# Mapping Flood-Based Farming Systems with Bayesian Networks

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## Abstract

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## 1. Introduction

- The diversity of FBFS settings: the diversity of FBFS settings in terms of floodwater availability, crop types, or social organization (e.g., spate irrigation in Tigray versus inundation canals in Kisumu) suggests that diagnostic elements aiming to operate at large scale should be framed into a conceptual model that can be applied in a wide range of contexts.
- The similarity of FBFS with other ecological systems: FBFS systems share characteristics with other ecological systems. They are similar to conventional irrigation in terms of supplementary irrigation, they resemble rainfed agriculture in terms of rainwater and growing period, and they share features with riparian vegetation in terms of extended growing period. These similarities indicate that valid concepts should be translated into flexible classification rules that can be used to highlight the most outstanding features of FBFS and discriminate them from the other ecological systems.
- The unpredictable nature of floods in FBFS: the large uncertainty in FBFS estimates, particularly in the areas these farming systems cover, implies the need for an approach that can detect agronomic flooding even in situations where flood events are not physically observable on satellite images. This is important because flood events may not leave a detectable trace of inundation, not only because the sensor can miss the flood event, but also because many FBFS have deep soils capable of storing large volumes of water. Agronomic flooding may also occur after the planting date, in which case it can be confused with other types of flood events because flood occurrence is largely unpredictable, and it is difficult to determine whether and how floods are used for FBFS purposes [3,4].

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, of which 567 km

^{2}(28.2%) is covered by water [24]. The central part of the county is relatively flat, surrounded by ridges reaching up to 1835 m above sea level. The relief of the county can be classified into three main topographic regions: the Kano lowland plains, the Maseno midlands, and the highlands of the Nyabondo Plateau. The Nyabondo Plateau constitutes the bulk of the area that is prone to flooding, particularly during periods of heavy rains. The floodplains are well suited for agriculture due to their relatively rich soils that have been formed by recurrent alluvial deposits.

#### 2.2. Conceptual Framework

#### 2.3. Acquisition of Nonspatial Data and Bayesian Network Specifications

#### 2.4. Acquisition and Preprocessing of Spatial Data

#### 2.5. Exploratory Analysis of the Normalized Difference Spectral Indices

#### 2.6. Computation of Spatial Data Metrics

#### 2.6.1. Slope and Flow Accumulation

#### 2.6.2. Vegetation Sensitivity to Water Variation

_{i}is the vegetation sensitivity to water variation at pixel i, and n is the total number of images in the time series, sd is the standard deviation. NDII6

_{i}, NDII7

_{i}, and NDVI

_{i}, respectively, are the NDII6, NDII7, and the NDVI time series at pixel i.

#### 2.6.3. Surface Sensitivity to Flooding

_{i}is the surface sensitivity to flood at pixel i, NDFI

_{i}is the NDFI time series at pixel i.

#### 2.6.4. Soil Water Content

_{i}is the soil water content at pixel i, and n is the total number of images in the time series. NDII6

_{i}, NDII7

_{i}, NDFI

_{i}, and NDVI

_{i}, respectively, are the NDII6, NDII7, NDFI, and the NDVI time series at pixel i.

#### 2.6.5. Surface Exposure to Wetness

#### 2.6.6. Temporal Variation in Vegetation

#### 2.6.7. Water Presence and Flood at the Beginning of the Rainy Season

#### 2.6.8. Power of Tools

#### 2.7. Computation of Spatial Data Nodes

#### 2.7.1. Step 1: Computation of Boxplot Ranges and Presence/Absence Data

#### 2.7.2. Step 2: Computation of Probabilities that Pixels Belong to a Boxplot Range Using Presence/Absence Data

#### 2.7.3. Step 3: Identification of Most Likely Pixel States

#### 2.7.4. Step 4: Deduction of State Values for Unclear Pixels

#### 2.8. Expert System, Outputs, and Validation

_{i}is the ith state of the variable X, and P(x

_{i}) is the probability of the ith state of the variable X.

## 3. Results

#### 3.1. Spatiotemporal Analysis of Water and Vegetation

#### 3.2. Prior Distributions of FBFS-Relevant Metrics

#### 3.3. Posterior Distribution of FBFS-Relevant Metrics

#### 3.4. Uncertainty of FBFS-Relevant Metrics

#### 3.5. FBFS Potential in Kisumu County and Tigray

#### 3.5.1. Spatial Coverage of FBFS and Prediction Uncertainty

#### 3.5.2. Validation and Uncertainty-Adjusted Predictions

## 4. Discussion

- The extent and dynamics of environmental problems at various spatial scales: Environmental problems (e.g., pollution, flood disasters) are often predicted using multiple proxy metrics, each of which represents a potential source of uncertainty. While the approach can be used to derive such proxy variables from remotely sensed data, one of its main strengths is the ability to transparently track the sources of uncertainty. In most conventional assessments, evaluation and mapping of environment problems are generally achieved using multivariate techniques (e.g., weighted overlay), which do not allow assessing uncertainty in a spatially explicit manner.
- Cognitive tools: The single and multilayer procedures can be used to generate exploratory analyses of an area of interest, producing results that are useful as supporting materials in expert elicitation workshops, focus group discussions, or participatory mapping. The exploratory analysis can be illustrated by maps, based on which local experts can explain specific issues or estimate the probabilities of certain variables regarding the areas of interest. Such maps can also be provided to local communities to identify specific features of local systems as well as to validate predictions concerning their community.
- Project impact assessment: Development interventions, and projects in general, often require quantitative assessment of impact pathways and project-related risks [22,51]. The approach proposed in this paper can be used for framing and assessing the chances of project success or failure in a spatially explicit manner. The approach can also be useful in limiting the spatial scope of development interventions to areas where the risk of project failure is below a certain threshold.
- Spatial crop modelling: The approach we discussed in this paper can be used to estimate a wide range of important variables for crop production. These variables can then be used as inputs for probabilistic crop models [52] (under review) to estimate crop yield at various spatial scales. The approach can be easily modified for studying the state of crop yield in relation to qualitative model inputs, based on a multinomial Bayesian network describing pixel-scale yield potentials as discrete yield values. Studies aiming to assess continuous yield distributions are usually based on deterministic models operating at pixel level. In this regard, one could use mathematical equations to describe crop yield and integrate these equations into a continuous Bayesian network see [27]. Hybrid Bayesian networks see [27] provide an opportunity for extracting information from both quantitative and qualitative variables.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Major features and typical flood-based farming system landscapes found in Kisumu County (Kenya) and in Tigray (Ethiopia).

**Figure 2.**Conceptual framework for probabilistic mapping of flood-based farming systems based on expert analysis in Kisumu County, Kenya and Tigray region, Ethiopia. Elliptic shapes mark nonspatial data components described by an expert-informed Bayesian network. GADM stands for Global Administrative Areas, MODIS stands for Moderate Resolution Imaging Spectroradiometer, SRTM stands for Shuttle Radar Topography Mission, hdf stands for Hierarchical Data Format, GDAL stands for Geospatial Data Abstraction Library, and FBFS stands for flood-based farming systems.

**Figure 3.**Bayesian network describing the causal reasoning used for mapping flood-based farming systems (FBFS) in Kisumu, Kenya and Tigray, Ethiopia. Each box represents a node. White bars and numbers are probabilities of the various node states indicated by the text on the left-hand side of each bar. Arrows indicate the direction of the causal relationships between nodes. The probability distributions are based on expert-elicited data regarding both Kisumu and Tigray.

**Figure 4.**Vegetation seasonality in Kisumu County, Kenya based on a 3-year time series of Normalized Difference Vegetation Index from Moderate Resolution Imaging Spectroradiometer data (MODIS NDVI). EGS = end of growing season; BGS = beginning of growing season; the indices (1 and 2) indicate the first and second season, respectively. The top plot describes the evolution of the NDVI of an average pixel over time, with red bars showing senescent vegetation and green bars showing active vegetation. The bottom plot illustrates the computation of the length of the growing season based on NDVI ratio values derived from the NDVI values.

**Figure 5.**Exploratory analyses for mapping flood-based farming systems in Kisumu County, Kenya and the Tigray region, Ethiopia. Strip shadings (left) are used to indicate different parts of the figure: (

**a**) boxplots of spectral index distributions based on random samplings of 10,000 pixels at each date, lines demarcate the median, the 25% and 75% quantiles, and the outlier limits; (

**b**) bar plots of monthly aggregates of loadings of principal components (PC) showing the temporal variability in PC. The sign of the first PC was fixed to be positive; (

**c**) maps showing the spatial variability of the PC. (

**d**,

**e**) Line and boxplots of representative samples of pixels corresponding to land use types.

**Figure 6.**Probability of different levels of vegetation and flooding in Kisumu County, Kenya, and Tigray, Ethiopia. Flood is estimated using the normalized difference flood index. Vegetation is estimated using the normalized difference vegetation index. The shadings highlight different states of flood and vegetation with Very low corresponding to the range of lower outliers, Low corresponding to the range from the lower bound of the confidence interval to the 25% quantile, Moderately low corresponding to the range from the 25% quantile to the median, Moderately high corresponding to the range from the median to the 75% quantile, High corresponding to the range from the 75% quantile to the upper bound of the confidence interval, and Very high corresponding to the range of upper outliers. This figure illustrates some parts of the computation of spatial data nodes. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries.

**Figure 7.**Prior estimates of spatial data inputs for an expert-informed Bayesian network used for mapping flood-based farming systems in Kisumu, Kenya and Tigray, Ethiopia. The spatial data nodes were computed using complex heuristics-based time series of normalized difference spectral indices of MODIS and elevation data of SRTM. Pixel values in the spatial data nodes map to the corresponding node states in the Bayesian network. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries.

**Figure 8.**Posterior distributions of relevant variables estimated using an expert-informed Bayesian network mapping procedure for flood-based farming systems in Kisumu County, Kenya and Tigray, Ethiopia. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries.

**Figure 9.**Uncertainty maps generated from an expert-informed Bayesian network mapping procedure for flood-based farming in Kisumu, Kenya and Tigray, Ethiopia. Uncertainty is expressed as Shannon entropy. The lower the value, the lower the uncertainty. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries.

**Figure 10.**Estimates of potential areas for flood-based farming in Kisumu County, Kenya and Tigray, Ethiopia using a mapping procedure based on an expert-informed Bayesian network. The FBFS potential maps show estimates of the suitability of each pixel for flood-based agriculture. Shannon entropy is used as a measure of uncertainty regarding the suitability of each pixel for flood-based agriculture. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries. Transparent black features are validation polygons.

**Figure 11.**Effect of uncertainty thresholds on prediction outcomes of an expert-informed Bayesian network mapping of flood-based farming in Kisumu County, Kenya and Tigray, Ethiopia. The optimistic prediction accounts for all pixels with a minimum probability of 0.5 of falling in at least the medium-suitability class. The pessimistic prediction accounts for all pixels with a minimum probability of 0.75 of falling in either the ‘likely suitable’ or the ‘very likely suitable’ class. Blue, light blue, and black lines, respectively, demarcate lakes, rivers, and administrative boundaries.

**Figure 12.**Evaluation of the joint effect of uncertainty thresholds and the detected state of FBFS potential on the proportion of false positive prediction outcomes of an expert-informed Bayesian network mapping of flood-based farming in Kisumu County, Kenya and Tigray, Ethiopia. This figure illustrates how imposing constraints on the states of FBFS potential detected at a given pixel and the probability at which this FBFS potential can be trusted affect the outcome of the prediction. A minimum FBFS potential of ‘Very low’ means that all states are considered in the prediction, a minimum FBFS potential of ‘Low’ means that the ‘Very low’ state is excluded, a minimum FBFS potential of ‘Medium’ means that ‘Very low’ and ‘Low’ states are excluded, and so on. A total of 91 evenly spaced points between 0.1 and 1 were considered as probability thresholds in the simulation.

**Table 1.**List of normalized difference spectral indices used to estimate several spatial data nodes to feed a Bayesian network for mapping FBFS in Kisumu County, Kenya, and Tigray region, Ethiopia.

Spectral Index | MODIS Bands | MODIS Spectral Range | Full Name |
---|---|---|---|

NDVI | B2, B1 | (NIR_{2} − VIS_{Red})/(NIR + VIS_{Red}) | Normalized Difference Vegetation Index [10] |

NDFI | B1, B6 | (NIR_{1} − SWIR_{1})/(NIR + SWIR_{1}) | Normalized Difference Flood Index [17] |

NDII6 | B2, B6 | (NIR_{2} − SWIR_{1})/(NIR_{2} + SWIR_{1}) | Normalized Difference Infrared Index—Band 6 [11] |

NDII7 | B2, B7 | (NIR_{2} − SWIR_{2})/(NIR_{2} + SWIR_{2}) | Normalized Difference Infrared Index—Band 7 [11] |

Gao NDWI | B2, B5 | (NIR_{2} − NIR_{5})/(NIR_{2} + NIR_{5}) | Normalized Difference Water Index (NDWI) [12] |

McFeeters NDWI | B4, B2 | (VIS_{green} − NIR_{2})/(VIS_{green} + NIR_{2}) | Normalized Difference Water Index (NDWI) [13] |

**Table 2.**Translation of 2-bit pixel level quality assessment in MODLAND [48] used to estimate pixel data quality.

2-Bit Encoded per Pixel QA Code | Decimal Value | Quality Attribute Meaning |
---|---|---|

00 | 0 | Pixel produced, good quality, not necessary to examine more detailed QA |

01 | 1 | Pixel produced, unreliable or unquantifiable quality, recommend examination of more detailed QA |

10 | 2 | Pixel not produced due to cloud effects |

11 | 3 | Pixel not produced primarily due to reasons other than cloud |

**Table 3.**Description of data used to validate a Bayesian network mapping procedure for FBFS in Kisumu County, Kenya, and Tigray region, Ethiopia.

Study Area | Validation Polygons | |||
---|---|---|---|---|

Land Use Type | Description | Number | Area (km^{2}) | |

Kisumu | FBFS fields | Water is mainly acquired via gravity from rivers or lakes | 11 | 48.9 |

Forests | More than 60% tree cover | 5 | 7.3 | |

Irrigated agricultural fields | Water is mainly acquired using pumps | 2 | 92.0 | |

Rainfed agricultural fields | Water mainly acquired via rainfall | 2 | 1.3 | |

Riparian vegetation | Vegetation close to water | 4 | 6.7 | |

Water bodies | Areas permanently covered by water | 2 | 164.9 | |

Tigray | FBFS fields | Water is mainly acquired via gravity from dry wadis | 9 | 65.7 |

Forests | More than 60% tree cover | 4 | 3.3 | |

Irrigated agricultural fields | Water is mainly acquired using pumps and wells | 4 | 9.9 | |

Rainfed agricultural fields | Water mainly acquired via rainfall | 2 | 38.0 | |

Riparian vegetation | Vegetation close to water | 4 | 1.6 | |

Water bodies | Areas permanently covered by water | 5 | 33.2 |

**Table 4.**Spatial coverage of flood-based farming systems (FBFS) in Kisumu County, Kenya and Tigray, Ethiopia derived from a classification algorithm based on an expert-informed Bayesian network.

Study Area | Area Covered by the Respective FBFS Potential Class (km^{2} and Share of Total Area) | ||||
---|---|---|---|---|---|

Very Low | Low | Medium | High | Very High | |

Kisumu County, Kenya | 873.3 (32.8%) | 552.7 (20.7%) | 72.5 (2.7%) | 495.5 (18.6%) | 670.8 (25.2%) |

Tigray region, Ethiopia | 9000.9 (17.1%) | 11,185.2 (21.3%) | 597.0 (1.1%) | 11,530.2 (21.9%) | 20,209.3 (38.5%) |

**Table 5.**Accuracy assessment of a map derived from an expert-informed Bayesian network mapping of flood-based farming systems (FBFS) potential in Kisumu County, Kenya and Tigray, Ethiopia.

Study Area | Validation Polygons | FBFS Potential | ||||||

Land use type | Number | Area (km^{2}) | Very low | Low | Medium | High | Very high | |

Kisumu | FBFS fields | 11 | 48.9 | 0.6% | 8.4% | 0.9% | 19.2% | 70.9% |

Forests | 5 | 7.3 | 50.0% | 44.6% | 0.6% | 2.8% | 1.9% | |

Irrigated agricultural fields | 2 | 92.0 | 14.4% | 29.1% | 2.9% | 22.1% | 31.5% | |

Rainfed agricultural fields | 2 | 1.3 | 21.3% | 52.5% | 0.6% | 25.0% | 0.6% | |

Riparian vegetation | 4 | 6.7 | 3.2% | 16.5% | 0.0% | 12.4% | 67.8% | |

Water bodies | 2 | 164.9 | 100.0% | 0.0% | 0.0% | 0.0% | 0.0% | |

Tigray | FBFS fields | 9 | 65.7 | 2.1% | 9.2% | 4.3% | 17.5% | 66.8% |

Forests | 4 | 3.3 | 36.1% | 34.7% | 0.0% | 16.5% | 12.7% | |

Irrigated agricultural fields | 4 | 9.9 | 15.0% | 32.7% | 1.7% | 24.3% | 26.3% | |

Rainfed agricultural fields | 2 | 38.0 | 41.9% | 41.7% | 0.4% | 14.0% | 2.0% | |

Riparian vegetation | 4 | 1.6 | 19.1% | 26.5% | 4.9% | 14.7% | 34.8% | |

Water bodies | 5 | 33.2 | 94.0% | 3.1% | 0.0% | 2.2% | 0.7% |

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## Share and Cite

**MDPI and ACS Style**

Liman Harou, I.; Whitney, C.; Kung’u, J.; Luedeling, E.
Mapping Flood-Based Farming Systems with Bayesian Networks. *Land* **2020**, *9*, 369.
https://doi.org/10.3390/land9100369

**AMA Style**

Liman Harou I, Whitney C, Kung’u J, Luedeling E.
Mapping Flood-Based Farming Systems with Bayesian Networks. *Land*. 2020; 9(10):369.
https://doi.org/10.3390/land9100369

**Chicago/Turabian Style**

Liman Harou, Issoufou, Cory Whitney, James Kung’u, and Eike Luedeling.
2020. "Mapping Flood-Based Farming Systems with Bayesian Networks" *Land* 9, no. 10: 369.
https://doi.org/10.3390/land9100369