Abstract: The purpose of this study was to use mechanistic modeling of soil-plant-atmosphere hydraulics to develop quantitative measures of post-establishment agricultural drought for subsistence sorghum production under soil and rainfall conditions typical of semi-arid Eastern Botswana. Daily AET/PET ratios were calculated for 120 days following each of 15 growing period start dates over 9 growing seasons (1981/82 through 1989/90). The resulting series for each start date were used to calculate values for the total occurrences when AET/PET ≤ 0.3 for 2, 4 and 6 consecutive days and values of agricultural drought days using baseline AET/PET ratios reported in the literature. These two agricultural drought measures were compared over 3 the high-rainfall seasons (1983/84 to 1985/86) and 3 low rainfall seasons (1987/88 to 1989/90) for the 15 start dates. The mean occurrences when AET/PET ≤ 0.3 over the dry seasons were markedly higher and tended to be more variable for all growing period start dates. The mean occurrences for the 3 dry seasons showed the same pattern over the 15 start dates for all durations, but the values decreased with increasing duration in a non-linear manner. The same was true for the wet season occurrences. Agricultural drought day means were always < 0 and were more negative for the dry seasons for all start dates. Although the patterns for all measures contained low mean values, there were no well-defined minima for either the dry or wet seasons.
Introduction
The climate of landlocked Botswana (between 22 and 26° south latitude and 21 and 28° east longitude in Southern Africa) is typical of the semi-arid tropics classified as Bsh according to the Koppen-Geiger-Pohl climatic classification system (Campbell, 1980). The Kgalagadi (also Kalahari) semi-desert covers about two-thirds of Botswana. Most of the population lives along the Kgalagadi's eastern fringe where the mono-modal spring/summer rainfall (from October through March) is sufficiently high and reliable to sustain traditional subsistence crop and livestock production.
Meteorological and agricultural droughts (also termed as agro-meteorological or agro-climatic drought) are constant expectations in this environment and are reflected in the overall productivity statistics for sorghum (Sorghum bicolor (L.) Moench), the staple food source in Botswana. The Agricultural Statistics Unit (ASU) of Botswana's Central Statistics Office (CSO) conducts annual agricultural surveys which are compiled into their annual agricultural survey reports (Shatera, 2001). Tabulated data for sorghum production from these reports (available from the ASU/CSO, Private Bag
0024, Gaborone, Botswana) for 20 years between 1979 through 2002 (except 1991, 1992, 1994 and 2000) showed that the mean and standard deviation of the area planted to sorghum by subsistence farmers in Botswana was 143,000±66,000 ha with range 23,000 to 279,000 ha. Corresponding values were 91,000±63,000 ha with range 13,000 to 244,000 ha for the area harvested, 60±19% with range 0.28 to 0.89 for the ratio of area harvested to area planted, 161±153 kg with range 40 to 684 kg for the yield per ha planted and 253±219 kg with range 108 to 1071 kg for the yield per ha harvested. On the other hand, several documents (DLFRS, 1978; Lightfoot, 1979, 1981; ATIP 1985a) available from the Botswana Department of Agricultural Research (Private Bag 0033, Gaborone, Botswana) and published manuscripts (Jones, 1987a-c; Harris, 1996; Setimela et al., 1998; Munamava and Riddoch, 2001) report a dryland yield potential under improved soil and crop management practices on research plots of 1500 to 2000 kg ha-1 for the local sorghum cultivar Segaolane that almost all subsistence farmers grow in Botswana. Segaolane is an open pollinated, drought tolerant, pure line, medium cycle (120-125 days to full maturity) variety (Chiduza, 1987, 2001).
Over generations of experience, Botswana's subsistence farmers have evolved traditional soil and crop management practices appropriate to their socio-economic circumstances to cope with the agricultural drought risk associated with large fluctuations of plant available soil water under the low, unpredictable and variable daily rainfall pattern during the growing period (Coulibaly and Vanderlip, 1994; Davis and Vanderlip, 1996; Rockstrom, 2000). Their practices are considered low-input compared to those associated with modern, intensive commercial agricultural husbandry such as use of commercial fertilizers, weed and pest control, rotations etc. (Pule-Meulenberg and Batisani, 2003; World Resources Institute, 2006). This would explain why the full potential yield of Segaolane and other local cutivars are not realized in subsistence sorghum production. Although socio-economic changes underway in Botswana are forcing agricultural intensification, the data presented in the previous paragraph indicate that this transition away from subsistence farming is still in progress.
Botswana's subsistence farming families grow an average 4 to 5 ha. Sorghum seed is broadcast at fairly high rates on the soil surface and incorporated using cattle or donkey teams pulling a single-furrow mouldboard plough (Lightfoot, 1981). High seeding rates are used to offset poor germination and/or post-emergence stand establishment that occur in about 40% of sowings, necessitating replanting several times and consequent increased labor costs and exhaustion of seed supplies (Chiduza 1993; Chiduza et al., 1995; Harris et al., 2001). This would reasonably explain the high year-to-year variability in area planted reported above. In addition, land tenure is communal and therefore crop fields are not fenced. Animals are allowed to graze until farmers in a community collectively agree to begin preparing the fields for sowing. The timing of rounding up and herding of the livestock is therefore dependent on communal perception of the reliability of the rains as the season progresses. Many farmers would be unwilling to take advantage of any early rains as their unprotected crops may be destroyed by livestock.
Subsistence dryland farmers in Botswana would generally like to plant as early as possible as this would permit the crop to reach the critical flowering and grain filling periods at times when the soil water and temperature regimes are more likely to be favorable (Davis and Vanderlip, 1996). On the other hand, planting too early or too late would produce growing degree day accumulation that are lower than the maximum possible value over the spring/summer period and this would result in delayed maturity or problems with seed set. Such decision-making considerations on planting raise the question: is agricultural drought risk after crop establishment related to the start-date of the growing period? The primary objective of this study was to attempt to quantitatively answer this question using cost-effective physics-based modeling of soil-plant-atmosphere hydraulics. It would be prohibitively costly and time consuming to conduct the multi-location, multi-year field plot studies needed to identify optimal planting periods (if these exist at all) and their frequency of occurrence.
Answering this question has both scientific and socio-economic implications for semi-arid eco-regions. The phenomenon of agricultural drought is embedded in the psyche of rural inhabitants in these areas and this is reflected in national governmental contingency plans to cope with its societal and economic impacts (UNDP/UNSO, 2000). In this connection it is most interesting to note that the name of the monetary unit in Botswana (the pula) means rain. Yet while there is universal agreement on the concept of agricultural drought as a function of the availability and accessibility of water in the rooting zone to meet crop transpiration requirements, there is no universal methodology in the scientific literature to quantify post-establishment agricultural drought occurrence and drought risk for annual crops in semi-arid, mono-modal rainfall climates. The long-recognized reason is that, unlike other natural hazards, agricultural drought is not episodic (i.e., no identifiable onset and end) but occurs continuously over extended and varying periods of time throughout the growing period (Tannehill, 1947; Wilhite and Glantz, 1985; Wilhite, 1995). The risk to crop production depends not only on the intensity and duration of agricultural drought but also on the crop growth stage (Doorenbos and Pruitt, 1977; Doorenbos and Kassam, 1979). In short, agricultural drought risk depends on the exposure i.e. the occurrence of various severity levels and their duration, in conjunction with the vulnerability of the crop at that severity level (Blaikie et al., 1994). Risk is therefore location and impact specific and vulnerability is determined to a large extent by the prevailing soil and crop management technology.
Given these characteristics, quantifying agricultural drought risk continues to present a challenge to scientists involved in agricultural drought monitoring and assessment programs associated with national contingency plans (Wilhite, 1991, 1992; Pandi et al., 2001). Nevertheless, any historical information on agricultural drought risk can help provide better insight and understanding needed to develop appropriate soil and crop husbandry technologies and mitigation programs.
The only previous attempt to quantify agricultural drought occurrence in Botswana that we were able to uncover was reported by Vossen (1990). The study was based on the Water Satisfaction Index (WSI) developed by Frere and Popov (1979) and adopted a rather generalized, coarse approach that did not take into account specific crop or growth stage sensitivity to drought stress. The soil water balance was calculated over 10-day periods and soil moisture was assumed to be equally available to meet actual evapo-transpiration requirements over the entire range of soil water content. This study sought a finer and more detailed approach.
Materials and Methods
Overview of Approach
In this study we first estimated the daily reference Potential Evapo-Transpiration
(PET) using a Penman-based equation with coefficients appropriate for
Botswana. Next, we used the soil hydro-physical HYDRUS-1D computer program
to dynamically integrate the weather, soil water hydraulics and plant
development to estimate daily Actual Evapo-Transpiration (AET) for subsistence
sorghum production on the predominant soil type in eastern Botswana. The
daily AET/PET ratio was taken as the measure for the intensity of agricultural
drought meaning the degree to which moisture availability and accessibility
in the root zone were inadequate to sustain plant growth. We then used
these ratios to develop post-establishment agricultural drought measures
and examined them in relation to a full range of growing-period start
dates.
Data
Daily meteorological data series of rainfall from January 1927 through
December 1997 and on maximum and minimum air temperature, relative humidity
at 0800 and 1400 h, daily bright sunshine hours and windrun for 1981 though
1990 were obtained for the agro-meteorological station located at the
headquarters (24°40' south latitude; 25°55' east longitude) of
the Meteorological Services Department (P.O. Box 10100, Gaborone, Botswana).
Data on measurements of the hydro-physical characteristics of a Ferric Luvisol (equivalent to a Kandic Paleustalf in the USDA Soil Taxonomy) in a field at the Agricultural Research Station at Sebele in Botswana (24°33' 40'' S, 25°56' 40'' E), were obtained from the Department of Agricultural Research (Private Bag 0033, Gaborone, Botswana). These measurements were made as part of the FAO-sponsored Botswana Soil Mapping and Advisory Services Project implemented between 1980 through 1990 (project numbers FAO/BOT/80/003 and FAO/BOT/85/011). Ferric Luvisols are the predominant soil type used for dryland cropping in Eastern Botswana and in large areas of semi-arid Africa (Dekkers, 1993). The data on dry bulk density, particle size distribution and soil water retention characteristics of this soil were measured on samples taken from the Ap/A (0- 33 cm), Bt1/Bt2 (33-97 cm) and Bt3 (97-180 cm) horizons of the soil profile using procedures detailed by the American Society of Agronomy (Black, 1965). The bulk density measurements were made on 5 replicate core samples from each horizon. Moisture retention values represented the mean of three measurements. At soil water tension < 100 kPa measurements were taken on soil cores and on the crushed < 2 mm fraction for tension ≥ 100 kPa. The particle size distribution was measured on disturbed samples by sieving and sedimentation analysis.
Meteorological Data Analysis
The annual rainfall total, the number of rain days, the rain depth
per rain day and the fraction of the annual rainfall total received between
July 1 and each of 15 specified growing period start dates were calculated
for the 70 rain years of record (rain year taken as July 1 through June
30). These start dates were day-of-year 274 (1 October), 288, 305, 309,
314, 319, 324, 329, 335, 339, 344, 349, 354, 359 and 365 (31 December).
The growing degree days accumulated for 120 days after each start date
using a base temperature of 10°C and a ceiling of 30°C were calculated
for 9 years (1981/82 through 1989/90) resulting in nine totals for each
planting date. The growing degree value for any day was taken as the daily
mean temperature minus 10°C. Mean temperature values below 10°C
were adjusted to 10°C and above 30°C were adjusted to 30°C.
Estimating PET
The Penman-based reference PET equation used was (Persaud et al.,
2006):
| (1) |
where PET = mean daily potential evapotranspiration in mm; Δ = slope of the saturation vapor pressure versus temperature curve in mb °K-1 at the value for the mean daily air temperature; γ = 0.66 mb°K-1; Ra in mm water = mean daily direct solar radiation under cloudless skies at a specified location; r = reflection coefficient for a particular surface; n = mean daily hours bright sunshine; N = mean daylength in hours for a given location; σ = 19.83x10-10 mm H2O day-1 °K-4; T = mean daily temperature in °K; es (T) = saturation vapor pressure in mb at temperature T (°K); e = mean daily vapor pressure in mb; u = mean daily windrun in km day-1.
The set of empirical coefficients, a1 through a9 and r in Eq. 1, were those in use by the Botswana Department of Meteorological Services (DMS). These were the FAO-recommended coefficients detailed by Doorenbos and Pruitt (1977) and Frere and Popov (1979) with some modifications (Vossen, 1988; Persaud et al., 2006). The values were a1= 0.28, a2 = 0.49, a3 = 0.34, a4 = 0.044, a5 = 0.10, a6 = 0.90, a7 = 0.27, a8 = 1.0, a9 = 1/100 and r = 0.25. The PET estimates included the correction of γ for altitude (McCulloch, 1965) and the C-factor adjustment to compensate for the site-specific effect of daytime to nightime wind run, net solar radiation, maximum relative humidity and daytime wind velocity so that one set of coefficients could be universally applicable for PET estimation (Doorenbos and Pruitt, 1977).
Estimating AET
The AET was estimated by modeling soil water dynamics using the HYDRUS-1D
software (Simunek et al., 2005) developed at the George E. Brown
Jr. Salinity Laboratory, Agriculture Research Service, US Department of
Agriculture (USDA/ARS). This software can be downloaded freely at their
website http://www.ars.usda.gov/services/software/software.htm.
It is a multi-purpose and flexible computer program developed to numerically
solve (inter alia) the partial differential equation governing unsteady
one-dimensional (1-D) water flow in variably-saturated soils. By appropriately
changing the program input parameters characterizing the flow domain and
describing the boundary conditions and physical processes, 1-D soil water
dynamics under specified weather conditions can be modeled for any given
soil profile to yield AET estimates for any crop of interest.
HYDRUS-1D implements a standard Galerkin linear finite element method (Celia et al., 1990) to numerically solve the Richards'-based partial differential equation governing one-dimensional unsteady water flow (Richards, 1931) with a generalized sink term to account for water uptake by plant roots. HYDRUS-1D was used to calculate the soil water content, pressure head and root water uptake over time starting October 1, 1981, for each element of the (rectangular) finite element mesh. Post-processing subroutines of HYDRUS-1D permitted integrating these ouput values to calculate the water balance components for any specified interval of the soil profile over a given time period.
The governing Richards'-based water flow equation was
| (2) |
where θ (z,t) is the volumetric water content [L3 L-3], h(h≤0) is the (negative) soil water pressure head [L], S is a sink term for the root water uptake [T-1], z is the Cartesian coordinate [L] representing depth below surface (z = 0), t is time [T], K(h) is the unsaturated hydraulic conductivity function [LT-1].
The soil hydraulic functions θ(h) and K(h) are required inputs to the numerical solution of Eq. 2. The θ(h) function used was
| (3) |
where θs is the volumetric water content at saturation, θr is the residual water content (i.e., the volumetric water content at which convective water flow was negligible, |h| is the soil water tension (i.e., the absolute value of the soil water pressure head in cm water); α is a fitting parameter that is related to the air entry pressure value, n is a fitting parameter related to the pore size distribution and m = 1-1/n (van Genutchen, 1980).
The K(h) function used was:
| (4) |
It defined K(h) in terms of the soil water retention parameters α and n and two additional parameters Ko and L (van Genuchten, 1980) based on the statistical pore-size distribution model of Mualem (1976). Here Ko (LT-1) = K(h = 0) is the fitted value at saturation (cm day-1) and can be interpreted as an estimate of the saturated hydraulic conductivity. The dimensionless parameter L is a fitted pore tortuosity/connectivity parameter and will be negative in most cases (Kosugi, 1999).
The value of θs was estimated from the measured soil
texture using the tabulation of Rawls et al. (1982). The parameters
θr, α and n for the θ(h) function were then
estimated by non-linear least squares fitting of the measured soil moisture
retention data to Eq. 3 using the RETC computer program
of van Genutchen et al. (1991). The parameters Ko and
L in the K(h) function were then estimated using the ROSETTA software
(Schaap and Leij, 2000). Both RETC and ROSETTA were developed at the USDA/ARS
George E. Brown Jr. Salinity Laboratory and can be downloaded freely at
their website
http://www.ars.usda.gov/
services/software/software.htm.
The root water uptake term S(z, t) in Eq. 2 was taken as S(z,t) = a [h(z,t)] Smax(z) where Smax (z) is the maximum root water extraction rate as a function of depth z (Feddes et al., 1978). The value of Smax(z) at a given time t was taken as constant = PET/L(t) where L(t) is the rooting depth as a function of time. Here L (t) was taken as the solution to the Verhulst (1838) logistic growth equation given as L(t) = (Lmax Lo])/ [e-rt (Lmax – Lo) + Lo] where Lmax is the maximum rooting depth (here taken as 100 cm) and Lo = L(t) at t = 0 taken as some small positive value (0.4 cm in this study) to avoid all zero values for L(t). The value of r was then computed by assuming L (t) = Lmax/2 when t = midpoint of the growing period (60 days in this case giving r = 0.092). The function a(h) was taken as a piecewise continuous function taking values between 0 and 1 depending on the soil water pressure head(h) at a given depth as described by Feddes et al. (1978). In this study a(h) was defined for a given horizon of the soil profile based on examination of the fitted water retention curve (defined by Eq. 3) and K(h) curve (defined by Eq. 4) and would be presented in the results and discussion.
Taking Smax(z) = PET/L(t) implies that bare soil evaporation was taken as zero in the HYDRUS-1D computations and the flux at the surface was equal to the rainfall. Subsistence farmers use high broadcast seeding rates in sorghum production since it results in rapid cover of the soil and weed suppression (Lightfoot, 1981). Plant populations can be as high as 20 plants m-2 (ATIP 1985a, b) and can produce a leaf area index as high as 5.0 at the end of the vegetative growth (Jagtap et al., 1998). This practice along with no control of weeds would tend to considerably reduce bare soil evaporation. Assuming zero soil surface evaporative flux may not be strictly true but was not unreasonable in the context and purpose of this study.
The measured volumetric water content at -1.5 MPa soil water pressure potential was taken as the initial condition i.e., θ(z,t) for 0 < z < profile depth and t = 0. The measured daily rainfall minus the bare soil evaporative flux (zero in this study) was specified as the time-dependent surface (z = 0) flux boundary condition. Internal drainage flux through the bottom (z = 1.80 m) of the profile was taken as zero. The Actual Evapo-Transpiration (AET) as a function of time was obtained by numerical integration of the root water uptake term S(z, t) between z = 0 and z = L(t).
The fitted function parameters obtained for the Ap/A, Bt1/Bt2 and Bt3 horizons of the 0-180 cm profile were entered using the HYDRUS-1D pre-processing program module; its post-processing module was used to calculate the AET. The daily AET/PET ratios were then calculated separately for 120 days after each of the abovementioned 15 growing period start dates i.e., day 274 (1 October), 288, 305, 309, 314, 319, 324, 329, 335, 339, 344, 349, 354, 359 and 365 (31 December). This was done for 9 years starting in 1981/82 through 1989/90 resulting in nine 120-day series of AET/PET ratios for each start date. The number of occurrences when the AET/PET ratio was = 0.3 for 2, 4 and 6 consecutive days duration were determined on each 120-day series for each growing period start date. Descriptive statistics of the occurrences over the 9 years for each growing period start date were examined and appropriate graphs prepared to show agricultural drought intensity occurrence (i.e., AET/PET ratio ≤0.3) and duration (2, 4 and 6 days) in relation to start date.
In the foregoing analysis the baseline agricultural drought intensity was fixed at AET/PET = 0.3. However, the tolerance of sorghum to agricultural drought varies with the growth stage (Doorenbos and Kassam, 1979). To take this into consideration the 120-day growing period was divided into 4 stages namely 0 to 20, 21 to 50, 51 to 90 and 91 to 120 days corresponding to the initial, developmental, mid-season and late-season divisions of the growing period for sorghum as described by Doorenbos and Kassam (1979). The baseline AET/PET ratios for these periods were taken as 0.3, 0.65, 1.0 and 0.55, respectively (Doorenbos and Kassam, 1979). Values of the calculated daily AET/PET ratio minus these baseline drought intensity values as appropriate were calculated and summed algebraically over the 120-day growing period for each year and start date. This accumulated total was taken as an integrated measure of agricultural drought days (analogous to the temperature-based growing degree day concept) over the growing period for each year for a given start date. The descriptive statistics of the agricultural drought days over the 9 years for each growing period start date were examined and appropriate graphs prepared to show agricultural drought days in relation to growing period start date.
Results and Discussion
Rainfall in Relation to Start Date
Figure 1 shows the accumulated rainfall (and as
a fraction of the annual July 1 through June 30 total) between 1 July
and each of the 15 growing period start dates averaged over 70 years (1927/28
through 1996/97) of record for the meteorological station located at the
headquarters of the Meteorological Services Department in Gaborone, Botswana.
As would be expected, the fraction of the annual total rainfall available
to carry the crop to maturity (1 minus the fractions shown in Fig.
1) decreased with increasing start date and the relationship was practically
linear. The rainfall depths corresponding to these mean fractional values
are shown on the right axis of Fig. 1. These depths
ranged from 21 to 221 mm for the earliest (October 1) to the latest (December
31) start dates. On the average, almost half of the total rainfall was
received prior to 31 December and probably explains why subsistence farmers
rarely replant after the beginning of the New Year. The 70 values of the
fractions in Fig. 1 were positive-skewed before November
20 (day of year 324), negative-skewed after December 20 (day of year 354)
and normally distributed in between, as evidenced by the coincidence of
the mean and median values.
| Fig. 1: | Mean and median of rainfall received between 1 July and each of 15 growing period start dates over 70 years (1927/28 through 1996/97) of record for the station. Bars indicate standard error of the mean |
| Fig. 2: | Mean and median of rainfall received 120 days after each of 15 growing period start dates over 70 years (1927/28 through 1996/97) of record for the station. Bars indicate standard error of the mean |
The spread about the mean was almost the same for all start dates as evidenced by the almost constant standard error (±1 to 1.5%) about the mean (Fig. 1). Figure 2 shows the rainfall received 120 days after each specified growing period start date averaged over the same 70 rain years. Over the 70 years of record, the mean rainfall total received over 120 days after a given growing period start date initially increased, leveled off and then decreased with increasing start date. The distributions of the 120-day totals were mostly skewed but there was no consistent pattern to the skew. The standard error of the mean showed these totals were quite variable and were not significantly different between the start dates (Fig. 2). Together, these results served to illustrate the possible importance of the growing period start date in relation to crop production in an unpredictable, mono-modal rainfall environment.
Growing Degree Days in Relation to Start Date
Figure 3 showing the estimated growing degree day
accumulation for each growing period start date, also serves to illustrate
the possible importance of the growing period start date for dryland crop
production in tropical semi-arid environments. As shown highest growing
degree days (above 2000) were accumulated for start dates November 5 through
November 25. On the other hand, the growing degree day totals were all
above the reported minimum of 1800 required for medium to late cycle sorghum
varieties (Chipanshi et al., 2003). Year-to-year variation in cloud
cover and night-time radiative cooling effects on average daily temperature
(taken as average of the maximum and minimum temperatures) may account
for the high skew shown in the distributions for the intermediate start
dates.
Soil hydraulic Functions
Table 1 shows the physical properties measured on
samples from the Ap/A, Bt1/Bt2 and Bt3 horizons taken from the typical
Ferric Luvisol profile at the Agricultural Research Station at Sebele
in Eastern Botswana. The profile horizons are typical for this soil group
consisting of an eluviated loamy sand to sandy loam Ap/A overlying several
illuviated sand loam to sandy clay loam Bt layers of varying thicknesses.
| Fig. 3: | Mean and median for growing degree day accumulated for 120 days following 15 growing period start dates using 70 years (1927/28 through 1996/97) of temperature record for the station. Bars indicate standard error of the mean |
| Fig. 4: | Particle size distributions for 3 horizons sampled in a Ferric Luvisol (Kandic Paleustalf) profile in Eastern Botswana |
The particle size distributions for the horizons sampled show the expected increase in fine particle size fractions with depth (Table 1 and Fig. 4). The smooth curves in Figure 4 are constructed natural cubic splines through the data points (de Boor, 1978).
| Table 1: | Physical properties measured on a typical Ferric Luvisol (Kandic Paleustalf) used for subsistence sorghum production in Eastern Botswana |
| 1 Code is reference profile number in Botswana
Soil Database. 2 VCS = Very coarse sand (2 |
|
The fitted parameters θr, α, n, Ko and L using the RETC and ROSETTA software for the θ(h) and K(h) functions are included in Table 1. The value of θs in the fitting procedures was fixed based on the soil texture at 0.41 for the sandy loam and 0.39 for the sandy clay loam (Rawls et al., 1982). The θ(h) and K(h) functions show that the soil volumetric water content and hydraulic conductivity decreased rapidly with increasing soil water tension (Fig. 5 and 6).
Root Water Uptake Function
The parameters for the Feddes (1978) piecewise a (h) function for
all 3 layers of the profile was taken as a(h) = 1 for |h| = 10 cm water
decreasing linearly to 0 at |h| = 1000 cm. Our choice of this form of
the piecewise a(h) function to quantify the effect of soil water
tension on root water uptake for all 3 layers was based on the foregoing
findings and results and some other considerations discussed in the next
paragraphs.
Sorghum is tolerant to waterlogged soil conditions so there was no reason to specify a non-zero value for h at which root uptake is inhibited due to anaerobic conditions. This choice is further supported by the historical rainfall statistics. The mean and standard deviation for the annual water
year (July 1 through June 30) total over 70 years was 527±151 mm with range 243 to 925 mm. Corresponding values for the number of raindays were 62±12 with range 42 to 97 and for the rain per rainday 8.5±2 mm with range 4.4 to 14.4 mm. These values in conjunction with the rapid internal drainage potential of the Ap/A horizons of the profile as indicated by Fig. 5 and 6, make it reasonable to assume that waterlogged conditions would be rare.
| Fig. 5: | Measured and fitted soil water retention curves for 3 horizons sampled in a Ferric Luvisol (Kandic Paleustalf) profile in Eastern Botswana |
| Fig. 6: | Fitted hydraulic conductivity functions for 3 horizons in a Ferric Luvisol (Kandic Paleustalf) profile in Eastern Botswana |
These considerations also factored into choosing 10 cm soil water tension as the threshold value for initiating the linear decrease in the a(h) function and 1000 cm water tension as the point when root water uptake would be zero. Furthermore, water uptake depends on both the availability and accessibility of the soil water to the plant roots to satisfy transpiration demand and these depend on the dynamic interaction between soil hydraulics, rainfall, evapo-transpiration and plant growth and development. The mean and median rainfall, PET and AET totals over 120 days after a given growing period start date averaged over the 9 years (July 1981 through June 90) are shown in Fig. 7. The mean and standard deviation of the 120-day rainfall totals in shown in Fig. 7 taken over all 15 start dates was 266±22 mm with range from 233 to 298 mm. Corresponding values for the 120-day PET totals were 672±38 mm with range 598 to 714 mm giving a rainfall to PET ratio of 0.40±0.02 with range 0.35 to 0.42. These results indicate that on the average over a growing season, the rainfall total to carry a sorghum crop to maturity was always less than one-half of the daily Penman-based PET estimates. This should be taken in the context of Fig. 6 which shows that K(h) was 1 mm day-1 when the soil water tension was 40 cm water in the Ap/A, 50 cm in the Bt1/Bt2 and 40 cm in the Bt3 layer of the soil profile. The estimated volumetric water contents corresponding to these soil water tension values were 0.21, 0.20 and 0.26, respectively (Fig. 5). Therefore, in this soil/atmosphere environment, even though there was available soil water, it may not be accessible at a high enough rate to meet the evapo-transpiration demand due to the low soil hydraulic conductivity. At |h| = 1000 cm of water the estimated volumetric water content was 0.09 for the Ap/A layer and 0.10 and 0.14 for the Bt1/Bt2 and Bt3 layers (Fig. 5). On the other hand the unsaturated hydraulic conductivity was essentially zero (Fig. 6).
The drought tolerance of sorghum is due to morphological and physiological characteristics. Plants have an extensive laterally spreading fibrous adventitious root system, wax-coated leaves and the ability to stop growth in periods of drought and resume when conditions become favorable (Krieg, 1983). These crop characteristics, the considerations discussed in the previous paragraphs and the low rainfall depth per rainday make it reasonable to hypothesize that most of the root water uptake would probably take place in the upper Ap/A layers. If this were true, it would imply that the AET ought to be very close to the rainfall received over the growing period even if the same a(h) function were used in the root water uptake term of the Richards-based equation (Eq. 2).
| Fig. 7: | The mean and median rainfall, PET and AET totals over 120 days following 15 growing period start dates for sorghum over the 9 seasons (1981/82 through 1989/90). Bars indicate standard error of the mean |
This hypothesis was supported by the AET estimates shown in Fig. 7 which reasonably matched the 120-day rainfall totals with respect to the mean, standard error and median. The mean and standard deviation the 120-day AET totals in shown in Fig. 7 taken over all 15 start dates was 250±17 mm with range from 221 to 272 mm. This gives a mean and standard deviation of the ratio of the 120-day total of the AET estimates to the 120-day rainfall totals taken over all 15 start dates in Fig. 7 of 0.94±0.03 with a range of 0.90 to 1.0. For any given growing period start date in a given growing season, the AET/rainfall ratios can be artificially brought close to 1 if the allowance was made for bare soil evaporation thereby reducing the net rainfall input at the soil surface. The foregoing results indicate that some bare soil evaporation should have been included in calculating the AET estimates. However, there was no quantitative data on the evolution of Leaf Area Index (LAI) over time for traditionally grown sorghum in Botswana and the effect of LAI on soil evaporation. Clearly, direct experimentation is needed to further refine the parameters used for the soil water dynamics model in this study.
Agricultural Drought Measures
The choice of AET/PET = 0.3 as a baseline value of agricultural drought
intensity was based on the report of Doorenbos and Kassam (1979). Based
on the overall 120-day AET to PET ratio shown in Fig. 7,
this choice turned out to be somewhat low but was nevertheless reasonable.
The mean and standard deviation of the ratio of the 120-day total of the
AET estimates to the 120-day PET totals taken over all 15 start dates
in Fig. 7 was 0.37±0.01 with a minimum of 0.33
and a maximum of 0.39.
Descriptive statistics of the nine values of the 2, 4 and 6 consecutive day occurrences of AET/PET ≤0.3 for a given start date showed that there was a reasonably well defined correlation with the total seasonal rainfall. There were 3 seasons with the high rainfall namely1987/88 through 1989/90 with totals of 640, 691 and 549 mm, respectively. There were also 3 seasons with low rainfall namely 1983/84 through 1985/86 with totals of 323, 243 and 316 mm, respectively. The 2, 4 and 6 consecutive day occurrences of AET/PET ≤0.3 over the wet and dry seasons were therefore compared for the 15 growing period start dates and graphed in Fig. 8. Similarly, Fig. 9 shows the comparison of the agricultural drought days over the wet and dry seasons over the 15 start dates.
As would be expected, the mean occurrences when AET/PET ≤0.3 over the dry seasons were markedly higher and tended to be more variable than that over the wet seasons for all growing period start dates. The mean occurrences for the 3 dry seasons behaved similarly over the 15 start dates for all durations, but the values appeared to decrease with increasing duration in a non-linear manner. The same was true for the wet season means. Low mean occurrences for the wet season were apparent for start dates from day of year 335 (December 1) through 354 (December 20) but a minimum was not well-defined (Fig. 8). Agricultural drought day means were always < 0. As expected, means were more negative for the dry seasons for all start dates. Although there appeared to be some semblance of minimal values for both the dry and wet season means in relation to start date, these minima were weakly defined more so for the dry years than the wet years (Fig. 8).
For all measures examined, no single start date or range of start dates after end October appeared to produce a strong, well-defined minimum for either the dry or wet seasons. Interestingly, this result (Fig. 8 and 9) tends to confirm Botswana's subsistence farmers' lore that anytime in November and December was equally appropriate for preparing their fields for planting (Jones, 1987b, c). It is possible that further study over many more years of record would be more revealing, but we opine that this may not be assured. Zhou et al. (2005) established in their in-depth analysis of daily rainfall over Botswana that the annual and semi-annual harmonics account for less than 10% of the total variance in all the records. The annual rainfall over the growing season is effectively a continuation of the dry season punctuated by temporally and spatially random, short duration, convective rainstorms.
| Fig. 8: | Mean 2, 4 and 6 consecutive day occurrences of AET/PET = 0.3 for 3 wet and 3 dry years during 120 days following 15 growing period start dates for sorghum. Bars indicate standard error of the mean |
| Fig. 9: | Mean agricultural drought days over 3 wet and 3 dry years during 120 days following 15 growing period start dates for sorghum. Bars indicate standard error of the mean |
Consequently, fairly long runs of dry days occur throughout the rainy season (Zhou et al., 2005). Their duration and frequency of occurrence would depend on the wetness of the season as indicated by the total rainfall. Wetness is determined primarily by the proximity of the high pressure cells over the Atlantic Ocean to the west and Indian Ocean to the East and their limiting effect on the southward advance of the inter-tropical convergence zone. This explains why the agricultural drought measures developed in this study effectively segregated between the dry and wet seasons but were not definitively differentiated for the sliding 120-day windows (i.e., the growing period for a given start date) within the season.
The measures developed in this study were based on fundamental physical processes involved in the hydraulics of the soil-plant-atmosphere continuum, imbuing considerable generality and universality to the approach presented herein for quantifying post-establishment agricultural drought for subsistence sorghum in Botswana. In their entirety, the results and findings of this study therefore demonstrate the feasibility of using mechanistic modeling of soil-plant-atmosphere hydraulics to develop generally applicable quantitative measures of post-establishment agricultural drought for annual crop production under the mono-modal rainfall climate of semi-arid tropical eco-zones.