Abstract
To simulate the large-scale impacts of wind farms, wind turbines are parameterized within mesoscale models in which grid sizes are typically much larger than turbine scales. Five wind-farm parameterizations were implemented in the Weather Research and Forecasting (WRF) model v4.3.3 to simulate multiple operational wind farms in the North Sea, which were verified against a satellite image, airborne measurements, and the FINO-1 meteorological mast data on 14 October 2017. The parameterization by Volker et al. underestimated turbulence and wind-speed deficit compared to measurements and to the parameterization of Fitch et al., which is the default in WRF. The Abkar and Porté-Agel parameterization gave close predictions of wind speed to that of Fitch et al. with lower magnitude of predicted turbulence, although the parameterization was sensitive to a tunable constant. The parameterization by Pan and Archer resulted in turbine-induced thrust and turbulence that were slightly less than that of Fitch et al., but resulted in a substantial drop in power generation due to the magnification of wind-speed differences in power calculation. The parameterization by Redfern et al. was not substantially different from Fitch et al. in the absence of conditions such as strong wind veer. The simulations indicated the need for a turbine-induced turbulence source within a wind-farm parameterization for improved prediction of near-surface wind speed, near-surface temperature, and turbulence. The induced turbulence was responsible for enhancing turbulent momentum flux near the surface, causing a local speed-up of near-surface wind speed inside a wind farm. Our findings highlighted that wakes from large offshore wind farms could extend 100 km downwind, reducing downwind power production as in the case of the 400-MW Bard Offshore 1 wind farm whose power output was reduced by the wakes of the 402-MW Veja Mate wind farm for this case study.
Abstract
To simulate the large-scale impacts of wind farms, wind turbines are parameterized within mesoscale models in which grid sizes are typically much larger than turbine scales. Five wind-farm parameterizations were implemented in the Weather Research and Forecasting (WRF) model v4.3.3 to simulate multiple operational wind farms in the North Sea, which were verified against a satellite image, airborne measurements, and the FINO-1 meteorological mast data on 14 October 2017. The parameterization by Volker et al. underestimated turbulence and wind-speed deficit compared to measurements and to the parameterization of Fitch et al., which is the default in WRF. The Abkar and Porté-Agel parameterization gave close predictions of wind speed to that of Fitch et al. with lower magnitude of predicted turbulence, although the parameterization was sensitive to a tunable constant. The parameterization by Pan and Archer resulted in turbine-induced thrust and turbulence that were slightly less than that of Fitch et al., but resulted in a substantial drop in power generation due to the magnification of wind-speed differences in power calculation. The parameterization by Redfern et al. was not substantially different from Fitch et al. in the absence of conditions such as strong wind veer. The simulations indicated the need for a turbine-induced turbulence source within a wind-farm parameterization for improved prediction of near-surface wind speed, near-surface temperature, and turbulence. The induced turbulence was responsible for enhancing turbulent momentum flux near the surface, causing a local speed-up of near-surface wind speed inside a wind farm. Our findings highlighted that wakes from large offshore wind farms could extend 100 km downwind, reducing downwind power production as in the case of the 400-MW Bard Offshore 1 wind farm whose power output was reduced by the wakes of the 402-MW Veja Mate wind farm for this case study.
Abstract
A severe derecho impacted the Midwestern United States on 10 August 2020, causing over 12 billion dollars in damage, and producing peak winds estimated at 63 m s−1, with the worst impacts in Iowa. The event was not forecast well by operational forecasters, nor even by operational and quasi-operational convection-allowing models.
In the present study, nine simulations are performed using the Limited Area Model version of the Finite-Volume-Cubed-Sphere model (FV3-LAM) with three horizontal grid spacings and two physics suites. In addition, when a prototype of the Rapid Refresh Forecast System (RRFS) physics is used, sensitivity tests are performed to examine the impact of using the Grell-Freitas (GF) convective scheme.
Several unusual results are obtained. With both the RRFS (not using GF) and Global Forecast System (GFS) physics suites, simulations using relatively coarse 13 and 25 km horizontal grid spacing do a much better job of showing an organized convective system in Iowa during the daylight hours of 10 August than the 3-km grid spacing runs. In addition, the RRFS run with 25-km grid spacing becomes much worse when the GF convective scheme is used. The 3-km RRFS run that does not use the GF scheme develops spurious nocturnal convection the night before the derecho, removing instability and preventing the derecho from being simulated at all. When GF is used, the spurious storms are removed and an excellent forecast is obtained with an intense bowing echo, exceptionally strong cold pool, and roughly 50 m s−1 surface wind gusts.
Abstract
A severe derecho impacted the Midwestern United States on 10 August 2020, causing over 12 billion dollars in damage, and producing peak winds estimated at 63 m s−1, with the worst impacts in Iowa. The event was not forecast well by operational forecasters, nor even by operational and quasi-operational convection-allowing models.
In the present study, nine simulations are performed using the Limited Area Model version of the Finite-Volume-Cubed-Sphere model (FV3-LAM) with three horizontal grid spacings and two physics suites. In addition, when a prototype of the Rapid Refresh Forecast System (RRFS) physics is used, sensitivity tests are performed to examine the impact of using the Grell-Freitas (GF) convective scheme.
Several unusual results are obtained. With both the RRFS (not using GF) and Global Forecast System (GFS) physics suites, simulations using relatively coarse 13 and 25 km horizontal grid spacing do a much better job of showing an organized convective system in Iowa during the daylight hours of 10 August than the 3-km grid spacing runs. In addition, the RRFS run with 25-km grid spacing becomes much worse when the GF convective scheme is used. The 3-km RRFS run that does not use the GF scheme develops spurious nocturnal convection the night before the derecho, removing instability and preventing the derecho from being simulated at all. When GF is used, the spurious storms are removed and an excellent forecast is obtained with an intense bowing echo, exceptionally strong cold pool, and roughly 50 m s−1 surface wind gusts.
Abstract
A scale-dependent dynamic Smagorinsky model is implemented in the Met Office/NERC Cloud (MONC) model using two averaging flavors, along Lagrangian pathlines and local moving averages. The dynamic approaches were compared against the conventional Smagorinsky–Lilly scheme in simulating the diurnal cycle of shallow cumulus convection. The simulations spanned from the LES to the near-gray-zone and gray-zone resolutions and revealed the adaptability of the dynamic model across the scales and different stability regimes. The dynamic model can produce a scale- and stability-dependent profile of the subfilter turbulence length scale across the chosen resolution range. At gray-zone resolutions the adaptive length scales can better represent the early precloud boundary layer leading to temperature and moisture profiles closer to the LES compared to the standard Smagorinsky. As a result, the initialization and general representation of the cloud field in the dynamic model is in good agreement with the LES. In contrast, the standard Smagorinsky produces a less well-mixed boundary layer, which fails to ventilate moisture from the boundary layer, resulting in the delayed spinup of the cloud layer. Moreover, strong downgradient diffusion controls the turbulent transport of scalars in the cloud layer. However, the dynamic approaches rely on the resolved field to account for nonlocal transports, leading to overenergetic structures when the boundary layer is fully developed and the Lagrangian model is used. Introducing the local averaging version of the model or adopting a new Lagrangian time scale provides stronger dissipation without significantly affecting model behavior.
Abstract
A scale-dependent dynamic Smagorinsky model is implemented in the Met Office/NERC Cloud (MONC) model using two averaging flavors, along Lagrangian pathlines and local moving averages. The dynamic approaches were compared against the conventional Smagorinsky–Lilly scheme in simulating the diurnal cycle of shallow cumulus convection. The simulations spanned from the LES to the near-gray-zone and gray-zone resolutions and revealed the adaptability of the dynamic model across the scales and different stability regimes. The dynamic model can produce a scale- and stability-dependent profile of the subfilter turbulence length scale across the chosen resolution range. At gray-zone resolutions the adaptive length scales can better represent the early precloud boundary layer leading to temperature and moisture profiles closer to the LES compared to the standard Smagorinsky. As a result, the initialization and general representation of the cloud field in the dynamic model is in good agreement with the LES. In contrast, the standard Smagorinsky produces a less well-mixed boundary layer, which fails to ventilate moisture from the boundary layer, resulting in the delayed spinup of the cloud layer. Moreover, strong downgradient diffusion controls the turbulent transport of scalars in the cloud layer. However, the dynamic approaches rely on the resolved field to account for nonlocal transports, leading to overenergetic structures when the boundary layer is fully developed and the Lagrangian model is used. Introducing the local averaging version of the model or adopting a new Lagrangian time scale provides stronger dissipation without significantly affecting model behavior.
Abstract
Recent studies suggest that the eddy kinetic energy is localized in the lee of significant topographic features in the Antarctic Circumpolar Current (ACC). Here we explore the importance of the local dynamics quantitatively using the outputs from the realistic ocean general circulation model hindcast with the aid of the modified Lorentz energy cycle. Results confirm the importance of energy transfer among reservoirs in the downstream region of standing meanders, showing that the major five standing meanders are responsible for more than 70% of the kinetic energy transfer to eddies and dissipation over the Antarctic Circumpolar Current region. The eddy kinetic energy is generated in the upper 3000-m depth downstream of the standing meanders and transported due to the vertical energy redistribution governed by the vertical pressure flux toward the deeper layer where the eddy energy is dissipated. Moreover, we also calculate the work done by the Ekman transport to confirm that the wind energy input works as the dominant energy source for the baroclinic energy pathway. The advantage of this quantity against the vertical mean density flux is that it is independent of the reference states defined arbitrarily. It is shown that the westerlies can supply sufficient energy locally to initiate baroclinic instability in the Indian and Pacific sectors of the ACC, whereas the nonlocal process is important in the Atlantic sector. Our results suggest that the five narrow regions associated with significant topography play key roles in the energy balance of the ACC region.
Significance Statement
The purpose of this study is to understand the eddy–mean flow interactions in the Antarctic Circumpolar Current from the energetic viewpoint. Our results show that the five narrow regions called “hotspots” in our study are responsible for the energy transfer from the mean flow to eddies. It is also found that the hotspots are important for the energy sink in the Southern Ocean. These findings suggest that the five hotspots are likely to play key roles in the responses of the Antarctic Circumpolar Current to the changes in westerlies in these decades.
Abstract
Recent studies suggest that the eddy kinetic energy is localized in the lee of significant topographic features in the Antarctic Circumpolar Current (ACC). Here we explore the importance of the local dynamics quantitatively using the outputs from the realistic ocean general circulation model hindcast with the aid of the modified Lorentz energy cycle. Results confirm the importance of energy transfer among reservoirs in the downstream region of standing meanders, showing that the major five standing meanders are responsible for more than 70% of the kinetic energy transfer to eddies and dissipation over the Antarctic Circumpolar Current region. The eddy kinetic energy is generated in the upper 3000-m depth downstream of the standing meanders and transported due to the vertical energy redistribution governed by the vertical pressure flux toward the deeper layer where the eddy energy is dissipated. Moreover, we also calculate the work done by the Ekman transport to confirm that the wind energy input works as the dominant energy source for the baroclinic energy pathway. The advantage of this quantity against the vertical mean density flux is that it is independent of the reference states defined arbitrarily. It is shown that the westerlies can supply sufficient energy locally to initiate baroclinic instability in the Indian and Pacific sectors of the ACC, whereas the nonlocal process is important in the Atlantic sector. Our results suggest that the five narrow regions associated with significant topography play key roles in the energy balance of the ACC region.
Significance Statement
The purpose of this study is to understand the eddy–mean flow interactions in the Antarctic Circumpolar Current from the energetic viewpoint. Our results show that the five narrow regions called “hotspots” in our study are responsible for the energy transfer from the mean flow to eddies. It is also found that the hotspots are important for the energy sink in the Southern Ocean. These findings suggest that the five hotspots are likely to play key roles in the responses of the Antarctic Circumpolar Current to the changes in westerlies in these decades.
Abstract
The energy and momentum balance of an abyssal overflow across a major sill in the Samoan Passage is estimated from two highly resolved towed sections, set 16 months apart, and results from a two-dimensional numerical simulation. Driven by the density anomaly across the sill, the flow is relatively steady. The system gains energy from divergence of horizontal pressure work
Abstract
The energy and momentum balance of an abyssal overflow across a major sill in the Samoan Passage is estimated from two highly resolved towed sections, set 16 months apart, and results from a two-dimensional numerical simulation. Driven by the density anomaly across the sill, the flow is relatively steady. The system gains energy from divergence of horizontal pressure work
Abstract
The high-resolution mooring observations reported here reveal a cascade process from internal solitary waves (ISWs) to turbulent mixing via high-frequency internal waves near the maximum local buoyancy frequency (near-N waves) in the deep water of the northern South China Sea (SCS). Riding on the parent ISW, near-N waves with a peak frequency of 20 cph emerged at the trough of the ISW and extended to the rear face of the ISW. Most of the near-N waves occurred around the thermocline, where the isothermal displacements induced by the near-N waves were largest with an amplitude of 12 m. The energy of near-N waves was 5% of that of the parent ISW, and instability investigations showed that due to the strong shear, Ri in the region of strong near-N waves was less than 1/4, suggesting that the near-N waves were unstable and might dissipate rapidly. Simulations based on the Korteweg–de Vries (KdV)–Burgers equation reproduced the formation of observed near-N waves due to the energy cascade from ISWs. Our observational results demonstrate a new energy cascade route from ISWs to turbulence in the deep water, deepening the understanding of the energy dissipation process of ISWs and their roles in the enhanced mixing in the northern SCS.
Abstract
The high-resolution mooring observations reported here reveal a cascade process from internal solitary waves (ISWs) to turbulent mixing via high-frequency internal waves near the maximum local buoyancy frequency (near-N waves) in the deep water of the northern South China Sea (SCS). Riding on the parent ISW, near-N waves with a peak frequency of 20 cph emerged at the trough of the ISW and extended to the rear face of the ISW. Most of the near-N waves occurred around the thermocline, where the isothermal displacements induced by the near-N waves were largest with an amplitude of 12 m. The energy of near-N waves was 5% of that of the parent ISW, and instability investigations showed that due to the strong shear, Ri in the region of strong near-N waves was less than 1/4, suggesting that the near-N waves were unstable and might dissipate rapidly. Simulations based on the Korteweg–de Vries (KdV)–Burgers equation reproduced the formation of observed near-N waves due to the energy cascade from ISWs. Our observational results demonstrate a new energy cascade route from ISWs to turbulence in the deep water, deepening the understanding of the energy dissipation process of ISWs and their roles in the enhanced mixing in the northern SCS.
Flippin’
χ
SOLO, an Upper-Ocean Autonomous Turbulence-Profiling FloatAbstract
A new autonomous turbulence profiling float has been designed, built, and tested in field trials off Oregon. Flippin’ χSOLO (FχS) employs a SOLO-II buoyancy engine that not only changes but also shifts ballast to move the center of mass to positions on either side of the center of buoyancy, thus causing FχS to flip. FχS is outfitted with a full suite of turbulence sensors—two shear probes, two fast thermistors, and pitot tube, as well as a pressure sensor and three-axis linear accelerometers. FχS descends and ascends with turbulence sensors leading, thereby permitting measurement through the sea surface. The turbulence sensors are housed antipodal from communication antennas so as to eliminate flow disturbance. By flipping at the sea surface, antennas are exposed for communications. The mission of FχS is to provide intensive profiling measurements of the upper ocean from 240 m and through the sea surface, particularly during periods of extreme surface forcing. While surfaced, accelerometers provide estimates of wave height spectra and significant wave height. From 3.5 day field trials, here we evaluate (i) the statistics from two FχS units and our established shipboard profiler, Chameleon, and (ii) FχS-based wave statistics by comparison to a nearby NOAA wave buoy.
Significance Statement
The oceanographic fleet of Argo autonomous profilers yields important data that define the state of the ocean’s interior. Continued deployments over time define the evolution of the ocean’s interior. A significant next step will be to include turbulence measurements on these profilers, leading to estimates of thermodynamic mixing rates that predict future states of the ocean’s interior. An autonomous turbulence profiler that employs the buoyancy engine, mission logic, and remote communication of one particular Argo float is described herein. The Flippin’ χSOLO is an upper-ocean profiler tasked with rapid and continuous profiling of the upper ocean during weather conditions that preclude shipboard profiling and that includes the upper 10 m that is missed by shipboard turbulence profilers.
Abstract
A new autonomous turbulence profiling float has been designed, built, and tested in field trials off Oregon. Flippin’ χSOLO (FχS) employs a SOLO-II buoyancy engine that not only changes but also shifts ballast to move the center of mass to positions on either side of the center of buoyancy, thus causing FχS to flip. FχS is outfitted with a full suite of turbulence sensors—two shear probes, two fast thermistors, and pitot tube, as well as a pressure sensor and three-axis linear accelerometers. FχS descends and ascends with turbulence sensors leading, thereby permitting measurement through the sea surface. The turbulence sensors are housed antipodal from communication antennas so as to eliminate flow disturbance. By flipping at the sea surface, antennas are exposed for communications. The mission of FχS is to provide intensive profiling measurements of the upper ocean from 240 m and through the sea surface, particularly during periods of extreme surface forcing. While surfaced, accelerometers provide estimates of wave height spectra and significant wave height. From 3.5 day field trials, here we evaluate (i) the statistics from two FχS units and our established shipboard profiler, Chameleon, and (ii) FχS-based wave statistics by comparison to a nearby NOAA wave buoy.
Significance Statement
The oceanographic fleet of Argo autonomous profilers yields important data that define the state of the ocean’s interior. Continued deployments over time define the evolution of the ocean’s interior. A significant next step will be to include turbulence measurements on these profilers, leading to estimates of thermodynamic mixing rates that predict future states of the ocean’s interior. An autonomous turbulence profiler that employs the buoyancy engine, mission logic, and remote communication of one particular Argo float is described herein. The Flippin’ χSOLO is an upper-ocean profiler tasked with rapid and continuous profiling of the upper ocean during weather conditions that preclude shipboard profiling and that includes the upper 10 m that is missed by shipboard turbulence profilers.
Abstract
A new set of CMIP6 data downscaled using the localized constructed analogs (LOCA) statistical method has been produced, covering central Mexico through southern Canada at 6-km resolution. Output from 27 CMIP6 Earth system models is included, with up to 10 ensemble members per model and 3 SSPs (245, 370, and 585). Improvements from the previous CMIP5 downscaled data result in higher daily precipitation extremes, which have significant societal and economic implications. The improvements are accomplished by using a precipitation training dataset that better represents daily extremes and by implementing an ensemble bias correction that allows a more realistic representation of extreme high daily precipitation values in models with numerous ensemble members. Over southern Canada and the CONUS exclusive of Arizona (AZ) and New Mexico (NM), seasonal increases in daily precipitation extremes are largest in winter (∼25% in SSP370). Over Mexico, AZ, and NM, seasonal increases are largest in autumn (∼15%). Summer is the outlier season, with low model agreement except in New England and little changes in 5-yr return values, but substantial increases in the CONUS and Canada in the 500-yr return value. One-in-100-yr historical daily precipitation events become substantially more frequent in the future, as often as once in 30–40 years in the southeastern United States and Pacific Northwest by the end of the century under SSP 370. Impacts of the higher precipitation extremes in the LOCA version 2 downscaled CMIP6 product relative to the LOCA downscaled CMIP5 product, even for similar anthropogenic emissions, may need to be considered by end-users.
Abstract
A new set of CMIP6 data downscaled using the localized constructed analogs (LOCA) statistical method has been produced, covering central Mexico through southern Canada at 6-km resolution. Output from 27 CMIP6 Earth system models is included, with up to 10 ensemble members per model and 3 SSPs (245, 370, and 585). Improvements from the previous CMIP5 downscaled data result in higher daily precipitation extremes, which have significant societal and economic implications. The improvements are accomplished by using a precipitation training dataset that better represents daily extremes and by implementing an ensemble bias correction that allows a more realistic representation of extreme high daily precipitation values in models with numerous ensemble members. Over southern Canada and the CONUS exclusive of Arizona (AZ) and New Mexico (NM), seasonal increases in daily precipitation extremes are largest in winter (∼25% in SSP370). Over Mexico, AZ, and NM, seasonal increases are largest in autumn (∼15%). Summer is the outlier season, with low model agreement except in New England and little changes in 5-yr return values, but substantial increases in the CONUS and Canada in the 500-yr return value. One-in-100-yr historical daily precipitation events become substantially more frequent in the future, as often as once in 30–40 years in the southeastern United States and Pacific Northwest by the end of the century under SSP 370. Impacts of the higher precipitation extremes in the LOCA version 2 downscaled CMIP6 product relative to the LOCA downscaled CMIP5 product, even for similar anthropogenic emissions, may need to be considered by end-users.
Abstract
Coupled data assimilation (CDA), which combines coupled models and observations from multiple Earth system domains, plays a critical role in climate studies by producing a four-dimensional estimation of Earth system states. Traditional ensemble Kalman filter (EnKF) CDA algorithms, while convenient to implement in multiple DA components in a coupled system, are however expensive and lack sufficient representativeness for low-frequency background flows. Here, a Multi-timeScale High-Efficiency Approximate filter with EnOI (MSHea-EnOI) scheme has been implemented with a global fully coupled model. It consists of stationary, low-frequency, and high-frequency filters constructed from the time series of a single-model solution with improved representativeness for low-frequency background error statistics and enhanced computational efficiency. The MSHea-EnOI is evaluated in a biased twin experiment framework with synthetic “observations” produced by another coupled model, and a three-decade coupled reanalysis experiment with real observations. Results show that with increased representativeness on multiscale background flows, while computationally costing only a small fraction of ensemble-based CDA, the MSHea-EnOI shows the potential to improve CDA quality with synthetic observations. The coupled reanalysis experiment with real observations also shows reasonable fittings to observations and comparable results to other reanalysis products using different DA schemes. While reconstructing a close-to-Rapid Atlantic meridional overturning circulation, the coupled reanalysis reproduces most of the atmosphere and ocean reanalysis signals such as the Hadley circulation and upper ocean heat content. The MSHea-EnOI could have good application potential in ensemble-based DA systems in terms of its multiscale property and computational efficiency.
Abstract
Coupled data assimilation (CDA), which combines coupled models and observations from multiple Earth system domains, plays a critical role in climate studies by producing a four-dimensional estimation of Earth system states. Traditional ensemble Kalman filter (EnKF) CDA algorithms, while convenient to implement in multiple DA components in a coupled system, are however expensive and lack sufficient representativeness for low-frequency background flows. Here, a Multi-timeScale High-Efficiency Approximate filter with EnOI (MSHea-EnOI) scheme has been implemented with a global fully coupled model. It consists of stationary, low-frequency, and high-frequency filters constructed from the time series of a single-model solution with improved representativeness for low-frequency background error statistics and enhanced computational efficiency. The MSHea-EnOI is evaluated in a biased twin experiment framework with synthetic “observations” produced by another coupled model, and a three-decade coupled reanalysis experiment with real observations. Results show that with increased representativeness on multiscale background flows, while computationally costing only a small fraction of ensemble-based CDA, the MSHea-EnOI shows the potential to improve CDA quality with synthetic observations. The coupled reanalysis experiment with real observations also shows reasonable fittings to observations and comparable results to other reanalysis products using different DA schemes. While reconstructing a close-to-Rapid Atlantic meridional overturning circulation, the coupled reanalysis reproduces most of the atmosphere and ocean reanalysis signals such as the Hadley circulation and upper ocean heat content. The MSHea-EnOI could have good application potential in ensemble-based DA systems in terms of its multiscale property and computational efficiency.
Abstract
Probabilistic forecasting is a common activity in many fields of the Earth sciences. Assessing the quality of probabilistic forecasts—probabilistic forecast verification—is therefore an essential task in these activities. Numerous methods and metrics have been proposed for this purpose; however, the probabilistic verification of vector variables of ensemble forecasts has received less attention than others. Here we introduce a new approach that is applicable for verifying ensemble forecasts of continuous, scalar and two-dimensional vector data. The proposed method uses a fixed radius near-neighbors search to compute two information-based scores, the ignorance score (the logarithmic score) and the information gain, which quantifies the skill gain from the reference forecast. Basic characteristics of the proposed scores were examined using idealized Monte Carlo simulations. The results indicated that both the Continuous Ranked Probability Score (CRPS) and the proposed score with a relatively small ensemble size (< 25) are not proper in terms of the forecast dispersion. The proposed verification method was successfully used to verify the Madden-Julian Oscillation index, which is a two-dimensional quantity. The proposed method is expected to advance probabilistic ensemble forecasts in various fields.
Abstract
Probabilistic forecasting is a common activity in many fields of the Earth sciences. Assessing the quality of probabilistic forecasts—probabilistic forecast verification—is therefore an essential task in these activities. Numerous methods and metrics have been proposed for this purpose; however, the probabilistic verification of vector variables of ensemble forecasts has received less attention than others. Here we introduce a new approach that is applicable for verifying ensemble forecasts of continuous, scalar and two-dimensional vector data. The proposed method uses a fixed radius near-neighbors search to compute two information-based scores, the ignorance score (the logarithmic score) and the information gain, which quantifies the skill gain from the reference forecast. Basic characteristics of the proposed scores were examined using idealized Monte Carlo simulations. The results indicated that both the Continuous Ranked Probability Score (CRPS) and the proposed score with a relatively small ensemble size (< 25) are not proper in terms of the forecast dispersion. The proposed verification method was successfully used to verify the Madden-Julian Oscillation index, which is a two-dimensional quantity. The proposed method is expected to advance probabilistic ensemble forecasts in various fields.
