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At least 271 records · Page 15

Stochastic Models of Tropical Rain-Rate Fields

Because of the extreme variability of rain rate in space and time and the difficulties with remote sensing methods of measuring rain rates, accurate determination of rainfall over large areas and time periods has long been a problem for hydrologists, meteorogists, and climatologists. A number of statistical models of rain have been developed in order to investigate the impact of rain variability on satellite remote sensing methods, validation of satellite rain products, and generation of rain maps with accompanying error estimates. These models may be useful in examining 'sub-grid scale' issues in representing precipitation in numerical mdoels. A stochastic model will first be described which can generate time-dependent high-resolution spatial rain fields with space and time correlations similar to those seen in rain data, as well as representing the presence of areas with zero rain rate and log-normally distributed rain rates where there is rain. A simpler model derived from this, formulated in the spectral domain, seems to imply fractal-like rain statistics at small scales when fit to rain data.

Bell, Thomas L.↗

Microphysics, Radiation and Surface Processes in the Goddard Cumulus Ensemble (GCE) Model

One of the most promising methods to test the representation of cloud processes used in climate models is to use observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and realistic representations of cloud microphysical processes, and they can reasonably well resolve the time evolution, structure, and life cycles of clouds and cloud systems (size about 2-200 km). The CRMs also allow explicit interaction between out-going longwave (cooling) and in-coming solar (heating) radiation with clouds. Observations can provide the initial conditions and validation for CRM results. The Goddard Cumulus Ensemble (GCE) Model, a CRM, has been developed and improved at NASA/Goddard Space Flight Center over the past two decades. The GCE model has been used to understand the following: 1) water and energy cycles and their roles in the tropical climate system; 2) the vertical redistribution of ozone and trace constituents by individual clouds and well organized convective systems over various spatial scales; 3) the relationship between the vertical distribution of latent heating (phase change of water) and the large-scale (pre-storm) environment; 4) the validity of assumptions used in the representation of cloud processes in climate and global circulation models; and 5) the representation of cloud microphysical processes and their interaction with radiative forcing over tropical and midlatitude regions. Four-dimensional cloud and latent heating fields simulated from the GCE model have been provided to the TRMM Science Data and Information System (TSDIS) to develop and improve algorithms for retrieving rainfall and latent heating rates for TRMM and the NASA Earth Observing System (EOS). More than 90 referred papers using the GCE model have been published in the last two decades. Also, more than 10 national and international universities are currently using the GCE model for research and teaching. In this talk, five specific major GCE improvements: (1) ice microphysics, (2) longwave and shortwave radiative transfer processes, (3) land surface processes, (4) ocean surface fluxes and (5) ocean mixed layer processes are presented. The performance of these new GCE improvements will be examined. Observations are used for model validation.

Tao, Wei-Kuo↗

Effects of Nonuniform Beam Filling on Rainfall Retrieval for the TRMM Precipitation Radar

The Tropical Rainfall Measuring Mission (TRMM) will carry the first spaceborne radar for rainfall observation. Because the TRMM Precipitation Radar (PR) footprint size of 4.3 km is greater than the scale of some convective rainfall events, there is concern that nonuniform filling of the PR antenna beam may bias the retrieved rain-rate profile. The authors investigate this effect theoretically and then observationally using data from the NASA Jet Propulsion Laboratory Airborne Rain Mapping Radar (ARMAR), acquired during Tropical Oceans Global Atmosphere Coupled Ocean Atmosphere Response Experiment in early 1993. The authors' observational approach is to simulate TRMM PR data using the ARMAR data and compare the radar observables and retrieved rain rate from the simulated PR data with those corresponding to the high-resolution radar measurements. The authors find that the path-integrated attenuation and the resulting path-averaged rain rate are underestimated. The reflectivity and rain rate near the top of the rainfall column are overestimated. The near-surface reflectivity can be overestimated or underestimated, with a mean error very close to zero. The near-surface rain rate, however, is usually underestimated, sometimes severely.

Durden, Stephen L.↗

The ground truth analysis of rain gauge data for the TRMM project

As a part of the Tropical Rainfall Measuring Missioin (TRMM) ground truth program to determine the diurnal variability of the area wide rain rates, the rain rate PDFs, and their effect on the area integral algorithm, rain rate data have been collected from a network of gages located in the area near the Cape Canaveral and Kennedy Space Center, in the period beginning in September 1987. In the preliminary statistical analysis, based on the rain rates derived from the eleven gages, the seasonal diurnal rainfall and network averaged rain rates are determined. The analysis was performed in two steps: determination of the hourly and daily rain accumulations and rain rates; and computation of the fraction of hourly and daily rain rates that exceed a particular threshold, and analysis of the hourly and daily rain rate PDFs for the network. The results indicate that there are diurnal and seasonal variations in the components which determine the network rain rate PDFs.

Kowalewsky, Karen J.↗

Sampling error study for rainfall estimate by satellite using a stochastic model

In a parameter study of satellite orbits, sampling errors of area-time averaged rain rate due to temporal sampling by satellites were estimated. The sampling characteristics were studied by accounting for the varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates. For a satellite of nominal Tropical Rainfall Measuring Mission (Thiele, 1987) carrying an ideal scanning microwave radiometer for precipitation measurements, it is found that sampling error would be about 8 to 12 pct of estimated monthly mean rates over a grid box of 5 X 5 degrees. It is suggested that an observation system based on a low inclination satellite combined with a sunsynchronous satellite simultaneously might be the best candidate for making precipitation measurements from space.

Shin, Kyung-Sup↗

Weekend Effect" in Summertime U.S. Rainfall: Evidence for Midweek Intensification of Storms by Pollution

Persistent and strong dependence of rain rate on the day of the week has been found in Tropical Rainfall Measuring Mission (TRMM) satellite estimates of summer afternoon rainfall over the southeast U.S. and the nearby Atlantic from 1998 to 2005. Midweek (Tue-Thu) rain rates and rain area appear to increase over land, and this increase is accompanied by a corresponding diminution of rainfall over nearby waters. Reanalysis data from atmospheric models, suggest that there is a corresponding weekly variation in atmospheric winds consistent with the changes in rainfall. These variations are almost certainly caused by weekly variations in human activity. The most likely cause of the observed changes in rainfall is the well documented weekly variation in atmospheric pollution. Particulate pollution is highest in the middle of the week. Considerable observational and modeling evidence has accumulated concerning the effects of aerosols on precipitation. Most of this evidence relates to the suppression of precipitation by aerosols, but it has been argued that storms in highly unstable moist environments can be invigorated by aerosols, and some modeling studies seem to confirm this. The strong weekly cycle in rainfall observed over the southeast U.S. along with what appears to be dynamical suppression of rainfall over the nearby Atlantic, and the lack of an observable cycle over the southwest U.S., are consistent with this theory.

Bell, Thomas L.↗

GPM Mission Overview

The Global Precipitation Measurement (GPM) Mission is an international satellite mission to unify and advance precipitation measurements from a constellation of research and operational sensors to provide "next-generation" precipitation products. Relative to current global rainfall products, GPM data products will be characterized by: (1) more accurate instantaneous precipitation measurements (especially for light rain and cold-season solid/snow precipitation), (2) more frequent sampling by an expanded constellation of microwave radiometers that include operational humidity sounders over land, (3) inter-calibrated microwave brightness temperatures from constellation radiometers within a unified framework, and (4) physical-based precipitation retrievals from constellation radiometers using a common a priori cloud hydrometeor database derived from GPM Core sensor measurements. The cornerstone of the GPM mission is the deployment of a Core Observatory in a unique 65 degree non-Sun-synchronous orbit to serve as a physics observatory and a calibration reference to improve precipitation measurements by a constellation of dedicated and operational passive microwave sensors. The Core Observatory will carry a KulKa-band Dual-frequency Precipitation Radar (DPR) and a multi-channel (10-183 GHz) GPM Microwave Radiometer (GMI). The combined use ofDPR and GMI measurements will place greater constraints on possible solutions to radiometer retrievals to improve the accuracy and consistency of precipitation retrievals from all constellation radiometers. As a science mission with integrated application goals, GPM is designed to (1) advance precipitation measurement capability from space through combined use of active and passive microwave sensors, (2) advance the knowledge of the global water/energy cycle and freshwater availability through better description of the space-time variability of global precipitation, and (3) improve weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of instantaneous precipitation rates and time-integrated rainfall accumulation. An overview of the GPM mission concept and science activities in the United States, together with an update on international collaborations in radiometer intercalibration and ground validation, will be presented.

Hou, Arthur Y.↗

Evidence of Convective Redistribution of Carbon Monoxide in Aura Tropospheric Emission Sounder (TES) and Microwave Limb Sounder (MLS) Observations

Vertical convective transport is a key element of the tropospheric circulation. Convection lofts air from the boundary layer into the free troposphere, allowing surface emissions to travel much further, and altering the rate of chemical processes such as ozone production. This study uses satellite observations to focus on the convective transport of CO from the boundary layer to the mid and upper troposphere. Our hypothesis is that strong convection associated with high rain rate regions leads to a correlation between mid level and upper level CO amounts. We first test this hypothesis using the Global Modeling Initiative (GMI) chemistry and transport model. We find the correlation is robust and increases as the precipitation rate (the strength of convection) increases. We next examine three years of CO profiles from the Tropospheric Emission Sounder (TES) and Microwave Limb Sounder (MLS) instruments aboard EOS Aura. Rain rates are taken from the Tropical Rainfall Measuring Mission (TRMM) 3B-42 multi-satellite product. Again we find a correlation between mid-level and upper tropospheric CO, which increases with rain rate. Our result shows the critical importance of tropical convection in coupling vertical levels of the troposphere in the transport of trace gases. The effect is seen most clearly in strong convective regions such as the Inter-tropical Convergence Zone.

Manyin, Michael↗

A model for estimating time-variant rainfall infiltration as a function of antecedent surface moisture and hydrologic soil type

Recent research indicates that the use of remote sensing techniques for the measurement of near surface soil moisture could be practical in the not too distant future. Other research shows that infiltration rates, especially for average or frequent rainfall events, are extremely sensitive to the proper definition and consideration of the role of the soil moisture at the beginning of the rainfall. Thus, it is important that an easy to use, but theoretically sound, rainfall infiltration model be available if the anticipated remotely sensed soil moisture data is to be optimally utilized for hydrologic simulation. A series of numerical experiments with the Richards' equation for an array of conditions anticipated in watershed hydrology were used to develop functional relationships that describe temporal infiltration rates as a function of soil type and initial moisture conditions.

Wilkening, H. A.↗

Hydrometeor Size Distribution Measurements by Imaging the Attenuation of a Laser Spot

The optical extinction of a laser due to scattering of particles is a well-known phenomenon. In a laboratory environment, this physical principle is known as the Beer-Lambert law, and is often used to measure the concentration of scattering particles in a fluid or gas. This method has been experimentally shown to be a usable means to measure the dust density from a rocket plume interaction with the lunar surface. Using the same principles and experimental arrangement, this technique can be applied to hydrometeor size distributions, and for launch-pad operations, specifically as a passive hail detection and measurement system. Calibration of a hail monitoring system is a difficult process. In the past, it has required comparison to another means of measuring hydrometeor size and density. Using a technique recently developed for estimating the density of surface dust dispersed during a rocket landing, measuring the extinction of a laser passing through hail (or dust in the rocket case) yields an estimate of the second moment of the particle cloud, and hydrometeor size distribution in the terrestrial meteorological case. With the exception of disdrometers, instruments that measure rain and hail fall make indirect measurements of the drop-size distribution. Instruments that scatter microwaves off of hydrometeors, such as the WSR-88D (Weather Surveillance Radar 88 Doppler), vertical wind profilers, and microwave disdrometers, measure the sixth moment of the drop size distribution (DSD). By projecting a laser onto a target, changes in brightness of the laser spot against the target background during rain and hail yield a measurement of the DSD's second moment by way of the Beer-Lambert law. In order to detect the laser attenuation within the 8-bit resolution of most camera image arrays, a minimum path length is required. Depending on the intensity of the hail fall rate for moderate to heavy rainfall, a laser path length of 100 m is sufficient to measure variations in optical extinction using a digital camera. For hail fall only, the laser path may be shorter because of greater scattering due to the properties of hailstones versus raindrops. A photodetector may replace the camera in automated installations. Laser-based rain and hail measurement systems are available, but they are based on measuring the interruption of a thin laser beam, thus counting individual hydrometeors. These systems are true disdrometers since they also measure size and velocity. The method reported here is a simple method, requiring far less processing, but it is not a disdrometer.

Lane, John↗

TRMM Microwave Radiometer Rain Rate Estimation Method with Convective and Stratiform Discrimination

Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima (T85min) in a regional map containing a Mesoscale Convective System (MCS). A map of surface rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85min, produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we have developed a TMI algorithm to retrieve convective and stratiform rain. In this algorithm, two parameters are used to classify three kinds of thunderstorms (Cbs) based on the T85 data: a) the magnitude of scattering depression deduced from local T85mi, and b) the mean horizontal gradient of T85 around such minima. Initially, the algorithm is optimized or tuned utilizing the PR and TMI data of a few MCS events. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (greater than or equal to 20 mm/hr) rain rates are retrieved on the average with an accuracy of about 15%. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.

Prabhakara, Cuddapah↗

A TRMM Rainfall Estimation Method Applicable to Land Areas

Methods developed to estimate rain rate on a footprint scale over land with the satellite-borne multispectral dual-polarization Special Sensor Microwave Imager (SSM/1) radiometer have met with limited success. Variability of surface emissivity on land and beam filling are commonly cited as the weaknesses of these methods. On the contrary, we contend a more significant reason for this lack of success is that the information content of spectral and polarization measurements of the SSM/I is limited. because of significant redundancy. As a result, the complex nature and vertical distribution C, of frozen and melting ice particles of different densities, sizes, and shapes cannot resolved satisfactorily. Extinction in the microwave region due to these complex particles can mask the extinction due to rain drops. Because of these reasons, theoretical models that attempt to retrieve rain rate do not succeed on a footprint scale. To illustrate the weakness of these models, as an example we can consider the brightness temperature measurement made by the radiometer in the 85 GHz channel (T85). Models indicate that T85 should be inversely related to the rain rate, because of scattering. However, rain rate derived from 15-minute rain gauges on land indicate that this is not true in a majority of footprints. This is also supported by the ship-borne radar observations of rain in the Tropical Oceans and Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA-COARE) region over the ocean. Based on these observations. we infer that theoretical models that attempt to retrieve rain rate do not succeed on a footprint scale. We do not follow the above path of rain retrieval on a footprint scale. Instead, we depend on the limited ability of the microwave radiometer to detect the presence of rain. This capability is useful to determine the rain area in a mesoscale region. We find in a given rain event that this rain area is closely related to the mesoscale-average rain rate. Based on this observation, in this study we have developed a method to estimate the mesoscale-average rain rate over land utilizing microwave radiometer data. Because of the high degree of geographic and seasonal variability in the nature and intensity of rain, this method requires some tuning with 15-minute rain gauge data on land. After tuning the method, it can be applied to an independent set of rain events that are close in time and space. We find that the mesoscale rain rates retrieved over the period of a month on land with this method shows a correlation of about 0.85 with respect to the surface rain-gauge observations. This mesoscale-average rain rate estimation method can be useful to extend the spatial and temporal coverage of the rainfall data provided by the Precipitation Radar on board the Tropical Rainfall Measuring Mission (TRMM) satellite.

Prabhakara, C.↗

An Update on Oceanic Precipitation Rate and its Zonal Distribution in Light of Advanced Observations from Space

This study contributes to the estimation of the global mean and zonal distribution of oceanic precipitation rate using complementary information from advanced precipitation measuring sensors and provides an independent reference to assess current precipitation products. Precipitation estimates from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and CloudSat cloud profiling radar (CPR) were merged, as the two complementary sensors yield an unprecedented range of sensitivity to quantify rainfall from drizzle through the most intense rates. At higher latitudes, where TRMM PR does not exist, precipitation estimates from Aqua's Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) complemented CloudSat CPR to capture intense precipitation rates. The high sensitivity of CPR allows estimation of snow rate, an important type of precipitation at high latitudes, not directly observed in current merged precipitation products. Using the merged precipitation estimate from the CloudSat, TRMM, and Aqua platforms (this estimate is abbreviated to MCTA), the authors' estimate for 3-yr (2007-09) nearglobal (80degS-80degN) oceanic mean precipitation rate is approx. 2.94mm/day. This new estimate of mean global ocean precipitation is about 9% higher than that of the corresponding Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) value (2.68mm/day) and about 4% higher than that of the Global Precipitation Climatology Project (GPCP; 2.82mm/day). Furthermore, MCTA suggests distinct differences in the zonal distribution of precipitation rate from that depicted in GPCPand CMAP, especially in the Southern Hemisphere.

profiling radar↗

The Effect of Environmental Conditions on Tropical Deep Convective Systems Observed from the TRMM Satellite

This study uses measurements of radiation and cloud properties taken between January and August 1998 by three Tropical Rainfall Measuring Mission (TRMM) instruments, the Clouds and the Earth's Radiant Energy System (CERES) scanner, the TRMM Microwave Imager (TMI), and the Visible and InfraRed Scanner (VIRS), to evaluate the variations of tropical deep convective systems (DCS) with sea surface temperature (SST) and precipitation. This study finds that DCS precipitation efficiency increases with SST at a rate of approx. 2%/K. Despite increasing rainfall efficiency, the cloud areal coverage rises with SST at a rate of about 7%/K in the warm tropical seas. There, the boundary layer moisture supply for deep convection and the moisture transported to the upper troposphere for cirrus-anvil cloud formation increase by approx. 6.3%/K and approx. 4.0%/K, respectively. The changes in cloud formation efficiency, along with the increased transport of moisture available for cloud formation, likely contribute to the large rate of increasing DCS areal coverage. Although no direct observations are available, the increase of cloud formation efficiency with rising SST is deduced indirectly from measurements of changes in the ratio of DCS ice water path and boundary layer water vapor amount with SST. Besides the cloud areal coverage, DCS cluster effective sizes also increase with precipitation. Furthermore, other cloud properties, such as cloud total water and ice water paths, increase with SST. These changes in DCS properties will produce a negative radiative feedback for the earth's climate system due to strong reflection of shortwave radiation by the DCS. These results significantly differ from some previous hypothesized dehydration scenarios for warmer climates, and have great potential in testing current cloud-system resolving models and convective parameterizations of general circulation models.

Lin, Bing↗

"Weekend-effect" evidence for intensification of storms by pollution over U.S.

Aerosols change the way precipitating clouds evolve, due to their effect on condensation and ice formation. The net effect of aerosols on precipitation varies depending on the local environment and synoptic situation, the types of aerosols, and also on how far downstream one looks for effects. Repeated experiments with controlled release of aerosols would be helpful in unraveling how aerosols affect precipitation. The weekly variation in human activity may provide just such a set of experiments. Using the rainfall estimates from the passive microwave instrument on the Tropical Rainfall Measuring Mission (TRMM), which has been orbiting for over eight years and can view areas as far north as about 40 degs, we find that there is indeed a weekly variation in summer (JJA) rainfall over the southeastern U.S. land area, with the average rain rate peaking in the middle of the week (Tue-Thu). Rainfall over nearby oceanic areas, on the other hand, seems to peak on weekends. A bootstrap statistical test indicates that the variations are unlikely to be due to chance. Physically related weekly variations in the statistics of ground-based measurements and model reanalysis data are found. The midweek peak in rainfall over land coincides with the well documented midweek peak in pollution around much of the U.S., and is unlikely to be due to other weekly variations in human influence. The midweek increase is also unlikely to be a consequence of the radiative heating or cooling of the atmosphere by the aerosols.

Bell, T. L.↗

Lightning and Precipitation: Observational Analysis of LIS and PR

Lightning flash rate can identify areas of convective rainfall when the storms are dominated by ice-phase precipitation. Modeling and observational studies indicate that cloud electrification and microphysics are very closely related and it is of great interest to understand the relationship between lightning and cloud microphysical quantities. Analyzing data from the Lightning Image Sensor (LIS) and the Precipitation Radar (PR), we show a quantitative relationship between microphysical characteristics of thunderclouds and lightning flash rate. We have performed a complete analysis of all data available over the Mediterranean during the TRMM mission and show a range of reflective profiles as a function of lightning activity for both convective and stratiform regimes as well as seasonal variations. Due to the increasing global coverage of lightning detection networks, this kind of study can used to extend the knowledge about thunderstorms and discriminate between different regimes in regions where radar measurements are readilly available.

Adamo, C.↗

A TRMM Microwave Radiometer Rain Rate Estimation Method with Convective and Stratiform Discrimination

Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima (T85min) in a regional map containing a Mesoscale Convective System (MCS). This is because of relatively small footprint size (approximately 5.5 km) and strong extinction properties in this channel of the TMI. A map of surface rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85(sub min), produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we infer empirically from TMI data the presence of three different kinds of thunderstorms or Cbs. These Cbs are classified as young, mature, and decaying types, and are assumed to have a scale of about 20 km on the average. Two parameters are used to classify these three kinds of Cbs based on the T85 data: a) the magnitude of scattering depression deduced from local T85(sub min) and b) the mean horizontal gradient of T85 around such minima. Knowing the category of a given Cb, we can estimate the rain rate associated with it. Such estimation is done with the help of relationships linking T85min to rain rate in each Cb type. Similarly, a weak background rain rate in all the areas where T85 is less than 260 K is deduced with another relationship linking T85 to rain rate. In our rain retrieval model, this background rain constitutes stratiform rain where the Cbs are absent. Initially, these relationships are optimized or tuned utilizing the PR and TMI data of a few MCS events. After such tuning, the model is applied to independent MCS cases. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (>= 20 mm/hr) rain rates are retrieved satisfactorily. Accuracy in the estimates of the light, moderate, and intense rain areas and the mean rain rates associated with such areas in these independent MCS cases is on the average about 15 %. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.

Prabhakara, C.↗

Impact of TRMM and SSM/I-derived Precipitation and Moisture Data on the GEOS Global Analysis

Current global analyses contain significant errors in primary hydrological fields such as precipitation, evaporation, and related cloud and moisture in the tropics. The Data Assimilation Office at NASA's Goddard Space Flight Center has been exploring the use of space-based rainfall and total precipitable water (TPW) estimates to constrain these hydrological parameters in the Goddard Earth Observing System (GEOS) global data assimilation system. We present results showing that assimilating the 6-hour averaged rain rates and TPW estimates from the Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/Imager (SSM/I) instruments improves not only the precipitation and moisture estimates but also reduce state-dependent systematic errors in key climate parameters directly linked to convection such as the outgoing longwave radiation, clouds, and the large-scale circulation. The improved analysis also improves short-range forecasts beyond 1 day, but the impact is relatively modest compared with improvements in the time-averaged analysis. The study shows that, in the presence of biases and other errors of the forecast model, improving the short-range forecast is not necessarily prerequisite for improving the assimilation as a climate data set. The full impact of a given type of observation on the assimilated data set should not be measured solely in terms of forecast skills.

Hou, Arthur Y.↗