, the spacings can change with time as instrument, processing, or assimilation characteristics change. Also, the term “typical” is purposefully vague here; for example, even if an observation type is thinned such that only a single observation is utilized in each 100 km × 100 km trapezoid subdomain covering a viewing domain, observations can still occur only a few kilometers apart on either side of a trapezoid edge. Neither the shortest or mean separation distance between nearest observations of a particular type is what the simulation algorithm here requires to defines its value of Δx. Also note that this requirement concerns horizontal separations of observations within the same NR periods, irrespective of the observation pressure level. For this latter reason, observation spacings are examined here for individual 30-min temporal bins, irrespective of observation height.

Real AMV locations for four AMV types are presented within subdomains of their viewing regions in Fig. 8. These are for Himawari-7 (Australia; Fig. 8a), Meteosat-10 (South Atlantic; Fig. 8b), GOES-13 (South Atlantic; Fig. 8c), and MODIS (Arctic; Fig. 8d). The observation periods shown are the 30-min periods, respectively, beginning at 0000 UTC 1 July 2015 and at 2230, 2230, and 2300 UTC 30 June 2015. Presentation of only subdomains allows the figures to display greater spatial resolution than global portraits permit.

Fig. 8.
Fig. 8.

Spacing of assimilated real AMVs obtained from images provided by (a) Himawari-7 VIS/IR views near Australia, (b) Meteosat-10 VIS/IR and (c) GEOS-13 IR over portions of Brazil and the South Atlantic, and (d) MODIS IR over the Arctic. These are for observations specified within the 30-min periods centered on 0000 UTC 1 Jul 2015 and 2230, 2230, and 2300 UTC 30 Jun 2015, respectively. Latitudes and longitudes are displayed for each panel.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

For Himawari-7, the observations appear on a regular grid in most regions, with a strict minimal spacing of 0.5° in both latitude and longitude in such places. For Meteosat-10, the spacing is more irregular, with “typical” separations of 100 km, but with some pairs of observations lying as close as 25 km, due to the GMAO DAS spatial thinning of this dataset. For GOES-13, the typical spacing is much closer, generally 25 km. For MODIS observations, the spacing is approximately 15 km. So, there is great variability in this metric among the AMV types.

Examples of simulated observation locations appear in Fig. 9 for the same AMV types, geographical regions, and times as in Fig. 8. Observation locations in corresponding figures are not expected to be collocated since the cloud and water vapor fields are expected to differ. Rather it is only some characteristics that should be similar, particularly those that the simulation and tuning algorithm are explicitly designed to mimic.

Fig. 9.
Fig. 9.

As in Fig. 8, but for observations simulated from the corresponding NR date for 2006.

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

For Himawari-7, the spacing in Fig. 9 is regular everywhere, drawn from the NR grid having regularly spaced latitudes and longitudes, with slightly greater spacing than for the real observations. This slight difference in spacing results from the way the simulated spacing has been determined for this high-resolution NR dataset by rounding up the grid spacing to the next highest integer number of grid spacings. The apparent irregularity of some real observation locations over Australia is not mimicked by the simulated locations that instead maintain regularity everywhere. Although at this time for this AMV type, the number of simulated locations is half the number of real ones, for other observation times during this same analysis period, there are many more simulated than real ones, such that the total numbers for this period are the same.

The simulated and real Meteosat locations display qualitatively similar typical separation distances and spacing irregularities. There are only a few simulated locations where adjacent ones clearly lie along identical meridians or parallels. Both real and simulated observations cover most of the presented subdomain.

For GOES IR, the simulated locations do not exhibit streaks with as densely located observations as seen for the real ones. Outside of those regions, however, the typical spacings of simulated and real observations of this AMV type appear qualitatively similar. Similar comments apply to the MODIS IR locations shown.

f. Histograms of derived NR fields

A very critical component of the tuning for the AMV location algorithm is the set of histograms of either cloud fractions or scaled, local water vapor variations. In conjunction with the other results discussed in this section, it is therefore appropriate to describe some characteristics of the histograms themselves. These are determined by the NR fields considering the prescribed spacings Δx, the geographic extents of the observation types, and the times of day that such observations occur in reality.

When parameters for the AMV simulation locations are determined separately for 19 AMV types (distinct satellites, instruments, etc.), separately for land versus water or sea ice locations, and divided into six latitudinal belts and seven pressure layers, there are 1596 histograms of f produced. Although only a few examples are presented here, the comments offered generally apply to observations of similar AMV types. Each histogram is presented here in terms of fractions of counts (ηi=Hi/iHi) that fall within each of the If = 21 bins of 0 ≤ f ≤ 1. Each is also presented as though it is a continuous, rather than discrete function (i.e., as a line rather than a set of bars).

Values of ηi for cloud fractions appear in Fig. 10 for considered viewing locations over water or ice for (i) GOES-15 between 0° and 30°N and (ii) MODIS between 60° and 90°N. For each set, results are presented for three separate pressure ranges: 143–286, 429–572, and 856–1000 hPa. The first and last ranges are those for which the fractions of clear-sky locations are smallest and the second where that fraction is largest. All the ηi are computed by considering NR fields at each half-hourly time during which observations of that AMV type are simulated as possibly present (i.e., accounting for the temporal availability as reported in connection with Fig. 1) throughout a 14-day period, so that the fractions represents a mean over 14 days of observations. The mean numbers of horizontal locations considered during each 6-h analysis period for the GOES-15 and MODIS simulations within this geographic area are 414 243 and 214 937, respectively (counting looks at the same geographic location but during different half-hourly viewing periods within each 6-h analysis period as distinct “locations”). These were determined using respective Δx of 25 and 10 km.

Fig. 10.
Fig. 10.

Histograms of numbers of cloud fraction values falling within each of 21 bins, presented as fractions of the total number of locations considered over water or ice for (a) GOES-15 in the band 0°–30°N and (b) MODIS north of 60°N for three separate pressure ranges: 143–286 (solid), 429–572 (dashed), and 856–1000 hPa (dotted).

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

Most populated is the bin for f < 0.025. It contains as much as 99% of considered locations for GOES-15 for 429 < p < 572 hPa to as little as 69% of considered locations for MODIS for 856 < p < 1000 hPa. For some AMV types within some layers, a smaller peak occurs for some bin with f > 0.9. Within the remaining bins, fractions for each AMV type and p layer considered are all small, with typically small variations between adjacent bins.

Histograms of ηi for f = swΔw appear in Fig. 11 for considered viewing locations over water or ice for Himawari-7 (Faig. 11) and Meteosat-10 (Fig. 11b) between 30°S and 0°. They use scaling factors sw = 2. The results are presented for two pressure ranges: 143–286 and 286–429 hPa. These ranges contain most of the observations for these AMV types. The mean numbers of horizontal locations considered during each 6-h analysis period for the Himawari-7 and Meteosat-10 WV simulations within this geographic area are 99 158 and 206 311, respectively. These considered spacings Δx of 30 and 25 km, respectively. The bin for swΔw < 0.025 is the most populated, with values shown ranging between 0.17 and 0.81. Fractions for swΔw > 0.075 generally decrease with increasing swΔw until swΔw > 0.975, where a small local maximum of the fraction occurs.

Fig. 11.
Fig. 11.

Histograms of numbers of values of swΔw falling within 21 bins, presented as fractions of the total number of locations considered over water in the band 30°S–0° for (a) Himawari-7 and (b) Meteosat-10 for the two separate pressure ranges: 143–286 (solid) and 286–429 hPa (dashed).

Citation: Journal of Atmospheric and Oceanic Technology 37, 3; 10.1175/JTECH-D-19-0079.1

g. Examples of tuned function parameters

For GOES-13 IR simulations, the function
P(f)=α(1|f12|)5,
with f = cn is selected by the parameter tuning algorithm for all latitudinal bands, underlying surfaces, and p layers considered. Different bands, surfaces, and layers have different values of α. These latter are presented in Table 2 for the bands where observations exist.
Table 2.

Values of parameters α for probability functions used to determine simulated IR observing locations for GOES-13 as a function of latitudinal band, surface type, and pressure layer (only the bottom p for each layer is listed).

Table 2.

Note that values differ between bands, surfaces, and layers. These differences are caused by variations in cloud-fraction histograms, target observation counts, numbers of locations considered, and the fractions of each surface type in differing latitude bands. The tiny values for land locations in the band 30°–60°N, for example, are due to the exclusion of observations over land north of 30°N in sets of real observations assimilated.

5. Summary

The simulation algorithm, as applied here, does not attempt to replicate all characteristics of real observations. In particular, it does not address some peculiarities of the GOES IR observation scanning or processing disk. It therefore does not necessarily produce the same variations of counts with time as real-image processing applications display, aside from considerations of solar zenith angle and diurnal cloudiness exhibited in the NR. It also does not consider that many trackable features may tend to persist from one considered time to the next, requiring that a probabilistic algorithm incorporate temporal correlations. If all the bins of f values are not sufficiently populated, it also cannot discriminate observation locations based on the NR fields; for example, dense observation streaks will be less prevalent than for real observations. It does, however, permit production of observations at multiple vertical levels at the same horizontal grid points since the tuned probability for each layer is not conditioned on the probabilities for those above.

Although the presented algorithm does not produce location characteristics identical to those for real observations in all respects, it appears to produce sufficient realism to be useful for OSSE simulations. In particular, it mimics time-mean counts as functions of surface type, latitude band, and pressure layer. It also produces observations only within those considered time intervals for which the template of real observations includes observations of the same AMV type. Although the typical geographic coverage and spacing of simulated locations are notably different from those for real observations for some AMV types, they at least can be termed qualitatively similar.

The AMV simulation algorithm does not require that the NR has sufficient spatial and, as importantly, temporal resolution to construct simulated images for application of feature-tracking algorithms. It can also effectively compensate for significant deficiencies in NR cloud or local moisture gradient fields, although not if such gradients are effectively absent. It remains sufficiently flexible that some additional properties, such as diurnal variations in counts, beyond simple consideration of solar zenith angle, can be incorporated if desired. The tuning of the probability function is fairly robust and computationally quick.

Acknowledgments

This work was supported by the cooperative agreement between NASA/GSFC, USRA/GESTAR and MSU/GESTAR. The manuscript’s reviewers also contributed helpful improvements. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at Goddard Space Flight Center.

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