effect of sowing date distributions on simulation of maize yields … · 1270 mm and two rainy...

Agricultural Systems 147 (2016) 10–23

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Agricultural Systems

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Effect of sowing date distributions on simulation of maize yields atregional scale – A case study in Central Ghana, West Africa

Amit Kumar Srivastava ⁎, Cho Miltin Mboh, Thomas Gaiser, Heidi Webber, Frank EwertInstitute of Crop Science and Resource Conservation, University of Bonn, Katzenburgweg 5, D-53115 Bonn, Germany

⁎ Corresponding author.E-mail addresses: [email protected] (A.K. S

(C.M. Mboh), [email protected] (T. Gaiser), [email protected]@uni-bonn.de (F. Ewert).

http://dx.doi.org/10.1016/j.agsy.2016.05.0120308-521X/© 2016 Elsevier B.V. All rights reserved.

a b s t r a c t
a r t i c l e i n f o
Article history:Received 26 March 2015Received in revised form 12 May 2016Accepted 16 May 2016Available online xxxx

In sub-Saharan Africa, with its high rainfall variability and rainfed agricultural production system of maize (Zeamays L), the estimation of its sowing date is a crucial decision for farmers. To support decision making in rainfedagriculture, differentmethods using “probabilistic approaches” for the selection of the sowing dates at the region-al level has beendevelopedwheremost of the timeswe only have information about the probable sowing period.The crop model LINTUL5 embedded into a general modelling framework, SIMPLACE (Scientific Impact Assess-ment and Modelling Platform for Advanced Crop and EcosystemManagement) has been combined with a mul-tilayer soil water balance model (SLIM) to simulate maize yields in Central Ghana. Different assumptions aboutthe sowing date distributions at the regional level were compared to the corresponding deterministic ap-proaches. The simulated regional maize yields with the probability-based approaches showed always thelower RMSE compared to the deterministic approaches, although significant in all cases. The approach A4-S4,where we assumed that sowing dates are normally distributed around the sowing day estimated with a rainfallbased rulewere the best approach in capturing the spatial and temporal variability ofmaize yields at the regionallevel. The assumption of a probabilistic distribution of sowing dates within a given sowing period tends to be su-perior to deterministic sowingdate selection because the decisions about sowing dates are oftendriven by factorslike availability of labor, capital or seeds and are hencemuchmore complex than those assumed in existing cropmodels.

© 2016 Elsevier B.V. All rights reserved.

Keywords:MaizeSowing dateProbabilistic modelling, sub-Saharan Africa

1. Introduction

Ghana, one of the sub-Saharan African (SSA) countries is character-ized by low-input agriculture. Several studies have shown that SSA is aregion with very low yield and crop water productivity (Liu, 2009),being at the same timevery vulnerable to climate change impacts on ag-ricultural production (Fader et al., 2010). Crop yield simulations areoften not in agreement with reported yields and production of cropsfor regions with low yields such as Ghana. One reason for the poor per-formance of crop models is due to the fact that they are generally cali-brated for high-yielding cultivars, which do not reflect varietiesusually grown in low-yield regions (Gaiser et al., 2010). Other underly-ing reasons could be poor data availability regarding soil properties, soildistribution, the spatial distribution of crop specific sowing dates, fertil-izer application rate, and spatial distribution, fallow availability etc.Hence, it is essential to calibrate crop growth parameters to local condi-tions and crop management practices. In terms of agricultural manage-ment strategies, sowing date is known to be of central importance for an

rivastava), [email protected] (H. Webber),

accurate simulation of crop growth and agricultural productivity as theresponse of yield to sowing date fluctuates widely among environ-ments.Many studies have reported the impact of the sowingdate exclu-sively or in combinationwith othermanagement factors (Marteau et al.,2011; Sacks et al., 2010; Bondeau et al., 2007; Stehfest et al., 2007). InSSA, the sowing date estimation, which is closely linked to the onsetof the rainy season, is an important decision as it determines the lengthof the plant growing period in the season and therefore also related tothe choice of crop and cultivar to plant (Waongo et al., 2014). In general,sowing dates can be set for the simulation in two different ways. Eitherobserved sowing dates or estimated sowing dates can be used as inputinto the crop model. Observed sowing date data are usually not avail-able for large-scale analyses in SSA.

Various approaches have been developed to estimate crop sowingdates. Among them, rainfall based approaches are currently in use inSSA (Laux et al., 2008; Dodd and Jolliffe, 2001; Diallo, 2001). For thesemethods, rainfall amounts andwet- and dry-spell occurrences at the be-ginning of the rainy season have been a key variable in deriving the suit-able sowing dates (Waongo et al., 2014; Tachie-Obeng et al., 2013; Lauxet al., 2008). These rainfall drove rule-based approaches for derivingsowing dates are easy to implement and are currently being used for ag-ricultural decision support tool at the Burkina Faso Directorate Generalof Meteorology. However, these approaches are not crop specific,

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11A.K. Srivastava et al. / Agricultural Systems 147 (2016) 10–23

since information about crop type and phenology is not explicitly con-sidered (Waongo et al., 2014). Moreover, rainfall driven rule-based ap-proach alone cannot fully explain farmer's choices about when to planttheir crops. Sowing dates are also often estimated based on a set of rulesdepending on crop- and climate-specific characteristics such as cropwater and temperature requirements (Waha et al., 2012; Bondeau etal., 2007). This corresponds to an optimization against temperatureranges and water demand, which does not take farmer's preferencesinto account and neglects other factors like risk distribution, the waterholding capacity of soils. Moreover, outcomes, of the optimizationmethod are largely dependent on the cropmodel used, adding extra un-certainties to the outcomes.

Another common approach is to run the crop model for each monthin a year and choose the month with the highest yield (Liu, 2009;Stehfest et al., 2007). However, this approach has various limitations:(a) the temporal resolution is quite coarse; (b) sowing might not takeplace in the optimal season, especially in regionswith two growing sea-sons, which is often the case in regions close to the equator in SSA. De-pending on the cropmodel and the optimizationmethod, this approachcan be computationally time demanding. To simplify this approach, as-sumptions are usually made. For instance, Folberth et al. (2012) esti-mated sowing dates by employing a crop model at a monthly andweekly time step. They also limited the sowingdate computation periodby using earliest and the latest sowing dates provided at the national orsub-national levels. Laux et al. (2010) have used another approachwhere he combines crop model and rainfall distribution characteristicswhere sowing dates are derived using rainfall events fulfilling specificagronomic criterions. Subsequently, optimized sowing dates are de-rived from a crop model as per the objectives. Recently, Waongo et al.(2014) have derived optimal maize sowing dates using “fuzzy logic”membership functions using cumulative rainfall amount and the wet-and dry-spell lengths. In Sub-Saharan African countries, usually, thereis a lack of daily rainfallmeasurements at regional level due to less num-ber of weather stations; therefore, “fuzzy logic” approach to determin-ing the sowing dates has limited application in such a case as it is adata intensive approach.

Moreover, spatial and temporal variability in sowing dates alsoexists at the regional level as investigated in several studies(Rukandema et al., 2008; Chmielewski et al., 2004; Harrison et al.,2000; Stephens and Lyons, 1998; Rauniyar and Goode, 1992). This

Fig. 1. Map of Africa showing simulation units and the 16 d

variability in sowing dates at the regional level could be attributedto the following reasons:

i) Spatial and temporal variability of water availability in the soilduring the sowing period.

ii) Spatial and temporal variability of the harvest of the precedingcrops or limited machinery and labor capacity.

iii) Temporal and spatial variability in the availability of seeds orother inputs like fertilizers.

Hence, the assumption can be made that the sowing dates within agiven regions follow certain probability distributions. In this paper,therefore, we are testing the effect of a “probabilistic approaches” forthe selection of the sowing dates on crop yields at the regional levelwhere most of the times we only have information about the mostprobable sowing period. Our objective, therefore, is to analyze the effectof different assumptions about the sowing date distributions at theregional level on crop yields and compare it to selected deterministicapproaches. In this study, we focus on maize (Zea mays L) as a testcrop in the Ashanti and Brong-Ahafo regions (Fig. 1), which are amajor agricultural production area in Ghana.

2. Materials and methods

2.1. Study regions and simulation units

Ashanti Region is an administrative region in Ghana centrally locat-ed in the middle belt of Ghana. It lies between longitudes 0.15 W and2.25W, and latitudes 5.50N and 7.46N and occupies a total land surfacearea of 24,389 km2. The region has an average annual rainfall of1270 mm and two rainy seasons. The major rainy season starts inMarch, with a major peak in May. There is a slight dip in July and apeak in August, tapering off in November. December to February isdry, hot, and dusty. The average annual mean temperature is about27 °C. Much of the region is situated between 150 and 300 m abovesea level. Brong-Ahafo Region is also an administrative region inGhana centred around latitude 7.75 N and longitude 1.5 W, occupyinga total land surface of 39,557 km2. The region has a tropical climate,with high temperatures averaging 23.9 °C and a double maxima rainfall

istricts of Brong-Ahafo and Ashanti regions in Ghana.

12 A.K. Srivastava et al. / Agricultural Systems 147 (2016) 10–23

pattern. Rainfall ranges, from an average of 1000 mm in the northernparts to 1400 mm in the southern parts.

In this study, the simulations were run at 38 × 38 km grid cells(i.e., simulation unit) across the two target regions (Ashanti andBrong-Ahafo) (Fig. 1). There were 23 and 39 grids cells in Ashantiand Brong-Ahafo regions respectively. Information about datasources, procedures to generate the data in detail are explained inSection 2.3. Maize yield was calculated for each simulation grid forthe period of 16 years (1992–2007) and aggregated from the simula-tion grid to the district level for comparing them with the observedyields provided by the Agriculture Statistics & Census Division, Min-istry of Agriculture, Ghana.

2.2. Model description, calibration, and evaluation

LINTUL5, a bio-physical model that simulates plant growth, biomassand yield as a function of climate, soil properties, and cropmanagementusing experimentally derived algorithms, have beenwidely used in var-ious studies at the field, country, and continental scale (Trawally et al.,2015; Eyshi Rezaei et al., 2015; Zhao et al., 2015; Webber et al., 2015;Gaiser et al., 2013; Franke et al., 2013). The applied version LINTUL5simulates potential crop growth (limited by solar radiation only)under well-watered conditions, ample nutrient supply and the absenceof pests, diseases, andweeds (Wolf, 2012). Biomass production is basedon intercepted radiation according to Lambert-Beer's law and light useefficiency. The produced biomass is partitioned among various crop or-gans (leaves, stems, storage organs and roots) according to partitioningcoefficients defined as a function of the development stage of the crop.The phenology is simulated by the accumulation of thermal timeabove a defined base temperature. Photosynthesis and total cropgrowth rate are calculated bymultiplying the intercepted light and radi-ation use efficiency (RUE). Total crop growth, root-shoot partitioning,and leaf area expansion are further influenced by water stress. Thephysiological plant age in the model is defined by development stage,which is characterized by formation and appearance of various organs.The development stage is expressed in a dimensionless variable, havingthe value 0 at seedling emergence, 1 at flowering and 2 at maturity(Wolf, 2012). To simulate a continuous cropping system, themodel was embedded into a general modelling framework, SIMPLACE(Scientific Impact Assessment and Modelling Platform for AdvancedCrop and Ecosystem Management) (Gaiser et al., 2013). The

Table 1Crop parameters of LINTUL5 used in the study for Obatanpa (variety1) and Dodzie (variety 2)

Name Description

Crop parametersTSUM1 Temperature sum from emergence to anthesisTSUM2 Temperature sum from anthesis to maturityTBASEM Lower threshold temperature for emergenceTEFFMX Maximum effective temperature for emergenceTSUMEM Temperature sum from sowing to emergenceRUE-0.0 Radiation use efficiency at development stage 0RUE-1.25 Radiation use efficiency at development stage 1.25RUE-1.50 Radiation use efficiency at development stage 1.50RUE-1.75 Radiation use efficiency at development stage 1.75RUE-2.0 Radiation use efficiency at development stage 2.0SLATB-0.0 Specific leaf area at development stage 0SLATB-0.9 Specific leaf area at development stage 0.9SLATB-1.0 Specific leaf area at development stage 1.0SLATB-2.0 Specific leaf area at development stage 2.0LAI critical Critical leaf area beyond which leaves die due to self-RGRLAI Maximum relative increase in LAIROOTDI Initial rooting depthROOTDM Maximum rooting depthRRDMAX Maximum rate of increase in rooting depthTDWI Initial total crop dry weight

SIMPLACE b LINTUL5-SLIM N solution of the modelling platform wasused in this study. SLIM is a conceptual soil water balance modelsubdividing the soil in a variable number of layers, substituting thetwo layer approach in Lintul5 (Addiscott and Whitmore, 1991). Waterstress occurs when the available soil water is between a defined criticalpoint andwilting point or higher than the field capacity (water logging).The critical point is a crop specific valuewhich is calculated according toAllen et al. (1998) and depends on crop development, soil water tensionand potential transpiration. Water, nutrients (NPK), temperature, andradiation stresses restrict the daily accumulation of biomass, rootgrowth, and yield. Stress indices are calculated daily forwater andnutri-ent limitations and range from 0.0 to 1.0. The estimation of the daily in-crease in crop biomass, considers, on a given day, the maximum stressindex among water, nitrogen, phosphorus and potassium stress.Water stress occurs when available water in the soil is below crop-water demand. The same holds for nitrogen stress, that is, when cropavailable nitrogen in the rooted soil profile is lower than crop nitrogendemand.

In this study, two sets of maize cultivar (namely Obatanpa andDodzie) related parameters (Table 1) were calibrated against fielddata collected from field trials in Northern Ghana. The field experi-ments were conducted under rainfed conditions with differentmaize varieties and levels of NPK application. The Maize (Z. mays)crop parameter dataset (provided with the WOFOST model), wasused as a starting point to establish a new parameter set for twoMaize varieties namely Obatanpa (long-cycle variety) and Dodzie(short-cycle variety). TSUM1 (thermal time requirement for both va-rieties from emergence to anthesis) and TSUM2 (thermal time re-quirement for both varieties from anthesis to maturity) were fixedto values obtained from daily temperature observations. For theother parameters, a plausible range over which they vary was ob-tained from the literature (Ceglar et al., 2011; Boons-Prins et al.,1993). For the other parameters, a plausible range over which theyvary was obtained from the literature. By systematically sampling avalue from the range of each parameter, a set containing all the pa-rameters of the model was obtained and evaluated by comparingthe simulated above ground biomass, LAI and the phenology to thecorresponding observations. The systematic sampling and evalua-tion was performed for the entire parameter space of all variablesand the parameter set with the smallest mean residual error waschosen.

varieties of maize.

Unit Valuevar. 1/var.2

°C day-1 1060/970°C day-1 990/830°C 8.0°C 30.0°C 56.0g MJ-1 3.8g MJ-1 3.8g MJ-1 3.0g MJ-1 2.0g MJ-1 1.4m2 g-1 0.022m2 g-1 0.03m2 g-1 0.032m2 g-1 0.02

shading m2 m-2 4ha ha-1 day-1 0.02m 0.1m 1m 0.012kg ha-1 5


As a measure of accuracy to compare statistical data and simulatedvalues the following objective function was used (Papula, 1982):

a. The mean relative error MR as:

MR ¼ 1n

Xni¼1

yi−xið Þxi

ð1Þ

b. The mean residual error ME as:

ME ¼ 1n

Xni¼1

yi−xi ð2Þ

Where n is the sample number, x is the observed and y is the simu-lated value. A value of 0 of mean residual error (ME) indicates no sys-tematic bias between simulated and measured values. The meanrelative error (MR) gives an indication of the mean magnitude of theerror in relation to the observed value. Small values indicate little differ-ence between simulated and measured values.

2.3. Dataset for model calibration

The data was collected from the experiment conducted at two lo-cations in the Tolon/Kumbungu district, one of the 18 districts of thenorthern region of Ghana. The area lies within the interior northernsavanna agro-ecological zone (i.e. Guinea and Sudan savannahzones) of Ghana on latitude 9o 25′ 141″N, longitude 0o 58′ 142″Wand an average elevation of 183 m above mean sea level (Lawsonet al., 2008). The sites were the experimental field of the Savanna Ag-ricultural Research Institute (SARI) of the Council for Scientific andIndustrial Research (CSIR) at Akukayili and a farmer's field atCheshegu. The weather data was obtained from the CSIR-SARI mete-orology unit for Nyankpala. Treatments consisted of a factorial com-bination of twomaize genotypes and three (3) levels of fertilizer. Thetwo maize genotypes – Dodzie with 75 days maturity (D) andObaatanpa with 110 days maturity (OB) – used were obtained from

Table 2Soil physical and chemical properties at two sites Akukayili and Cheshegu characterized as Lix

Depth (m) BD (g/cm3) FC (cm/cm3) WP (cm/cm3) OC (%) NH

Akukayili0.1 1.43 0.17 0.08 0.31 0.20.2 1.49 0.17 0.09 0.33 0.20.3 1.43 0.15 0.06 0.35 0.10.4 1.50 0.17 0.10 0.36 0.10.5 1.50 0.18 0.12 0.26 0.10.6 1.46 0.21 0.14 0.33 0.10.7 1.50 0.21 0.15 0.29 0.20.8 1.50 0.23 0.17 0.34 0.10.9 1.51 0.24 0.17 0.31 0.11.0 1.53 0.24 0.17 0.56 0.1

Cheshegu0 1 1.38 0.17 0.07 0.38 0.10.2 1.40 0.17 0.07 0.32 0.10.3 1.41 0.18 0.08 0.35 0.10.4 1.42 0.20 0.10 0.34 0.10.5 1.46 0.21 0.11 0.33 0.10.6 1.43 0.22 0.15 0.28 0.10.7 1.53 0.13 0.08 0.30 0.20.8 1.51 0.19 0.14 0.31 0.10.9 1.51 0.18 0.12 0.3 0.11.0 1.52 0.18 0.13 0.29 0.1

BD= Bulk Density; FC = Field Capacity; WP = Wilting Point; OC = Organic Carbon.

the CSIR-Savanna Agricultural Research Institute in Nyankpala andallotted to main plots. The three (3) levels of fertilizer (0-0-0, 60-40-40 and 90-60-60 kg ha−1 Nitrogen (N), Phosphorous (P2O5)and Potassium (K2O) used for the experiment were allotted to thesubplots. Soils at Akukayili and Cheshegu were characterized asLixisol and Plinthosol respectively (Table 2).

2.4. Datasets used at regional level

2.4.1. Climate dataPrecipitation data as model input was derived from the Africa Rain-

fall Climatology Version 2 (ARC2) daily rainfall product (Novella andThiaw, 2012) at a resolution of 0.1°. This product has been developedfrom Eumetsat's Meteosat satellite data and GTS (Global Telecommuni-cations System) rain gauge data. To obtain daily rainfall for specificpoints in our study area, a piecewise cubic interpolation was performedon the ARC2 product. Available rain gauge-measured daily rainfall fromthree stations (Kumasi, Sunyani, and Wenchi) in the area of interestcompared well with the interpolation results (Fig. 2). For the net Globalradiation, we used data from Global Energy and Water Cycle Experi-ment (http://www.gewex.org/srbdata.htm) at a 1-degree spatial reso-lution. To get the net solar radiation for points in the study area foreach, the nearest neighbor interpolation was performed over the dailynet solar radiation product to achieve a resolution of 0.3125° (pointsin our study area are spaced at 0.3125° Longitude and Latitude). Asour region of interest is not too far from the equator (latitude 6.0885–8.5863° N), the net Solar Radiation for areas within a degree change oflatitude is not expected to vary very much. The nearest neighbor inter-polation from a 1° Dataset is, therefore, sufficient. For minimum andmaximum temperature, wind speed and relative humidity, the reanaly-sis data at ~38 km resolution provided by the National Centre for Envi-ronmental Prediction's Climate Forecast System Reanalysis (CFSR) wasused (Saha et al., 2010).

2.4.2. Soil dataValues for relevant soil parameters (sand, silt, clay, cation exchange

capacity, pH, organic carbon and bulk density) were extracted from thesoil property maps of Africa at 1 km × 1 km resolution (http://www.isric.org/data/soil-property-maps-africa-1-km). Other parameters suchas soil water at field capacity, wilting point, and saturation point, VanGenuchten parameters were computed (Rawls et al., 1993).

isol and Plinthosol respectively used for model calibration and validation in the study.

4 mg kg N03 mg kg Sand (%) Silt (%) Clay (%) Gravel (%)

3 6.15 57.8 31.9 10.3 33.01 4.32 59.8 25.9 14.3 39.07 2.14 61.8 29.9 8.3 41.89 2.40 57.6 22.2 20.2 57.59 2.32 49.6 22.2 28.2 71.08 2.19 41.6 24.2 34.2 68.51 1.80 39.6 20.2 40.2 68.06 1.50 39.6 18.2 42.2 63.92 1.21 39.6 16.2 44.2 61.85 1.22 41.6 16.2 42.2 58.8

9 3.31 62.0 31.0 7.0 16.07 2.59 62.0 31.0 7.0 11.06 1.83 58.0 33.0 9.0 13.06 1.99 54.0 33.0 13.0 15.07 2.12 54.0 29.0 17.0 23.37 2.14 36.0 21.0 43.0 81.00 1.99 56.0 23.0 21.0 89.77 1.59 39.8 17.9 42.3 87.14 1.21 41.8 19.9 38.3 88.84 1.22 41.8 19.9 38.3 85.9

http://www.gewex.org/srbdata.htmhttp://www.isric.org/data/soil-property-maps-africa-1-kmhttp://www.isric.org/data/soil-property-maps-africa-1-km

Fig. 2. Comparison of rain gauge measured and interpolated rainfall data in the crop growth period in the study a) Kumasi (16 years of data from 1992 to 2007 are plotted), b) Sunyani(9 years of data from 1999 to 2007 are plotted) and c) Wenchi (16 years of data from 1992 to 2007 are plotted).


2.4.3. Crop yield dataDistrict level maize yields (Mg ha−1) over 16 years (1992–2007)

from all the districts in the two regions (Ashanti and Brong-Ahafo)have been collected from Agriculture Statistics & Census Division, Min-istry of Agriculture, Ghana. As no significant trends in crop yield data(e.g., due to technological developments) from 1998 to 2007 could bedetected, no de-trending has been applied.

2.4.4. Data on maize varieties and fertilizer applicationTwo maize varieties were used in the study namely Obatanpa (a

long cycle variety) and Dodzie (short cycle variety) assuming that thefarmers use long cycle variety in the major rainy season and a shortercycle variety in the minor season. Low fertilizer application of

Fig. 3. Schematic representation of uniform probability distribution in which each sowingwindow is assigned an equal probability.

4.0 kg ha−1 and no irrigation as practiced by local farmers was applied(Tachie-Obeng et al., 2013; EarthTrends, 2003).

2.5. Approaches for crop sowing date estimation

The sowingperiod (i.e., fromonset to the endof sowing) ofmaize formajor and minor sowing seasons were extracted from crop calendarprovided by FAO (2010) database. The sowing period for both thesowing seasons stretches out to about 52 days. We divided the entiresowing period into five equal sowing windows (refer Fig. 3).

Approach 1 (A1): Mean date of the region specific sowing period.Approach 2 (A2): Rule-based sowing within the sowing window(The first day of a spell of 7 days in which at least 20 mm of rainfalls, on condition that no dry period of N7 days occurs in the follow-ing 30 days).Approach 3 (A3): Optimal sowing date based on maximum yieldachieved.Approach 4 (A4): Probabilistic distribution of sowing dates withinthe sowing window. Four scenarios of this approach have been test-ed, are as follows:Scenario 1 (A4-S1): Sowing dates having uniform probability distri-bution: The assumption is that the occurrence of each sowing datewithin the sowing range has equal probability.Scenario 2 (A4-S2): Sowing dates having normal probability distri-bution: The assumption is that the occurrence of sowing withinthe sowing window is normally distributed with the mean of thedistribution in the middle of the sowing window.Scenario 3 (A4-S3): The sowing window with the maximum simu-lated yield in the respective year k (as in approach A3) is assignedto have the highest probability in year k.

Fig. 4. Schematic representation of Gaussian probability distribution (a, b, c, d, and e) inwhich thefirst, second, third, fourth andfifth sowingwindows are respectively assigned thehighestprobability.


Scenario 4 (A4-S4): The sowingwindowwith the simulated yield inyear k estimated from the Rule based approach (i.e., A2) has thehighest probability in year k.

2.6. Analysis method

The performance of the approaches for the crop sowing date estima-tion was evaluated by comparing the simulated outputs for the years1998 to 2007 to the observed yields for the same time period assumingfarmers practice low-input agriculture with low fertilizer applicationrates and no irrigation.

As crop yields are sensitive to sowing date, the yield Yk of a district ina particular year will depend on the proportion of the surface areaplanted within each sowing window. As all farmers are unlikely toplant on the same date, in this paper we investigate the effect of differ-ent sowing distributions on the simulated crop yield. For approaches A1,A2 and A3 simulated yields were aggregated at the district level andcompared to the observed yields. For Approach A4, the whole sowingperiodwas divided into 5windows and the four scenarios of probabilis-tic distribution were used to calculate the yield per year as follows (Fig.4):

Yk ¼X5i¼1

MiPi ð3Þ

Table 3Observed and simulatedAboveground biomass (AGB), Grain yield , Day of Anthesis (DOA), Dayof replicates for the Obatanpa and Dodzie variety in the two sites of central Ghana namely Aku

Site Variety Treatment N DOAObserved

DOASimulated

DOMObserved

DOMSimulated

GrOb(M

Akukayili Obatanpa Control 4 59 56 103 103 0.3Fertilized 4 56 56 103 103 2.6

Dodzie Control 4 55 52 92 92 0.2Fertilized 4 51 52 92 92 2.1

Cheshegu Obatanpa Control 4 60 56 111 103 0.3Fertilized 4 56 56 111 103 2.7

Dodzie Control 4 54 52 91 92 0.2Fertilized 4 50 52 91 92 2.0

Pi ¼ f iX5n¼1

f i

!−1ð4Þ

f i ¼1

σffiffiffiffiffiffi2π

p e−Xi−μð Þ2σ2

2

ð5Þ

where,

Yk simulated Crop yield in the kth year (Mg ha−1)Mi average yield of the ith sowing window (Mg ha−1)Pi Probability assigned to the ith sowing windowfi Gaussian probability density of the ith windowXi the score of the ith windowμ assumed mean of sowing windows score or score of sowing

window of highest probabilityσ assumed standard deviation of sowing windows score.

The probability assigned to a specific window (Pi) in this context re-fers to an assumed proportion of the surface area planted with maizewithin this window relative to the total surface area of a district. To cal-culate the assumedprobability of eachwindow from theGaussian prob-ability density function (Eq. (5)) scores were assigned to each windowsuch that the central score is 0. That is −2,−1, 0, 1 and 2 was respec-tively assigned for windows 1 to 5 (Fig. 4). In addition to that, we alsoassumed a constant standard deviation of 1 for the sowing window.

ofMaturity (DOM),mean residual error (ME), andmean absolute error (MR), N=numberkayili and Cheshegu.

ain Yieldservedg ha-1)

Grain YieldSimulated(Mg ha-1)

MEGrainYield(Mgha-1)

MRGrainYield

AGBObserved(Mgha-1)

AGBSimulated(Mgha-1)

ME AGB(Mgha-1)

MRAGB

1.0 0.7 2.3 2.4 1.8 −0.6 −0.253.5 0.9 0.3 6.7 6.4 −0.3 −0.04

2 1.0 0.8 3.5 1.42 1.62 0.2 0.142.6 0.5 0.2 5.5 5.1 −0.4 −0.071.1 0.8 2.7 2.12 2.08 −0.04 −0.023.3 0.6 0.2 6.7 6.2 −0.42 −0.060.9 0.7 3.5 1.3 1.7 0.4 0.312.4 0.4 0.2 5.1 4.7 −0.4 −0.08

Fig. 5. Observed and simulated leaf Area Index (LAI) of Obatanpa and Dodzie varieties for the two sites Akukayili and Cheshegu in central Ghana under fertilized and control productionsystem.


This means a deviation of 1 sowingwindow relative to the sowingwin-dow of highest probability of sowing is assumed. The different distribu-tions were obtained by varying the mean of the Gaussian probability

density function (Eq. (5)). For instance, if−2 (the score of the first win-dow) is chosen as themean (score of highest probability), a distributionin Fig. 4a is obtained. Likewise, considering−1 (the score of the second

Fig. 6. The Simulated yield of maize variety Obatanpa in five different sowing windows at four districts in Ghana (Ejura, Kintampo North, Kumasi, and Sunyani).


window) as the mean, a distribution skewed towards the second win-dow is obtained as in Fig. 4b. Hence adopting the score of a specific win-dow as the mean gives a distribution in which that window has thehighest probability. Fig. 3 illustrates the case of scenario 1, where a uni-form distribution is assigned to all sowing windows. Fig. 4c illustratesthe scenario 2 where a normal Gaussian distribution is always assignedacross the sowingwindows. For scenario 3 either the distribution in Fig.4a,b,c,d, or e can be used for calculating district yields depending onwhether the first, second, third, fourth, or fifth sowing window respec-tively has themaximum simulated yield. Figs. 3 and 4 enable readers tograsp the connection sowingwindow scores and the different probabil-ity distributions tested. These figures help the readers to understandEqs. (3) to (5) in the context of sowingwindowdistributions.Moreover,without these figures equations, 3–5 will not be very meaningful to areader without a sound background in elementary probabilityprinciples.

The agreement between simulated and observed yield was statisti-cally evaluated using root mean square error (RMSE). The minimumvalue of RMSE which is 0 indicates that simulated and measured valuesare identical.

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xni¼1

Si−Oið Þ2vuut

where, Si and Oi are the simulated and the observed values and n is thenumber of observations.

3. Results

3.1. Model calibration and evaluation

Yields of two maize varieties Obatanpa (a long cycle variety) andDodzie (a short cycle variety) on two contrasting soil types, under fertil-ized and unfertilized conditions during the year 2011, were simulatedwith the parameterized LINTUL5 model. For both the varieties, the ob-served and simulated day of anthesis and day of maturity under fertilizedand control (unfertilized) production treatments agreed well with an ex-ception for Obatanpa in Cheshegu, where model underestimates the dayof maturity by 8 days under both fertilized and control production treat-ments (Table 3). The simulated and observed Leaf Area Index (LAI) forboth varieties agrees well under fertilized and control production treat-ments in both the sites (Fig. 5). The mean of simulated aboveground bio-mass agrees very well under fertilized treatments in both the siteswhereas, under unfertilized (control) treatments the discrepancy be-tween simulated and observed values varies from 2% to 31% for boththe varieties across the sites and treatments. The simulated yield wasoverestimated by 20–30% under fertilized condition for both the varietiesand sites, whereas, the model did not capture the grain yield under con-trol condition as observed grain yield was exceptionally low.

3.2. Model sensitivity to the sowing dates

To examine the sensitivity of themaize yields to the choice of the sow-ing dates, the yield of maize varieties (Obatanpa and Dodzie) was

Fig. 7. The simulated yield of maize variety Dodzie in five different sowing windows at four districts in Ghana (Ejura, Kintampo North, Kumasi, and Sunyani).


simulated using the SIMPLACE b LINTUL5-SLIM N modelling solution foreach of the five sowing windows for 16 districts in Ghana, over a periodof 16 years (1992–2007). Figs. 6 and 7 shows the sensitivity of the simu-lated yield of bothmaize varieties to sowing dates for four of the districts

Table 4Root mean square error (RMSE in Mg ha−1) and R2 values of different approaches of sowing d

R RMSE (Mg ha-1) of approaches for sowing date estimation

Districts A1 A2 A3

RMSE R2 RMSE R2 RMSE R2

Ahafo Ano South 0.26 0.4 0.28 0.3 0.62 0.7Amansie West 0.46 0.5 0.44 0.5* 0.77 0.8Asante Akim North 0.48 0.5 0.54 0.5* 0.58 0.6*Asante Akim South 0.35 0.4 0.29 0.3 0.65 0.6Asunafo North 0.31 0.3 0.31 0.3 0.42 0.4Asutifi 0.40 0.5 0.37 0.5 0.76 0.8Atebubu-Amantin 0.43 0.5* 0.45 0.5 0.46 0.6Atwima 0.29 0.3 0.30 0.3* 0.50 0.5*Dormaa 0.41 0.4 0.47 0.4 0.36 0.4Ejura Sekyedumase 0.39 0.4 0.37 0.3* 0.75 0.8Kintampo North 0.45 0.5 0.53 0.5* 0.29 0.4Kumasi 0.40 0.4 0.31 0.4* 0.71 0.7Offinso 0.28 0.3 0.35 0.3 0.65 0.6*Sekyere East 0.25 0.3 0.28 0.2* 0.51 0.5Sunyani 0.22 0.6 0.28 0.6 0.54 0.8Tano North 0.38 0.4* 0.40 0.4* 0.54 0.5Sum of RMSE 5.78 5.95 9.12Average of RMSE 0.36 0.37 0.57

R2 values with * are significant at p ≤ 0.05.

and four years. For a representative sample of the whole study area, thefour districts were chosen from the north, south, west and east of ourstudy area respectively. Figs. 6 and 7 clearly show that the yields vary spa-tially across the districts and temporarily within each district. The Dodzie

ate estimation in the 16 districts of Ghana over 16 years (1992–2007).

A4-S1 A4-S2 A4-S3 A4-S4

RMSE R2 RMSE R2 RMSE R2 RMSE R2

0.26 0.3 0.26 0.4 0.34 0.4 0.24 0.30.46 0.5 0.47 0.5 0.56 0.6 0.39 0.40.48 0.5* 0.48 0.5* 0.47 0.5* 0.53 0.5*0.33 0.3 0.33 0.3 0.42 0.4 0.29 0.30.31 0.3 0.31 0.3 0.30 0.3 0.35 0.40.40 0.5 0.41 0.5 0.48 0.6 0.36 0.40.38 0.5* 0.38 0.5* 0.37 0.5* 0.45 0.5*0.26 0.3* 0.27 0.3* 0.35 0.3* 0.20 0.2*0.38 0.4 0.38 0.4 0.34 0.3 0.45 0.50.34 0.3* 0.35 0.4* 0.44 0.4 0.28 0.3*0.48 0.5 0.47 0.5 0.40 0.5 0.52 0.50.32 0.3 0.33 0.3 0.40 0.4 0.29 0.3*0.30 0.3 0.31 0.3 0.36 0.4 0.24 0.20.22 0.2* 0.23 0.2 0.30 0.3 0.17 0.2*0.24 0.6 0.25 0.6 0.32 0.6 0.21 0.50.34 0.3 0.34 0.3 0.37 0.4 0.36 0.45.52 5.57 6.23 5.330.34 0.35 0.39 0.33

Fig. 8. Comparison of Observed and simulated maize yield in 16 districts of Ghana over 16 years under approach A1 versus A4-S2.


variety of maize is seemingly more sensitive to sowing date than theObatanpa variety. The spatial average of the highest attainable yield is1.84 Mg ha−1 compared to the mean observed yield of 1.46 Mg ha−1.These discrepancies in the performance of the LINTUL5-SLIM modelcould be an indication of the poor assessment of the soil and crop waterstatus during the reproductive and maturation critical phases. Model re-sponses are quite dependent on parameters such as soil water holding ca-pacity and rooting depth, none of which were measured. Hence, thediscrepancies may be related to the quality of input data. While our sim-ulations suggest that the two varieties ofmaize exhibit differences in theirsensitivity to sowing date (Figs. 6 and 7),we, however, have no separatelyobserved yields for each variety. Averaging both varieties and comparingwith the observed yields may lead to discrepancies in districts where aparticular variety is dominantly cultivated.

3.3. Comparative analysis of sowing date approaches

Maize yields were simulated with different approaches of sowingdate estimation (for details of approaches, refer Section 2.5) for 16

districts in Ashanti and Brong-Ahafo regions in central Ghana for thetime period of 16 years (1992–2007) and compared to the respectiveobserved yields. Root mean square error (RMSE) values of simulatedmaize yield were used to compare the performance of different ap-proaches. In general, the approach A4-S4 of estimating the sowingdates across the districts was best as simulated maize yield agree wellto the observed yields resulting in the lowest RMSE value of5.33 Mg ha−1 (Table 4). However, pairwise comparison of RMSE valuesof all the approaches using Fisher's LSD (Least Significant Difference)test shows that they are not significantly different from each other ex-cept approach A3 (significance was regarded at 0.05 level). Figs. 8, 9and 10 graphically illustrate the pairwise comparisons. The compari-sons were chosen to compare the deterministic methods with a corre-sponding probabilistic method in which the window chosen by thedeterministic method is assigned the highest probability. The objectivewas to underscore the errors whichmight arise in ignoring the fact thatall farmers cannot plant on a specific date as supposed by the determin-istic approaches. Because of difference in farmer behaviour and timeavailability, sowing is expected to follow some form of a distribution

Fig. 9. Comparison of observed and simulated maize yield in 16 districts of Ghana over 16 years under approach A2 versus A4-S4.


over a region. Bymaking these comparisons we suppose that the deter-ministic methods represent at best themean behaviour of such a distri-bution and that the distribution of sowing dates is Gaussian.

Comparing the approach A1 with A4-S2, we found that A4-S2 cap-tured well the spatial and temporal variability of maize yields inGhanadistricts (Fig. 8). The approachA4-S2 performed better or equallywell in 11 out of 16 districts showed in the lower RMSE values com-pared to the RMSE values estimated for approach A1 (Table 4). Table 5also indicates that approach A4-S2 performed better or equally goodin 13 out of total 16 years temporarily compared to approach A1. Bycombining probabilistic approach with approach A1, a reduction of0.21 Mg ha−1 in RMSE was estimated in absolute terms across the dis-tricts. Similarly, approach A4-S4 better captured the observed maizeyields across all the districts when compared to approach A2 (Fig. 9).The RMSE was reduced by 0.62 Mg ha−1 using probabilistic approach(A4-S4) compared to the A2 approach (Table 4). While comparing ap-proach A3 with A4-S3 (Fig. 10), the observed yields were better cap-tured in all the 16 districts by using approach A4-S3 (Table 5) asRMSE was reduced by 3.02 Mg ha−1.

4. Discussion

When comparing the different approaches, probability-based ap-proaches (i.e., A4-S1; A4-S2 and A4-S4) except A4-S3 tend to performbetter than the deterministic approaches A1, A2 and A3 as the formerhave lower RMSE values than the latter (Table 4). The higher RMSEvalues ofmethods A3 andA4-S3 could be attributed to the optimistic as-sumption that all the farmers in a certain region planted during optimalsowing conditions (i.e., in a sowing window where the simulated yieldis highest). This may not be the case because such a scenario entails thatfarmers have a good knowledge of optimal sowing conditions. In sub-Saharan Africa, a good proportion of farmers is peasants with a basicknowledge of optimal agronomic conditions for sowing. Most farmerstend to rely on agronomic knowledge transferred from their ancestors.In precipitation-limited regions, sowing generally occurs around thestart of the rainy season. In particular, maize is usually planted whenmonthly average precipitation reaches 80–140 mm month−1 (Sackset al., 2010). However, there is considerable spread in these relation-ships between sowing date and precipitation, which, therefore,

Fig. 10. Comparison of Observed and simulated maize yield in 16 districts of Ghana over 16 years under approach A3 versus A4-S3.


overemphasizes the difference between regions and hence suggests,using precipitation driven rule-based approaches for estimating sowingdates at a regional scale with care. Sacks et al., 2010 reported a case ofnorthern Nigeria where maize is generally planted in May and June, co-inciding with the start of the rainy season there, but a more detailedstudy showed that even within small areas, sowing dates could varysubstantially between farmers. In addition to climatic factors, other ag-ronomic factors influence sowing date decisions, especially in precipita-tion-limited regions. Despite the similar time of rain onset, sowing datescan differ between places due to farmer's family size. Farmerswith largefamilies can plant earlier because of greater availability of labor. Finally,farmers plant about aweek earlier if they are planning to grow a secondcrop after the main maize crop (Hassan, 1996). Therefore, the assumedclimatic relationships canmask the true drivers of sowing decisions. Thetimingof the rainy season places a broad constraint on sowingdates, butagronomic, socio-economic and cultural factors can shift sowing datesby a month or more from what might be expected based on climaticconditions alone (Sacks et al., 2010). Adding further to the limitationsof climate-based approaches, it only addresses the ‘main’ growing

season of a particular crop, not the ‘secondary’ growing season in a dou-ble-cropping system which is frequently a case with Sub-Saharan Afri-can cropping systems.

The results obtained in this study also indicate that the estimation ofsowing dates at the regional level is not solely driven by climatic factors(approach A2). The best estimates of sowing dates are obtained by com-bining the A2 approach and the probabilistic approach (i.e., A4-S4)resulting in lowest RMSE value of 5.33 compared to 5.95 obtainedusing approach A2 solely. This outcome indicates that most of thefarmers in central Ghana wait for the first rain events within the usualsowingperiod receiving at least 20mm(within a spell of 7 days) for car-rying out the sowing. However, due to reasons of labor availability orother constraints as discussed above, many farmers are not able tosow all their plots at this optimal date and on many plots, the sowingis delayed. Thus, by introducing a spread of sowing dates around the op-timal sowing date in terms of rainfall, the probability approach can im-prove the simulatedmaize yield across the regions. A previous study forthe Sahel evaluated different local and regional climatic criteria for sow-ing dates using a high potential yield millet variety with constant cycle

Table 5Root means square error (RMSE in Mg ha−1) value of different approaches of sowing date estimation in 16 years of simulation across all 16 districts.

RMSE (Mg ha-1) of approaches for sowing date estimation

Years A1 A4-S2 A2 A4-S4 A3 A4-S3

1992 0.48 0.47 0.61 0.33 0.88 0.551993 0.34 0.31 0.36 0.32 0.48 0.321994 0.64 0.58 0.54 0.54 0.86 0.661995 0.42 0.39 0.34 0.38 0.67 0.471996 0.29 0.29 0.32 0.29 0.58 0.351997 0.32 0.33 0.44 0.34 0.46 0.341998 0.33 0.20 0.29 0.18 0.53 0.261999 0.39 0.36 0.33 0.39 0.40 0.332000 0.22 0.21 0.21 0.21 0.40 0.222001 0.34 0.34 0.39 0.36 0.58 0.372002 0.33 0.31 0.31 0.34 0.45 0.322003 0.31 0.31 0.31 0.33 0.44 0.322004 0.27 0.27 0.31 0.27 0.49 0.322005 0.40 0.42 0.43 0.45 0.58 0.452006 0.42 0.40 0.37 0.40 0.68 0.452007 0.34 0.38 0.41 0.36 0.70 0.44Sum of RMSE 5.82 5.58 5.97 5.49 9.19 6.17Average of RMSE 0.36 0.35 0.37 0.34 0.57 0.39


and highlighted a strong sensitivity of yields to the choice of sowingdate (Sultan et al., 2005). Waha et al., 2012 also found that close agree-ment between simulated and observed sowing dates of maize for largeparts of temperate regions where mechanization of sowing is predomi-nant can be realized based on climatic conditions only. However, theagreement is poor in tropical regions where, despite a possible season-ality, climatic conditions are favorable throughout the year, and in re-gions characterized by multiple-cropping systems.

The investigation of the relationships between the onset and thesowing dates raises several important issues. The onset date is equivocalsince several definitions exist at different scales (Marteau et al., 2011)and its estimation always needs subjective tuning (namely amount ofrainfall and length of the initial wet spell, length and intensity of post-onset dry spell, etc.). The relationships between sowing and onsetdates on one hand and yield variability, on the other hand, are evenmore complicated. We cannot estimate the intra-districts variance ofrainfall, but can be hypothesized that a large fraction of the intra-dis-tricts variance in yields is not directly related to the rainfall variabilitybut could be to the biotic factors or soil fertility.

Among other assumptions made in the simulation study, model cal-ibration was carried out based on the field experiment data of only twomaize varieties, which generally makes available reference data forlarge areas. Hence, this study can be significantly refined by interactingwith local experts so that well-adapted cultivars could be simulated asopposed to the idealized types simulated within this exercise. Produc-tion systems were abstracted at the level of a single crop, ignoring pos-sible interactions within crop rotations. If cropping systems wereanalyzed instead, crop performance in a given simulation unit wouldresult from its performance in different rotations and under different in-puts of resources. Additionally, we assumed that the fertilizer applica-tion rates were uniformly distributed across the regions which mayhave substantial effect on temporal and spatial variability of crop yields.

Besides the aforementioned assumptions, the physical inconsistencyemanating from the combination of multiple sources of meteorologicalvariables is another source of uncertaintywhichmight affect the results.

5. Conclusion

A new approach to derive crop sowing dates at the regional scale ispresented and applied for the first time to maize crop in West Africa.By analyzing different approaches to estimating sowing dates at the re-gional scale, we have found that the decisions about sowing dates areoften driven by factors that aremuchmore complex that those assumedin existing cropmodels. Probability approach A4-S4,wherewe assumedthe rainfall based estimated sowing dates are normally distributed,

resulted in best approach capturing the spatial and temporal variabilityof maize yields at the regional level. The prediction could substantiallybe improved if farmers can supply the data related to the crop varietiessown (so that we can have an idea about variety distribution across theregion) and the crop management (fertilizer application rates).

Acknowledgements

Work carried out under the project BiomassWeb of GlobeE. Fundingby FederalMinistry of Education and Research (BMBF) (FKZ 031A258B)is highly acknowledged. We also extend our thanks to Dr. Wilson AgyeiAgyare from Kwame Nkrumah University of Science and Technology,Kumasi, Ghana for providing maize yield data at regional scale.

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Effect of sowing date distributions on simulation of maize yields at regional scale – A case study in Central Ghana, West A...1. Introduction2. Materials and methods2.1. Study regions and simulation units2.2. Model description, calibration, and evaluation2.3. Dataset for model calibration2.4. Datasets used at regional level2.4.1. Climate data2.4.2. Soil data2.4.3. Crop yield data2.4.4. Data on maize varieties and fertilizer application

2.5. Approaches for crop sowing date estimation2.6. Analysis method

3. Results3.1. Model calibration and evaluation3.2. Model sensitivity to the sowing dates3.3. Comparative analysis of sowing date approaches

4. Discussion5. ConclusionAcknowledgementsReferences

effect of sowing date distributions on simulation of maize yields … · 1270 mm and two rainy...

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