Dynamic NDVI Modeling in Malawi: Insights for Climate-Adapted Agriculture

Unpacking Malawi’s Geography

Landlocked Country in Southeastern Africa
- Borders: Tanzania, Zambia, Mozambique
- Diverse topography: Highlands and lowlands

Agriculture: Main Source of Livelihood

Employs ~80% of the Population
Key Crops:
- Maize
- Groundnut
- Tobacco

Figure 2: A female farmer in Malawi (Flickr)

Climate Vulnerabilities and Impacts

Increasing Climate Variability
- Average temperatures in Malawi have risen by 0.9°C–1.2°C since 1960 (World Bank, 2021).
Frequent droughts and floods
- Six major droughts in the past 30 years, affecting 24+ million people (UNICEF, 2020).
- Floods have doubled in frequency since 1990 (UNDP, 2022).

Figure 3: Flooding in Nsanje, Malawi, 16 March 2023 (Flickr)

Agricultural Vulnerabilities

Impact on Crop Yields
- Maize yields decreased by 25%–40% (Lobell et al., 2011).
  - Projected to decline by 11%–30% by 2050 (Portmann, Burger, & Läderach, 2014).
Limited irrigation infrastructure
- Only 3% of farmland is irrigated (IFPRI, 2017).

Figure 4: A Malawian Farmer Assessing Drought-Affected Maize Crops in 2015. (Source)

Economic and Food Security Challenges

Economic Impacts
- Droughts reduce GDP by 1% annually (World Bank, 2017).
Reliance on Rain-Fed Agriculture
- 95% of farmland depends on rain (ActionAid, 2006).
- Leads to food insecurity during droughts and erratic rainfall (Zulu et al., 2014).
- Affecting smallholder farmers the most.

Figure 5: Drought-affected farmland in Malawi (2015). (Source)

NDVI: Proxy for Vegetation Health and Agricultural Productivity

Normalized Difference Vegetation Index (NDVI)

\[ \text{NDVI} = \frac{\text{NIR} - \text{RED}}{\text{NIR} + \text{RED}} \]

Widely used to monitor vegetation health.
Reflects photosynthetic activity and biomass.
Ranges from -1 to 1.

Figure 6: NDVI explained through vegetation conditions: withered, stressed, and healthy (Source)

Limitations of NDVI Monitoring for Agricultural Analysis

NDVI patterns are frequently disrupted by extreme events like floods and droughts. Limitations of Current Models: Existing NDVI models struggle to account for:

Short-term impacts (e.g., crop failures during disasters).
Long-term recovery trends critical for sustainable agricultural planning.
Spatial variability in NDVI dynamics across regions.
Data Limitations: Sparse ground observations and limited satellite coverage.

Figure 7: Spatial and temporal challenges in NDVI monitoring across Malawi. (Source)

Why a Dynamic Framework Is Necessary?

Figure 8: Framework for addressing climate change impacts on agriculture in Malawi

Research Questions

How can advanced stochastic models capture the impact of extreme weather events (e.g., flooding, droughts) on NDVI dynamics in Malawi?

Does combining stochastic modeling with machine learning improve NDVI prediction accuracy under stable and extreme conditions?

Methodology: Establishing a Baseline

Simple Time Series Models (AR(1))

\[ \text{NDVI}_t = \phi \cdot \text{NDVI}_{t-1} + \epsilon_t \] where:

\(NDVI_t\): Observed NDVI at time \(t\)
\(NDVI_{t-1}\): NDVI at the previous time step \(t-1\)
\(\phi\): Autoregressive coefficient
\(\epsilon_t\): Random Error term

Purpose: Establish a basic trend in NDVI.
Limitations: Unable to capture abrupt changes due to extreme weather.

Methodology: Dynamic Linear Model (DLM)

State Equation (1)

Describes the evolution of NDVI over time:

\[ NDVI_{t+1, i} = \phi \cdot \text{NDVI}_{t, i} + \mathbf{\beta} \cdot \mathbf{X}_{t, i} + \epsilon_{t, i} \] Observation Equation (2)

Links the true NDVI state to observed NDVI with noise:

\[Observed \ NDVI_{t, i} = \text{NDVI}_{t, i} + \eta_{t, i}\]

where:

\(\mathbf{X}_{t, i}\) : Vector of environmental predictors (e.g., precipitation, temperature, soil moisture) for location \(i\) at time \(t\).

\(\phi\) : Autoregressive coefficient capturing temporal dependency.

\(\mathbf{\beta}\) : Coefficients for the predictors.

\(\epsilon_{t, i} \sim \mathbb{N}(0, \sigma^2_\epsilon)\) : Process noise, accounting for unexplained variability.

\(\eta_{t, i} \sim \mathbb{N}(0, \sigma^2_\eta)\) : Observation noise reflecting measurement uncertainty.

Enhanced Spatio-Temporal Dynamic Model (STDM)

Accounts for both spatial and temporal variability in NDVI dynamics.

State Equation

\[ \text{NDVI}_{t+1, i} = \phi \cdot \text{NDVI}_{t, i} \\ + \rho \cdot \sum_{j\in \mathbb{N}(i)} w_{ij} \cdot \text{NDVI}_{t, j} \\ + f(\mathbf{X}_{t, i}; \mathbb{\beta}) + \epsilon_{t, i} \] Observation Equation \[\text{Observed NDVI}{t, i} = \text{NDVI}{t, i} + \eta_{t, i}\]

where:

\(\rho\) : Spatial dependency coefficient, capturing influence from neighboring locations.

\(\mathbb{N}(i)\) : Set of neighboring locations for \(i\) .

\(w_{ij}\) : Spatial weights.

\(f(\mathbb{X}_{t, i}; \mathbf{\beta})\) : Non-linear function of predictors (e.g., precipitation, temperature).

\(\epsilon_{t, i} \sim \mathbb{N}(0, \sigma^2_\epsilon)\) : Process noise.

\(\eta_{t, i} \sim \mathbb{N}(0, \sigma^2_\eta)\) : Observation noise.

NDVI Forecasting (DLM & ARIMA) Using MODIS

Figure 9: Forecast of NDVI for 10 years using AutoARIMA, with observed NDVI (green), forecasted NDVI (orange), and the 95% confidence interval (shaded area)

Figure 10: Dynamic Linear Model (DLM) forecast evaluation of NDVI. Training data (green) and validation data (black) are compared to the forecasted NDVI (blue dashed line)

The dataset consists of dekadal NDVI indicators from NASA’s MODIS collection 6.1, aggregated to sub-national administrative units in Malawi, including current NDVI values, long-term averages, and percentage anomalies, to monitor vegetation trends and productivity.
The AutoARIMA model highlights long-term NDVI predictions, incorporating seasonal patterns but with increasing uncertainty in the forecast horizon (wide confidence intervals).
The DLM model effectively validates predictions with observed data, showing stronger alignment to trends and seasonality.

Comparing Observed and Predicted NDVI: LSMS vs. PlanetScope

Figure 11: Average observed NDVI for 2018 based on LSMS (Living Standards Measurement Study) data, aggregated at the district level in Malawi.

Figure 12: Predicted NDVI for 2018 using the Spatio-Temporal Dynamic Model (STDM) with PlanetScope imagery as input.

The LSMS NDVI data provides district-level observed vegetation productivity.
The model comparison highlights spatial variability, with certain districts showing strong agreement between observed and predicted NDVI, while others reveal discrepancies.
Discrepancies between observed and predicted values point to opportunities for refining models, improving both short-term and long-term NDVI predictions.

Conclusion

Summary & Key Insights

Dynamic Linear Models (DLMs) provide a baseline for NDVI modeling.
Enhanced Spatio-Temporal Dynamic Models (STDMs) capture spatial and temporal variability.
Combined model approach improves NDVI modeling in Malawi under variable conditions.

Future Directions

Machine Learning Enhancement
Expand model to other regions and include more environmental variables.

Q&A

Thank you!

Refrences

McSweeney, C., New, M., & Lizcano, G. (2010). UNDP Climate Change Country Profiles: Malawi. Retrieved from https://gcfsi.isp.msu.edu/files/1014/8545/9985/Zulu_-_Climate_Variability_LAN_1.cmts_ewc.pdf
ActionAid. (2006). Climate Change and Smallholder Farmers in Malawi.
Government of Malawi. (2015). Post-Disaster Needs Assessment Report.
Zulu, L. C., & others. (2014). Climate Variability and Change in Malawi: A Focus on Agriculture. Global Center for Food Systems Innovation. Retrieved from https://gcfsi.isp.msu.edu/files/1014/8545/9985/Zulu_-_Climate_Variability_LAN_1.cmts_ewc.pdf
Lobell, D. B., Burke, M. B., Tebaldi, C., et al. (2008). Prioritizing climate change adaptation needs for food security in 2030. Science.
Jones, P. G., & Thornton, P. K. (2009). The potential impacts of climate change on maize production in Africa and Latin America in 2055. Global Environmental Change.
International Food Policy Research Institute (IFPRI). (2017). Malawi Policy Note: Irrigation. Retrieved from https://massp.ifpri.info/files/2017/08/MaSSP-Policy-Note-28-_Irrigation-formatted-revised.pdf
(IFPRI, 2017).
World Bank. (2017). Turn Down the Heat: Climate Extremes, Regional Impacts, and the Case for Resilience. Retrieved from https://documents.worldbank.org/en/publication/documents-reports/documentdetail/260191515082979489/turn-down-the-heat-climate-extremes-regional-impacts-and-the-case-for-resilience