Search NASA⌕ Search

SEARCH · Search NASA

Results for “Atmospheric river”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Airborne Hyperspectral Sensing of Monitoring Harmful Algal Blooms in the Great Lakes Region: System Calibration and Validation

Harmful algal blooms (HABs) in Lake Erie have been prominent in recent years. The bloom in 2014 reached a severe level causing the State of Ohio to declare a state of emergency. At that time NASA Glenn Research Center was requested by stakeholders to help monitor the blooms in Lake Erie. Glenn conducted flights twice a week in August and September and assembled and distributed the HAB information to the shoreline water resource managers using its hyperspectral imaging sensor (in development since 2006), the S􀂱3 Viking aircraft, and funding resources from the NASA Headquarters Earth Science Division. Since then, the State of Ohio, National Oceanic and Atmospheric Administration (NOAA), and U.S. Environmental Protection Agency (EPA) have elevated their funding and activities for observing, monitoring, and addressing the root cause of HABs. Also, the communities and stakeholders have persistently requested NASA Glenn􀂶s participation in HAB observation. Abundant field campaigns and sample analyses have been funded by Ohio and NOAA, which provided a great opportunity for NASA to advance science and airborne hyperspectral remote sensing economically. Capitalizing on this opportunity to advance the science of algal blooms and remote sensing, NASA Glenn conducted the Airborne Hyperspectral Observation of harmful algal blooms campaign in 2015 that was, in many respects, twice as large as the 2014 campaign. Focusing mostly on Lake Erie, but also including other small inland lakes and the Ohio River, the campaign was conducted in partnership with a large number of partners specializing in marine science and remote sensing. Airborne hyperspectral observation of HABs holds promise to distinguish potential HABs from nuisance blooms, determine their concentrations, and delineate their movement in an augmented spatial and temporal resolution and under clouds􀂲all of which are excellent complements to satellite observations. Working with collaborators at several Ohio and Michigan institutions as well as one in South Dakota and one in Alabama, this effort was able to provide next-day georeferenced estimates of cyanobacteria and scum concentrations. Very prompt processing and analysis of the hyperspectral imagery is necessary for the information to be acted upon. For example, a next-day report of an overflight over the Ohio River indicated that a bloom could be present as far downstream as the Cincinnati intake, but the Ohio EPA had not received visual reports of a bloom that far downstream. Water samples were obtained at the Cincinnati water intake, based on the flight data, and detected microcystins in the source water. The flight data helped State and municipal authorities realize the potential extent of that bloom, and triggered response sampling, before the visual river-wide scums started forming. The present document describes the process that was utilized to take raw remote sensing data and create information products; this includes system calibration and validation, efforts to correct atmospheric effects, and algorithms that produce the data products. Furthermore, successful research into improved algorithms for expanding the capability to delineate in water constituents is included. Finally, comparisons that show expected relationships between ground-based measurements and hyperspectral imager version 2 (HSI2) data results are presented, giving confidence in the remote sensing products.

Hyperspectral Imaging↗

Iron and sulfur in the pre-biologic ocean

Tentative geochemical cycles for the pre-biologic Earth are developed by comparing the relative fluxes of oxygen, dissolved iron, and sulfide to the atmosphere and ocean. The flux of iron is found to exceed both the oxygen and the sulfide fluxes. Because of the insolubility of iron oxides and sulfides the implication is that dissolved iron was fairly abundant and that oxygen and sulfide were rare in the atmosphere and ocean. Sulfate, produced by the oxidation of volcanogenic sulfur gases, was the most abundant sulfur species in the ocean, but its concentration was low by modern standards because of the absence of the river-borne flux of dissolved sulfate produced by oxidative weathering of the continents. These findings are consistent with the geologic record of the isotopic composition of sedimentary sulfates and sulfides. Except in restricted environments, the sulfur metabolism of the earliest organisms probably involved oxidized sulfur species not sulfide.

Review↗

Recent Changes in Land Water Storage and Its Contribution to Sea Level Variations

Sea level rise is generally attributed to increased ocean heat content and increased rates glacier and ice melt. However, human transformations of Earth's surface have impacted water exchange between land, atmosphere, and ocean, ultimately affecting global sea level variations. Impoundment of water in reservoirs and artificial lakes has reduced the outflow of water to the sea, while river runoff has increased due to groundwater mining, wetland and endorheic lake storage losses, and deforestation. In addition, climate-driven changes in land water stores can have a large impact on global sea level variations over decadal timescales. Here, we review each component of negative and positive land water contribution separately in order to highlight and understand recent changes in land water contribution to sea level variations.

Reservoir impoundment↗

Assessing the Geomorphic Evolution and Hydrographic Changes Induced by Winter Storms along the Louisiana Coast

The influence that cold front passages have on Louisiana coastal environments, including land loss and land building processes, has been the primary topic of this multidisciplinary research. This research has combined meteorological, remote sensing, and coastal expertise from the University of Wisconsin (UW) and Louisiana State University (LSU). Analyzed data sets include remotely sensed radiometric data (AVHRR on NOAA-12,13,14, Multispectral Atmospheric Mapping Sensor (MAMS) and MODIS Airborne Simulator (MAS) on NASA ER-2), U.S. Army Corps of Engineers (USACE) water level data, water quality data from the Coastal Studies Institute (CSI) at LSU, USACE river discharge data, National Weather Service (NWS) and CSI wind in sitzi measurements, geomorphic measurements from aerial photography (NASA ER-2 and Learjet), and CSI ground based sediment burial pipes (for monitoring topographic change along the Louisiana coast) and sediment cores. The work reported here-in is a continuation of an initial investigation into coastal Louisiana landform modification by cold front systems. That initial effort demonstrated the importance of cold front winds in the Atchafalaya Bay sediment plume distribution (Moeller et al.), documented the sediment transport and deposition process of the western Louisiana coast (Huh et al.) and developed tools (e.g. water types identification, suspended solids estimation) from multispectral radiometric data for application to the current study. This study has extended that work, developing a Geomorphic Impact Index (GI(sup 2)) for relating atmospheric forcing to coastal response and new tools to measure water motion and sediment transport.

Menzel, W. Paul↗

Carbonate Mineral Formation on Mars: Clues from Stable Isotope Variation Seen in Cryogenic Laboratory Studies of Carbonate Salts

The geologic history of water on the planet Mars is intimately connected to the formation of carbonate minerals through atmospheric CO2 and its control of the climate history of Mars. Carbonate mineral formation under modern martian atmospheric conditions could be a critical factor in controlling the martian climate in a means similar to the rock weathering cycle on Earth. The combination of evidence for liquid water on the martian surface and cold surface conditions suggest fluid freezing could be very common on the surface of Mars. Cryogenic calcite forms readily when a rise in pH occurs as a result of carbon dioxide degassing quickly from freezing Ca-bicarbonate-rich water solutions. This is a process that has been observed in some terrestrial settings such as arctic permafrost cave deposits, lakebeds of the Dry Valleys of Antarctica, and in aufeis (river icings) from rivers of N.E. Alaska. We report here the results of a series of laboratory experiments that were conducted to simulate potential cryogenic carbonate formation on the planet Mars. These results indicate that carbonates grown under martian conditions (controlled atmospheric pressure and temperature) show enrichments from starting bicarbonate fluids in both carbon and oxygen isotopes beyond equilibrium values with average delta13C(DIC-CARB) values of ~20.5%0 which exceed the expected equilibrium fractionation factor of [10(sup 3) ln alpha = ~13%0] at 0 degC. Oxygen isotopes showed a smaller enrichment with delta18O(H2O-CARB) values of ~35.5%0, slightly exceeding the equilibrium fractionation factor of [10(sup 3) ln alpha = ~34%0 ] at 0degC. Large kinetic carbon isotope effects during carbonate precipitation could substantially affect the carbon isotope evolution of CO2 on Mars allowing for more efficient removal of 13C from the Noachian atmosphere enriched by atmospheric loss. This mechanism would be consistent with the observations of large carbon isotope variations in martian materials despite the relative paucity of carbonate minerals in the martian crust.

Socki, Richard↗

Earth observations during Space Shuttle flight STS-26: Discovery's mission to earth - September 29-October 3, 1988

During the late September-early October, 1988 flight of the Space Shuttle Discovery, astronauts took 1505 photographs of earth using handheld cameras. The resulting pictures provide an overview, not available from any other source, of dynamic environmental phenomena on five continents. The Discovery photographs show that: (1) atmospheric clarity has improved in the Northern Hemisphere, (2) widespread burning of natural vegetation throughout the Southern Hemisphere continues to generate immense smoke palls and extensive sedimentation in rivers and estuaries, and (3) although the drought in Africa was partially relieved by heavy rains in autumn, 1988, Lakes Chad and Nasser are at the lowest levels ever seen from space.

Wood, C. A.↗

Isotopic Tracers for CO 2 Produced During A Planetary Impact Into Limestone Target Rocks

Terrestrial meteorite impacts have been directly linked with multiple mass extinction events throughout Earth’s history. Among these impacts, those that land in sedimentary target rocks are thought to generate large quantities of CO 2 via decarbonation. This injection of CO 2 into the atmosphere has the potential to alter the climate and threaten terrestrial habitability. The magnitude of this change depends upon the net amount of CO 2 released, which is controlled by how much CO 2 is produced by the impact, how much CO 2 is removed by back-reactions after the impact, and other post-impact CO 2 sinks. To interrogate the behavior of CO 2 release into the impact atmosphere, we present carbon (δ 13 C), oxygen (δ 18 O), and clumped (Δ 47 ) isotope results from carbonate clasts preserved within the impact breccia of the Steen River Impact Structure (SRIS) in Alberta, Canada. These clasts exhibit a ~65‰ range in δ 13 C and a ~5‰ variation in δ 18 O. However, while δ 13 C and δ 18 O are positively correlated, Δ 47 unexpectedly has a negative relationship with δ 13 C and δ 18 O. Based on prior assumptions, there would either be (1) no relationship with carbonate Δ 47 and the bulk ratios because Δ 47 would be reset at extreme impact temperatures, or (2) Δ 47 would have a positive correlation with the bulk ratios, reflecting gradual Δ 47 ‘resetting.’ To reconcile the SRIS result with these expectations, we conducted a series of in vacuo heating experiments at temperatures above calcite decomposition. As predicted by Rayleigh fractionation, these heating experiments generated depletions in δ 13 C and δ 18 O that increased with reaction time. Mimicking the SRIS results, these experiments also produced concomitant increases in Δ 47 . Using an adaptation of a mechanistic model for decomposition fractionation (Hayles & Killingsworth, 2022) we hypothesize that these exotic isotope trends are caused by Rayleigh fractionation and a Δ 47 kinetic isotope effect that results from the disproportionation of O to CaO and CO 2 during thermal decomposition. This high Δ 47 CO 2 subsequently exchanges with the residual CaCO 3 . This work highlights a potential pathway for identifying and quantifying CO 2 generation by impacts and builds on the relatively limited literature characterizing the behavior of carbonate clumped isotopes at very high geologic temperatures.

Multi-isotope systems↗

Inland Water Greenhouse Gas Budgets for RECCAP2: 2. Regionalization and Homogenization of Estimates

Inland waters are important emitters of the greenhouse gasses (GHGs) carbon dioxide (CO 2 ), methane (CH 4 ), and nitrous oxide (N 2 O) to the atmosphere. In the framework of the 2 nd phase of the REgional Carbon Cycle Assessment and Processes (RECCAP-2) initiative, we synthesize existing estimates of GHG emissions from streams, rivers, lakes and reservoirs, and homogenize them with regard to underlying global maps of water surface area distribution and the effects of seasonal ice cover. We then produce regionalized estimates of GHG emissions over 10 extensive land regions. According to our synthesis, inland water GHG emissions have a global warming potential of an equivalent emission of 13.5 (9.9-20.1) and 8.3 (5.7-12.7) Pg CO 2 -eq. yr -1 at a 20 and 100 year horizon (GWP 20 and GWP 100 ), respectively. Contributions of CO 2 dominate GWP100, with rivers being the largest emitter. For GWP 20 , lakes and rivers are equally important emitters, and the warming potential of CH4 is more important than that of CO2. Contributions from N 2 O are about two orders of magnitude lower. Normalized to the area of RECCAP-2 regions, S-America and SE-Asia show the highest emission rates, dominated by riverine CO 2 emissions.

Ronny Lauerwald↗

Mechanism of Torrential Rain Associated with the Mei-yu Development during SCSMEX-98

A case of torrential precipitation process in the Mei-yu front, an Asian monsoon system east to the Tibetan Plateau, is studied with the coupled Penn State University/NCAR MM5 and NASA/GSFC PLACE (Parameterization for Land - Atmosphere - Cloud Exchange) models. Remote and local impacts of water vapor on the location and intensity of Mei-yu precipitation are studied by numerical experiments. Results demonstrate that the water vapor source for this heavy precipitation case in Yangtze river basin is derived mostly from the Bay of Bengal, transported by the southwesterly low-level Jet (LLJ) southeast to the Tibetan Plateau. The moist convection is a critical process in the development and maintenance of the front. The meridional and zonal secondary circulations resulted from Mei-yu condensation heating both act to increase the wind speed in the LLJ. The condensation induced local circulation strengthens the moisture transport in the LLJ, providing a positive feedback to sustain the Mei-yu precipitation system. It is found that local precipitation recycling shifts heavy rain toward the warm side of the Mei-yu front. This shift of rainfall location is due to the pronounced increase of atmospheric moisture and decrease of surface temperature over the warm side of the front.

Qian, Jian-Hua↗

Spatiotemporal Methane Emissions from Global Reservoirs

Methane (CH4) is a greenhouse gas which contributes significantly to global warming and has atmospheric concentrations which have increased considerably in the last few decades, primarily due to human-induced emissions. Natural sources such as wetlands and inland aquatic systems (i.e., reservoirs, lakes, rivers) contribute substantially to global emissions but these natural systems comprise the most uncertain components of the CH4 budget. This study addresses multiple gaps and uncertainties associated with global CH4 emissions from reservoirs and undertakes a spatial and temporal assessment of global reservoir emissions. The results from this study suggest that reservoirs occupy a global area about 300,000 km2 (comparable to the size of the country of Italy) and emit 10.1 Tg CH4 yr-1. We identify data and methodological elements of previous estimates that indicate they may overestimate these emissions. This work provides a suite of global data sets, gridded at 0.25° × 0.25°, considering reservoir surface area, spatial distribution, eco-climatic system type, and the full annual cycle of daily CH4 emissions.

Spatiotemporal↗

Calculations of cosmogenic nuclide production rates in the Earth's atmosphere and their inventories

The production rates of cosmogenic isotopes in the Earth's atmosphere and their resulting terrestrial abundances have been calculated, taking into account both geomagnetic and solar-modulatory effects. The local interstellar flux was assumed to be that of Garcia-Munoz, et al. Solar modulation was accounted for using the heliocentric potential model and expressed in terms of the Deep River neutron monitor count rates. The geomagnetic field was presented by vertical cutoffs calculated by Shea and Smart and the non-vertical cutoffs calculated using ANGRI. The local interstellar particle flux was first modulated using the heliocentric potential field. The modulated cosmic-ray fluxes reaching the earth's orbit then interacted with the geomagnetic field as though it were a high-pass filter. The interaction of the cosmic radiation with the Earth's atmosphere was calculated utilizing the Bolztmann transport equation. Spallation cross sections for isotope production were calculated using the formalism of Silberberg and Tsao and other cross sections were taken from standard sources. Inventories were calculated by accounting from the variation in solar modulation and geomagnetic field strength with time. Results for many isotope, including C-14, Be-7 and Be-10 are in generally good agreement with existing data. The C-14 inventory, for instance, amounts to 1.75/sq cm(e)/s, in excellent agreement with direct estimates.

Obrien, K.↗

Atmospheric soundings during the Washita 1992 campaign

During the period June 9 through June 18, 1992, an intensive radiosounding program was conducted to measure atmospheric profiles of the wind velocity, the temperature and the specific humidity. The launch site was located near site MS000 in the northeastern part of the catchment of the Little Washita River; this location was selected in order to ensure that the measured profiles would reflect the catchment's surface features for the prevailing southwesterly winds during this time of the year. The launch times of the rawinsondes are shown.

Brutsaert, W.↗

An Automatic Cloud Mask Algorithm Based on Time Series of MODIS Measurements

Quality of aerosol retrievals and atmospheric correction depends strongly on accuracy of the cloud mask (CM) algorithm. The heritage CM algorithms developed for AVHRR and MODIS use the latest sensor measurements of spectral reflectance and brightness temperature and perform processing at the pixel level. The algorithms are threshold-based and empirically tuned. They don't explicitly address the classical problem of cloud search, wherein the baseline clear-skies scene is defined for comparison. Here, we report on a new CM algorithm which explicitly builds and maintains a reference clear-skies image of the surface (refcm) using a time series of MODIS measurements. The new algorithm, developed as part of the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm for MODIS, relies on fact that clear-skies images of the same surface area have a common textural pattern, defined by the surface topography, boundaries of rivers and lakes, distribution of soils and vegetation etc. This pattern changes slowly given the daily rate of global Earth observations, whereas clouds introduce high-frequency random disturbances. Under clear skies, consecutive gridded images of the same surface area have a high covariance, whereas in presence of clouds covariance is usually low. This idea is central to initialization of refcm which is used to derive cloud mask in combination with spectral and brightness temperature tests. The refcm is continuously updated with the latest clear-skies MODIS measurements, thus adapting to seasonal and rapid surface changes. The algorithm is enhanced by an internal dynamic land-water-snow classification coupled with a surface change mask. An initial comparison shows that the new algorithm offers the potential to perform better than the MODIS MOD35 cloud mask in situations where the land surface is changing rapidly, and over Earth regions covered by snow and ice.

Lyapustin, Alexei↗

Teleconnection, Regime Shift, and Predictability of Climate Extremes: A Case Study for the Russian Heat Wave and Pakistan Flood in Summer 2010

In this talk, we present observational evidence showing that the two major extremes events of the summer of 2010, i.e., the Russian heat wave and the Pakistan flood were physically connected. We find that the Pakistan flood was contributed by a series of unusually heavy rain events over the upper Indus River Basin in July-August. The rainfall regimes shifted from an episodic heavy rain regime in mid-to-late July to a steady heavy rain regime in August. An atmospheric Rossby wave associated with the development of the Russian heat wave was instrumental in spurring the episodic rain events , drawing moisture from the Bay of Bengal and the northern Arabian Sea. The steady rain regime was maintained primarily by monsoon moisture surges from the deep tropics. From experiments with the GEOS-5 forecast system, we assess the predictability of the heavy rain events associated with the Pakistan flood. Preliminary results indicate that there are significantly higher skills in the rainfall forecasts during the episodic heavy rain events in July, compared to the steady rain period in early to mid-August. The change in rainfall predictability may be related to scale interactions between the extratropics and the tropics resulting in a modulation of rainfall predictability by the circulation regimes.

Lau, W. K.↗

Diagnosing Warm Season Precipitation Over the GCIP Region from a GCM and Reanalysis

A 45 year simulation using a global general circulation model (GCM), the National Center for Atmospheric Research (NCAR) Community Climate Model v.3 (CCM3), forced with observed sea surface temperatures (SST), and 39 years of global National Centers for Environmental Prediction (NCEP) reanalyses were analyzed to determine Mississippi River basin warm season (May, June, July or MJJ) wet and dry year composites in the water and energy budgets. Years that have increased MJJ soil moisture over the GEWEX (Global Water and Energy Experiment) Continental Interior Project (GCIP) region also have high precipitation, lower surface temperature, decreased Bowen ratio, and reduced 500 hPa geopotential height (essentially reduced MJJ ridging). The reverse is true for years that have reduced MJJ soil moisture. Wet years are also accompanied by a general increase in moisture transport from the Gulf of Mexico into the central U.S. There is some indication (though weaker) that soil moisture may then affect precipitation and other quantities and be affected in turn by 500 hPa geopotential heights. The correlations are somewhat low, however, demonstrating the difficulty in providing definitive physical links between the remote and local effects. Analysis of two individual years with an extreme wet event (1993) and an extreme dry event (1988) yields the same general relationships as with the wet and dry composites. The composites from this study are currently serving as the basis for a series of experiments aimed at determining the predictability of the land surface and remote SST on the Mississippi River basin and other large-scale river basins.

Oglesby, Robert↗

Assimilation of NASA’s Airborne Snow Observatory Snow Measurements for Improved Hydrological Modeling: A Case Study Enabled by the Coupled LIS/WRF-Hydro System

he NASA LIS/WRF-Hydro system is a coupled modeling framework that combines the modeling and data assimilation (DA) capabilities of the NASA Land Information System (LIS) with the multi-scale surface hydrological modeling capabilities of the WRF-Hydro model, both of which are widely used in both operations and research. This coupled modeling framework builds on the linkage between land surface models (LSMs), which simulate surface boundary conditions in atmospheric models, and distributed hydrologic models, which simulate horizontal surface and sub-surface flow, adding new land DA capabilities. In the present study, we employ this modeling framework in the Tuolumne River basin in central California. We demonstrate the added value of the assimilation of NASA Airborne Snow Observatory (ASO) snow water equivalent (SWE) estimates in the Tuolumne basin. This analysis is performed in both LIS as an LSM column model and LIS/WRF-Hydro, with hydrologic routing. Results demonstrate that ASO DA in the basin reduced snow bias by as much as 30% from an open-loop (OL) simulation compared to three independent datasets. It also reduces downstream streamflow runoff biases by as much as 40%, and improves streamflow skill scores in both wet and dry years. Analysis of soil moisture and evapotranspiration (ET) also reveals the impacts of hydrologic routing from WRF-Hydro in the simulations, which would otherwise not be resolved in an LSM column model. By demonstrating the beneficial impact of SWE DA on the improving streamflow forecasts, the article outlines the importance of such observational inputs for reservoir operations and related water management applications.

Hydrologic modeling↗

Assimilation of NASA's Airborne Snow Observatory Snow Measurements for Improved Hydrological Modeling: A Case Study Enabled by the Coupled LIS/WRF-Hydro System

The NASA LIS/WRF-Hydro system is a coupled modeling framework that combines the modeling and data assimilation (DA) capabilities of the NASA Land Information System (LIS) with the multi-scale surface hydrological modeling capabilities of the WRF-Hydro model, both of which are widely used in both operations and research. This coupled modeling framework builds on the linkage between land surface models (LSMs), which simulate surface boundary conditions in atmospheric models, and distributed hydrologic models, which simulate horizontal surface and sub-surface flow, adding new land DA capabilities. In the present study, we employ this modeling framework in the Tuolumne River basin in central California. We demonstrate the added value of the assimilation of NASA Airborne Snow Observatory (ASO) snow water equivalent (SWE) estimates in the Tuolumne basin. This analysis is performed in both LIS as an LSM column model and LIS/WRF-Hydro, with hydrologic routing. Results demonstrate that ASO DA in the basin reduced snow bias by as much as 30% from an open-loop (OL) simulation compared to three independent datasets. It also reduces downstream streamflow runoff biases by as much as 40%, and improves streamflow skill scores in both wet and dry years. Analysis of soil moisture and evapotranspiration (ET) also reveals the impacts of hydrologic routing from WRF-Hydro in the simulations, which would otherwise not be resolved in an LSM column model. By demonstrating the beneficial impact of SWE DA on the improving streamflow forecasts, the article outlines the importance of such observational inputs for reservoir operations and related water management applications.

Timothy M. Lahmers↗

Hydrologic models for land-atmosphere retrospective studies of the use of LANDSAT and AVHRR data

The use of a Geographic Information System (GIS) and LANDSAT analysis in conjunction with the Simulator for Water Resources on a Rural Basin (SWRRB) hydrologic model to examine the water balance on the Little Washita River basin is discussed. LANDSAT analysis was used to divide the basin into eight non-contiguous land covers or subareas: rangeland, grazed range, winter wheat, alfalfa/pasture, bare soil, water, woodland, and impervious land (roads, quarry). The use of a geographic information system allowed for the calculation of SWRRB model parameters in each subarea. Four data sets were constructed in order to compare SWRRB estimates of hydrologic processes using two methods of maximum LAI and two methods of watershed subdivision. Maximum LAI was determined from a continental scale map, which provided a value of 4.5 for the entire basin, and from its association with the type of land-cover (eight values). The two methods of watershed subdivision were determined according to drainage subbasin (four) and the eight land-covers. These data sets were used with the SWRRB model to obtain daily hydrologic estimates for 1985. The results of the one year analysis lead to the conclusion that the greater homogeneity of a land-cover subdivision provides better water yield estimates than those based on a drainage properties subdivision.

Duchon, Claude E.↗