Climatological Model Research Articles

Assessing Hurricane Rainfall Mechanisms Using a Physics-Based Model: Hurricanes Isabel (2003) and Irene (2011)

Abstract We examine a recently developed physics-based tropical cyclone rainfall (TCR) model and apply it to assess the mechanisms that dominate the magnitude and spatial distribution of TC rainfall, with Hurricanes Isabel (2003) and Irene (2011) as study cases. We evaluate the TCR model using Weather and Research Forecasting (WRF) Model simulations. TCR-generated rainfall fields for the two storms compare well with WRF estimates in terms of both azimuthal mean and spatial distributions. When coupled with a hydrologic model, TCR generates flood peaks over the Delaware River basin for Irene as accurately as WRF. TCR accounts for four major rainfall mechanisms: surface frictional convergence, vortex stretching, interaction of the storm with topography, and interaction of the storm with large-scale baroclinity. We show that these rainfall mechanisms affected the rainfall pattern differently for Isabel and Irene. Frictional convergence is the dominant factor, while other mechanisms are also significant. The frictional convergence depends on the boundary layer formulation, which is relatively simple in TCR and may require calibration of boundary layer parameters. Furthermore, we find that the TC rainfall distribution is strongly dependent on the temporal and spatial variation of the TC wind field, mediated by the physical mechanisms represented by TCR. When coupled with various analytical wind models, TCR generally captures the rainfall distribution, with the Holland wind model performing the best. Given its high computational efficiency, TCR can be coupled with an analytical wind model, a hydrological model, and a TC climatology model to generate large numbers of synthetic events to assess the risk associated with TC rainfall and inland flooding.

Detection of Severe Weather Events in a High-Resolution Ensemble Prediction System Using the Extreme Forecast Index (EFI) and Shift of Tails (SOT)

Abstract The extreme forecast index (EFI) and shift of tails (SOT) are commonly used to compare an ensemble forecast to a reference model climatology, in order to measure the severity of the current weather forecast. In this study, the feasibility and the relevance of EFI and SOT computations are examined within the convection-permitting Application of Research to Operations at Mesoscale (AROME-France) ensemble prediction system (EPS). First, different climate configurations are proposed and discussed, in order to overcome the small size of the ensemble and the short climate sampling length. Subjective and objective evaluations of EFI and SOT for wind gusts and precipitation forecasts are then presented. It is shown that these indices can provide relevant early warnings and, based on a trade-off between hits and false alarms, optimal EFI thresholds can be determined for decision-making.

On the Coupling between Barotropic and Baroclinic Modes of Extratropical Atmospheric Variability

Abstract The baroclinic and barotropic components of atmospheric dynamics are usually viewed as interlinked through the baroclinic life cycle, with baroclinic growth of eddies connected to heat fluxes, barotropic decay connected to momentum fluxes, and the two eddy fluxes connected through the Eliassen–Palm wave activity. However, recent observational studies have suggested that these two components of the dynamics are largely decoupled in their variability, with variations in the zonal mean flow associated mainly with the momentum fluxes, variations in the baroclinic wave activity associated mainly with the heat fluxes, and essentially no correlation between the two. These relationships are examined in a dry dynamical core model under different configurations and in Southern Hemisphere observations, considering different frequency bands to account for the different time scales of atmospheric variability. It is shown that at intermediate periods longer than 10 days, the decoupling of the baroclinic and barotropic modes of variability can indeed occur as the eddy kinetic energy at those time scales is only affected by the heat fluxes and not the momentum fluxes. The baroclinic variability includes the oscillator model with periods of 20–30 days. At both the synoptic time scale and the quasi-steady limit, the baroclinic and barotropic modes of variability are linked, consistent with baroclinic life cycles and the positive baroclinic feedback mechanism, respectively. In the quasi-steady limit, the pulsating modes of variability and their correlations depend sensitively on the model climatology.

Mean circulation of the Mid-Atlantic Bight from a climatological data assimilative model

The along-shelf momentum balance of the Mid-Atlantic Bight (MAB) coastal ocean includes a significant contribution from the along-shelf gradient in sea level. This sea level tilt, of order 10−7, and other features of the mean sea level are not captured well in global mean dynamic topography (MDT) derived from hydrographic observations or satellite altimetry and gravity data, and is poorly represented in global and basin scale dynamical models. This is problematic for applications that would use coastal satellite altimeter data to estimate total water level above datum. We have produced a MDT for the MAB using the Regional Ocean Modeling System (ROMS) with 4-dimensional variational (4D-Var) data assimilation configured to obtain climatological annual and monthly mean results. The observations assimilated were a regional hydrographic climatology of temperature and salinity, and long-term mean velocity from HF-radar, shipboard ADCP, and current-meters. Assimilation adjusts the 3-dimensional ocean state, boundary conditions, and air-sea fluxes to minimize the model-data misfit. The assimilation of mean velocity data is vital to obtaining a realistic circulation result. The MDT exhibits a strong across-shelf sea level slope in geostrophic balance with the southwestward mean flow. The subtle along-shelf tilt is recovered and is relatively uniform throughout the MAB inside the 50 m isobath, but on the southern outer shelf it reverses sign and drives significant across-isobath flow, partially draining the southward mean transport. In the north, across-shelf flow is offshore in the surface and bottom Ekman layers, but largely balanced locally by inflow in the interior depth range.

Solar Wind and Seasonal Influence on Ionospheric Currents From Swarm and CHAMP Measurements

AbstractWe present a new climatological model of the ionospheric current system, determined from magnetic measurements taken by the Challenging Minisatellite Payload (CHAMP) and Swarm satellites. The model describes the horizontal currents in the ionosphere, below the satellites, and the field‐aligned (Birkeland) currents that connect the ionosphere with the magnetosphere. The model provides ionospheric current values at any location as continuous functions of solar wind speed, interplanetary magnetic field, dipole tilt angle, and the F10.7 index of solar flux. Geometric distortions due to variations in the Earth's main magnetic field are taken into account, thus allowing for precise comparisons between the two hemispheres. The model is the first of its kind to describe the full 3‐D electric currents and not only the field‐aligned or the equivalent horizontal current. We use this capability to demonstrate a key difference between seasons: During winter, the total horizontal current is almost entirely confined to the auroral oval, for all interplanetary magnetic field orientations, where it connects upward and downward Birkeland currents. During more sunlit conditions, the horizontal current extends beyond the auroral oval and is a sum of currents connecting Birkeland currents and currents that circulate in the ionosphere. The westward electrojet is the only large‐scale current structure that is persistent across seasons. Comparison with average convection maps suggests that it is comprised largely of Hall currents, which connect to Birkeland currents in the winter but not in summer.

Empirical forecast of quiet time ionospheric Total Electron Content maps over Europe

An accurate forecast of the atmospheric Total Electron Content (TEC) is helpful to investigate space weather influences on the ionosphere and technical applications like satellite-receiver radio links. The purpose of this work is to compare four empirical methods for a 24-h forecast of vertical TEC maps over Europe under geomagnetically quiet conditions.TEC map data are obtained from the Space Weather Application Center Ionosphere (SWACI) and the Universitat Politècnica de Catalunya (UPC). The time-series methods Standard Persistence Model (SPM), a 27 day median model (MediMod) and a Fourier Series Expansion are compared to maps for the entire year of 2015. As a representative of the climatological coefficient models the forecast performance of the Global Neustrelitz TEC model (NTCM-GL) is also investigated. Time periods of magnetic storms, which are identified with the Dst index, are excluded from the validation.By calculating the TEC values with the most recent maps, the time-series methods perform slightly better than the coefficient model NTCM-GL. The benefit of NTCM-GL is its independence on observational TEC data. Amongst the time-series methods mentioned, MediMod delivers the best overall performance regarding accuracy and data gap handling. Quiet-time SWACI maps can be forecasted accurately and in real-time by the MediMod time-series approach.

Improved model for correcting the ionospheric impact on bending angle in radio occultation measurements

Abstract. The standard approach to remove the effects of the ionosphere from neutral atmosphere GPS radio occultation measurements is to estimate a corrected bending angle from a combination of the L1 and L2 bending angles. This approach is known to result in systematic errors and an extension has been proposed to the standard ionospheric correction that is dependent on the squared L1 ∕ L2 bending angle difference and a scaling term (κ). The variation of κ with height, time, season, location and solar activity (i.e. the F10.7 flux) has been investigated by applying a 1-D bending angle operator to electron density profiles provided by a monthly median ionospheric climatology model. As expected, the residual bending angle is well correlated (negatively) with the vertical total electron content (TEC). κ is more strongly dependent on the solar zenith angle, indicating that the TEC-dependent component of the residual error is effectively modelled by the squared L1 ∕ L2 bending angle difference term in the correction. The residual error from the ionospheric correction is likely to be a major contributor to the overall error budget of neutral atmosphere retrievals between 40 and 80 km. Over this height range κ is approximately linear with height. A simple κ model has also been developed. It is independent of ionospheric measurements, but incorporates geophysical dependencies (i.e. solar zenith angle, solar flux, altitude). The global mean error (i.e. bias) and the standard deviation of the residual errors are reduced from -1.3×10-8 and 2.2×10-8 for the uncorrected case to -2.2×10-10 rad and 2.0×10-9 rad, respectively, for the corrections using the κ model. Although a fixed scalar κ also reduces bias for the global average, the selected value of κ (14 rad−1) is only appropriate for a small band of locations around the solar terminator. In the daytime, the scalar κ is consistently too high and this results in an overcorrection of the bending angles and a positive bending angle bias. Similarly, in the nighttime, the scalar κ is too low. However, in this case, the bending angles are already small and the impact of the choice of κ is less pronounced.

A comparative study of ionospheric IRIEup and ISP assimilative models during some intense and severe geomagnetic storms

Three-dimensional (3-D) electron density matrices, computed in the Mediterranean area by the IRI climatological model and IRIEup and ISP nowcasting models, during some intense and severe geomagnetic-ionospheric storms, were ingested by the ray tracing software tool IONORT, to synthesize quasi-vertical ionograms. IRIEup model was run in different operational modes: (1) assimilating validated autoscaled electron density profiles only from a limited area which, in our case, is the Mediterranean sector (IRIEup_re(V) mode); (2) assimilating electron density profiles from a larger region including several stations spread across Europe: (a) without taking care of validating the autoscaled data in the assimilation process (IRIEup(NV)); (b) validating carefully the autoscaled electron density profiles before their assimilation (IRIEup(V)).The comparative analysis was carried out comparing IRI, IRIEup_re(V), ISP, IRIEup(NV), and IRIEup(V) foF2 synthesized values, with corresponding foF2 measurements autoscaled by ARTIST, and then validated, at the truth sites of Roquetes (40.80°N, 0.50°E, Spain), San Vito (40.60°N, 17.80°E, Italy), Athens (38.00°N, 23.50°E, Greece), and Nicosia, (35.03°N, 33.16°E, Cyprus). The outcomes demonstrate that: (1) IRIEup_re(V), performs better than ISP in the western Mediterranean (around Roquetes); (2) ISP performs slightly better than IRIEup_re(V) in the central part of Mediterranean (around Athens and San Vito); (3) ISP performance is better than the IRIEup_re(V) one in the eastern Mediterranean (around Nicosia); (4) IRIEup(NV) performance is worse than the IRIEup(V) one; (5) in the central Mediterranean area, IRIEup(V) performance is better than the IRIEup_re(V) one, and it is practically the same for the western and eastern sectors.Concerning the overall performance, nowcasting models proved to be considerably more reliable than the climatological IRI model to represent the ionosphere behaviour during geomagnetic-ionospheric storm conditions; ISP and IRIEup(V) provided the best performance, but neither of them has clearly prevailed over the other one.

Spatial and Temporal Features of the Topside Ionospheric Electron Density by a New Model Based On GPS Radio Occultation Data

AbstractA new method for probing the spatial and temporal features of the topside ionosphere is presented. The Vary‐Chap model given by linear functions was used to discover and report features of the topside scale height and its gradient. Based on the global coverage of the radio occultation data, spherical harmonic functions were applied to detect some spatial features of the estimated topside. In addition, a Fourier time‐dependent method was applied in 10 consecutive years to both estimate and predict the temporal evolution of the topside. As a result, the temporal variation of the peak height showed high correlation with the scale height. And on the other hand, the electron density peak showed a strong anticorrelation with the gradient of the scale height. This suggests that the equatorial topside was mainly controlled by the E × B equatorial vertical drift, which increases the scale height in the equatorial region, and the diffusion of the electrons along the geomagnetic field lines, which reduces the gradient of the scale height. Also, a 1 year prediction with a reasonable accuracy showed that the proposed model can be considered a practical and useful tool for predicting features of the topside ionosphere, which may have special interest for the development of climatological models.

Limited predictability of extreme decadal changes in the Arctic Ocean freshwater content

Predictability of extreme changes in the Arctic Ocean freshwater content and the associated release into the subpolar North Atlantic up to one decade ahead is investigated using a CMIP5-type global climate model. The perfect-model setup consists of a 500 year control run, from which selected 10 year long segments are predicted by initialized, perturbed ensemble predictions. Initial conditions for these are selected from the control run to represent large positive or negative decadal changes in the total freshwater content in the Arctic Ocean. Two different classes of ensemble predictions are performed, one initialized with the ‘observed’ ocean globally, and one initialized with the model climatology in the Arctic Ocean and with the observed ocean elsewhere. Analysis reveals that the former yields superior predictions 1 year ahead as regards both liquid freshwater content and sea ice volume in the Arctic Ocean. For prediction years two and above there is no overall gain in predictability from knowing the initial state in the Arctic Ocean and damped persistence predictions perform just as well as the ensemble predictions. Areas can be identified, mainly in the proper Canadian and Eurasian basins, where knowledge of the initial conditions gives a gain in predictability of liquid freshwater content beyond year two. Total freshwater export events from the Arctic Ocean into the subpolar North Atlantic have no predictability even 1 year ahead. This is a result of the sea ice component not being predictable and LFW being on the edge of being predictable for prediction time 1 year.

Incorporating Radiation Effects Into AE9/AP9

This paper describes a framework for incorporating linear radiation effects into the statistical machinery of the AE9/AP9 radiation climatology model software via “kernel” files. Users can provide their own kernels without modification of the software. Kernels can be applied to a variety of radiation effects such as proton single-event effect rate, internal charging current, ionizing dose, and nonionizing dose. Kernels can be generated for custom shielding geometry and materials and for custom parts or material susceptibilities.

June Solstice Equatorial Spread F in the American Sector: A Numerical Assessment of Linear Stability Aided by Incoherent Scatter Radar Measurements

AbstractPrevious studies have suggested that weakening downward plasma drifts can produce favorable conditions for the ionospheric Generalized Rayleigh‐Taylor (GRT) instability and explain the occurrence of postmidnight equatorial spread F (ESF). We evaluated this hypothesis using numerical simulations aided by measurements and attempted to explain ESF events observed in the American sector during June solstice, low solar flux conditions. We analyzed plasma drifts and ESF measurements made by the incoherent scatter radar of the Jicamarca Radio Observatory (11.95° S, 76.87° W, ∼1° dip). We found adequate measurements during a prototypical, quiet time event on 4–5 June 2008 when the downward drifts weakened and a fully developed ESF appeared. The measured drifts were used as input for the SAMI2 model. SAMI2 reproduced an “apparent” uplift of the ionosphere based on h F measurements that was consistent with expectations and observations. SAMI2 also provided parameters for estimation of the flux tube linear growth rates of GRT instability associated with the weakening drift event. We found that the weakening drifts did produce unstable conditions with positive growth rates. The growth rates, however, were slower than those obtained for typical, premidnight ESF events and those obtained for similar drift conditions in other longitude sectors. We show, however, that departures in the wind pattern, from climatological model predictions, can produce favorable conditions for instability development. Following the hypothesis of Huba and Krall (2013) and using SAMI2 simulations, we show that equatorward winds, when combined with weakening drifts, could have contributed to the unstable conditions responsible for the postmidnight ESF events.

Changes in AE9/AP9-IRENE Version 1.5

This paper describes version 1.5 of the AE9/AP9 family of space radiation climatology models. The most significant update is the inclusion of new data sets that change the flux maps. These new data include measurements from Van Allen Probes, Azur, and the HiLET sensor on the TWINS-2 spacecraft. In recognition of international contributions to the models, we introduce the IRENE nomenclature for International Radiation Environment Near Earth.

Wind storminess in the Adriatic Sea in a climate change scenario

In this work we assess the quality of the wind fields provided over the Adriatic Sea by the Regional Climate Model COSMO-CLM with reference to a control (CTR) period from 1971 to 2000 and to a future period from 2071 to 2100 under IPCC RCP 8.5 scenario (SCE), focusing on the implications for wave climate characterisation. Model skills have been assessed by comparing CTR results in terms of gross statistical properties and storm features against wind data from coastal observatories along the whole Italian Adriatic coast, showing a satisfactory capability of capturing the main features of mean observed seasonal variability. Significant achievements with reference to existing climatological models have been observed especially in terms of wind directionality, with unprecedented performances in reproducing the bimodal dominance of Bora (from northeast) and Sirocco (from southeast) in the northern basin, and the typical patterns of Bora jets flowing from the mountain ridges enclosing the Adriatic Sea on its eastern side. Future projections generally confirm the tendency to a decreasing energy trend envisaged by previous studies, with a more marked effect for extreme events in the northern basin. Based on the comparison between climatological wind fields and the results of a SWAN wave model run forced by COSMO-CLM, we also define and test a criterion for a rapid identification of some relevant case studies for dedicated wave modelling experiments, without the need of running entire climatological wave simulations. This permits to focus the analysis of climatological oceanographic extreme events to a limited number of selected cases, allowing remarkable saving of computational effort especially if an ensemble approach is desired.

Atmospheric Dynamic and Thermodynamic Processes Driving the Western North Pacific Anomalous Anticyclone during El Niño. Part I: Maintenance Mechanisms

The western North Pacific anomalous anticyclone (WNPAC) is an important low-level circulation system that connects El Niño and the East Asian monsoon. In this study, the mechanisms responsible for the formation and maintenance of the WNPAC are explored. Part I of this study focuses on the WNPAC maintenance mechanisms during El Niño mature winter and the following spring. Moisture and moist static energy analyses indicated that the WNPAC is maintained by both the remote forcing from the equatorial central-eastern Pacific via the atmospheric bridge and the local air–sea interactions. Three pacemaker experiments by a coupled global climate model FGOALS-s2, with upper-700-m ocean temperature in the equatorial central-eastern Pacific restored to the observational anomalies plus model climatology, suggest that about 60% (70%) intensity of the WNPAC during the winter (spring) is contributed by the remote forcing from the equatorial central-eastern Pacific. The key remote forcing mechanism responsible for the maintenance of the WNPAC is revealed. In response to El Niño–related positive precipitation anomalies over the equatorial central-eastern Pacific, twin Rossby wave cyclonic anomalies are induced to the west. The northern branch of the twin cyclonic anomalies advects dry and low moist enthalpy air into the tropical western North Pacific, which suppresses local convection. The suppressed convection further drives the WNPAC.

GLOBALLY-APPLICABLE PREDICTIVE WILDFIRE MODEL A TEMPORAL–SPATIAL GIS BASED RISK ANALYSIS USING DATA DRIVEN FUZZY LOGIC FUNCTIONS

Abstract. This study (van den Dool, 2017) is a proof of concept for a global predictive wildfire model, in which the temporal–spatial characteristics of wildfires are placed in a Geographical Information System (GIS), and the risk analysis is based on data-driven fuzzy logic functions. The data sources used in this model are available as global datasets, but subdivided into three pilot areas: North America (California/Nevada), Europe (Spain), and Asia (Mongolia), and are downscaled to the highest resolution (3-arc second). The GIS is constructed around three themes: topography, fuel availability and climate. From the topographical data, six derived sub-themes are created and converted to a fuzzy membership based on the catchment area statistics. The fuel availability score is a composite of four data layers: land cover, wood loads, biomass, biovolumes. As input for the climatological sub-model reanalysed daily averaged, weather-related data is used, which is accumulated to a global weekly time-window (to account for the uncertainty within the climatological model) and forms the temporal component of the model. The final product is a wildfire risk score (from 0 to 1) by week, representing the average wildfire risk in an area. To compute the potential wildfire risk the sub-models are combined usinga Multi-Criteria Approach, and the model results are validated against the area under the Receiver Operating Characteristic curve.

Modelling ionospheric vertical drifts over Africa low latitudes using Empirical Orthogonal functions and comparison with climatological model

For the first time, empirical model of daytime vertical E×B drift based on Empirical Orthogonal functions (EOF) decomposition technique is presented. Day-to-day variability of E×B drift inferred from horizontal (H) geomagnetic field data around dip latitude for the period of 2008–2013 is used to both develop and validate the model. Results show that the EOF technique is promising with modelled values and data giving correlation coefficient values of at least 0.90 for geomagnetic conditions of both Kp⩽3 and Kp>3 within 2008–2013. Independent model validation shows that in situ E×B values from ion velocity meter (IVM) instrument on-board C/NOFS satellite are closer to model E×B estimates than the climatological Scherliess-Fejer (SF) model incorporated within the International Reference Ionosphere (IRI).

Kinematic parameters of internal waves of the second mode in the South China Sea

Abstract. Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

Bio-physical characterisation of polynyas as a key foraging habitat for juvenile male southern elephant seals (Mirounga leonina) in Prydz Bay, East Antarctica.

Antarctic coastal polynyas are persistent open water areas in the sea ice zone, and regions of high biological productivity thought to be important foraging habitat for marine predators. This study quantified southern elephant seal (Mirounga leonina) habitat use within and around the polynyas of the Prydz Bay region (63°E– 88°E) in East Antarctica, and examined the bio-physical characteristics structuring polynyas as foraging habitat. Output from a climatological regional ocean model was used to provide context for in situ temperature-salinity vertical profiles collected by tagged elephant seals and to characterise the physical properties structuring polynyas. Biological properties were explored using remotely-sensed surface chlorophyll (Chl-a) and, qualitatively, historical fish assemblage data. Spatially gridded residence time of seals was examined in relation to habitat characteristics using generalized additive mixed models. The results showed clear polynya usage during early autumn and increasingly concentrated usage during early winter. Bathymetry, Chl-a, surface net heat flux (representing polynya location), and bottom temperature were identified as significant bio-physical predictors of the spatio-temporal habitat usage. The findings from this study confirm that the most important marine habitats for juvenile male southern elephant seals within Prydz Bay region are polynyas. A hypothesis exists regarding the seasonal evolution of primary productivity, coupling from surface to subsurface productivity and supporting elevated rates of secondary production in the upper water column during summer-autumn. An advancement to this hypothesis is proposed here, whereby this bio-physical coupling is likely to extend throughout the water column as it becomes fully convected during autumn-winter, to also promote pelagic-benthic linkages important for benthic foraging within polynyas.

Functional inverted Wishart for Bayesian multivariate spatial modeling with application to regional climatology model data.

Modern environmental and climatological studies produce multiple outcomes at high spatial resolutions. Multivariate spatial modeling is an established means to quantify cross-correlation among outcomes. However, existing models typically suffer from poor computational efficiency and lack the flexibility to simultaneously estimate auto- and cross-covariance structures. In this article, we undertake a novel construction of covariance by utilizing spectral convolution and by imposing an inverted Wishart prior on the cross-correlation structure. The cross-correlation structure with this functional inverted Wishart prior flexibly accommodates not only positive but also weak or negative associations among outcomes while preserving spatial resolution. Furthermore, the proposed model is computationally efficient and produces easily interpretable results, including the individual autocovariances and full cross-correlation matrices, as well as a partial cross-correlation matrix reflecting the outcome correlation after excluding the effects caused by spatial convolution. The model is examined using simulated data sets under different scenarios. It is also applied to the data from the North American Regional Climate Change Assessment Program, examining long-term associations between surface outcomes for air temperature, pressure, humidity, and radiation, on the land area of the North American West Coast. Results and predictive performance are compared with findings from approaches using convolution only or coregionalization.