IMPROVING THE LAND SURFACE GENERAL DROUGHT INDEX MODEL

Drought affects all human activities and ecosystems. Nearly 40 percent of the world’s population inhabit Drylands, and they depend on agriculture for their food, security and livelihoods. Among the remote sensing indices developed, the Land Surface General Drought Index (LSGDI) was recently proposed. This paper proposes an improved model of LSGDI to face the issue of drought in semi-arid and arid regions. The experiment was conducted for the Maga’s floodplain, in NorthCameroon. The method uses satellite images of Landsat in 1987, 2003 and 2018, for January and March or April, corresponding to the middle and the end of the dry season. A Vegetation Moisture Index (VMI) and a Normalized Difference Soil Drought Index (NDSoDI) are both developed. On an orthogonal plan, their projections give a drought line that expresses the improved LSGDI (LSGDI2) as the root sum square of the NDSoDI and the VMI. The LSGDI2 results are ranged in [0.09 – 0.14] interval, which is used to define the threshold and ease the qualifiers for drought classes. The visual patterns easily match the sandy areas of the original Landsat images with the highest values, while the vegetation and water areas match the lowest values. Compared with the LSGDI and Second Modified Perpendicular drought Index (MPDI1), the new index reflectance values are higher. Finally, although LSGDI2 curve’s evolution follows the NDSoDI one at 94%, the new spectral index values depends on the both components, helping to map highest values of drought and moisture in Maga’s floodplain, for a sustainable rice culture expansion. * Corresponding author (stats.n.maps.expertise@gmail.com) The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W11, 2020 PECORA 21/ISRSE 38 Joint Meeting, 6–11 October 2019, Baltimore, Maryland, USA This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLII-3-W11-101-2020 | © Authors 2020. CC BY 4.0 License. 101


INTRODUCTION
Drought refers to an extended period, i.e. a season, a year, or several years, of deficient rainfall, relative to the statistical multi-year average for a region (Graham, S. 2000). Although there are dozens of definitions covering meteorological and hydrological aspects, this study addresses the agricultural effects of drought, in terms of the risk of low soil moisture and crop needs in the semiarid regions. This affects all human activities and ecosystems, and more than 2 billion people, nearly 40 percent of the world's population (White and Nackoney, 2003), inhabit Drylands. These populations depend on agriculture for their food, security and livelihoods. Over the years, Earth Observation (EO) sciences have been efficient in spatializing drought areas. Spectral indices are among the most important approaches.
From the vegetation moisture view, the Normalized Difference Vegetation Index (NDVI) and its derivatives such as the Soil Adjusted Vegetation Index (SAVI) and the Modified Adjusted Vegetation Index (MSAVI), based on the red and near infrared (NIR) wavelengths, were developed to monitor the vegetation cover and stage of growth. The Normalized Difference Water Index (NDWI) (Gao, 1996), the Anomaly Vegetation Index (AVI), the Vegetation Condition Index (VCI) (Kogan, F., 1995), and the Vegetation Health Index (VHI) (Kogan, F., 1997), help with assessing vegetation stress and health. Further, the Normalized Difference Drought Index (Gu, Y. et al., 2007) was used to assess the covered land surface dryness.
From the perspective of soil drought or moisture, the Normalized Multi-band Drought Index (NMDI) (Wang, L. and Qu, J.J., 2007) and the Perpendicular Drought Index (PDI)  were developed. The PDI was modified through the MPDI  and the MDPI1 (Li, Z. and Tan, D., 2014).
The main goal of this paper is to assess the land surface drought, through another spectral model that assesses the covered and the uncovered land dryness. Its gives a second technical approach of the Land Surface General Drought Index, LSGDI (Ngandam Mfondoum and Gbetkom, 2019), for sustainable agriculture expansion in arid and semi-arid regions.

Research location
The research was conducted on the site of Maga's floodplain, located between latitudes 10º37' -10º54' N, and longitudes 14º40' -15º10'E, in northern-Cameroon (Central Africa). It is an artificial floodplain extended on 1560 hectares and more than 200000 hectares with its surroundings, where a project of irrigated rice cultivation was launched in 1985 to promote national production. According to the national bioclimatic map, Maga's floodplain belongs to the Sudano-sahelian or semi-arid zone ( Figure 1). Yearly, the rainfall is around 500 mm, and temperatures vary between 15º and 41º Celsius. Natural vegetation is made of savannah that exposes the soil. The soil is loamy, clay and alluvial, characterized by sediments deposits. Several types of soil degradation have been identified, modelled and mapped (Ngandam Mfondoum, A.H. et al., 2016;Ngandam Mfondoum, A.H. and Gbetkom, P.G., 2019;Gbetkom, P.G. et al., 2019). However, there is still a need for EO support to anticipate the risk of increased silting, salinization and sodisation during the irrigated rice project's expansion planned by Cameroon's government.   Pre-processing help to minimize the effects of sensor, solar, atmospheric and topographic distortions. The images used are Level-1 products, which are delivered as digital numbers, DNs. Bands blue, green, red, near infrared, and both shortwave infrared were stacked. Applying the Cosine Solar TAUZ (COST) radiometric calibration model to the stacked image, the DNs were converted from at-sensor radiance to top-of-atmosphere (TOA) reflectance via solar correction, and rescaled from 64-bit to 8-bit. Atmospheric corrections and haze reduction have helped to remove other noises and then approximate values of surface reflectance. The last step concerned the topographic correction to lower altitude artifacts.

Experiment design
Ngandam Mfondoum and Gbetkom (2019) assume that balancing the moisture of the vegetated area with the dryness of the bare soil, is necessary to learn about the general drought retrieved from remote sensing techniques. They propose the Land Surface General Drought Index (LSGDI) as a normalized difference written as follows: Where the NDSoDI is the Normalized Difference Soil Drought Index and the VMI is the Vegetation Moisture Index. The subtraction of the normalized difference from 1 is suggested in order to: i) invert the values of soils from lower to higher values in the VMI; ii) keep highest values of the soil drought in the NDSoDI.
The NDWI is sensitive to changes in liquid water content and in spongy mesophyll of vegetation canopies (Gao, 1996). Its values usually exhibit a quicker response to drought conditions than NDVI (Gu et al., 2007). In sparse vegetation cover conditions characterizing semiarid zones, the SAVI is most suitable to assess vegetation cover and stages of growth and for adjusting the background soil reflectance through constant L value.
Spectral space plot between the NDWI and the SAVI for the main land cover categories, i.e. sandy soil, other soil, water body and rice crops, shows that they are highly correlated by the vegetation (Figure3 When visually compared to the NWDI and the SAVI, the VMI shows more efficiency in keeping vegetation moisture, lowering surface water, and being more sensitive to vegetation, soil features and sediments deposits at the lake's bottom (Figure 4).

The Normalized Difference Soil Drought Index (NDSoDI)
Its computation is based on the spectral behaviour of soils according to their moisture. Lobell and Asner (2002) have demonstrated that the soil reflectance varies according to its moisture through the following exponential model: Where R is the soil reflectance at a particular wavelength, ⍬ is the volumetric soil water content, Rdry is the reflectance of dry soil (at ⍬ = 0.0), c describes the rate of soil reflectance change with moisture, and f is the ratio of the saturated to dry reflectance. A local spectral library was constructed. Figure 5 shows the land surface reflectance variation of the four training samples types of soils according to their predicted moisture.

Figure 5. Reflectance of the four types of soils dryness
The evolution the "two periods" moving average trend lines built for each type of soil delimits the suitable electromagnetic spectrum wavelengths between the middles of the green and the SWIR2 (black square), while the most suitable is the SWIR1 (green square ). These lines also highlight the Red-NIR's slope (green brace) as the transition between the first period going from the SWIR2 to NIR and the second period going from the NIR to the green. From the green to the blue, there is no trend change, signs of end of the slope. Complementary analysis is made through the reflectance space between bands, sampling the four major land cover objects, i.e. sandy soil, other soils, water body and vegetation. Plots between the blue, the red and the SWIR1 bands in the six periods of the study.  The reflectance differences among water and sandy soils spectral curves are also to be noticed between in the three concerned wavelengths (Figure 7).

Figure 7. Reflectance curves for April 2018
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W11, 2020 PECORA 21/ISRSE 38 Joint Meeting, 6-11 October 2019, Baltimore, Maryland, USA From these views, it is assumed that, sand and soil features would be highlighted, when adding the red and SWIR1 bands, showing a strong positive convergence along a soil slope. The moisture would be assessed by subtracting the blue band and adjusting the water and soil reflectance values. The adjustment factor's values are settled according to the reflectance difference between the sand's spectral curve, which has the highest bare soil reflectance, and the water body's curve, in the blue, the red and SWIR1 bands for each month. (1 + ∑ ) Where ∑L is the sum of the differences between the sandy soil and the water body curves in the blue, red and SWIR1 bands. The highest values describe soil dryness and the lowest values its moisture, as shown on figure 8.

Figure 8. NDSoDI visual patterns
Accordingly, this index can be called the Soil Adjusted Moisture Index (SAMI) when the lowest values are to be considered.

The improved Land Surface General Drought Index (LSGDI2)
From the above reasoning, it is hypothesized that adding the drought of the land vegetated area with the one of the bare soil will provide better information regarding general droughts. When combining the VMI and NDSoDI spectral space, dry and wet surfaces can be represented on x-y orthogonal axes to locate the LSGDI2 (Figure 9). The moisture square includes the water body in both VMI and NDSoDI lower values, and its diagonal, the moisture line, separates two triangles representing the both indices areas of influence. The value needed equals to the triangles right angles projection, named the drought line, and corresponding to the LSGDI2. According to Pythagorean Theorem, it should be expresses as the square root of sum of squares of the NDSoDI and the VMI, such as: The value 0.1 helps adjusting the values below 1, to ease the interpretation of the results.

Dynamic ranges and visual patterns appraisal
The LSGDI2 global range dynamics are between 0.097 and 0.137 ≈ 0.14 for the studied period (Figure10). The difference with the LSGDI is that from the obtained values, it is easy to affect qualifiers to classes of drought. Therefore, the resulting image was reclassified and the thresholds were defined, using the five descriptors from Palmer's drought severity classification: [Exceptional drought -Extreme drought -Severe drought -Moderate drought -Abnormally drought]. With maximums of 0.137 and 0.134 respectively in January and March, 2003 was the drier year. It could be predicted that all values from 0.13 and above (≥ 0.13) are classified "exceptional drought", and those below 0.1 (0.9) are classified "abnormally drought" or moist areas.
Moreover, the visual patterns compared with the original Landsat images demonstrate that highest values correspond to sand and lower values to water body and rice crops ( Figure 10). Figure 10. Visual patterns of the LSGDI2

Reflectance efficiency and its statistical impact
A comparison was run with the LSGDI and the MDPI1 (Li, Z. and Tan, D., 2014). As reminding, MDPI1 processing also assesses the soil and vegetation moisture/drought in one algorithm: The three indices values were resampled in the interval [0 -1] to ease the comparison. After that, fifteen (15) pixels were sampled on each stretched image, with correspondence in all the five (05) classes of drought. It appears that LSGDI2 reflectance neatly enhances those given by the MDPI1 and LSGDI ( Figure 11). Figure 11. Reflectance of the three indices for April 2018 A statistical analysis with each class confirms the LSGDI2 efficiency in detecting drought, by varying comparatively to visual patterns interpretation and the two others indices ( figure 12). For instance, its "Abnormally drought" class areas for January 2003 and April 2018, are respectively 1/6 (16716 ha / 92976 ha) and 1/7 (9658 ha/69257 ha), less than LSGDI ones. Concerning the MDPI1, its areas for the "Exceptional drought" class values has been almost the same, i.e. around 52680 hectares during the six periods ( Figure 12).

Drought and moisture informative analysis
LSGDI2 values come from both the NDSoDI and VMI. It appears on fifteen (15) sampled points that LSGDI2 curve is distinct from its two components' ones (Figure13). Therefore, they both contribute to the model.

CONCLUSIONS
The aim of this paper was to improve the LSGDI, formerly assessed as a normalized difference. The main methodology point has been to sum the vegetation moisture and the soil drought, both assessed through the VMI and the NDSoDI, to express the general drought. The proposed LSGDI2 appeared to be the square root of sum of squares of the two previous. The analysis of its results shows that its reflectance values in each class of drought is higher than MDPI1 and LSGDI.

AKNOWLEDGEMENTS
Authors are grateful to USGS for the satellite images freely available. They especially appreciate the support of StatsN'Maps management, for initiating and directing this work since its presentation to PECORA21/ISRSE38.