The first step for SPAM is to disaggregate crop statistics of agricultural production (e.g., the yield, harvested area, and total production) by administrative-unit levels (k), crop type (j), and farming system (l) from coarser scale to finer scale (illustrated by orange shapes in Fig. 2). For example, the national-level statistics are disaggregated into subnational levels, statistics for crop aggregates are divided into individual crop types, and the crop statistics are further separated by rainfed and irrigated conditions. Disaggregation is a nonspatial module. For the administrative unit (ADM), we consider three levels – k=0 (national level), 1 (subnational level 1), and 2 (subnational level 2) – and refer to the country-specific administrative level as the statistical reporting units (SRUs; SRU =k0, k1 or k2). In general, the SPAM model will have better performance if crop statistics are more disaggregated by the ADM. Therefore, we prefer to collect crop statistics for ADM1 and ADM2, despite statistics mostly being available at the ADM0 level and the subnational coverage always being less complete. Comparing to the previous SPAM products, the subnational coverage percentage has increased markedly for SPAM2010, which is described in detail in Sect. 4.1.

We improve the model capacity in SPAM2010 as well: we simultaneously allocate 42 crops and crop aggregates (versus the 20 crops and crop aggregates in SPAM2000) and consider four farming systems for each crop (Fig. 2). In SPAM2010, we keep the farming systems conceptualized for SPAM2000, which have proven to be useful to represent the different crop performances under different management systems; e.g., the irrigated yields of a particular crop are likely to be substantially different from the corresponding rainfed yields. The four farming systems are defined as follows:

The irrigated farming system (I) refers to the crop area equipped with either full or partial control irrigation. Normally the crop production on the irrigated fields uses a high level of inputs such as modern varieties and fertilizer as well as advanced management such as soil and water conservation measures.

For irrigated farming systems, the crop-specific shares are derived by dividing the harvested area cultivated under full-control irrigation obtained from AQUASTAT, MIRCA, and country-level statistics by the overall harvested area. For rainfed farming systems, crop-specific shares are primarily estimated based on generalized assumptions for individual countries and crops. For example, all cereals in western Europe are produced with high inputs, whereas 20 % of cereals in sub-Saharan Africa are grown under a subsistence farming system. We also assume fertilization as a proxy for high-input use, so if irrigated crop areas and overall fertilized and nonfertilized areas of a crop are known, it is possible to deduce rainfed–high shares by subtracting the irrigated areas from fertilized areas. The remainder of fertilized area will be then classified as rainfed–high, and the nonfertilized areas will be further split between rainfed–low and rainfed–subsistence. In addition, the shares of rainfed–subsistence are assigned when there is not enough suitable area for rainfed–low conditions to satisfy the completeness of disaggregated crop statistics in terms of area extent and/or production quantity. In such cases a portion of the rainfed–low statistics were assumed to stem from rainfed–subsistence. Although disaggregation is a nonspatial module of SPAM, it is applied interactively with the spatial modules by the support of multiple spatial data and nonspatial data, which are elaborated in detail in the section “Data preparation for SPAM2010”.

The core part of the SPAM model is the cross-entropy module (illustrated by the dashed green frame in Fig. 2), which is used to achieve the allocation for each spatial grid (i). It works by (iteratively) minimizing the error between the preallocated shares of physical area (πijl) and the allocated shares of physical area (sijl) in each pixel i by crop j and production system l: 1min⁡{sijl}CEsijl,πijl=∑i∑j∑lsijlln⁡sijl-∑i∑j∑lsijlln⁡πijl, where CE is the abbreviation for cross-entropy, which is defined as the log function of probability. The difference between {sln⁡s} versus {sln⁡π} means the estimated probability s and its prior probability π are minimized subject to certain constraints. i.

Constraint specifying the range of allocated physical-area shares:20≤sijl≤1,∀i∀j∀l;

πijl indicates the decision to produce a particular crop under a specific production system, which is normally dependent on both biological and economic factors. However, subsistence farmers mainly grow crops for their own consumption, largely uncoupled from price, market access, or crop-potential-suitability conditions. Therefore, we first assume that the prior allocation for subsistence physical area (CropA‾ijS) in grid i by crop j under this circumstance is simply dependent on rural population density: 9CropA‾ijS=AdjCropAjkS×AggRurPopi∑i∈kAggRurPopi∀i∀j, where AdjCropAjkS is the generated physical area for crop j at the subsistence farming system for the given SRU k, and AggRurPopi is the rural population density at grid i (see the detailed description in Sect. 4).

Then for the three remaining farming systems, we assume that the potential unit revenue of planting a certain crop (Revijl) would affect farmers' crop choices: 10Revijl=AdjCropAjlkSRU∑iAdjCroplandi×Pricej×Accessi×PotYieldijl, where AdjCroplandi, Pricej, Accessij, and PotYieldijl are the adjusted cropland area, market price, accessibility parameter, and potential-yield values for crop j in farming system l and grid i (see the detailed description in the following Sect. 4).

Then we assume that the priors for the remaining three farming systems are mainly influenced by the estimated revenue, cropland area, and irrigated area.

For an irrigated farming system (I), 11CropA‾ijI=AdjIrrAreai×RevijI∑jRevijI∀i∀j. For rainfed–high (H) and/or a rainfed–low (L) farming systems, 12CropA‾ijl=AdjCropLandi-AdjIrrAreai-CropA‾ijS×Revijl∑jRevijl,l=HL∀i∀j, where AdjCropLandi and AdjIrrAreai are the cropland area and irrigated area at grid i (see the detailed description in the following Sect. 4).

Finally, the main inputs for the optimization procedure are converted to shares and written as 13πijl=CropA‾ijl∑i∈kSRUCropA‾ijl. The optimization module in SPAM2010 is almost the same as that in previous versions. We apply the cross-entropy process in the General Algebraic Modeling System (GAMS), which ensures that the optimization procedure iterates until a solution is found. Once the allocation is successful, meaning that an optimal or locally optimal solution has been found, the routine immediately returns the allocated physical area (AllocAijl) by grid i, crop j, and farming system l, and the program continues with postprocessing automatically (Fig. 2). If the solution is infeasible or nonoptimal, the program stops, allowing for manual scrutiny, adjustment, and rerun (see data harmonization in the following section).

Using the results of the optimization, the allocation module produce maps of harvested area (AllocHijl), yield (AllocYijl), and production quantity (AllocPijl) for each grid i by crop j and farming system l (Fig. 2). For harvested area, we convert the allocated physical area (AllocAijl) to allocated harvested area (AllocHijl) by multiplying by cropping intensity (CropIntensityjlk): 14AllocHijl=AllocAijl×CropIntensityjlk. For yield, we first calculate an average potential yield (PotYield‾jlkSRU) within an SRU using the allocated harvested area as weight, then the allocated yield (AllocYijl) is estimated as 15AllocYijl=AdjPotYieldijl×AdjCropYjlkSRUPotYield‾jlkSRU, where the average potential yield is calculated as 16PotYield‾jlkSRU=∑i∈SRUAdjPotYieldijl×AllocHijl∑i∈kSRUAllocHijl. We finally estimate the production quantity (AllocPijl) as 17AllocPijl=AllocHijl×AllocYijl.

Disaggregation of crop statistics is the first step for running the SPAM model. Table 3 summarizes the disaggregated rice harvested area and yield (area-weighted) for global rice production by four farming systems in SPAM2010. At the global level, the world has harvested about 160×106 ha of rice around 2010. The majority of rice production area is irrigated, i.e., about 98×106ha, which accounts for 61.2 % of the total rice harvested area. This share is followed by the high-input rainfed farming system (17.3 %, approximately 27 million ha), subsistence farming system (16.0 %, approximately 26 million ha), and low-input rainfed farming system (5.5 %, approximately 9 million ha). The global-average rice yield is 4374 kg/ha, which stands at the average yield between the irrigated farming system (5528 kg/ha) and high-input rainfed farming system (3663 kg/ha) and is much higher than the average yield of low-input rainfed farming system (1810 kg/ha) and the average yield of subsistence farming system (1604 kg/ha). At the regional level, Asia (South Asia, South East Asia, East Asia together) is the largest rice-producing region, which has harvested approximately 142 million ha of rice around 2010. The majority of Asian rice production area is also irrigated, and the share, i.e., 63.7 %, is close to the global share of irrigated rice farming system. South Asia has more rice area harvested (approximately 60 million ha) than South East Asia (approximately 49 million ha) and East Asia (approximately 33 million ha). However, the average rice yield in South Asia (3553 kg/ha) is lower than South East Asia (4125 kg/ha) and East Asia (6566 kg/ha). Consequently, the total rice production in these regions is very close to each other. Rice production in North America is completely irrigated, and the average yield is relatively high in this region. Subsistence rice production is mainly in sub-Saharan Africa (SSA) and South Asia, and the rice yield under subsistence conditions is also the lowest among the four farming systems.

After applying the optimization model in GAMS, the disaggregated crop statistics are spatially allocated to produce the SPAM maps. Figures 3 and 4 present the maps of harvested area and yield (after adjustment) for maize, respectively. For all farming systems, as shown in Fig. 3e, maize area is highly concentrated in northern China and North America. However, maize production in North America is mainly rainfed with high input, while in China, the rainfed farming system is mainly located in the northeastern part (Fig. 3e), and the irrigated farming system is mainly found in the north-central part (Fig. 3a). The rainfed low-input farming system (Fig. 3c) and subsistence farming system (Fig. 3d) for maize production are mainly located in South America and SSA, while the rainfed high-input maize farming system is also widely distributed outside China and northern America, including Central America, Europe, and other regions (Fig. 3b). As shown in Fig. 4e, the average maize yield is very high in North America and Europe and is relatively high in South America and Asia.

The first SPAM product was the regional-level agricultural-production maps produced for Brazil circa 1994 (You et al., 2006). Since then the model and products of SPAM have been continuously improved and updated. Besides the evolution of the method (see Sect. 3), the evaluation of SPAM model performance is also improving. In one of our early works, the uncertainty in the model, i.e., the variance explained by the cross-entropy approach, is evaluated by comparing it with the performance of simplified proportional approaches, which have been used by Monfreda et al. (2008) for producing the M3 dataset. It was proven that the cross-entropy approach was more successful in estimating crop areas than the proportional approaches, no matter the proportion to the total land area, to the cropland area, or to the amount of (biophysically) suitable land for the production of each crop (You et al., 2006). Moreover, many researchers believed that the inclusion of economic factors, i.e., market, would increase the performance of the crop disaggregation model (see the discussion in You et al., 2014), though it does not automatically guarantee that model's outputs. This partly explained the considerable discrepancies between SPAM2000 and M3 (Anderson et al., 2015) and partly confirmed that using more sophisticated approaches for production allocation would reduce uncertainty (Donaldson and Storeygard, 2016). In one of our recent works, the sensitivity of the variant of the standard SPAM model output to a few methodological-data choices had been evaluated. These include the spatial allocation method, the crop coverage, the treatment of a “rest-of-crops” aggregate, the incorporation of a “crop potential suitability” data layer, the inclusion of rudimentary economic elements, and the administrative-unit details of the primary source statistics. It showed that the standard SPAM estimates are unsensitive to the inclusion of crude economic elements, moderately sensitive to the set of crops or crop aggregates being modeled, and mostly dependent on the degree of disaggregation of the underlying national and subnational production statistics (Joglekar et al., 2019). This implies that the improvements to the methodological aspect of SPAM have limited effect on reducing uncertainty. By contrast, the quality and accuracy of the underlying statistics used to prime the model are particularly pertinent (Joglekar et al., 2019).

SPAM products are estimates with various uncertainty. Inaccuracy surely exists and varies from region to region and even from crop to crop. Although there were efforts paid to the evaluation of model conceptualization and performance, those previous validations should not be taken for granted for the latest updates. Therefore, we carried out extensive validation work to assess the accuracy of the output maps of SPAM2010. Firstly, we relied on a system through which we are able to send the crop maps to collaborators and users alike for comments or assessment. For example, the CGIAR is a global partnership which unites 15 centers engaged in agricultural research. Each center has its own mandate crops, e.g., IRRI (International Rice Research Institute) for rice and CIMMYT (International Maize and Wheat Improvement Center) for maize and wheat. We took advantage of their vast network of field offices and local expertise to help us to validate the SPAM results. Many researchers from these institutes have been involved in the production of SPAM2010, which increases the reliability of the results. The Chinese Academy of Agricultural Sciences (CAAS) undertook the regional-level validation for SPAM2010 following the approaches they have applied for the evaluations of previous SPAM products (Liu et al., 2013; Li et al., 2016; Chen et al., 2016). Moreover, field-level validating information has either been collected by crowdsourcing tools such as Geo-Wiki (Fritz et al., 2012) and eFarm (Yu et al., 2017a) or through field trips and workshops on-site or online, where local experts were asked to confirm or validate the crop production maps by providing handwritten comments or posting comments online at the our MapSPAM website. Most of these reports were collected crop by crop and country by country. An example of the detailed validation process is provided in the Supplement (see Sect. S16). The complete validation process could take a great deal of effort and time, but these users' feedback is quite important and valuable. We took this feedback and rerun SPAM model and further released the updated versions of SPAM. The previous SPAM products have been updated substantially with the help of those comments. For example, SPAM2000 and SPAM2005 are at version 3.07 and version 3.20, respectively. The current product, i.e., SPAM2010v1.10, was already released after extensive validations; it is still open and ready to receive more comments. Such an iterative process would enable a continued update to improve the product quality.

Secondly, we qualitatively evaluated the uncertainty in the input data. Like any models, the results depend on the input data and the modeling process. For SPAM, the most important input data are the subnational crop data, which have a large impact on the final product accuracy as mentioned before. We built our SPAM uncertainty rating mainly on the availability and confidence of our subnational data. In addition, we added the parameters and constraints we have to adjust to solve the SPAM model. For example, we sometimes have to abandon some crop-potential-suitability constraints in order to solve a country. For some countries, we may have to allow cropland per pixel to increase by 5 % or even 10 % of the original input to make the model run. In addition, we collected feedback and comments from users, local experts, and collaborators as discussed above. They are sporadic but very useful. We combine all the information together to give a subjective rating on how confidence we, the SPAM team, think of our final crop maps (both area and yield) based on the judgment of the reliability of input data. Figure 5 shows the country-level uncertainty rating with 5 categories (1 represents the lowest uncertainty, 5 the highest). The complete rating list is presented in Sect. S17 in the Supplement. Not surprisingly, the uncertainty in Africa and South East Asia is higher than that in countries in Europe and America. Although such a validation process is not vigorous, the result is convincing, and such a rating is highly demanded and explicitly requested by users.

Thirdly, we quantitatively evaluated the results by cross-comparing the results with statistics at another administrative level that has not been used in running the model. We ran SPAM with complete statistics (ADM0, ADM1, and ADM2) and then ran them with only ADM0 and ADM1 statistics to see how the aggregated results to ADM2 compare to the original statistics at ADM2, or at least to the aggregated original results at ADM2. The runs were all done at ADM1 and then combined to give results for the whole country. We then calculated the coefficient of determination (R2) between the values allocated from model and obtained from statistics to assess the model performance. In general, a higher R2 indicates a better performance. This approach has already been used for evaluating the performance of SPAM2000 (You et al., 2014). The upper part of Fig. 6 shows the results of such an approach applied to Brazil in SPAM2000 for its main food crops, while the bottom part of Fig. 6 shows the results of the same approach applied to the same country for the same crops in SPAM2010. The figure clearly indicates that the model performed better in allocating rice than other crops. Moreover, the performance improved greatly from SPAM2000 to SPAM2010, especially for soybean and potato. We further selected a few smaller countries in Asia and Africa to undertake the same assessment, which are believed to have a relatively higher uncertainty in terms of input data (Fig. 5). Bangladesh, Benin, Senegal, and Tanzania were selected as they have good statistical data coverage in SPAM2010. Figure 7 shows that the R2 for selected crops (i.e., maize, rice, and cotton) ranged between 0.66 and 0.94, suggesting that the overall performance of SPAM2010 is good in these selected countries for those selected crops.

Finally we did regional-level quantitative validations when third-party independent crop maps were available, given that it is impossible for us to collect the true spatial distribution of crops (both area and yield) for the time of 2010 on a global scale. Among the limited third-party independent spatial crop distribution data, the Cropland Data Layer (CDL; https://nassgeodata.gmu.edu/CropScape/, last access: 11 December 2020) is a crop-specific land cover dataset created for the continental United States using moderate-resolution satellite imagery and extensive agricultural ground truth, which has been applied to validate our SPAM2010 product at the regional scale by correlating the grid-level crop area. We focus on the three most popular staple crops in the United States, i.e., maize, wheat, and soybean, and obtain the crop area maps of 2009, 2000, and 2011 from CDL. We calculate the 2009–2011 average crop areas at a 5 arcmin resolution for CDL according to the scheme of SPAM2010 and further calculate the coefficient of determination (R2) and the root mean square error (RMSE) between the grid-level values derived from the two datasets (Fig. 8). The values of R2 are between 0.71 and 0.91, and the values of RMSE are between 231 and 307 ha, indicating a relatively high reliability. In particular, the higher R2 and lower RMSE suggest our maize and soybean maps are more reliable than the wheat map. There are potentially many factors affecting the different results if we treat CDL as the truth, for example, the different accuracy or availability of input data, suitability layers, and parameters for the area shares and yield ratios. Another possible reason is that we did not distinguish spring wheat and winter wheat in SPAM, which partly explains why the agreement for wheat is lower than that for maize and soybean. Moreover, the National Land Cover Dataset (NLCD) of China mapped paddy field distribution as a special cropland cover at a 1 × 1 km grid level (http://www.resdc.cn/data.aspx?DATAID=99, last access: 11 December 2020). By assuming paddy fields will be mostly used for growing rice, we evaluate the rice area map in China by correlating SPAM2010_rice and NLCD2010_paddy according to the same scheme described above. The value of R2 is 0.49, and the value of RMSE is 1024 ha (Fig. 9). Although this result does not seem as good as the results from the United States by using CDL, it is fairly acceptable because NLCD measures land cover rather than land use and is in a relatively coarse spatial resolution. Moreover, the R2 is substantially increased comparing to its predecessors. For example, the R2 is assessed as 0.42 for SPAM2005 by using the same approach according to Liu et al. (2013). In addition, there are regional-level crop distribution maps produced by independent efforts on interpreting remotely sensed images. For example, Zhang et al. (2017) provided annual paddy area time series from 2000 to 2010 based on satellite remote sensing for China and India. We compared these remote-sensing-derived paddy maps with the rice area estimated by SPAM for the year 2010. The R2 values are 0.36 and 0.34 for China and India, respectively (Fig. 10). We could expand this quantitative evaluation when more third-party independent crop maps are available. However, it should be noted that errors might exist in the third-party independent crop maps as well; hence this quantitative evaluation approach also might result in uncertainty. Our results show that the uncertainty gradually increases when applying CDL, NLCD, and Zhang et al. (2017).

There are a few reports which compare SPAM with M3, MIRCA, and GAEZ, especially their output maps circa 2000 (Anderson et al., 2015; Donaldson and Storeygard, 2016). Although it is difficult to make statements about which one is better, there are several features that distinguish SPAM products from the M3, MIRCA, and GAEZ data. First, the estimates from SPAM can be customized using user-provided data for one or more of the input variables and return results to the provider in a short turnaround period. Second, although SPAM runs mainly at a 5 arcmin resolution, it can be run at higher resolutions provided that at least some of the rasterized inputs also have higher-resolution data to support such an exercise. Third, considerable effort is made to compile subnational crop statistics at administrative level 2 (e.g., district or county) for all possible countries. Fourth, if there is knowledge of crop existence in any area for any crop, this can be incorporated into the model to make a more accurate crop allocation. Moreover, SPAM does not have a large coverage of crops (compared to M3) and does not include detailed biophysical parameters (compared to MIRCA and GAEZ); instead it focuses more on agricultural production by providing data on crop harvested area and yield disaggregated by farming systems. Finally, SPAM results are readily available on the internet in several formats (also tabular) for all interested users. We are currently building a SPAM model in the cloud, where we let any user supply his or her own input data and run SPAM on his or her own under the GitHub platform. This SPAM in the cloud will be published and communicated to the SPAM user community once it is ready.

Anderson et al. (2015) conclude that substantial discrepancies exist across these four global spatially explicit crop production datasets circa 2000, and the disagreement between models serves as a reminder of the ongoing challenges to the creation of spatially explicit estimates of harvested area and yield based on crop statistics. However, it is more challenging to assess the disaggregated farming system results such as irrigated rice vs. rainfed rice and subsistence maize vs. high-input rainfed rice, which have not been systematically explored in Anderson et al. (2015). We collected additional global datasets which are relevant to agricultural-production mapping, e.g., the average irrigated and rainfed yields (ca. 2000) from Siebert and Döll (2010) and the harvested area and yield for four crops (ca. 2005) from http://www.earthstat.org/ (last access: 11 December 2020). We compared these datasets with our SPAM products for the corresponding period. We found that the results are differed from crop to crop and from farming system to farming system. In general, the yield estimates on maize and wheat are better than the other crops, and the irrigated yields are better than the rainfed yields (Figs. 11 and 12).

However, as M3, MIRCA, and GAEZ do not provide subsequent global spatially explicit crop production ca. 2000, it is impossible to compare the current SPAM2010 with other data products. In order to illustrate the continuity of SPAM products, we present a grid-by-grid comparison between SPAM2010 and SPAM2005. Figure 13 shows that rice production in 2010 increased notably in eastern Europe, Africa, northeastern China, northwestern India, southern Australia, etc., while it decreased notably in central Asia and South America. Maize production displays an overall increase across the globe between 2005 and 2010, except for some places in central Asia, which have shown a decreasing trend. It is also noticeable that maize production in the US and Europe has kept relatively stable. This result is accordant with the “maize boom” which had taken place around the globe (Herrmann, 2013), especially in the developing countries (Cairns et al., 2013; Ornetsmüller et al., 2019). It should be noted that the current type of comparison may not be a perfect comparison (because differences exist in methodologies and data input applied in SPAM2005 and SPAM2010) and that the current comparison only shows the rate of change; thus a higher value does not necessarily indicate a huge change in absolute crop production.

In addition, we compared the changes in crop area between SPAM products and the abovementioned regional-level independent crop maps once they were available in time series. We calculated the area changes in maize, wheat, and soybean by overlaying CDL2005 and CDL2010 and undertook the same procedure for SPAM. We then plot these changes (i.e., ΔCDL and ΔSPAM) in Fig. 14. Likewise, we compared the changes in SPAM rice area and the changes in paddy rice area obtained from Zhang et al. (2017; Fig. 15). Figures 14 and 15 both show that the coefficient of determination is extremely low between changes yielded from different data products, which further reminds us that it is inappropriate to directly compare SPAM products over time, although we are confident of the spatial accuracy of SPAM products at each time stage. This is mainly because SPAM requires a large number of input data, yet the sources of these multiple data inputs cannot be guaranteed to be the same across different time stages. Therefore, such changes reflected by SPAM products over time not only mix real changes on the ground but also largely depend on the input data. For example, the cropland layers (one of the most important data inputs) are accessed from different sources to make sure the cropland data and the statistical data are adopted for the same year. We did not evaluate the continuity of these input data, which is almost impossible and is beyond the purpose of SPAM. Consequently, it is suggested to use the SPAM products with, at least, acknowledgement to the corresponding cropland layer, e.g., Lu et al. (2020) for SPAM2010. Moreover, we do not recommend users to cross-compare the SPAM products over time because the differences may have more input data errors or inaccuracies than detecting the real change on the ground.

As stated previously, the SPAM estimates are dependent on the extent and veracity of the primary input data like most models (Joglekar et al., 2019). SPAM2010 requires data on 42 crops in over 200 countries for the production season. Ideally, these data should be collected at an ADM2 level; however this is not always possible. It is particularly difficult to a few countries such as Somali and Nigeria, where reliable data are not available, or different input data just conflict with each other. For example, only one crop area (i.e. millet) for a district is already larger than the total cropland area, yet we know there are still five more crops growing in this district. In these cases, we have to adjust the conflicting data using expert judgment to make the model solvable. Since most cropping statistics are not delineated by farming system, estimates of the shares of production under each of the four systems in question are required. To convert harvested-area statistics to the physical-area statistics used in the model, additional data on cropping intensities by crop and farming systems must be collected. We have made every effort to collect official or published data, and we reply on expert judgments as the last resort when we simply could not find other sources. For example, no country publishes official statistics on crop yield ratio (yield conversion factor) between irrigated vs. rainfed crops. We surveyed published papers, personal communication with the FAO's Agriculture to 2030 team, and gray literature to collect such data. While indeed a series of expert judgments are used, the scope (e.g., crops and regions) is quite limited in the overall input data. Once the data on disaggregate cropping practices are compiled, several variables at a gridded scale are needed to disaggregate these cropping statistics into the desired spatial units. These data include estimates of cropland, irrigated land, suitable area and yield, population density, and protected areas. The variety and sheer volume required to run the SPAM (and related) models raise questions of reliability and comprehensiveness of estimates across different cropping statistics, geographic areas, and countries.

In terms of reliability, different sources of information may lead to inconsistent and even incompatible information. For example, the data on the estimated cropland extent within a grid are compiled from several sources, which in turn deploy different methods to generate their estimates. The extent of cropland within a grid is crucial information for the allocation model, but the confidence regarding its actual location varies regionally (see Lu et al., 2020). Crop statistics on area harvested and yield may not have been consistently collected and processed across different countries, so these major data may be unreliable to begin with. Additionally, two of the major conversion factors used, farming system shares and cropping intensities, are often not available for each crop and farming system within a country. Lacking raw data on these statistics for a particular crop–country combination, these data were simply assigned from a similar crop or country or created using expert judgment. Neither data on cropping intensities nor farming system shares have been validated for reliability. In terms of comprehensiveness, notably less subnational coverage exists in developing countries, and only global-average commodity price data were used to account for the economic influences on crop production.

The wide range of data sources, coverage, and regional nuances of crop production have methodological implications. First, there are possible trade-offs between data consistency and data reliability. For example, there are requirements of the model (i.e., cropping intensities and farming system shares) that are not consistently available within a country at the administrative level needed. Often, these numbers are taken from national-level values, even though they may not reflect the reality at the administrative level. Secondly, multi- and intercropping are not handled in a sophisticated manner within SPAM. These types of cropping patterns are only accounted for using a single cropping intensity value per crop, farming system, and (possibly) subnational unit. Finally, the market is important for both subsistence farmers and commercial ones (Losch et al., 2012). In SPAM, we rely on population density for an indirect representation of market proximity. We use the rural population to calculate a prior for the subsistence portion of a crop (i.e., subsistence among the four farming systems). For subsistence farmers, by definition they mostly consume what they produce, and so we indeed assume their production is closely correlated with their rural population size. For all other farmers, we assume they produce for the market (local, regional, or even international markets). The assumption of using rural population as a proxy for market access was to break down the total cropland into individual crop areas in the prior revenue calculation. We did not, explicitly or implicitly, assume a rural population (even subsistence farmers) is entirely fed by local agriculture. Instead, we applied rural population density as a proxy for market access, which allows crop-specific tuning depending on how crops are distributed across the four farming systems. As this crop-specific revenue is divided by the total revenue within a pixel in Eqs. (9) and (10), the prior is not affected by market accessibility if it is not crop-specific. In other words, crop-specific market accessibility is preferable for the current SPAM model. Yet such accessibility data at the global scale do not exist now. We would consider including a more direct representation of market proximity by actual travel times to markets or road networks as the global roads and railways databases are becoming available (Koks et al., 2019). Several trade-offs were made to ensure that the complex allocation method was tractable, and it is important to recognize that these trade-offs likely affect the plausibility of results.

Last but not least, we admit that it is inappropriate to compare SPAM products directly across time stages (Figs. 13–15), although we have paid every effort to guarantee the spatial accuracy of SPAM products at each time stage. It is largely because the system errors exist across various data products. In a latest publication, Iizumi and Sakai (2020) released a time series product of global gridded crop yields. Although they applied a different approach (i.e., spatial adjustment) which is conceptually different from the spatial disaggregation approach applied in SPAM, it provides great implications to further integrate and standardize the SPAM and the similar gridded earth system datasets for broader applications. There is an ongoing consortium called The Land Use Change Knowledge Integration Network (LUCKiNet; http://www.luckinet.org, last access: 11 December 2020). The SPAM team is part of this consortium, which aims to integrate tools and standardize approaches across various ongoing projects that develop gridded information on land use dynamics for applications in food security, climate change, biodiversity, and other related issue areas. Not only LUCKiNet aims to create crop maps comparable over time, but we also want to have these maps consistent across land uses such as cropland, grassland, and forest. The modeling techniques would consider the spatiotemporal dynamics of different land use forms in an integrative framework.

In this paper, we present SPAM2010, the latest global gridded agricultural-production dataset in 2010. SPAM2010 uses an updated cross-entropy approach to make plausible estimates of crop distribution for 42 crops and four farming systems within disaggregated units, which shows great improvement over its predecessors: SPAM2000 and SPAM2005. For example, the expanded crop list enables the analysis for not only staple food crops but also cash crops. A recent study has analyzed the global beer supply by using SPAM2000 (Xie et al., 2018). It will be very promising to analyze the global coffee and tea supply by using the latest dataset as these crops are newly included in SPAM2010 and are in increasing demand with superior economic value but also highly sensitive to climate change (Bunn et al., 2015).

SPAM2010 substantially extends the SPAM family and fills the gap for the work of global agricultural-production mapping by successfully creating a global gridscape at the confluence between earth and farming systems. In particular, it helps to better understand land management practices characterized by concomitant data and knowledge gaps (e.g., crop selection and element of crop harvest; Erb et al., 2017). It not only allows analysts and policymakers to better target agricultural and rural development policies and investments, increasing food security and growth with minimal environmental impacts, but also enables scientists to better address the global-change challenges within the anthroposphere and beyond by providing the only possibility for updating the global agricultural and environmental assessments from 2000 (when M3, MIRCA, GAEZ, and SPAM2000 are available) to 2005 and 2010 (when SPAM2005 and SPAM2010 are available as well). All the SPAM maps and tabular data in multiple time stages are freely available on the MapSPAM website (http://mapspam.info/  last access: 11 December 2020), which also acts as a platform for validating and improving the performance of the SPAM maps by collecting feedback from users.