Hydrologic budget of North Americu

9. BLOKHINOV, E. G. (1967): N e w techniques for estimation of parameters of accidental fluctua- tions of streamflow using longterm observation data, Trudy Gosudarstvennogo gidrologiches- kogo instituta, Vypusk 143, Problems of regulation and use of rivers (in Russian).

10. KRITSKY, S. N. and MENKEL, M.F. (1948): O n conformity of thcroretical probability dictribu- tion curves with streamflow observation data, Problemy regulirovaniya rechnogo stoka, Vypusk 3, Publ. AN SSSR (in Russian).

11. KRITSKY, S.N. and MENKEL, M.F. (1956): O n estimation of probable recurrence of rarely observed hydrological events, Problemy regulirovaniya rechnogo stoka, Vypusk 6, Pubi. AN SSSR (in Russian).

12. BLOKHINOV, E. G. (1966): On the special features of distribution of sampling estimates of streaniflow parameters, Trudy Gosudarstvennogo gidrologicheskogo instituta, Vypnsk 134.

13. KRITSKY, S.N. and MENKEL, M.F. (1967): On some techniques of statistical analysis of hydro- logical observation ranges, Trudy Gosudarstvennogo gidrologicheskogo instituta, Vypusk 143, Problems of regulation and use of rivers (in Russian).

14. YEVJEVICH, V.M. (1964): Fluctuations of wet and dry years, Part 11, Analysis by serial correlation, Colorado State University Hydrology Paper No. 4.

15. EFIMOVICH, P. A. (1936): Problems of water resources calculations in hydrology, Gosenergoiz- dat (in Russian).

16. SHARASHKINA, N. S. (1960): Study of the cycle character of annual streamflow values as applied to water power problems, Probleiny gidroenergetiki i regulirovaniya rechnogo stoka, Publ. AN SSSR (in Russian).

17. HURST, H.E., (1952): TheNile, a general account of the river and theutilization of its waters, London.

Hydrologic budget of North America and sub-regions formulated using atmospheric vapor flux data

G.P. Malhotra' and P. Bock'

SUMMARY: The atmospheric water vapor flux divergence has been computed to obtain water balances of parts of North America for the period May 1, 1958 to April 30, 1963. Eleven areas were studied ranging in size from 8.5 million square kilometers (3.3 million square miles) to 150 O00 square kilometers (58 O00 square miles). The data included mean monthly vertically integrated distribution of flux divergence and

precipitable water, regional averages of runoff, and isohyetal averages of precipitation. The atmospheric data were used to estimate F E , the mean difference between precipitation

and evapotranspiration. These values of F E further yielded values of mean monthly evapo- transpiration, and indirectly yielded mean monthly change in the surface and subsurpace water storage, and the yearly pattern of the cumulative storage. The results of the study indicate that the patterns of monthly evapotranspiration and storage

as computed from atmospheric data become questionable if the size of area is reduced below about 550 O00 square kilometers (200 O00 square miles).

Presently with Bcas Designs Organization, Nangal Township, Punjab-Jndia. Formerly with University of Connccticut, Storrs, Connecticut, USA and The Travelers Research Corporation, Hartford, Connecticut, USA. Presently with University of Connecticut. Formerly with the Travelers Research Center, inc.

501

G. P. Mcilhorro utid P. Dock

BUDGET HYDROLOCI@UE D E L’AMERI@UE BU NORD ET DE SOUS-REGIONS FORMULE EN UTfLISANT LES DONNEES D U FLUX DE VAPEUR D’EAU IIIkUMk : La ((divergence)) du flux de In vapeur d’eau atmosphériqiie it été évaluée pour obtenir le bilan d’eau de parties de l’Amérique du Nord pour la période du I Mai 1958 ULL 30 avril 1963. Onze superficies ont été étudiées : ellcs préseiitaicnt des surfacas allani de 8,5 millions de kin’ (3,3 millions de milles carris) & 100 O00 k m 2 (58,000 milles carrés). Les données comprenaient la distribution intégrée de la ((divergence)) moyenne mensuelle

verticale du Aux et de l’eau précipitable, les moyennes régionales de l’écoulement et les moyennes des isohyètes des précipitations. Les données almosphériques ont été utilisées pour estimer F E , la diKérence moyenne entre

ia précipitation et I’évapotranspiratioii. Ces valeurs de P-E permettaient alors d’obtenir des valeurs de I’évapotranspiration mensuelle moyenne et inc!irectement les modifications moyennes mensuelles de I’emmagasinemcnt d’eau superficiel et souterrain, ainsi que Ia figure annuelle de I’emmagasinement Cumulatif.

Les résultats de l’étude montrent que les figures de I’évapotranspiration mensuelle et de I’emmagasinement évaluées d’apres les données atmosphériques peuvent être mises en doute si l’étendue de la surface est réduite en-dessous de 550 O00 kmz (200 000 milles carrés).

BALANCE HIDROLÓGICO DE AMERICA DEL NORTE Y DE SUS SUBREGIONES FORMULADO UTILIZANDO LOS DATOS DEL FLUJO D E VAPOR ATMOSFERICO RESUMES: La divergencia del flujo de vapor de agua atmosrérico ha sido calculada para obtener balances hidrológicos de ciertas partes de América del Norte durante ei período comprendido entre el 1 ” de mayo de 1958 y el 30 de abril de 1963. Sc estudiar on once zonas cuyas dimensiones varian entre 8,5 millones de kilómetros cuadrados (3,3 millones de millas cuadradas) y 150.000 kilómetros cuadrados (58.000 millas cuadradas). Los datos incluían la distribución media mensual verticalmente integrada de la divergmeia

del flujo y de agua precipitable, medias regionales de la escorrentía y medias isohiéticas de la precipitaciôn. Los datos atmosféricos se utilizaron para calcular P-E, es decir la diferencia entre la precipi-

tación y la evapotranspiración. Estos valores de P-E dieron. también valores de la evapotranspi- ración media mensual, e in.directamen.te el cambio mensual medio en el almacenamiento de agua superficial y subsuperficial, así como la distribución anual del almacenamiento acumulativo. Los resultados del estudio indican que las distribuciones dc la evapotranspiración y almacena-

miento mensuales, calculadas a partir de datos atmosféricos, son diodusas si las dimensiones de la zona se reducen a menos de nuos 550.000 kilöinctros cuadrados (200.000 millas cuadradas)

502

Hvdrologic brrùget (~f North Aniericci

I. TERRESTRIAL AND ATMOSPHERIC BR A N C H E S OF THE HYDROLOGIC CYCLE

The hydrologic cycle lias two major branches, the terrestrial and the atmospheric. The terrestrial branch consists of the inflow, outflow, and storage of water in its various forms on and in the earth, while the atmospheric branch is concerned with the same phenomena in the atmosphere. These two branches of the hydrologic cycle are joined at lhe interface between the atmosphere and tlie earth surfaces including tlie ocean. The terrestrial branch

Fig. 1. Terrestrial Branch of the Hydrologic Cycle.

o1 the hydrologic cycle is illustrated Idiagrainniatically in a simplified form in figure I which shows a terrestrial area bounded by XX and YY. During a given unit of time, precipitaticn (P), falls on this area from the atmosphere, whereas evapotranspiration (E) goes back to the atniospliere. Surface runoff (X) flows out of the area, and a change in surface and subsurface storage (AS) in the area takes place. Tliis change may be positive or negative. During the same unit of time, the movement of ground water in the area causes an influx (C',), aiid outflow (Go) of the ground water. Also, some transferals and withdrawals of water through man-made diversion structures may take place. Such transfers and diversions are indicated by T and W. Applying the principle of continuity to the various components of the terrestrial

branch of the hydrolosic cycle, we can write the balance equation as:

P+T+G,= E+R+dS+W+G" (1)

in which increase in storage is denoted as positive aiid the bar-denotes the average values of the components during unit time considered. If a large enough piece of earth's surface is considered such that the difference in

Ci and Go is negligitle, and the amounts of T and W are inconsequential, the balance equation for the terrestrial branch, involving the components representing the spatial averages denoted by () can te written as:

(P) = (Ë) + (R) + (ds) (2) or

(P-E) = (a) + (AS) in which increase in storage is denoted as positive.

compared to the other terms. Equation (7) is then reduced to: If long periods of time and large areas are considered, then AS tends to be small

(E) = (P) - (R) (3)

503

G. P. Mulhotru und P. Bock

Traditionally, the quantities of major interest to the engincer have bccn runoff (R) and precipitation (P). These two quantities generally are measurable. The measurement of evapotranspiration (E), and storage change (AS), however,

has been neglected primarily because it is so very difficult. While semi-empirical estimates of these quantities are made for local areas, there is an increasing need for the large-area estimates of evapotranspiration and soil moisture storage for use in planning more efficient irrigation systems, water resources projects, and optimum use of available water. For thc estimation of E and AS, hydrologists are now turning to the atmospheric

branch of the water cycle. In figure 2 is shown a region of atmosphere bounded by X‘X’ and Y’Y’. In a given unit of time, water vapor Qi enters the region and Q, is transported out of the region through the movement of air. During this time, a change in the precipitable water content (A W) takes place. Also, precipitation (P) falls out of the atmospheric region and the evapotranspiration (E) enters the region from the earth’s surface below.

Y’ I I

-t-c

Fig. 2. Atmospheric Branch of the Hydrologic Cycle.

The mass-balance equation for the various components of the atmosplieric branch of the hydrologic cycle, representing the spatial and time average components, can be written as:

where increase in precipitable water content is denoted as positive. The quantity (Q, - Qi) is generally denoted as V.Q and is called “divergence”, if it has

a positive value. When Qi exceeds Q,, the quantity (Q, - Qi) is negative and is called “convergence. ” Equaion (4) can thus be written as:

( F E ) = -(=) - (dw) or

and-also

(E) = (p) - [-<v. Q + AW)] (7)

Thus, if the quantity within the brackets in equation 7 is estimated from the atmospheric data, we can compute (P-) from equation (6). Precipitation (P) being a measured quantity, we can then estimate E as a residual.

504

Hydrologic budget of North Americri

Also, combining equations (2) and (.6):

-(V .Q + AW) = (E) + (AS) or

Runoff (R), is a measurable quantity. With the inclusion of atmospheric data, we can compute AS, the change in surface and subsurface storage, from equation (8). In the discussion in the following chapters, the symbols R, P, V . Q, etc.,represent

(R), (p), (v . Q), etc., unless otherwise stated. For a long period of time and a reasonably large area, the change in the surface and

subsurface storage is usually assumed as negligible. Equation (8) can then be written as:

-

Thus, runoff can also be computed from the atmospheric data. For a long period of time, the change in the precipitable water content of the atmosphere can also be assumed as negligible. Equation (9) can then be further simplified as:

For the purpose of this study, the mean value of V ’ Q for a large study area was computed by a program on I B M 7030 (STRETCH) based essentially on iterative inter- polation (between the individual station values) which satisfies the Poisson’s equations in finite difference form. A description of the procedure is given in [5, 251.

2. PREVIOUS INVESTIGATIONS USING ATMOSPHERIC VAPOR FLUX

The first attempt to study the water balance of a region utilizing the atmospheric flux data was probably made by Benton, Blackburn and Snead [I], who studied the water balance of the Mississippi watershed (3 million square kni) for the year 1946. The study offered a qualitative appraisal of the role of the atmosphere in the hydrologic cycle. Benton and Estoque [2] computed the net moisture flux across the boundaries of a major portion of the North American continent for the calendar year 1949 by using the geo- strophic approximation and considering the integrated flux up to the 400-mb level using twice-daily observations of radiosonde data. The computed value of the runoff was found to be 36% lower than the estimated water discharge in the rivers. In another study by Benton and Dominitz [3], the evapotranspiration for parts of

central United States and Canada were-computed for a one-year period (calendar year 1949) both from atmospheric data and by the semi-empirical method developed by Thomthwaite [?O]. The atmospheric data from twenty-two radiosonde stations recorded twice a day were used for the study. It was concluded that reasonable monthly and annual totals of evapotranspiration can be obtained from atmospheric data when very large areas of almost continental size are considered. Hutchings [ll] computed the water vapor flux and its divergence during the three-

month period June through August 1954 over a quadrangular area of 90,000 square kilometers in England. Atmospheric data recorded at four aerological stations at the vertices of the area at 50-mb intervals were used from the surface up to 350 mb. Hut-

5 O5

ching’s study shows that the aerological inetliod gives results that are comparable with those obtained by othcr methods for computing E- i‘ over u reasonably large area und for a period of from one to Lhrec months. The possibility of estimating the changc in thc surfacc and subsurface storage was indicated in this study. During this period, the general circulation of the atmospheric water vapor flux and its

role in the hydrologic cycle were studied by Starr and White [17], Starr, Peixoto and Livador [i 81, and Starr aiid Peixoto [19]. They computed the meridional and zonal fluxes and tlie Aux divergence of water vapor on a global scale for the calendar year 1950, using daily data for ninety aerological stations over the globe. Recently, Rasmusson [i 61 computed the atmospheric water balance for the North

American continent and for regions within the continent. His study covered a two-year period, May I961 through April 1963. From vertically integrated vapor Aux divergence derived from twice-daily air data, he computed mean monthly, seasonal, and annual values of the mean difference between evaporation and precipitation, (E-). H e concluded that the results of water balance studies deteriorate rapidly as the area is decreased below lo6 square kilometers (,386 O00 square miles). The present study involves essentially the same area as studied by Rasmusson, but the period of study has been extended over 5 years. Väisänen [23], Palmén and Söderman [13], Bradbury [6], Ferruza [9], Brock [7], and

Rasmussen [15] have studied different areas around the globe and for different periods of time. Some of the results obtained from atmospheric water balance for small areas and short periods of time indicated reasonable agreement with the independently confirmed results of evapotranspiration, etc. These studies have quite different objectives-from the estimation of evapotranspiration

and slorage change in the cases of Palmén and Söderman [13] and Viiisiinen [23] to the water budget of individual storm systems in the cases of Bradbury [6] and Ferruza [9]. Palmén and Söderman’s study covered an area of 304 O00 square kilometers in the

Baltic region and spanned a period of one year-October 1961 through September 1962. They used twice-daily air data from six aerological stations. Of the study area, 77% is cwered by water. They found that the mean monthly and mean annual values of evapo- transpiration for the area were in very good agreement (+3% for annual values) with those computed from “well established empirical formulas for the evaporation” in the region. Brock [7] studied an area of 2.9 m.illion square kilometers in the western United States

for the single month of February 1962. H e compared the observed daily values of precipi- tation with those computed from flux divergence (using twice-daily air data) using pan evaporation data for actual evapotranspiration without any adjustments to the data. He found significant positive correlation tetween the two values of precipitation. He further concluded that when daily water vapor flux divergence estimates of evapotrans- piration or precipitation are averaged over periods of at least 6 days, “reasonably reliable results” can be obtained for areas of the order of 3 million square kilometers (1.2 million square miles). H e also concluded that the daily analyses of estimates of E-P from vapor Aux data do not represent the true field. Rasmussen [15] studied the IJpper Colorado River Basin (0.63 million square kilo-

meters) for winter time accumulation of water for a period of seven winter seasons, 1957 through 1963. H e also compared the values of precipitation as observed by rain gauges and those estiinated from atinosplieric flux divergence computed from twice daily atmosphcric data. H e concluded that the gauge data underestimate the basin precipitation by about 50%. A review of the various aspects of the atmospheric water balance are discussed by

Palinén [14] in a report of the World Meteorological Organization. This monograph outliiics the progress iliade over the past two decades in thc study of the water balance of the atmosphere.

506

fi-vdrologic budget of NuriJi Anrericu

3. DATA AND STUDY AREAS

This study is based on the mean monthly values of divergence, vertically integrated moisture [5], precipitation, and runoff for the 5-year period from May 1958 to April 1963. Although this period is marked in its later stages by a drought in the eastern parts of the United States, it is long enough to compare the 5-year mean monthly values of evapo- transpiration, surface and subsurface water storage, etc., with other semi-empirical and observational methods. In a hydrological sense, this 5-year period is not very long, but it does provide a more adequate base for water balance studies and is the longest period of time for which such studies have so far been attempted. The total area and its sub-division for which the water vapor transport study has been

made are shown in figure 3. The area includes almost all of the continental USA excluding

W Weslern Region. ' E Eastern Region. \vi Area 01 Jntcrnal Drainage. ,E 1 \\,Z Restern Region exïluuivc E? Curnlxrkind and Tennessev

u[ Internal Drainage Aren. C Cenlrnl Ilcgion.

Chio Basin.

Rircr Dashs. ~:3 crest L Z ~ ; ~ S nepi,,.

. .

Fig. 3. Study Areas and Sub-divisions.

the coastal areas. The coastal area strip which has been excluded is defined by the location of the streamgaging stations on the rivers. Also included are portions of southern Canada. The total study area is 3.28 million square miles (8.50 million square kilometers). This study area was chosen because data required for a water balance study are readily

available for the area. Also, the area has a very adequate network of aerological stations that compares well with any such network in the world, and therefore represents an area for which the observed atmospheric data could be used for this type of study withreasona- bly adequate reliance.

507

G. P. Mrrlltotr(r ( r i i d I'. Rock

The sludy area is broken down into three major regions: (a) Eastern Region, 834 O00 sq miles (3. I6 m sq kin) (b) Central Region, I 604 O00 sq miles (4.1 5 m sq kni) (c) Western Region, 846 O00 sq iniles (2.19 m sq km)

(E) (C) (W)

The study was extended Lo the following further sub-divisions of these re&' 'ions:

1. Ohio River Bash up to Metropolis, Illinois: (E-1)

This area of 203 O00 sq miles (530 000 sq km) lies wholly within the Eastern Region.

Combined area of these two river basins is 58 000 sq miles (150 O00 sq km) and is part of the Ohio River Basin.

This area includes the surface area of lakes and the tributary watersheds up to Cornwall, Ontario on the main stem of the Ct. Lawrence River. The total area of this subdivision is 296 O00 sq miles (766 O00 sq km).

2. Tennessee and Cumberland River Basin: (E-2)

3. Great Lakes Area: (E-3)

4. Area of Internal Drainage in the Western Region: (W-i)

An area of 211 300 sq miles (546 O00 sq km) located in the western region drains internally. A separate study has been made for this area.

5. Western Region excluding the This truncated western region has an area of 634 500 sq miles (1.64 m sq km). area of Internal Drainage: ( W-2)

Studies have also been made for the following combinations of the major subdivisions:

1. Eastern and Central Regions combined. (C+ E)

2. Eastern and Central and Western regions combined (total study areaj

3. Total Study Area excluding the internal drainage area in the Western Region. [(W-2) + Cf E]

The Eastern Region includes the United States east of approximately 89" longitude, and southern portions of the provinces of Quebec and Ontario. The coastal areas excluded on the eastern and southern coasts are based on the selection of 35 stream-flow gaging stations on different rivers in the region. The choice of these stations has been made such that they are nearest to the m.outh of the river but at the same time beyond the tidal reach. The Central Region comprises the area of the United States between the eastern region

and the Rocky Mountains. It also includes the southern halves of the provinces of Alberta, Saskatchewan, and Manitoba, and the southwestern corner of the province of Ontario. The coastal areas of Louisiana and Texas have been excluded because of the choice of the stream gaging stations on the rivers flowing out to the Gulf of Mexico. The considerations for the selection of the 13 streamgages have been the same as inen- tioned for the Eastern Region. The Western Region includes the continental United States west of the Rocky Mountains

and the southern portion of the province of British Colum.bia. The coastal strip on lhe west coast has been excluded. The south boundary of the region is alinosl lhe same ;is the U.S.-Mexican border. The Western Region is gaged by 14 stream. gaging stations. About a quarter of the total area of the western region drains internally. The internal

drainage areas incliide the south-eastern arcas of the state of Oregon, western Ulah, almost all of thc state uf Nevada and parts of southern California. Addilioilul studies

508

Hydrologic hirùget of’ North Aniericu

have been made for the area of internal drainage, and also for the western region excluding the area draining internally. One of the biggest obstacles to the hydron~eteorological analyses of the water budget

in the past has been the non-availability of quantities like the vertically integratedprecipi- table water and atmospheric flux divergence for a reasonably long period of time. The previous studies [il, 18, 191 therefore, were necessarily limited to a fraction of a year or one single year. Rasmusson [i 61 was the first to extend the hydrometeorological studies over a two-year period. The atmospheric data for a 5-year period published in December 1966 [5] was an

attempt to compute a comprehensive mass of information regarding the moisture and moisture transport statistics for North America. These computations are based on the meteorological observations at J 76 rawinsonde stations in North America and adjacent oceans. Such observations were taken twice daily at 0000GMT and 1200GMT. For the purpose of vertical integration of moisture content and flux divergence of

moisture, the rawinsonde data are required at various levels through the atmosphere. The mean water vapor flux computed at any station, at the time of observation and at a given pressure level, is q? where (I is the specific humidity and V is the wind vector. The usual errors introduced are instrumentation errors, wind measurement errors, and sampling errors arising through the use of arithmetic mean of two observations a day (used in this study). Investigations by Hutchings [i i], Hodge and Harmantas [lo], and Rasmusson [I 61

seem to indicate that instrument errors produce negligible differences in the mean inonthly flux. However, the systemutic error in flux divergence introduced by the use of once- or twice-a-day observations to approximate the mean daily flux, seem not to be negligible, but is an important factor in determining the smallest area to which the atmospheric water balance equations can be successfully applied.

- _.

4. THE WATER BALANCES

The analyses of the atmospheric water vapor flux and other hydrologic data and the water balance for the various study regions are discussed in this section. Table 1 shows the arrangement of the data used of the water balances for the Eastern

Region. This arrangement of data is typical and such a table has been computed for each study area. Col 1 shows the year and month for the total period of study, 60 months (May 1958

through April 1963). Col 2 gives the values of “divergence” (V . Q) in cm/cm2. These values are computed

from the twice daily radiosonde data in accordance with the method given in [19]. Col 3 gives the value of the change in the precipitable water content in the atmosphere

(A W). These values represent the change between the first and the last day values of W obtained from published values of w[5]. Col 4: P-E = - (V. Q+A W) is computed from the values in col 2 and 3. Col 5 gives the monthly values of runoff for the region coinputed from the U.S.G.S.

runoff data published in Surface Water Records. The total runoff from a study region is divided by the total area of the region and the units have been reduced to cm/sqcm. Col 6 gives the values of the average monthly precipitation over the study region in

cm/cm2. These values have been derived from the Weather Bureau (US) and Meteorologi- cal Department (Canada) isohyetal maps. Cols 2 through 6 essentially represent the data as measured in the atmosphere and on

the earth’s surface. Cols 7 through 12 represent the computed values of the non-measured elements of the hydrologic cycle.

509

G. Y. Mulhorru und Y. Bock

Col 7 in table 1 gives the values of AS computed from cols 4 and 5 in accordance with equation 8. Considering the storage level at the bcginning of the study period as datum (O.OO), the values of storage ,S in cm/cm2 are computed in col 8 from values in col 7. These accumulative estimated values of S are plotted as a dotted line in figure 4 for the Eastern Region.

It can be seen from ñgure 4 that the storage level goes progressively downward till at the end of 5 years the depletion in the ground storage levels in the entire region appears to have reached about 42 c m (plotted as dotted line). The values of the estimates of such depletions or rise in the water storage levels in the other study areas are tabulated in table 2 and the progressive monthly change in estimated S are shown dotted in figure 2 for the Total Study Area. Similar information for other areas is given by Malhotra [12]. The total storage changes as tabulated and plotted appear to be excessive in either

direction. Possible explanations of these changes could be as follows: (I) that such changes did indeed occur because of imbalance between precipitation and evapotranspiration; (2) that these storage level changes are due to underground flow from one region to the other. Thus, the assumption made in the development of water balance equations that AG is negligible, does not actually hold; (3) that the storage level changes as estimated are not true and are a result of errors in atmospheric data on account of inadequate space and time spredd of radiosonde stations and observations; (4) parts of 1, 2 and 3 above are true. If the explanation No. 1 was true, it would mean that over a period of 5 years (1958-

1963) there has been an average depletion of about 45 cni (assuming a porosity = 1.0) in ground water over the entire Eastern Region which covers an area of about 2.16 million sq km. Further, such a depletion in the Ohio River Basin which is spread over 530 O00 sq km, is of the order of 2.1 m over the entire area. Again, according to the statement No. I, the general rise in the ground storage level

of the Central Region is over 45 c m over an area of 4. I5 million sq k m and in the internal drainage areas of the West which. cover over 500 O00 sq km, the increase in ground water storage levels is about 180 cm during the 5-year period. Although there is no reasonably good method lo check the validity of the figures

mentioned above, some dircction is given by the ground water levels published monthly

510

H,vdrologic huùger o/' North America

Table 1. Eastern Region (E)-Observed and Computed Data

Month 2 M a y

June July August September October November December January February March Aniil

Units: cm

-0.97 h.56 -3.46 -0.42 -6.88 t0.91 +0.07 -0.74 F0.73 -0.23 t0.62 -1.31 -2.89 -CP.61 -1.27 +0.29 -3.51 -0.25 -5.15 t0.37 -3.75 +0.37 -2.91 -0.08

(4)

-0.59 +3.88 +5.87 +0.67 -0.50 +0.69 t3.50 tO.L.8 +3.76 +4.18 +3.38 +2.99

1 (5) I (6) I (7) I (8) I (9) 1 (10) I (11) I (12) 5.27 7.80 -5.86 -5.86 -5.16 -5.16 +O.Il 7.69 2.58 10.50 +1.30 - 4.56 +2.00 - 3.16 t4.58 5.92 3.09 14.00 +2.78 - 1.78 C3.48 + 0.32 e6.57 7.43 4.66 9.80 -3.99 - 5.77 -3.29 - 2.97 +1.37 8.43 1.88 9.00 -2.38 - 8.15 -1.68 - 4.65 + O 2 0 8.ßO 1.92 6.00 -1.23 - 9.38 -0.53 - 5.18 +1.39 4.61 1.92 7.50 +1.58 - 7.80 12.28 - 2.90 +4.20 3.30 2.07 5.70 -1.09 - 8.89 -0.39 - 3.29 t1.68 4.02 3.91 8.60 -0.15 - 9.04 +O.% - 2.74 +4.46 4.34 3.93 7.20 bO.87 - 8.19 +1.55 - 1.19 +5.48 1.72 3.78 8.20 -0.40 - 8.59 +0.30 - 0.88 +4.08 4.12 4.50 8.30 -1.51 -10.10 ' -0.81 - 1.70 +3.69 4.61

~~~ ~

May June July August September October November December January February March Aorll

May June July Auguet September October November December January February March April

~

-5.19 +2.83 -2.57 -0.88 -3:n9 -5.34 -0.65 -4.96 -4.35 -5.86 -4.72 -4.14

-3.64 -1.28 12.89 -1.90 -0.24 -0.13 -0.53 -2.23 -0.42 -8.97 -6.38 4.75

~~

+2.05 -0.28 -0.09 +0.30 -0.74 -1.83 -0.46 -0.14 tO.48 -0.49 +0.79 to.64

+O.ll, +0.83 -0.27 +0.88 -1.86 t0.74 -1.34 t0.65 -0.47 +0.21 +O.% -0.06

+3.14 -2.35 r2.66 +O.% +4.63 +7.17 +1.11 +5.10 +3.87 +6.35 +3.93 +3.50

+3.53 +0.45 -2.62 t1.02 +2.10 -0.81 +1.87 +1.58 CO.89 +0.76 t5.80 +4.81

3.16 9.28 2.68 7.61 1.98 10:45 1.81 10.13 1.67 9.35 2.26 12.88 2.70 7.78 3.78 7.96

4.56 8.80 4.29 6.74 6.06 7.54

3.95 10.20 2.72; 13.00 2.54 9.80 2.12 H.60 2.00 8.40 1.77 6.40 1.85 -6.10 1.97 4.90 2.40 4.40 3 , s 10.00 6.91 10.30 5.93 9.90

3.84 :n.o8

-0.02 -10.12 -5.23 -15.35 +0.68: -14.67 -1.23 -15.90 +2.96 -12.94 +4.91 - 8.03 -1.59 - 9.62 +1.32 - 8.30 +0.03 - 8.27 +1.19 - 6.48 -0.36 - 6.84 -2.56 - 9.40 -0.42 - 9.82 -2.27 -12.09 -5.16 -17.25 -1.10 -18'35 t0.10 -18.25 -2.38 -20.63 +O.OZ -20.61 -0.39 -21.00 -1.51 -22.51 t5.22 -17.29 -111 -18.40 -1.12 -19.52

__-

+O.M -4.53 +1.38 -0.53 -3.66 +5.61 -0.89 +2.02 +0.73 +2.49 +0.34 -1.86

+0.28 -1.57 -4.46 -0.40 +0.80 -1.68 +0.72 10.31 -0.81 +5.92 -0.u -0.42

-

- 1.02 - 5.55 - 4.17 - 4.70 - 1.04 + 4.57 + 3.68 + 5.70 + 6.43 + 8.92 1 9.26 t 7.40

+ 7.88 + 6.11 + 1.65 + 1.25 + 2.05 + 0.37 + 1.09 + 1.40 + 0.59 + 6.51 + 6.10 + 5.68

d.84 -1.85 +3.36 t1.28 +5.33 11.87 +1.81 +5.80 +4.57 +1.05 +4.63 +4.20

+4.23 +1.15 -1.92 +1.72 .+2.80 co.09 +2.51 +2.28 +1.5s +9.48 +6.50 +5.51

__

5.42 9.46 1.09 8.85 4.02 5.01 5.97 2.16 3.51 1.75 2.11 3.34

5.97 11.85 1l.l.Z 6.88 5.60 6.91 3.53 2.62 2.81 0.54 3.80 4.39

-

May -0.44 June -2.09 July -2.33 August -1.99 September -3.44 October -0.65 November -3.36 December -6.5H January -5.51 February -8.24 March -3.48 Anri 1 -2.01

+1. o1 C0.42 10.55 +0.06 -1.05 -0.50 -1.10 tO.04 -0.04 +0.47 t0.34 +1.09

-0.57 +1.67 +1.78 +1.93 c4.49 +1.15 i4.46 +6.54 +5.55 t7.77 +3.14 +0.92

5.10 8.30 3.12 11.00 2.64 10.60 2.26 9.50 1.92 7.20 1.73 5.10 1.98 7.70 3.98 10.60 4.41 9.60 4.01 9.10 8.70 7.00 6.11 8.30

-5.61 -25.19 -1.45 -26.64 -0.86 -27.50 -0.33 -27.83 +2.57 -25.26 -0.58 -25.84 +2.48 -23.36 +2.56 -20.80 +1.14 -19.66 +3.76 -15.90 -5.56 -21.48 -5.19 -26.65

-4.97 -0.75 -0.16 c0.37 +3.27 LO.12 +3.18 t3.26 41.84 +4.46 -4.86 4.49

+ 0.71 - 0.04 - 0.20 + 0.17 + 3.44 + 3.56 + 8.74 +10.00 +11.84 +I630 +11.44 + 6.95

10.13 8.17 +2.37 8.63 +2.48 8.12 +2.62 6.87 +5.19 2.01 +1.85 3.15 +5.16 2.54 +7.24 3.36 +8.25 3.35 +8.47 0.63 +3.84 3.16 +1.62 6.68

..

May June July Augurrt September October November December January February March Aprii

+0.07 -0.30 +2.75 -1.24 +0.09 -0.30 -1.55 -2.85 -2.49 '-2.53 -5.99 -0.84

-0.22 -0.34 C0.28 +0.71 -1.88 -0.48 -0.17 -0.47 +0.30 -0.04 +O.% +0.40

+0.15 +O34 -3.03 +0.53 +1.79 +0.78 b1.72 +3.32 c2.19 +2.57 +5.45 +0.?4

2.83 6.80 2.07 8.70 1.96 9.00 1.66 7.40 1.52 9.40 1.85 7.20 2.34 6.40 2.22 6.60 2.82 5.90 2.66 4.80 5.98 10.80 3.74 6.60

-2.68 -29.33 -1.43 -30.76 -4.99 -35.75 -1.13 -36.88 t0.27 -36.61 -1.07 -37.68 -0.62 -38.30 +1.10 -37.20 -0.63 -37.83 -0.09 -37.92 -0.53 -38.45 -3.30 -41.75

-1.98 + 4.97 +OB5 -0.73 +44.23. +I34 -4.29 - 0.05 -2.33 -0.43 - 0.48 +1.23 +0.97 + 0.49 +2.49 -0.37 + 0.12 +l.48 +0.08 + 0.20 +2.42 +1.80 + 2.00 M.O2 +0.07 t 2.07 +2.89 +0.61 + 2.68 +3.27 t0.17 + 2.85 +6.15 -2.60 - 0.25 C1.14

5.95 7.36 11.33 6.17 6.91 5.72 3.98 2.58 3.01 1.53 4.05 5.48

511

G. P. hícrltiotrci utid P. Uock

Table 2. First Estimate of the Total Change in the Surface and Subsurface at the End of 5-Year Period Computed From Water Vapor Balance.

I

-1á.l.I

-1l.i

I 7 , ,-,

- 1 1 . 1

.LI.'

by the U.S. Geological Survey in the "Water Resources Review". For the Tennessee and Cumberland basins (1 50 O00 sq km), the waler vapor balanceestimate shows (table2) a fall in storage level of 106 c m (about 3.5 ftj. Checking with. the levels in the observation wells in the State of Tennessee which are located in the study region, it appears that the change in the well levels has either been negligible or there has been a slight increase in these level during the period of study. Similarly, for the Eastern Region, the ground water levels during the 5-year period are

reported as about average in the annual summaries of the "Water Resources Review" . The above information suggests that during 5-year period there was no tremendous

fall in the ground water level of the Eastern Region as indicated by the water vapor balance. It appears that all points are toward rejecting the hypothesis in explanation No. 1. If the changes in ground water storages were due to inter-regional underground flows,

they would likely be identified by the Geological Survey records. Also, such Bows would be of more permanent nature than being a particular feature of the 5-year study period. The volume of such flows can be estimated from figures given in table 2. According to

these figures 0.8 c m has flown in per month in the central area of 4.153 million sq km. This represents a uniform inflow of about 15 O00 cubic meters per second. Calculations suggest that this rate of flow is unrealistic. There is no evidence of such treniendous ground flows. ïhis hypothesis, is, therefore, also rejected. From the previous discussion and evidence in U.S. Geological Survey reports, it is

indicated that during the study period, the ground water levels in the United States have remained about average and that depletions of substantial nature in local areas have occurred mostly due to severe pumping. The storage changes indicated by water vapor balance equations might well be the

result of erroneous atmospheric data due to the inadequate number of radiosonde stations and errors in the measurements of wind velociíies, specific humidity, etc. at various levels of pressure. This error could also have been introduced because of the twice-daily measure- ment of these data.

512

H-vdrologic hudget q f North Americn

it, therefore, appears reasonable to assume tl-iat the change in the storage levels in the various study areas severally and jointly was negligible for the total 5-year study period. Based on the foregoing reasoning, the monthly values of AS as estimated at first have

been modified so that for the 5-year period,

This has been done by subtracting froin each monthly value of AS in a study region, the corresponding value shown in the last column of table 2. The adjusted values of AS for a typical case are shown in col 9 of table 1. The adjusted value of cumulative storage Sis shown in col 10. This adjusted value of monthly AS has been used for the water balance studies in the

following sections. Similarly, the values of - (V . Q + A W ) shown in col 4 of table 1 have been adjusted

by subtracting the corresponding value for a region from the last column in table 2 and are shown in col II of table J . These adjusted values of - (V . Q + A W) are referred to as adjusted V . Q in the following discussion. Eastern Region and Total Study Area are shown plotted in figures 4 and 5. The dotted

lines show the non-adjusted values of the storage as estimated from the observed atmos- pheric data. The solid lines show the adjusted values of the surface and subsurfacestorage estimated on the basis of From the adjusted values of storage, it can be seen that the storage appears to fluctuate

around an arbitrary datum during a typical year. These fluctuations are more in line with the observed indications of groundwater as sunmarized in the U.S. Geological Survey, "Water Resources Review". In the typical data sheet shown in table I , the value of evapotranspiration (E) is

computed in col 12 from the atmospheric water balance equation (6):

A S = O over the 5-year study period.

using the modified value of

from col 11. -tV*Q+AW)

Fig. 5. Estimated Monthly Surface and Subsurface Storage, S, for the 5-Year Period-Total Study Area.

51 3

G. P. Mulhotrci und P. Bock

For the eleven study regions, mean monthly values of the various adjusted water vapor balance components have been computed and are given in table 3 for the Total Study Area. Two sets of curves for each study region have also been plotted showing the 60 monthly values of these components for the study period. The first set of curves shows the values of (P-E) computed from the modified values of vapor flux divergence and runoff, R; and the second set shows the values of precipitation, P, and evapotranspiration, E. These curves are shown in figure 6 for the Total Study Area. For any given month the difference between (P-E) and (R) or between (P) and (E) represents the change in surface and subsurface storage (AS). The cumulative values of (AS) for each study region are shown as solid-line curves.

Fig. 6. Monthly Values of Wattr Balance Cornponents- 5-Year Period-Total Study Area.

As an illustrative example, the water balance of the Total Study Area and its salient features are discussed in the following paragraphs. Balances for the other areas are described by Malhotra [12]. The total area of study which covers U.S. and Southern Canada (excluding the coastal

areas) is spread over 3.3 million sq miles (8.5 million sq kilometers). Over this part of the world, mean annual precipitation varies from less than 15 c m to over 250 c m and mean annual runoff varies from zero to over 100 cm. The seasons of the highest and lowest flow differ locally but for the area as a whole the maximum runoff occurs in spring and minimum in fall. Mean monthly runoff during the study period ranged from 0.96 c m (September) to 2.33 c m (April). The mean monthly values of the components computed and estimated from water

vapor balance are shown in table 3. The quantity (P- E) stands for - (V . Q + A W) and represents convergence. The march of the monthly values of (P-E) and R; as also (E) and (P) over the

5-year period of study are shown in figures 6(a) and 6(b). The pattern of winter time stream-flow during the ñrst four years is slightly different than during the last year (1962-1963). During the first 4 years there are marked increases from the fail minimum through the winter. In the year 1962-1963, howevcr, there is little change in average strcam-flow from the fall minimum until the following spring. It is interesting to note that unlike the first four years, there is no convergence peak during the last year until March 1963.

514

Hydrologic hiidget of Norfh Americtr

Table 3. Computed Mean Monthly Water Balance for 5 Years (May 1958 to April 1963). Total Study Area (W+C+E)

Unitß: cm

(R)

2.25

1.89

1.52

1.27

r,.nri

1.07

1.07

1.28

1.15

1.61

2.20

2.33

1ß.9U

Month

May

June

July

August

Sep t e m ber

October

November

December

,January

February

March

April

(AS>*

-0.Ç4

-1.49

-1.57

-0.94

1.16

0.G4

lJ.70

0.84

0.20

1.77

0.62

-1.21

Annual

G.GO

7.03

7.12

5.95

6.26

5.24

4.58

,1.3G

3.86

4.84

5.10

(P - E)' _ _ ~ _ 1.61

0.40

-0.05

0.33

2.12

1.71

1.77

2.12

1.72

3.38

2.83

1.13

19.07

. ~ __

-~ 4.99

6.63

7.17

5.62

4.14

3.53

2.81

2.24

2.14

I.4G

2.27

-2.13

-3.70

-.1.G4

-3.48

-2.84

-2.14

-1.30

-1.10

'O.fi7

'1.29

-u.m

'Adjusted values 'As oí end oí monlh. Changc ironi M a y 1

As a whole, (P - E) shows a more irregular pattern, and greater seasonal changes, than those in the runoff. In general, maximum values occur during the winter and minimum during the summer. As can be seen from table 3, almost throughout the year there is inflow of moisture flux in the area. Only during the month of July a slight outflow of moisture i.e., divergence is indicated. Consequently, precipitation exceeds evapotrans- piration during all months except July when P and E almost balance each other. From table 3 and also from figure 6 it appears that the difference between (P-E)

and R changes sign from winter to summer. Thus, values under the component (AS) in table 3 show that there is an accumulation of water in the form of surface and subsurface storage over this area from September through March, which is lost again during the summer months. These fluctuations in storage during the 5 years are clearly shown in figure 4 (Adjusted S). That these fluctuations in storage agree with the known behavior of this quantity has already been discussed in the preceding sections. Soil moisture, as well as the water table, reach their highest value over most of the area in spring, and the surface storage in the form of snow reaches a maximum in late winter and early spring. Late spring and summer are characterized by periods of high evapotranspiration and decrease in storage. The lowest value of storage occurs in late summer or early fall. The values of evapotranspiration computed from V . Q and plotted in figure 6(b) show

a remarkably regular pattern over the 5-year period. The maximum evapotranspiration occurs during the month of July and minimum in February, which is reasonable and expected. From the foregoing it appears that the patterns of evapotranspiration and storage

515

G. P. Molhotru and P. Bock

computed from water vapor balance equations for the Total Study Area follow a logicul pattern. Similar analyses were made for the other 10 study areas ranging in size down to 150 O00

sq kin for the Tennessee and Cumberland Basins (ET). The conclusions are summarized below.

(E) Eastern Region

The agreements between convergence and runoff lend credence to the water vapor balance approach.

(E-1 j Ohio Basin, (E-2) Tennessee arid Cumberland River Basin, (E-3) Great Lakes

These subregions are located entirely within the Eastern Region. Subregion E-2 is located entirely within E-i. The analyses indicate that although the precipitation and runoff pattern of the areas E,

E-1, E-2 are on the same general lines, the patterns of V . Q and of the parameters evapo- transpiration and storagc as derived from V . Q for the area E-2 do not conform to the larger areas which surround it. It, therefore, appears to be indicated that the area E-2 is too small (58 O00 sq mi) to be amenable to a reasonable estimation of the movement of water vapor flux. There are an inadequatenumber of radiosonde stations to estimate V . Q for smaller areas. There are a total of 22 aerological stations in area E, of which 6 are in area E-I, one in E-2, and 5 in E-3.

It may be of interest to mention here that Bruce and Rogers [8] in 1962 estimated the mean annual evaporation from the Great Lakes System as 3.05 feet (93 cm). The computed annual mean evaporation is only 53 c m for a 5-year study period. This represents either an under-estimation of evaporation from Great Lakes from atmospheric data (- 43%) or an over-estjmation by conventional evaporation estimation techniques. Since a correct estimate of evaporation from the Great Lakes is important from the point of view of water resources, it is desirable that a greater coverage of the Great Lakes area by aerologi- cal stations be planned for more reliable hydrological results.

(C) Central Region

Components of the water vapor balance form a logical pattern. The parameters computed from V . Q values are in agreement from year to year and thus lend credence to the water vapor approach for this region.

( W) Western Region, ( W-i) Internal Drainage Area, ( W-2) Western Region Exclitcling Internal Drainage Area

The Western Region is roughly the size of the Eastern Region and is made of areas of very high precipitation to deserts. The stream Ilow pattern generally conforms to the pattern of the Tola1 Study Area and the Central and the Eastern Region. The precipitation pattern is entirely different from the Eastern Region. The yearly ( P - E) pattern is very irregular. Because ni" the highly non-homogeneous nature of the Western Region climat- ically, the spatial mean values of observed convergencc, runoff, precipitation, etc. require very careful interpretation and these may not produce coherent mass balancc analyses. One of the arcas within thc Western Region which appears to be coiitiibtiting to the

516

H.vdrologic budget of North Americci

climatological non-homogeneity of the Western Region is the area of internal drainage labeled as W-1 and covering 2J 1 O00 sq miles (546 O00 sq kilometers). None of the runoff from this area flows to the sea but is ultimately stored as surface or subsurface storage in the region. The mean annual precipitation (2.25 cm) is the minimum of all the study area. The computed value of the evapotranspiration is greater than precipitation. This is partly due to tlie fact that for many months during the study period the value of convergence (P-E) exceeds the value of precipitation P. This indicates a negative value for E. In such cases, evapotranspiration has teen assumed to be zero as the physical process of negative evapotranspiration could not be comprehended. However, if we assume that the mean monthly values of evapotranspiration shown as positive by Vapor balance computations have the same pattern of error as those shown negative, the latter may not be assumed as zero. Results of ccmputaticns made ky keeping negative values of evapotranspiration intact yield mean annual evapotranspiration identically equal to mean annual precipitation. In this case there is no underground inflow and the water budget of the area is in perfect balance. It is very hard to say if the water vapor balance of this area (as computed by assumin g

computed negative values of E to be zeroj forms a logical pattern and whether some reliance could be placed on the estimated mean figures. If computed negative values of evapotranspiration are assumed as zero, the value of mean annual evapotranspiration for this area is 31.34 c m and mean annual precipitation is 22.57 cm. The fact of the mean annual evapotranspiration exceeding the mean annual precipitation, however, has teen suggested foi, desert areas around the globe, in general, by Starr and Peixoto, 1958 [19]. The question of how the water talance at and below the surface of the deserts maintains itself in order to permit this large annual loss, is still unanswered. A possible hypothesis is that suficient inflow of ground water OCCUJS into the region from the surrounding areas, but this explanation would require further careful study.

(C+E) The Combined Central and Eustern Region

The patterns of the mean monthly convergence, precipitation, runoff, evapotranspiration follow tlie same pattern of the individual Eastern and Central Regions. For areas of size (C+E), the errors on account of the regional averaging of various components appear to be evened out.

The Total Study Aren Ex-cíirriing the Internal Drainage Areci iir flle Westerii Region

The results of this study show a slight improvement over those for the total study area. The mean monthly runoff, evapotranspiration, and storage patterns during the year are the same for the total area.

5. EVAPOTRANSPIRATION AND GROUND STORAGE USING THO RNTH WAITE’ S ESTIMATE

Thornthwaite and Associates [21,22] have published the point values of monthly potential and actual evapotranspiration and also the soil water changes for stations all around the globe. Of stations for which these values have been computed for the U.S. and Southern Canada by Thornthwaite, 750 were selected in his study for computing regional values of “actual evapotranspiration” and “soil moisture”. Almost all the stations falling within the study area were selected. Table 4 shows typical values of E and S as worked out by water vapor balance and as

computed from Thornthwaite’s published values for the Eastern Region. The water vapor values are tlie 5-year monthly means.

51 7

G. P. Malliofru utid P. Hock

As illustrative examples, figiircs 7, 8, 9, and 10 show theplots of E, (meanvapor balance values) and E,,, (computed from Thornthwaite's pubiishcd data) for areas E-2, E-3, W and W-I. Similarly, figures Il, 12, 13, and 14 show the plots of S, and ,YTII. For all study areas exccpt the Cumberland and Teimessee basins in íhe Eastern region

(E-2) and the Western sub-regions ( W, W-í, and W-2) the trend of the maxima and minima of the evapotranspiration by the two methods are generally similar. The evapotranspira- tion reaches a maximum in the month of July and minimum in the winter months, For seven study regions in which the similarity between the E, and E,, is visible,

it is also evident that Thornthwaite's values are higher than the vapor balance values in summer and lower in winter. For the total study area, E,, (max) in July is about 40 percent high than E, (max), and E,, (min) is almost negligible but E, (min) is 1 to 2 cms in winter months. This typical difference can be traced to certain assumptions and procedures inherent in

the Thornthwaite method. For computation of the monthly value of evapotranspiration, the most important factor according to Thornthwaite is the mean monthly temperature.

16

(Wi) I*TIUILDUNCiC IRE>. rmix m i " mom (W) --~aC'm

ËTH: Thornthwaite

Ëv: vapor ùahnce

n I I i l I I

Fig. 10.

14 - 12

in

ik2-

M J d A S O N D J F M A M .I J A S O N D J F M A

Fig. 9.

Mean Monthly Evapotranspiration, E.

518

H.vclrologic hiiript of North Atmrieci

-2.1

.5.0

According to his method if the mean monthly temperature is - I "C or lower, no evapo- transpiration takes place during that month. In the areas under study, however, il is not hard to visualize regions where the mean monthly temperature falls below - I "C in January and February, but still have days during these months when the temperature rises high enough for the phenomena of evapotranspiration to take place. This may partly explain why Thornthwaite's values of evapotranspiration are lower in the winter. Similarly, the mean monthly summer temperatures may be artificially boosted by a few

extra warm days during July and August. Evapotranspiration computed on the basis of these mean temperatures may therefore be higher than what has occurred on the day-to- day basis during the month. For the four study areas for which the trends of maxima and minima between E,,

and E,., do not match, it is hard to label the Thornthwaite values as less correct. As far as E,, values are concerned, these are consistent for the eleven study regions. It is the E,, values which appear to have shown illogical patterns for these four study regions. As far as study region E-2 (58 O00 sq miles) is concerned, it may be too small an area for a water vapor balance treatment. The Western region ( W) and the region W-2 (Western Region excluding the area of internal drainage), do not show a sine-wave distribution of evapotranspiration during the year and seem to have an almost uniform rate of evapo- transpiration throughout. For the desert area, W-1, Eu values show the most dissimilarily. It indicates a high rate

of evapotranspiration during winter and almost negligible during the months of July and August. Somewhat similar indications are given by Starr andPeixoto (1958) [i91 when they remarked " ... it is tempting to draw the somewhat startling conclusion that the desert

- 8 . 1

- :<.I

Table 4. Study Region: Eastern Region-Mean Monthly Values of Evapotranspiration and Storage

Unit: cm

Month

~~

April

May

June

.Jul?.

Aupus1

Septemhei

Octoher

Novcmher

Deccrnher

Januar?.

Februar?

March

April

Annual

Vapur Balance

li2.0

_. 8 "

~ ~

0.00

-2.23

-3.35

4.1fi

-.i.n?!

4 . G 2

-:J. I !I

-2.11

-0.71

-0.2::

.7.78

-1 .H!i

-0.15

__ ET" __ ~

8.6

12.2

13.5

11.5

8.4

4.fi

I .3_

0.3

0.3

o. 1

1 .:I

3.9 ~~

G6.1

Thornthwsiie =qx- I: -2.Y - 3.9

-3.6

-2.7 -1fl.2

-10.3

519

areas are on a par with oceans as major sources of moisture for out hcniispheric regime of precipitation ”. Figures I l through 14 show the plots of the mean monthly storage based on the 5-

year atmospheric flux data (S,) and from Tliornthwaite’s published data (STI{). For 8 of the 11 study areas, the plots for S, and S,,, show similar tendencies for

maxima and minima. The surface and subsurface storage appears to be minimum in August/September and maximum in February/March. Thornthwaite’s values are consist- ently lower than the water vapor balance values in the low season and higher in the high storage season. The storage graphs as shown in these figures assume datum at the beginning of the

month of May. This is purely arbitrary. For study areas E-2 (Great Lakes), and W-1 (Area of internal drainage in the Western

Region), similarities between the two graphs are either only partial or none. The greater dissimilarity exists for area W-1 (fig. 14). Whereas the vapor balance shows a maximum storage in August-September-October period, the Thornthwaite values schow a minimum of storage during these months (the same trend as for other regions and areas). This could be explained as due to the fact that in the regional water vapor balance for W-1 , the runoff is zero and thus the entire P-E over this area ultimately ñnds its way to the surface and sub-surface. Therefore, a high storage volume is indicated by the vapor balance approach particularly because it is a regional balance. The Thornthwaite method is based on point values of AS which in turn is balanced on the basis of point values of runoff which may be positive. The S,,r values therefore, follow a more conventional pattern in this area.

U L 1- 1 -1-uLLl \I I I \ 5 1 1 ’. II I I

Fig. 1 1 Mean Monthly values of Surface and Subsurface Storage, S.

520

6. CONCLUSIONS

\ ~ \! sTii: Thornthuaite-l Í c t -

\ I \ I \ I

\ 1 I

\ I \ I \. ‘

- I - - I -

. J - - - -

I I I I I I I I I I I

From the water balance studies for a large part of the North American continent and ils subregions, using 5 years of atmospheric vapor flux data together with observed slream flow and precipitation, lhe following conclusions are advanced:

I. A systematic bias has been found in the surface and sub-surface storage as computed from the atmospheric vapor flux data For the period May 1958 to April 1963. This bias is present in both the larger and smaller study areas although it tends lo be magnified as the areas get smaller. The bias in storage appears to accrue from a systematic error

-12 M J .I A s o N D %r ~i

Fig. 13. Monthly Values of-.Water Balance Components- 5-Year Period-Total Study- Area.

pattern in the mean monthly values of flux divergence. A similar inference has been drawn by Rasmusson [16] from a study of flux divergence maps. He states ... “maps of the vertically integrated flux divergence for North America and the Central American Sea exhibit systematic diurnal variations, and also a systematic error pattern.” In this study, this error pattern is adjusted from coinputed values of the systematic bias in the surface and sub-surface storage by making Lhe assumption (physically realistic in the absence of contravening evidence) that the net change in the storage over the 5-year period is negligible.

52 1

C. P. Mtilliotrii urrd P. Bock

2.

3.

4.

5.

6.

7.

8.

9.

Using the existing network. of aerological stations in the North American continent, the atmospheric vapor flux balance approach yields logical results when the areas are large (greater than 550 000 sy km). For smaller areas the computed values of evapotranspiration and storage become less logical and require careful interpretation. Adjustments are required. Similar inferences have been drawn by Rasmusson [i61 and Brock [7]. However, J. L. Rasmussen [15] concludes that meaningful computations can be performed from atmospheric water balance for areas as small as 200 000 sq km over periods ranging from days to seasons. However, his computed balances are only for winter season. Palnién and Söderman [13] and Väisänen [23] have also obtained fairly good results for smaller areas of Baltic region and Finland from mean monthly atmospheric data.

The Western Region of the United States and Southern Canada, although 2. J 9 million sq km in area, has yielded very confusing results. This appears to be because of its highly non-homogeneous climatological characteristics. However, with the exclusion of the internally draining areas (546 000 sq km), the results became more defined and logical.

The internally-draining areas of the West show an interesting result: that in these desert areas, the mean annual evapotranspiration exceeds the mean annual precipi- tation. This indicates large sources of underground water. This conclusion is similar to that derived by Starr and Peixoto in 1958 [19] for the Sahara region. Further study is required.

Exclusion of the internally-draining areas of the West from the total study area has very little effect on the results of the water balance.

For the total study area (United States and Southern Canada), computed values of ( F E ) from the atmospheric flux data and the observed streamflow from the area gave an average storage (table 3) whose spring maximum and late summer minimum differ by about 6 cm. Against this, van Hylckama [24], using Thornthwaite’s technique computed a difference of around 19 cm.

From a comparison of the values of evapotranspiration (E) and surface and sub- surface (Sj computed froin atmospheric data with the regional averages computed by the Thornthwaite Method, it is seen that: (a) In general, the values of evapotranspiration computed by the two methods agree; (bj However, the values of evapotranspiration computed from the atmospheric flux

data give lower values in summer and higher values in winter than the Thornth- waite values; and

(c) The surface and sub-surface storage values computed from the flux data show a much smaller difference between the maximum and minimum values than those by the Thornthwaite method.

Statistical analyses results Malhotra [12] show that both the hydrological and the aerological data have similar stochastic properties.

The results of this study leave little doubt that the atmospheric flux data coupled with the standard surface hydrological observations can be applied to great advantage for large scale hydrological and water resources investigations. If good atmospheric data exist for a region, estimates of regional evapotranspiration and storage can be obtained which are very difficult, if not impossible, to obtain by any other method. However, these data must be used on a time and space scale which is compatible with the density of observation stations.

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Hyrlrologic budget oJ' Nor/h America

10. Not only is a larger network of aerological stations indicated but the existing data might yield improved results by the daily analyses on a number of pressure surfaces together with a careful consideration of topography. Further meteorological research is indicated in these areas.

11. Further hydrological research in understanding the physical phenomena which gene- rate the various components of the hydrological cycle will surely help in better inter- pretation of the results of studies like the present which attempt to link more than one branch of the all-pervasive Hydrological Cycle.

7. ACKNOWLEDGEMENTS

This paper summaries the dissertation [I21 of the senior author that was submitted in partial Fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Connecticut, 1969. The work was initiated at The Travelers Research Center, Hartford, Connecticut and continued at the University of Connecticut, Department of Civil Engineering and Institute of Water Resources. Constructive suggestions were given by Dr. Eugene M. Rasmusson, Professor E. Palmén, Professor C. J. Posey, Mr. Howard Frazier and Mr. James Welsh.

REFERENCES

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7. BENTON, G.S. and ESTOQUE, M. A. (1954): Water vapor transfer ovcr the North American continent, Joirrnal of Meteorology, Vol. 11.

3. BENTON, G. S. and DOMINITZ, J. (1 956): Measuring evapotranspiration from atmospheric data, Journal of !lie Hydruirlic Diuision, Arnerican Society of Ciuil Engineers. Airgirst.

4. BLEEKER, W. and ANDRE, M. J. (1951): O n the diurnal variation of precipitation, particularly over the Central USA, Qrrarterly Journal of the Royal Meteorological Society, Vol. 77.

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6. BRADBURY, D. L. (1957): Moisture analysis and water budget in three different typcs of storms, Journal of Meteorology, Vol. 1 i.

7. BROCK, BYRON, Eugene (1968): Daily divergence of water vapor transport. M.S. Thesis, Department of Meteorology, MIT, Cambridge, Massachusetts.

8. BRUCE, J.P. and RODGERS, G.K. (1962): Water balance of the Great Lakes System. Publica- tion No. 71, Grecrt Lakes Americnn Association for the Aduaiicerneni of Science.

9. FERRUZA, D. (1967): Analysis of synoptic scale water vapor transport, S.M. Thesis, MIT Department of Meteorology, Cambridge, Massachusetts.

10. HOGDE, M. W. and HARMANTAS, C. (1965): Compatibility of U. S. radiosondes, Monrh1.v Weather Review, Vol. 93.

11. HUTCHINIX, J.W. (1957): Water vapor flux and flux divergencc over southern England: summer 1954, Qirart. J. Roy. Meteor. Soc., Vol. 83.

12. MALHOTRA, G.P. (1969): Hydrologic cycle of North America formulated by the analysis of water vapor transport data. A dissertation submitted in partial fulfillment of the requirements for the Degree of Doctor or Philosophy, the Civil Engineering Department, the University of Connecticut, Storrs, Connecticut.

13. PALM~N, E. and SODERMAN, D. (1966): Computation of the evaporation over the Baltic Sea from the flux of water vapor in the atmosphere, Geophysico, Vol. 8, No. 4.

14. PALMEN, E. (1967): Evaluation of atmospheric moisture transport for hydrological purposes. World Me/eorological Orgaiiisatioit Reporl. International Hydrological Decade.

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N, J. L. (1968): AtmosphcriL water balance of Lhe npper Colorado basin, A f n m - p/zeric .Science Tecliriical Paper No. 1 - 1 , Colorado State University, Ft. Collins.

16. RASMUSSON, E. M. (1966): Atmospheric watcr vapor transport aiid the hydrology of North America, Mri.c..rrrc/rrr.sf/t,s Institirle of T ~ c / I ~ ~ J ~ Q J , Rcport No. A- I , Planctary C¡rculations Project.

17. STARR, V.P. and WHITE, R. M. (1955): Direct measurement or thc hemispheric poleward flux of watcr vapor, J. Mur. Res., Vol. 14.

18. STARR, V.P., PEIXOTO, J.P. and LivAfiAs, G. (1958): O n Lhe meridional flux of watcr vapor in the northern heinispherc, Geo]: P w n e Appl., Vol. 39.

19. STARK, V. P. and PEIXOTO, J.P. (1958): O n the global balance ofwater vapor and lhe hydrology of descrts, Tellus, Vol. 10.

20. THORNTHWAITE, C. W. and KENNETH HARE, F. 11965): The loss of water to thc air, Mefeor. Monogrcrp/m, Vol. 6, No. 28. American Meteorological Society, Boston.

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Water balance peculiarities of karst areas

O. L. Markova, State Hydrological Institute, Leningrad, USSR

SUMMARY: The paper dcals with peculiarities of water balance of regions with covered karst and gives some examples of quantitative estimate of karst cffect on river runoff.

PARTICULARITÉS DU BILAN D’EAU DES KÉGIONS KARSTIQUES KL SUM^ : On expose les particularités du bilan d’eau dans les régions karstiques; des exemples d’estimation quantitative de l’influence du Karst sur l’écoulement sont donnés.

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