text:
Q: Consolidate does not work with my subquery
Possible Duplicate:
SQL Subquery , One to Multiple rows

Following query I have written returns the result as expected, example 121350 rows.
SELECT dbo.Articles_in_Consignment.Consignment_id,
  dbo.ORDER_D.Orders_boxsize,
  dbo.ORDER_D.Orders_boxweight,
  dbo.ORDER_D.Orders_boxlength,
  dbo.ORDER_D.Orders_boxwidth,
  dbo.ORDER_D.Orders_boxdepth,
  dbo.ORDER_D.Order_dispatchment_id,
  SUM(
    ISNULL(
       dbo.COMPONENT.Component_weight, 0) *
       ISNULL(dbo.ORDER_ALLOCATE.Order_allocate_qty, 0)
  ) AS Component_weight,
  COUNT_BIG(*) AS _ic
FROM dbo.Articles_in_Consignment
   INNER JOIN dbo.ORDER_D
     ON  dbo.Articles_in_Consignment.Order_dispatchment_id = dboRDER_D.Order_dispatchment_id
   INNER JOIN dbo.ORDERS
     ON  dbo.ORDER_D.Order_dispatchment_id = dbo.ORDERS.Order_dispatchment_id
   INNER JOIN dbo.ORDER_ITEMS
     ON  dbo.ORDERS.Orders_id = dbo.ORDER_ITEMS.Orders_id
   INNER JOIN dbo.ORDER_ALLOCATE
     ON  dbo.ORDER_ITEMS.Order_items_id = dbo.ORDER_ALLOCATE.Order_items_id
   INNER JOIN dbo.STOCKIN
     ON  dbo.ORDER_ALLOCATE.Stockin_id = dbo.STOCKIN.Stockin_id
   INNER JOIN dbo.COMPONENT
    ON  dbo.STOCKIN.Component_id = dbo.COMPONENT.Component_id
WHERE  (dbo.ORDERS.Cold = 'No')
GROUP BY
  dbo.Articles_in_Consignment.Consignment_id,
  dbo.ORDER_D.Orders_boxsize,
  dbo.ORDER_D.Orders_boxweight,
  dbo.ORDER_D.Orders_boxlength,
  dbo.ORDER_D.Orders_boxwidth,
  dbo.ORDER_D.Orders_boxdepth,
  dbo.ORDER_D.Order_dispatchment_id

However,WHEN i TRY TO ADD a subquery following SELECT statement the resulted ROWS increases TO 155550 row due TO subquery returning one TO many ROWS.
,(
  SELECT CASE
    WHEN EXISTS (
      SELECT *
      FROM   dbo.ORDER_ITEMS
      WHERE  Component_id IN (1111, 1111)
             AND Orders_id = dbo.ORDERS.Orders_id
    ) THEN CAST(1 AS BIT)
    ELSE CAST(0 AS BIT)
    END
  ) AS DG

Ordering by OrderId.
How can I solve this so that my consolidation of first query does not break due to subquery?
Current result I am getting with subquery...
Consignment_id    Order_boxsize   Order_dispatchment_id   Component_weight   _ic   DG

--------------    -------------   --------------------    ----------------   ---  --

125                L                121212                    0.639           21   0
125                L                121212                    0.639           21   0

expected result with consolidation.
Consignment_id    Order_boxsize   Order_dispatchment_id   Component_weight   _ic   DG

--------------    -------------   --------------------    ----------------   ---  --

125                L                121212                    1. 278         42   0

https://stackoverflow.com/questions/14352512/sql-subquery-one-to-multiple-rows


text:
Il Cantone di Legé era una divisione amministrativa dell'Arrondissement di Nantes.

È stato soppresso a seguito della riforma complessiva dei cantoni del 2014, che è entrata in vigore con le elezioni dipartimentali del 2015.

Comprendeva i comuni di:

 Corcoué-sur-Logne
 Legé
 Touvois

Note

Collegamenti esterni
Statistiche sul sito dell'INSEE

Lege

redpajama_set_name: RedPajamaWikipedia


Get in control of pests and insects with pest and insect control products from California Gardens in Howden. Pest control is part and parcel of your gardening life, and it's pretty certain that at some point you'll need to defend yourself against an attack from six-legged beasties as intent on eating your produce as you are.
Your Humberside garden centre is here to help in the war against pests: they've got every pest control weapon you could need to tackle outbreaks of nasties from slugs to aphids and mealybugs to spider mites. Bring in pictures or samples and the team will be happy to diagnose your problem and help you tackle it effectively.
Barriers keep pests off before they even get started. Lightweight horticultural fleece, available off the roll or in handy packets at California Gardens here in Howden, is a great pest control for keeping carrot fly off, while insect-proof mesh over the brassica bed excludes pigeons and cabbage white butterflies too.
Small colonies of aphids are easily squished between thumb and forefinger: but for larger infestations you'll need a bottle of insecticidal soap from California Gardens. It's derived from plant-based fatty acids so completely organic: spray onto plants in dry weather and repeat as necessary.
You can also protect entire beds by harnessing the power of Mother Nature. Among the best selling products in the range of biological pest controls at California Gardens is a slug-eating nematode you just water onto the ground every six weeks for season-long control. Ask the staff at the garden centre for a demonstration: we guarantee you won't look back.


text:
Epic Mickey 2 to feature muscial numbers, 2D levels return, first boss battle revealed
New gameplay footage from Epic Mickey 2: The Power of Two has been released, confirming that 2D levels will return in the upcoming sequel and also revealing the game's first boss encounter.
Pete's Dragon headlines
Pete's Dragon latest

redpajama_set_name: RedPajamaCommonCrawl


text:
Rubio shifts to the offensive in an effort to slow Trump
THOMAS BEAUMONT and STEVE PEOPLESThe Associated Press
A flood of mainstream Republican officials and donors have lined up behind Marco Rubio in the week since former Florida Gov. Jeb Bush suspended his campaign for president.
KENNESAW, Georgia — A flood of mainstream Republican officials and donors have lined up behind Marco Rubio in the week since former Florida Gov. Jeb Bush suspended his campaign for president.
And yet Rubio's team concedes that neither the influx of support, nor the conversion of many of Bush's wealthy donors, is enough to stop Donald Trump.
Instead of riding the wave of new support alone, Rubio has been forced to speed up plans for an all-out assault on the billionaire businessman's character.
Rubio had hoped to wait until the chaotic Republican nominating campaign had shrunk to a two-man race. But with a growing sense of urgency among GOP stalwarts to settle on a Trump alternative, the young Florida senator is trying to simultaneously slow Trump and cast himself the savior of the party's future.
"I will never quit. I will never stop until we keep a con man from taking over the party of Reagan and the conservative movement," Rubio thundered at a rally with 2,000 people in Oklahoma City on Friday.
It is a delicate balance.
Rubio, a 44-year-old first-term U.S. senator, is trying to project leadership in the party while also going after Trump using his own game, marked by mockery and uncanny aim for his opponent's vulnerabilities.
But it's a necessary one, says Rubio's latest big endorsement, Tennessee Gov. Bill Haslam.
"Rubio looked around and thought, 'Well, I might not like it, but that's what the media is covering and that's what people are responding to.'"
But Rubio is quickly getting a feel for what he began during Thursday's debate, launching a direct challenge to Trump's appeal to working class voters.
In recent days, Rubio has dished about Trump's on-stage perspiration and alluded, jokingly, that Trump may have wet his pants. He's also taken to referring to the billionaire businessman as a "con artist" dozens of times a day while campaigning.
"It's amazing to me. A guy with the worst spray tan in America is attacking me for putting on makeup," Rubio charged as he campaigned in Georgia on Saturday. "Donald Trump likes to sue people. He should sue whoever did that to his face."
But make no mistake: Rubio's new tack is a fight for survival.
He trails Trump in virtually all of the 11 states holding nominating contests on March 1, known as Super Tuesday. The Florida senator has finished in no better than second place in the first four primary contests. Trump has won three out of four. And Texas Sen. Ted Cruz remains a top-tier contender, even after finishing in third place in the last three contests.
Given Trump's momentum, Rubio's team says publicly the senator's best chance for the nomination might be a contested national convention in July. That could happen only if Rubio prevents Trump from accumulating the majority of delegates in the months-long primary season that extends through June.
But Rubio said Saturday he expects to win the nomination outright.
"It'll take a few days to realize the game he's running. He's going to start to lose support, maybe not in time for Tuesday, but certainly in time for all states," Rubio said of Trump to reporters in Alabama, during a blur of Super Tuesday state stops. "I really believe the voters will decide."
And with Bush now out of the race, Rubio has begun reeling in donors once loyal to the former governor.
Some Florida-based donors, as well as top donors and fundraisers in Washington, D.C., Chicago and elsewhere were ready to join Rubio's team immediately after Bush left the race. Rubio also attended a fundraiser in Midland, Texas, a longtime Bush stronghold, on Friday that featured several former Bush donors.
"There are a number of us, now that Gov. Bush is out of the race, who were very impressed with his debate Thursday, and see him as the one to take down Trump," said Chicago investor Craig Duchossois, who shifted from Bush to Rubio. "He showed he's not going to take any crap from him."
Rubio aides confirmed Sunday that Chicago investor Muneer Satter, a former leading Bush campaign donor, had joined Rubio's campaign as a member of his national fundraising leadership.
In the past two weeks, Rubio has also won the backing of four governors and 20 members of Congress, more than all of his Republican rivals combined.
Rubio had hoped to forestall a one-on-one brawl with Trump until there were only two. Cruz, Ohio Gov. John Kasich and retired neurosurgeon Ben Carson remain in the race, although none have the level of support from as many governors and members of Congress as Rubio.
In a year of the outsider, however, it's unclear how much that will boost his momentum.
And in the meantime, Rubio's assault on Trump's character continues.
Audiences in Super Tuesday states Oklahoma, Georgia and Alabama ate up the tough talk as he whipped through Southern states.
"It's about time he take his gloves off and start fighting," said Gary Baker from Okmulgee, Oklahoma. "I think he should have started punching sooner."
Better late than never, said Greg Strimple, a Republican pollster and former adviser to the National Republican Senatorial Committee.
"The Rubio campaign needs to set-up a contrast on Trump, equate Trump to the culture of corruption Americans hate — where the rich get richer and middle class pays the price," Strimple said.
Rubio says there's time, but none to waste.
"If you sense a sense of urgency, it's not just about winning," Rubio said. "It's about the idea that the party of Reagan and the conservative movement could fall into the hands of a con man, who's pulling the ultimate con job on the American people."


text:
package com.zaradai.lattrac

import com.zaradai.lattrac.capture._
import com.zaradai.lattrac.store.Observer

class LatencyServiceDecorator(builder: LatencyBuilder) extends LatencyTracerService {
  private[this] lazy val service = builder.buildWithAutoLifecycle

  override def trace(id: String, location: String): Unit =
    service.trace(id, location)

  override def observe(observer: Observer[TraceEvent]): Unit =
    service.observe(observer)
}

object FineLatencyTracer extends LatencyServiceDecorator(LatencyTracerBuilder.nanos.inMemory.disruptored)

object FineLatencyTracerBackedByMongo extends LatencyServiceDecorator(LatencyTracerBuilder.nanos.usingMongo().disruptored)

object CourseLatencyTracer extends LatencyServiceDecorator(LatencyTracerBuilder.millis.inMemory.queued)

object CourseLatencyTracerBackByMongo extends LatencyServiceDecorator(LatencyTracerBuilder.millis.usingMongo().queued)

redpajama_set_name: RedPajamaGithub


Hot on the heels of his excellent new EP for @free-love-digi, we've secured a fantastic new mix from LA producer @moralz. Blending footwork, halftime D&B and hip-hop for an exuberant take on the 170BPM sound, the mix features cuts from Moralz and fellow FLD associates Thomas B and Ghast alongside beats from Fracture, Om Unit, Machinedrum, Moresounds and many more. Future jungle business!


21. And what more does the Word contribute to our salvation than the Son, if, as they hold, the Son is one, and the Word another? For the command is that we should believe, not in the Word, but in the Son. For John says, 'He that believes in the Son, has everlasting life; but he that believes not the Son, shall not see life John 3:36.' And Holy Baptism, in which the substance of the whole faith is lodged, is administered not in the Word, but in Father, Son, and Holy Ghost. If then, as they hold, the Word is one and the Son another, and the Word is not the Son, Baptism has no connection with the Word. How then are they able to hold that the Word is with the Father, when He is not with Him in the giving of Baptism? But perhaps they will say, that in the Father's Name the Word is included? Wherefore then not the Spirit also? Or is the Spirit external to the Father? And the Man indeed (if the Word is not Son) is named after the Father, but the Spirit after the Man? And then the Monad, instead of dilating into a Triad, dilates according to them into a Tetrad, Father, Word, Son, and Holy Ghost. Being brought to shame on this ground, they have recourse to another, and say that not the Man by Himself whom the Lord bore, but both together, the Word and the Man, are the Son; for both joined together are named Son, as they say. Which then is cause of which? And which has made which a Son? Or, to speak more clearly, is the Word a Son because of the flesh? Or is the flesh called Son because of the Word? Or is neither the cause, but the concurrence of the two? If then the Word be a Son because of the flesh, of necessity the flesh is Son, and all those absurdities follow which have been already drawn from saying that the Man is Son. But if the flesh is called Son because of the Word, then even before the flesh the Word certainly, being such, was Son. For how could a being make other sons, not being himself a son, especially when there was a father ? If then He makes sons for Himself, then is He Himself Father; but if for the Father, then must He be Son, or rather that Son, by reason of Whom the rest are made sons.


You need more than just a good knowledge of the hotel industry to become successful in hotel manager in Bangladesh. Not only this but you also need to develop excellent management, time management, interpersonal and research skills, and good interpersonal skills.
Although a good hotel manager knows how to delegate, always keeps a close eye on every aspect of the business like kitchen, service, cleaning, maintenance, front desk etc. Also, you need to become a good communicator and to actively seek information about what's going on in the hotel, the industry, and in the wider society if you want to be successful in this career.
And you'll keep a very close eye on every aspect of the business as a good hotel manager. So, if you have these qualities then you must be successful in hotel management.
You should think about the jobs when you're a hotel manager in Bangladesh and for you is that there are job opportunities might also be found in other accommodation and tourism businesses, including resorts, health farms, cruise ships, inns or motels. If that's where you want to go then any of these can also provide a pathway to a position in a large hotel.
Apart from these, other opportunities may exist in the non-profit sector. These may include, for example, hospitals, aged care centers, orphanages, women's refuges or refugee centers. A qualification in hospitality or sometimes, in management is one of the common career paths in this industry through education.
Although this can start you off with sound skills and knowledge, you can apply while gaining necessary experience. And with suitable qualifications and experience, you might later go in a completely different direction.
In addition of these, there is another career path through an experience where you can find work in any area of a hotel and work your way up if you can demonstrate your commitment, abilities and personal qualities.
As those people will be thoroughly trained in that hotel's ethics, standards and procedures, many top hotel chains prefer people to work their way up at the hotel. So, while starting with any job in a hotel you can start your career of a hotel manager in Bangladesh.
You need a bachelor's degree in hospitality or hotel management if you want to be a hotel manager in Bangladesh. Also, you may be hired with an associate's degree or a certificate in hotel management if hotels with fewer services and less complicated operations.
Besides, there are many types of lodging and the salaries vary according to industry, level of responsibility and geographic location.
Although hotel managers earned a median annual income of $51,840, the bottom 10 percent of earners in the field earned around $28,870, while the top 10 percent earned over $96,570. On the other hand, hotel managers in larger establishment earned the most, with an average annual wage of $98,570.
Hotel managers may be assigned different roles and tasks by different employers while giving the differences in kinds and sizes of hotels. And in this case, a hotel manager in Bangladesh may be assigned different roles and tasks by different employers.
When they are coordinating their activities with those of managers in other sections and someone may manage only one section of a hotel. While the deal with the many problems that arise in this business, you'll continually monitor guest satisfaction.
And if the guests are satisfied then you're going to the top with your hotel management soon. Well, let's know some steps to become a hotel manager in Bangladesh.
When some people say don't bother, some other think hospitality degrees are worth it. Before sinking a lot of money into a hospitality degree, you should consider a few important factors. But, a degree might be necessary to separate yourself from the pack for some of the most coveted hotel management jobs.
As plenty of colleges offer courses in hotel management programs, the best way to find out what type of degree your hotel values the most is to simply ask. Also, those who have produced hotel managers for them in the past, they may have a relationship with a college.
If you think a hotel management is a job that students land right out of undergraduate school then you're in the wrong. In a series of increasingly responsible positions, most properties prefer managers with on-the-job experience.
For example, a desk clerk might get promoted to chief room clerk and after that front office manager, sales and promotion manager and finally, a hotel manager in Bangladesh.
Although employees who show leadership potential and have several years of experience can sometimes move into assistant manager jobs, employers typically reserve management-training spots for college-educated candidates. So, you should look for experience through part-time summer jobs and internships as an aspiring hotel manager.
Slower than the average growth of 7% for all jobs, jobs for hotel managers will grow 4% from 2016 to 2026, according to the statistics.
The hotel sector will move toward more limited-service properties with fewer amenities and features to manage as the tourism industry will expand. Apart from these, hotel operators are scaling back on management to slash costs. As there are fewer competitors for management openings, employment prospects will be best at smaller hotels.
If you can become an apprentice or if they provide some form of leadership training then going the extra mile can include directly asking the current management.
When you want to make the hotel better and will more than likely try to accommodate you, management will love seeing that. If the apprentices complete a six-week rotation through each department in a hotel then they choose a department to focus on for about four months. They make a presentation to the executive committee after the apprenticeship ends and even receive a certificate that is recognized across the industry.


text:
2. The divergence and curl operators
a. The grid and coordinate system
b. Vector operators
3. Governing equations
4. Conservation principles
a. Conservation of the domain-mean mass and tracer
b. Conservation of the tracer variance
c. Conservation of total energy
1) Conservation of kinetic energy under advection
2) The energy conversion term
5. Properties of the finite-difference operators
6. Numerical tests
7. Discussion and conclusions
Comparison of Numerical Schemes
Mass equation
OS_Vor-Div scheme
NS_Vor_Div scheme
Vorticity equation
Divergence equation
Export References
Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical process of the UCLA general circulation model. Methods in Computational Physics. J. Chang, Ed., Vol. 17. Academic Press, 173–265.
Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical process of the UCLA general circulation model. Methods in Computational Physics. J. Chang, Ed., Vol. 17. Academic Press, 173–265.)| false
Arakawa, A., and V. R. Lamb, . 1981: A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Wea. Rev., 109 , 18–36.
Arakawa, A., and V. R. Lamb, . 1981: A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Wea. Rev., 109, 18–36.)| false
Baumgardner, J. R., and P. O. Frederickson, 1985: Icosahedral discretization of the two-sphere. SIAM J. Numer. Anal., 22 , 1107–1115.
Baumgardner, J. R., and P. O. Frederickson, 1985: Icosahedral discretization of the two-sphere. SIAM J. Numer. Anal., 22, 1107–1115.)| false
Giraldo, F. X., 2000: Lagrange–Galerkin methods on spherical geodesic grids: The shallow water equations. J. Comput. Phys., 160 , 336–368.
Giraldo, F. X., 2000: Lagrange–Galerkin methods on spherical geodesic grids: The shallow water equations. J. Comput. Phys., 160, 336–368.)| false
Heikes, R., 1993: The shallow water equations on a spherical geodesic grid. Department of Atmospheric Science Tech. Rep. 524, Colorado State University, 175 pp.
Heikes, R., 1993: The shallow water equations on a spherical geodesic grid. Department of Atmospheric Science Tech. Rep. 524, Colorado State University, 175 pp.)| false
Heikes, R., and D. A. Randall, 1995a: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests. Mon. Wea. Rev., 123 , 1862–1880.
Heikes, R., and D. A. Randall, 1995a: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests. Mon. Wea. Rev., 123, 1862–1880.)| false
Heikes, R., and D. A. Randall, . 1995b: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy. Mon. Wea. Rev., 123 , 1881–1887.
Heikes, R., and D. A. Randall, . 1995b: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy. Mon. Wea. Rev., 123, 1881–1887.)| false
Masuda, Y., and H. Ohnishi, 1987: An integration scheme of the primitive equations model with an icosahedral-hexagonal grid system and its application to the shallow water equations. Short- and Medium-Range Numerical Weather Prediction, T. Matsuno, Ed., Universal Academy Press, 317–326.
Masuda, Y., and H. Ohnishi, 1987: An integration scheme of the primitive equations model with an icosahedral-hexagonal grid system and its application to the shallow water equations. Short- and Medium-Range Numerical Weather Prediction, T. Matsuno, Ed., Universal Academy Press, 317–326.)| false
Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed. Springer-Verlag, 710 pp.
Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed. Springer-Verlag, 710 pp.)| false
Randall, D. A., 1994: Geostrophic adjustment and the finite-difference shallow water equations. Mon. Wea. Rev., 122 , 1371–1377.
Randall, D. A., 1994: Geostrophic adjustment and the finite-difference shallow water equations. Mon. Wea. Rev., 122, 1371–1377.)| false
Randall, D. A., R. Heikes, and T. D. Ringler, 2000: Global atmospheric modeling using a geodesic grid with an isentropic vertical coordinate. General Circulation Model Development, D. A. Randall, Ed., Academic Press, 509–538.
Randall, D. A., R. Heikes, and T. D. Ringler, 2000: Global atmospheric modeling using a geodesic grid with an isentropic vertical coordinate. General Circulation Model Development, D. A. Randall, Ed., Academic Press, 509–538.)| false
Ringler, T. D., and D. A. Randall, 2002: The ZM grid: An alternative to the Z grid. Mon. Wea. Rev., 130 , 1411–1422.
Ringler, T. D., and D. A. Randall, 2002: The ZM grid: An alternative to the Z grid. Mon. Wea. Rev., 130, 1411–1422.)| false
Ringler, T. D., R. P. Heikes, and D. A. Randall, 2000: Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores. Mon. Wea. Rev., 128 , 2471–2490.
Ringler, T. D., R. P. Heikes, and D. A. Randall, 2000: Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores. Mon. Wea. Rev., 128, 2471–2490.)| false
Sadourny, R., and P. Morel, 1969: A finite-difference approximation of the primitive equations for a hexagonal grid on a plane. Mon. Wea. Rev., 97 , 439–445.
Sadourny, R., and P. Morel, 1969: A finite-difference approximation of the primitive equations for a hexagonal grid on a plane. Mon. Wea. Rev., 97, 439–445.)| false
Sadourny, R., A. Arakawa, and Y. Mintz, 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedal-hexagonal grid for the sphere. Mon. Wea. Rev., 96 , 351–356.
Sadourny, R., A. Arakawa, and Y. Mintz, 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedal-hexagonal grid for the sphere. Mon. Wea. Rev., 96, 351–356.)| false
Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 375 pp.
Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 375 pp.)| false
Stuhne, G. R., and W. R. Peltier, 1996: Vortex erosion and amalgamation in a new model of large scale flow on a sphere. J. Comput. Phys., 128 , 58–81.
Stuhne, G. R., and W. R. Peltier, 1996: Vortex erosion and amalgamation in a new model of large scale flow on a sphere. J. Comput. Phys., 128, 58–81.)| false
Stuhne, G. R., and W. R. Peltier, . 1999: New icosahedral grid-point discretizations of the shallow water equations on the sphere. J. Comput. Phys., 144 , 23–58.
Stuhne, G. R., and W. R. Peltier, . 1999: New icosahedral grid-point discretizations of the shallow water equations on the sphere. J. Comput. Phys., 144, 23–58.)| false
Thuburn, J., 1997: A PV-based shallow-water model on a hexagonal-icosahedral grid. Mon. Wea. Rev., 125 , 2328–2347.
Thuburn, J., 1997: A PV-based shallow-water model on a hexagonal-icosahedral grid. Mon. Wea. Rev., 125, 2328–2347.)| false
Williamson, D. L., 1968: Integration of the barotropic vorticity equation on a spherical geodesic grid. Tellus, 20 , 642–653.
Williamson, D. L., 1968: Integration of the barotropic vorticity equation on a spherical geodesic grid. Tellus, 20, 642–653.)| false
Williamson, D. L., . 1969: Numerical integration of fluid flow over triangular grids. Mon. Wea. Rev., 97 , 885–895.
Williamson, D. L., . 1969: Numerical integration of fluid flow over triangular grids. Mon. Wea. Rev., 97, 885–895.)| false
Winninghoff, F. J., 1968: On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis. Ph.D. thesis, University of California, Los Angeles, 161 pp.
Winninghoff, F. J., 1968: On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis. Ph.D. thesis, University of California, Los Angeles, 161 pp.)| false
Export Figures
Grid points, shown as circles, can be connected to form a triangular grid shown by the dashed lines. Alternatively, cell walls can be positioned halfway between grid points to form a hexagonal grid shown by the solid lines. The hexagonal grid is the dual of the triangular grid
The grid is composed of hexagons (and possibly pentagons) with scalars defined at the cell centers and vectors defined at the cell corners. Each vector is described in the (e1, e2) coordinate system that is placed at each cell corner. The normal vectors to the cell walls are nc+ and nc−, where the c+ direction is in the counterclockwise direction from c and c− is in the clockwise direction. The area associated with each corner, Ac, is defined by the line segments connecting the grid-cell centers. R0c is the portion of Ac owned by cell 0. The area associated with the grid-cell center, Ai, is defined by the perimeter of the hexagon
The symbol hi for 0 ≤ i ≤ 2 represents an averaging of mass to the cell wall shared by grid cell i and i + 1. The area of the triangle is divided into three parts, Ric. The unit vectors normal to each cell-wall segment are given as ni and point from cell center i to cell center i + 1
Log base 10 of (top) the fractional change in total energy and (bottom) the mass-weighted potential enstrophy for each numerical simulation
(top) Energy power spectrum and (bottom) enstrophy power spectrum at day 40 for each numerical simulation, plotted as functions of total wavenumber. The open circles show the initial energy and enstrophy power spectra
(top) Total energy power spectrum and (bottom) enstrophy power spectrum averaged over days 950–1050. The open circles show the initial energy and enstrophy power spectra. Also shown in each panel, by a dashed line, is the theoretical prediction of the slope of the respective spectrum. The solid line denotes the equivalent wavenumber of the Rossby radius of deformation
The evolution of the relative vorticity field over the first 1000 days of integration. The relative vorticity scales range from approximately ±2.0 × 10−5, ±1.5 × 10−5, ±1.0 × 10−5, and ±3.0 × 10−6 s−1 at t = 0, t = 10, t = 100, and t = 1000 days, respectively.
View raw image
A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid
Todd D. Ringler
Todd D. RinglerDepartment of Atmospheric Science, Colorado State University, Fort Collins, Colorado
Search for other papers by Todd D. Ringler in
David A. Randall
David A. RandallDepartment of Atmospheric Science, Colorado State University, Fort Collins, Colorado
Search for other papers by David A. Randall in
https://doi.org/10.1175/1520-0493(2002)130<1397:APEAEC>2.0.CO;2
Using the shallow water equations, a numerical framework on a spherical geodesic grid that conserves domain-integrated mass, potential vorticity, potential enstrophy, and total energy is developed. The numerical scheme is equally applicable to hexagonal grids on a plane and to spherical geodesic grids. This new numerical scheme is compared to its predecessor and it is shown that the new scheme does considerably better in conserving potential enstrophy and energy. Furthermore, in a simulation of geostrophic turbulence, the new numerical scheme produces energy and enstrophy spectra with slopes of approximately K−3 and K−1, respectively, where K is the total wavenumber. These slopes are in agreement with theoretical predictions. This work also exhibits a discrete momentum equation that is compatible with the Z-grid vorticity-divergence equation.
Corresponding author address: Todd Ringler, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. Email: todd@atmos.colostate.edu
A spherical geodesic grid is a tessellation of the sphere that is generated by using the icosahedron as a starting point (e.g., Heikes and Randall 1995a). The potential applicability of spherical geodesic grids to the simulation of the atmospheric general circulation has been recognized since the 1960s (Sadourny et al. 1968; Williamson 1968, 1969; Sadourny and Morel 1969). Recently there has been renewed interest in this idea (Baumgardner and Frederickson 1985; Masuda and Ohnishi 1987; Heikes 1993; Heikes and Randall 1995a,b; Stuhne and Peltier 1996, 1999; Thuburn 1997; Giraldo 2000; Randall et al. 2000; Ringler et al. 2000).
Sadourny and Morel (1969) proposed that an optimal grid structure on the sphere should be as uniform as possible while preserving the isotropy of the spherical geometry. Spherical geodesic grids come close to meeting these ideal specifications. In terms of uniformity, a spherical geodesic grid can be constructed such that grid cell areas vary by less than 5% over the entire sphere (Heikes 1993). In terms of isotropy, relative to any given grid cell center all cell neighbors are nearly equidistant, and all the neighbors lie across cell walls (Randall et al. 2000). While Sadourny and Morel (1969) chose the spherical geodesic grid because of its uniformity, Williamson (1969) chose a spherical geodesic grid because the grid could be gradually distorted in space to produce increased resolution in critical regions such as the Gulf Stream.
In contrast to spherical geodesic grids, conventional latitude–longitude grids are neither uniform nor isotropic. The grid-pole singularities of latitude–longitude grids result in grid-cell areas that vary by O(1) over the globe. Furthermore, since latitude–longitude grids have cell neighbors that lie across both cell walls and cell corners, the grids are not isotropic.
While the merits of the spherical geodesic grid may have been appreciated decades ago, only recently have these merits been realized in simulations with full atmospheric general circulation models (AGCMs). Attempts to use spherical geodesic grids to solve the nondivergent shallow-water equations were successful (Sadourny et al. 1968; Williamson 1968). The difficulties involved in modeling the divergent shallow-water equations on the spherical geodesic grid were not overcome, however, until Masuda and Ohnishi (1987) proposed using the vorticity-divergence form of the equations. The vorticity-divergence formulation requires inverting elliptic equations at every time step to obtain the velocity field. The computational overhead required to do this with finite-difference models was generally considered prohibitive. Heikes and Randall (1995a,b, hereafter HR95) overcame this significant difficulty by implementing a multigrid method to invert the elliptic equations in a computationally efficient manner. Ringler et al. (2000) extended this framework from the shallow-water equations to the full 3D primitive equations and incorporated the physical parameterizations required for climate simulations.
Williamson (1969) chose to tile the sphere with triangles by connecting the grid points of the spherical geodesic grid (see Fig. 1). Alternatively, Sadourny and Morel (1969) used the inverse, or dual, of the triangular grid, which results in hexagonal grid cells also shown in Fig. 1. The lineage of work leading to the creation of a full AGCM based on a spherical geodesic grid in Ringler et al. (2000) emphasized the use of the hexagonal grid cells. An alternative line of research that emphasized the use of the triangular grid cells originated with both Williamson (1969) and Baumgardner and Frederickson (1985). The more recent works by Stuhne and Peltier (1996, 1999) and Giraldo (2000) use triangular finite elements to construct their numerical schemes. The present study makes extensive use of both the hexagonal and triangular grids.
As discussed by Arakawa and Lamb (1977), the problem of designing a numerical scheme for a general circulation model can be conceptually separated into the design of the linear properties of the scheme, and the design of its nonlinear properties. The numerical simulation of linear wave phenomena in geophysical fluid dynamics can be analyzed in terms of the geostrophic adjustment process (Winninghoff 1968; Arakawa and Lamb 1977; Randall 1994). The atmosphere is continually adjusting to forcings, such as diabatic heating, by the radiation of inertia–gravity waves, which leave behind an "adjusted" state that is close to geostrophic balance. In order to produce realistic results, a numerical scheme must faithfully reproduce this adjustment process. Following the lead of Masuda and Ohnishi (1987), HR95 used the "Z grid," on which vorticity, divergence, and mass are prognosed, in part because, as shown by Randall (1994), the Z grid simulates geostrophic adjustment very well; that is, schemes based on the Z grid have good linear properties. HR95 used a finite-volume method which guarantees conservation of mass, including tracer mass, as well as potential vorticity. HR95 did not discuss the conservation of nonlinear functions of the prognostic fields, such as the kinetic energy, total energy, and potential enstrophy.
The present study is aimed at modifying the scheme of HR95 so as to guarantee conservation of kinetic energy, total energy, and potential enstrophy under frictionless processes. Such conservation properties are particularly important in long-term simulations such as those that are needed for the study of climate. On long timescales, sources and sinks of energy and other quantities are fundamental to the circulation. Small but systematic spurious sources and sinks of fundamental quantities, such as energy, can lead to unrealistic circulation regimes.
The continuous two-dimensional nonlinear shallow-water equations are highly constrained in terms of their energy and enstrophy cascades. The net effect of advection is to transfer energy from shorter to longer spatial scales, while transferring enstrophy from longer to shorter spatial scales. Arakawa and Lamb (1977, 1981) point out that we have little hope of accurately simulating such energy cascades and the associated energy spectra if the numerical schemes do not conserve energy and potential enstrophy. They show that conserving basic quantities, such as mass, potential vorticity, potential enstrophy, and energy, can dramatically increase the overall accuracy of long numerical simulations, even with no change in the local "order of accuracy" of the schemes. While schemes of higher-order accuracy are generally to be preferred, all other things being equal, a formal increase in order of accuracy should not be chosen at the expense of the conservation principles. Arakawa and Lamb (1977) provide an example of a lower-order conservative numerical scheme that produces a more realistic simulation than a higher-order nonconserving scheme.
The scheme presented in this paper is equally applicable to planar hexagonal grids (see Fig. 1) and a spherical geodesic grid. The spherical geodesic grid is quite similar to the hexagonal grid; all the grid cells are hexagons, with the exception of 12 grid cells that are pentagons (Sadourny and Morel 1969). In section 2 we construct some of the building blocks of the numerical scheme, namely the divergence, and curl operators, from their respective definitions. We then use these basic operators, in section 3, to obtain a discrete form of the shallow-water equations. In section 4 we show that this discrete system conserves a number of important quantities: mass, potential vorticity, potential enstropy, and total energy. In section 5 we demonstrate some properties of our finite-difference operators. This numerical scheme has been implemented in a shallow water model on a doubly periodic plane. Results are shown in section 6, and these results are compared and contrasted to those produced with the numerical scheme currently used in the Colorado State University (CSU) AGCM (Ringler et al. 2000). Section 7 gives a discussion that places our numerical scheme into context.
The numerical scheme developed below is defined on a grid of polygons that are either hexagonal or pentagonal in shape. When discretizing the surface of a plane, all the polygons are hexagons. When discretizing the sphere, all of the polygons are hexagons with the exception of 12 polygons that are pentagons.
All scalars, such as the fluid depth, are defined at the centers of the grid cells and are referenced with the subscript i, while all vectors, such as the velocity vector, will be defined at the cell corners and referenced with the subscript c. When we wish to analyze a specific corner, we will set c = γ as shown in Fig. 2 and use the data from the surrounding numbered cell centers. In addition to cell centers and cell corners, we will need to reference segments of the cell walls defined by the symbol d. We will use the subscripts c+ and c− to denote the cell wall segments on d in the counterclockwise and clockwise directions from corner c, respectively. The unit vectors nc+ and nc− denote the directions perpendicular to dc+ and dc−, respectively, and point outward relative to cell center 0.
At each corner we have placed an arbitrary orthogonal coordinate system defined by the unit vectors (e1, e2). The area fluxes across the dc+ and dc− wall segments are Vc · nc+dc+, and Vc · nc−dc−, respectively. We use the symbols Ai and Ac to represent the total areas associated with the grid cell centers and corners, respectively. The area of the shaded region in Fig. 2, denoted by Ric, is the portion of Ac that is associated with cell center i.
With the coordinate system defined in Fig. 2, we can derive numerical approximations to the divergence and curl operators from their respective analytic definitions.1 The analytic form of the divergence operator is
The divergence operator yields a scalar, which will be defined at cell centers, by summing over the dot product of vector data defined at cell corners. Referring to Fig. 2, we can approximate the divergence operator at the cell centers as
where the summation is over all cell corners associated with grid cell i. The variable nc is equal to 6 for hexagons and 5 for pentagons. If we define
then we can rewrite (2) in the more compact form
The definition of the curl operator is
where we have explicitly selected the "vertical" component of the curl by dotting with k. Since the curl is a scalar quantity, it will be defined at grid-cell centers. We can approximate (5) as
where, as with the divergence operator, the summation is over all cell corners associated with the cell center i.
The shallow-water equations can be written as
where h is the fluid depth, hs is the height of the surface, V is the vector velocity, K is the kinetic energy, and η is the absolute vorticity. Equation (9) describes the evolution of an arbitrary tracer τ, where τ is a mixing ratio. Alternatively, we can take the curl and divergence of (8) to generate equations for the vorticity and divergence:
Here η ≡ f + k · ∇ × V is the absolute vorticity and δ ≡ ∇·V is the divergence. In the continuous equations, the vector momentum formulation and the vorticity-divergence formulation are equivalent. Given η and δ we can determine V in two steps. First, we solve the elliptic equations
for the streamfunction, ψ, and velocity potential, χ. We then compute the velocity using the relation
Vkψχ. (14)
Given the discrete analogs to the divergence and curl operators derived in section 2, we can write the discrete forms of (7), (8), and (9) as
where (15) and (17) describe the evolution of mass and mass-weighted tracer within a grid cell. Equation (16) describes the evolution of the velocity at a cell corner. For clarity we reiterate our notation: terms with a subscript i are defined at cell centers, terms with a subscript c are defined at cell corners, and terms with a subscript c+ or c− are defined at the cell walls. The terms hc+, τc+, hc−, and τc− should be interpreted as averages of mass and tracer from the cell centers to the cell wall segment c+ and c−. The term ηc is the average of absolute vorticity from the cell centers to the cell corners. All of these symbols are undefined at this point. The form of the kinetic energy, Ki, is undefined, as is the discrete form of the gradient operator.
The discrete forms of the vorticity and divergence equations can be written down by analogy with the analytic forms shown in (10) and (11):
Since we have not yet specified the form of the discrete gradient operator, the discrete Laplacian operator is unspecified. In section 5 we will show that (18) and (19) can, alternatively, be derived from the discrete form of the momentum equation. As a result, the discrete momentum formulation will be entirely consistent with the discrete vorticity-divergence formulation.
In the shallow-water equations the potential vorticity, q, is equal to the absolute vorticity divided by the layer thickness, h, so we can rewrite (18) as
which is identical in form to the tracer equation.
While the continuous equations allow an infinite number of quantities to be conserved, this is not possible within the discrete system. In this section we will show that with the appropriate choices of hc+, τc+, hc−, τc−, ηc, Ki, and the gradient operator, the discrete shallow-water equations shown above can be implemented such that the following quantities are conserved in the domain mean: mass, mass-weighted tracer, and mass-weighted potential vorticity, mass-weighted tracer variance, mass-weighted potential enstrophy, and total energy.
The domain-integrated mass, mass-weighted tracer, and mass-weighted potential vorticity are conserved simply by virtue of their flux forms, written in (15), (17), and (20), respectively. The only stipulation is that hc+, τc+, hc−, τc−, qc+, and qc− have the same values when referenced by either of the cell centers that share a given cell wall. This is equivalent to the requirement that the flux out of one cell is identical to the flux into its neighbor. This will become more explicit later when we more precisely define these quantities.
In order to show how the mass-weighted tracer variance can be conserved, we must start with the advective form of the tracer equation. The advective form is obtained by taking (17) − τi × (15) to yield
Following Arakawa and Lamb (1977) we introduce a function G = G(τ) that depends only on τ. We can construct an equation for G by taking (15) × G(τ) and adding it to (21) × dG/dτ. This results in
If we choose c = γ, as shown in Fig. 2, and recognize that Fc+ represents the flux between cell 0 and cell 2, while Fc− represents the flux between cell 0 and cell 1, we can see that G will be conserved if
Solving (23) for τc+ and (24) for τc−, we obtain
As an example, if we choose G(τ) = τ2 we can solve (25) and (26) for τc+ and τc− to obtain
Note that no additional constraints on hc+ or hc− are required.
Since the potential vorticity equation, (20), is identical in form to the tracer equation, (17), we can use the results of (27) and (28) to guarantee the conservation of potential enstrophy in the discrete system. We can write the vorticity equation by using the lhs of (18) and the rhs of (20) to yield
Instead of averaging vorticity to the cell walls, we average potential vorticity to the cell walls using (27) and (28) and then multiply by the averaged mass.
The total energy in the discrete shallow-water equations is conserved. We show this in two steps: first, that kinetic energy is conserved under the process of advection, and second, that the energy conversion term neither creates nor destroys total energy.
In this section we will find the form of the gradient operator that guarantees that the process of advection neither creates nor destroys kinetic energy. First, we must form the kinetic energy equation by taking the scalar product of Vc and the momentum equation given in (16):
This equation is valid for every cell corner. The first term on the rhs of (30) is identically zero at every cell corner because Vc is perpendicular to k × Vc, even in the discrete case. Recall that while the momentum equation is defined at cell corners, the kinetic energy is a scalar and will, therefore, be defined at cell centers. To move (30) from the corners to the centers, we weight each momentum point by the area, Ric, as defined in Fig. 2 and sum over all corners associated with grid cell i to yield
where we have multiplied by the cell mass, hi, after summing over the corners. Equation (31) holds at every cell center.
We now multiply the continuity equation, (15), by Ki to obtain
where we have moved the cell area, Ai, to the lhs of the equation. Equations (31) and (32) are both defined at cell centers, so we can add them together to yield
where we have used (3) to express (33) completely in terms of the velocity. The last term on the rhs of (33) is an energy conversion term. At this point we will drop the last term on the rhs of (33). We return to this term in the next section.
Summing both sides of (33) over the entire domain yields
where it is understood that the outside summation is over all the grid cell centers and the inside summation is over the corners associated with a given cell center i.
We will now show that the rhs of (34) sums to zero at the corner labeled c = γ in Fig. 2. Symmetry then implies that the sum is zero at every corner. Note that in Fig. 2 there is no way to tell whether the grid cells that share the corner c = γ are hexagons or pentagons. Both types of polygons are accounted for in this numerical scheme without exception.
At this point it is convenient to adopt a new naming convention as shown in Fig. 3. Since we are choosing a specific corner, we will drop the subscript c. The area of the triangle is partitioned into three subareas, Ri, for 0 ≤ i ≤ 2. The vectors normal to each cell-wall segment, ni, point away from cell center i toward cell center i + 1, where i + 1 is cyclic. The averaging of mass to cell walls, hi, denotes a yet-unspecified averaging from cell centers to the cell-wall segment shared by cell center i and i + 1.
If we sum (34) over all grid cells but keep only the terms in the summation that have c = γ and expand, we are left with
where we require that the expression will sum to zero. Now let
for all i between 0 and 2, and let S = R0 + R1 + R2. We can then rewrite (35) in the compact form of
where there is an implied sum over the index i and i − 1 is cyclic. We can factor out the velocity and rewrite (37) as
We want (38) to be true for an arbitrary vector velocity field, so (38) reduces to
If we take the dot product of (39) with the unit vectors that define the local coordinate system and solve for the components of ∇K, we find
Equations (40) and (41) serve as the definition of the gradient operator. Note that the form of K is still unspecified; the rhs of (34) sums to zero for arbitrary scalar fields. We will return to the gradient operator in the next section.
We can now write (34) as
If we interpret (42) as two terms in a chain rule expansion, we have
This will be true if we define the kinetic energy as
Equations (36), (39), and (44) are the constraints that allow kinetic energy to be conserved under advection.
In addition to showing that advection does not create or destroy kinetic energy, we must show that the terms that represent the conversion of energy between its kinetic and potential forms do not create or destroy energy. In order to do this we must derive the potential energy equation by multiplying gAi(hs + hi) through (15) to obtain
In an approach similar to that used above, we will show that the rhs of (45) and the last term in (33) cancel at every cell corner. Combining the rhs of (45) and the last term on the rhs of (33) and summing over the domain, we want to ensure that
If we compare (46) to the rhs of (34), we see that the two expressions are identical, except that K in (34) is replaced by g(hs + h) in (46). Since we have already shown that the rhs of (34) sums to zero for an arbitrary scalar, (46) is satisfied provided that we use an expression analogous to (39) to compute the gradient of g(hs + h).
The form of total energy that is conserved in this discrete system is
which is consistent with the continuous shallow-water equations.
We have shown that we can conserve total energy by choosing (39) as the discrete gradient operator. In this section we will show that (39) has an alternative geometric interpretation as the slope of the plane fit through the surrounding three data points. For clarity, we will assume a regular hexagonal grid in this section, but note that we have verified our findings on both distorted hexagonal grids and spherical geodesic grids.
Referring to Fig. 2 and assuming a regular hexagonal grid, if we take the dot product of (39) with the unit vector nc+, we find that
where Δl is the distance between grid cells 2 and 0. Equation (48) can be interpreted as the slope of the plane fit through (K0, K1, K2) in the nc+ direction. Taking the dot product of (39) with nc− yields
Equations (48) and (49) are sufficient to prove that (39) is the slope of the plane fit through (K0, K1, K2).
Once we interpret (39) as the slope of the plane fit through the surrounding data, the vector identity,
follows immediately in the discrete system. The physical interpretation of the curl operator shown in (5) and (6) is a line integral of the component of a vector field along the path of integration. In Fig. 2, if we start at γ and follow ∇K along the perimeter of grid cell 0, we return to where we started. Hence, (50) holds in the discrete system. While this is a rough argument, we have proven (50) rigorously.
With the divergence and gradient operators specified, we can determine the form of the discrete Laplacian operator as ∇2K = ∇·∇K, where K is a scalar field. If we define the vector V in (2) as ∇K and use (39) as the form of the gradient operator, we find that
where Δt is the length of the line segment connecting grid cell corners. Equation (51) can be simplified to
which is exactly the same form as derived by HR95.
Along with the vector identity shown in (50) and the definition shown in (52), we require two more equations to hold in the discrete system:
We simply note here that (53) and (54) hold in the discrete case solely because we assume that the vector V is perpendicular to the vector k.
Equations (50), (52), (53), and (54) suffice to derive the discrete vorticity and divergence equations [(18) and (19)] from the discrete momentum equation (16). Thus we conclude that the discrete momentum formulation is consistent with the discrete vorticity-divergence formulation.
We will show results from three numerical models. Two of the models are based on the framework developed above. The first uses the discrete vorticity-divergence formulation [Eqs. (15), (18), and (19)] and we will refer to this model as NS_Vor-Div. The second uses the discrete vector momentum formulation [Eqs. (15) and (16)] and will be referred to as NS_Momentum. The third model is based on the scheme developed by Masuda and Ohnishi (1987) and HR95. This scheme uses the vorticity-divergence formulation of the shallow-water equations and will be referred to as OS_Vor-Div. A fairly complete comparison of OS_Vor-Div and NS_Vor-Div is contained in the appendix.
The models are situated on a doubly periodic f plane with f0 = 1.4 × 10−4 s−1. The plane is discretized using a regular hexagonal grid of 128 × 128 (see Fig. 7). The distance between cell centers, Δn, is 100 km. The time-stepping scheme for all three models is third-order Adams–Bashforth with a time step of 100 s. All three models are started from the same initial condition, of the form
The first values on the rhs of (55), (56), and (57) are the respective domain mean values and the second values are the maximum perturbations from the means. The perturbations were generated by a random number generator. The initial conditions are highly unbalanced. Given the absolute vorticity and divergence fields, the discrete analogs of (12) and (13) are used to solve for the streamfunction and velocity potential, respectively. For the NS_Momentum model, we use the discrete gradient operator to differentiate the streamfunction and velocity potential to obtain the initial velocity field. The time rates of change of all prognostic variables are zero at t = 0. The surface topography is random and has the form hs = 0 ± 20 m. With gravity set to 9.81 m s−2, we obtain a Rossby radius of deformation of approximately 700 km. With Δn = 100 km, we marginally resolve eddies on this scale. All three models are inviscid in the sense that no explicit dissipation is introduced.
Figure 4a measures the error in domain-integrated total energy over a 40-day integration. The y axis is log base 10 of the absolute value of the fractional change in domain-integrated total energy. All of the simulations show substantial variability during the first few days of integration. During this period the state of the system is rapidly changing while it moves toward geostrophic balance. The time truncation error is relatively large during this period and we have verified that it accounts for the variations of the total energy over the first several days of integration. After 40 days, the NS_Vor-Div and NS_Momentum simulations have a total energy that is within 0.5% of the initial value. The total energy in the OS_Vor-Div simulation continues to drift and after 40 days the total energy has doubled.
Figure 4b shows the fractional change in domain-integrated mass-weighted potential enstrophy. Both the NS_Vor-Div and NS_Momentum simulations conserve mass-weighted potential enstrophy to within 0.05% after 40 days of integration. The NS_Vor-Div simulation displays a slow modulation of this quantity that is due to truncation error in the elliptic solver [(12) and (13)]. If we make the convergence threshold in the elliptic solver sufficiently stringent, we can eliminate this modulation. The OS_Vor-Div simulation shows a steady drift in potential enstrophy and after 40 days of integration the potential enstrophy has also doubled.
Figure 5a shows the wavenumber spectrum of total energy at the end of the 40-day integration for each simulation. Figure 5a also shows the energy spectrum at t = 0, which is the same of all simulations. Consistent with the white noise initial condition, the initial energy spectrum is also white. Figure 5b shows the enstrophy spectrum of each simulation after 40 days and also shows the initial enstrophy spectrum. The purpose of Fig. 5 is to show whether there is anomalous buildup of energy or enstrophy at any given wavenumber. In terms of energy, both the NS_Vor-Div simulation and NS_Momentum simulation show an appropriate upscale transport of energy with no apparent buildup of energy at the grid scale. The OS_Vor-Div simulation also shows the upscale cascade, but the lack of conservation of total energy is readily apparent. In terms of enstrophy, both the NS_Vor-Div simulation and NS_Momentum simulation show no buildup of enstrophy at the smallest scales. The OS_Vor-Div simulation shows a buildup of enstrophy at both the smallest and largest scales.
Now we wish to determine whether the new numerical scheme produces the appropriate energy and enstrophy cascades. In order to test this, we must include a sink of enstrophy at the smallest resolved scales in order to generate a downscale cascade of enstrophy. Using the NS_Momentum model, we do this by including a ∇6 diffusion in the momentum equation.2 The coefficient on the diffusion is 1 × 1024 m6 s−1; scale analysis suggests that this value is sufficient to dissipate a vorticity or divergence perturbation of size 1 × 10−4 s−1, with a spatial scale of 2Δn, in several hours. The model is initialized with the same initial condition shown above, but there is no topography. Figure 6 shows the energy and enstrophy spectra averaged over days 950–1050. Dimensional analysis suggests that, within the inertial range, the energy spectrum should decay as K−3, where K is the total wavenumber, and the enstrophy spectrum should decay as K−1 (Pedlosky 1987; Salmon 1998). Figure 6 indicates that the numerical model is accurately capturing both the upscale cascade of energy and the downscale cascade of enstrophy. After 1000 days of integration, the total energy has changed by only 0.5% (not shown). So while the ∇6 diffusion operator continues to destroy enstrophy, it destroys very little energy. Figure 7 shows the relative vorticity field at four stages of the integration: t = 0, t = 10, t = 100, and t = 1000 days. This figure qualitatively confirms the spectral analysis shown in Fig. 6. The flow continually evolves into larger structures. Also consistent with Fig. 6, we do not see any spurious buildup of energy or enstrophy at the grid scale.
We have constructed a shallow-water model, for use on a spherical geodesic grid, that conserves mass, potential vorticity, potential enstrophy, and total energy. We have demonstrated these conservation properties in a numerical simulation of geostrophic turbulence on an f plane. In addition to conserving energy and potential enstrophy to within the time truncation error, our numerical scheme was able to accurately capture the spectral distributions of energy and enstrophy in a simulation of geostrophic turbulence.
In the introduction we stated that conserving these basic quantities is only one necessary component of a robust numerical scheme; faithful simulation of the geostrophic adjustment process and numerical convergence are the other two necessary components. Looking at these other two necessary components will provide some context for the work we have completed here.
In a study of the geostrophic adjustment process, Randall (1994) discretizes the vorticity-divergence form of the shallow-water equations on the Z grid. The Z grid entails the use of the vorticity-divergence formulation with all scalar quantities defined at the grid-cell centers. He compares the discrete dispersion relation obtained using the Z grid to the dispersion relations obtained using the A, B, C, D, and E grids (Arakawa and Lamb 1977). The A–E grids entail the use of the momentum formulation. Randall (1994) clearly shows that the Z grid more accurately simulates the geostrophic adjustment process than any of the A–E-grid systems. On the Z grid, the discrete equations involve no spatial averaging and only a discrete Laplacian operator is required [see Randall (1994), Eqs. (4)–(6)]. As shown in (52), the Laplacian operator derived here is identical to that used by HR95. Furthermore, this Laplacian operator is consistent with the formulation used in Randall (1994). We conclude that the framework developed here not only conserves the quantities listed above, but is also consistent with the Z-grid discretization and, thus, does a better job of simulating the geostrophic adjustment process than the A–E-grid systems. This topic is more fully explored in Ringler and Randall (2002).
The order of accuracy of this numerical scheme is determined by three aspects: the accuracy of the interpolations [Eqs. (27), (28), and (36)], the accuracy of the vector operators [Eqs. (2), (6), and (39)], and the properties of the grid. On a regular hexagonal grid, all of these approximations are formally second-order accurate.
We interpreted the approximation to the gradient operator in two ways: first, the gradient ensures conservation of kinetic energy under the process of advection, and second, the gradient operator measures the slope of the plane fit through the surrounding three data points.
This work has shed light on the relationship between the Z grid and its discrete analog in the momentum equations. We have exhibited a momentum equation that is compatible with the Z grid. In the continuous system, we can move between the momentum formulation and vorticity-divergence formulation in a seamless manner using basic vector operators. Both forms contain the same information and yield the same result. In this work we were able to manipulate the discrete form of the vector momentum equation using discrete analogs of the gradient, divergence, and curl operators to derive a discrete form of vorticity-divergence equations. Since the derived vorticity-divergence equations are the Z-grid vorticity-divergence equations, we are guaranteed that the discrete momentum equation is consistent with the Z grid. The momentum analog to the Z grid (call it the ZM grid) solves the full momentum equation at every grid-cell corner.
On the hexagonal grid there are twice as many grid-cell corners as there are grid-cell centers. An easy way to see this is as follows. Each cell center is associated with an area, Ai, and each cell corner is associated with an area, Ac. On a regular hexagonal grid Ai = 2Ac, so in order to cover the same area there must be twice as many cell corners as there are cell centers. Since the ZM grid solves the momentum equation at every cell corner and the continuity equation at every cell center, there are twice as many momentum points as there are mass points. The redundancy of the momentum equation allows for the existence of computational modes. We define computational modes as solutions to the discrete equations that have no analogs in the continuous system. We are addressing the redundancy of the ZM grid in separate work by analyzing the linear geostrophic adjustment process on a hexagonal grid (Ringler and Randall 2002).
We have implemented the numerical scheme outlined in this paper on a spherical geodesic grid and we are currently conducting the standard suite of shallow-water test cases as well as several other tests.
We would like to thank Ross Heikes and Alistair Adcroft for useful discussions and for comments on an earlier draft of this paper. This work was supported by the U.S. Department of Energy's Climate Change Prediction Program under Grant DE-FG03-98ER62611 to Colorado State University.
In this appendix we compare the OS_Vor-Div scheme developed by Masuda and Ohnishi (1987) and HR95 to our new scheme, NS_Vor-Div. For this comparison we will assume a regular hexagonal grid where the distance between grid-cell centers is Δn and the distance between grid-cell corners is Δt.
Both schemes express the mass equation as fluxes across the cell walls and we will denote these fluxes as Fj, where the flux points from cell 0 to cell j. For both schemes, the mass equation for the fluid thickness at cell center 0 can be written as
The schemes will differ in the formulation of the flux, Fj.
The flux across cell walls can be express as
The first term on the rhs of (A2) represents the flux of mass across the cell wall shared by grid cells 0 and j due to divergent motion. The second term on the rhs of (A2) represents the flux across the cell wall due to rotational motion. Substituting (A2) into (A1) yields
The flux across each cell wall, Fj, is broken into two parts: one part associated with the corner j − 1, and one part associated with the corner j. The mass equation can be written just like (A1), but the fluxes are expressed as
Substituting (A4) into (A1) and doing some algebra yields
Comparison with (A3) shows that the rotational motion is modeled exactly as before, but that a slight modification to the flux due to divergent motion is introduced.
Similar to the mass equation, the vorticity equation for both schemes can be written as
where, similar to Fj in the mass equation [(A1)], Hj is the flux of absolute vorticity across the cell walls. In fact, the vorticity equation is identical to the mass equation, expect h is replaced by η. Furthermore, in both schemes the averaging of absolute vorticity is done in exactly the same manner as the averaging of mass. Instead of duplicating the same manipulations we just completed, we can simply state that the OS_Vor-Div scheme integrates the vorticity equation as shown in (A3) and the NS_Vor-Div scheme integrates the vorticity equation as shown in (A5).
For clarity, we reiterate the continuous form of the divergence equations:
which we can write symbolically as
In section 5 we show that both the OS_Vor-Div and NS-Vor-Div schemes use the same discrete Laplacian operator; therefore, regarding term 2, the only differences between the two schemes could be the form of kinetic energy, K. In comparing the two schemes we need to identify any differences in the treatment of term 1 or the formulation of K.
This scheme approximates term 1 as
Masuda and Ohnishi (1987) express the kinetic energy in continuous form as
Equation (A10) is derived in Heikes (1993). If we use the formulation developed by Masuda and Ohnishi (1987) we can write the discrete form of (A10) at cell center 0 as
In the process of manipulating the discrete analog of (A10) into (A11), we combined the first two terms on the rhs of (A10) into the first term on the rhs of (A11). The third and fourth terms on the rhs of (A10) were combined into the second term on the rhs of (A11). And finally, the last term on the rhs of (A10) was expanded to form the last two terms on the rhs of (A11). We can now write (A11) in terms of the velocity components as
where R and D are the rotational and divergent velocities, respectively. The subscripts N and T are the normal and tangent directions relative to each cell wall, respectively. For example, RT is the rotational part of the velocity vector in the tangent direction. There are several points to note. First, (A12) is not positive definite; the last two terms can be negative. Second, (A12) is biased in the sense that certain components of the velocity vector, such as RT and DN, more strongly control the value of K0 than other components of the velocity, such as RN and DT.
In comparing this to OS_Vor-Div we see that the part of term 1 due to divergent motion is modeled exactly the same in the two schemes, but the part due to rotational motion is different.
The form of kinetic energy used in NS_Vor-Div is shown in (44). When we use the vorticity-divergence formulation, we can rewrite (44) using (14) as
In practice, we use the gradient operator to compute (∇ψ)j and (∇χ)j at each corner, then we construct the velocity vector as each corner. We compute the kinetic energy as the sum of (1/2)(Vj · Vj) over the cell corners. The important point to note is that our formulation uses the full, unbiased, velocity vector to compute the kinetic energy.
Citation: Monthly Weather Review 130, 5; 10.1175/1520-0493(2002)130<1397:APEAEC>2.0.CO;2
We could also derive an approximation to the gradient operator from its analytical definition. Instead, we will use the constraint of conservation of total energy (section 4) to define the form of the gradient operator.
If we use the NS_Vor-Div model with a ∇6 diffusion operator of vorticity and divergence, our findings are the same.
https://journals.ametsoc.org/view/journals/mwre/130/5/1520-0493_2002_130_1397_apeaec_2.0.co_2.xml


text:
Anna Caputo (from left), Sutton Cadman, Gracie Chaves and Carson Hucks are part of the Alexander High School Habitat for Humanity chapter in Douglasville that is leading their community to raise $90,000 to build a home for a veteran. (Photo by Phil Skinner)
Photo: Phil Skinner
Douglasville teens take charge of a Habitat home build for a veteran
Laura Berrios, For the AJC
Who hasn't had the experience of the neighborhood kid asking for help with a fundraiser for a school trip or a sports team? In Douglas County, students are asking their neighbors to chip in for a new house. Not just any house, but a Habitat Humanity home to be built for a military veteran.
The Habitat for Humanity chapter club at Alexander High School has taken on a house project. Students plan to fund and help build a Habitat home for a local veteran's neighborhood, and they'll need to raise $90,000 before a spring build deadline.
If that seems like an impossible goal and a lot of hard work, don't tell them.
Alexander English teacher and club sponsor, Debbie Rager, said she is "amazed at the determination and tenacity of these students to chip away at their fundraising goal."
They've organized yard sales and raffles, asked for donations and sponsorships, and sold T-shirts. And in the process, they've left a lasting impression on the adults.
"They seek opportunities to share their vision, rather than sit and wait and hope fortune smiles their way," Rager said.
Sophomore Sutton Cadman started the charter this school year with some of his friends and classmates. Sutton said he wanted more community service opportunities in high school and heard from a relative about a Habitat chapter at Walton High School in Cobb County. He thought it would be cool to start one at his school.
After forming their club, students asked the Northwest Georgia Habitat for Humanity if they could take charge of building the fourth house in Veterans Place, a Douglas County neighborhood that will eventually have eight Habitat houses set aside for veterans. It's one of only two veterans-only Habitat neighborhoods being built in the country.
Once granted permission, students hit the ground running to raise the money needed for building supplies for the 1,800-square-foot house. So far, they've collected about one-third of their goal.
Long-time Habitat volunteer Jimmy Haddle of Douglasville has been involved with dozens of home builds over the past two decades. Raising the money is the hardest part, he said, "but these kids have taken the bull by the horns."
"It's very unusual for a group of kids this young to do this. They're learning that it takes plain old hard work getting it done yourself," said Haddle, who serves as a mentor to the school chapter.
Frank Moran, another Douglasville Habitat volunteer, is helping the students by introducing them to community leaders and giving them a platform to speak. He's quick to point out that the teens are doing all the work, and that impresses him.
Club officers have spoken to the Douglas County Chamber of Commerce, and before church and civic groups. They have written grants, and are planning a golf tournament and a poker night. Parents organized a booster club to provide guidance.
"Sutton and his team have renewed our faith in young people," Moran said. "It's more than just raising money, I've watched a young man grow, building his confidence as he meets with all these different groups,"
Booster parent Kelly Cadman, Sutton's mom, said it is a pleasure to see these teens learn how to organize, market, and finance something of this magnitude.
"I know that aside from the impact they will have after this project and projects to come with Habitat, they will take away so much more in character and leadership," she said.
The homeowner, who has yet to be selected, will be a veteran from Douglas County. The goal is to have the home built by late spring. Alexander students will work on the build, as will other teams from the community. The work is typically completed over nine Saturdays, with hired professionals, like plumbers and electricians, working during the week.
Said Haddle: "A bunch of us are really pulling for these kids; we want them to finish it."
WHAT INSPIRES ALEXANDER HIGH'S HABITAT CHAPTER?
Sutton Cadman: "I went to an elementary and middle school that were really involved in community services, but when I got to high school there weren't as many opportunities. I thought it would be a great thing to start this and get involved in the community."
Carson Hucks: "I recently built a (Habitat) house, and I really enjoyed it. I was just happy and glad to be there. I've been involved in other community service, and I like it."
Gracie Chaves: "I want to help (the veteran) get a house, a place to have a home and have memories. It feels good to help people."
Teacher Debbie Rager: "A group of kids, many who are not even licensed car drivers, are working as change agents. Am I inspired by them? You better believe it. These kids stand in the gap for those who need help, and this is the message of hope they bring."
HELP US INSPIRE ATLANTA
We recognize a big part of our journalistic mission is to shine a spotlight on wrongdoings and to hold our public officials accountable.
But we also understand the importance of celebrating our region's moments, milestones and people. That's exactly what we hope to accomplish with Inspire Atlanta.
Each week, Inspire Atlanta will profile a person that makes metro Atlanta a better place in which to live.
Of course, we can't do this alone: We need your help in finding extraordinary people and identifying inspiring stories across our region. We learned about Habitat for Humanity chapter club at Alexander High School from Kelly Cadman, who said she was impressed to see these teens engage in such productive, meaningful work in their community.
Know someone who inspires you or makes metro Atlanta a better place for others?
Email us at inspireatlanta@ajc.com.
If you want to donate to the Alexander High School Habitat for Humanity chapter, go to nwmetroatlantahabitat.org/alexander


text:
Q: Oracle - exchange partitions with a table I try to create a table2 on Oracle 11g.2.0.3 with:
CREATE table2
LOGGING TABLESPACE TS_table1_2014 PCTFREE 10 INITRANS 1 STORAGE ( INITIAL 65536 NEXT 1048576 MINEXTENTS 1 MAXEXTENTS UNLIMITED BUFFER_POOL DEFAULT ) NOCOMPRESS
as (select * from table1 where date_text <= '2015-12-31');

and I have received error below when I try to exchange this table2 with a partitioned table3:
alter table table3 exchange partition partition_name WITH TABLE table2;

    Error report -
    SQL Error: ORA-14097: column type or size mismatch in ALTER TABLE EXCHANGE PARTITION
    14097. 00000 -  "column type or size mismatch in ALTER TABLE EXCHANGE PARTITION"
    *Cause:    The corresponding columns in the tables specified in the
               ALTER TABLE EXCHANGE PARTITION are of different type or size
    *Action:   Ensure that the two tables have the same number of columns
               with the same type and size.

I have test diferences with query below:
Select a.COLUMN_NAME
  , a.DATA_TYPE, b.DATA_TYPE
  , a.data_length, b.data_length
  , a.data_precision, b.data_precision
  , a.data_scale, b.data_scale
  , a.nullable, b.nullable
from ALL_TAB_COLUMNS a
full outer join ALL_TAB_COLUMNS b on a.column_name=b.column_name
 and b.owner=user and b.table_name='&table2'
 where  a.owner=user and a.table_name='&table1'
 and (
    nvl(a.data_type,'#')!=nvl(b.data_type,'#')
    or nvl(a.data_length,-1)!=nvl(b.data_length,-1)
    or nvl(a.data_precision,-100)!=nvl(b.data_precision,-100)
    or nvl(a.data_scale,-100)!=nvl(b.data_scale,-100)
    or nvl(a.nullable,'#')!=nvl(b.nullable,'#')
   )
;

Some differences resulted are in a column size. This syntax "create as select" didn't keep order and size for new table created.
How can I create table2 as select from table1 with force keep same size columns as primary table1 source?
Thanks!

A: I can't find any differences in your DDL.  What I suggest is to use the same DDL to create table2, then do:
insert into table2 select * from table1;

A: You need to use dbms_metadata package or query number of data dictionary views like all_tab_columns and etc to get metadata about existing table so you can construct correct sql for swap-table (used in exchange partition operation). CTAS does not transfer DEFAULT values for example and constraints except NOT NULL checks.
The best practice is to create/re-create/modify this table simultaneously with partitioned table.

redpajama_set_name: RedPajamaStackExchange


text:
Агне́сса (Аньес) Францу́зская (около 1260 — 19 декабря 1327) — младшая дочь Людовика IX и Маргариты Прованской. Была регентом Бургундии при малолетнем сыне.

Семья
Агнесса была младшей из одиннадцати детей, восемь из которых дожили до взрослого возраста. В 1279 году вышла замуж за Роберта II, герцога Бургундии, и стала матерью восьми детей:
 Бланка (1288—1348), замужем за Эдуардом, графом Савойским.
 Маргарита (1290—1315), замужем за королём Людовиком X.
 Жанна (около 1290—1348), замужем за Филиппом VI.
 Гуго V (герцог Бургундии) (1294—1315).
 Эд IV (герцог Бургундии) (1295—1350).
 Людовик, король Фессалоникский (1297—1316), женат на Матильде Эно.
 Мария (1298—1336) замужем за Эдуардом I, графом Бара
 Роберт, граф Тоннера (1302—1334), женат на Жанне, наследнице Тоннера.

Двое детей умерли в юном возрасте: Жан (1279 † 1283) и Маргарита (1285).

После смерти мужа Агнесса была регентшей при своём малолетнем сыне, Гуго, с 1306 по 1311 год. Она умерла в Кот-д'Ор 19 или 20 декабря 1327 года и похоронена в Аббатстве де Сито.

В популярной культуре
Агнесса Французская является одной из второстепенных героинь цикла исторических романов «Проклятые короли» французского писателя Мориса Дрюона. Упоминается во всех романах, но на сцену выходит лишь один раз в конце романа «Негоже лилиям прясть».

Генеалогия

Примечания

Капетинги (главная ветвь)
Женщины-регенты
Принцессы крови
Герцогини Бургундии


In a quiet environment , this apartment of 20 m² (about 215 ft²), built in 2001 contains 1 room, 1 shower room and 1 toilet. It is equipped with a kitchenette. It's located on the 2nd floor. Heating : individual electric. Others : intercom.


So, you think you might like to have LASIK surgery? There are many things to take into consideration when deciding if LASIK is right for you? Is your prescription stable? Are you an ideal candidate? Who is the best surgeon? And high on the list is considering whether or not the cost of LASIK is the right investment for you?
In the United States, the national average cost of LASIK eye surgery ranges anywhere from $1,500 to $4,5001 per eye. It's important that you find out what your actual LASIK will be at the LASIK practice you are researching. Once you know your cost of LASIK from a practice, you need to look at your return on investment (ROI) quantitatively but also in the quality of your lifestyle.
How do I determine the cost of LASIK?
When you begin evaluating LASIK eye surgery cost, it is important to make sure you find a practice that understands your unique situation, both your vision and your finances, and a surgeon that you trust with your eyes. Patients should research different practices and have a comprehensive LASIK consultation with at least two LASIK surgeons before selecting the right fit. Determining the cost of LASIK can be challenging as it varies based on the practice, their technology and expertise. Some practices will require you to come in for the consultation in order to calculate your cost of LASIK as it is based on your prescriptions, if you have astigmatism, and sometimes what type of technology is used. Other practices have a flat pricing structure so you can get a straightforward answer over the phone.
Be sure to compare prices to make sure it is an apples-to-apples comparison.
Look at technology, surgeon experience, postoperative appointments, and patient care.
Look carefully and ask questions to avoid any hidden fees or "starting at" prices.
Lastly, it is important to consider the lifetime value of LASIK versus the one-time LASIK cost.
In the chart below, we help you compare the costs of LASIK at Providence Eye over a lifetime versus contact lenses or glasses. We think you'll quickly see the return on investment (ROI) in LASIK eye surgery.
At Providence Eye & Laser Specialists, we believe in being straightforward about pricing. We won't surprise you with additional costs or hidden fees. We understand the cost of LASIK eye surgery is a major consideration. So, instead, we meet with our patients to discuss our flat-rate prices up front.
Contact us today to schedule your complimentary consultation with Dr. Mozayeni. We'll discuss your LASIK eye surgery cost options and more.
What is the Cost of LASIK vs Glasses & Contacts?


Jerusalem (AFP) – Prime Minister Benjamin Netanyahu faces a graft probe some believe could force him from office, but the four-term premier has overcome legal troubles in the past and remains a towering figure in Israeli politics.
Police questioned Netanyahu for some three hours at his official residence in Jerusalem on Monday night over tens of thousands of dollars in gifts allegedly given to him by wealthy supporters.
While an inquiry has been ongoing for months, it has now been elevated to a criminal probe and news of his questioning shook the Israeli political scene, setting off speculation over whether it will lead to his downfall.
But some analysts argued that the threat seemed more substantial than in previous cases.
"The last couple of times that he was in this situation, he tried to say, 'You go after my wife, you go after my personal life, it's an illegal way to try to reverse democratic elections,'" Gayil Talshir, a political science professor at Jerusalem's Hebrew University, told AFP.
Much remains unknown about the investigation being overseen by Attorney General Avichai Mandelblit.
He has confirmed that Netanyahu is suspected of receiving "gifts from businessmen," but has provided few other details.
US billionaire and World Jewish Congress president Ronald Lauder has been among those questioned in the probe over gifts he allegedly gave Netanyahu and alleged spending on trips for him, Israeli media reported.
Lauder, whose family founded the Estee Lauder cosmetics giant, has long been seen as an ally of Netanyahu.
Netanyahu has also acknowledged receiving money from French tycoon Arnaud Mimran, who was sentenced to eight years in prison in France over a scam involving the trade of carbon emissions permits and taxes on them.
Netanyahu's office said he had received $40,000 in contributions from Mimran in 2001, when he was not in office, as part of a fund for public activities, including appearances abroad to promote Israel.
The allegations have put the right-wing premier's opponents — both from within his party and elsewhere — on alert for signs of his support among the public weakening.
Recent polls have suggested that if elections were held now, his Likud party would finish behind the centrist Yesh Atid, but that voters still prefer Netanyahu as prime minister.
Many analysts say that can be attributed to voters not seeing a viable alternative to the 67-year-old's leadership, but warn that could change quickly once a campaign is under way.
There is a recent example to draw lessons from, with Netanyahu's predecessor Ehud Olmert forced to resign while dogged by corruption allegations and now serving 27 months in prison.
"With Ehud Olmert, there was a moment in which his otherwise substantial following abandoned him because they increasingly became convinced that the allegations were solid," Amotz Asa-El, a former Jerusalem Post executive editor and currently a columnist for the paper, told AFP.
"I don't see this now with Prime Minister Netanyahu," he added, though cautioned that further revelations could change that.
Netanyahu and his family have overcome legal troubles in earlier years — and involving similar accusations.
In 2000, prosecutors decided there was insufficient evidence to indict Netanyahu and his wife Sara following an investigation.
The probe then looked at whether they unlawfully kept gifts presented to Netanyahu during his first term as prime minister from 1996 and 1999.
It also investigated whether they had promised a Jerusalem contractor he would be paid out of the public purse for work done on their private home.
On Monday night, while Mandelblit confirmed Netanyahu was being investigated over the alleged gifts, he at the same time listed a series of other accusations that investigators had looked into and decided to drop.
Sara Netanyahu has however again come under scrutiny in recent months. In December, police questioned her for several hours over allegations that the couple used public funds to cover personal spending, Israeli media reported.
Netanyahu has served as premier for a total of nearly 11 years, fast approaching revered founding father David Ben-Gurion's 13, and shown himself to be a shrewd politician.
But if damaging details emerge from the probe, his considerable survival skills could be put to the test.
Such details could "puncture his public persona and portray him as a desperate and thus pathetic seeker of perks," Chemi Shalev of Israeli newspaper Haaretz wrote.


Remodeling your bathroom doesn't have to be a massive, budget-breaking endeavor. Just making a few small changes can make a huge difference in the way it looks while also adding greater functionality and convenience.
An over-the-toilet storage shelf gives you added space.
You also can add shelving around the top of the wall, even above your combo tub and shower to store towels and toiletries.
Baskets, baskets, baskets. Use small baskets or fabric bins to keep a small bathroom organized. They're also a great way to make up for not enough drawer space.
Does your bathroom look outdated?
A fresh coat of a light colored paint on the walls can go a long way to giving your bathroom a new and brighter feel.
Replace brass fixtures with brushed nickel or chrome.
Capitalize on an older bathroom by adding décor that gives it a nostalgic, retro feel. Instead of hating that green bathtub, embrace it as the focus of your bathroom. Add a striped or chevron-print shower curtain as an accent.
If your bathroom is large enough, create a vanity area with a small mirror for makeup, hair products and styling tools. Use small glass jars to organize small clips and products.
Consider finding a new "home" for things that contribute to the clutter. For example, store medicines and first aid supplies on a shelf in your linen closet instead of the bathroom cabinet.
An inexpensive spice rack hung on the wall or side of the bathroom cabinet will keep toiletries and products handy but off of the counter.
Place a nice hamper with a lid just outside the bathroom door to hide dirty clothes and towels.
Keep a small stash of cleaning supplies handy in the bathroom. Sanitizing wipes are the simplest solution for quick cleaning because they do a great job on almost all surfaces. Use one wipe every morning to stop messes before they start.
As you can see, it doesn't take a lot to put a brand new smiley face on your bathroom, and even bigger smile on your face. Contact Arnold & Sons today for a free in-home consultation and price quote on the new and improved bathroom experience you have in mind.
Previous Post3 Types of Plungers, and What They're For.


text:
Trump Picks a Fight with the Facts on His First Full Day
Submitted by Mary Bottari on January 23, 2017 - 5:16pm
For those who hoped the Trump administration would become more "presidential" after the pomp and ceremony of the swearing-in, the Trump team cleared up any confusion by peddling outright lies from the White House podium.
Trump Travels to Langley as Millions March in Protest
On January 21, the day after his swearing in, Trump traveled to Langley, Virginia.
The mission? To mend fences with the CIA. A secondary mission? To give the press something else to report on than the millions of women in pink "pussyhats" gathering in cities and towns across America.
Trump had a lot of mending to do. He had repeatedly slammed U.S. intelligence agencies, casting aspersions on their finding that Russia was behind the hacks on the Democratic National Committee, and comparing intelligence chiefs to "Nazi Germany" when a memo containing allegations that the Russians might be in a position to blackmail Trump hit the media.
As he took to a podium with his back to the wall of stars commemorating CIA agents killed in the line of duty, Trump chose not to speak of history or individual acts of heroism, but of himself.
"Trust me, I'm like a smart person," Trump told the crowd which may have included an imported cheering section, reports CBS.
Facing a wall emblazoned with the biblical injecture "Ye shall know the truth and the truth shall make you free," Trump chose a different path.
Trump slammed the media as "among the most dishonest people on earth" and stated "like a million, million and a half people" attended his inauguration. By the time he made these statements Saturday morning, images like this one of 2009 vs. 2017 inaugural crowds had been widely circulated by the nation's major newspapers, including the Washington Post and the New York Times. They clearly show that Trump crowds were much smaller than Obama's, a fact team Trump should have been prepared for.
Trump also said his dispute with the intelligence agency was "manufactured by the media," when, in truth, Trump has publicly excoriated the intelligence services most recently comparing them to Nazi Germany in a Tweet.
Trump said he was "hit by a couple of drops" as he began his address on Inauguration Day, but the sky quickly cleared. "And the truth is, it stopped immediately, and then became sunny," he said. "And I walked off, and it poured after I left. It poured." According to the New York Times, "it began to rain lightly almost exactly as Mr. Trump began to speak and continued to do so throughout his 18 minute long speech."
It was a "despicable display of self-aggrandizement in front of CIA's Memorial Wall of Agency heroes," said former CIA Director John Brennan through an aide. Another senior former CIA officer characterized to NBC News as a "free-wheeling, narcissistic diatribe."
His performance at the CIA only "made relations with the intelligence community worse," one government official told CBS News.
It was downhill from there. Trump's media team took to the airwaves to defend their boss and each other.
#SpicerFacts: White House Press Secretary Lies in First Press Conference
Later in the day, press secretary Sean Spicer called his first White House Press conference. Spicer kept the media waiting for an hour, and came out loaded for bear.
The visibly angry Spicer skewered a Time reporter who mistakenly tweeted that a MLK bust was removed from the Oval Office (an assertion the reporter corrected and apologized for), condemned the media for focusing on crowd size at the inauguration, and issued a series of statements geared toward convincing the media that the crowd was larger than reported.
Spicer began by ripping into the press for publishing photos of Trump's inauguration that "made it appear" less people were in attendance. White tarp grass coverings "had the affect of highlighting any areas where people were not standing" -- a bizarre argument, as even without tarps the parameters of crowds can be easily seen.
Spicer dragged out specific data points to make his case. For instance, he cited official-sounding ridership numbers from WMATA, the D.C. public-transit system. "We know that 420,000 people used D.C. Metro public transit yesterday, which compares to 317,000 that used it for President Obama's last inaugural."
This too is false. WMATA officials, told the Washington Post that 570,557 riders used the Metro system between its 4 a.m. opening and its midnight closure on Friday. That contrasts with President Obama's 2009 and 2013 inaugurations, which saw 1.1 million trips and 782,000 trips respectively.
Spicer was not even close.
Politico's headline? "Five Untruths in Five Minutes" and Politifact dissected the performance and awarded Spicer the second "Pants on Fire" of his career.
Not an auspicious start for a White House Press Secretary whose key currency is credibility. Spicer capped off this performance by storming out without taking any questions.
#ALTfacts: KellyAnne Conway Defends Spicer, Says Spicer Presented "Alternative Facts"
On Sunday, Trump's top advisor KellyAnne Conway told Chuck Todd on NBC's Meet the Press that Spicer was merely giving "alternative facts" in describing the crowd size for Trump's swearing in.
#Altfacts quickly became a hashtag on social media, an appropriate accompaniment to the #Altright propaganda peddled by Steve Bannon, formerly of Breitbart News, who is now Trump's "chief strategist and senior advisor."
But the "Alt" gave a hip sheen to the ugly business.
NBC's Todd responded to Conway incredulously, "four of the five facts he uttered were just not true," and a moment later "alternative facts are not facts, they are falsehoods."
The Truth About Crowds
On Monday, the Trump team tried to make amends. Spicer kept his cool and had a long press conference answering a wide range of questions.
When asked point-blank by ABC's Jonathan Karl, "Is it your intention to always tell the truth?" Spicer said "it is."
But he undercut himself a moment later by saying "but sometimes we can disagree with the facts."
The facts are these.
Crowd scientists at Manchester Metropolitan University in Britain hired by the New York Times put the Trump inauguration turnout at about 160,000.
This compares to media estimates of 1.9 million for Barack Obama's 2008 inauguration.
This compares to the 470,000, calculated by the crowd scientists, for the Women's March on Washington D.C.
This compares to the 3.1 to 4.6 million, tallied by academics in a spreadsheet, of people participating in Women's Marches across the country.
This compares to the 2.9 million people who delivered the popular vote to Hillary Clinton, the widest margin of any losing presidential candidate.
And it is likely this last number is bedeviling Trump.
Later in the day, he confirmed this by telling Congressional leaders "that between 3 million and 5 million illegal votes caused him to lose the popular vote." There is zero evidence for this claim. If this claim were true it would upend elections across the country not just the presidential.
DonorsTrust Pumped $142 Million into Right-Wing Causes in 2018
Koch Foundations Increased Media Investments in 2018
Trump's "Social Media Summit" Allies Spread Propaganda Attacking Impeachment
Trump Attacks on First Amendment Are Un-American
Propaganda U.S. Congress Health U.S. Government Democracy Public Relations Corporations International Human Rights War / Peace Marketing Secrecy Ethics Economy ALEC Exposed Politics Lobbying Wisconsin Climate Change Activism Right Wing Journalism Media Iraq Environment


Nothing recalls long walks on the beach like artistic renderings of the shore! From the feel of warm sand under your toes to the cool water offering you some respite from the hot sun, most beach memories are built where the land meets the sea. Brynn Casey's landscape scenes, created exclusively for Maine Cottage, are real and understandable, but her expressive, abstract style leaves an ambiguousness to her work that allows for deeply thoughtful and evocative responses.


When you connect the battery, the voltage in the wire is 1.5 volts, and when you disconnect it, the voltage is zero volts. By connecting and disconnecting a battery quickly, you create a square wave that fluctuates between 0 and 1.5 volts.
A sine wave fluctuates smoothly between, for example, 10 volts and -10 volts.
By creating a sine wave and running it through a wire, you create a simple radio transmitter. It is extremely easy to create a sine wave with just a few electronic components -- a capacitor and an inductor can create the sine wave, and a couple of transistors can amplify the wave into a powerful signal (see How Oscillators Work for details, and here is a simple transmitter schematic). By sending that signal to an antenna, you can transmit the sine wave into space.