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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1985

Active and passive microwave measurements in Hurricane Allen

The NASA Langley Research Center analysis of the airborne microwave remote sensing measurements of Hurricane Allen obtained on August 5 and 8, 1980 is summarized. The instruments were the C-band stepped frequency microwave radiometer and the Ku-band airborne microwave scatterometer. They were carried aboard a NOAA aircraft making storm penetrations at an altitude of 3000 m and are sensitive to rain rate, surface wind speed, and surface wind vector. The wind speed is calculated from the increase in antenna brightness temperature above the estimated calm sea value. The rain rate is obtained from the difference between antenna temperature increases measured at two frequencies, and wind vector is determined from the sea surface normalized radar cross section measured at several azimuths. Comparison wind data were provided from the inertial navigation systems aboard both the C-130 aircraft at 3000 m and a second NOAA aircraft (a P-3) operating between 500 and 1500 m. Comparison rain rate data were obtained with a rain radar aboard the P-3. Evaluation of the surface winds obtained with the two microwave instruments was limited to comparisons with each other and with the flight level winds. Two important conclusions are drawn from these comparisons: (1) the radiometer is accurate when predicting flight level wind speeds and rain; and (2) the scatterometer produces well behaved and consistent wind vectors for the rain free periods.

Delnore, V. E.↗
NASA NTRS1993

Precipitation measurement using SIR-C: A feasibility study. Investigation at nadir

The most significant limitation of the imaging SAR in rain measurements is the ground return coupled to the rain cell. Here we report a study of the possibility of using the X-SAR and the C-band channel of SIR-C for rain measurement. Earlier signal-to-clutter calculations rule out the use of X-SAR at steeper off-vertical angles of incidence (i.e., 20 less than theta less than 50). Only rain rates greater than 30 mm/hr at angles of incidence greater than 60 degrees showed good signal-to-clutter ratio (SCR). This study involved calculations at vertical incidence. There is adequate signal-to-noise ratio (SNR) at vertical incidence, but the presence of high-range side-lobe levels leads to small SCR for measurement over oceans at both X and C bands. For larger rain thickness (greater than two km), the SCR gets better and smaller rain rates (greater than 10 mm/hr) can be measured. However, rain measurements over forests seem to be feasible at nadir even for smaller rain thickness (less than two km). We conclude that X band may be usable over the forest at vertical incidence to measure rain rates greater than five mm/hr even for shallow rain thickness and over ocean for large rain thickness.

Ahamad, Atiq↗
NASA NTRS1992

A comparison of airborne and ground-based radar observations with rain gages during the CaPE experiment

The vicinity of KSC, where the primary ground truth site of the Tropical Rainfall Measuring Mission (TRMM) program is located, was the focal point of the Convection and Precipitation/Electrification (CaPE) experiment in Jul. and Aug. 1991. In addition to several specialized radars, local coverage was provided by the C-band (5 cm) radar at Patrick AFB. Point measurements of rain rate were provided by tipping bucket rain gage networks. Besides these ground-based activities, airborne radar measurements with X- and Ka-band nadir-looking radars on board an aircraft were also recorded. A unique combination data set of airborne radar observations with ground-based observations was obtained in the summer convective rain regime of central Florida. We present a comparison of these data intending a preliminary validation. A convective rain event was observed simultaneously by all three instrument types on the evening of 27 Jul. 1991. The high resolution aircraft radar was flown over convective cells with tops exceeding 10 km and observed reflectivities of 40 to 50 dBZ at 4 to 5 km altitude, while the low resolution surface radar observed 35 to 55 dBZ echoes and a rain gage indicated maximum surface rain rates exceeding 100 mm/hr. The height profile of reflectivity measured with the airborne radar show an attenuation of 6.5 dB/km (two way) for X-band, corresponding to a rainfall rate of 95 mm/hr.

Satake, Makoto↗
NASA NTRS1992

A comparison of airborne and ground-based radar observations with rain gages during the CaPE experiment

The vicinity of KSC, where the primary ground truth site of the Tropical Rainfall Measuring Mission (TRMM) program is located, was the focal point of the Convection and Precipitation/Electrification (CaPE) experiment in July and Aug. 1991. In addition to several specialized radars, local coverage was provided by the C-band (5 cm) radar at Patrick AFB. Point measurements of rain rate were provided by tipping bucket rain gage networks. Besides these ground-based activities, airborne radar measurements with X- and Ka-band nadir-looking radars on board an aircraft were also recorded. A unique combination data set of airborne radar observations with ground-based observations was obtained in the summer convective rain regime of central Florida. We present a comparison of these data intending a preliminary validation. A convective rain event was observed simultaneously by all three instrument types on the evening of 27 July 1991. The high resolution aircraft radar was flown over convective cells with tops exceeding 10 km and observed reflectivities of 40 to 50 dBZ at 4 to 5 km altitude, while the low resolution surface radar observed 35 to 55 dBZ echoes and a rain gage indicated maximum surface rain rates exceeding 100 mm/hr. The height profile of reflectivity measured with the airborne radar show an attenuation of 6.5 dB/km (two way) for X-band, corresponding to a rainfall rate of 95 mm/hr.

Satake, Makoto↗
NASA NTRS2000

On Utilization of NEXRAD Scan Strategy Information to Infer Discrepancies Associated With Radar and Rain Gauge Surface Volumetric Rainfall Accumulations

To evaluate the Tropical Rainfall Measuring Mission (TRMM) monthly Ground Validation (GV) rain map, 42 quality controlled tipping bucket rain gauge data (1 minute interpolated rain rates) were utilized. We have compared the gauge data to the surface volumetric rainfall accumulation of NEXRAD reflectivity field, (converting to rain rates using a 0.5 dB resolution smooth Z-R table). The comparison was carried out from data collected at Melbourne, Florida during the month of July 98. GV operational level 3 (L3 monthly) accumulation algorithm was used to obtain surface volumetric accumulations for the radar. The gauge records were accumulated using the 1 minute interpolated rain rates while the radar Volume Scan (VOS) intervals remain less than or equal to 75 minutes. The correlation coefficient for the radar and gauge totals for the monthly time-scale remain at 0.93, however, a large difference was noted between the gauge and radar derived rain accumulation when the radar data interval is either 9 minute, or 10 minute. This difference in radar and gauge accumulation is being explained in terms of the radar scan strategy information. The discrepancy in terms of the Volume Coverage Pattern (VCP) of the NEXRAD is being reported where VCP mode is ascertained using the radar tilt angle information. Hourly radar and gauge accumulations have been computed using the present operational L3 method supplemented with a threshold period of +/- 5 minutes (based on a sensitivity analysis). These radar and gauge accumulations are subsequently improved using a radar hourly scan weighting factor (taking ratio of the radar scan frequency within a time bin to the 7436 total radar scans for the month). This GV procedure is further being improved by introducing a spatial smoothing method to yield reasonable bulk radar to gauge ratio for the hourly and daily scales.

Roy, Biswadev↗
NASA NTRS1990

The effect of convective life cycle stage on microwave brightness temperature/rainrate relations as determined from 3-D cloud model results

The relationship between the rain rate and the brightness temperature (Tb) was investigated using a cloud model/microwave radiative transfer model combination to obtain the rain-rate/Tb relations for four different frequencies: 10, 19, 37, and 86 GHz. The results at 19, 37, and 86 GHz were found to be significantly affected by ice in the modeled convective system, while the results at 10 GHz showed very little effect. Nonprecipitating cloud water was found to affect Tb in two ways. First, at low rain rates, the presence of significant cloud water produced higher Tb values than in cases with little cloud water. The second effects occurs at 19, 37, and 86 GHz at higher rainrates associated with significant ice formation; the scattering by ice lowered the Tb.

Adler, Robert F.↗
NASA NTRS1986

Rain cell size statistics derived from radar observations at Wallops Island, Virginia

An investigation of two-dimensional rain cell size statistics has analyzed regression relations relating radar-determined rain rates to disdrometer data. This has yielded least-squares fits of radar reflectivity factors, and the application of a contouring program has generated 22,000 contours in which each isopleth belongs to predefined rain-rate intervals. An abundance of total and cell contours were observed belonging to all rain-rate categories. Both the computed number distributions and the conditional cumulative distributions as a function of contour diameter were found to be represented with good approximation by given exponential functions.

Goldhirsh, J.↗
NASA NTRS1982

Results of 11.7-GHz CTS rain attenuation measurements at Waltham, Massachusetts

Satellite-to-earth rain attenuation at 11.7 GHz was measured at Waltham, Massachusetts (42.4 deg N, 71.3 deg W; elevation angle 25 deg), utilizing the Communications Technology Satellite beacon signal. This paper summarizes 29 months of measurements by presenting attenuation and rain rate distributions, fade duration distributions, fading rate distributions, and statistical relationships between attenuation and rain rate. For a two-year statistical base, rain attenuation exceeded 9.7 dB for 0.01 percent of the time and 2.0 dB for 0.1 percent of the time.

Nackoney, O. G.↗
NASA NTRS2006

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.↗
NASA NTRS1995

Passive microwave algorithm development and evaluation

The scientific objectives of this grant are: (1) thoroughly evaluate, both theoretically and empirically, all available Special Sensor Microwave Imager (SSM/I) retrieval algorithms for column water vapor, column liquid water, and surface wind speed; (2) where both appropriate and feasible, develop, validate, and document satellite passive microwave retrieval algorithms that offer significantly improved performance compared with currently available algorithms; and (3) refine and validate a novel physical inversion scheme for retrieving rain rate over the ocean. This report summarizes work accomplished or in progress during the first year of a three year grant. The emphasis during the first year has been on the validation and refinement of the rain rate algorithm published by Petty and on the analysis of independent data sets that can be used to help evaluate the performance of rain rate algorithms over remote areas of the ocean. Two articles in the area of global oceanic precipitation are attached.

Petty, Grant W.↗
NASA NTRS2010

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↗
NASA NTRS2010

Methods and Results for a Global Precipitation Measurement (GPM) Validation Network Prototype

As one component of a ground validation system to meet requirements for the upcoming Global Precipitation Measurement (GPM) mission, a quasi-operational prototype a system to compare satellite- and ground-based radar measurements has been developed. This prototype, the GPM Validation Network (VN), acquires data from the Precipitation Radar (PR) on the Tropical Rainfall Measuring Mission (TRMM) satellite and from ground radar (GR) networks in the continental U.S. and participating international sites. PR data serve as a surrogate for similar observations from the Dual-frequency Precipitation Radar (DPR) to be present on GPM. Primary goals of the VN prototype are to understand and characterize the variability and bias of precipitation retrievals between the PR and GR in various precipitation regimes at large scales, and to improve precipitation retrieval algorithms for the GPM instruments. The current VN capabilities concentrate on comparisons of the base reflectivity observations between the PR and GR, and include support for rain rate comparisons. The VN algorithm resamples PR and GR reflectivity and other 2-D and 3-D data fields to irregular common volumes defined by the geometric intersection of the instrument observations, and performs statistical comparisons of PR and GR reflectivity and estimated rain rates. Algorithmic biases and uncertainties introduced by traditional data analysis techniques are minimized by not performing interpolation or extrapolation of data to a fixed grid. The core VN dataset consists of WSR-88D GR data and matching PR orbit subset data covering 21 sites in the southeastern U. S., from August, 2006 to the present. On average, about 3.5 overpass events per month for these WSR-88D sites meet VN criteria for significant precipitation, and have matching PR and GR data available. This large statistical sample has allowed the relative calibration accuracy and stability of the individual ground radars, and the quality of the PR reflectivity attenuation correction in convective and stratiform precipitation to be evaluated. We will present results of PR-GR reflectivity and rain rate bias comparisons for each OR site, and for different rain types, for the full data set and as time series. The capabilities of the statistical analysis and vertical cross section tools for display and analysis of individual site overpass event data will be described, and examples of the tools' outputs will be shown.

Morris, Kenneth R.↗
NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗
NASA NTRS2000

Monthly Oceanic Rainfall from TRMM Microwave Imager (TMI) Data

We evaluated the performance of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) at-launch algorithm for monthly oceanic rain rate using two years (January 1998 - December 1999) of TMI data. The TMI at-launch algorithm is based on Wilheit et al.'s technique for estimating monthly oceanic rainfall that relies on histograms of multichannel microwave measurements. Comparisons with oceanic monthly rain rates derived from the Defense Meteorological Satellite Program (DMSP) F-13 and F-14 Special Sensor Microwave Imager (SSM/I) data show the average rain rates over the TRMM region (between 400S and 40N) are 3.0, 2.85 and 2.89 mm/day, respectively for F-13, F-14 and TMI. Based on the latest version of TB data (version 5), both rainrate and freezing height derived from TMI are similar to those from the F-13 and F-14 SSM/I data. However, regionally the differences are statistically significant at the 95% confidence. Three hourly monthly rainrates are also computed from 3-hourly TB histograms to examine the diurnal cycle of precipitation. Over most of the oceanic TRMM area, a distinct early morning rainfall peak is found. A harmonic analysis shows that the amplitude of the 12h harmonic is significant and comparable to that of the 24h harmonic.

Chang, Alfred T. C.↗
NASA NTRS2018

Aerosol Midlatitude Cyclone Indirect Effects in Observations and High-Resolution Simulations

Aerosol-cloud interactions are a major source of uncertainty in inferring the climate sensitivity from the observational record of temperature. The adjustment of clouds to aerosol is a poorly constrained aspect of these aerosol-cloud interactions. Here, we examine the response of midlatitude cyclone cloud properties to a change in cloud droplet number concentration (CDNC). Idealized experiments in high-resolution, convection-permitting global aquaplanet simulations with constant CDNC are compared to 13 years of remote-sensing observations. Observations and idealized aquaplanet simulations agree that increased warm conveyor belt (WCB) moisture flux into cyclones is consistent with higher cyclone liquid water path (CLWP). When CDNC is increased a larger LWP is needed to give the same rain rate. The LWP adjusts to allow the rain rate to be equal to the moisture flux into the cyclone along the WCB. This results in an increased CLWP for higher CDNC at a fixed WCB moisture flux in both observations and simulations. If observed cyclones in the top and bottom tercile of CDNC are contrasted it is found that they have not only higher CLWP but also cloud cover and albedo. The difference in cyclone albedo between the cyclones in the top and bottom third of CDNC is observed by CERES to be between 0.018 and 0.032, which is consistent with a 4.6-8.3 Wm(exp -2) in-cyclone enhancement in upwelling shortwave when scaled by annual-mean insolation. Based on a regression model to observed cyclone properties, roughly 60% of the observed variability in CLWP can be explained by CDNC and WCB moisture flux.

Mccoy, Daniel T.↗
NASA NTRS2008

Seeking Augmented Information Content Concerning Diurnal Precipitation Achieved by Combining TRMM-PR and CloudSat-CPR Radar Data Sets

The CloudSat satellite's Cloud Profiling Radar (CPR) is a highly sensitive 94 GHz (W-band) nadir viewing radar system flown in retrograde sun synchronous orbit useful for determining the vertical structure of cloud hydrometeors down to sensitivity of approx. -30 dBZ reflectivity factor. Given this sensitivity, it is possible to unambiguously measure precipitation rates in clouds over a spectrum extending from approx. 0.08 - 3.0 mm hr (sup -1) down to altitudes of 0.5 km with approx.0.25 km vertical binning. This enables an effective means to measure a great deal of the drizzle and light rain spectrum. However, because of its near-polar sunsynchronous orbit, CloudSat cannot sample the diurnal cycle of precipitation, nor with its nadir-only CPR view can it obtain a high duty cycle in sampling precipitation at fixed local times over fixed positions. On the other hand, the TRMM satellite, which is flown in a non-sunsynchronous 35-degree inclined orbit carrying the 13.8 GHz KU-band Precipitation Radar (PR) scanning through nadir over an approx. 225 km swath, can sample both the diurnal cycle and with a much improved duty cycle relative to CloudSat. Moreover, the PR and CPR have the same 0.25 km vertical binning capability. The PR's greatest shortcoming is its approx. +17 dBZ sensitivity, which eliminates the possibility of measuring rain rates below -0.3-0.5 mm hr(sup -1), which can involve rainfall accumulations of up to 50% of the total over some regions. This begs the question of whether by combining CPR and PR data sets, whether it is possible to obtain an augmented measurement of the diurnal precipitation cycle. By collecting complimentary datasets during CloudSat and TRMM satellite orbit crossings within a delta t = 45-min proximity window, it is possible to demonstrate that whenever TRMM detects a precipitation signal, the correlations along the vertical axis between the reflectivities acquired from the CPR and PR are in inverse proportion to the magnitude of the delta t proximity window. By taking advantage of these underlying correlations, it is possible to develop a functional which can be used to broaden the reflectivity spectrum, concomitantly the rain rate spectrum, of the PR measurements based on the inherently broader reflectivity spectrum of the CPR at the lower reflectivity end of the spectrum, concomitantly at lighter rain rates. With the functional in place, it is then possible to produce synthetic CloudSat precipitation imagery over the PR track and thus over the diurnal time period. These augmented data are then used to study the spectral-vertical diurnal properties of precipitation over oceanic regions observed by TRMM.

Smith, Eric A.↗
NASA NTRS2002

Convection and Easterly Wave Structure Observed in the Eastern Pacific Warm-Pool during EPIC-2001

During September-October 2001, the East Pacific Investigation of Climate Processes in the Coupled Ocean-Atmosphere System (EPIC-2001) ITCZ field campaign focused on studies of deep convection in the warm-pool region of the East Pacific. In addition to the TAO mooring array, observational platforms deployed during the field phase included the NOAA ship RN Ronald H. Brown, the NSF ship RN Horizon, and the NOAA P-3 and NCAR C-130 aircraft. This study combines C-band Doppler radar, rawinsonde, and surface heat flux data collected aboard the RN Brown to describe ITCZ convective structure and rainfall statistics in the eastern Pacific as a function of 3-5 day easterly wave phase. Three distinct easterly wave passages occurred during EPIC-2001. Wind and thermodynamic data reveal that the wave trough axes exhibited positively correlated U and V winds and a slight westward phase tilt with height. A relatively strong (weak) northeasterly deep tropospheric shear followed the trough (ridge) axis. Temperature and humidity perturbations exhibited mid-to upper level cooling (warming) and drying (moistening) in the northerly (trough and southerly) phase. At low levels warming (cooling) occurred in the northerly (southerly) phase with little change in the relative humidity, though mixed layer mixing ratios were larger during the northerly phase. When composited, radar, sounding, lightning and surface heat flux observations suggest the following systematic behavior as a function of wave phase: approximately zero to one quarter wavelength ahead of (behind) the wave trough in northerly (southerly) flow, larger (smaller) CAPE, lower (higher) CIN, weaker (stronger) tropospheric shear, higher (lower) conditional mean rain rates, higher (lower) lightning flash densities, and more (less) robust convective vertical structure occurred. Latent and sensible heat fluxes reached a minimum in the northerly phase and then increased through the trough, reaching a peak during the ridge phase (leading the peak in CAPE). From a radar echo coverage perspective, larger areas of light rain and slightly larger (10%) area averaged rain rates occurred in the vicinity of, and just behind, the trough axes in southerly flow. Importantly, the transition in convective structure observed across the trough axis when considered with the relatively small change in area mean rain rates suggests the presence of a transition in the vertical structure of diabatic heating across the easterly waves examined. The inferred transition in heating structure is supported by radar diagnosed divergence profiles that exhibit convective (stratiform) characteristics ahead of (behind) the trough.

Peterson, Walter A.↗
NASA NTRS1993

Probability-matched reflectivity-rainfall relations for a hurricane from aircraft observations

The relation between the distribution of equivalent reflectivity, Z(sub e), measured by an airborne C-band radar and that for rain rate, R, measured concurrently by a disdrometer on the same aircraft in the eyewall and outer bands of Hurricane Anita (1977) was investigated using the probability-matching method (PMM). It was found that the pdf of R is much narrower in the outer rainbands of Hurricane Anita than in the eyewall, and that the mean rain rates are also much smaller. It is shown that the use of PMM provides more realistic relations than the conventional power-law Z-R regression relations based upon scatter-plots of disdrometer measurements, showing higher eyewall reflectivities for the same rain rates at rates in excess of 6.3 mm/h.

Marks, Frank D., Jr.↗