COMPUTATION OF THE EVAPORATION OVER THE BALTIC SEA FROM THE FLUX OF WATER VAPOR IN THE ATMOSPHERE

Transcription

1 COMPUTATION OF THE EVAPORATION OVER THE BALTIC SEA FROM THE FLUX OF WATER VAPOR IN THE ATMOSPHERE E. PALMÉN Academy of Finland ABSTRACT The water budget of a fixed volume of the atmosphere is determined by the evaporation from the earth's surface, the precipitation and the flux of water vapor, liquid and solid water across the boundary of the volume. The amount of water in liquid and solid form is, on the average, relatively small in comparison with the amount of water vapor and cannot be determined from the regular observations. For practical purpose it is convenient to select a volume limited by vertical walls and extending from the earth's surface with the pressure po to an upper level where the moisture content is sufficiently small, pressure pu. If the horizontal area of the volume is denoted by A and the length of its periphery by L the difference between the mean evaporation Ë and precipitation "p over the area is determined by p a p o E - P = - dp + - / qvndp gj Tit gaj Here g is the gravity constant, 7/ the mean specific humidity at a given isobaric surface, p the pressure and qv n the mean horizontal flux of water vapor normal to the boundary L. If the mean intensity of precipitation, the change of q and the net outflux of water vapor are computed from observations the formula gives the mean evaporation at the synoptic time considered. The evaluation was performed over the Baltic region marked in the figure for the two daily synoptic times for every day with sufficiently good observations for the year October 1, 1961-September 30, Due to different sources of error the individual values of E for the synoptic times were not quite satisfactory, but averaged over extended periods, e.g. months or the whole year, the computed mean evaporation seems to be in very good agreement with previous computations made with well known empirical formulae. For the whole year the total evaporation over the area in the figure amounted to 510 mm or 510 kg/m 2. RÉSUMÉ Le bilan d'eau d'un volume fixé de l'atmosphère est déterminé par Pévaporation de la surface terrestre, les précipitations et le flux de vapeur d'eau, de l'eau liquide et solide au travers des limites du volume. Le montant d'eau sous forme liquide et solide est, en moyenne, relativement faible en comparaison avec le montantdevapeur d'eau et ne peut être déterminé par les observations régulières. Pour des buts pratiques, il est préférable de choisir un volume limité par des parois verticales et s'étendant de la surface terrestre avec une pression po jusqu'à un niveau supérieur, où l'humidité est suffisamment réduite, de pression pu- Si la surface horizontale du volume estappelée À et la longueur du périmètre L, la différence entre l'évaporation moyenne E et la précipitation ~p (moyenne), sur la surface est donnée par : p a _ - 1 r Ôq L (' ^ E-P=t- J-dP + ^ l 1 V^IP H où g est l'accélération terrestre, q est l'humidité spécifique moyenne pour une surface isobarique donnée, p est la pression et qv n est le flux moyen horizontal de vapeur d'eau, normal à la surface L. 244 p a

2 Si l'intensité moyenne des précipitations, la variation de q et le flux net de vapeur d'eau sont déduits des observations, la formule donne l'évaporation moyenne, au temps considéré. L'évaluation a été faite sur la région baltique marquée sur la figure pour deux instants par jour, avec des observations suffisamment bonnes du 1er octobre 1961 au 30 septembre A cause des différentes sources d'erreurs les valeurs individuelles de E pour des instants déterminés n'étaient guère satisfaisantes, mais leurs moyennes sur certaines périodes (par exemple des mois ou l'année) correspondaient très bien avec des évaluations précédentes faites avec des formules empiriques connues. Pour l'année totale, l'évaporation totale sur l'aire de la figure était de 510 mm ou 510 kg/m INTRODUCTION The water budget of a fixed volume of the atmosphere is determined by the évapotranspiration from the earth's surface, the precipitation and the flux of water vapor, liquid and solid water across the atmospheric boundary of the volume. The flux of liquid and solid water cannot be computed from regular meteorological observations, but is generally quite small compared with the flux of water vapor. It has therefore been neglected in the computations presented here. For a fixed synoptic time the difference between the mean evapo-transpiration, E, and the mean precipitation, p, over the earth's surface of the selected volume is equal to the net outflux of water vapor across the boundary of the volume plus the change per unit time of the total content of water vapor in the volume. For practical use of this principle it is convenient to select the volume so that it is limited by vertical walls extending from the earth's surface, pressure po, to a level with sufficiently small moisture content, pressure PH- If the horizontal area of the volume is denoted by A and the length of its periphery by L the difference E P is determined by E-P=~ I dp + / qvndp (1) s J- ^ A sl % P H Here g is the acceleration of gravity, q denotes the mean specific humidity at a fixed isobaric level, p the pressure and qv n the mean horizontal water vapor flux normal to the vertical boundary along the periphery L. In Eq. (1) the first right-hand term represents the mean change of "precipitable water" per unit time above the area A and the second term the net mean horizontal outflux of water vapor from the volume. Formula (1) is very convenient in hydrology, especially if it is used for extended areas and over periods of time not too short. It permits a direct determination of the runoff and storage of water in the soil per unit time from aerological measurements since A(p ~-~E) = Runoff + Storage. (2) This new method has already been successfully applied on hydrological problems by many scientists. Because the formula determines the instantaneous difference between evapo-transpiration and precipitation and neglects the storage of liquid and solid water in clouds, it should not be applied on very short periods of time, especially because the first right-hand term in Eq. (1) cannot be estimated for shorter periods than 6-12 hours from regular aerological data. However, if used properly, the method is in principle superior to other methods if the areas considered are sufficiently large to reduce the errors due to short-period fluctuations in winds and moisture content. ft is very difficult to get satisfactory measurements of the mean évapotranspiration from large regions, and, especially in regions with strong orographic effects 245

3 on precipitation, also the mean precipitation often cannot be determined with satisfactory accuracy. In such cases it should be recommended to compute the mean évapotranspiration for selected periods with no precipitation, or to compute the mean precipitation for selected synoptic cases with intense rain and very weak evaporation. Formula (1) can also, using Gauss's theorem, be transformed into -/> = - 1>n "H "H v U.qVdp where now the last term represents the integrated mean divergence of the water vapor flux. The above equation can be transformed into P, -^0 0,» 0 E-F = - -4-dp + - qu-vdp + - / y.yqdp. v sj v àt g J g J P H P H This formula shows that the second right-hand term containing the horizontal wind divergence often is of great importance due to the correlation between V V and q in the vertical. By using geostrophic winds instead of real winds this term cannot be considered, and consequently the geostrophic assumption could result in large errors. P H 2. AREA OF COMPUTATION Eq. (1) was applied on the southern part of the Baltic area, essentially on the Baltic Sea proper. The total area is 30.3 x 10 4 km 2 large and limited by the boundary marked in figure 1. The area forms a polygon between the six aerological stations Jokioinen, Stockholm, Copenhagen, Greifswald, Kaliningrad and Riga marked in the figure. Unfortunately the stations are not exactly on the shore of the Baltic Sea. Of the total area limited by the polygon about 23 per cent was land and 77 per cent sea. Since we are in this case interested in the evaporation from the sea, the computed values have to be reduced in order to eliminate, as well as possible, the influences of the land areas. I shall return to this question later on. The computation of both right-hand terms in Eq. (1) was performed twice a day for the period October I, 1961-September 30, The flux of water vapor was evaluated for earth's surface, 1000, 850, 700, 500 and 400 mb. The normal flux across the bounding line between two stations was considered equal to the arithmetic mean of qv n between every pair of stations. The corresponding change of water vapor content, the first right-hand term in Eq. (1), was computed from the change of the mean specific humidity of the standard surfaces at the six stations from one synoptic time to the following time. This method is naturally quite crude, but since we are essentially interested in the mean evaporation for periods of e.g. one month, the influence of this term is of minor importance. The integration was extended up to 400 mb; above that level the ^-values became generally so small that the flux of water vapor in the upper part of the atmosphere could be neglected. All computations of the flux term and the total water vapor content were performed by a high-speed electronic computer. In this way the difference p was computed for every synoptic time during the whole year. A similar computation was made assuming geostrophic winds instead of real winds. However, some of the synoptic times had to be excluded because of lack of observations from one or several of the stations. Generally between 10 and 20 per cent of the regular synoptic times were thus excluded in the different months, 246

4 Fig. 1 Area of the Baltic region used for computation of the mean evaporation. The area, km 2 large, is limited by the straight lines between the six aerological stations used for the computation. The stations are : Jokioinen in Finland, Stockholm in Sweden, Copenhagen in Denmark, Greifswald in Germany and Kaliningrad, Riga in USSR. and we must hope that no systematic errors were introduced through this exclusion. To determine the evaporation the mean precipitation over the whole area for the selected synoptic times had to be estimated. Fortunately, there are many islands with satisfactory rain gauges in the Baltic area. By using the data from these islands and from a considerable number of coastal stations it was possible to get a good estimate of the mean precipitation intensity at the synoptic times from the measured precipitation during the whole period from 6 hours before to 6 hours after the corresponding synoptic time. 3. RESULTS OF THE COMPUTATIONS The computed mean evaporation from the Baltic Sea for the synoptic times 00 h and 12 h GMT are not, as already was pointed out, quite satisfactory because oj different errors in the computed values of the terms in Eq. (1). However, in the mean monthly values most of the random errors are obviously eliminated. From the mean values the influence of the evapo-transpiration over the land areas could be eliminated 247

5 by using approximate values for this part of the whole area A. Over land the annual variation of the evapo-transpiration deviates very strongly from the annual variation of evaporation from the sea. Already Witting (1918) showed that the evaporation from the Baltic Sea reached its highest values in late autumn and its lowest values in late spring and early summer. Over land, on the other hand, the highest evapo-transpiration occurs in late spring and early summer, whereas in winter the mean evapotranspiration is very small. In Table 1 the computed values of the mean monthly evaporation according to Eq. (1) are presented and in addition the corrected values, assuming the land area to be 23 per cent of the total area A in figure 1. The monthly values in this table are smoothed according to formula El = l/4( o+ 2 i + 2) (5) TABLE 1 Mean monthly evaporation from the total area A in figure 1, E, and corrected mean evaporation, E$. Land area 23 per cent of A. Month Emm s mm Correction January February March April May June July August September October November December Year According to the corrected values the total evaporation from the Baltic Sea, if the land areas in figure 1 are considered, amounted to 510 mm during the investigated period October 1, 1961-September 30, The computed and corrected values are graphically presented in figure 2. Both values show a strong seasonal variation with very high evaporation during November-January and low evaporation during April-June. Since the computations were made for only one singular year, the mean monthly evaporation values are not quite representative as mean values for longer time periods. The year considered here was in many respect unusual. For instance, October was characterized by very high air temperature over the Baltic area, and hence the evaporation could be expected to be smaller than usual during this time of the year. As a consequence of the mild autumn the Baltic Sea had an unusually high surface temperature in December. During this month, however, several strong outbreaks of cold air occurred, and hence the situation was very favourable for strong evaporation. 248

6 Fig. 2 Monthly mean values of the evaporation from the total area A in figure 1, E, and mean values of the evaporation from the sea areas, E s. All values are given in mm/month. The total evaporation from the sea areas during the period October 1, 1961-September 30, 1962 amounted to 510 mm, and the corresponding total precipitation to 470 mm. 249

7 4. COMPARISON WITH PREVIOUS ESTIMATES OF EVAPORATION To get an idea of the reliability of the evaporation computed with aid of Eq. (1) the above results should be compared with estimates of the evaporation from the Baltic Sea performed in other ways. Most other computations of evaporation from seas have been made by using empirical formulae of the type (Jacobs, 1942) : E = kva(e s - e a ). Here k is an empirical constant, V a is the wind velocity at "anemometer level", e s the water vapor pressure at the sea surface (determined by the water temperature) and e a the corresponding vapor pressure in air. For the lighthouse Bogskâr in the northern Baltic Sea Simojoki (1948) computed the mean monthly evaporation for a period of 13 years by aid of Eq. (6). Similar computations were made by Brogmus (1952) for the central region of the Baltic Sea (Gotland Sea) using approximately the same value o f k. For comparison their results and the values from table 1 are presented in table 2. TABLE 2 Comparison of mean evaporation from the Baltic Sea determined by Simojoki, Brogmus and Palmén Month Simojoki Emm Brogmus mm Palmén Es mm V 2 (SB) - P mm January February March April May June July August September October November December Year The last column in table 2 gives the difference between the combined values according to Simojoki and Brogmus and my own values. The largest absolute differences are those for October and December. The cause of this difference was already discussed before; it can obviously be explained by the special weather conditions in October and December The total annual evaporation values according to table 2 are in almost complete agreement. This is surprising when considering the completely different methods used by Simojoki and Brogmus on one side and by myself on the other side. During the period October 1, 1961-September 30,1962 the total precipitation amounted to 470 mm 250

8 (Fig. 2), which is the value computed by Brogmus (1952) for the central part of the Baltic. The agreement indicates that the precipitation values in Eq. (1) are approximately correct. The agreement gives strong support to the usefulness of Eq. (1) for computation of the evaporation from the flux of water vapor in the atmosphere. On the other hand, the agreement between the mean values of table 2 also indicates that both methods, at present time, give about equally good estimates of the mean evaporation, at least during extended periods of time. However, it should be stressed that the aerological method, applied in the present investigation on the Baltic Sea, equally well can be applied on land areas, whereas Jacob's empirical formula, or other similar formulae, are applicable only for computation over water. Over land areas obviously the aerological method is superior to all other methods if sufficiently reliable aerological data are available. The mean evaporation from the Baltic area was also, as already mentioned, computed for the same year by using geostrophic winds instead of real winds. The geostrophic method gave a much larger mean evaporation, or 712 mm instead of 510 mm. There can be no question of that 712 mm is a much too large value. In discussing Eq. (4) 1 already pointed out that this shortcoming of the geostrophic method essentially depends on the impossibility to consider the divergence term in Eq. (4) when using geostrophic winds. Some systematic errors in the computed evaporation could result from the impossibility to consider the net flux of liquid and solid water in clouds. Especially in cases of strong outbreaks of cold air this additional flux could result in an underestimate of the evaporation, but no attempt was made to estimate the possible effect of this. 5. EXAMPLES OF VERY STRONG EVAPORATION As Eq. (6) shows, very strong evaporation is to be expected in weather situations with strong outbreaks of cold air in winter, when the surface water of the Baltic Sea still is relatively warm. Such a situation occurred during the period December 18, 12 h- December 22,00 h GMT. The computed values of E during this period are presented in table 3. TABLE 3 Evaporation during a period of a strong outbreak of cold air over the Baltic. Time Dec h Dec h 12 h Dec h 12 h Dec h 12 h Dec h 12 h Mean E mm/12 h (mm/12h) The mean evaporation over the whole area A in figure 1 was during this period of 4 days 4.8 mm/12 h, corresponding to about 12 mm/day if corrected for the land area. This mean evaporation corresponds to a flux of latent heat of 0.5 cal per cm 2 and minute. It shows the strong influence of the Baltic sea as a heat source for the surrounding coastal regions, especially when considering that the simultaneous transfer of sensible heat amounted to about the same value. 251

9 REFERENCES (!) BROGMUS, W., 1952: Eine Revision des Wasserhaushaltes der Ostsee. Kieler Meeresforschungen, Band IX, 1. ( 2 ) JACOBS, W. C., 1942: On the energy exchange between sea and atmosphere. Journal of "Marine Research, Vol. V, No. 1, pp ( 3 ) SIMOJOKI, H., 1948 : On the evaporation from the Northern Baltic. Geophysica, No. 3, pp ( 4 ) WITTING, R., 191 s : Hafsytan, geoidytan och landhôjningen utmed Baltiska Habvet och vid Nordsjôn. Fennia 39, No