Agrometeorological and Soil Criteria for Defining Workable Days for Rational Mechanized Sugarcane Harvest in Southern Brazil

The number workable days (NWD) for agricultural field operations is of great importance for sizing agricultural machinery fleets. This is especially pivotal for sugarcane harvest, which extends from 8 to 10 months/year. In light of this, the current study aimed at defining criteria for obtaining the NWD for rational sugarcane harvest at different sites in the state of São Paulo, southern Brazil, taking into account both a general and a specific criteria. For this purpose, data from harvest interruption of 30 sugar mills in southern Brazil throughout periods ranging from two to five years were used. The following variables were tested as criteria for defining harvest interruption: minimum precipitation (PREC); soil water holding capacity (SWHC); and the limit of the ratio between actual soil moisture (SM) and SWHC. Based on such a specific criterion ascribed to each site along with a general criterion, NWD maps were prepared for the state of São Paulo, Brazil. The results showed that there were variations from the definition criteria of NWD at the different sites in the state. However, the use of a general criterion for harvest interruption, based on PREC ≥ 3 mm, SWHC = 40 mm and SM/SWHC ≥ 90%, provided accurate results. During the validation of these criteria, the NWD maps generated from the individual criterion proposed for each site resulted in an average error of 24.9 days/year, whereas the map generated from the general criterion culminated in an average error of 4.4 days/year.


Introduction
The study of workable days for the completion of field operations with agricultural machinery and implements turns out to be of extreme importance to minimize possible impacts of machinery traffic on soils whenever they contain high moisture contents in order to prevent soil compaction [1] [2].
The climatic study dealing with the frequency of suitable days to diverse works with agricultural machinery has been done on the basis of meteorological historical data and soil information, providing technical support to planning, selection and rationalization of mechanized field operations, although such a strategy is not always taken into account at the stage of fleets' sizing [3].
In the sugar-energy industry sector, fleets' sizing has been done based on economic and logistic criteria without, however, taking into consideration how many effective days are suitable for field activities. Thus, in order to size the number of agricultural fleets necessary for a given activity or available effective time for such machinery to perform a specific operation, it is pivotal to scrutinize soil water content and also its influence on such a field operation. This defines the actual magnitude of how many effective workable days are to be considered in the crop growing season for such an operation.
Under the current high-intensity agriculture model, it is indispensable that the growers acquire some knowledge of actual time availability for the performance of field operations throughout crop growing seasons [4] [5]. This is the first step to obtaining the greatest efficiency in the execution of these operations, which are subjected to variations in local meteorological conditions, mainly rainfall regimes. Rainfall and its influence on soil water status at a given site directly impinged upon the number of available days for work with agricultural machinery [6] [7].
According to [8], a simple empirical analysis of dry days within a long-term precipitation series already provides useful information for plenty of agricultural applications. Duration of dry periods is an important input variable to define management strategies of agricultural practices, such as soil preparation, sowing and harvest planning, fertilizer application and phytosanitary control. Nevertheless, information regarding soil water availability is also crucial, since the main problem caused by indiscriminate traffic of machinery in the fields is soil compaction, which in turn depends directly on soil moisture conditions [1].
The criteria for determining workable days for field operations at Central Nigeria, Africa, were proposed by [9]. These authors found a good agreement between observed and estimated workable days by assessing a 30-cm soil layer in conjunction with soil water storage less than 95% of available water capacity plus daily rainfall below 5 mm. Similarly, the number of days potentially useful for work with forest machinery as a function of soil water balance at Guanhães, MG, Brazil, was determined by [10]. cordance with the field operation to be carried out. The following criteria were used by [11] for assessing workable days for soil preparation and management: precipitation of the day lower than 5 mm along with a limit of the ratio between actual soil moisture (SM) and soil water holding capacity (SWHC) between 40 and 90%. According to these authors, the number of workable days varied from place to place and also from season to season, with a predominance of 11 to 20 workable days per month at Piracicaba, SP, Passo Fundo, RS, and Dourados, MS, whereas at Londrina, PR, a lower number of workable days of up to 10 days per month throughout the year prevailed. Similar criteria to those employed by [11] were utilized by [6] for determination of the probability of workable days for rice cultivation in Southern Brazil. On the other hand, [12] just used the ratio between SM and SWHC of 80% in a computational system to predict workable days for several field operations in Sudan.
Several studies report methodologies for determining the number of workable days, with the majority of them reported by [2]; however, in most cases such methodologies are solely regionally applicable and were not always validated by means of observed data obtained from production fields. Also, São Paulo State, Brazil, does not possess a full analysis of the determination of the number of workable days for mechanized harvest of sugarcane. This emphasizes the importance of a scientific study in order to assist mechanized harvest planning to be adopted by many sugarcane-mills that are installed all over the state.
Thus, the hypothesis of the current research was to verify whether it is possible to develop site-specific and/or general criteria for the definition of workable days to carry out the mechanized harvest of sugarcane in Southern Brazil by means of local meteorological data in conjunction with information on soil type and water balance. The aim of the current study, therefore, was to propose agrometeorological criteria, both site-specific and general ones, for the estimation of the number of workable days (NWD) for the mechanized harvest of sugarcane, as well as to validate such criteria by comparing estimated NWD with independent observed values obtained from sugarcane mills at different sites in the State of São Paulo, Brazil. Based on the criteria defined in this study, mapping of the mean NWD for mechanized harvest of the crop was also elaborated in order to assist the scaling of harvesters.

Material and Methods
For the definition of agrometeorological criteria aimed at determining the NWD for the mechanized harvest of sugarcane in the State of São Paulo, Brazil, data on grinding interruption hours due to rainfall from 30 sugarcane mills allotted within the State (Figure 1) was collected. Grinding interruption hours due to rainfall are highlighted by the industry; however, this type of stoppage only occurs whenever there is interruption of harvest in the field. Therefore, it was assumed that grinding interruption at the cane mills depicting a suspension of harvest in the field was a plausible assumption, as well as the resumption of  Figure 1 shows the distribution of sugarcane mills which provided data on grinding interruption due to rainfall. It was observed that there is an excellent distribution of these mills, representing the great majority of sugarcane-producing areas in the State of São Paulo. Further in Figure 1, 23 sites are presented where cane mills are located, which indicates that there were locations that hosted more than one single cane mill. Daily data of stoppage hours due to rainfall were grouped into monthly hours. After the summation of total monthly hours with stoppage, the total was divided by 24 hours in order to determine throughout the month how many equivalent days were not taken as workable due to the occurrence of rainfall along with high soil moisture conditions. The determination of the number of workable days throughout the month was obtained by means of subtraction of the overall days computed during the crop growing season for each month in relation to stoppage days. Such data were referred to as the observed  To determine effective soil water status, a sequential climatological water balance (WBSeq) approach was applied in accordance with the method proposed by [13], similarly to what was done by [4]. Firstly, WBSeq on a daily basis scale was elaborated for all the sites under scrutiny (Figure 1) [19]. According to [7] and [20], meteorological information generated by gridded climate data set was satisfactory to represent the water balance and the trafficability conditions for field operations.
In order to come up with the best criterion for determining the NWD for the mechanized harvest of sugarcane, 27 combinations were taken into account by employing: three precipitation thresholds (PREC); three thresholds of the relationship between actual soil moisture and soil water holding capacity (SM/SWHC); and three levels of SWHC (Table 1). This kind of analysis was only made for the sugarcane harvest periods when stoppage hours due to rainfall were reported by the sugar mills.
Variations of SWHC aimed to simulate the combination of different soil types or root depths under compaction effects. Thus, a SWHC = 40 mm was adopted as the representative of a sandy loam soil or shallow depth, a SWHC = 80 mm for an intermediate soil texture or medium depth, and a SWHC = 120 mm for a clay loam soil or deep soil. The definition of thresholds for PREC and SM/SWHC for a given day to be considered as a workable day was made on the basis of the contributions published by [6] [11] [21].
On the basis of the criteria illustrated in Table 1, a set of the combination of To define the best criterion for determining NWD a comparative analysis between monthly values observed at sugarcane mills (NWD Obs) and estimated from the criteria presented in Table 1 (NWD Est) was made. The performance of NWD estimates was assessed by means of the following statistical parameters: mean error (ME); mean absolute error (MAE); Willmott agreement index (d) revealing exactness of the estimates; coefficients of determination (R 2 ) and Pearson correlation (r) which indicate precision or accuracy of the estimates; and performance index (C) proposed by [22].
Statistical analyses were made with the software R, whereas elaboration of graphs was performed by making use of the software Statistica 11.0. From the results obtained, the best three models associated with the lowest MAE for each site were classified. In case of a MAE tie, we took into consideration the C index to make a decision, which in turn is calculated by the product between d, proposed by [23], and r.
After evaluation of the three best models by means of statistical analyses, a creation function of Box Plot with the software Statistica 11.0 was utilized in the search for a sole model that could be applied all over the State of São Paulo, by assessing individually each single variable. In this particular case, the SWHC, PREC and SM/SWHC criteria were evaluated using all datasets available for the study, regardless of the site or region under scrutiny and considering the MAE values of each criterion. Therefore, the SWHC, PREP and SM/SWHC that possessed the lowest MAE when all data was analyzed with no regional discrimination, comprised the general model proposed to determine the number of workable days.
As the study aimed to propose agrometeorological criteria for the assessment of NWD for the mechanized harvest of sugarcane, shortly after the determination of individual criteria for each site, such criteria were interpolated and spatialized by means of the Voronoi method [24], making used of the Open Source Quantum GIS (QGIS).
Once developed, validation of both individual and general criteria by means of the comparison of NWD estimates with observed independent data was made.
Such a validation procedure employed the same statistical parameters previously To make maps of annual average NWD for the State of São Paulo, the values of such a variable obtained by either site-specific or general criteria were determined for the historical series (1983-2014) and correlated to geographical coordinates (latitude-φ, longitude-λ, and altitude-ξ) by means of a multiple linear regression analysis, as well as with an integration of these inputs along with their values raised to the power of two (φ*λ, φ*ξ, λ*ξ, φ 2 , λ 2 e ξ 2 ): where a corresponds to the linear coefficient and b, c, d, e, f, g, h, i and j are the angular coefficients of the multiple regression equation; and ε is the error associated with the estimates.
The multiple linear regression model generated to provide information on annual average NWD both from a site-specific and general criterion was processed under the ArcGis software, version 10.3. This kind of procedure is an accurate method for interpolating climate-related variables [25]. After the completion of the determination procedure of the latitude, longitude and altitude layers for each pixel, it was possible to start the NWD spatialization process. Latitude and longitude maps in conjunction with altitude were employed in the making of NWD maps for the mechanized harvest of sugarcane determined by both site-specific and general criteria, by means of the algebra of maps, as preconized by [25]. For such, Spatial Analyst-Options and Spatial Analyst-Raster Calculator tools were employed in the ArcGis, version 10.3, together with the NWD multiple linear regression models, having latitude, longitude and altitude as independent variables.
Mean annual NWD maps built for the mechanized harvest of sugarcane, tak-  Table 2). For such analysis, the same statistical parameters previously described (ME, MAE, d, R 2 , r, C), along with the root mean square error (RMSE) [22] [23], were employed to give support and consistency to the outcomes obtained in the current study.

Definition of Criteria for Determining the Number of Workable Days for the Mechanized Harvest of Sugarcane
Simulations with the 27 criteria combinations taking into account three levels of PREC, SWHC and SM/SWHC for each of the 30 cane mills allowed us to propose the best models for NWD estimation for the mechanized harvest of sugarcane. Table 3 shows the relation of the three best combinations for each one of the sites from which MAE and C were calculated. For cases from which there was more than one single observed data for a given site, the outcomes chosen were those that resulted in the lowest MAE on average for the month or in case of a tie, the highest C was taken into consideration for decision-making. On the L. H. de Souza Vieira et al. Table 3. Classification of the three criteria combinations for determining the number of workable days for the mechanized harvest of sugarcane along with its respective values of mean absolute error (MAE) and performance index (C) for each site. For the "Criteria" column the first number refers to SWHC, the second to precipitation limit for the day to be considered as workable, and the third to ratio limit SM/SMHC.  Table 3, the first number refers to SWHC, the second to precipitation limit for the day considered to be workable, and the third to ratio limit SM/SWHC.   Table 4, it is possible to verify that a SWHC of 40 mm shows up as the pivotal value for determining NWD in 87% of the sites, whereas for PREP a 3 mm value was found to be the most frequent (74%). For the criterion related to SM/SWHC, such predominance is not as evident as it is for the other criteria.

According to
The most frequent occurrence for SM/SWHC was attributed to a threshold of 90%, having been considered as the most suitable one in 48% of the sites followed by a threshold of 80% occurring in 30% of the sites.
In order to assure a better understanding of the impact of each one of the criteria proposed in the current study for determining NWD, MAE related to each  Such a result turns out to be similar to that obtained by [21] who in turn made use of a threshold of PREC of 5 mm and SM/SWHC of 90%. Similar thresholds for PREC and SM/SWHC were also adopted by [11] to define the interruption of soil preparation operations with agricultural machinery. In this case, the afore-  non-favorable conditions for soil management were established as also assumed by [21], since risks associated with compaction of soil layers right underneath tillage depth were eminent. Nevertheless, the threshold of 90% for SM/SWHC is higher than the one adopted by [12] in rainfed areas of Sudan, which was 80%, the second most frequent threshold in our study.
Spatial distribution of site-specific criteria for the mechanized harvest of sugarcane at each producing site in the State of São Paulo obtained from interpolation proposed by the Voronoi approach can be seen in Figure 2.
According to the map shown in Figure 2, no particular predominance of a given criteria combination in the state was detected, however, it was possible to delimitate coverage areas for each one of the combinations. The observed variation is a result of differences in soil characteristics such as soil texture and structure, as well as soil hydric physical attributes, relief/topography, and weather conditions. As to the weather influences at hotter areas, there is a proclivity for the soil to start to dry off earlier, favoring, therefore, anticipation of the resumption of activities related to machinery traffic [5] [27].
It is important to emphasize that many areas belonging to the state lack scien- A model for field operations of machinery that requires a simulation technique for discrete events in order to evaluate the performance of machines on the basis of daily status of soil workability throughout a series of years was developed by [28]. The results of this model were compared with those obtained from a simpler method based on mean values of the probability of workable days available for agricultural operations at different growing seasons and the authors reached the conclusion that such a simpler method, due to its simplicity, gener-

Validation of the Criteria Employed for Determining the Number of Workable Days for the Mechanized Harvest of Sugarcane
One way to assure utilization feasibility of the proposed criteria (specific and general) is by means of their validation by comparing NWD estimates with data observed in the cane-mills. Table 6  both procedures is quite similar; as is also the performance of the models in terms of precision and accuracy. Despite this, as it was expected a priori, the specific criteria generated MAE slightly lower (3.8 days) than that obtained from general criteria (4.4 days). In general, both specific and general criteria were able to explain between 78 and 79% of the NWD variation among different sites in the state, which evidences a satisfactory performance of such criteria. This might also be confirmed by the values of d and C indices, with the latter classified as "Good" for the two procedures in accordance with the classification proposed by [22].
By analyzing Table 6, it is possible to observe that the determination of NWD obtained by specific criteria for each single site tends to underestimate NWD   Table 7 shows the mean number of workable days determined by specific and general criteria for the evaluated sites. The determination of NWD on the basis of general criteria for the majority of the sites tends to overestimate NWD when compared to estimated values obtained by site-specific approaches. By comparing both criteria for each particular site in absolute terms, that is, by bearing in mind NWD determined by both adopted criteria without therefore taking into consideration whether there is an overestimation or underestimation, a mean difference of 25 workable days might be observed. Also shown in Table 8, specific criteria culminated in a higher variation of NWD among different regions/sites (ranging from 203 to 298 days month −1 ), whereas such a variation was lower whenever NWD was estimated by general criteria/approach (varying from 260 to 290 days month −1 ).
For 50 scrutinized sites (

Spatialization of the Number of Workable Days for the Mechanized Harvest of Sugarcane in the State of São Paulo
Equation (2)  For the aforementioned NWD linear model the standard error was of 3.8 days, which is considered to be low given the magnitude of the total mean NWD throughout the year (278 days), depicting less than 2% and evidencing therefore a better performance ascribed to the use of general criteria in comparison to site-specific criteria when NWD is to be associated with variations in geographical locations. This might be explained by the fact that general criteria for determining NWD basically vary as a function of climatic inputs, which demonstrates that there is a strong correlation between environmental variables and geographical space (r = 0.89). Further, for the NWD determined by the site-specific approach, besides climate fluctuations, SWHC also varies affecting the ratio SM/SWHC, which cannot be explained by the geographical coordinates. Figure 3 and Figure 4 illustrate the maps of NWD for the mechanized harvest of sugarcane in the State of São Paulo, taking into consideration both site-specific and general criteria, respectively. These maps display a great spatial variation of NWD, both indicating an increase of such a variable from South to North and also from East to West of the state. This shows that integration of the results with geographical information systems is useful to create geo-referenced maps for ease of interpretation, as observed by [30] in a study dealing with the  effects of soil attributes and rainfall data on workability time of agricultural machinery. According to [7], maps of soil trafficability provide baseline data for further researches and risk assessment.
By comparing the maps of Figure 3 and Figure 4, expressive discrepancies might be noticed, for instance, in Southern São Paulo State in conjunction with Pontal do Paranapanema, which evidenced roughly 40 to 45 days less NWD for the map based on the site-specific criteria. In general, NWD obtained by the site-specific criteria tends to trigger a more pronounced variation in the outcomes, with NWD ranging from 220 to over 300 days ( Figure 3). Conversely, the NWD map based on general criteria presents a variation of 255 to 295 days ( Figure 4).
Examining the number of workable days for agricultural operations with machinery in planted forests as a function of meteorological variables, [10]  To define which maps best depict NWD spatial variation for harvest of sugarcane a validation of such maps was performed taking into consideration an independent dataset. Mean values of NWD corresponding to the pixels at which 16 sites demonstrated in Table 3 are located, were extracted from the maps illustrated in Figure 3 and Figure 4. These data, defined as "NWD estimated", were compared to "NWD calculated" by both criteria (site-specific and general), making use of meteorological data along with sequential water balance corresponding to each studied site. Table 8 shows both NWD calculated and estimated values for the 16 sites employed on the validation of the maps of Figure 3 and Figure 4. Table 9 presents a statistical analysis of the maps of NWD validation, when generated from both site-specific and general criteria. The outcomes obtained from the map generated from the general criteria resulted in lower errors (MAE Moreover, ME of the map generated from site-specific criteria turned out to be of the same magnitude of MAE, which reveals systematic errors leading to a lower precision of the estimates with d = 0.81. On the other hand, for the map generated with general criteria, d index was 0.92. Finally, by assessing the values Table 9. Mean error (ME), mean absolute error (MAE), agreement index (d), coefficient of determination (R 2 ), coefficient of correlation (r), performance index (d), and root mean square error (RMSE) of the estimates of the number of workable days (NWD) for mechanized harvest of sugarcane in the State of São Paulo, considering values extracted from the maps (NWDEst) in comparison to those calculated (NWDCalc) for both site-specific and general criteria (40-03-90). of C we found that the performance of NWD estimates obtained by means of the map based on the general criteria was considered to be very good (C = 0.80), according to the classification proposed by [22]. The best performance of the NWD linear model determined by general criteria might be possibly attributed to an alternation of criteria for determining NWD by means of site-specific criteria-a fact that does not always represent reality, since the macro-regions delimitated by spatialization given by the Voronoi method are very large, involving different types of soil, which in turn affect SWHC and SM/SWHC thresholds to define NWD [1]. On the other hand, the NWD linear model based on the general criteria better represents the average NWD for the State of São Paulo, generating errors of a lower magnitude.

Conclusions
The results of the present study allowed concluding that: 1) To determine NWD, lower values of SWHC are to be considered by a recommendation of 40 mm; 2) It is possible to determine NWD by making use of site-specific and general criteria for the entire State of São Paulo; 3) Site-specific criteria for determining NWD, as expected, varied from site to site, noting however a prevailing condition of SWHC = 40 mm. For general criteria the best combination was the one that employed a SWHC of 40 mm along with thresholds for PREC and SM/SWHC of 3 mm and 90%, respectively; 4) NWD estimation based on agrometeorological and soil criteria was shown to be a useful tool with an intermediate complexity in such a way as to generate reliable results supported by performance index C; 5) The maps generated from a multiple linear regression analysis are a suitable tool for understanding spatial variability of NWD for the mechanized harvest of sugarcane in the State of São Paulo, particularly when general criteria were employed (SWHC = 40 mm, PREC ≤ 3 mm and SM/SWHC ≤ 90%); 6) Mean NWD varied in the State of São Paulo, increasing from South to North and from East to West, with values ranging from 203 to 298 by means of the map based on regional site-specific criteria, and from 260 to 290 in compliance with the map generated from general criteria, which was shown to be better during the validation process.