Detecting Agricultural and Meteorological Drought With Gross Primary Production Recovery Including Spatiotemporal Statistical Analysis in East Africa's Lake Victoria Basin

Drought imposes severe, long-term effects on global environments and ecosystems. A better understanding of how long it takes a region to recover to pre-drought conditions after drought is essential for addressing future ecology risks. In this study, drought-related variables were obtained using remote sensing and reanalysis products for 2003 to 2016. The meteorological drought index (standardized precipitation evapotranspiration index [SPEI]) and agricultural drought index (vegetation condition index [VCI]) were employed to estimate drought duration time (DDT) and drought recovery time (DRT). To the basin’s west, decreasing rainfall and increasing potential evapotranspiration led to decreasing SPEI. On the east side, decreasing soil moisture from each depth effects vegetation condition, which results in a decreasing gross primary productivity and VCI. Extreme meteorological drought events are likely to occur in the basin’s northeastern and middle western areas, while the southern basin is more likely to suffer from extreme agricultural drought events. The mean SPEI-based DDT (2.45 months) was smaller than the VCI-based DDT (2.97 months); the average SPEI-based DRT (2.02 months) was larger than the VCI-based DRT (1.63 months). Most of the area needs 1 or 2 months to recover from drought except for the basin’s northwestern area, where the DRT is more than 8 months. DDT is the most important parameter in determining DRT. These results provide useful information about regional drought recovery that will help local governments looking to mitigate potential environmental risks and formulate appropriate agricultural policies in Lake Victoria Basin. values VCI, Decreasing eastern area.


Introduction
As a devastating hazard, drought not only imposes extensive and long-term effects on the global environmental system, it also causes signi cant losses to the economy and human life ( (Schwalm et al., 2017). Regional drought effects are compounded if a new drought event occurs before recovery from a preceding drought event is complete (Seneviratne and Ciais, 2017). Therefore, accurate DRT assessments are essential for understanding possible ecological risks.
DRT is de ned as the time required for a region to fully return to its pre-drought conditions (Schwalm et al., 2017). Drought identi cation and recovery parameter selection are the key steps in DRT calculations.
To identify a drought event, previous studies used the meteorological drought index (Standardized Precipitation Evapotranspiration Index, SPEI) and Drought Severity Index (DSI) Schwalm et al., 2017;Yu et al., 2017). Climate data-based SPEI is easy to estimate for long-term analysis but it is not linked to plant condition (Vicente-Serrano et al., 2010). Satellite-based DSI includes greenness information with high spatial resolution. However, DSI data is only available from 2000 to 2011 with uncertainties from the satellite (cloud cover, atmospheric aerosols, and low solar illumination) and single input data (Mu et al., 2013).
Many factors such as water quantity (stream ow and total water storage), water quality (water temperature, turbidity, and dissolved oxygen), ecosystem uxes (carbon and energy uxes), and gross primary productivity (GPP) are used in drought recovery assessments (Ahmadi et  found that most of the world can recover from a drought in less than six months. Unlike a conventional drought, a ash drought typically occurs during warm seasons and can occur more frequently -in one or two months (Ford and Labosier, 2017). Therefore, DRT should be examined in more detailed studies at a high spatiotemporal resolution. Yu  To better understand drought recovery in the Lake Victoria Basin, our objectives are 1) check the seasonal patterns and trends of drought-related variables; 2) capture drought events using meteorological (SPEI) and agricultural (vegetation condition index [VCI]) drought indices from 2003 to 2016; 3) investigate SPEI based-and VCI based-DRT for high spatiotemporal resolution; and 4) examine parameter importance for determining DRT across the Lake Victoria Basin. To the best of our knowledge, this is the rst comprehensive study to quantify agricultural DRT at a high spatiotemporal resolution.

Study area
As the second largest freshwater lake in the world, Lake Victoria supports one of the world's poorest and densest populations. Its catchment covers a 194,200 km 2 area and has a total population of 30 million people (Mailu, 2001). Basin agriculture supports more than 70% of the local population (Zhou et al., 2014). Figure 1 shows the land cover distribution in the Lake Victoria Basin. Grassland (16%) is predominantly in the west, open water (26%) in the middle, and cropland (36%) in the east. Maize is the main crop (Zhou et al., 2014).
The Victoria Basin is shared by 5 agricultural East African nations: Kenya, Uganda, Tanzania, Rwanda, and Burundi. Kenya is in the northeastern part of the basin, and contains three provinces: Nyanza, Western, and Rift Valley. They are predominantly cropland. The northwest comprises central Ugandan districts Masaka and Mpigi, which are characterized by large farming communities. Tanzania, located in the basin's south, also has a large cropland area. Most of the farmland is located in the Mwanza and Mara provinces, though it also covers the Kagera region, a key region for food production and distribution whose landcover is a mixture of cropland and grassland. Rwanda is located in the western part of the study area and is mainly covered by cropland. Burundi is also in the western basin and is half cropland.
According to the Köppen-Geiger climate classi cation (Peel et al., 2007), Lake Victoria Basin's climate zone is tropical with four distinct seasons: hot dry (Dec. to Feb., DJF), major rainy (Mar. to May, MMA), short dry (Jun. to Aug., JJA) and short rainy (Sept. to Nov., SON) (Awange JL, 2006). Annual precipitation ranges between 670 and 2,200 mm, with a mean value of 1,202 mm (Kizza et al., 2009). Several studies discuss droughts in the Lake Victoria Basin during the twentieth century's last two decades (Funk et  Next, we used the GLDAS-based PET and rainfall data from TRMM-3B43 to compute SPEI. In this study, we used the GLDAS_NOAH025_M _V2.1 dataset (Beaudoing and Rodell, 2020) for soil moisture (0-10cm, 10-40cm, 40-100cm, and 100-200cm) data, net radiation ux, ground heat ux, air temperature, and surface pressure. GLDAS combines ground and satellite data via assimilation methods along with land surface models. The National Centers for Environmental Prediction (NCEP), National Aeronautics and Space Administration (NASA), and National Oceanic and Atmospheric Administration (NOAA) created GLDAS (Rodell et al., 2004) (http://disc.sci.gsfc.nasa.gov/hydrology/data-holdings).
TRMM is a two-country collaboration between NASA and Japan's National Space Development Agency that gathers information related to tropical and subtropical precipitation (Tropical Rainfall Measuring Mission. 2011). The TRMM mission became defunct in 2015 and was succeeded by the Global Precipitation Mission (GPM), with some TRMM products continuing with GPM, such as TRMM-3B43 (Huffman et al., 2007). TRMM-3B43-Monthly gives the best latitudinal precipitation estimate and is available at 0.25° spatial resolution with a 1 month granule size. Data has been collected from 1998 to the present and covers 50° N to 50° S (https://disc.gsfc.nasa.gov/datasets/TRMM_3B43_7/summary). Kogan (1990) proposed and modi ed NDVI to VCI to normalize NDVI values relative to their minimum and maximum. We estimated VCI from NDVI using one of Terra Moderate Resolution Imaging Spectroradiometer (MODIS)'s standard products, the MODIS Vegetation Indices (MOD13C2). It has a temporal and spatial resolution of 1 month and 500 m, respectively. TRMM data and MOD13C2 have the same temporal coverage. The MODIS NDVIs are processed from atmospherically recti ed two-way surface re ectance values that have been suppressed for cloud shadows, heavy aerosols, clouds, and water (Didan, 2015). The MODIS NDVI product can be accessed from the Oak Ridge National Laboratory Distributed Active Center (http://daac.ornl.gov/MODIS/).
To estimate DRT, we used the Global Monthly GPP from an Improved Light Use E ciency (LUE) Model (GMPILUEM) between 1982-2016 with an 8 km spatial resolution (Madani and Parazoo, 2020). This GPP product uses climate data from the Modern-Era Retrospective Analysis for Research and Applications Version 2, canopy and fraction of photosynthetically active radiation data from Global Inventory Modeling and Mapping Studies (GIMMS 3g), and improved LUE based on ux tower data. The dataset can be downloaded from https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=1789. All dataset spatiotemporal resolution was converted to 0.05° × 0.05° (monthly). Detailed information about this study's dataset is shown in Table 1. 3. Methods

Potential evapotranspiration
In this study, we calculated PET using the PT method (Eq. (1)) (Priestley and Taylor, 1972) because it only requires wind and relative humidity climate data. Additionally, PT model PET estimates in tropical areas were found to be acceptable in Gunston and Batchelor, (1983). The PET is estimated as shown below: where Δ is the slope vapor pressure curve (kPa/˚C); R n is net radiation (MJ/m 2 /day); γ is a psychrometric constant (kPa/˚C); G is the soil heat ux (MJ/m 2 /day); λ is the latent heat of vaporization (MJ/kg); and α is the PT coe cient, usually with a default value of 1.26 (Priestley and Taylor, 1972). Kogan (1990) proposed the VCI equation using current, minimum, and maximum NDVI values for each pixel:

Drought indices
where VCI amy is the value of VCI assigned to pixel a for the duration of month m for year y; NDVI amy is a value of the monthly NDVI for pixel a for month m and year y; and NDVI a, min and NDVI a, max are the multiyear minimum and maximum NDVI, respectively, corresponding to pixel a. The observed values' resulting percentage is positioned between the maximum and minimum values of prior years. Higher and lower values signify good and bad vegetation state conditions, respectively.
SPEI is a meteorological drought index based on the log-logistic distribution of the difference between precipitation and PET (Vicente-Serrano et al., 2010). To estimate SPEI, the monthly difference between precipitation and PET is calculated rst: where d i is the difference between precipitation (P i ) and PET in month i. Next, the probability density function of the log-logistic distributed variable f(x), which has three parameters (Singh et al., 1993), is shown as: where , , and are scale, shape, and origin parameters, respectively, for d values in the range ( >d<∞); is the gamma function; are probability-weighted moments for order i; and n is sample size. Following this, we can estimate the probability distribution function of d as: Finally, SPEI can be estimated by converting F(x) into corresponding SPEI 1-month Z-standardized normal values (Abramowitz and Stegun, 1965): According to SPEI classi cation (McKee et al., 1993), the drought severity scale from − 2 to 2 is divided into 7 levels, with less than − 2 indicating extreme drought and larger than 2 indicating extreme wet conditions. With the same drought severity scale as SPEI, VCI has only 5 levels (Kogan, 1995). Detailed information about their classi cations can be found in Table 2.

Drought Recovery Time (DRT)
We determined DRT using a combination of monthly drought index (SPEI or VCI) and GPP values for each pixel in the 14-year period from 2003 to 2016. A drought starts when SPEI − 1 (VCI 30), and ends when SPEI − 1 (VCI 30). These conditions have to persist for at least 3 months for it to be considered a drought event. After de ning a drought event using SPEI or VCI, DRT can be estimated

Boruta algorithm
We used the Boruta algorithm to examine which parameters are most important when determining DRT. The Boruta method selects variables and ranks them in order of importance while rejecting parameters that do not improve -or adversely affect -the model's accuracy. Boruta operates by initially adding randomness to a dataset by creating shu ed duplicates of all parameters. These are termed 'shadow parameters' (Kursa and Rudnicki, 2010). The extended dataset is then trained with a random forest classi er using decision trees to select appropriate class. The appropriate class is reached by applying a measure that determines each parameter's importance. A higher result translates to more important class. The algorithm performs iterations where it checks whether the real parameter has a higher importance than the best shadow feature at every stage. This is done by comparing "z scores"; the real parameter must have a higher z score than the maximum shadow parameter z score. In this process, parameters considered unimportant are eliminated. The algorithm terminates when all parameters are con rmed or  (Table 3).
As shown in Fig. 2 Generally, JJA showed low rainfall, GPP, SM, VCI, and SPEI, the driest season. SM from 0 to 100 cm increased when rainfall increased and decreased when there was less rainfall.

Annual drought conditions
To assess drought conditions in the study area, we estimated SPEI and VCI annual spatial distribution (Fig. 4). Generally, mean SPEI and VCI values indicate that near-normal conditions imply a potentially stable canopy cover and greenness. As shown in Fig. 4a, SPEI mean annual spatial distribution showed near-normal conditions with very moderate drought tendencies. For example, in 2007, the entire basin was almost normal. But drought prevalence has progressed since then, with conditions peaking in 2016 when the majority of the basin experienced moderate to severe drought conditions.
VCI mean annual spatial distribution shows almost no drought, with light to moderate drought occurring in the southeastern part of the basin (Fig. 4b) This is because VCI is an indicator of greenness, whereas SPEI considers PET and rainfall climate factors. That fundamental difference in approach implies a time lag in the results (Fig. 4)

Monthly drought conditions
We calculated monthly SPEI and VCI spatial distributions to assess detailed monthly drought variation with a scale denoting drought severity from "extreme wet" to "extreme drought" (Fig. 5). The results shown in Fig. 2, Fig. 4, and Fig. 5 are consistent with the evidence from several reports referenced in Table 4. From 2003 to 2016, July has consistently experienced the most severe to extreme drought conditions. Generally, JJA has the most signi cant drought conditions, which are consistent with the results shown in Fig. 2 To evaluate drought condition results, we analyzed recorded drought years for different countries in the study area, as shown in Table 4 . The drought variation's spatial extent is shown in Fig. 5. It is notable that Fig. 5 shows a onemonth delay in 'dry' conditions predominant from June to August using the SPEI index and from July to September, even extending into October, with the VCI index. This is because SPEI relies on meteorological data whereas VCI relies on vegetation conditions, implying drought is rst observed meteorologically before it's observed in vegetation.

Drought event identi cation based on drought severity
To understand drought event history based on SPEI and VCI results, we calculated the percentage of different drought events based on severity (Table 3). Spatial distribution is shown in Fig. 6. The most moderate SPEI drought events ( ) were in the southern part of the study area (Fig. 6). Most of the study area has up to 70% possibility of experiencing moderate drought and a 10 to 20% possibility of experiencing a severe drought ( ). Extreme drought events ( mostly occurred in the eastern and northeastern tip of the study area (Fig. 6). Overall trends indicate that the basin has a higher spatial area percentage prone to moderate drought. Using VCI data, 50 to 80% of the study area may experience a moderate drought ( ) except for regions in the southeast and southern tip, where the percentage is only 10 to 30%. VCI-predicted severe drought ( is similar to SPEI. The majority of the study area has a 10 to 20% chance of experiencing extreme drought ( ) except for the southeast region, which shows a 40 to 70% likelihood (Fig. 6). Both VCI-and SPEI-based percentage coverage trends for moderate (M), severe (S), and extreme (E) drought are similar where the spatial drought coverage percentage decreases from moderate to severe. There are some differences, however, in the southeast region for SPEI_M, VCI_M, and SPEI_E, VCI_E which show an inverse trend. This is because VCI indicates drought based on actual vegetation conditions whereas SPEI indicates drought based on meteorological conditions. Overall, more moderate and severe drought events occurred in the southern part of the study area; the eastern and western parts of the basin experienced extreme drought events. As previously discussed, the western area is mostly farming communities in Uganda, Tanzania, Rwanda, and Burundi, including large food crop (maize) belts in central and eastern Uganda. The areas prone to moderate, severe and extreme drought events (Fig. 6) should be considered high-risk drought areas and likely future bottlenecks for water balance. Drought mitigation strategies are imperative in these areas.

Drought duration and recovery time based on SPEI and VCI
Using SPEI and VCI drought indices, we calculated and compared mean DDT and DRT spatial distributions in the Lake Victoria Basin from 2003 to 2016 (Fig. 7). The mean SPEI-DDT ranges from 2 to 4 months with a 2.45-day average value. The northeastern and southwestern study area were most likely to suffer from meteorological drought (i.e., SPEI) for at least 3 months, compared to 2 months in other areas. The VCI-DDT spatial distribution (2.97 months) was similar to SPEI-DDT (2.45 months) except for the southeast study area, where VCI-DDT is 2 months longer than SPEI-DDT. This means the southeastern part of the basin is more likely to suffer a long agricultural drought. The SPEI-DRT mean value is 2.02 months, though there are a few instances in the northwest basin area where SPEI-DRT took more than 8 months (black). The VCI-DRT mean value is 1.63 months, which is 0.39 months shorter than the SPEI-DRT mean value.
The study area's mean DDT is higher than the mean DRT, though the mean DDT and mean DRT are

Factors affecting DRT
We ranked the importance of DDT, SM depths, PET, GPP, rainfall, and drought indices on DRT (Fig. 8). We selected and ranked these factors using a "z score" for SPEI-DRT and VCI-DRT, where a higher value means the factor is more important. The shadow Min, shadow Mean and shadow Max (blue box plots) add randomness to the data to allow for more precise parameter ranking. The green box plots show that each features' z score is higher than the shadow value, which means they are all signi cantly important in determining SPEI-DRT and VCI-DRT.
DDT is the most important parameter for determining DRT for SPEI-DRT followed by GPP, PET, SPEI, and rainfall. Soil moisture, though still relevant, is the least important parameter for DRT determination. DDT is also the most crucial parameter for determining DRT for VCI-DRT followed by VCI and rainfall. Soil moisture is again classi ed as the least important parameter, though still important. Based on these results, DDT is the most important factor for determining DRT, regardless of drought indices. We examined DRT spatial distribution after 1, 2-, 3-, 4-, and 5-month drought events to understand the DDT and DRT relationship (Fig. 9). After a one-month drought, SPEI-DRT (SPEI_DRT_1) shows that the entire basin needs to recover from the drought event, with DRTs ranging from 1 to 4 months with some scattered pockets requiring up to 6 months. For a 2-month drought, SPEI_DRT_2, less areas need to recover from drought than for the SPEI_DRT_1 scenario, though there are some isolated pockets in the far east study area that require more than 8 months. SPEI_DRT_3 indicates similar DRTs to SPEI_DRT_2, but the area requiring longer time was larger than for SPEI_DRT_1 or SPEI_DRT_2.

Conclusions
Access to accurate drought duration and recovery time information is vitally important in drought-prone areas used for agricultural purposes. Using grid-based data with high resolution, we investigated seasonal patterns in drought-related variables, identi ed drought events, and examined both SPEI-and VCI-based DRTs in the Lake Victoria Basin from 2003 to 2016. This study is the rst to determine meteorological and agricultural DRTs for the Lake Victoria Basin on a 0.05° monthly scale. Of the four seasons, JJA was the driest, with lower values of rainfall, GPP, SM, VCI, and SPEI. Decreasing GPP and VCI is caused by increasing PET and decreasing SM from each depth in the basin's eastern area.
Decreasing SPEI is due to decreasing rainfall and increasing PET in the basin's western area. Drought indices SPEI and VCI showed that 2016 and 2007 were Lake Victoria Basin's driest and wettest years in the study range. Meteorological drought calculations showed that moderate droughts occurred at higher frequency in the southeastern part of the basin, whereas the northeastern and mid-western areas were more likely to suffer from extreme drought events. Agricultural drought measurements showed that extreme drought events occurred at higher frequency in the basin's southern areas. On average, SPEIbased DRT (2.02 months) was longer than VCI-based DRT (1.63 months). SPEI-DRT and VCI-DRT showed similar spatial distribution though SPEI-based DRT (2.02 months) was longer than VCI-based DRT (1.63 months) on average. DDT is the most important parameter for determining DRT, though regions with higher PET, SPEI, GPP, and precipitation values are also associated with shorter recovery times. These results improve understanding of drought on an ecosystem level. Nevertheless, a global DRT product with high accuracy and good spatial and temporal resolution remains challenging, and requires additional investigation.
Declarations 57. Zhang D, Liu X, Bai P (2019) Assessment of hydrological drought and its recovery time for eight tributaries of the Yangtze River (China) based on downscaled GRACE data.