Yield analysis of the Mwea Irrigation scheme

Study area

The MIDP has a gazzetted area of 30 350 acres out of which 26 000 acres is dedicated to paddy rice cultivation. The main scheme in the gazzeted area is divided into five main sections (hydraulic and administrative units): Karaba, Mwea, Teberre, Thiba, and Wamumu. These sections are further divided into 47 blocks in total. The scheme is located along the drainage basins of Rivers Nyamindi and Thiba, which also supply the irrigation water to the scheme ( figure 1).

Kenya experiences two rainy seasons that are linked to the kusi monsoon wind patterns: 

• the long rains from March to May; and
• the short rains from October to December.

The kaskazi winds bring drier conditions. The Thiba Dam was built to provide a year-round water supply for the MIS, expanding irrigation and allowing for double cropping. 

^{Figure 2: Methodology worklflow}

Data

WaPOR data: from the version 3 of the dataset (available in the portal from the beggining of 2024 to date, with data going as far back as 2018) was acquired from the WaPOR portal to carry out the analysis. The layers used were: 

• AETI (actual evapotranspiration and interception): the combined water loss from a surface through evaporation from soil and water bodies, transpiration from plants, and interception of water by vegetation canopies, expressed in millimeters of water per unit of time (mm/month*); and 
• NPP (net primary production): the amount of carbon that vegetation captures through photosynthesis after subtracting the carbon used for plant respiration, expressed as grams of carbon per square meter per unito of time (gC/m²/dekad*). In essence, NPP refers to how much the plants grow and accumulate biomass over the observed time frame.

* The data was downloaded at the monthly and dekadal (10 days) time-steps, then aggregated to the period of study: from May to December.

Local data: 

• yield data by section, that was used for the validation. The field data used in this analysis was collected through a multi-stage stratified random sampling approach. Sections served as strata, from which blocks/units were randomly selected, followed by random selection of farms. The exact aggregation methodology from sample plots to section-level yields is not clearly documented in public sources we consulted. 
• boundaries of the irrigation scheme (shapefile). 

This data was provided by the NIA, that has collaborated with this study and facilitaded greatly its execution. 

Study period

The MIS practices 2 to 2.5 rice growing seasons annually. The main season runs from July (sometimes earlier) to December. A secondary, shorter season occurs from March to July, and a ratoon crop can also be grown between December and February. Based on reports by the NIA for the period of interest, the growing period considered spanned from 01 May to 15 December.

The multi-year approach adopted in this study seeks to compare these main growing seasons accross four years: from 2019 to 2022. This period for the four years was chosen due to the availability of field data from the NIA. 

^{Equations 1 and 2: formulas for calculatting total biomass production and yield}

Analysis

The analyses were conducted using python and QGIS. The work done using python rested on the freely available WaPORIPA 3 repository developed by IHE Delft, a partner of the WaPOR project. QGIS was used for the data preparation. 

Besides are the formulas used to calculate TBP (total biomass production) and Y (yield). 

Terms of the equations:

• TBP, in tons/ha, expresses the total amount of dry matter produced over the season;
• NPP, in gC/m2 /season, espresses how much dry matter crops actually keep and store after using some of their energy for basic survival functions like breathing. It's the net growth they achieve;
• 45 is a conversion factor that transforms NPP into TBP by accounting for the fact that carbon typically makes up about 45% of plant dry matter;
• 1000 converts the units from gC/m2/season to tons/ha;
• HI is the harvest index; it is unitless. It refers to the ratio that shows what percentage of the NPP ends up as harvestable crop;
• AOT is the above ground total biomass production, also unitless. It refers to the plant matter that grows above the soil surface (stems, leaves, branches, and the harvestable parts like grains or fruits) and excludes what is underground (the roots);
• f_c is the light use efficiency correction factor, which adjusts the biomass calculation to account for local conditions that might affect how efficiently plants convert sunlight into biomass. This factor was obtained from the litterature;
• M_c is the moisture content factor, which converts dry matter biomass to fresh weight biomass by accounting for the water content in the harvested crop. The Mc is crop-specific and was found in the litterature;
• Y, in ton/ha/season, expresses the amount of harvestable crop: it's the useful part of the NPP that can be sold or consumed. 

In order to answer this question, the AETI of the irrigated area (total water lost from crops and soil through evaporation, transpiration, and rainfall pooled in the canopy) of the area of interest (AOI) was observed for each month of the growing seasons over the 4-year study period. 

The AETI time series for the main growing seasons in 2019, 2020, 2021 and 2022 (figure 3) demonstrates a consistent seasonal pattern that closely aligns with the rice crop calendar.

• 1️⃣: AETI values are typically low during land preparation and early planting phase (May–June),
• 2️⃣: rise sharply during the vegetative and reproductive phases (July–October),
• 3️⃣: and gradually decline during crop maturity and harvest (November–December).

This trend reflects that the phenological stages of rice growth is captured well and is observed consistently across all four years. All five sections within the irrigation scheme—Karaba, Mwea, Tebere, Thiba, and Wamumu—follow this general trend, with variations in magnitude and in the timing of the stages (1️⃣,2️⃣ and 3️⃣).

Notably, Wamumu and Karaba seem to consistently higher AETI values (4️⃣) despite their smaller land area. This is potentially due to better irrigation infrastructure, more intensive cultivation, or a higher proportion of irrigated rice fields.

For the 2022 and 2023 seasons, however, there is a slight increase in AETI observed toward the end of each main season (October–December) (5️⃣). This could be attributed to the onset of short rain season in Kenya, residual soil moisture, or continued irrigation, including land preparation for the subsequent season. These factors contribute to sustained evapotranspiration even after the crop reaches physiological maturity.

High AETI values observed at the start of the 2022 and 2023 seasons can be explained by a variety of potential factors. The start and end of season dates (SOS and EOS) used in this study were determined by reports by the NIA, and could correspond more to planned dates than actual dates that typically vary year-to-year. This could mean that the these two years' seasons may have started a bit later (6️⃣) on the ground. The implication is that the AETI and NPP values (from which yield is derived) may include a short lapse of time that corresponds to the previous season, which has the potentinal to bias the subsequent yield analysis for those two years.

Considering double cropping is practiced in MIS, the initial decline in AETI followed by an increase likely might reflect the chosen SOS including late crop stages from the preceding double-cropping cycle.

However, due to limited spatial granularity of the validation data, these are interpretations are primarily based on temporal trends observed in the AETI datasets. Furthermore, satellite-derived AETI estimates may also capture evapotranspiration from non-crop vegetation, standing water, or fallow fields with residual moisture, potentially leading to overestimations during initial phases of the crop growth cycle. 

Overall, AETI time series provide valuable insights into crop phenology. 

^{Figure 3b: AETI time series (view 1: individual years)}

In order to answer this question, the yield data provided by the NIA at the section level was compared to the yield data estimated using WaPOR data for each main growing season over the 4 year study period. The WaPOR-based seasonal yield was obtained by summing the dekadal data.

Several metrics were calculated to assess the relationship between estimated and observed yields over the 4-year period:

• Percent bias (PBIAS = -0.45%) The PBIAS measures the average tendency of predictions to be larger or smaller than observations. The value of -0.45% is close to zero, indicating that WaPOR estimates are, on average, virtually unbiased compared to field yields, with a very slight tendency towards underestimation.
  
• Mean error (ME = -0.03 t/ha) The mean error represents the average difference between predictions and observations (without taking absolute values). At -0.03 t/ha, this confirms minimal systematic bias, with errors distributed symmetrically around zero, which means that some overestimations and some underestimations largely cancel out.
  
• Mean absolute error (MAE = 0.795 t/ha) The MAE expresses the average magnitude of prediction errors in the same units as yield. With typical yields around 6 t/ha (as shown in Figure 5), an MAE of 0.795 t/ha represents approximately 13% error, indicating that individual predictions deviate from observed values by about 0.8 t/ha on average.
  
• Normalized root mean square error (nRMSE = 15.30%) nRMSE quantifies error magnitude relative to mean observed yield and, unlike MAE, penalizes larger errors more strongly. At 15.3%, this indicates the model has moderate predictive accuracy. That is, reasonable for yield estimation models but with non-negligible error that should be considered when using these estimates for decision-making. For average yields of roughly 6 t/ha, this suggests approximately 68% of estimates fall within ±0.92 t/ha of the true yield (roughly 5.1 - 6.9 t/ha) and 95% fall within ±1.8 t/ha (roughly 4.2 - 7.8 t/ha).
  
• Standard deviation of yields (WaPOR = 0.456 t/ha vs. observed = 0.490 t/ha): the similarity in standard deviations indicates that WaPOR captures not only the mean yields well, but also their temporal variability across seasons, which is important for understanding local and temporal yield dynamics.

Overall, the model demonstrates minimal systematic bias with moderate prediction errors of approximately 15% relative error, which represents typical performance for remote sensing-based yield estimation.

^{Figure 4: scatter plot of WaPOR-based yield estimate compared to the field measured yields}