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A simple aridity equation for agricultural purposes in marginal zones
Journalof Arid Environments (1990) 19,353-362
A simple aridity equation for agricultural purposes in marginal zones Enrique Troyo-Dieguez", Francisco de Lachica-Bonilla* & Jose L. Fernandez-Zayas'] Accepted 30 November 1989 Analysis of the widelyused drynessindex proposed by Budyko revealsits limited usefulness in evaluating aridity of regions with very low precipitation coupled with high evaporation rates. Such is the case of a region in BajaCaliforniaSur, Mexico, where a better aridity index is needed to describe weather during months of limited, or null, rainfall. An improved aridity index is proposed, retaining the physicalmeaning of null precipitation, a typical condition of many deserts. This is attained by preserving the inverse relationship of aridity and precipitation. A regionalization of La Paz, Baja California Sur, illustrates the quality of the proposed index. Subranges of aridity can be defined with a better fitting accordingto desertic needs.
Introduction Agriculture is a technological activity through which matter is transformed from several sources, employing various forms of energy (solar, chemical and mechanical). Its main purpose is to produce biomass of economical importance. This activity is guided by different types of information, such as the genetic code of each kind of plant, cultural practices, soil properties and the climatological character of each region. This definition implies that agriculture depends on biotic and abiotic factors that explain the processes involved, either in an isolated or a connected way. The more relevant abiotic factors are solar radiation, water in the form of rain, or through irrigation, and soil, the substrate and nutrients reservoir for biotic factors. These factors are usually studied separately, although they interact with each other in several ways.
Relationship between climate and agriculture The elements of climate that have the most important effects on agriculture are solar radiation, and rain in rain-fed agriculture. Both contribute to the formation and development of soils in continental regions as well as in microregions, through a number of processes that operate even in microscale dimensions. Of these processes, climate is of primary importance. While the parent rock, plants and edaphon contribute the materials from which soils are made, climate determines the process of soil development (Cargo & Mallory, 1977). There is a causal relationship between the world-wide distribution of • Centro de Investigaciones Bio16gicas de Baja California Sur, Apartado Postal 128. La Paz, Baja California Sur,Mexico, C.P. 23000. t Instituto deIngenieria, Universidad Naciona1 Aut6noma deMexico (UNAM), Cd. Universitaria. Coyoacan, Mexico, D. F., C.P.04510. 0140-1963/90/060353 +
10 $03'00/0
© 1990 Acadetnic Press Litnited
E. TROYO-DIEGUEZ ET AL.
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edaphic orders and climatic regions. In the study of pedogenetic processes, a basic hypothesis is set up by the statement that atmosphere is a primary pedogenetic element (Steila, 1987). For agricultural purposes, soil fertility is not an isolated nor static factor modified by the nutrient-extracting crops, but is a condition which depends, among other factors, on the local weather. Soil humidity varies in different quantities: a minimum value known as the permanent wilting point (PWP), and a maximum known as field capacity (FC). The magnitude of these parameters, PWP and FC, is different for each type of soil. The availability of this water for plants is a function of evapotranspiration which is modified by solar radiation, rain, soil type and the physiological mechanisms of each plant. According to Prescott (1958), two major soil zones exist: (1) humid zones where the mean rainfall in every month is adequate to meet potential evapotranspiration and (2) desert regions where mean monthly rainfall never exceeds that required to keep the soil moisture above the wilting point of plants (PWP). From an understanding of the soil-atmosphere relationship, it can be argued that in rain-fed agriculture the availability of water in the edaphic environment and consequently the crop success depend largely on weather; this is because under dry conditions the water deficit reaches a level which decreases the plant growth processes and the root system becomes unable to extract water at a sufficient rate to sustain the transpirational demand (Jones & Zur, 1984). Consequently, this kind of agriculture requires that soil quality (physical and chemical) analysis in a site must be completed within adequate climatological parameters (Revelle, 1981). From the hydrological viewpoint, the use of the equation proposed by Landsberg (1984), cited by Barradas & Fanjul (1985), establishes an adequate reference of the water balance. This equation is given by:
a
OCt
+ dt) = [OCt) + Pp - E - Dr - Ro]/Z
(1)
where is the volumetric content of water in soil (given up during the range of) time t + dt, and Pp, E, Dr, Ro and Z are the total precipitation, evapotranspiration, deep percolation, runoff and root depth, respectively. Although deep percolation and runoff are relevant processes of the water balance in an ecosystem, they are relatively insignificant in the agricultural arid plains of Baja California Sur. Desert climatology is of considerable importance in the agricultural development of the arid lands of Baja California. However, adequate descriptions of aridity for conditions in Baja California have not been forthcoming. Drought has been defined in many ways, including precipitation deficit, periods of wide extend or great severity, occurring on a variety of spatial scales. These events are the result oflarge-scale subsidence which inhibits precipitation-producing mechanisms (Landsberg, 1984, cited by Robinson & Fesperman, 1987). If such climate fluctuations could be predicted well in advance, agriculturalists and planners might be able to take action to minimize the deleterious consequences (Nicholls, 1985). Intensive case studies of individual droughts are a prerequisite to an understanding of their initiation, maintenance, and demise (Namias, 1978). A variety of aridity indexes have been formulated; formerly, the term 'Aridity Index' refers to the 1948 work of Thornthwaite (Stadler, 1987). It might be appropriate to mention that desertic climate is most often defined in terms of low precipitation and humidity. It follows that an adequate representation of dryness, or aridity, must clearly reflect water scarcity. Arid zones in Mexico are extensive, covering more than 60% of the country. Agricultural activities in these lands have a limited availability of water. The aridity, understood as a condition of water deficiency, has to be evaluated so as to plan adequately for agriculture in these zones and objectively to ration the use of hydrological resources. According to Mcsific-Aleman (1966), the genesis of north-western Mexican arid zones,
A SIMPLE ARIDITY EQUATION
355
with emphasis on the Baja California peninsula, depends on the occurrence of cold oceanic currents from California: dynamics at the ocean-atmosphere interface cause an absence of condensation and a lack of rain, a typical condition of this arid zone. Recent studies indicate that this phenomenon is modified by El Nino-Southern Oscillation (ENSO) events, which show a positive correlation with the seasonal variations of precipitation (Reyes-Coca & Rojo-Salazar, 1985). Thus, an ENSO event may have the potential for long-range prediction (Nicholls, 1986). Statistical information pertaining to the historical occurrence of ENSO events is a useful basis for speculative long-range forecasts a year, and more, in advance (Quinn et al., 1978). The merits of an adequate aridity index are highlighted in this work by the evaluation of the aridity of La Paz basin, B.C.S., Mexico. The index is derived from a simple equation that seeks to express the relationship between rainfall and evaporation. Study area and methods The climatological data used in this study, including temperature, precipitation and evaporation values for La Paz, were obtained from Divis6n Hidrometrica de Baja California Sur, Mexico, of the Secretaria de Agricultura y Recursos Hidraulicos. The La Paz weather station is located at 24° 09'N and 110° 20'W, and is the main source of climatological information for the farmers and rangers in the La Paz area. Two sets of precipitation data, from 1906 to 1911 and 1917 to 1986, (Salinas & Leyva, 1988), and a set of temperature data, from 1921 to 1986 were considered (Salinas & Leyva, 1989). No precipitation data were found in the available records for the period from 1912 to 1916. According to historical records, maximum precipitation in any month was 381'6 mm in September 1943, and the maximum precipitation on any day was 137·0 mm on 30 September 1976. Monthly values of temperature, precipitation, evaporation and aridity are shown in Table 1. Global characterization of aridity was based on monthly mean values. The calculation of the aridity, D, was done first by solving the equation -proposed by Budyko (1974) according to the methodology developed by Joseph & Ganor (1986). The values of total solar radiation were obtained from Galindo & Chavez (1977) and Fernandez-Zayas (1987). This information was combined with other data (Hastings, 1964; Hastings & Humphrey, 1969) and then analysed by means of the Statgraphics computer program. A modified aridity index A, is calculated by means of a water balance using the ratio precipitation/evaporation as the main water deficit estimator. For the case at hand, mean daily evaporation is 5'87 mm/day, or approximately 176 mm/month (Table 1). For agricultural purposes, a balanced condition (null aridity) was considered when precipitation equalled evaporation; in this case, index A = 0, the minimum value of aridity. A maximum value of aridity implies that precipitation is zero for any study period. An aridity scale was selected in order to obtain a suitable set of ranges for agricultural purposes; however, different aridity scales can be adopted to suit specific requirements of any activity, as in the case of marine aquaculture, where a scale of the balance precipitation/evaporation with higher resolution is needed to avoid increases in salinity.
Aridity models The first approach to a study ofweather in a locality is generally based on an interpretation of maps and symbols used in common climatological classification systems. The Koppen system, modified by Garcia (1964), is widely used in Mexico. According to this classification system, the climate of La Paz, Mexico, can be represented by the code BW(h')hw(e), which is interpreted as very dry weather with a principal rainy season in
43·5
Mean Max
Total
2·0
2·0 2·5 3·0 4·5 8·5 10·0 13·0 13·0 12·0 12·0 6·5 2·0
32·5 35·0 36·0 39·0 39·5 42'5 43·0 43·0 43·0 43·5 37·5 36·0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Min
Minimum
Maximum
Month
Temperature CCC)
23'6 29·5 17·5
17·5 18·0 19·7 22·0 24·3 26·5 29·2 29·5 29·0 26·1 22·2 18·9
Mean
15·05 59·90 0·70 180·60
12·5 42·6 59·9 13·7 9·2 20·4
1-8
12·1 5'0 2·0 0'7 0·7
Precipitation 290·6 337·5 393·8 431·3 450·0 468'8 450·0 431-3 393·8 346·9 300·0 262·5 379·7 468·8 262·5 4556·5
176·1 192·3 155·9 2113'3
Net radiation (Rn) cal/cmvday
Radiation
169·2 155·9 184·8 172·8 173·2 170'2 182·9 192·3 182·8 182·8 172·9 173.5
Evaporation
Hydrological data (mm)
0·277 1·107 0·011 0·004
0·041 0·115 0·337 1·058 H07 0·449 0·062 0'018 0·011 0·044 0'056 0·022
D
Aridity A
3·66 3·98 2·69 3·66
3·71 3·87 3·96 3·98 3·98 3·96 3·73 3·11 2·69 3·70 3·79 3·53
Table 1. Thermo-pluoiometric and radiational data ofLa Paz weather station for theperiods 1906-1911 and 1917-1986, and estimated aridity
UJ
VI
t-
).
'-l
ttl
tTl N
o c
m-
-6
0 0< 0
..,:;:gtrl
0-.
A SIMPLE ARIDITY EQUATION
357
summer and a secondary one in winter; precipitation in general is very scarce all year long; winter precipitation is less than the summer one; warm climate, with annual thermal oscillation from 7 to 14°C (Garcia & Mosino, 1968). It is necessary to remember, however, that this information is very generalized and inadequate for planning agricultural practices. There is a 5-year fluctuation of drought or extreme aridity in the climatological record of La Paz weather station, a fluctuation not evident in common classification systems of weather. In this work, for the estimation of Budyko's aridity index, net radiation was calculated through the equation Rn = (l - a)(Rt)
(2)
where Rn is the net radiation, Rt the total solar radiation, and a is the albedo value, in this case 0'25 (Sellers, 1965). Estimated net radiation values were applied for the computation of the aridity index (Galindo & Chavez, 1977). It was noted that a maximum value of net radiation occurs in June (468'75 cal/cmvday) and a minimum in December (262'5). According to these theoretical data, annual mean Rn in La Paz, B.C.S., is 379'69 cal/cmvday, among the highest in Mexico. A widely used aridity index proposed by Budyko in 1951 (Stadler, 1987), expressed as a radiational index of dryness, is the following: D
= Rn/(LP)
(3)
where D is the radiational index of dryness, Rn the mean net radiation received in callcm2/ day, L the latent heat of vaporization, and P the amount of precipitation in mm. A common limitation of aridity indexes is that they ignore the capacity of the soil to accumulate water. It is generally accepted that this shortcoming cannot be easily eliminated. . Considering L in this equation as a function of temperature and selecting a fixed value of albedo, suitable for annual crops or short vegetation under arid conditions, equation (3) can be re-written as: D
= Rn/(b
- eT) (P)
(4)
where b is the total heat ofvaporization in callg (b = 595,5), cis an empirical factor varying with temperature in °C (c = 0'609), and P is the amount of precipitation in mm that occurred in the study period. Applying the last equation for an annual period in the study area and considering Rn = 379'69, T = 23'6 and P = 180'6, the equation renders D = 0'0036 as a result of the influence of the higher values of P, in this case that of August and September. As shown, D is strongly sensitive to rain values and is extremely low, and cannot demonstrate an adequate representation of the aridity fluctuation in this dry, arid zone. Annual variation of D (Budyko's index of dryness) as well as precipitation pattern is presented in Fig. 1 (precipitation values were divided by 100 to obtain a suitable scale). Minimum and maximum values of the dryness index correspond to September and May, the inverse of the precipitation values. The dryness index pattern presents a growing tendency towards April and is the inverse to that of precipitation. It should be noted that if P = 0, D is numerically undefined (in La Paz, Mexico, the periods from February to June and from October to December are dry seasons with null precipitation; nevertheless, they are important agricultural seasons). This condition renders Budyko's model useless in arid zones, where null rainless periods are common. In fact, this model can only be applied for analysis of mean annual values of historical series; month by month analysis may not be done, because of the possible occurrence of months with zero precipitation. Minimum and maximum mean monthly values of precipitation were 0'7 and 59·9 mm
E. TROYO-DIEGUEZ ET AL.
358
r-----------------------,
1·2
Dryness pattern
1·1
"
-g'" ~
o
0·9 0·8
~
0·7
o-,
0·6
'"
0·5
c '"
0
~»
-c
~
CO
Pre cip i tatian pattern
0·4 0·3 0'2
0'\ 0'
JAN
t-+===+-+
FEB
MAR
APR
MAY
JUN
JUL AUG
SEP OCT
NOV
DEC
Time
Figure 1. Annualvariation of Budyko'sDryness Indexand precipitation pattern of La Paz, B.C.S., Mexico.
for May and September, respectively; for most months precipitation is very low, near zero, accordingly to the historical series (Salinas & Leyva, 1988). Annual isohyetes of La Paz and adjacent stations show the area likely to have a global precipitation deficit (Fig. 2). Annual value of D in equation (4) is low (D = 0'0036), much lower than the same index for September (D = 0'011), the month with most rain (60 mm). In consequence, there could be a wrong interpretation. This characteristic arises because the value of annual precipitation represents the sum of individual values of all months. Consequently, the resulting estimated aridity value, D, on the basis of annual analysis is actually an extrapolation of added values, not really an average index; in this case D underestimates the aridity in the study region. In order to evaluate diverse arid zones for agricultural purposes in Baja California Sur, Mexico, the following equation is proposed in this work: IIOOW Gulf of California
24°
24°
Pacific Ocean 25 km
Figure 2. Annual isohyetes for the southern part of BajaCalifornia Sur, Mexico.
359
A SIMPLE ARIDITY EQUATION 5,---------------.====r-------, Proposed index (A) 4
Annual A
Budyka's index (D)
+-+ +.-+/
<;
AnnualD
JAN
I
I
FEB
MAR
I APR
I MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Time
Figure 3. Annual variation of the proposed index around its annual value as compared with the Budyko's dryness index.
A = N(1 - F)
(5)
where A is the proposed aridity index; F is the ratio of precipitation/evaporation for a period of time, F = PIE; andN is the number of categories to be established according to local agroclimatological conditions. N is the maximum value of aridity previously fixed. In this equation, if P = 0, then A = N. If P > E, then A renders a negative value which is to be interpreted as a condition of null aridity. Considering N = 4 and mean monthly evaporation as a constant parameter (176 mm), according to the available data for La paz (Table I), the last equation can be simplified to: A = 4 - (0'02273)(P)
(6)
where A is the aridity index proposed for La Paz region (monthly) and P is the mean monthly precipitation in mm. In order to obtain a positive value of the aridity index, the condition 0 :s;:; P < 176 must be satisfied. According to this equation, if P - 176 mm! month, then A = 0; as the precipitation balances the mean monthly evaporation (PIE = 1), the resulting number describes a non-arid condition.
Other results The fluctuation of A around its annual mean as compared with the fluctuation of D is presented in Fig. 3. It is clearly depicted in the figure how the proposed index yields high values at the time of high dryness, and decreases as the rainy season arrives. Notice in the figure how Budyko's index trend diverges from the observed rainfall pattern; the annual value of dryness, D, does not really indicate an arid condition because of its low value. Six suggested subranges of aridity for La Paz region according to equation (6) are shown in Table 2. The geographic pattern of aridity in the study region according to equation (6) is presented in Fig. 4 for the subhumid period (August-September); for the rest of the year (October-July), the equation renders a condition of extreme aridity (EA) for most of the region.
E. TROYO-DIEGUEZ ET AL.
360
Table 2. Proposed subranges ofaridity according to equation (5) Aridity index (A)
Precipitation (P, in mm/month)
Classification
3·5 to 4·0 3·0 to 3·5 2·0 to 3·0 1·0 to 2·0 0·0 to 1·0 negative values
o to 22 22 to 44 44 to 88 88 to 132 132 to 175 p> 175
EA: Extreme aridity (desert) A: Arid SA: Semi-arid DS: Dry-subhumid MS: Moist-subhumid H: Humid (aridless)
Conclusion The equation of aridity developed here can readily identify regional differences of aridity and is applicable to any arid zone. It can be complementary to common climatological classification systems or other similar measures. The proposed equation is robust at low values of precipitation; the resulting aridity index is strongly correlated with precipitation deficit. The maximum and minimum values of A for La Paz region are 3·98 for May, the month with the lowest precipitation, and 2·69 for September, the month with the highest precipitation (Fig. 3); these values appear to be strongly correlated with the latent and active periods of vegetation respectively. Monthly fluctuations of A and D for the area under study are shown in Fig. 3. It can clearly be noticed how the proposed index A yields high values at the time of high dryness, a high risk agricultural season, and lower values when the rainy season arrives; for the study region, the proposed index A is robust (resistant) at low values of precipitation. The equation presented in this work can readily identify regional differences of aridity and become an analytical tool for agricultural planners in arid zones (see Fig. 4). More studies need to be conducted for a better explanation of aridity fluctuation under normal and abnormal conditions, and to account for the potential for soil accumulation of water.
GULF OF CALIFORNIA
PACIFIC OCEAN
25
Figure 4. Agroclimatological provinces of Southern Baja California Sur according to the aridity condition (sub-humid period).
A SIMPLE ARIDITY EQUATION
361
This work was financed by Consejo Nacional de Ciencia yTecnologia (CONACyT) and Secretarfa de Programaci6n y Presupuesto (SPP) of Mexico. Thanks are due to BioI. Cesar Salinas-Zavala for providing valuable temperature and precipitation data as well as for a critical review of some aspects of the paper. We would also like to thank Dr Claude Grenot, from Ecole Normale Superieure, Paris, for critical reading of the manuscript and helpful suggestions.
References Barradas, V. L. & Fanjul, L. (1985). Equilibrio hidrico y evapotranspiraci6n en una selva baja caducifolia de la Costa de jalisco, Mexico. Biotica(Mexico), 10: 199-210. Budyko, M. I. (1974). Climate and Life. New York and London: Academic Press. International Geophysics Series, 18: 525 pp. Cargo, D. N. & Mallory, B. F. (1977). Man and His Geologic Environment. Menlo Park, California: Addison-Wesley. 581 pp. Chang, jen-hu. (1987). Agroclimatology. In: Oliver, J. E. & Fairbridge, R. W. (Eds) , The Encyclopedia of C limatology, pp. 16-22. Encyclopedia of Earth Sciences, Vol. XI. New York: Van Nostrand Reinhold. 986 pp. Fernandez-Zayas, J. L. (1978). Introducci6n al estudio de los sistemas solares activos. Series del Instituto de Ingenieria, No. D-26. UNAM, Mexico. 109 pp. Galindo, I. G. & Chavez, A. (1977). EstudiodelClimaSolaren la Republica Mexicana. I.-Radiaci6n Solar Total. Instituto de Geofisica, UNAM, Mexico. 17 charts. Garcia, E. (1964). Modificaciones al Sistemade Clasificacion Climdtica de Koppen. (Para Adaptarloa lasCondiciones dela RepublicaMexicana). Institute de Geografia, UNAM, Mexico, D.F. 246 pp. Garcia, E. & Mosifio, P. A. (1968). Los dimas de la Baja California. In: Del Arenal C., R. (Ed.), Memoria 1966-1967 del Comite Mexicano para el Decenio Hidrologico Intemacional. pp. 29-56. Instituto de Geofisica, UNAM, Mexico. Hastings, J. R. (Ed). (1964). Climatological data for Baja California. Technical Report on the Meteorology and Climatology of Arid Regions, 14: 1-141. Institute of Atmospheric Physics, University of Arizona. Hastings, J. R. & Humphrey, R. R. (1969). Climatological data and statistics for Baja California. Technical Report on the Meteorology and Climatology of Arid Regions, 18: 1-96. Institute of Atmospheric Physics, University of Arizona. Jones, J. W. & Zur, B. (1984). Simulation of possible adaptive mechanisms in crops subjected to water stress. Irrigation Science,S: 251-264. Joseph, J. H. & Ganor, E. (1986). Variability of climatic boundaries in Israel, use of modified Budyko-Lettau aridity index. Journal of Climatology, 6: 69-82. Koppen, W. (1948). Climatologia - (Grundriss der Klimatology 1923, 1931) Transl Perez, P. H. Mexico: Fondo de Cultura Econ6mica. 478 pp. Landsberg, J. J. (1984). Physical aspects of the water regime of wet tropical vegetation. In: Medina, E., Mooney, H. A. & Vazquez-Yanez, (Eds), Physiological Ecology of Plantsof theWet Tropics. pp. 13-26. The Hague: W. Junk. 254 pp. Maderey, L. E. (1983). Clima, hidrologia y agricultura. Anuariode Geografia, UNAM, 23: 41-50. Mosino-Aleman, P. (1966). Factores Determinantes delClimaenla RepublicaMexicanacon Referencia Especial a lasZonasAridas. Departamento de Prehistoria, INAH, SEP, Mexico. 22 pp. Namias, J. (1978). Recent drought in California and Western Europe. Reviews of Geophysics and SpacePhysics, 16: 435-458. Nicholls, N. (1985). Impact of the Southern Oscillation on Australian crops. Journal of Climatology, 5: 553-560. Nicholls, N. (1986). Use of the Southern Oscillation to predict Australian sorghum yield. Agricultural and Forest Meteorology, 38: 9-15. Nieuwolt, S. (1986). Agricultural droughts in the tropics. Theoretical and Applied Climatology, 37: 29-38. Prescott, J. A. (1958). Climatic indices in relation to the water balance. In: Climatology and Microclimatology. Proceedings of the Canberra Symposium. pp. 48-51. Arid Zone Research, UNESCO. Quinn, W; H., Zopf, D.O., Short, K. S. & Kuo Yang, R. T. W. (1978). Historical trends and statistics of the southern oscillation, El Nino, and Indonesian droughts. Fishery Bulletin, 76: 663678.
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Revelle, R. R. (1981). Uses of climatic knowledge in the food systems of developing countries. In: Slater, L. E. & Levin, S. K. (Eds), Climate's Impact on Food Supplies. pp. 39-44. American Association for the Advancement of Science. Washington, D. C. 243 pp. Reyes-Coca, S. & Rojo-Salazar, P. (1985). Variabilidad de la precipitaci6n en la Peninsula de Baja California. Reoista de Geofisica, 22/23: 111-128. Robinson, P. J. & Fesperman, J. N. (1987). On the mesoscale distribution of precipitation deficits. Theoretical andAppliedClimatology, 38: 119-126. Salinas, C. & Leyva, A. (Eds), (1989). Promedios Mensuales de Temperatura en Baja California Sur. Centro de Investigaciones Biol6gicas de Baja California Sur, A. C. (CIB) y Secretaria de Agricultura y Recursos Hidraulicos. Informe tecnico del CIB. La Paz, BCS, Mexico. 211 pp. Salinas, C. & Leyva, A. (Eds). (1988). Totales Mensuales dePrecipitacion Pluvial en Baja California Sur. Centro de Investigaciones Biol6gicas de Baja California Sur, A.C. (CIB) y Secretaria de Agricultura y Recursos Hidraulicos, Informe tecnico del cm. La Paz, BCS, Mexico. 211 pp. Sellers, W. D. (1965). Physical Climatology. pp. 123-126. Chicago: University of Chicago. Stadler, S. J. (1987). Aridity indexes. In: Oliver, J. E. & Fairbridge, R. W. (Eds), TheEncyclopedia of Climatology. pp. 102-107. Encyclopedia of Earth Sciences, Vol XI. New York: Van Nostrand Reinhold. 986 pp, Steila, D. (1987). Soils and climate. In: Oliver, J. E. & Fairbridge, R. W. (Eds), TheEncyclopedia of Climatology. pp. 769-773. Encyclopedia of Earth Sciences, Vol. XI. New York: Van Nostrand Reinhold. 986 pp. Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical Review, 38: 55-94. Thornthwaite, C. W. (1958). Introduction to arid zone climatology. In: Climatology and Microclimatology. Proceedings of theCanberra Symposium, pp. 15-22. Arid Zone Research, UNESCO.
A simple aridity equation for agricultural purposes in marginal zones Enrique Troyo-Dieguez", Francisco de Lachica-Bonilla* & Jose L. Fernandez-Zayas'] Accepted 30 November 1989 Analysis of the widelyused drynessindex proposed by Budyko revealsits limited usefulness in evaluating aridity of regions with very low precipitation coupled with high evaporation rates. Such is the case of a region in BajaCaliforniaSur, Mexico, where a better aridity index is needed to describe weather during months of limited, or null, rainfall. An improved aridity index is proposed, retaining the physicalmeaning of null precipitation, a typical condition of many deserts. This is attained by preserving the inverse relationship of aridity and precipitation. A regionalization of La Paz, Baja California Sur, illustrates the quality of the proposed index. Subranges of aridity can be defined with a better fitting accordingto desertic needs.
Introduction Agriculture is a technological activity through which matter is transformed from several sources, employing various forms of energy (solar, chemical and mechanical). Its main purpose is to produce biomass of economical importance. This activity is guided by different types of information, such as the genetic code of each kind of plant, cultural practices, soil properties and the climatological character of each region. This definition implies that agriculture depends on biotic and abiotic factors that explain the processes involved, either in an isolated or a connected way. The more relevant abiotic factors are solar radiation, water in the form of rain, or through irrigation, and soil, the substrate and nutrients reservoir for biotic factors. These factors are usually studied separately, although they interact with each other in several ways.
Relationship between climate and agriculture The elements of climate that have the most important effects on agriculture are solar radiation, and rain in rain-fed agriculture. Both contribute to the formation and development of soils in continental regions as well as in microregions, through a number of processes that operate even in microscale dimensions. Of these processes, climate is of primary importance. While the parent rock, plants and edaphon contribute the materials from which soils are made, climate determines the process of soil development (Cargo & Mallory, 1977). There is a causal relationship between the world-wide distribution of • Centro de Investigaciones Bio16gicas de Baja California Sur, Apartado Postal 128. La Paz, Baja California Sur,Mexico, C.P. 23000. t Instituto deIngenieria, Universidad Naciona1 Aut6noma deMexico (UNAM), Cd. Universitaria. Coyoacan, Mexico, D. F., C.P.04510. 0140-1963/90/060353 +
10 $03'00/0
© 1990 Acadetnic Press Litnited
E. TROYO-DIEGUEZ ET AL.
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edaphic orders and climatic regions. In the study of pedogenetic processes, a basic hypothesis is set up by the statement that atmosphere is a primary pedogenetic element (Steila, 1987). For agricultural purposes, soil fertility is not an isolated nor static factor modified by the nutrient-extracting crops, but is a condition which depends, among other factors, on the local weather. Soil humidity varies in different quantities: a minimum value known as the permanent wilting point (PWP), and a maximum known as field capacity (FC). The magnitude of these parameters, PWP and FC, is different for each type of soil. The availability of this water for plants is a function of evapotranspiration which is modified by solar radiation, rain, soil type and the physiological mechanisms of each plant. According to Prescott (1958), two major soil zones exist: (1) humid zones where the mean rainfall in every month is adequate to meet potential evapotranspiration and (2) desert regions where mean monthly rainfall never exceeds that required to keep the soil moisture above the wilting point of plants (PWP). From an understanding of the soil-atmosphere relationship, it can be argued that in rain-fed agriculture the availability of water in the edaphic environment and consequently the crop success depend largely on weather; this is because under dry conditions the water deficit reaches a level which decreases the plant growth processes and the root system becomes unable to extract water at a sufficient rate to sustain the transpirational demand (Jones & Zur, 1984). Consequently, this kind of agriculture requires that soil quality (physical and chemical) analysis in a site must be completed within adequate climatological parameters (Revelle, 1981). From the hydrological viewpoint, the use of the equation proposed by Landsberg (1984), cited by Barradas & Fanjul (1985), establishes an adequate reference of the water balance. This equation is given by:
a
OCt
+ dt) = [OCt) + Pp - E - Dr - Ro]/Z
(1)
where is the volumetric content of water in soil (given up during the range of) time t + dt, and Pp, E, Dr, Ro and Z are the total precipitation, evapotranspiration, deep percolation, runoff and root depth, respectively. Although deep percolation and runoff are relevant processes of the water balance in an ecosystem, they are relatively insignificant in the agricultural arid plains of Baja California Sur. Desert climatology is of considerable importance in the agricultural development of the arid lands of Baja California. However, adequate descriptions of aridity for conditions in Baja California have not been forthcoming. Drought has been defined in many ways, including precipitation deficit, periods of wide extend or great severity, occurring on a variety of spatial scales. These events are the result oflarge-scale subsidence which inhibits precipitation-producing mechanisms (Landsberg, 1984, cited by Robinson & Fesperman, 1987). If such climate fluctuations could be predicted well in advance, agriculturalists and planners might be able to take action to minimize the deleterious consequences (Nicholls, 1985). Intensive case studies of individual droughts are a prerequisite to an understanding of their initiation, maintenance, and demise (Namias, 1978). A variety of aridity indexes have been formulated; formerly, the term 'Aridity Index' refers to the 1948 work of Thornthwaite (Stadler, 1987). It might be appropriate to mention that desertic climate is most often defined in terms of low precipitation and humidity. It follows that an adequate representation of dryness, or aridity, must clearly reflect water scarcity. Arid zones in Mexico are extensive, covering more than 60% of the country. Agricultural activities in these lands have a limited availability of water. The aridity, understood as a condition of water deficiency, has to be evaluated so as to plan adequately for agriculture in these zones and objectively to ration the use of hydrological resources. According to Mcsific-Aleman (1966), the genesis of north-western Mexican arid zones,
A SIMPLE ARIDITY EQUATION
355
with emphasis on the Baja California peninsula, depends on the occurrence of cold oceanic currents from California: dynamics at the ocean-atmosphere interface cause an absence of condensation and a lack of rain, a typical condition of this arid zone. Recent studies indicate that this phenomenon is modified by El Nino-Southern Oscillation (ENSO) events, which show a positive correlation with the seasonal variations of precipitation (Reyes-Coca & Rojo-Salazar, 1985). Thus, an ENSO event may have the potential for long-range prediction (Nicholls, 1986). Statistical information pertaining to the historical occurrence of ENSO events is a useful basis for speculative long-range forecasts a year, and more, in advance (Quinn et al., 1978). The merits of an adequate aridity index are highlighted in this work by the evaluation of the aridity of La Paz basin, B.C.S., Mexico. The index is derived from a simple equation that seeks to express the relationship between rainfall and evaporation. Study area and methods The climatological data used in this study, including temperature, precipitation and evaporation values for La Paz, were obtained from Divis6n Hidrometrica de Baja California Sur, Mexico, of the Secretaria de Agricultura y Recursos Hidraulicos. The La Paz weather station is located at 24° 09'N and 110° 20'W, and is the main source of climatological information for the farmers and rangers in the La Paz area. Two sets of precipitation data, from 1906 to 1911 and 1917 to 1986, (Salinas & Leyva, 1988), and a set of temperature data, from 1921 to 1986 were considered (Salinas & Leyva, 1989). No precipitation data were found in the available records for the period from 1912 to 1916. According to historical records, maximum precipitation in any month was 381'6 mm in September 1943, and the maximum precipitation on any day was 137·0 mm on 30 September 1976. Monthly values of temperature, precipitation, evaporation and aridity are shown in Table 1. Global characterization of aridity was based on monthly mean values. The calculation of the aridity, D, was done first by solving the equation -proposed by Budyko (1974) according to the methodology developed by Joseph & Ganor (1986). The values of total solar radiation were obtained from Galindo & Chavez (1977) and Fernandez-Zayas (1987). This information was combined with other data (Hastings, 1964; Hastings & Humphrey, 1969) and then analysed by means of the Statgraphics computer program. A modified aridity index A, is calculated by means of a water balance using the ratio precipitation/evaporation as the main water deficit estimator. For the case at hand, mean daily evaporation is 5'87 mm/day, or approximately 176 mm/month (Table 1). For agricultural purposes, a balanced condition (null aridity) was considered when precipitation equalled evaporation; in this case, index A = 0, the minimum value of aridity. A maximum value of aridity implies that precipitation is zero for any study period. An aridity scale was selected in order to obtain a suitable set of ranges for agricultural purposes; however, different aridity scales can be adopted to suit specific requirements of any activity, as in the case of marine aquaculture, where a scale of the balance precipitation/evaporation with higher resolution is needed to avoid increases in salinity.
Aridity models The first approach to a study ofweather in a locality is generally based on an interpretation of maps and symbols used in common climatological classification systems. The Koppen system, modified by Garcia (1964), is widely used in Mexico. According to this classification system, the climate of La Paz, Mexico, can be represented by the code BW(h')hw(e), which is interpreted as very dry weather with a principal rainy season in
43·5
Mean Max
Total
2·0
2·0 2·5 3·0 4·5 8·5 10·0 13·0 13·0 12·0 12·0 6·5 2·0
32·5 35·0 36·0 39·0 39·5 42'5 43·0 43·0 43·0 43·5 37·5 36·0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Min
Minimum
Maximum
Month
Temperature CCC)
23'6 29·5 17·5
17·5 18·0 19·7 22·0 24·3 26·5 29·2 29·5 29·0 26·1 22·2 18·9
Mean
15·05 59·90 0·70 180·60
12·5 42·6 59·9 13·7 9·2 20·4
1-8
12·1 5'0 2·0 0'7 0·7
Precipitation 290·6 337·5 393·8 431·3 450·0 468'8 450·0 431-3 393·8 346·9 300·0 262·5 379·7 468·8 262·5 4556·5
176·1 192·3 155·9 2113'3
Net radiation (Rn) cal/cmvday
Radiation
169·2 155·9 184·8 172·8 173·2 170'2 182·9 192·3 182·8 182·8 172·9 173.5
Evaporation
Hydrological data (mm)
0·277 1·107 0·011 0·004
0·041 0·115 0·337 1·058 H07 0·449 0·062 0'018 0·011 0·044 0'056 0·022
D
Aridity A
3·66 3·98 2·69 3·66
3·71 3·87 3·96 3·98 3·98 3·96 3·73 3·11 2·69 3·70 3·79 3·53
Table 1. Thermo-pluoiometric and radiational data ofLa Paz weather station for theperiods 1906-1911 and 1917-1986, and estimated aridity
UJ
VI
t-
).
'-l
ttl
tTl N
o c
m-
-6
0 0< 0
..,:;:gtrl
0-.
A SIMPLE ARIDITY EQUATION
357
summer and a secondary one in winter; precipitation in general is very scarce all year long; winter precipitation is less than the summer one; warm climate, with annual thermal oscillation from 7 to 14°C (Garcia & Mosino, 1968). It is necessary to remember, however, that this information is very generalized and inadequate for planning agricultural practices. There is a 5-year fluctuation of drought or extreme aridity in the climatological record of La Paz weather station, a fluctuation not evident in common classification systems of weather. In this work, for the estimation of Budyko's aridity index, net radiation was calculated through the equation Rn = (l - a)(Rt)
(2)
where Rn is the net radiation, Rt the total solar radiation, and a is the albedo value, in this case 0'25 (Sellers, 1965). Estimated net radiation values were applied for the computation of the aridity index (Galindo & Chavez, 1977). It was noted that a maximum value of net radiation occurs in June (468'75 cal/cmvday) and a minimum in December (262'5). According to these theoretical data, annual mean Rn in La Paz, B.C.S., is 379'69 cal/cmvday, among the highest in Mexico. A widely used aridity index proposed by Budyko in 1951 (Stadler, 1987), expressed as a radiational index of dryness, is the following: D
= Rn/(LP)
(3)
where D is the radiational index of dryness, Rn the mean net radiation received in callcm2/ day, L the latent heat of vaporization, and P the amount of precipitation in mm. A common limitation of aridity indexes is that they ignore the capacity of the soil to accumulate water. It is generally accepted that this shortcoming cannot be easily eliminated. . Considering L in this equation as a function of temperature and selecting a fixed value of albedo, suitable for annual crops or short vegetation under arid conditions, equation (3) can be re-written as: D
= Rn/(b
- eT) (P)
(4)
where b is the total heat ofvaporization in callg (b = 595,5), cis an empirical factor varying with temperature in °C (c = 0'609), and P is the amount of precipitation in mm that occurred in the study period. Applying the last equation for an annual period in the study area and considering Rn = 379'69, T = 23'6 and P = 180'6, the equation renders D = 0'0036 as a result of the influence of the higher values of P, in this case that of August and September. As shown, D is strongly sensitive to rain values and is extremely low, and cannot demonstrate an adequate representation of the aridity fluctuation in this dry, arid zone. Annual variation of D (Budyko's index of dryness) as well as precipitation pattern is presented in Fig. 1 (precipitation values were divided by 100 to obtain a suitable scale). Minimum and maximum values of the dryness index correspond to September and May, the inverse of the precipitation values. The dryness index pattern presents a growing tendency towards April and is the inverse to that of precipitation. It should be noted that if P = 0, D is numerically undefined (in La Paz, Mexico, the periods from February to June and from October to December are dry seasons with null precipitation; nevertheless, they are important agricultural seasons). This condition renders Budyko's model useless in arid zones, where null rainless periods are common. In fact, this model can only be applied for analysis of mean annual values of historical series; month by month analysis may not be done, because of the possible occurrence of months with zero precipitation. Minimum and maximum mean monthly values of precipitation were 0'7 and 59·9 mm
E. TROYO-DIEGUEZ ET AL.
358
r-----------------------,
1·2
Dryness pattern
1·1
"
-g'" ~
o
0·9 0·8
~
0·7
o-,
0·6
'"
0·5
c '"
0
~»
-c
~
CO
Pre cip i tatian pattern
0·4 0·3 0'2
0'\ 0'
JAN
t-+===+-+
FEB
MAR
APR
MAY
JUN
JUL AUG
SEP OCT
NOV
DEC
Time
Figure 1. Annualvariation of Budyko'sDryness Indexand precipitation pattern of La Paz, B.C.S., Mexico.
for May and September, respectively; for most months precipitation is very low, near zero, accordingly to the historical series (Salinas & Leyva, 1988). Annual isohyetes of La Paz and adjacent stations show the area likely to have a global precipitation deficit (Fig. 2). Annual value of D in equation (4) is low (D = 0'0036), much lower than the same index for September (D = 0'011), the month with most rain (60 mm). In consequence, there could be a wrong interpretation. This characteristic arises because the value of annual precipitation represents the sum of individual values of all months. Consequently, the resulting estimated aridity value, D, on the basis of annual analysis is actually an extrapolation of added values, not really an average index; in this case D underestimates the aridity in the study region. In order to evaluate diverse arid zones for agricultural purposes in Baja California Sur, Mexico, the following equation is proposed in this work: IIOOW Gulf of California
24°
24°
Pacific Ocean 25 km
Figure 2. Annual isohyetes for the southern part of BajaCalifornia Sur, Mexico.
359
A SIMPLE ARIDITY EQUATION 5,---------------.====r-------, Proposed index (A) 4
Annual A
Budyka's index (D)
+-+ +.-+/
<;
AnnualD
JAN
I
I
FEB
MAR
I APR
I MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Time
Figure 3. Annual variation of the proposed index around its annual value as compared with the Budyko's dryness index.
A = N(1 - F)
(5)
where A is the proposed aridity index; F is the ratio of precipitation/evaporation for a period of time, F = PIE; andN is the number of categories to be established according to local agroclimatological conditions. N is the maximum value of aridity previously fixed. In this equation, if P = 0, then A = N. If P > E, then A renders a negative value which is to be interpreted as a condition of null aridity. Considering N = 4 and mean monthly evaporation as a constant parameter (176 mm), according to the available data for La paz (Table I), the last equation can be simplified to: A = 4 - (0'02273)(P)
(6)
where A is the aridity index proposed for La Paz region (monthly) and P is the mean monthly precipitation in mm. In order to obtain a positive value of the aridity index, the condition 0 :s;:; P < 176 must be satisfied. According to this equation, if P - 176 mm! month, then A = 0; as the precipitation balances the mean monthly evaporation (PIE = 1), the resulting number describes a non-arid condition.
Other results The fluctuation of A around its annual mean as compared with the fluctuation of D is presented in Fig. 3. It is clearly depicted in the figure how the proposed index yields high values at the time of high dryness, and decreases as the rainy season arrives. Notice in the figure how Budyko's index trend diverges from the observed rainfall pattern; the annual value of dryness, D, does not really indicate an arid condition because of its low value. Six suggested subranges of aridity for La Paz region according to equation (6) are shown in Table 2. The geographic pattern of aridity in the study region according to equation (6) is presented in Fig. 4 for the subhumid period (August-September); for the rest of the year (October-July), the equation renders a condition of extreme aridity (EA) for most of the region.
E. TROYO-DIEGUEZ ET AL.
360
Table 2. Proposed subranges ofaridity according to equation (5) Aridity index (A)
Precipitation (P, in mm/month)
Classification
3·5 to 4·0 3·0 to 3·5 2·0 to 3·0 1·0 to 2·0 0·0 to 1·0 negative values
o to 22 22 to 44 44 to 88 88 to 132 132 to 175 p> 175
EA: Extreme aridity (desert) A: Arid SA: Semi-arid DS: Dry-subhumid MS: Moist-subhumid H: Humid (aridless)
Conclusion The equation of aridity developed here can readily identify regional differences of aridity and is applicable to any arid zone. It can be complementary to common climatological classification systems or other similar measures. The proposed equation is robust at low values of precipitation; the resulting aridity index is strongly correlated with precipitation deficit. The maximum and minimum values of A for La Paz region are 3·98 for May, the month with the lowest precipitation, and 2·69 for September, the month with the highest precipitation (Fig. 3); these values appear to be strongly correlated with the latent and active periods of vegetation respectively. Monthly fluctuations of A and D for the area under study are shown in Fig. 3. It can clearly be noticed how the proposed index A yields high values at the time of high dryness, a high risk agricultural season, and lower values when the rainy season arrives; for the study region, the proposed index A is robust (resistant) at low values of precipitation. The equation presented in this work can readily identify regional differences of aridity and become an analytical tool for agricultural planners in arid zones (see Fig. 4). More studies need to be conducted for a better explanation of aridity fluctuation under normal and abnormal conditions, and to account for the potential for soil accumulation of water.
GULF OF CALIFORNIA
PACIFIC OCEAN
25
Figure 4. Agroclimatological provinces of Southern Baja California Sur according to the aridity condition (sub-humid period).
A SIMPLE ARIDITY EQUATION
361
This work was financed by Consejo Nacional de Ciencia yTecnologia (CONACyT) and Secretarfa de Programaci6n y Presupuesto (SPP) of Mexico. Thanks are due to BioI. Cesar Salinas-Zavala for providing valuable temperature and precipitation data as well as for a critical review of some aspects of the paper. We would also like to thank Dr Claude Grenot, from Ecole Normale Superieure, Paris, for critical reading of the manuscript and helpful suggestions.
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