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Comparing Evaporative Sources of Terrestrial Precipitation and Their Extremes in MERRA Using Relative Entropy

A quasi-isentropic back trajectory scheme is applied to output from the Modern Era Retrospective-analysis for Research and Applications and a land-only replay with corrected precipitation to estimate surface evaporative sources of moisture supplying precipitation over every ice-free land location for the period 1979-2005. The evaporative source patterns for any location and time period are effectively two dimensional probability distributions. As such, the evaporative sources for extreme situations like droughts or wet intervals can be compared to the corresponding climatological distributions using the method of relative entropy. Significant differences are found to be common and widespread for droughts, but not wet periods, when monthly data are examined. At pentad temporal resolution, which is more able to isolate floods and situations of atmospheric rivers, values of relative entropy over North America are typically 50-400 larger than at monthly time scales. Significant differences suggest that moisture transport may be the key to precipitation extremes. Where evaporative sources do not change significantly, it implies other local causes may underlie the extreme events.

Climatological Distributions↗

The Response of the South Asian Summer Monsoon Circulation to Intensified Irrigation in Global Climate Model Simulations

Agricultural intensification in South Asia has resulted in the expansion and intensification of surface irrigation over the twentieth century. The resulting changes to the surface energy balance could affect the temperature contrasts between the South Asian land surface and the equatorial Indian Ocean, potentially altering the South Asian Summer Monsoon (SASM) circulation. Prior studies have noted apparent declines in the monsoon intensity over the twentieth century and have focused on how altered surface energy balances impact the SASM rainfall distribution. Here, we use the coupled Goddard Institute for Space Studies ModelE-R general circulation model to investigate the impact of intensifying irrigation on the large-scale SASM circulation over the twentieth century, including how the effect of irrigation compares to the impact of increasing greenhouse gas (GHG) forcing. We force our simulations with time-varying, historical estimates of irrigation, both alone and with twentieth century GHGs and other forcings. In the irrigation only experiment, irrigation rates correlate strongly with lower and upper level temperature contrasts between the Indian sub-continent and the Indian Ocean (Pearson's r = -0.66 and r = -0.46, respectively), important quantities that control the strength of the SASM circulation. When GHG forcing is included, these correlations strengthen: r = -0.72 and r = -0.47 for lower and upper level temperature contrasts, respectively. Under irrigated conditions, the mean SASM intensity in the model decreases only slightly and insignificantly. However, in the simulation with irrigation and GHG forcing, inter-annual variability of the SASM circulation decreases by *40 %, consistent with trends in the reanalysis products. This suggests that the inclusion of irrigation may be necessary to accurately simulate the historical trends and variability of the SASM system over the last 50 years. These findings suggest that intensifying irrigation, in concert with increased GHG forcing, is capable of reducing the variability of the simulated SASM circulation and altering the regional moisture transport by limiting the surface warming and reducing land-sea temperature gradients.

amplification↗

Southeast Greenland Winter Precipitation Strongly Linked to the Icelandic Low Position

Greenland's largest precipitation flux occurs in its southeast (SE) region during the winter, controlled primarily by easterly winds and frequent cyclogenesis in the North Atlantic. Several studies have attempted to link SE Greenland precipitation to the North Atlantic Oscillation (NAO) but results are inconsistent. This work uses reanalysis, automatic weather station data, and regional climate model output to show that the east-west position of the Icelandic low is a better predictor of SE Greenland precipitation (average correlation of r equals -0.48 in DJF (December January February)) than climate indices such as the NAO (r equals -0.06 in DJF). In years when the Icelandic low is positioned extremely west, moisture transport increases up to approximately 40 percent (or up to 40 kilograms per meter per second) off the SE Greenland coast compared to when the low is in an extreme east position. Furthermore, in years when the Icelandic low is positioned extremely west, storm track density and intensity increase just off the SE coast of Greenland. Thus, the Icelandic low's longitudinal position dominates SE Greenland ice sheet's wintertime precipitation, a positive term in the ice sheet mass balance. Given SE Greenland's importance in the overall ice sheet mass balance, the position of the Icelandic low is therefore important for making projections of future sea level.

Arctic↗

Recent Rainfall Decline in West Africa Due to Enhanced Biomass Burning and Dust Emission

Rainfall in West Africa during boreal summer is primarily controlled by the low-level southerly monsoon flow that transports moisture from the Gulf of Guinea to the region and the African Easterly Jet that modulates the convective systems. However, the role of aerosols in rainfall variability of this region, despite the large emissions of dust and black carbon in Africa, is not well-understood. Our study reveals a decline in precipitation over Southern West Africa (SWA) in the past two decades that its trend and interannual variability present an indirect relationship with the aerosols loadings. Examining the local and remote sources of aerosols, we found that the latter have a larger contribution. We have used MERRA-2 large scale atmospheric dynamics and physics data to determine the mechanisms responsible for aerosol-rainfall interactions in the region. Our results have important implications for the people and ecosystem as the increasing rates of land use change, deforestation and urbanization in the continent are expected to enhance the aerosols. This will result in an increase in the frequency and intensity of the extreme events including droughts.

Dezfuli, Amin↗

TPSAS-NF1676L-30053-DND

The 2016-17 Arctic sea ice growth season (October-March) exhibited one of the lowest end-of-season sea ice volume and extent of any year since 1979. An analysis of MERRA2 atmospheric reanalysis data and CERES radiative flux data reveals that a record warm and moist Arctic atmosphere supported the reduced sea ice growth through two pathways. First, numerous regional episodes of increased atmospheric temperature and moisture, transported from lower latitudes, increased the cumulative energy input from downwelling longwave surface fluxes. Second, in those same episodes, the efficiency that the atmosphere cooled radiatively to space was reduced, increasing the amount of energy retained in the Arctic atmosphere and reradiated back toward the surface. Overall, the Arctic radiative cooling efficiency shows a decreasing trend since 2000. The results presented highlight the increasing importance of atmospheric forcing on sea ice variability demonstrating that episodic Arctic atmospheric rivers, regions of elevated poleward water vapor transport, and the subsequent surface energy budget response is a critical mechanism actively contributing to the evolution of Arctic sea ice.

Bradley Hegyi↗

Effect of Irrigation on Humid Heat Extremes

Most studies of irrigation as an anthropogenic climate forcing focus on its cooling effects. However, irrigation also increases humidity, and so may not ameliorate humid heat and its extremes. We analyzed global climate model results over hot locations and seasons at high temporal resolution to estimate the impact of irrigation on humid heat extremes, quantified as different percentiles of wet-bulb temperature (T(sub w)), under contemporary conditions. We found that although irrigation reduced temperature, the median and higher percentiles of T(sub w) on average did not decrease. Increases in T(sub w) percentile values and increases in frequency of dangerous T(sub w) of several days per year due to irrigation were found in some densely populated regions, including the central United States and the Middle East, while the Ganges basin saw reduced T(sub w). Changes in T(sub w) were partly associated with the differential regional impacts of irrigation on moisture transport. These results underline the importance of considering impacts of climate forcings on humidity as well as temperature in evaluating associated effects on heat extremes.

Irrigation↗

Soil moisture-atmosphere feedbacks mitigate declining water availability in drylands

Global warming alters surface water availability (precipitation minus evapotranspiration, P–E) and hence freshwater resources. However, the influence of land–atmosphere feedbacks on future P–E changes and the underlying mechanisms remain unclear. Here we demonstrate that soil moisture (SM) strongly impacts future P–E changes, especially in drylands, by regulating evapotranspiration and atmospheric moisture inflow. Using modelling and empirical approaches, we find a consistent negative SM feedback on P–E, which may offset ~60% of the decline in dryland P–E otherwise expected in the absence of SM feedbacks. The negative feedback is not caused by atmospheric thermodynamic responses to declining SM; rather, reduced SM, in addition to limiting evapotranspiration, regulates atmospheric circulation and vertical ascent to enhance moisture transport into drylands. This SM effect is a large source of uncertainty in projected dryland P–E changes, underscoring the need to better constrain future SM changes and improve the representation of SM–atmosphere processes in models.

precipitation↗

A Strong Atmospheric River Responsible for the 2019 Record Floods in the Middle East

Atmospheric rivers (ARs) cause some of the weather-related disasters around the world. While many studies have shown the contribution of ARs to precipitation in the coastal regions such as western Europe and the U.S. West Coast, little is known about their mechanisms and impacts on flooding in the Middle East. This study shows that an AR was responsible for the record floods during March 2019 across the Middle East. Iran in particular was hit hardest with the floods that left a death toll of at least 76 and an early estimate of $2.5 billion (U.S. dollars) damage to its infrastructures. The heavy precipitation produced by this AR made the 2018/19 rainy season the wettest in the past four decades. By contrast, the prior year (2017/18) was the driest over the same period. This is a compelling example of rapid dry-to-wet transitions that may enhance the chance of landslides and impose challenges to water resources management. The AR originated in the Atlantic Ocean and propagated across North Africa and the Arabian Peninsula before its final landfall over the Zagros Mountains. On its nearly 9000 km journey, the AR received additional moisture from the Mediterranean, Red, and Arabian Seas, and the Persian Gulf. Moisture transport by this AR during 24-25 March 2019 is estimated at more than 150times the aggregated discharge of the four major rivers in the region, that is, the Tigris, Euphrates, Karun, and Karkheh. Anomalously warm sea surface temperatures in all surrounding basins and coincidence of a midlatitude system and a subtropical jet provided the necessary ingredients for formation of this strong AR. This work underlines the fact that the impacts of rain-producing ARs are not limited to the coastal regions. Such ARs can travel very long distances away from the oceans and affect remote arid and semi-arid regions like the Middle East. This study examined an individual AR, though one associated with record floods. However, it attempts to draw attention to the need for more AR-related research over the Middle East.

Atmospheric Rivers↗

Planetary Boundary Layer Height Estimates From ICESat-2 and CATS Backscatter Measurements

The lowest layer of the atmosphere in which all human activity occurs is called the Planetary Boundary Layer (PBL). All physical interactions with the surface, such as heat and moisture transport, pollution dispersion and transport happen in this relatively shallow layer. The ability to understand and model the complex interactions that occur in the PBL is very important to air quality, weather prediction and climate modeling. A fundamental and physically important property of the PBL is its thickness or height. This work presents two methods to obtain global PBL height using satellite lidar data from the Ice, Cloud and land Elevation Satellite-2 (ICESat-2) and the Cloud-Aerosol Transport System (CATS). The first method is a straightforward backscatter threshold technique and the second is a machine learning approach known as a Convolutional Neural Network. The PBL height retrievals from the two methods are compared with each other and with PBL height from the NASA GEOS MERRA-2 reanalysis. The lidar-retrieved PBL heights have a high degree of spatial correlation with the model heights but are generally higher over ocean (∼400 m) and over northern hemisphere high latitude regions (∼1,000 m). Over mid-latitude and tropical land areas, the satellite estimated PBL heights agree well with model mid-day estimates. This work demonstrates the feasibility of using satellite lidar backscatter measurements to obtain global PBL height estimates, as well as determining seasonal and regional variability of PBL height.

Stephen P Palm↗

High Latitude Atmospheric Rivers: Teleconnections and Impacts

Atmospheric rivers (ARs) are long, narrow synoptic scale features that act as moisture transport vehicles by moving water vapor poleward. They are typically found in storm tracks and often have profound implications for regional hydroclimate. For high latitude locales such as Antarctica and the Arctic, ARs are fewer in number but often have an outsized impact by either producing significant snow accumulation events, or, depending on their thermal characteristics, initiating melt events on ice sheets, ice shelves, and sea ice. In this study, we apply both reanalysis and climate model data to evaluate high latitude ARs for both the Arctic and Antarctic in the context of teleconnections and modes of variability. Specifically, we fold in both MERRA-2 and ERA5 reanalysis as well as historical and climate change simulations from the CESM2 (Community Earth System Model, Version 2) and E3SMv2 (Energy Exascale Earth System Model, v2) with multiple ensemble members to better understand natural variability versus climate change signals. An overview of AR climatology and impacts will be presented, including a baseline uncertainty quantification analysis using data from ARTMIP (the Atmospheric River Tracking Method Intercomparison Project). AR impacts during specific modes of variability will be characterized by diagnosing precipitation and boundary layer temperature associated with Ars influencing the cryosphere. Modes of variability investigated include the SAM (Southern Annular Mode), PDO (Pacific Decadal Oscillation), PSA2 (Pacific South American Mode 2), the IOD (Indian Ocean Dipole), and the AO (Arctic Oscillation).

Atmospheric Rivers↗

Quantifying Spatial Drought Propagation Potential in North America Using Complex Network Theory

Droughts have a dominant three-dimensional (3-D) spatiotemporal structure typically spanning hundreds of kilometers and often lasting for months to years. Here, we introduced a novel framework to explore the 3-D structure of the evolution of droughts based on network theory concepts. The proposed framework is applied to identify critical source regions responsible for large-scale drought onsets during 1901–2014 for the North American continent using the Standardized Precipitation Evaporation Index (SPEI). We built a spatial network connecting the drought onset timings for the North American continent. Using a spatially weighted network partitioning algorithm, the whole continent is then classified into regional spatial drought networks (RSN), where droughts are more likely to propagate within these regional systems. Finally, a customized network metric was applied to identify locations (source regions) where the drought onsets further propagate to other areas within the regional spatial network. Our results indicated that the West coast, Texas coastal region, and Southeastern Arkansas as major source regions through which atmospheric drought propagates to Western, South Central, and Eastern North America. The formation of drought source regions are due to presence of high pressure ridges and anomalous wind patterns. Furthermore, our results indicate that the drought propagation from these source regions may be due to inadequate moisture transport. The proposed framework can help to develop an early warning detection system for droughts and other spatially extensive extreme events such as heatwaves and floods.

Goutam Konapala↗

Synergy of Satellite Radiation, Precipitation, and Other Meteorological Variable Observations for Global Mean Sea Surface Turbulent Heat Flux Estimation

Sea surface turbulent heat flux is one of the key components in global freshwater and energy balances and plays an important role in atmospheric dynamics, thermodynamics and general circulation. This turbulent heat flux is dominantly decided by sea surface latent heat release with some contribution from sensible heat exchange. The flux and its anomaly could significantly affect ocean heat storage and ocean circulation. They are part of and have great impacts on climate variability. Though the turbulent heat flux is extremely important for the climate and weather systems, only very limited ship and buoy observations of the flux are available over open oceans. There are no global, operational, direct measurements of this crucial meteorological variable. Global estimates are, basically, indirectly calculated from bulk turbulent flux parameterization with a combination of satellite column water vapor, sea surface water temperature, and wind speed observations. Critical parameters such as sea surface air temperature and humidity are estimated from empirical relations of theses variables with the water vapor and sea surface water temperature, respectively. Lacking accurate knowledge on surface air temperature and humidity, uncertainties in the parameterization and potential changes in the non-linear turbulent processes with long-term climate variations could cause large errors in estimated long-term turbulent fluxes from the indirect method as shown in current global sea surface turbulent flux datasets. This study uses synergized data of satellite global radiation, precipitation, and other meteorological variable observations to estimate sea surface turbulent heat fluxes. The radiation observations are made by the satellite Clouds and the Earth’s Radiant Energy System (CERES) sensors, while the global precipitation data is from NASA’s satellite Global Precipitation Climatology Project (GPCP). Other data includes satellite sea surface water temperature and wind speed observations. These datasets are obtained from a wide range of space sensors from passive to active instruments and from visible and near infrared to thermal infrared and microwave spectral sounders. One significant feature of these datasets is that they have multi-decades long climate records. Top-of-atmosphere (TOA) radiation and its anomaly represents the net heat energy input to the climate system, and the oceanic precipitation and ocean-land moisture transport can be used to quantify sea surface latent heat release. Based on the synergized datasets and the principle of global water and energy balances, global mean turbulent heat fluxes are estimated. The turbulent heat anomalies for the first two decades of the 21st century are, then, obtained mainly from global CERES radiation and GPCP precipitation anomalies, along with CERES derived ocean-land heat transports. Analysis indicates that the uncertainties in the estimated turbulent flux anomalies may be reduced considerably. The results suggest a strong needs in synchronized and synergized observations of atmospheric radiation, precipitation, and oceanic meteorological variables for long-term climate studies.

Bing Lin↗

Influence of Lower Tropospheric Moisture on Local Soil Moisture-Precipitation Feedback Over the U.S. Southern Great Plains

Land-atmosphere coupling (LAC) has long been studied focusing on land surface and atmospheric boundary layer processes. However, the influence of lower tropospheric (LT) humidity on LAC remains largely unexplored. In this study, we use radiosonde observations from the U.S. Southern Great Plains (SGP) site and an entrained parcel buoyancy model to investigate the impact of LT humidity on LAC there during the warm season (May–September). We quantify the effect of LT humidity on convective buoyancy by measuring the difference between the 2–4 km vertically integrated buoyancy with and without the influence of background LT humidity. Our results show that, under dry soil conditions, anomalously high LT humidity is necessary to produce the buoyancy profiles required for afternoon precipitation events (APEs). These APEs under dry soil moisture cannot be explained by commonly used local land-atmosphere coupling indices such as the convective triggering potential/low-level humidity index (CTP/HI Low ), which do not account for the influence of the LT humidity. On the other hand, consideration of LT humidity is unnecessary to explain APEs under wet soil moisture conditions, suggesting the boundary layer moisture alone could be sufficient to generate the required buoyancy profiles. These findings highlight the need to consider the impact of LT humidity, which is often decoupled from the humidity near the surface and largely controlled by moisture transport, in understanding land-atmospheric feedbacks over dry soil conditions, especially during droughts or dry spells over the SGP.

Gaoyun Wang↗

SaltStone Wastewater Cement Study Using Isothermal Calorimetry, Standard Concrete Characterization Techniques, and CemGEMS - 25169

Cementitious reagents are used to solidify/stabilize aqueous radioactive, hazardous, and mixed salt solutions, and sludges to meet low-level radioactive waste (LLW) and Resource Conservation and Recovery Act (RCRA) requirements for disposal at Department of Energy (DOE). It is flexible enough to solidify radioactive wastewater saturated in complex species that include but are not limited to radioactive isotopes from the bombardment of neutrons in reactor operation, corrosion products from metallic components, and a variety of soluble organic compounds. [1,2]. Waste form testing typically includes processing or fresh properties, cured properties, compressive strength and hydraulic properties, porosity, density, saturated and unsaturated moisture transport, and leachability of contaminants in the waste form pore solution. Properties are collected over a relatively limited time, typically 28 to 365 days [3]. In addition, changes in the waste form as the result of time and changing conditions are important for concrete engineers to predict overall performance of the forms and potential release of contaminants in the disposal process via unintended filtration into the environment [4]. These predictions are determined/calculated characterizing young waste forms (relative to the standard age of concrete) and are based on transport through soluble ions in pore solutions. Characterization methods include X-ray, SEM, and isothermal calorimetry among other methods used to define the composition, amorphous vs. crystalline nature of the components, and the energetic formation mechanisms for multi-phase mineral systems. [5–7] Isothermal calorimetry is a well standardized technique for cements and concretes and can be used to predict the timing and nature of the hydration reactions.[8] The technique can measure long term energetic

Bustamante, Michael E. [Savannah River National La↗

Seasonal delay of Sahelian rainfall driven by an east–west contrast in radiative forcing in idealized CESM experiments

Recent studies suggest the observed seasonal delay of rainfall over the Sahel is mainly driven by anthropogenic aerosol forcing, which features a robust east–west contrasting changes in recent decades, with negative and positive top-of-the-atmosphere shortwave radiative forcing in South and East Asia (SA&EA) and in North America and Europe (NA&EU), respectively. Their individual effects on the Sahel rainfall annual cycle remain unclear. Here, by designing idealized sensitivity experiments based on Community Earth System Model (CESM1.2), we show that both negative radiative forcing over SA&EA and positive radiative forcing over NA&EU contribute to the delayed phase and enhanced amplitude of Sahel rainfall annual cycle. To understand the underlying physical processes, both the convective quasi-equilibrium (CQE) and atmospheric energetic frameworks are utilized. Both frameworks can well explain the seasonal delay in the rainfall annual cycle over the Sahel under the regional radiative forcings, with the CQE framework showing stronger explanatory power. Based on the insights from both frameworks, we conducted a moisture budget analysis and found that the negative radiative forcing over SA&EA causes an anomalous low-level anticyclonic circulation, which transports more moisture to the Sahel. As the anomalous anticyclone is stronger in summer and fall compared to spring, rainfall is delayed in the Sahel. Further, under the influence of the positive radiative forcing over NA&EU, more warming in the northern hemisphere causes northward transport of moisture to the northern tropics associated with the cross-equatorial transport of energy. The moisture transport increases relativehumidity over the Sahel and enhances the effective atmospheric heat capacity that delays the seasonal rainfall.

54 ENVIRONMENTAL SCIENCES↗

Simulation of the modern arctic climate by the NCAR CCM1

The National Center of Atmospheric Research (NCAR) Community Climate Model Version 1 (CCM1's) simulation of the modern arctic climate is evaluated by comparing a five-year seasonal cycle simulation with the European Center for Medium-Range Weather Forecasts (ECMWF) global analyses. The sea level pressure (SLP), storm tracks, vertical cross section of height, 500-hPa height, total energy budget, and moisture budget are analyzed to investigate the biases in the simulated arctic climate. The results show that the model simulates anomalously low SLP, too much storm activity, and anomalously strong baroclinicity to the west of Greenland and vice versa to the east of Greenland. This bias is mainly attributed to the model's topographic representation of Greenland. First, the broadened Greenland topography in the model distorts the path of cyclone waves over the North Atlantic Ocean. Second, the model oversimulates the ridge over Greenland, which intensifies its blocking effect and steers the cyclone waves clockwise around it and hence produces an artificial circum-Greenland trough. These biases are significantly alleviated when the horizontal resolution increases to T42. Over the Arctic basin, the model simulates large amounts of low-level (stratus) clouds in winter and almost no stratus in summer, which is opposite to the observations. This bias is mainly due to the location of the simulated SLP features and the negative anomaly of storm activity, which prevent the transport of moisture into this region during summer but favor this transport in winter. The moisture budget analysis shows that the model's net annual precipitation (P-E) between 70 deg N and the North Pole is 6.6 times larger than the observations and the model transports six times more moisture into this region. The bias in the advection term is attributed to the positive moisture fixer scheme and the distorted flow pattern. However, the excessive moisture transport into the Arctic basin does not solely result from the advection term. The contribution by the moisture fixer is as large as from advection. By contrast, the semi-Lagrangian transport scheme used in the CCM2 significantly improves the moisture simulation for this region; however, globally the error is as serious as for the positive moisture fixer scheme. Finally, because the model has such serious problems in simulating the present arctic climate, its simulations of past and future climate change for this region are questionable.

Bromwich, David H.↗

Solution-processed tungsten diselenide as an inorganic hole transport material for moisture-stable perovskite solar cells in the n-i-p architecture

Some of the obstacles to the commercialization of perovskite solar cells (PSCs) are their long-term moisture stability and material cost of the constituent layers, such as the commonly used spiro-OMeTAD hole transport layer (HTL). Replacing the spiro-OMeTAD with low-cost inorganic hole transport materials (HTMs) are important to further elevate the attractiveness of PSCs for commercialization. Perovskite-compatible, solution-exfoliated two-dimensional (2D) transition metal dichalcogenides (TMDCs) are being considered as viable candidates for inorganic HTMs. We consider one such TMDC, WSe 2 which was chemically exfoliated using dichlorobenzene (DCB), a perovskite-compatible solvent, as it was integrated with triple cation perovskite absorbers within the solar cell stack. Here, the WSe 2 HTL required heat treatment processes to be maintained below 100°C in order to preserve the integrity of the underlying perovskite; despite this lower temperature post treatment process, the structural morphology of the film revealed its dense and pinhole-free nature. Temperature-dependent transport studies conducted on the WSe 2 film provided evidence of its semiconducting character and its ability to extract holes well from the underlying triple-cation Cs 0.05 FA 0.79 MA 0.16 PbI 2.45 Br 0.55 absorber. The inorganic HTL offered better environmental stability in moisture-rich environments of up to 60% relative humidity, in comparison to spiro-OMeTAD HTL-based devices which degraded faster as a result of pinholes

14 SOLAR ENERGY↗

The modification and application of Kuo's parameterization of cumulus convection in middle latitudes

An evaluation to reveal physical insight into the involved mechanisms through a combination of the large scale heat and moisture budgets and formulation of the latent heat released was performed. To improve upon the treatment of the interaction of deep convection with the environment, modifications consisting of considerations of the large scale moisture supply and of the vertical transport of moisture and of dry static energy inside the cloud are made. Also, a two layer cloud ensemble model is combined with the modified scheme. An examination of the modified scheme is performed by combining the large scale heat and moisture budgets and the modified formulation of the latent heat released. The modified parameterization procedures are compared with the original scheme, and the results of tests of both schemes are discussed. A variational optimization scheme is developed to analyze the wind field such that the integrated continuity equation and the global boundary condition are satisfied.

Liang, W. J.↗