A Multispectral Camera Suite for the Observation of Earth’s Outgoing Radiative Energy

Abstract

As part of the Earth Climate Observatory space mission concept for the direct observation from space of the Earth Energy Imbalance, we propose an advanced camera suite for the high-resolution observation of the Total Outgoing Radiation of the Earth. For the observation of the Reflected Solar Radiation, we propose the use of two multispectral cameras covering the range from 400 to 950 nm, with a nadir resolution of 1.7 km, combined with a high-resolution RGB camera, with a nadir resolution of 0.57 km. For the observation of the Outgoing Longwave Radiation, we propose the use of six microbolometer cameras, with each a spectral bandwidth of 1 μm in the range from 8 to 14 μm, with a nadir resolution of 2.2 km.

1. Introduction

The Earth Energy Imbalance (EEI) is defined as the small difference between the incoming energy received by the Earth from the Sun and the outgoing energy lost by the Earth to space. Both the incoming solar and the terrestrial outgoing energy are of the order of 340 W/m² at the global annual mean level [1], while the EEI is of the order of 0.9 W/m² [2,3]. The EEI is accumulated in the Earth’s climate system, particularly in the oceans which have a high heat capacity, and results in global temperature rise.

The monitoring of the EEI is of prime importance for a predictive understanding of climate change [4,5].

Despite its fundamental importance, the EEI is currently poorly measured from space, due to two fundamental challenges.

The first fundamental challenge is that the EEI is the relatively small difference between two opposite terms with large and nearly equal amplitude. Currently, incoming solar radiation and outgoing terrestrial radiation are measured with separate instruments, which means that their calibration errors are added, and overwhelm the signal to be measured. The current error on the direct measurement of the EEI is of the order of 5 W/m² [1], significantly larger than the signal to be measured of the order of 0.9 W/m². In order to make significant progress in this challenge, a differential measurement using identically designed, intercalibrated instruments—so-called wide-field-of-view (WFOV) radiometers—to measure both the incoming solar radiation and the outgoing terrestrial radiation is needed [6].

The second fundamental challenge is that outgoing terrestrial radiation has a systematic diurnal cycle [7,8,9]. From 2003 to 2023, the diurnal cycle of the outgoing terrestrial radiation was sampled from the so-called morning and afternoon Sun synchronous orbits, complemented by geostationary imagers [10,11]; recently, the sampling from the morning orbit had to be abandoned [12]. The Geostationary Earth Radiation Budget Experiment [13] resolves the detailed diurnal variations in the ERB but lacks global coverage for the connection to the EEI. The sampling of the global diurnal cycle can be improved by using two orthogonal 90° inclined orbits [14] which provide both global coverage and a statistical sampling of the full diurnal cycle at the seasonal (3-month) time scale. For calculating the global annual mean EEI, the satellite measurements are first averaged temporally per latitude/longitude gridbox; next, the gridbox yearly averages are averaged spatially with an appropriate weighting factor to obtain the global annual mean. Details are provided in Reference [14].

The wide-field-of-view radiometer will make accurate low-spatial-resolution measurements of the Total Outgoing Radiation (TOR) of the Earth. Auxiliary visible and thermal imagers will be used to increase the spatial resolution of the radiometer observations and to separate the TOR spectrally in the Reflected Solar Radiation (RSR) and the Outgoing Longwave Radiation (OLR).

The so-called narrowband multispectral imagery from the cameras can be combined using, e.g., linear regression techniques, to estimate the so-called broadband radiance, either the OLR radiance from the thermal cameras or the RSR radiance from the visible cameras. The narrowband-to-broadband conversion principle has a long heritage from missions such as AVHRR [15], HIRS [16], MODIS [17], and SEVIRI [18].

After the narrowband-to-broadband conversion, the cameras measure the angular distribution of the OLR and RSR radiance, measured accurately via the radiometer. This radiance distribution can be used, e.g., for correcting small imperfections in the cosine response of the radiometer. In turn, the radiometer can be used for a bias correction of the camera-derived broadband radiances.

With the bias-corrected directional radiance distribution, it is possible to derive additional secondary objective data products, e.g., maps of fluxes. This is routinely performed in several satellite products, for instance, CERES [19] and GERB [20], and is achieved through the development of Angular Dependency Models (ADMs) [21]. Such ADMs can be derived from the multiangular views of multispectral cameras. Beyond these traditional approaches to mapping radiance to flux, and given the intended 2036 launch time frame, it may be interesting to develop new algorithms based on deep learning (DL) [22,23], which is currently seeing many applications in the remote sensing domain.

Figure 1 shows a multiannual mean TOR at 1° resolution, Figure 2 shows the corresponding RSR, and Figure 3 shows the corresponding OLR.

A reference design of the visible imager is described in [24].

A reference design of the thermal imager is described in [25].

A new space mission concept, called the Earth Climate Observatory (ECO), for the accurate and stable monitoring of the EEI is currently elaborated upon, building further on the basic concepts in [6,24,25].

In this paper, we describe an advanced multispectral camera suite with performance that goes beyond [24,25]’s reference designs in terms of spectral information content. In Section 2, we describe the advanced shortwave camera suite. In Section 3, we describe the optical design for a new visible high-resolution camera used in the advanced shortwave camera suite. In Section 4, we develop the advanced longwave camera suite. We discuss our results in Section 5 and provide our conclusions in Section 6.

2. Shortwave Camera Suite

In [24]’s reference design, the shortwave (SW) camera—also called solar camera—consists of an RGB CMOS detector array with a wide-field-of-view lens allowing us to view the Earth from limb to limb. The field of view is 140 °. The wide-field-of-view (WFOV) lens design is illustrated in Figure 4. The nadir resolution is 2.2 km. The f-number is 3. The used RGB CMOS spectral responses are illustrated in Figure 5. On a stand alone basis, the RSR can be estimated from an RGB CMOS imager through spectral regression with a noise level of 3%.

The only on-board calibration source for the SW camera suite will be a shutter, allowing us to verify the dark current and also allowing us to shield the camera from direct solar illumination during solar pointing. The camera spectral gains and dark current will be determined preflight during ground calibration. The stability of the RGB spectral responses and the gains will be monitored and, if needed, adjusted in flight through vicarious calibration monitoring stable Earth targets similar to those in [26,27,28]. The stability of the shortwave cameras does not influence the accuracy of the global annual mean EEI, which depends on the radiometer.

The spectral regression noise level, through which the RSR broadband radiance can be estimated, can be improved by increasing the number of narrowband spectral channels used as input for the regression. In [29], a commercially available CMOS sensor with 4 × 4 filter bands in the VIS (470–620 nm) is described. Also, a commercially available CMOS sensor with 5 × 5 filter bands in the VIS-NIR (650–975 nm) is described.

The newly proposed ECO Shortwave Camera Suite (SCS) consists of three separate shortwave (SW) cameras. Cameras 2 and 3 can be based on the same CMOSIS CMV2000 sensor array. Since the size of the detector is comparable to that of the detector used in [24], the reference wide-field-of-view lens from Figure 4 can be reused. Camera 1 can be realized using the higher-resolution CMOSIS CMV12000 sensor array. Since the size of the CMV12000 sensor is about three times larger than the detector size used in [24], a new lens design is appropriate and will be presented in Section 3. The three shortwave cameras have different spectral responses, by using different filters directly integrated on the CMOS chip, with spatial patterns illustrated in Figure 6.

The three ECO SW cameras are the following:

1.

ECO SW Camera 1 will be the RGB high-resolution SW camera, formed of a CMOS sensor, with spectral response between 400 and 1000 nm, with standard ‘RGGB’ Bayer pattern. The active area of the CMOS sensor will be 3000 × 3000 pixels, yielding a nadir resolution for a single pixel of 0.57 km and a nadir resolution for the 2 × 2 RGGB pixels of 1.1 km. The pixel pattern of SW Camera 1 is illustrated in the left part of Figure 6.

2.

ECO SW Camera 2 will be the VIS SW camera from [29]. The nadir resolution of the 4 × 4 VIS filter pattern—illustrated in the middle part of Figure 6—is 6.8 km.

3.

ECO SW Camera 3 will be the VIS-NIR SW camera from [29], using the same underlying CMOS sensor as Camera 2. The nadir resolution of the 5 × 5 VIS-NIR filter pattern—illustrated in the right part of Figure 6—is 8.5 km.

The detectors from [29], considered for Cameras 2 and 3, are also considered for the CubeMAP [30] and Hyperscout-H [31] space missions.

3. Optical Design High-Resolution SW Camera

The SW camera uses the CMOSIS CMV12000 4K CMOS detector with pixel size 5.5 μm. For the envisioned FOV of ${140}^{\circ }$, we use a circular area of 16.5 mm diameter, corresponding to 3000 pixels. For a WFOV lens with field angle ${140}^{\circ }$ observing the Earth from an altitude of 700 km, the size of the nadir pixel is 0.57 km. Considering that the sensor is used with a Bayer color filter, the RMS spot size we require should be smaller than 2 pixels—corresponding to 11 μm. The barrel distortion is considered to be corrected in postprocessing.

3.1. The Design Parameters

The lens train—illustrated in Figure 7—consists of six lenses, two of which form an achromatic doublet. The doublet along with the third lens works as a chromatic aberration correction system along with focusing the image on the image plane. The main lens properties are summarized in

Table 1. Lens data: surface type, material, thickness, and diameters. Three aspherical surfaces. s-s-s-d-s format.

Lens Order (Singlet/Doublet)	Front Surface Type	Rear Surface Type	Material	Thickness (mm)	Diameter (mm)
First lens (s: singlet)	Aspherical	Spherical	LAK14	3.7	32
Second lens (s)	Spherical	Spherical	LAK14	5	23
Third lens (s)	Spherical	Spherical	SF6	5	12
Fourth lens (d: doublet)	Spherical	Spherical	N-FK51A	2.7	7.6
Fifth lens (d)	Spherical	Aspherical	N-SF6	2	7.6
Sixth lens (s)	Spherical	Aspherical	LAK14	2.2	11.4

. The lens materials were selected from the SCHOTT^® catalog. The LAK14 is a crown glass with relatively high refractive index, and SF6 is a flint glass with high refractive index, as well.

There are three aspherical surfaces on the system: the first surface, the last surface, and the final surface of the achromatic doublet. This is conducted to ensure increased light collection and to reduce spherical aberrations. The initial reference design for this lens train was the one shown in Figure 4 [24].

The system was designed and optimized using the Zemax 2018 OpticStudio^® software. Only a few parameters were constrained, namely, the ‘Effective focal length’, at 15.6 mm, and the lens thickness minimum at 2 mm. The initial merit function for spot size was conducted through the ‘Quick focus’ function provided by Zemax. Once a substantial percentage of criteria was fulfilled during optimization and satisfactory RMS values along with a good relative illumination were achieved, further optimization was performed using the ‘Hammer optimization’ function provided by Zemax.

3.2. Optical Performance

3.2.1. RMS Error

The RMS error—see Figure 8—shows the root mean square deviation of a bunch of rays of light from its intended spot of incidence. For a preservation of the spatial information captured via the detector at a resolution of 2 pixels, corresponding to a nadir resolution of 1.1 km, this value should be below 11 μm approximately. This is widely true for the said lens train and only reaches 12 μm for the 400 nm wavelength at the extreme ${70}^{\circ }$ incidence angle.

3.2.2. Seidel Aberrations

The Seidel aberrations—see Figure 9—apart from distortion have been optimized and kept low. The distortion/barrel distortion is to be corrected on the ground as postprocessing.

3.2.3. Point Spread Function (PSF)

The optical PSF is the characterization of how a point of light is transformed when passing through an optical system. The optical PSF is related to the RMS spot size as shown in Figure 8, which mostly lies below the desired 11 μm. The average optical PSF of all wavelengths is given in Figure 10.

To evaluate the joint effect of the optical PSF and the pixel shape, the convolution of the optical PSF with the detector pixel shape is calculated. We use a layer of fixed size containing several pixels of the same type, either red/blue active pixels or green-green active pixels. The two types of pixels exist due to the presence of the Bayer filter. The individual pixels have sizes of 5.5 μm, but to emulate real pixels, an active area of 80% of the nominal pixel size, as shown in Figure 11, is used. We assume the variation in the optical PSF is negligible within the layer of pixels.

The convolution of these pixel layers with the optical PSF for the $0^{\circ }$ incidence angle is shown in Figure 12. It can be seen that, after the convolution, individual pixels are still recognizable.

From the RMS in Figure 8, the 400 nm wavelength at ${70}^{\circ }$ incidence angle and 500 nm at ${38}^{\circ }$ incidence angles have high RMS spot radii. The PSFs and convolutions at these particular wavelengths and angles are examined in detail.

The optical PSF for light with a wavelength of 400 nm incident at ${70}^{\circ }$ is shown in the left of Figure 13. The convolution of this optical PSF with the blue-type active pixel layer is shown in the right of Figure 13.

The optical PSF for light with a wavelength of 500 nm incident at ${38}^{\circ }$ is shown in the left of Figure 14. The convolution of this optical PSF with the green-type active pixel layer is given in the right of Figure 14.

The light spreads towards the top and bottom of the pixels in the right part of Figure 13 and Figure 14. Following [24], the required minimum spatial effective resolution of the cameras is 5 km. The current design meets this requirement with ample margin.

3.3. Simulated Performance for Earth Observation

3.3.1. SNR High-Resolution 4K-RGB Camera

For Camera 1, with a nadir resolution of 570 m and a nominal satellite altitude of 700 km, Lambertian Earth leaving flux is attenuated towards the entrance of the camera by a factor of ${(0.57/700)}^2/\pi =2.11\times {10}^{-7}$. Within the optical system, with a 0° radiometric aperture diameter of 5.38 mm and a detector pixel size of 5.5 micron, the entrance flux is amplified towards the detector by a factor of $\pi /4\times {(5.38/5.5\times {10}^{-3})}^2=7.5\times {10}^5$. Assuming no light loss, the ratio between the detector flux and the Earth flux is then $2.11\times {10}^{-7}\times 36.7\times {10}^4=0.16$. Assuming a 50% light loss, the ratio becomes $0.16\times 0.5=0.08$.

The detector for Camera 1 is the CMOSIS CMV12000 CMOS detector array, with $4096\times 3072$ pixels and a full well capacity of 1485 counts, corresponding to approximately 10.5 bit per pixel. For a $3000\times 3000$ pixel subarray, it can be read out at a maximum frame rate of 400 fps, corresponding to a minimum readout time for a single frame of 2.5 ms. We calculate the maximum integration time before saturation occurs for the theoretical case of 100% diffuse reflection for an incident solar irradiance of 1500 W/m². The wavelength-dependent saturation times for red, green, and blue wavelengths with peaks at 634 nm, 547 nm, and 453 nm, respectively, are 16.7 μs, 18.9 μs, and 26 μs, respectively. An average quantum efficiency of 0.45 is assumed.

Before motion blurring occurs, a further time averaging is allowed within a time period of 0.57 km/(7 km/s) = 81.4 ms, so over 81.4 ms/2.5 ms ≈ 32 frames. The SNR as a function of wavelength for 32 integrations of 15 μs each for red, green, and blue wavelengths is $47\times {10}^3$, $41\times {10}^3$, and $30\times {10}^3$, respectively. If we follow the procedure of [24] to estimate the RSR from the RGB camera measurements, the quantization errors corresponding to these SNR values cause an error on the RSR of 0.04 W/m². This 0.04 W/m² quantization error is small compared to [24]’s spectral regression error of 3%, which for the reference scene of 1500 W/m² corresponds to 3% × 1500 W/m² = 45 W/m².

3.3.2. SNR Multispectral Cameras

For Cameras 2 and 3, with a nadir resolution of 1.71 km and a nominal satellite altitude of 700 km, Lambertian Earth leaving flux is attenuated towards the entrance of the camera by a factor of ${(1.71/700)}^2/\pi =1.9\times {10}^{-6}$. Within the optical system, with a 0° radiometric aperture diameter of 1.14 mm and a detector pixel size of 5.5 micron, the entrance flux is amplified towards the detector by a factor of $\pi /4\times {(1.14/5.5\times {10}^{-3})}^2=3.37\times {10}^4$. The ratio between the detector flux and the Earth flux is then $1.9\times {10}^{-6}\times 3.37\times {10}^4=0.064$ without light loss and $0.064\times 0.5=0.032$ with 50% light loss.

The detector for Cameras 2 and 3 is the CMOSIS CMV2000 CMOS detector array, with 1024 × 2048 pixels and a full well capacity of 1012.5 counts, corresponding to ≈10 bit per pixel. For a 1000 × 1000 pixel subarray, it can be read out at a maximum frame rate of 680 fps, corresponding to a minimum readout time for a single frame of 1.47 ms. Before motion blurring occurs, a further time averaging is allowed within a time period of 1.71 km/7 km/s = 243 ms, so over 243 ms/1.47 ms ≈ 166 frames. The Signal-to-Noise Ratio (SNR) as a function of wavelength for 166 readouts of 400 μs each is illustrated in Figure 15. For the least sensitive wavelength at 950 nm, the SNR for a single readout is 771 and the SNR for 166 readouts is $128\times {10}^3$.

4. Longwave Camera Suite

4.1. Multispectral Thermal Cameras

A reference design of the thermal imager is described in [25]. The thermal imager consists of a microbolometer detector array with a WFOV lens allowing us to view the Earth from limb to limb. The WFOV lens design is illustrated in Figure 16. The nadir sampling distance is 2.2 km, and the nadir effective resolution is 4.4 km. Using a single wavelength band of 8–14 micron, on a stand alone basis the OLR can be estimated from the thermal imager with an accuracy of 5%.

Longwave (LW) cameras are equipped with a shutter with known temperature and known high emissivity. The shutter is made of aluminum covered with Nextel 811-21 black paint [32]. This shutter will act as a flat black body. Combined with the deep space view, a two-point in-flight calibration for the longwave cameras will be implemented. The shutter view will be used for the characterization of the thermal offset as a function of the lens temperature. The deep space view will be used for an in-flight verification of the gain, which will also be measured on the ground before flight.

For improving the spectral regression OLR noise level, the number of ECO LW channels can be increased. This will be conducted by using multiple cameras, with filters inserted in front of the microbolometer detector array. In [33], the TIRI/HERA space instrument is described using the same detector as in [25] and a filter wheel with six filters each having a bandwidth of approximately 1 μm. For ECO, we will adopt similar filters, listed in

Table 2. ECO longwave spectral bands. The limits are defined at the FWHM (Full Width at Half Maximum) of the spectral bands.

Band	Limits
LW-1	8–9 μm
LW-2	9–10 μm
LW-3	10–11 μm
LW-4	11–12 μm
LW-5	12–13 μm
LW-6	13–14 μm

.

The six ECO filter spectral responses are also similar to the filter responses used for the SEVIRI/MSG [34] and FCI/MTG [35] instruments.

The ECO LW Camera Suite (LCS) will be formed of six separate LW cameras, each consisting of the same microbolometer array and WFOV lens and each equipped with a different filter realizing the spectral responses from Table 2. For the microbolometer array, the Lynred 1024 × 768 array with 17 μm pixel pitch [36] can be used.

The LW spectral responses are illustrated in Figure 17.

4.2. Noise-Equivalent Differential Temperature (NEDT)

For thermal cameras with a nadir sampling distance of 2 km and a nominal satellite altitude of 700 km, Lambertian Earth leaving flux is attenuated towards the entrance of the camera by a factor of (2/700)² = 8.2 × ${10}^{-6}$. Within the optical system, with a 0° radiometric aperture diameter of 6.61 mm and a detector pixel size of 17 micron, the entrance flux is amplified towards the detector by a factor of $\pi$/4 × (6.61/17 × ${10}^{-3}$)² = 119 × ${10}^3$. Assuming no light loss, the ratio between the detector flux and the Earth flux is then 8.2 × ${10}^{-6}$× 119 × ${10}^3$ = 0.97. Assuming 50% light loss, the ratio becomes 0.97 × 0.5 = 0.49.

The Lynred 1024 × 768 microbolometer detector array has an NEDT of 50 mK for f/1 optics at 300 K and at 30 Hz. For the above calculated optical magnification of 0.49, the NEDT will be increased to 50 mK/$\sqrt{0.49}$ = 72 mK. Before motion blurring occurs, the microbolometer signal can be integrated during 4.4 km/7 km/s = 0.63 s. After 0.63 s averaging, the NEDT will be reduced to 72 mK/0.63 s $\sqrt{\times 30\mathrm{Hz}}$ = 17 mK for a hypothetical microbolometer without a spectral filter. From the ECO spectral filters—illustrated in Figure 17 and quantized via Equation (3)—the fractions measured for an ideal black body at 300 K are calculated, and the respective resulting NEDTs are calculated and listed in

Table 3. Longwave filter fraction and NEDT.

	Band 1	Band 2	Band 3	Band 4	Band 5	Band 6
Fraction of black body radiation	0.1087	0.1155	0.1083	0.0908	0.0643	0.0362
NEDT per band (mK)	51.55	50.03	51.66	56.40	67.02	89.3785

.

4.3. Longwave Spectral Regression

In [25], the OLR was estimated from a single narrowband irradiance $I_{nb}$ measurement via the following steps:

1.

Conversion of the narrowband irradiance $I_{nb}$ to a narrowband brightness temperature $T_{nb}$.

2.

Conversion of the narrowband brightness temperature $T_{nb}$ to a broadband brightness temperature $T_{bb}$.

3.

Conversion of the broadband brightness temperature $T_{bb}$ to the OLR.

Here, we will generalize this approach using six narrowband irradiances $I_{nb,i}$, for i = 1, …, 6. The six narrowband irradiances are obtained from the six thermal cameras with spectral responses illustrated in Figure 17. Using the sigmoid function $s\left(x\right)$, with

$$s\left(x\right)=\frac{1}{1+e^{-x}}$$

(1)

we define the synthetic microbolometer spectral response $f_{mb}\left(\lambda \right)$

$$f_{mb}\left(\lambda \right)=s((\lambda -7.5 \mathsf{\mu }\mathrm{m})\ast 4)\ast s(\lambda -13 \mathsf{\mu }\mathrm{m})$$

(2)

with $\lambda$ being the wavelength, and we define the synthetic narrowband spectral responses $f_{nb,i}\left(\lambda \right)$, for i = 1, …, 6, as

$$\begin{array}{c}\hfill f_{nb,1}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -8 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -9 \mathsf{\mu }\mathrm{m})\ast 10)\\ \hfill f_{nb,2}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -9 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -10 \mathsf{\mu }\mathrm{m})\ast 10)\\ \hfill f_{nb,3}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -10 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -11 \mathsf{\mu }\mathrm{m})\ast 10)\\ \hfill f_{nb,4}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -11 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -12 \mathsf{\mu }\mathrm{m})\ast 10)\\ \hfill f_{nb,5}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -12 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -13 \mathsf{\mu }\mathrm{m})\ast 10)\\ \hfill f_{nb,6}\left(\lambda \right)=f_{mb}\left(\lambda \right)\ast s((\lambda -13 \mathsf{\mu }\mathrm{m})\ast 10)\ast s(-(\lambda -14 \mathsf{\mu }\mathrm{m})\ast 10)\end{array}$$

(3)

For a given general spectral irradiance distribution $I\left(\lambda \right)$, the narrowband irradiance $I_{nb,i}$ is given by

$$I_{nb,i}=\int I\left(\lambda \right)f_{nb,i}\left(\lambda \right)d\lambda$$

(4)

And the broadband irradiance, also known as the OLR, is given by

$$OLR=\int I\left(\lambda \right)d\lambda$$

(5)

For the specific case of black body radiation, the irradiance distribution is given by the Planck curve and depends only on the temperature T of the black body, $I\left(\lambda \right)=I_{BB}(T,\lambda )$. We define the brightness temperature $T_{nb,i}$ from an exponential fit to this black body radiation:

$$\int I_{BB}(T,\lambda )f_{nb,1}\left(\lambda \right)d\lambda \approx {(a_i\ast T_{nb,i})}^{b_i}$$

(6)

And we define the broadband brightness temperature $T_{bb}$ from Planck’s law:

$$OLR=\sigma \ast T_{bb}^4$$

(7)

For the general narrowband radiance $I_{nb,i}$ given by Equation (4), the narrowband brightness temperature $T_{nb,i}$ is obtained by inverting the exponential fit from Equation (6):

$$T_{nb,i}=\frac{{\left(I_{nb,i}\right)}^{\frac{1}{b_i}}}{a_i}$$

(8)

And the broadband brightness temperature $T_b$ is obtained by inverting Planck’s law:

$$T_{bb}={\left(\frac{OLR}{\sigma }\right)}^{\frac{1}{4}}$$

(9)

Similar to [25], we use the libradtran radiative transfer simulation tool to simulate the narrowband irradiances and OLR for 15 reference scenes, listed in column 1 of

Table 4. Longwave reference scenes, OLR, and OLR regression error.

Scene	OLR (W/m2)	OLR Error (%)
US standard—clear sky	257.59	0.21
Tropical—clear sky	284.46	$-0.44$
Midlatitude summer—clear sky	277.87	$-0.25$
Midlatitude winter—clear sky	227.95	$-0.46$
Subarctic summer—clear sky	260.81	$-0.11$
Subarctic winter—clear sky	197.04	$-0.17$
US standard—water cloud	214.31	0.61
US standard—thin ice cloud	184.32	0.04
US standard—thick ice cloud	124.75	$-0.61$
Midlatitude winter—water cloud	200.64	$-0.52$
Midlatitude winter—thin ice cloud	171.44	$-0.49$
Midlatitude winter—thick ice cloud	125.25	0.23
Subarctic summer—water cloud	227.57	$-0.42$
Subarctic summer—thin ice cloud	196.57	$-0.07$
Subarctic summer—thick ice cloud	142.98	$-0.08$

.

For the ensemble of these 15 reference scenes, we regress $T_{bb}$ as a linear function of $T_{nb,i}$:

$$T_{bb}\approx c_0+\sum _{i=1}^6{c}_i\ast T_{nb,i}$$

(10)

Next, we evaluate the OLR from $T_{bb}$ using Planck’s law—using Equation (9). The resulting OLR regression error is given in column 3 of Table 4. It lies within the range +/−0.61%.

The general recipe for estimating the OLR from measured narrowband irradiances $I_{nb,i}$, for i = 1, …, 6, is:

1.

Convert $I_{nb,i}$ to $T_{nb,i}$ using Equation (8).

2.

Estimate $T_{bb}$ from $I_{nb,i}$, using Equation (10).

3.

Convert $T_{bb}$ to the OLR, using Equation (7).

5. Discussion

The monitoring of the Earth Energy Imbalance is one of the most critical aspects of mastering our planet’s climate change [4,5] and is the main mission objective of the Earth Climate Observatory (ECO) space mission concept. The ECO payload concept consists of four WFOV radiometers as main instruments, targeting an accurate differential measurement of the EEI as the difference of the ISR and the TOR, at a low spatial resolution of approximately 6000 km for a single measurement of the TOR. As auxiliary ECO instruments, cameras are proposed, allowing us to spectrally separate the TOR into RSR and OLR and to resolve the RSR and the OLR at a spatial resolution of at least 5 km at nadir, allowing us to distinguish clear-sky from cloudy scenes. In [24], a 1500 × 1500 RGB CMOS camera was proposed, providing a nadir resolution of approximately 1 km for a single pixel and allowing us to estimate the RSR with a spectral regression error of 3% at the 2 × 2 pixel level. In [25], a 750 × 750 microbolometer camera was proposed, providing a nadir resolution of approximately 2 km and allowing us to estimate the OLR with a spectral regression error of 5% at the pixel level. In this paper, we are introducing some improvements in the ECO camera concept, building further on [24,25]’s baseline designs.

For a SW camera, in [24], a single RGB camera—with pixel size of 3.2 μm and image diameter of 1536 pixels, corresponding to 1536 × 3.2 μm = 4.9 mm—was used. The accuracy by which high-resolution RSR radiance can be estimated from this camera is limited to 3% by the information contained in the three spectral channels, the red, green, and blue channels with typical spectral responses shown in Figure 5.

Here, we have proposed a dramatic improvement in the number of spectral channels by adopting the IMEC multispectral cameras described in [29], which we adopt as our SW Cameras 2 and 3. Cameras 2 and 3 provide a total of 41 spectral channels, in the form of a 4 × 4 VIS and 5 × 5 VIS-NIR Multispectral Filter Array (MSFA), respectively, as illustrated in Figure 6. IMEC multispectral detectors are based on the CMOSIS CMV2000 detector, with a pixel size of 5.5 μm and image diameter of 1000 pixels, corresponding to 1000 × 5.5 μm = 5.5 mm. For the SW camera lens, we can use the optical design of [24], with a scaling of 5.5/4.9 = 1.1.

The use of MSFA-based cameras requires a demosaicing algorithm, for which deep learning (DL)-based methods are currently an active area of research [37,38]. The quality of demosaicing will improve if we can provide additional high-resolution input information. For this purpose, we propose to include SW Camera 1, a high-resolution RGB camera based on the CMOSIS CMV12000 detector, with a pixel size of 5.5 μm and image diameter of 3000 pixels, corresponding to 3000 × 5.5 μm = 16.5 mm. For this camera, we need a new optical design, which is presented in Section 3 and Figure 7.

For a thermal or longwave (LW) camera, in [25], a single ‘broadband’ microbolometer camera with spectral response between 8 and 14 μm—see the purple curve in Figure 17—is proposed. The corresponding OLR spectral regression error is 5%. Here, we propose to use six different copies of this basic camera—using the same microbolometer detector array and WFOV LW lens, see Figure 16—with six different filters in front of it. Inspired by the TIRI instrument [33] to be launched as part of the Hera mission [31], we choose six adjacent filters with a width of 1 μm, with spectral responses illustrated in Figure 17.

Extending the methodology of [25], with the newly proposed six-channel LW camera concept, in Section 4.3, we evaluate the OLR radiance spectral regression error to be 0.6%. Thus, comparing our newly proposed LW camera design to the one of [25], by going from 1 to 6 channels, we reduce the OLR spectral regression error from 5% to 0.6%.

A detailed analysis of the optical performance of the newly designed high-resolution SW camera, as well as an evaluation of the SNR of all SW cameras and the NEDT of all LW cameras, is given in Section 3.2. The optical performance is well above what is required for the ECO mission’s scientific objectives.

6. Conclusions

We propose in this work an update to the work previously performed for the ECO space mission to measure what can be considered as the most essential of all climate variables: the Earth Energy Imbalance. The proposed payload consists of a combination of highly accurate but low-resolution radiometers measuring incoming solar radiation and total outgoing terrestrial radiation in a differential way, enhanced with lightweight uncooled camera systems aiming to separate the total outgoing terrestrial radiation spectrally in reflected solar, or shortwave, and emitted thermal, or longwave, radiation, and to increase the spatial resolution to 5 km at nadir or better.

The primary mission objective is to measure the global annual mean EEI with an accuracy of 1 W/m² and a stability of 0.2 W/m²dec; in principle, this objective can be reached with stand alone radiometers. The addition of auxiliary cameras will allow for a secondary mission objective of deriving high-resolution maps of the RSR and OLR. These secondary mission objectives will require the development of narrowband-to-broadband regressions and angular dependency modeling. Although not critical for the primary mission objective, a calibration of the cameras is foreseen to serve the secondary mission objectives. For the calibration of the visible cameras, we foresee deep space views and vicarious calibration. For the calibration of the thermal cameras, we foresee deep space calibrations and a shutter acting as a flat-plate black body.

Compared to our earlier proposal for the camera system, which consisted of a single SW camera and a single LW camera, we now propose a suite of three SW cameras and six LW cameras, with strongly improved spectral information content. The 2 × 2 pixel nadir spatial resolution of the highest-resolution SW camera has improved from 2.2 km in the earlier design to 1.1 km in the current design. For the LW cameras, the number of spectral channels has increased from 1 to 6, and the OLR spectral regression error has gone down from 5% to 0.6%. For the SW cameras, the number of spectral channels has increased from 3 to 44.