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INTROThe role of precipitation within the hydrological cycle is evidently important. Precipitation provides the element that triggers several processes like surface runoff, rapid sub-surface flow and ground water restoration. In order to have precipitation these steps must be accomplished: 1) supply of moisture, 2)cooling below the point of condensation, 3) condensation 4) growth of particles. ADDIN EN.CITE <EndNote><Cite><Author>TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources</Author><Year>2007</Year><RecNum>11</RecNum><DisplayText>(TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources 2007)</DisplayText><record><rec-number>11</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433909525">11</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources,</author></authors></contributors><titles><title>Hydrology of catchments, rivers and Delta&apos;s; CT5450</title></titles><pages>144 blz.</pages><keywords><keyword>collegedictaat</keyword><keyword>tkj</keyword></keywords><dates><year>2007</year></dates><pub-location>Delft</pub-location><publisher>TU Delft</publisher><urls></urls></record></Cite></EndNote>(TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources 2007).The supply and influence of moisture in precipitation has been studied in depth in recent decades. Precipitation in an area is said to be composed by moisture advected and water evaporated that reached the atmosphere, the percentage of contribution of the evaporated water to the total precipitation is the recycling ratio. Precipitation or moisture recycling refers to the contribution of evaporation within a region to precipitation in that same region ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993).Precipitation recycling has been linked to the potential degree of interaction between atmosphere and surface hydrology, it can also be used as an indicator for sensitivity of climate to land use ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993), ADDIN EN.CITE <EndNote><Cite><Author>Savenije</Author><Year>1995</Year><RecNum>5</RecNum><DisplayText>(Savenije 1995)</DisplayText><record><rec-number>5</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430299958">5</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Savenije, Hubert H. G.</author></authors></contributors><titles><title>New definitions for moisture recycling and the relationship with land-use changes in the Sahel</title><secondary-title>Journal of Hydrology</secondary-title></titles><periodical><full-title>Journal of Hydrology</full-title></periodical><pages>57-78</pages><volume>167</volume><number>1–4</number><dates><year>1995</year><pub-dates><date>5//</date></pub-dates></dates><isbn>0022-1694</isbn><urls><related-urls><url>(94)02632-L</electronic-resource-num></record></Cite></EndNote>(Savenije 1995).The link between precipitation and evaporation has been studied in several regions, the understanding of their interaction have changed throughout the years. ADDIN EN.CITE <EndNote><Cite><Author>Benton</Author><Year>1950</Year><RecNum>13</RecNum><DisplayText>(Benton, Blackburn et al. 1950)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433917864">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Benton, George S.</author><author>Blackburn, Robert T.</author><author>Snead, Vernon O.</author></authors></contributors><titles><title>The role of the atmosphere in the hydrologic Cycle</title><secondary-title>Eos, Transactions American Geophysical Union</secondary-title></titles><periodical><full-title>Eos, Transactions American Geophysical Union</full-title></periodical><pages>61-73</pages><volume>31</volume><number>1</number><dates><year>1950</year></dates><isbn>2324-9250</isbn><urls><related-urls><url>;(Benton, Blackburn et al. 1950) show that in previous works of Horton he writes that “little or no vapour of truly oceanic origin may ever reach small tributary areas at the headwaters of large rivers”, which suggest that the water present in the continents is mainly of local origin. ADDIN EN.CITE <EndNote><Cite><Author>Benton</Author><Year>1950</Year><RecNum>13</RecNum><DisplayText>(Benton, Blackburn et al. 1950)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433917864">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Benton, George S.</author><author>Blackburn, Robert T.</author><author>Snead, Vernon O.</author></authors></contributors><titles><title>The role of the atmosphere in the hydrologic Cycle</title><secondary-title>Eos, Transactions American Geophysical Union</secondary-title></titles><periodical><full-title>Eos, Transactions American Geophysical Union</full-title></periodical><pages>61-73</pages><volume>31</volume><number>1</number><dates><year>1950</year></dates><isbn>2324-9250</isbn><urls><related-urls><url>;(Benton, Blackburn et al. 1950) argued against this statement. They proposed the lifting mechanism as an important factor for the occurrence of precipitation, stating that the increase of water vapour in the atmosphere does not necessarily increase precipitation. ADDIN EN.CITE <EndNote><Cite AuthorYear="1"><Author>McDonald</Author><Year>1962</Year><RecNum>14</RecNum><DisplayText>McDonald (1962)</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433918605">14</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>McDonald, James E.</author></authors></contributors><titles><title>THE EVAPORATION-PRECIPITATION FALLACY</title><secondary-title>Weather</secondary-title></titles><periodical><full-title>Weather</full-title></periodical><pages>168-177</pages><volume>17</volume><number>5</number><dates><year>1962</year></dates><publisher>Blackwell Publishing Ltd</publisher><isbn>1477-8696</isbn><urls><related-urls><url> (1962) pointed out that the contribution of evaporation to local precipitation was smaller than what was previously believed, he attributed this to misconceptions due to the incomplete understanding of the mechanisms of rainfall, and to an overlook of the scale of the phenomenon.Precipitation recycling is a concept that helps to better understand the water cycle, as this is the most basic of all geochemical cycles. It influences on other cycles and affects global circulation in the atmosphere and in the ocean, shaping weather and climate ADDIN EN.CITE <EndNote><Cite><Author>Eagleson</Author><Year>1986</Year><RecNum>4</RecNum><DisplayText>(Eagleson 1986)</DisplayText><record><rec-number>4</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298857">4</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eagleson, Peter S.</author></authors></contributors><titles><title>The emergence of global-scale hydrology</title><secondary-title>Water Resources Research</secondary-title></titles><periodical><full-title>Water Resources Research</full-title></periodical><pages>6S-14S</pages><volume>22</volume><number>9S</number><dates><year>1986</year></dates><isbn>1944-7973</isbn><urls><related-urls><url>;(Eagleson 1986).Precipitation recycling has been studied as a means to estimate the degree of potential interaction between surface hydrology and the atmospheric branch ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994). ADDIN EN.CITE <EndNote><Cite AuthorYear="1"><Author>Savenije</Author><Year>1995</Year><RecNum>5</RecNum><DisplayText>Savenije (1995)</DisplayText><record><rec-number>5</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430299958">5</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Savenije, Hubert H. G.</author></authors></contributors><titles><title>New definitions for moisture recycling and the relationship with land-use changes in the Sahel</title><secondary-title>Journal of Hydrology</secondary-title></titles><periodical><full-title>Journal of Hydrology</full-title></periodical><pages>57-78</pages><volume>167</volume><number>1–4</number><dates><year>1995</year><pub-dates><date>5//</date></pub-dates></dates><isbn>0022-1694</isbn><urls><related-urls><url>(94)02632-L</electronic-resource-num></record></Cite></EndNote>Savenije (1995) studied the role of vegetation in the hydrological cycle in the Sahel, and argued that the albedo influences the partition of energy, and that this is strongly dependant on the vegetation and dryness of the soil surface, which at the same time varies with precipitation and soil processes. ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994) motivated by the possible interactions between hydrology and climate studied the precipitation recycling in the Amazon Basin, and concluded that the precipitation recycling is a portion of the diabatic heating associate with condensation of water vapour that is contributed by evaporation in the Amazon Basin. ADDIN EN.CITE <EndNote><Cite><Author>SHUKLA</Author><Year>1982</Year><RecNum>16</RecNum><DisplayText>(SHUKLA and MINTZ 1982)</DisplayText><record><rec-number>16</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433993874">16</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>SHUKLA, J.</author><author>MINTZ, Y.</author></authors></contributors><titles><title>Influence of Land-Surface Evapotranspiration on the Earth&apos;s Climate</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>1498-1501</pages><volume>215</volume><number>4539</number><dates><year>1982</year><pub-dates><date>March 19, 1982</date></pub-dates></dates><urls><related-urls><url>;(SHUKLA and MINTZ 1982) concluded that a change of vegetation cover have a significant influence on climate, if the magnitude and extent of the change is large, however the response will vary and depend on the modification of the large scale circulation.The interaction of atmosphere and surface hydrology varies with time and location, in winter the continental areas act as sinks of moisture and during summer they become sources of atmospheric water that feed convective rains.The studies of precipitation recycling have been based in the use and development of analytical and numerical models. The first model was developed by Budiko and Drozdov in 1953 ADDIN EN.CITE <EndNote><Cite><Author>Burde</Author><Year>2001</Year><RecNum>6</RecNum><DisplayText>(Burde and Zangvil 2001)</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430365993">6</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Burde, G. I.</author><author>Zangvil, A.</author></authors></contributors><titles><title>The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>2497-2508</pages><volume>14</volume><number>12</number><dates><year>2001</year><pub-dates><date>2001/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Burde and Zangvil 2001), where they studied precipitation recycling for the European part of the USSR, they estimated that the contribution of evaporation to precipitation is 10%. ADDIN EN.CITE <EndNote><Cite><Author>Lettau</Author><Year>1979</Year><RecNum>18</RecNum><DisplayText>(Lettau, Lettau et al. 1979)</DisplayText><record><rec-number>18</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1434340173">18</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Lettau, Heinz</author><author>Lettau, Katharina</author><author>Molion, Luiz Carlos B.</author></authors></contributors><titles><title>Amazonia&apos;s Hydrologic Cycle and the Role of Atmospheric Recycling in Assessing Deforestation Effects</title><secondary-title>Monthly Weather Review</secondary-title></titles><periodical><full-title>Monthly Weather Review</full-title></periodical><pages>227-238</pages><volume>107</volume><number>3</number><dates><year>1979</year><pub-dates><date>1979/03/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0027-0644</isbn><urls><related-urls><url>(1979)107&lt;0227:AHCATR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0493(1979)107&lt;0227:AHCATR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/06/14</access-date></record></Cite></EndNote>(Lettau, Lettau et al. 1979) studied precipitation recycling in the amazon region, they found that 88% of the water precipitation in the westernmost region falls at least a second time from the atmosphere. ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993) modified Budiko’s model and turned it into a 2D model, their results showed good agreement to those of Budiko for the Eurasian region; for the North American region (to the east of the continental divide and within the Mississippi Basin) the peaks occurred during July and October, while the lowest values occurred during winter months. The range for recycled precipitation in the Mississippi Basin region varied from 15% to 34%. In the South American region their results were compatible to those of ADDIN EN.CITE <EndNote><Cite><Author>Lettau</Author><Year>1979</Year><RecNum>18</RecNum><DisplayText>(Lettau, Lettau et al. 1979)</DisplayText><record><rec-number>18</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1434340173">18</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Lettau, Heinz</author><author>Lettau, Katharina</author><author>Molion, Luiz Carlos B.</author></authors></contributors><titles><title>Amazonia&apos;s Hydrologic Cycle and the Role of Atmospheric Recycling in Assessing Deforestation Effects</title><secondary-title>Monthly Weather Review</secondary-title></titles><periodical><full-title>Monthly Weather Review</full-title></periodical><pages>227-238</pages><volume>107</volume><number>3</number><dates><year>1979</year><pub-dates><date>1979/03/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0027-0644</isbn><urls><related-urls><url>(1979)107&lt;0227:AHCATR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0493(1979)107&lt;0227:AHCATR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/06/14</access-date></record></Cite></EndNote>(Lettau, Lettau et al. 1979), Brubaker found that the recycling ratio was 30%, while Lettau 47% , the difference may be attributed to the size of the area of study. In the African continent the results of recycling ratio correspond with the values of evaporation, as these are the highest when evaporation is high. They range from 10% to 48%. ADDIN EN.CITE <EndNote><Cite><Author>Savenije</Author><Year>1995</Year><RecNum>5</RecNum><DisplayText>(Savenije 1995)</DisplayText><record><rec-number>5</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430299958">5</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Savenije, Hubert H. G.</author></authors></contributors><titles><title>New definitions for moisture recycling and the relationship with land-use changes in the Sahel</title><secondary-title>Journal of Hydrology</secondary-title></titles><periodical><full-title>Journal of Hydrology</full-title></periodical><pages>57-78</pages><volume>167</volume><number>1–4</number><dates><year>1995</year><pub-dates><date>5//</date></pub-dates></dates><isbn>0022-1694</isbn><urls><related-urls><url>(94)02632-L</electronic-resource-num></record></Cite></EndNote>(Savenije 1995) studied moisture recycling in the Sahel and concluded that 90% of the rainfall is the result of moisture recycling, this result is attributed to the formulation of the model, which balances atmospheric influx only with runoff. ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994) developed a spatially distributed model for the estimation of precipitation recycling in an area, they studied the Amazon region, and they found that the recycling ratio goes from 25% to 35% depending of the month. ADDIN EN.CITE <EndNote><Cite><Author>Dominguez</Author><Year>2006</Year><RecNum>9</RecNum><DisplayText>(Dominguez, Kumar et al. 2006)</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430381328">9</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dominguez, Francina</author><author>Kumar, Praveen</author><author>Liang, Xin-Zhong</author><author>Ting, Mingfang</author></authors></contributors><titles><title>Impact of Atmospheric Moisture Storage on Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1513-1530</pages><volume>19</volume><number>8</number><dates><year>2006</year><pub-dates><date>2006/04/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>;(Dominguez, Kumar et al. 2006) presented an elegant model (dynamic model) that in contrast to other previous models considers the change in atmospheric storage, which allows to perform calculations in smaller time-scales. When comparing the results of their model to those produced with Brubaker’s and Eltahir’s models, they found that almost identical spatial and temporal patterns are produced, but the values of the recycling ratio increased in a range from 12% to 33%. ADDIN EN.CITE <EndNote><Cite><Author>Bisselink</Author><Year>2009</Year><RecNum>19</RecNum><DisplayText>(Bisselink and Dolman 2009)</DisplayText><record><rec-number>19</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1437374478">19</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Bisselink, B.</author><author>Dolman, A. J.</author></authors></contributors><titles><title>Recycling of moisture in Europe: contribution of evaporation to variability in very wet and dry years</title><secondary-title>Hydrol. Earth Syst. Sci.</secondary-title></titles><periodical><full-title>Hydrol. Earth Syst. Sci.</full-title></periodical><pages>1685-1697</pages><volume>13</volume><number>9</number><dates><year>2009</year></dates><publisher>Copernicus Publications</publisher><isbn>1607-7938</isbn><urls><related-urls><url>;(Bisselink and Dolman 2009)studied the influence of evaporation from soil moisture to precipitation recycling in Europe, with the help of the dynamic model. They compared the results of the recycling ratio for two years with similar climatology but different pre-seasons, being both of them dry and warm years but with dry pre-season (2003) and with wet pre-season(2006). Their results confirmed their findings from 2008, ADDIN EN.CITE <EndNote><Cite><Author>Bisselink</Author><Year>2008</Year><RecNum>20</RecNum><DisplayText>(Bisselink and Dolman 2008)</DisplayText><record><rec-number>20</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1437377641">20</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Bisselink, B.</author><author>Dolman, A. J.</author></authors></contributors><titles><title>Precipitation Recycling: Moisture Sources over Europe using ERA-40 Data</title><secondary-title>Journal of Hydrometeorology</secondary-title></titles><periodical><full-title>Journal of Hydrometeorology</full-title></periodical><pages>1073-1083</pages><volume>9</volume><number>5</number><dates><year>2008</year><pub-dates><date>2008/10/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>1525-755X</isbn><urls><related-urls><url>;(Bisselink and Dolman 2008)where they showed in a monthly timescale that evaporation contributes to precipitation only in dry years. The analysis at a daily timescale allowed them to hypothesize that the precipitation recycling plays an important role in triggering of precipitation in dry spells even if the total amount of precipitation is small, creating a negative feedback, as long as there is enough moisture stored in the soil. Motivation:Illinois is one of the regions with more data available from direct observations, several studies have focused in the determination of terrestrial water balances. This project will examine the atmospheric branch of the hydrological cycle, with the help of moisture recycling models.Hypotheses and research questions:-How much of the precipitation that occurs in Illinois is sustained by the local evaporation?-From the models for estimating precipitation recycling, which one provides the most accurate results?-What is the origin, travel distances and travel times of water precipitated in Illinois?DefinitionPrecipitation recycling is defined as the contribution of precipitation falling in a region which originates from evaporation within the same region ADDIN EN.CITE <EndNote><Cite><Author>van der Ent</Author><Year>2010</Year><RecNum>2</RecNum><DisplayText>(van der Ent 2010)</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430295199">2</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>van der Ent, R. J., H. H. G. Savenije, B. Schaefli, and S. C. Steeele Dunne</author></authors></contributors><titles><title>Origin and fate of atmospheric moisture over continents</title><secondary-title>Water Resources Research</secondary-title></titles><periodical><full-title>Water Resources Research</full-title></periodical><pages>12</pages><volume>46 </volume><number>W09525</number><dates><year>2010</year></dates><urls></urls><electronic-resource-num>10.1029/2010WR009127</electronic-resource-num></record></Cite></EndNote>(van der Ent 2010). Precipitation in an area is assumed to be composed by two parts:P=Pr+Pa(1)Where P is the total precipitation in an area, Pr is the precipitation of water vapour evaporated in the same area, Pa is precipitation of water vapour that is advected to that area.Precipitation recycling is represented by the precipitation recycling ratio, this can be local (ρ), regional (r) and continental (R).The local precipitation ratio ρ is said to be specific for a point (x, y) in a region, ADDIN EN.CITE <EndNote><Cite><Author>Burde</Author><Year>2001</Year><RecNum>6</RecNum><DisplayText>(Burde and Zangvil 2001)</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430365993">6</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Burde, G. I.</author><author>Zangvil, A.</author></authors></contributors><titles><title>The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>2497-2508</pages><volume>14</volume><number>12</number><dates><year>2001</year><pub-dates><date>2001/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Burde and Zangvil 2001), but in reality is the recycling ratio of the cell that contains that specific point. The choice of the region of study influences the results of ρ, through its area and shape. The value of ρ varies with time and is defined as:ρ (t,x,y)=Pm (t,x,y)P (t,x,y)(2)Where Pm is the precipitation that comes from evaporation in the present area, and P is total precipitation.The regional recycling ratio r is defined for a region, it is representative for the whole area. This ratio is dependent of time t, the size of the region A, and its shape. It can be defined as:r=Pm t,x,ydAPt,x,ydA(3)The continental recycling ratio ADDIN EN.CITE <EndNote><Cite><Author>van der Ent</Author><Year>2010</Year><RecNum>2</RecNum><DisplayText>(van der Ent 2010)</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430295199">2</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>van der Ent, R. J., H. H. G. Savenije, B. Schaefli, and S. C. Steeele Dunne</author></authors></contributors><titles><title>Origin and fate of atmospheric moisture over continents</title><secondary-title>Water Resources Research</secondary-title></titles><periodical><full-title>Water Resources Research</full-title></periodical><pages>12</pages><volume>46 </volume><number>W09525</number><dates><year>2010</year></dates><urls></urls><electronic-resource-num>10.1029/2010WR009127</electronic-resource-num></record></Cite></EndNote>(van der Ent 2010) is a modification of the local recycling ratio in which the limiting factor of shape and area is overcome by using the continental surface as the region of study.The continental recycling ratio generally makes the distinction between precipitation of water vapour from continental origin and precipitation of water vapour from oceanic origin instead of locally evaporated and advected water vapour.P=PC+PO(5)The continental recycling ratio is defined as:ρc (t,x,y)=PC (t,x,y)P (t,x,y)(4)Models for moisture recycling:The models for estimation of precipitation recycling can be classified according to the treatment given to the time derivative of precipitable water, or depending on the direction of the flux in the area.The starting point for the models is the atmospheric water balance AWB in any of its forms.?w?t+?uw?x+?vw?y=E-P(5)Where:w = precipitable water [L3]u = wind velocity in the x direction [L3/T]v = wind velocity in the y direction [L3/T]P = precipitation [L3/T]E = evaporation [L3/T]The first term represents the change of the precipitable water (storage) in time, while the second and third the change of the vertically integrated moisture influx I in the x and y directions, respectively.?uw?x=Ix=LyρLgpupsqudp (6)?vw?y=Iy=LxρLgpupsqvdp (7)Where:Ly= Horizontal length perpendicular to the x direction [L]Lx= Horizontal length perpendicular to the y direction [L]g = gravity [L/T2]q = specific humidity [M/M]p = pressure [M/(T2*L)] ; pu= pressure when vapor content is negligible; ps= pressure at surface ρL= density of liquid water [L3/M]Andw=AρLgpupsqdp (8)Qx=1gpupsqudp (9)Qy=1gpupsqvdp (10)Qx= vertically integrated flux vector in the x direction [M L-1 T-1]Qy= vertically integrated flux vector in the y direction [M L-1 T-1]Note the difference in the units between (6), (7), and (9), (10), the first group is the result of the integration of Q/ρ along the borders of the area.Due to the complexity of the process of moisture recycling and of the phenomena involved, several assumptions had been adopted in the studies of precipitation recycling in order to simplify the calculation of the precipitation recycling ratio.These are ADDIN EN.CITE <EndNote><Cite><Author>Burde</Author><Year>2001</Year><RecNum>6</RecNum><DisplayText>(Burde and Zangvil 2001)</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430365993">6</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Burde, G. I.</author><author>Zangvil, A.</author></authors></contributors><titles><title>The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>2497-2508</pages><volume>14</volume><number>12</number><dates><year>2001</year><pub-dates><date>2001/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Burde and Zangvil 2001):Use of time averaged dataThis assumption is especially important for the determination of the moisture influx in monthly time scale. Most of the data used for the calculation of Influx is measured by satellite. The measurements are taken 4 times per day and then processed into daily and monthly values. ADDIN EN.CITE <EndNote><Cite><Author>Fitzmaurice</Author><Year>2007</Year><RecNum>7</RecNum><DisplayText>(Fitzmaurice 2007)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430370007">7</key></foreign-keys><ref-type name="Thesis">32</ref-type><contributors><authors><author>Jean Anne Fitzmaurice</author></authors></contributors><titles><title>A critical analysis of bulk precipitation recycling models</title><secondary-title>Civil and Environmental Engineering</secondary-title></titles><volume>Ph. D.</volume><dates><year>2007</year></dates><pub-location>Cambridge</pub-location><publisher>Massachusetts Institute of Technology</publisher><urls></urls></record></Cite></EndNote>(Fitzmaurice 2007) identified two possible ways of processing the data, they are called the time-averaged method and accumulated method.The first one refers to this assumption, here the influx is calculated from a unique value of Q which is the result of averaging all the instantaneous Q.The accumulated method calculates the monthly influx as the average of instantaneous influx.The use of the accumulated method is more realistic and overrides the necessity of this assumption.Storage of atmospheric water vapor is small compared to the atmospheric water vapor fluxesThis assumption refers to the time scale used for the analysis, ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994) demonstrated that for a monthly time-scale the variation of precipitable water is small when compared with the fluxes in an area.The pitfall of this assumption is that the use of large time-scales i.e. monthly neglects the daily variation of moisture storage changes, which can influence in the results for precipitation recycling as has been demonstrated by ADDIN EN.CITE <EndNote><Cite><Author>Fitzmaurice</Author><Year>2007</Year><RecNum>7</RecNum><DisplayText>(Fitzmaurice 2007)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430370007">7</key></foreign-keys><ref-type name="Thesis">32</ref-type><contributors><authors><author>Jean Anne Fitzmaurice</author></authors></contributors><titles><title>A critical analysis of bulk precipitation recycling models</title><secondary-title>Civil and Environmental Engineering</secondary-title></titles><volume>Ph. D.</volume><dates><year>2007</year></dates><pub-location>Cambridge</pub-location><publisher>Massachusetts Institute of Technology</publisher><urls></urls></record></Cite></EndNote>(Fitzmaurice 2007) and ADDIN EN.CITE <EndNote><Cite><Author>Dominguez</Author><Year>2006</Year><RecNum>9</RecNum><DisplayText>(Dominguez, Kumar et al. 2006)</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430381328">9</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dominguez, Francina</author><author>Kumar, Praveen</author><author>Liang, Xin-Zhong</author><author>Ting, Mingfang</author></authors></contributors><titles><title>Impact of Atmospheric Moisture Storage on Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1513-1530</pages><volume>19</volume><number>8</number><dates><year>2006</year><pub-dates><date>2006/04/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>;(Dominguez, Kumar et al. 2006).The atmosphere is assumed to be mixedThe assumption of a well-mixed atmosphere implies that the particles of advected and evaporated moisture have the same probability of precipitating. This means that the ratios of advected to evaporated particles are the same in a rainfall event and in the precipitable water in the atmosphere.In the early years of research of precipitation recycling this assumption was accepted and widely used, however the increase of computational power allowed the formulation of more detailed transport models ADDIN EN.CITE <EndNote><Cite><Author>Bosilovich</Author><Year>2002</Year><RecNum>10</RecNum><DisplayText>(Bosilovich 2002)</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430382126">10</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Bosilovich, M. G.</author></authors></contributors><titles><title>On the vertical distribution of local and remote sources of water for precipitation</title><secondary-title>Meteorology and Atmospheric Physics</secondary-title><alt-title>Meteorol Atmos Phys</alt-title></titles><periodical><full-title>Meteorology and Atmospheric Physics</full-title><abbr-1>Meteorol Atmos Phys</abbr-1></periodical><alt-periodical><full-title>Meteorology and Atmospheric Physics</full-title><abbr-1>Meteorol Atmos Phys</abbr-1></alt-periodical><pages>31-41</pages><volume>80</volume><number>1-4</number><dates><year>2002</year><pub-dates><date>2002/06/01</date></pub-dates></dates><publisher>Springer-Verlag</publisher><isbn>0177-7971</isbn><urls><related-urls><url>;(Bosilovich 2002) which demonstrated that the mixing in the atmosphere doesn’t occur quickly after evaporation as Budyko(1974) and others proposed. ADDIN EN.CITE <EndNote><Cite><Author>Fitzmaurice</Author><Year>2007</Year><RecNum>7</RecNum><DisplayText>(Fitzmaurice 2007)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430370007">7</key></foreign-keys><ref-type name="Thesis">32</ref-type><contributors><authors><author>Jean Anne Fitzmaurice</author></authors></contributors><titles><title>A critical analysis of bulk precipitation recycling models</title><secondary-title>Civil and Environmental Engineering</secondary-title></titles><volume>Ph. D.</volume><dates><year>2007</year></dates><pub-location>Cambridge</pub-location><publisher>Massachusetts Institute of Technology</publisher><urls></urls></record></Cite></EndNote>(Fitzmaurice 2007) proposed a method to relax this assumption, but it introduces coefficients difficult to determine.PaPm=wawm or PmP=wmw(12)Stationary models: The stationary models neglect the change in time of the precipitable water, the results for recycling ratio can only be obtained for monthly, seasonal and yearly time-scales.Budyko: Developed the first model for precipitation recycling. This model considers rectangular regions traversed by parallel uniform atmospheric flow. The variables for precipitation and evaporation are assumed to be constant and equal to their average values. The 1D models solve a modified version of the AWB, where all the processes are considered along a single straight streamline, in the x direction the equation is as follows:dwudx=E-P(11)Budyko used the assumption of a well-mixed atmosphere for average values, and defined the parameter β which is calculated as:β=wwa=PPa(13)β mathematically shows the proportion of precipitation that the evaporation adds to the advected water vapour. With the application of boundary conditions to eq.(11) a solution for the regional recycling ratio is obtained, and finally the regional recycling ratio is defined as (14)r=1-β-1=ELEL+2Qx(14)Where L represents the length of the region along the stream line.Brubaker: The model suggested by ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993) was a modification to Budyko’s one. This model still treats the values of E, Pa, and Pm as constants equal to their average values, and assumes that the fluxes in the region Q, are equal to the arithmetic mean of the incoming and outgoing moisture, which implies the assumption of a linear variation of Q within the region.This model is considered to be 2D ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993), because it considers the influx to a region along 2 directions (I),however the process followed to arrive to an expression for the regional recycling ratio starts from the eq (11). Moreover method used to calculate the influx is appropriate only for a region traversed with parallel airflow and boundaries that are not parallel to the streamlines because of the assumptions previously mentioned that neglect 2D effects and moisture redistribution within the area. However it allows a non-uniform distribution of flow going into the region ADDIN EN.CITE <EndNote><Cite><Author>Burde</Author><Year>2001</Year><RecNum>6</RecNum><DisplayText>(Burde and Zangvil 2001)</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430365993">6</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Burde, G. I.</author><author>Zangvil, A.</author></authors></contributors><titles><title>The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>2497-2508</pages><volume>14</volume><number>12</number><dates><year>2001</year><pub-dates><date>2001/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(2001)014&lt;2497:TEORPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Burde and Zangvil 2001).The formula for regional recycling ratio proposed by ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993) is as follows:r=ELEL+2I=11+2IEA(15)Eltahir and Bras: Introduced a model that estimates the local recycling ratio form a grid based calculation.The equations of conservation of mass used are those shown in (16),?wi?t=Ii+E-Oi-Pi?wo?t=Io-Oo-Po(16)Where I represents the flux coming in and O the flux going out of the region, the subscripts i indicate from within the region and o from outside the region. I and O are the summation of the components of the flux in the horizontal directions.The formula used for estimation of ρ is:ρ=Iw+EIw+E+I0(17)As the data used for calculations is monthly or larger the time derivative is neglected, together with the assumption of a well-mixed atmosphere, the spatial distribution for ρ can be estimated. The estimation procedure consist of an iteration process. The area of study is divided with a grid where the values of E, P, I are interpolated into the nodes, ρ will be estimated in the middle of the nodes. Then an initial value is assigned for all ρ. With the data and the first assigned value of ρ a new improved estimate is obtained, this process id repeated until the values of ρ converge.The advantage of this model is the possibility of using values that are spatially distributed, which is a more realistic approach than the previous models.Non Stationary modelsThese models take into account the time derivative of the atmospheric water content, which allows the reduction of the time-scale of analysis to days or even hours.Fitzmaurice: This model is based in the one proposed by ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994), it uses the first eq. of (16) and the one shown below:?w?t=I+E-O-P(18)Then a backward differentiation scheme is applied to both differential equations and then to ρ. This model also uses the assumption of well mixed atmosphere, the final expression isρt=wt-?tρt-?t+E?t+Ii?twt-?t+I?t+E?t(19)Eq (19) depends on time, the estimation procedure for ρ is similar to the one described for Eltahir’s model, with the difference that now a time-step Δt is required. The choice of this Δt, is dependent on the size of the cells and the average speed of wind.Dynamic: ADDIN EN.CITE <EndNote><Cite><Author>Dominguez</Author><Year>2006</Year><RecNum>9</RecNum><DisplayText>(Dominguez, Kumar et al. 2006)</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430381328">9</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dominguez, Francina</author><author>Kumar, Praveen</author><author>Liang, Xin-Zhong</author><author>Ting, Mingfang</author></authors></contributors><titles><title>Impact of Atmospheric Moisture Storage on Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1513-1530</pages><volume>19</volume><number>8</number><dates><year>2006</year><pub-dates><date>2006/04/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>;(Dominguez, Kumar et al. 2006) proposed a model for the calculation of the local recycling ratio ρ. This model is derived from the AWB, combined with the assumption of well mixed atmosphere.The equation for mass conservation for water vapour that has its origin within the region as shown in (20) is later written in terms of (1-ρ) with the help of the well mixed assumption, as show in (21)?wi?t+?uwi?x+?vwi?y=E-Pi(20)w?(1-ρ)?t+wu?(1-ρ)?x+wv?(1-ρ)?y=-E(1-ρ)(21)Then to facilitate the arrival to a solution a new coordinate system is introduced:χ=x-utξ=y-vtτ=t(22)After substitution of the new system and the application of chain rule to eq.(21) the final expression for a modified recycling ratio is obtained:Rχ, ξ, τ=1-exp-oτεχ, ξ, τωχ, ξ, τ?τ'(23)Where: Rχ, ξ, τ, ε(χ, ξ, τ), ω(χ, ξ, τ), represent ρ(x,y,t), E(x,y,t), w(x,y,t) respectively, the value of R can be transformed into the original ρ with the use of eqs.(22).Water Accounting Model (WAM) ADDIN EN.CITE <EndNote><Cite><Author>van der Ent</Author><Year>2010</Year><RecNum>2</RecNum><DisplayText>(van der Ent 2010)</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430295199">2</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>van der Ent, R. J., H. H. G. Savenije, B. Schaefli, and S. C. Steeele Dunne</author></authors></contributors><titles><title>Origin and fate of atmospheric moisture over continents</title><secondary-title>Water Resources Research</secondary-title></titles><periodical><full-title>Water Resources Research</full-title></periodical><pages>12</pages><volume>46 </volume><number>W09525</number><dates><year>2010</year></dates><urls></urls><electronic-resource-num>10.1029/2010WR009127</electronic-resource-num></record></Cite></EndNote>(van der Ent 2010) proposed a model based in the AWB, this model is capable of tagging water so its origin can be determined; the AWB for the tracing of sources is as follows:?wΩ?t+?uwΩ?x+?vwΩ?y=EΩ-PΩ(24)Where the subscript Ω denotes the area of origin of the water vapour. The WAM model performs the calculations for the local recycling ratio ρ in a grid, when the grid covers the continental area the model calculates the continental recycling ratio ρc, It is possible to obtain the regional recycling ratio r if the local recycling ratio is multiplied by the weighted precipitation in the area and then are added.Area of study:The state of Illinois is located in the Central Plains and within the Mississippi Basin. It’s surrounded by Wisconsin in the north, Iowa and Missouri in the west Indiana and Lake Michigan in the east. Its topography is relatively flat; the highest point has 376.4 m, while the lowest 85m.Illinois covers an area of 143,962 km2, it spans for 619.59 Km from north to south (42.4951°N-36.9540°N) and for 350.83 miles from east to west (91.4244°W – 87.3840°W).The area used for the present analysis covers a larger region, as the data of evaporation was obtained from water balances and this method is sensitive to the size of the region analysed ADDIN EN.CITE <EndNote><Cite><Author>Rasmusson</Author><Year>1968</Year><RecNum>21</RecNum><DisplayText>(Rasmusson 1968)</DisplayText><record><rec-number>21</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1438153557">21</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Rasmusson, Eugene M.</author></authors></contributors><titles><title>ATMOSPHERIC WATER VAPOR TRANSPORT AND THE WATER BALANCE OF NORTH AMERICA</title><secondary-title>Monthly Weather Review</secondary-title></titles><periodical><full-title>Monthly Weather Review</full-title></periodical><pages>720-734</pages><volume>96</volume><number>10</number><dates><year>1968</year><pub-dates><date>1968/10/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0027-0644</isbn><urls><related-urls><url>(1968)096&lt;0720:AWVTAT&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0493(1968)096&lt;0720:AWVTAT&gt;2.0.CO;2</electronic-resource-num><access-date>2015/07/29</access-date></record></Cite></EndNote>(Rasmusson 1968). The area considered for this study is 236,785 km2, it extends for 555.17 from north to south (42.50N – 37.50N) and 426.51 from east to west (92.50W-87.50W), as can be seen in the figure below_________.Illinois has a continental climate, with cold winters, warm summers and frequent short fluctuations in temperature, humidity, cloudiness and wind direction. Five climatic controls have been identified for Illinois, these are: the sun, weather systems, topography, urban areas and Lake Michigan ADDIN EN.CITE <EndNote><Cite><Author>Angel</Author><Year>2008</Year><RecNum>22</RecNum><DisplayText>(Angel 2008)</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1438157723">22</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Angel, Jim</author></authors><tertiary-authors><author>Illinois State Water Survey</author></tertiary-authors></contributors><titles><title>Climate of Illinois Narrative</title></titles><pages>5</pages><dates><year>2008</year></dates><urls><related-urls><url>;(Angel 2008).The temperature in Illinois has been historically higher in the south, where the average annual temperature is 14.4°C while in the north it is 8.8°C. January is coldest month and July the hottest ADDIN EN.CITE <EndNote><Cite><Author>Angel</Author><Year>2008</Year><RecNum>22</RecNum><DisplayText>(Angel 2008)</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1438157723">22</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Angel, Jim</author></authors><tertiary-authors><author>Illinois State Water Survey</author></tertiary-authors></contributors><titles><title>Climate of Illinois Narrative</title></titles><pages>5</pages><dates><year>2008</year></dates><urls><related-urls><url>;(Angel 2008)Illinois experiences about 29 tornadoes per year, peaking in April-June season ADDIN EN.CITE <EndNote><Cite><Author>Angel</Author><Year>2008</Year><RecNum>22</RecNum><DisplayText>(Angel 2008)</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1438157723">22</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Angel, Jim</author></authors><tertiary-authors><author>Illinois State Water Survey</author></tertiary-authors></contributors><titles><title>Climate of Illinois Narrative</title></titles><pages>5</pages><dates><year>2008</year></dates><urls><related-urls><url>;(Angel 2008). In normal conditions the wind speeds vary from 8 km/h to 20.9 km/h. Wind speeds reach maximums during winter and early spring, and minimums during summer. The dominant direction during summer is south to southwest, while during the rest of the year is less clear. ADDIN EN.CITE <EndNote><Cite><Author>Wendland</Author><Year>1981</Year><RecNum>23</RecNum><DisplayText>(Wendland 1981)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1438231714">23</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Wendland, W. M.</author></authors></contributors><titles><title>Illinois Windpower program</title></titles><dates><year>1981</year></dates><urls><related-urls><url>;(Wendland 1981)Results:From Brubaker’s modelFor this model, data Given the shape of the area, it’s recommended that these results are handled and analysed with care.Results obtained with evaporation from TWBThe long term average of the regional recycling ratio is 0.021. The seasonal cycle shows that the lowest values occur from October to March. From2004 to 2010 the behaviour in between years is in the form of peaks and drops, in a staggered manner, and all smaller than the long term average. In 2012 the yearly recycling ratio reaches the highest yearly average and then declines again. Among the years 2012 is the year with most months that have the highest recycling ratio, which occur in March through May and November. Whereas 2007 and 2008 have the largest number of months with the lowest recycling ratios.It can be seen that there is a correspondence with peaks and lows between the recycling ratio and the influx and out flux. The convergence presents an inverse relationship, when the convergence is maximum the recycling ratio is minimum, and when the convergence is minimum the recycling ratio is maximum.Results obtained with evaporation from AWBThe long term average of the recycling ratio for the region is 0.0249. The seasonal cycle shows that the lowest values occur from October to March; from April until July the general trend is ascending, after July the ratio decreases again, with the exception of a peak value in September.The year with the largest number of months with the minimum recycling ratios is 2010, while 2009 has the largest number of months with the maximum recycling ratios.The lowest yearly average of the recycling ratio happens in 2010. In this 10 year period there are two peaks in 2009 and 2012.Just like with the TWB there is an inverse correspondence between convergence and the recycling ratio.left173607When comparing the results obtained with the two evaporations, a disperse correlation is obtained, r=0.64.This confirms the results obtained from the sensitivity analysis, which showed that for Brubaker’s model the most influential term is the evaporation. Since the evaporation obtained from the AWB is larger, the majority of the points are located under the line for r=1. Sensitivity analysis.r=EAEA+2Ix=EA*(EA+2Ix)-1Changing the notation:r=α*β-1Where:α=EAβ=EA+2IxApplying the law of propagation of errors, the relative error of the regional recycling ratio (r) is:rr2=rα2+(-1)2rβ2=rα2+rβ2rα2=rE2+rA2Applying the definition of relative error:rβ2=σββ2Applying the theory of propagation of errors:σβ2=?β?E2σE2+?β?I2σI2σβ2=A2σE2+22σI2rβ2=A2σE2(EA+2I)2+4σI2(EA+2I)2Then the final expression for the relative error of the precipitation recycling of Brubaker’s model is:rr2=σEE2+σAA2+A2σE2(EA+2I)2+4σI2(EA+2I)2But σA=0 because it can be assumed to be completely accurate:rr2=σEE2+A2σE2(EA+2I)2+4σI2(EA+2I)2Re-arranging the terms:rr2=A2(EA+2I)2+1E2σE2+4(EA+2I)2σI2Changing the notation for simplicityrr2=γσE2+εσI2rr=γσE2+εσI2Analysis with E from TWBγ/10σE2/10-3γ* σE2ε/10-47σI2/1021ε*σI2/10-25rrJanuary368.971.214.463.883.581.392.11February21763.300.47102.1013.231.471.9410.10March664.840.382.522.805.501.541.59April18.860.910.171.613.270.530.41May14.740.950.140.784.420.350.37June9.750.250.020.546.240.340.16July8.050.060.000.852.860.240.07August8.080.300.020.963.190.310.16September15.580.330.051.434.100.580.23October40.650.600.241.153.870.450.49November227.590.210.492.502.140.540.70December9487.531.39132.203.044.141.2611.50Analysis with E from AWBγ/10σE2/10-3γ* σE2ε/10-47σI2/1021ε*σI2/10-25rrJanuary304.680.341.033.843.581.371.01February442.480.220.9912.711.471.870.99March90.640.180.172.725.501.490.41April46.910.840.391.673.270.550.63May10.370.930.100.774.420.340.31June6.131.880.120.536.240.330.34July4.950.440.020.822.860.240.15August6.450.530.030.943.190.300.18September6.601.540.101.354.100.550.32October17.910.350.061.113.870.430.25November43.420.510.222.392.140.510.47December330.920.280.932.964.141.230.96The results from the calculations of the error propagation for the recycling ratio estimated with the Brubaker’s model show that the biggest influence in the result comes from the values of evaporation, it’s order of magnitude completely overrides the uncertainty attained to the value of the influx. The multiplier of the variance of the evaporation depends on the squared value of the area and the inverse of the squared mean evaporation, in the case of a small evaporation, this multiplier increases. This is the case with the months of February and December in the TWB where half of the population size has negative values. The relative errors calculated with the Evaporation from the AWB are less disperse and also show that the evaporation is the dominant term with respect to the uncertainty.From Eltahir’s modelEltahir’s model provides results in a spatially distributed grid, they are called the local recycling ratio, and are obtained after an iterative process which requires as data the influx of water vapor to the area and evaporation. This model, in contrast to Brubaker’s, has the advantage of using spatially distributed data. However the data used here was the monthly state average, which means that a constant evaporation along the entire area was assumed. The main reason to use the state average is because of the uncertainty in the values from other sources, and to close the water balance ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994).When the results of the local recycling ratio are obtained, they are multiplied by a weighted factor of precipitation in that area and then added together to obtain the regional recycling ratio. I did this with data downloaded from ERA-Interim, the variable downloaded is “Total precipitation”, according to the manual this variable is obtained from forecast, so I followed the steps recommended to determine the monthly average but the results turned out to be underestimated. I’m checking again what mistake could I have done. The results showed below use these underestimated values, as I didn’t realize that on time. Once I find my error I’ll generate them again and update the results. Results obtained with evaporation from AWBLong term average: 0.0256Results obtained with evaporation from TWBLong term average: 0.0238Eltahir’s model:ρ=Iw+EI+E=Iw+E*I+E-1Changing the notation:ρ=α*β-1Where:α=Iw+Eβ=I+EApplying the law of propagation of errors, the relative error of the local recycling ratio (ρ) is:rρ2=rα2+(-1)2rβ2=rα2+rβ2Applying the definition of relative error:rρ2=σαα2+σββ2Applying the theory of propagation of errors:σαα2=?α?Iw2σIw2(Iw+E)2+?α?E2σE2(Iw+E)2σαα2=σIw2(Iw+E)2+σE2(Iw+E)2σββ2=?β?I2σI2(I+E)2+?β?E2σE2(I+E)2σββ2=σI2(I+E)2+σE2(I+E)2The final expression for the relative error is:rρ2=1(Iw+E)2σIw2+1(I+E)2σI2+1(Iw+E)2+1(I+E)2σE2rρ2=θ2σIw2+μ2σI2+θ2+μ2σE2The formula above shows that the multiplier of the variance of the evaporation is the largest among all. The values of the influx are in the order of 1011 m3/month, while evaporation is in the order of 109 m3/month, which results in a multiplier of the order of magnitude of 10-23. The variances of the influx are in the order of magnitude of 1021, and for the evaporation in the order of 1013. Finally the major contribution to the uncertainty in the recycling ratio from Eltahir’s model is the influx, as the product of this and its multiplier results in value of order 10-2 whereas from the evaporation it is 10-10. Regional water cycleTerrestrial Water Balance6286504000516,43116,43364264078578316,43116,433142.6142.68028021719AtmosphereLandBrubakerEltahir16,43116,43364264078578316,43116,433142.6142.68028021719AtmosphereLandBrubakerEltahirAtmospheric Water Balance6286503873516,30916,31076576490890716,30916,310142.6142.69309302223AtmosphereLandBrubakerEltahir16,30916,31076576490890716,30916,310142.6142.69309302223AtmosphereLandBrubakerEltahirThe values presented in the tables were calculated as an entire area, from the annual average of a 10 years’ time series.Evaporation was obtained from the air water balance and terrestrial water balance.The sum of 1 and 2 correspond to the total influx of atmospheric water vapour entering to the area.The flux 4 represents the precipitation in the area, while 3 is the value of water vapour evaporated from the area that is added to the precipitation, its value is calculated as the product of the recycling ratio and the precipitation.The flux represented by 2 is the advected precipitation that reaches the area, it can be calculated as the subtraction of 4 and 3.The value of 1 is the amount of water vapour that passes through the area, it is obtained from the subtraction of 2 from the influx.The flux represented by 7 is the evaporation that leaves the area of study, it can be estimated as evaporation – 3.From Brubaker’s model and Evaporation from the TWBFluxValueUnitInflux17216mm/yearOut flux17073mm/yearConvergence142mm/yearEvaporation659mm/yearPrecipitation802mm/yearRecycling ratio 1.85%FluxValue [mm/year]1164292787315480251436164297645From Brubaker’s model and Evaporation from the AWBFluxValueUnitInflux17216mm/yearOut flux17073mm/yearConvergence142mm/yearEvaporation787mm/yearPrecipitation930mm/yearRecycling ratio 2.3%FluxValue [mm/year]1163072909321493051436163087766For the calculation of the recycling ratio with Brubaker’s model the data used was evaporation and the vertically integrated water vapour in x and y directions. The data of evaporation was provided by Fritzi and was obtained with 2 different methods, the AWB and the TWB.Due to the nature of the data of evaporation (comes from a water balance), it is assumed that for the area and the period of study the water balance closes, that’s why the value of precipitation is the one that closes the water balance, obtained after trial and error. In order to verify the validity of the results, I think a good method is to compare the values here assumed with those used in the TWB and in the AWB. The value of precipitation presented above are in accordance with the value presented in Hydroclimatology of Illinois, where the annual precipitation from 1983 to 1994 is 974.8mm, at least for the case of AWB.Previous studies:The literature available about precipitation recycling for the present area of study as shown below is very limited and almost inexistent. ADDIN EN.CITE <EndNote><Cite><Author>Brubaker</Author><Year>1993</Year><RecNum>3</RecNum><DisplayText>(Brubaker, Entekhabi et al. 1993)</DisplayText><record><rec-number>3</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430298523">3</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brubaker, Kaye L.</author><author>Entekhabi, Dara</author><author>Eagleson, P. S.</author></authors></contributors><titles><title>Estimation of Continental Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1077-1089</pages><volume>6</volume><number>6</number><dates><year>1993</year><pub-dates><date>1993/06/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</url></related-urls></urls><electronic-resource-num>10.1175/1520-0442(1993)006&lt;1077:EOCPR&gt;2.0.CO;2</electronic-resource-num><access-date>2015/04/29</access-date></record></Cite></EndNote>(Brubaker, Entekhabi et al. 1993) studied the precipitation recycling in the North American region, in an area that lies to the east of the continental divide and within the Mississippi Basin, its size was 1’948,138.5Km2, while the area considered in this study has 236,785Km2, which means that the area in Brubaker’s study is 8.22 times bigger.The results obtained by Brubaker vary from 0.15 to 0.34, depending on the month. ADDIN EN.CITE <EndNote><Cite><Author>Benton</Author><Year>1950</Year><RecNum>13</RecNum><DisplayText>(Benton, Blackburn et al. 1950)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433917864">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Benton, George S.</author><author>Blackburn, Robert T.</author><author>Snead, Vernon O.</author></authors></contributors><titles><title>The role of the atmosphere in the hydrologic Cycle</title><secondary-title>Eos, Transactions American Geophysical Union</secondary-title></titles><periodical><full-title>Eos, Transactions American Geophysical Union</full-title></periodical><pages>61-73</pages><volume>31</volume><number>1</number><dates><year>1950</year></dates><isbn>2324-9250</isbn><urls><related-urls><url>;(Benton, Blackburn et al. 1950) analysed the role of the atmosphere in the hydrological cycle for the Mississippi Basin, the area studied had 3,237,308 km2.The process followed by ADDIN EN.CITE <EndNote><Cite><Author>Benton</Author><Year>1950</Year><RecNum>13</RecNum><DisplayText>(Benton, Blackburn et al. 1950)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1433917864">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Benton, George S.</author><author>Blackburn, Robert T.</author><author>Snead, Vernon O.</author></authors></contributors><titles><title>The role of the atmosphere in the hydrologic Cycle</title><secondary-title>Eos, Transactions American Geophysical Union</secondary-title></titles><periodical><full-title>Eos, Transactions American Geophysical Union</full-title></periodical><pages>61-73</pages><volume>31</volume><number>1</number><dates><year>1950</year></dates><isbn>2324-9250</isbn><urls><related-urls><url>;(Benton, Blackburn et al. 1950) was the formulation of a water balance for the basin, where a distinction was made between air from maritime and continental origin. The recycling ratio for the Mississippi Basin was estimated to be 0.10 Being the recycling ratio dependent on the size of the area, various researches had attempted to formulate equations that would give an estimate of it, given the area or the length scale of the dominant flow. ADDIN EN.CITE <EndNote><Cite><Author>Eltahir</Author><Year>1994</Year><RecNum>8</RecNum><DisplayText>(Eltahir and Bras 1994)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430377400">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eltahir, E. A. B.</author><author>Bras, R. L.</author></authors></contributors><titles><title>Precipitation recycling in the Amazon basin</title><secondary-title>Quarterly Journal of the Royal Meteorological Society</secondary-title></titles><periodical><full-title>Quarterly Journal of the Royal Meteorological Society</full-title></periodical><pages>861-880</pages><volume>120</volume><number>518</number><dates><year>1994</year></dates><publisher>John Wiley &amp; Sons, Ltd</publisher><isbn>1477-870X</isbn><urls><related-urls><url>;(Eltahir and Bras 1994) proposed an equation based on their results from the research carried out in the Amazon Basin. ρ=0.0056LWhere L = the magnitude of the linear scale of the region [Km] ADDIN EN.CITE <EndNote><Cite><Author>Dominguez</Author><Year>2006</Year><RecNum>9</RecNum><DisplayText>(Dominguez, Kumar et al. 2006)</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app="EN" db-id="rtzw25fad5vs2revfty5ta0dtapwr0f0avwv" timestamp="1430381328">9</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dominguez, Francina</author><author>Kumar, Praveen</author><author>Liang, Xin-Zhong</author><author>Ting, Mingfang</author></authors></contributors><titles><title>Impact of Atmospheric Moisture Storage on Precipitation Recycling</title><secondary-title>Journal of Climate</secondary-title></titles><periodical><full-title>Journal of Climate</full-title></periodical><pages>1513-1530</pages><volume>19</volume><number>8</number><dates><year>2006</year><pub-dates><date>2006/04/01</date></pub-dates></dates><publisher>American Meteorological Society</publisher><isbn>0894-8755</isbn><urls><related-urls><url>;(Dominguez, Kumar et al. 2006) proposed an equation developed from the results obtained after the application of the dynamic model to the United States.ρ=0.0573*Ln(A/1000)-0.2748Where A = Size of the area [Km2]When the later formula was deduced, its lower limit for applicability is 25,000 Km2.The application of this formula results in an annual regional recycling ratio of 0.03.In conclusion the existing literature does not provide with enough information about values of the recycling ratio, because they were done for larger areas in the same basin or for different basins that have different climatology. ReferenceRecycling RatioObservationsBenton0.10From water balance, entire Mississippi basinBrubaker0.15 – 0.34Area 8 times larger than present area, not a reliable modelDominguez0.03Dynamic model, Illinois areaDirmeyer0.07Back trajectory analysisReferences: ADDIN EN.REFLIST Benton, G. S., R. T. Blackburn and V. O. Snead (1950). "The role of the atmosphere in the hydrologic Cycle." Eos, Transactions American Geophysical Union 31(1): 61-73.Brubaker, K. L., D. Entekhabi and P. S. Eagleson (1993). "Estimation of Continental Precipitation Recycling." Journal of Climate 6(6): 1077-1089.Burde, G. I. and A. Zangvil (2001). "The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models." Journal of Climate 14(12): 2497-2508.Dominguez, F., P. Kumar, X.-Z. Liang and M. Ting (2006). "Impact of Atmospheric Moisture Storage on Precipitation Recycling." Journal of Climate 19(8): 1513-1530.Eagleson, P. S. (1986). "The emergence of global-scale hydrology." Water Resources Research 22(9S): 6S-14S.Eltahir, E. A. B. and R. L. Bras (1994). "Precipitation recycling in the Amazon basin." Quarterly Journal of the Royal Meteorological Society 120(518): 861-880.Lettau, H., K. Lettau and L. C. B. Molion (1979). "Amazonia's Hydrologic Cycle and the Role of Atmospheric Recycling in Assessing Deforestation Effects." Monthly Weather Review 107(3): 227-238.McDonald, J. E. (1962). "THE EVAPORATION-PRECIPITATION FALLACY." Weather 17(5): 168-177.Savenije, H. H. G. (1995). "New definitions for moisture recycling and the relationship with land-use changes in the Sahel." Journal of Hydrology 167(1–4): 57-78.SHUKLA, J. and Y. MINTZ (1982). "Influence of Land-Surface Evapotranspiration on the Earth's Climate." Science 215(4539): 1498-1501.TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources (2007). Hydrology of catchments, rivers and Delta's; CT5450. Delft, TU Delft. ADDIN EN.REFLIST Angel, J. (2008). Climate of Illinois Narrative: 5.Benton, G. S., R. T. Blackburn and V. O. Snead (1950). "The role of the atmosphere in the hydrologic Cycle." Eos, Transactions American Geophysical Union 31(1): 61-73.Bisselink, B. and A. J. Dolman (2008). "Precipitation Recycling: Moisture Sources over Europe using ERA-40 Data." Journal of Hydrometeorology 9(5): 1073-1083.Bisselink, B. and A. J. Dolman (2009). "Recycling of moisture in Europe: contribution of evaporation to variability in very wet and dry years." Hydrol. Earth Syst. Sci. 13(9): 1685-1697.Bosilovich, M. G. (2002). "On the vertical distribution of local and remote sources of water for precipitation." Meteorology and Atmospheric Physics 80(1-4): 31-41.Brubaker, K. L., D. Entekhabi and P. S. Eagleson (1993). "Estimation of Continental Precipitation Recycling." Journal of Climate 6(6): 1077-1089.Burde, G. I. and A. Zangvil (2001). "The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models." Journal of Climate 14(12): 2497-2508.Dominguez, F., P. Kumar, X.-Z. Liang and M. Ting (2006). "Impact of Atmospheric Moisture Storage on Precipitation Recycling." Journal of Climate 19(8): 1513-1530.Eagleson, P. S. (1986). "The emergence of global-scale hydrology." Water Resources Research 22(9S): 6S-14S.Eltahir, E. A. B. and R. L. Bras (1994). "Precipitation recycling in the Amazon basin." Quarterly Journal of the Royal Meteorological Society 120(518): 861-880.Fitzmaurice, J. A. (2007). A critical analysis of bulk precipitation recycling models. Ph. D., Massachusetts Institute of Technology.Lettau, H., K. Lettau and L. C. B. Molion (1979). "Amazonia's Hydrologic Cycle and the Role of Atmospheric Recycling in Assessing Deforestation Effects." Monthly Weather Review 107(3): 227-238.McDonald, J. E. (1962). "THE EVAPORATION-PRECIPITATION FALLACY." Weather 17(5): 168-177.Rasmusson, E. M. (1968). "ATMOSPHERIC WATER VAPOR TRANSPORT AND THE WATER BALANCE OF NORTH AMERICA." Monthly Weather Review 96(10): 720-734.Savenije, H. H. G. (1995). "New definitions for moisture recycling and the relationship with land-use changes in the Sahel." Journal of Hydrology 167(1–4): 57-78.SHUKLA, J. and Y. MINTZ (1982). "Influence of Land-Surface Evapotranspiration on the Earth's Climate." Science 215(4539): 1498-1501.TU Delft Faculteit Civiele Techniek en Geowetenschappen. Section Water Resources (2007). Hydrology of catchments, rivers and Delta's; CT5450. Delft, TU Delft.van der Ent, R. J., H. H. G. Savenije, B. Schaefli, and S. C. Steeele Dunne (2010). "Origin and fate of atmospheric moisture over continents." Water Resources Research 46 (W09525): 12.Wendland, W. M. (1981). Illinois Windpower program. ................
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