HySIMU: An Open-Source Toolkit for Hyperspectral Remote Sensing Forward Modelling

Highlights

What are the main findings?

• HySIMU, an open-source and modular Python-based hyperspectral remote sensing forward modelling starter toolkit that integrates various non-proprietary modules and libraries into an established processing workflow.

What are the implications of the main findings?

• HySIMU enables the community to perform sensitivity tests for various survey scenarios to optimize mission planning and design.
• HySIMU provides synthetic image generation capabilities to support and enhance image-processing algorithm development.

Abstract

Hyperspectral remote sensing (HRS) is gaining widespread adoption within the geoscience and Earth observation communities. It fosters diverse applications, including precision agriculture, soil science, mineral exploration, and carbon detection, to name a few. Recent technological advancements facilitated a growing number of satellite missions as well as an increase in the availability of commercial sensors and platforms, such as drones. A significant challenge in deploying the varied platforms and sensors is the design and optimization of the hyperspectral surveys. Forward modelling simulators are valuable for optimizing mission parameters and estimating imaging performance. Limited accessibility of open-source simulators presents an obstacle for users who seek to benefit from such tools. To bridge this gap, HySIMU (Hyperspectral SIMUlator) was developed and described herein. It is an open-source, forward modelling toolkit that combines and integrates a primary processing pipeline with various open-source packages into a transparent and modular workflow. It offers a cost-effective approach to evaluating the performance of hyperspectral surveys. HySIMU is designed to simulate hyperspectral imagery based on user-defined targets, platforms, and sensor parameters. Features include (i) a ground truth data cube builder for customizable input parameters, (ii) a terrain-based solar and view geometry calculator for illumination modelling, (iii) integrated open-source radiative transfer models for incorporating atmospheric effects, and (iv) spatial resampling filters. In this manuscript, the initial framework for HySIMU is presented with some example applications, including two validation studies with real hyperspectral images. As remote sensing technologies advance, forward modelling toolkits such as HySIMU play a crucial role in refining mission designs and assessing survey feasibility. The scalability for arbitrary hyperspectral sensors, platforms, and spectral libraries ensures broad applicability. Of particular importance is support for parameter optimization for both scientific and commercial HRS campaigns.

1. Introduction

Hyperspectral remote sensing (HRS) paved the way for various innovative applications in Earth observation (EO) fields, including but not limited to agriculture, geology, water resources, and land cover [1]. This review includes studies from spaceborne missions such as the decommissioned Hyperion (EO-1 platform) and TianGong-1, and the ongoing PRISMA (PRecursore IperSpettrale della Missione Applicativa), EnMAP (Environmental Mapping and Analysis Program), and HISUI (Hyperspectral Imager SUIte). Moreover, compared to satellite missions, airborne HRS missions have provided relatively higher spatial resolution since their introduction in the late 1980s and have delivered promising results across a wide range of applications [1,2]. These airborne missions include Hyperspectral Mapper (HyMAP), chim (CASI), and Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS). For additional information on HRS satellite and airborne missions and applications, see [1,2,3,4,5].

Recent advancements in hyperspectral imaging (HSI) technologies facilitated the acquisition of higher-spatial-resolution data from spaceborne platforms that may eventually compete with airborne missions. Commercial companies such as Pixxel [6], Wyvern [7], and Orbital Sidekick [8] promise satellite-based hyperspectral imagery with spatial resolutions as high as 5 m. Correspondingly, there has been an increase in the availability and accessibility of public and commercial datasets. In recent years, the rapid development of UAV (Uncrewed Aerial Vehicle) systems and the miniaturization of HSI sensors enabled this type of platform to enter the HRS scene, offering a lower-cost alternative for acquiring higher-resolution imagery. Despite limited spatial coverage, the popularity of UAV-based HRS missions for specialized applications has increased [9,10]. Adão et al. [11] outline a range of hyperspectral sensors that are compatible with UAV platforms and associated applications. Zhong et al. [12] list common fixed-wing, helicopter multirotor, and hybrid UAVs considered for hyperspectral missions and corresponding specifications. These aforementioned developments, along with the increasing trend in the number of publications on hyperspectral remote sensing in general [13,14] or in specialized applications such as agriculture [15] over the past decade, indicate exciting times ahead for the future of HRS.

The growing variety of HRS platforms and sensors adds more complexity to decision-making and mission planning. To achieve products that meet certain scientific or industrial standards, a comprehensive assessment of target resolvability and mission feasibility is critical during the planning process, particularly given the vast array of data sources and configuration options. As HRS systems and technologies continue to evolve and more missions are planned, a deeper understanding of how different system parameters influence overall performance is essential [16]. Given the complex relationship between the inputs and outputs of HRS systems, along with budgeting constraints, a simulation approach is often preferred to support the detailed system design, optimization, and evaluation of mission parameters [17].

An HRS mission requires a realistic assessment of target resolvability, from analyses through the acquisition of high-fidelity hyperspectral images for various targets and background materials, which are often impractical due to time and cost constraints [18]. Given the cost associated with acquiring high-resolution hyperspectral imagery, it is often unfeasible to conduct flight tests to evaluate multiple configurations and determine the optimal parameters for specific applications [19,20]. These constraints amplify the necessity of simulation tools for designing new EO imaging systems. Forward simulation approaches, which model the imaging system of a new sensor and generate sensor-like output data, are instrumental in testing and refining sensor designs before deployment [21]. The ability to simulate a remote sensing system’s process allows for the adaptation and optimization of sensor and observation conditions [17] and helps users to pick the parameters that provide the most cost-effective configuration. By constructing and validating models, users can reinforce their understanding of the complexities of HSI systems and processes [22]. This capability is invaluable for both theoretical research and practical applications, ensuring that hyperspectral imaging systems are designed and operated within their optimal performance metrics.

Over the years, various hyperspectral remote sensing simulators, designed based on either analytical approaches or physics-based modelling schemes, have been developed with various primary objectives. The Forecasting and Analysis of Spectroradiometric System Performance (FASSP) is a statistical approach to modelling surface spectral reflectances that are propagated through an end-to-end remote sensing system [23]. FASSP identifies the components of a spectral imaging system analytical model, including scene, sensor, and processing models. The Digital Imaging and Remote Sensing Image Generation (DIRSIG) is an extensive physics-based image and data simulator designed to generate synthetic multi-hyperspectral imagery across the visible to thermal infrared spectrum [24,25]. The Software Environment for the Simulation of Optical Remote sensing systems (SENSOR) consists of three parts that describe the geometrical relationship between the Sun, target, and remote sensing system, the radiometry, and the optical and electrical sensor model [17]. Some simulators are also designed specifically to support the development of a satellite mission, such as the EnMAP End-to-End Simulation Tool (EeteS) [21,26]. These simulators are intended for EO, but their architectural framework can also be used to simulate hyperspectral imagery for other planets, as demonstrated by [22] through their simulator for the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) instrument. There are more hyperspectral simulators than this short introduction is able to cover; however, Zahidi et al. [18] provide a comprehensive overview of some hyperspectral simulators, including the Cranfield Hyperspectral Image Modelling and Evaluation System (CHIMES).

Some of these simulators are either commercialized or include trademarked components, while a few others were developed specifically in support of a publicly funded HRS mission. The rest, due to numerous reasons, are not readily accessible to the remote sensing community. While publicly funded spaceborne and airborne missions are usually able to include a specialized simulator in their planning phase, UAV missions are rarely equipped with such toolkits, and survey sensitivity analysis is often ignored. For these reasons, it is difficult for the research community or small to medium-sized enterprises to utilize the benefits of an HRS simulator. With the variety of datasets from public missions, the diverse options of platforms and sensors previously outlined, and the inaccessibility of the simulators, there is a need for a fully open-source, modular, and sensor- and platform-independent HRS forward modelling toolkit. This simulator should be designed to evaluate the optimum performance metrics of an HRS mission across a variety of target settings, atmospheric conditions, and sensor characteristics. In this study, we aim to establish a starting framework for such a simulator that integrates a primary processing workflow with various non-proprietary modules or libraries, called HySIMU. This framework is established to start and provide easy access to an HRS simulator that produces reliable synthetic images for the remote sensing community, where users can simulate various mission scenarios and test system performance against their specific parameters. The open-source nature of the toolkit hopefully motivates users in the community to test it for various applications, as well as encourages improvements and additional modules. HySIMU is designed to be independent of target scale, platform or camera. Note that this manuscript is intended to introduce the toolkit rather than study specific applications or conduct sensitivity studies. Applications of the previous versions of the toolkit can be found in [27,28,29]. The manuscript is structured as follows: Section 1 outlines the motivation and objective, Section 2 describes HySIMU’s framework and modules, Section 3 discusses sample results and validation studies, and Section 4 summarizes the toolkit and its advantages.

2. Methods: HySIMU Framework

We developed the HySIMU framework following the general architecture provided by FASSP [23] with a focus on the scene and sensor models, the forward modelling flow by SENSOR [17], and the modules of EeteS [21,26]. HySIMU simulates at-sensor radiance datacubes from synthetic or realistic surface reflectance maps with the assumption that the image is geometrically calibrated. It is designed to be sensor- and platform-independent, and with its modularity, the end user will be able to incorporate a sensor with preferred specifications according to their requirements. However, it should be noted that simulations should focus on the required spectral and spatial parameters to avoid excessive computational burdens.

The simulator is written in Python v3.11.5, integrates open-source libraries, and supports parallelization on High-Performance Computing (HPC) clusters. It is not categorized as an end-to-end simulation system because it does not include sensor calibration and electronic noise modules. However, the modular nature of the simulator allows for any additional module to be added by users.

Figure 1 shows the general workflow diagram of HySIMU, which is composed of several modules. The main modules of HySIMU are: (i) ground truth builder, (ii) datacube texturing, (iii) solar and view geometry computation, (iv) radiative transfer modelling, and (v) spatial resampling. These Python modules are executed sequentially through the main HySIMU script that takes and distributes the inputs and passes them into each corresponding module. Outputs from a module are automatically passed into the subsequent module. Future updates and community integrations can be added to the HySIMU GitHub repository as standalone modules or scripts imported into the main script.

2.1. Ground Truth Builder

HySIMU requires an initial map that represents regions of material distribution or “spectral zones”. This map serves as the “ground truth” from which a synthetic surface reflectance datacube will be derived. While constructing a surface reflectance scene can be complex, HySIMU applies a general implementation, with an approach to bridging the deterministic-geometrical and the stochastic-statistical approaches together [16,30]. This module within the HySIMU framework follows, with some adjustments, the “frequency synthesis of landscapes” algorithm [31] to randomly generate fractal fields. The process is as follows:

i.

A set of Discrete Fourier Transform (DFT) frequencies using a Fast Fourier Transform (FFT) algorithm is created for a user-specified grid.

ii.

A power spectrum synthesis is then computed from these frequencies according to the power law Equation (1) [32]:

$$P=k^{-\left(2H+1\right)},$$

(1)

where P is the power spectrum coefficient, k is the FFT frequency, and H is the Hurst exponent. The configurable Hurst exponent is introduced to control the overall “roughness” or complexity of the map, with lower values representing more complex clustering. Random noise (within the modelled frequency range) is added to the coefficients.

iii.

An Inverse Discrete Fourier Transform (IDFT) is performed to transform the coefficients that have been generated from the frequency grid and scaled with the noise into the spatial domain, yielding a representation of a random two-dimensional (2D) fractal field.

iv.

The fractal field is subsequently discretized based on pixel values and indexed into distinct regions to represent the spectral zones. Each index is associated with the corresponding material spectra from the input.

If preferred, the generated fractal fields can also serve as an input Digital Elevation Model (DEM) to delineate the intrinsic spatial relationships between topography and material distribution, as in the case of geological surface targets in mineral exploration. This ground truth-building approach, with a simple statistical parameter to represent the complexity, allows for better control in sensitivity studies, enabling users to systematically test and adjust the response of their systems to various scenarios [22]. Samples of spectral zone maps produced by HySIMU are shown in Figure 2. Alternatively, the ground truth can also be imported as a user input or generated by discretizing an input DEM. The ground truth scene must be of a higher or identical spatial resolution than the desired sensor spatial resolution.

This module also contains a function to initialize texture augmentation of the ground truth, to simulate the presence of spatial variations or heterogeneity within each of the spectral zones. Within each zone, spatially correlated noise is added using a clustered Gaussian random field generated using the GSTools library [33]. The Gaussian distribution is based on a study which demonstrated, from a set of real-world scenes, that the higher-frequency spatial components of hyperspectral imagery could be described by Gaussian mixture models [34]. A covariance nugget is provided as a customizable parameter to vary the degree of correlation. These clusters are populated with synthetic spectra of the same endmember material, generated by the following module, to eventually add texture to the surface reflectance datacube.

2.2. Datacube Texturing

The ground truth scene produced by the previous module is populated with spectral reflectance data from user input or randomly selected samples, categorized by class types, from the ECOSTRESS library [35] integrated into the Spectral Python package [36]. The input reflectance data must be spectrally oversampled in order to yield an accurate resampling to the sensor spectral resolution. In creating synthetic imagery for use in multi-/hyperspectral remote sensing, it is important to realistically reproduce the presence of texture arising from variations within a specific land cover class [37]. HySIMU provides a module to synthesize new spectral reflectance data from the input, following a method described in [37]. The method utilizes a set of reflectance spectra from the same class to derive a mean spectrum and a covariance matrix. Random samples are drawn from a multivariate normal (MV-N) distribution calculated from the covariance matrix with the mean spectrum as the base. Manolakis et al. [38] showed that an MV-N distribution can categorize HSI data accurately.

Figure 3 shows a set of sample results from this HySIMU module. Figure 3a shows the reflectance spectra of five arbitrary Alunite samples taken from the USGS spectral library [39]. The black spectrum (present in all plots) is the mean computed from the five samples. Using the mean and the covariance matrix, 10 new spectra are synthesized, as shown in Figure 3b. While appropriate statistics for each specific class derived from real imagery are ideal [16] for a simulation study, these statistics are often not easily obtainable, and only one endmember spectrum is available. To manage this, HySIMU also implements a simplified approach. Instead of calculating a mean spectrum, the input spectra serve as the base, and a number of intermediate spectra are computed using a specified standard deviation. The same steps as previously described then follow. Synthetic spectra produced using this approach are shown in Figure 3c. While the synthesized spectra are more consistent with the base spectrum compared to Figure 3b, they can be a sufficient representation of spectral texture for the simulated datacube and provide an optional parameter for users to calibrate.

The synthetic spectra, representing spectral variability, are created from the input endmembers and are then allocated to the ground truth model. The ground truth model is based on the previously determined spectral regions blended with spatially correlated Gaussian noise produced in the previous module. Figure 4 shows two false-colour images of a synthetic surface reflectance datacube populated with six arbitrary mineral spectra from the USGS library. Figure 4a shows a non-textured or smooth datacube, while Figure 4b shows a textured datacube, where each spectral region is divided further into twenty-five spatially correlated subregions.

2.3. Solar and View Geometry Calculations

Another source of texture in hyperspectral imagery comes from variations in the solar angle of incidence due to topography [37]. Using the generated DEM or an input DEM (which must be of the same resolution as the ground truth), HySIMU corrects the angle of incidence from the sun zenith angle for each pixel, using the haversine library [40] to correct the coordinates based on the provided reference coordinates, the pvlib library [41,42] to determine the solar position (azimuth and elevation) at the specified simulation location and time, and the insolation library [43] to determine the slope aspects, slope gradients, and solar vectors. The corrected angle is calculated based on the formula used to compute the angle of incidence on an inclined surface [44]:

$$\cos \theta =\cos {\theta }_z\cos \beta +\sin {\theta }_z\sin \beta \cos \left({\gamma }_s-\gamma \right),$$

(2)

where $\theta$ is the angle of incidence, ${\theta }_z$ is the solar zenith angle, $\beta$ is the slope angle, ${\gamma }_s$ is the solar azimuth angle, and $\gamma$ is the surface azimuth angle. The corrected solar and view angle serve as input for the radiative transfer model in the following module. Figure 5 shows the effects of solar geometry correction on the final product of HySIMU. Without the correction, details related to terrain shadowing and terrain effects are not modelled, resulting in a less realistic image. This can significantly affect interpretation and classification in variable terrain scenarios.

2.4. Radiative Transfer Modelling

Using Lambertian surfaces and previously computed solar and view geometry models, atmospheric effects are applied to the generated surface reflectance datacube, pixel-by-pixel, using an integrated Radiative Transfer Model (RTM) to generate the at-sensor radiance datacube. The HySIMU workflow incorporates two open-source RTMs: 6S (the Simulation of a Satellite Signal in the Solar Spectrum) [45] and libRadtran (the library for Radiative transfer) [46,47]. Both RTMs have been validated in previous studies over the years (see [48,49,50] for 6S and [51,52] for libRadtran), and both perform better than other RTMs for specific applications [53]. The option to pick and choose the RTM provides more flexibility to the users and depends on their applications/goals. It should be noted that both RTMs require a different input parameter setup.

A vector version of the original 6S code (6SV1.1) RTM is implemented in the workflow through a Python wrapper called py6S [54]. This version can simulate the atmospheric radiative transfer of polarised and non-polarised visible and infrared radiation under different atmospheric conditions. HySIMU also implements libRadtran through a Python wrapper called pyLRT [55]. The model supports various solvers, with DISORT (Discrete Ordinates Radiative Transfer) being the one integrated into HySIMU, which allows high-resolution computation of radiance in the VIS-NIR-SWIR (visible light, near-infrared, and shortwave infrared) range. In addition to standard atmospheric parameters, HySIMU allows users to customize the gaseous properties of the atmosphere, such as H₂O, CO₂, and CH₄ concentrations, as supported by libRadtran.

Both RTMs are suitable for any kind of remote sensing platform (e.g., UAVs, aircraft, satellites). While the Lambertian surface assumption can be considered a simplified approach, both RTMs provide options to use Bidirectional Reflectance Distribution Functions (BRDFs) that are available within their respective modules, but these are not yet included in HySIMU as of now.

Additionally, HySIMU provides a module to compute radiance without incorporating an RTM, following the inverse of the reflectance formula [56]:

$${\rho }_{\lambda }= {\displaystyle \frac{\pi L_{\lambda }{d}^2}{{ESUN}_{\lambda }\mathit{cos}{\theta }_z}} ,$$

(3)

where ${\rho }_{\lambda }$ is the Top-Of-Atmosphere (TOA) reflectance (unitless), $L_{\lambda }$ is the at-sensor spectral radiance (W/m² sr μm), $d$ is the Earth-Sun distance in astronomical units, ${ESUN}_{\lambda }$ is the exoatmospheric solar irradiance (W/(m² μm)), and ${\theta }_z$ is the solar zenith angle. For this function, solar irradiance values are sourced from the global reference spectrum of the ASTM G173-03 Standard Spectrum [57] dataset included in the pvlib library. Sample images generated from all three radiance computation options available in HySIMU are shown in Figure 6a, and the corresponding radiance spectra from an arbitrary pixel are shown in Figure 6b. Pixel-based Spectral Angle Mapper (SAM) [58] analysis performed on the radiance spectra for all pairs of images produced an overall mean score below 6% (after normalization to 1 radian): libRadtran-6S at 3.245% (0.102 rad), libRadtran-noRTM at 5.455% (0.171 rad), and 6S-noRTM at 3.955% (0.124 rad), indicating a high degree of similarity. Nevertheless, these values depend on the land cover of the scene as well as the atmospheric conditions during the acquisition. These examples show RTM-dependent radiance differences, larger differences in the shorter wavelengths, and smaller for the longer wavelengths. The option of using different RTMs in HySIMU thus allows for an uncertainty estimation due to varying model performance.

2.5. Spatial Resampling

Following the incorporation of atmospheric effects, the full-resolution at-sensor datacube is resampled to the desired sensor’s spatial resolution. Typically, HSI imagery is spatially downsampled using spatial resampling algorithms such as pixel aggregate, nearest neighbour, bilinear, and cubic convolution or using more complex algorithms specialized for data fusion [20]. Although these resampling approaches can downsample imagery to any desired pixel size, the imagery captured by the sensor does not necessarily represent the scene accurately, with small feature details blurred relative to larger features [59]. This effect is characterized by the sensor’s net Point Spread Function (PSF). Consequently, when only using a spatial downsampling technique as mentioned above, these methods fail to account for the characteristics of the simulated sensor. Rather, spatial resampling should be performed using a weighted average of the PSF of the simulated sensor [20]. This approach can be found in [60], where a convolution of the synthetic HSI scene with the sensor PSF was implemented to preserve the sensor’s characteristics.

A sensor’s PSF (PSF_net) is composed of four components [59]:

i.

An optical PSF introduced by the energy distribution spread in the sensor’s focal plane.

ii.

An image motion PSF caused by a shift during the motion of the sensor during the integration time.

iii.

A detector PSF that represents the non-zero spatial area of each detector in the sensor.

iv.

An electronic PSF introduced by the electronic filter of the sensor.

The total PSF_net is computed by convolving these four PSF components.

HySIMU provides an option to compute a simplified PSF_net, which is a combination of only the optical and the detector PSFs, to accommodate the possibility that users might not have detailed sensor and platform parameters. Although the optical PSF theoretically is represented by an Airy pattern, HySIMU implements an approximation using a Gaussian function [59], as follows:

$${PSF}_{opt}\left(x,y\right)= {\displaystyle \frac{1}{2\pi ab}}{e}^{-x^2/a^2} e^{-y^2/b^2},$$

(4)

where x and y are positional variables, and a and b are the widths of the PSF in the cross-track and in-track directions, respectively. Moreover, the detector PSF is modelled using a rectangular function [59]:

$${PSF}_{det}\left(x,y\right)=rect\left(x/w\right) rect\left(y/w\right),$$

(5)

where x and y are positional variables, and $w$ is the width of the PSF. Thus,

$${simplfied PSF}_{net}={PSF}_{opt} \ast {PSF}_{det},$$

(6)

A significant portion of the signal received by each pixel originates from materials outside the pixel’s defined spatial extent [19]. The values of a Gaussian function decrease with distance, and at distances larger than three times the mean, the values become negligible. This implies that there is no advantage to using a Gaussian window larger than six times the mean [61]. Correspondingly, HySIMU uses a Gaussian kernel with a size equal to three times the spatial size of the sensor pixel as a default; however, it can be adjusted accordingly.

HySIMU also integrates the sensor-independent SR² function developed by Inamdar et al. for pushbroom sensors [20]. The SR² function combines optical PSF, image motion PSF, and detector PSF with several assumptions: (i) the PSF_net is wavelength-independent, (ii) the aircraft is flying at a constant speed in a perpendicular direction to the detector array, (iii) the spatial response is uniform over pixel spatial boundaries, and (iv) the data is georeferenced. While the function relies on these assumptions, it allows users to incorporate more detailed sensor parameters as well as platform motion parameters. It has been shown that the SR² is effective in downsampling HSI data and that potential improvements can still be added [20].

The difference between images generated by each of the PSF functions is shown in Figure 7. The simplified PSF appears to produce a blurrier image when using the established kernel size. Further calibration of the kernel size is possible to fit users’ specifications and applications. After the PSF_net has been computed, the full-resolution at-sensor radiance/reflectance datacube that has been generated by HySIMU in the previous module is convoluted with the PSF_net to maintain the sensor characteristics. Subsequently, the convolved datacube is downsampled to the sensor’s resolution using a traditional downsampling technique with interpolation orders from 1 to 5.

3. Discussion: Validation and Potential Applications

An ideal validation scheme for HySIMU would require a hyperspectral image accompanied by a corresponding higher resolution ground truth map, endmember spectra covering a broader spectral range than the sensor, and statistical parameters for each spectral zone. However, such a complete dataset practically does not exist. This is the main challenge we encountered during the development of this toolkit. A linear simulator, such as HySIMU, is highly dependent on the input ground truth and spectra provided. In response to this, we set up a more straightforward validation scheme using an AVIRIS image, albeit with a limited spatial resolution. Here, we only focus on an aircraft image simulation, as previous works have already covered UAV and satellite applications [27,28,29].

This section presents a validation study using the Jasper Ridge hyperspectral image taken by the AVIRIS mission in 1992 (referred to as JR). A 100 × 100-pixel subset of the full reflectance image (Figure 8e) has been previously classified in previous works [62,63,64]. The abundance map and endmember spectra are shown in Figure 8a and Figure 8b, respectively. Since the abundance image was derived from the hyperspectral image, the spatial resolution is still not adequate to create an appropriate and realistic ground truth map that can be downsampled to the sensor resolution; thus, simplification approaches are needed, and careful consideration is required when interpreting the results.

From the abundance map, we derived two simplified ground truth maps (GT1 and GT2) using the following methods: (i) GT1 was created by assigning each pixel to the spectral class with the highest abundance; (ii) GT2 was created by upscaling the ground truth to 200 × 200 pixels using a nearest neighbour algorithm and introducing three additional spectral classes in pixels lacking a single dominant class (>75% abundance). The three additional classes are dominated by both Tree and Soil classes. These classes represent mixtures of both endmembers with varying ratios (75%/25%, 25%/75%, and 50%/50%) and add more complexity to the ground truth data, which are shown in Figure 8c (GT1) and Figure 8d (GT2). The ground truth maps and endmember spectra sets were input into the HySIMU workflow, with parameters based on the AVIRIS sensor and the ER-2 platform, as listed in

Table 1. AVIRIS-based Jasper Ridge (JR) simulation parameters used in the validation study.

Parameter	Value
Sensor	AVIRIS-based
Bands	224
Spectral range	370–2500 nm
Flight altitude	20,000 m
Spatial resolution	20 m
Acquisition date	2 September 1992
Acquisition time	12:00:00 PST
View azimuth angle	90°
View zenith angle	5°
Image output	Reflectance
RTM	libRadtran
Atmospheric profile	mid-latitude summer
Aerosol profile	rural
PSF option	simplified
Platform speed	206 m/s
Sensor FOV	36°
Sensor integration time	0.087 s

. The DEM from the time of the survey was not available; hence, the simulations herein assume a flat DEM. Two synthetic hyperspectral reflectance images (REF1 and REF2) were generated using this setup, and are shown in Figure 8f,g. Computational performances of both REF1 and REF2 simulations are provided in

Table 2. HySIMU computing performance metrics for REF1 and REF2 simulations. The MaxRSS parameter represents the maximum resident set size and indicates the peak amount of memory used by any process during the simulation.

	REF1	REF2
GT image size	100 × 100 pixels	200 × 200 pixels
Spectral bands	224
Processor	Intel® Xeon® Processor E7-8867 v3 @ 2.5 GHz
Cores	64	64
Runtime	01:02:59	03:57:12
CPU time	2–19:10:56	10–16:32:00
MaxRSS	35.36 GB	35.97 GB

. Note that these simulations did not include DEM-based solar view geometry computation, the SR² filter, and radiance computation. Simulation runtimes are expected to increase if any of these functions are included.

The results show strong qualitative correlations between the Jasper Ridge reflectance and the simulated images. While the other three spectral classes exhibit colours similar to the JR image, the spectral zones of trees appear darker in both REF1 and REF2. This discrepancy may result from the shadowing effects of the vegetation canopy and the variability in vegetation types in the reflectance image, which could influence the derived Tree endmember spectrum during the unmixing process. Due to the limited resolution of the ground truth, the simulated images appear more pixelated than the true reflectance image. This is a result of reduced mixing across the pixels, in addition to the atmospheric effects on the simulated images.

Figure 9 shows scattergrams of reflectance values from a near-infrared (NIR) band and a Red band for all three images. It is important to point out that, due to different value calibrations, the scattergrams are not plotted on identical scales. Real images, due to various factors such as sensor noise, topographic shading, and subpixel mixing, often produce a diffuse scattergram [59], indicating substantial mixing. This effect can be observed in the JR (Figure 9a), with “clouds” of data points and no observable clustering. This observation is less prominent in both REF1 (Figure 9b) and REF2 (Figure 9c) scattergrams. REF1 displays more clustered data points, indicating weak mixing between the spectra. This is to be expected because REF1 is simulated directly from the abundance image. On this note, REF2 exhibits stronger mixing than REF1, because of a higher resolution ground truth and mixed spectra as inputs. Intrascene variability is expected to increase as the diversity of mixed spectra represented in the ground truth becomes greater (e.g., adding more mixed proportions such as 60% Tree and 40% Soil spectra). Outliers are also more apparent in the JR image, consistent with real-life characteristics of remote sensing images. These observations demonstrate that, despite its dependence on the spatial resolution of the ground truth, HySIMU can effectively mix the spectra, making it a reliable tool for simulating images from an input ground truth.

The JR reflectance image is atmospherically corrected while REF1 and REF2 are not; thus, a direct quantitative comparison to the simulated images is difficult. Correcting for atmospheric effects in REF1 and REF2 is counterproductive. Here, we opted for comparison metrics that do not rely on absolute values but rather on the monotonic relationships between image values using Spearman rank correlation (r_s) [65] and on image structural information using Structural Similarity Index Measure (SSIM) [66]. The results for these metrics are shown in

Table 3. Comparison metrics r_s and mean SSIM between JR and REF1 and REF2.

	JR–REF1	JR–REF2
rs	0.740	0.741
Mean SSIM	0.460	0.404

. r_s values signify consistent trends between REF1 and REF2 relative to the JR, while mean SSIM values, albeit modest, still indicate that all images are positively correlated.

Furthermore, we performed Principal Component Analysis (PCA) on all three images to reduce dimensionality and simplify the comparison, allowing the majority of the information to be represented in the first few principal components [67]. This is to mitigate the data calibration and atmospheric correction differences. All principal component values are normalized before plotting. Figure 10 illustrates the scattergrams of the first principal component (PC1) of JR plotted against PC1 of REF1 (Figure 10a) and REF2 (Figure 10b). R² values approaching 1 for both plots indicate that all first principal components have linear relationships; however, the steep slope and horizontal shearing of the clusters highlight more spectral variability on the x-axis, a feature consistent with more mixing contained in the JR image.

The design of two ground truth maps with differing complexities and resolutions highlights HySIMU’s ability to handle scenarios with varying levels of complexity and scale. It should be noted that having a realistic and high-resolution ground truth might not be necessary if the goal is only to test the response of various system parameters rather than performing a full classification scheme, considering that high-resolution ground truth will require longer computing time. This validation scheme demonstrates how HySIMU can be utilized to generate hyperspectral imagery from a set of realistic parameters and evaluate the effects of changing parameters for an HRS mission. In contrast, real atmospheric effects contain a high degree of uncertainty, particularly in the Blue bands (~450 nm) [68], and thus are difficult to model appropriately and often lead to underestimation. To mitigate the propagation of these errors throughout the processing chain, the use of alternative atmospheric correction algorithms besides 6S or libRadtran is recommended when inverse modelling HySIMU images.

An additional validation simulation (REF-A1) using the Urban dataset (UR) with ground truth and endmember spectra derived by [69], acquired with the Hyperspectral Digital Imagery Collection Experiment (HYDICE) instrument [70,71], is provided in the Supplementary File. Unlike the Jasper Ridge simulations, the Urban simulation does not include ground truths with different complexity levels. However, the analyses follow the same approach and order as those used for the Jasper Ridge simulations, and the results should therefore be interpreted in the same manner.

Previous iterations of HySIMU, which were specifically designed for UAV applications without integrated RTMs and implemented in MATLAB (R2020b) as a closed-source codebase, have demonstrated practical utility in mineral exploration [27] and soil sensing [28]. In addition, for satellite applications, Beaulne et al. [29] utilized the newer version of HySIMU for simulation studies to compare the performance of the PRISMA and PACE-OCI (Plankton, Aerosol, Cloud, ocean Ecosystem–Ocean Color Instrument) satellite systems for algal bloom monitoring. Using real algal spectra from the GLORIA (GLObal Reflectance community dataset for Imaging and optical sensing of Aquatic environments) dataset [72,73], this study concluded that while simulated PRISMA imagery offered improved finer-scale detection, their performance metrics were not consistently better. This shows the potential benefit of HySIMU by giving users a tool to evaluate the effectiveness of various satellite HRS products for their specific applications. HySIMU can serve as a complementary toolkit to various open-source hyperspectral analysis and processing tools, e.g., [74,75], contributing to the development of a comprehensive and transparent HSI workflow. Additionally, we envision several future application areas for HySIMU, including the generation of synthetic datasets to train machine-learning (ML) algorithms aimed at detecting atmospheric carbon from satellite imagery. In collaboration with an industry partner, we generated synthetic satellite hyperspectral images (using PRISMA satellite parameters) with varying levels of atmospheric methane in selected regions. These images were processed using libRadtran and provided to the partner’s in-house ML algorithm. The objective was to train the algorithm on synthetic data to enable its application to real satellite imagery. The results were promising, highlighting potential for further developments.

4. Conclusions

The increase in the availability of hyperspectral remote sensing sensors and platforms presents a need for an open-source simulator that is readily accessible to the remote sensing research community and small and medium-sized enterprises. In this study, HySIMU is presented as a framework for an open-source, modular, and sensor- and platform-independent HRS simulator toolkit that combines and integrates a primary processing pipeline with various open-source packages into a validated and modular workflow. HySIMU can simulate data for any spectral and spatial resolution and at any spatial and spectral scale. It allows users to have greater control over the parameters and thus provides a tool for sensitivity studies to determine the optimum survey parameters and conditions. The ability to produce reliable synthetic images can also be beneficial for training ML algorithms for various applications.

The main challenge in the process of developing HySIMU is the absence of high-resolution hyperspectral data and ground truth maps. This prevents the simulator from being used to its full extent and restricts its validation process. However, the performance of HySIMU was successfully validated, albeit more straightforwardly, by simulating the AVIRIS Jasper Ridge and HYDICE Urban reflectance images. The two simulations presented herein show that HySIMU can generate synthetic hyperspectral imagery at any scale and is applicable for sensitivity studies (for any single or multiple parameter choices) during mission planning.

It is important to note that real hyperspectral scenes often contain uncertainties from multiple sources, and an ideal simulator without simplifications is rather difficult to achieve. This toolkit implements several approximations; therefore, its effectiveness is determined by the input data and the specific context of the application. Furthermore, to categorize this toolkit as an end-to-end simulator, several other modules could be integrated in the upcoming versions, i.e., camera calibration and electronic noise modules. Additionally, while the randomly generated maps produced by HySIMU are more of a statistical representation than a real-life map, as more thematic or land classification remote sensing images become openly available, there is a potential to add an ML-driven, realistic map generator function in the future.

Despite these limitations, the integration of many previously developed community tools made HySIMU a flexible and fully customizable toolkit. Therefore, applications in other fields, such as vegetation mapping, agriculture, carbon detection, and environmental monitoring, are feasible. HySIMU is a starting framework that can provide both the remote sensing community and their users with a useful tool for specific applications, with a focus on mission design, target requirements, or sensor selection. HySIMU is developed with the community in mind, and users are encouraged to express ideas for improvements, add modules and algorithms, and apply the toolkit to new applications. The code is made available via GitHub under the GNU General Public License version 3 (GPLv3).