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NASA NTRS2008

The Super Tuesday Outbreak: Forecast Sensitivities to Single-Moment Microphysics Schemes

Forecast precipitation and radar characteristics are used by operational centers to guide the issuance of advisory products. As operational numerical weather prediction is performed at increasingly finer spatial resolution, convective precipitation traditionally represented by sub-grid scale parameterization schemes is now being determined explicitly through single- or multi-moment bulk water microphysics routines. Gains in forecasting skill are expected through improved simulation of clouds and their microphysical processes. High resolution model grids and advanced parameterizations are now available through steady increases in computer resources. As with any parameterization, their reliability must be measured through performance metrics, with errors noted and targeted for improvement. Furthermore, the use of these schemes within an operational framework requires an understanding of limitations and an estimate of biases so that forecasters and model development teams can be aware of potential errors. The National Severe Storms Laboratory (NSSL) Spring Experiments have produced daily, high resolution forecasts used to evaluate forecast skill among an ensemble with varied physical parameterizations and data assimilation techniques. In this research, high resolution forecasts of the 5-6 February 2008 Super Tuesday Outbreak are replicated using the NSSL configuration in order to evaluate two components of simulated convection on a large domain: sensitivities of quantitative precipitation forecasts to assumptions within a single-moment bulk water microphysics scheme, and to determine if these schemes accurately depict the reflectivity characteristics of well-simulated, organized, cold frontal convection. As radar returns are sensitive to the amount of hydrometeor mass and the distribution of mass among variably sized targets, radar comparisons may guide potential improvements to a single-moment scheme. In addition, object-based verification metrics are evaluated for their utility in gauging model performance and QPF variability.

Molthan, Andrew L.↗

NASA NTRS2017

Aerosol EnKF at GMAO

In the GEOS near real-time system, as well as in MERRA-2 which is the latest reanalysis produced at NASAs Global Modeling and Assimilation Office(GMAO), the assimilation of aerosol observations is performed by means of a so-called analysis splitting method. In line with the transition of the GEOS meteorological data assimilation system to a hybrid Ensemble-Variational formulation, we are updating the aerosol component of our assimilation system to an ensemble square root filter(EnSRF; Whitaker and Hamill (2002)) type of scheme.We present a summary of our preliminary results of the assimilation of column integrated aerosol observations (Aerosol Optical Depth; AOD) using an Ensemble Square Root Filters (EnSRF) scheme and the ensemble members produced routinely by the meteorological assimilation.

MERRA-2 EnSRF↗

NASA NTRS2022

Investigation of the Potential Saturation of Information from Global Navigation Satellite System Radio Occultation Observations with an Observing System Simulation Experiment

The potential impact of large numbers of Global Navigation Satellite System radio occultation (GNSS-RO) observations on numerical weather prediction is investigated using a global observing system simulation experiment (OSSE). The hybrid four-dimensional ensemble variational Gridpoint Statistical Interpolation (GSI) data assimilation system and Global Earth Observing System (GEOS) model are used to ingest up to 100,000 GNSS-RO soundings per day in addition to the current suite of conventional and radiance data. Analysis quality, forecast skill, and forecast sensitivity to observation impact are examined with differing quantities of additional GNSS-RO profiles. It is found that saturation of information from additional RO soundings has not been reached with 100,000 soundings per day. There are some indications of suboptimal performance of the GSI in handling GNSS-RO observations particularly in the middle and lower tropospheric extratropics.

GNSS-RO↗

NASA NTRS1999

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Keppenne, Christian L.↗

NASA NTRS2011

Effect of Cross-Correlation on Geomagnetic Forecast Accuracies

Surface geomagnetic observation can determine up to degree L = 14 time-varying spherical harmonic coefficients of the poloidal magnetic field. Assimilation of these coefficients to numerical dynamo simulation could help us understand better the dynamical processes in the Earth's outer core, and to provide more accurate forecast of geomagnetic secular variations (SV). In our previous assimilation studies, only the poloidal magnetic field in the core is corrected by the observations in the analysis. Unobservable core state variables (the toroidal magnetic field and the core velocity field) are corrected via the dynamical equations of the geodynamo. Our assimilation experiments show that the assimilated core state converges near the CMB, implying that the dynamo state is strongly constrained by surface geomagnetic observations, and is pulled closer to the truth by the data. We are now carrying out an ensemble of assimilation runs with 1000 years of geomagnetic and archeo/paleo magnetic record. In these runs the cross correlation between the toroidal and the poloidal magnetic fields is incorporated into the analysis. This correlation is derived from the physical boundary conditions of the toroidal field at the core-mantle boundary (CMB). The assimilation results are then compared with those of the ensemble runs without the cross-correlation, aiming at understanding two fundamental issues: the effect of the crosscorrelation on (1) the convergence of the core state, and (2) the SV prediction accuracies. The constrained dynamo solutions will provide valuable insights on interpreting the observed SV, e.g. the near-equator magnetic flux patches, the core-mantle interactions, and possibly other geodynamic observables.

Kuang, Weijia↗

NASA NTRS2023

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

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

Soil moisture↗

NASA NTRS2018

Atmosphere-Ocean Coupled Data Assimilation Using NASA GEOS: Estimation of Air-Sea Interface State Variables

Air-sea interface variables, such as the skin Sea Surface Temperature (SST) are essential for atmosphere-ocean coupling. In the NASA GMAO Data Assimilation System (DAS), the skin SST and 3-D atmospheric state are jointly estimated [1]. This presentation is focused on the prior or background error covariance that is used in this analysis. The GEOS DAS uses an ensemble-variational assimilation strategy. In that, specification of a climatological background (CB) error covariance for SST relies on the NOAA's OI SST, with estimates of standard deviation and correlation length scales based on weekly analyses of the bulk SST at 1 degree resolution. However, present analysis system is striving to resolve SST diurnal variability with six hourly analyses and assimilates a vast number of in-situ and satellite observations. The first part of this presentation re-derives the CB error covariance using OSTIA SST analyses and illustrates the impact of this update on assimilating satellite observations. In a hybrid assimilation system the CB error covariances are appended with a flow-dependent background error covariance estimate implied by the underlying ensemble. The second part of this presentation refers to: a. treatment of the skin SST in the ensemble members, b. corresponding ensemble spread, and c. impact of these additions on the data assimilation system. [1] S. Akella, et al. (2017), doi:10.1002/qj.2988

Akella, Santha↗

NASA NTRSDate not supplied

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

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

GC99↗

NASA NTRS2013

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Data Assimilation↗

NASA NTRS2016

Benefit of Modeling the Observation Error in a Data Assimilation Framework Using Vegetation Information Obtained From Passive Based Microwave Data

A primary operational goal of the United States Department of Agriculture (USDA) is to improve foreign market access for U.S. agricultural products. A large fraction of this crop condition assessment is based on satellite imagery and ground data analysis. The baseline soil moisture estimates that are currently used for this analysis are based on output from the modified Palmer two-layer soil moisture model, updated to assimilate near-real time observations derived from the Soil Moisture Ocean Salinity (SMOS) satellite. The current data assimilation system is based on a 1-D Ensemble Kalman Filter approach, where the observation error is modeled as a function of vegetation density. This allows for offsetting errors in the soil moisture retrievals. The observation error is currently adjusted using Normalized Difference Vegetation Index (NDVI) climatology. In this paper we explore the possibility of utilizing microwave-based vegetation optical depth instead.

Vegetation↗

NASA NTRS2017

GEOS S2S-2_1: GMAO's New High Resolution Seasonal Prediction System

A new version of the modeling and analysis system used to produce sub-seasonal to seasonal forecasts has just been released by the NASA Goddard Global Modeling and Assimilation Office. The new version runs at higher atmospheric resolution (approximately 12 degree globally), contains a substantially improved model description of the cryosphere, and includes additional interactive earth system model components (aerosol model). In addition, the Ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter. Here will describe the new system, along with the plans for the future (GEOS S2S-3_0) which will include a higher resolution ocean model and more interactive earth system model components (interactive vegetation, biomass burning from fires). We will also present results from a free-running coupled simulation with the new system and results from a series of retrospective seasonal forecasts. Results from retrospective forecasts show significant improvements in surface temperatures over much of the northern hemisphere and a much improved prediction of sea ice extent in both hemispheres. The precipitation forecast skill is comparable to previous S2S systems, and the only trade off is an increased double ITCZ, which is expected as we go to higher atmospheric resolution.

Molod, Andrea↗

NASA NTRS2018

Sub-Seasonal Forecasting of the Stratospheric Wave Events, Sudden Stratospheric Warmings, and Their Influence on the Troposphere

Stratospheric wave events and major sudden stratospheric warming (SSW) events are well captured in high-resolution global forecasts out to 10 days. Tropospheric influences of SSW include statistically significant shifts in the storm tracks and associated surface temperature and precipitation pattern changes. Since these events can in turn influence the troposphere on time scales of 30-60 days the ability to predict these events and the subsequent long-term response on time scales beyond 10 days is of interest. Here we examine the prediction of stratospheric wave events and their evolution using the NASA GMAO (Global Modeling and Assimilation Office) Sub-Seasonal to Seasonal (S2S) system. This is a recently released subseasonal to seasonal forecast system, GEOS-S2S version 2.1. Compared to GMAO's previous system, the new version runs at higher atmospheric resolution (approximately 1/2 degree globally), contains a substantially improved model of the cryosphere, includes additional interactive aerosol model components, and the ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter. Results are based on a comprehensive series of hindcasts starting from the year 2000. They show that while the S2S system is not as accurate at 10 days in forecasting major SSW events as the NASA GMAO Forward Processing system, it can usefully predict stratospheric anomalies out to 20 days and the subsequent stratospheric/tropospheric evolution beyond 30 days.

Coy, L.↗

NASA NTRS2018

GEOS S2S-2_1: The GMAO High Resolution Seasonal Prediction System

A new version of the coupled modeling and analysis system used to produce near real time subseasonal to seasonal forecasts was recently released by the NASA/Goddard Global Modeling and Assimilation Office. The new version runs at higher atmospheric resolution than the previous, (approximately 1/2 degree globally), contains a substantially improved model description of the cryosphere, and includes additional interactive earth system model components (aerosol model). In addition, the Ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter, and now includes the assimilation of along-track sea surface height. Here will describe the new system, along with the plans for the future (GEOS S2S-3_0) which will include a higher resolution ocean model and more interactive earth system model components (interactive vegetation, biomass burning from fires). We will also present results from a series of retrospective seasonal forecasts. Results show significant improvements in surface temperatures over much of the northern hemisphere and a much improved prediction of sea ice extent in both hemispheres. Analysis of the ensemble spread shows improvements relative to the previous system, including generally better reliability. The precipitation forecast skill is comparable to previous S2S systems, and the only tradeoff is an increased "double ITCZ", which is expected as we go to higher atmospheric resolution.

Molod, Andrea↗

NASA NTRS2020

Impact of Satellite Microwave Radiance Data Assimilation on GEOS Atmospheric Analysis and Forecasts in Tropics

The NASA Global Modeling and Assimilation Office (GMAO) has developed a system to assimilate all-sky microwave radiance data in the Goddard Earth Observing System (GEOS). The system provides additional constraints on the analysis process near the storm regions and adjusts the geophysical parameters such as precipitation, cloud, moisture, surface pressure, and wind by combining information from microwave radiance measurements and model forecasts in an optimal manner. The system proved that assimilating the all-sky microwave radiance data improve the GEOS atmospheric analyses and forecasts. This all-sky data framework has been included in the GEOS Forward Processing (FP) system and currently assimilating all-sky GMI data in real-time for GEOS global analysis and forecast production at the GMAO. This presentation describes the methodologies to assimilate cloud- and precipitation-affected microwave radiances in GEOS data assimilation system based on hybrid four-dimensional ensemble-variational (4D-EnVar) configuration. In the current operational GEOS-FP system, the addition of all-sky GMI radiances has the largest impact in the Tropics. Specific humidity is significantly improved in the short term (0-72 hours) forecasts. Similar improvements are seen in the Tropical and lower tropospheric temperature and winds. More detailed results on all-sky microwave radiance data impact on GEOS analysis and forecasts are discussed in this presentation.

Kim, Min-Jeong↗

NASA NTRS2019

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydro-meteorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

radar backscatter↗

NASA NTRS2011

Multi-Scale Hydrometeorological Modeling, Land Data Assimilation and Parameter Estimation with the Land Information System

The Land Information System (LIS; http://lis.gsfc.nasa.gov) is a flexible land surface modeling framework that has been developed with the goal of integrating satellite-and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. As such, LIS represents a step towards the next generation land component of an integrated Earth system model. In recognition of LIS object-oriented software design, use and impact in the land surface and hydrometeorological modeling community, the LIS software was selected as a co-winner of NASA?s 2005 Software of the Year award.LIS facilitates the integration of observations from Earth-observing systems and predictions and forecasts from Earth System and Earth science models into the decision-making processes of partnering agency and national organizations. Due to its flexible software design, LIS can serve both as a Problem Solving Environment (PSE) for hydrologic research to enable accurate global water and energy cycle predictions, and as a Decision Support System (DSS) to generate useful information for application areas including disaster management, water resources management, agricultural management, numerical weather prediction, air quality and military mobility assessment. LIS has e volved from two earlier efforts -- North American Land Data Assimilation System (NLDAS) and Global Land Data Assimilation System (GLDAS) that focused primarily on improving numerical weather prediction skills by improving the characterization of the land surface conditions. Both of GLDAS and NLDAS now use specific configurations of the LIS software in their current implementations.In addition, LIS was recently transitioned into operations at the US Air Force Weather Agency (AFWA) to ultimately replace their Agricultural Meteorology (AGRMET) system, and is also used routinely by NOAA's National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC) for their land data assimilation systems to support weather and climate modeling. LIS not only consolidates the capabilities of these two systems, but also enables a much larger variety of configurations with respect to horizontal spatial resolution, input datasets and choice of land surface model through "plugins". LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling be enabling ensembles of land surface states to be tested against multiple representations of the atmospheric boundary layer. LIS has also been demonstrated for parameter estimation, who showed that the use of sequential remotely sensed soil moisture products can be used to derive soil hydraulic and texture properties given a sufficient dynamic range in the soil moisture retrievals and accurate precipitation inputs.LIS has also recently been demonstrated for multi-model data assimilation using an Ensemble Kalman Filter for sequential assimilation of soil moisture, snow, and temperature.Ongoing work has demonstrated the value of bias correction as part of the filter, and also that of joint calibration and assimilation.Examples and case studies demonstrating the capabilities and impacts of LIS for hydrometeorological modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems

Peters-Lidard, Christa D.↗

NASA NTRS2013

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

EnKR↗

NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗