Optimizing Soil Moisture Station Networks for Future Climates

Soil moisture is central to local climate on land. In situ soil moisture observations are vital for observing vegetation‐relevant root‐zone soil moisture. However, stations included in the International Soil Moisture Network are sparse in regions with strong land‐atmosphere coupling. We apply a machine‐learning‐based procedure for informing future station placement using virtual soil moisture stations in future CMIP6 projections. Stations are placed where the climate is currently most under‐represented. This strategy outperforms random station placement and station placement according to geographical distance. Doubling the current number of stations using this method alleviates the uneven global distribution of stations, increases the skill in the estimation of inter‐annual variability and trends in dry‐season soil moisture, and reduces its differences across climates in future projections. Stations are predominantly placed in tropical climates, especially when optimizing for drying trends. The results can inform future station placement to support climate change mitigation efforts.

volunteer basis and includes observations from a wide variety of sampling depths, sensors, and regional networks. Quality flagging is applied to ensure the plausibility of the measurements. Sampling depths from 0.05 to 2 m are available, but they are not harmonized across stations and only a few stations have sampling depths below 1 m (W. A. Dorigo et al., 2011). The collection is currently mostly used for evaluating, developing, and validating remote sensing observations or models (W. Dorigo et al., 2021). For example, it has been used for uncovering climate interactions (Brocca et al., 2014;Hirschi, 2014) or real-time drought monitoring on country level (Gruber et al., 2018;Mozny et al., 2012;Rassl et al., 2022) (for a full review see W. Dorigo et al. (2021)).
For many monitoring purposes, however, the in situ stations included in the ISMN collection are too sparse in space and time. Furthermore, a central challenge of these observations is that they are not evenly distributed across the globe, favoring Europe and the US. This leads to an over-representation of the temperate Cs Köppen-Geiger climate. Historical efforts by the Soviet Union led to a dense station network in Eurasia, but these efforts ceased with its dissolution in 1991. As a consequence, 40% of reference regions defined for the intergovernmental panel on climate change (IPCC regions hereafter, see Iturbide et al. (2020)) and 76% of all countries do currently not have a single soil moisture station in the ISMN. In these countries, soil moisture may still be monitored through national observation networks, but copyright limitations, language barriers, and other practical hurdles may prohibit this valuable data to be incorporated into the ISMN. Consequently, the station density of the ISMN is well below the proposed necessary densities for interpolation (30 stations per million km 2 (Kloster et al., 2012;Oki et al., 1999;Seneviratne et al., 2010)) for 89% of the countries and 87% of the IPCC regions and only dense enough for data assimilation (141 stations per million km 2 , (Gruber et al., 2018)) in Western North-America, Greece, Hungary, Austria, South Korea, Puerto Rico, and Rwanda. Thus, soil moisture is unobserved in the majority of the global land area, leading to biases in the ISMN collection and missing soil moisture information on whole climate zones, regions, and countries.
With a rapidly warming climate, soil moisture drying is projected in many regions (Arias et al., 2021) and droughts are projected to increase in frequency, duration, extent, and severity (Lu et al., 2019;Prudhomme et al., 2014;Spinoni et al., 2020;Wang et al., 2021). However, soil moisture trends are uncertain in many regions (Arias et al., 2021;Cook et al., 2020). In Arias et al. (2021) low agreement in the change is prevalent for large parts of the world, and in many regions attributed to limited observational data. Thus, missing observations and uncertain future trends are inherently linked: An incomplete observation of local soil moisture dynamics may lead to an incomplete representation in climate models, high variability across models, and a low uncertainty of future change. This uncertainty then cannot be reduced due to a local lack of observations for validation and evaluation of climate models. This way, the missing information carries the uncertainty forward into the future until the gaps in the measurement network are sufficiently closed.
To overcome the limitations of sparse in situ observation networks of terrestrial climate variables, several classes of methods exist that transform point-scale data into gridded, spatially complete data products. These methods include data assimilation, spatial interpolation, and statistical up-scaling. They are employed in different contexts: Data assimilation is used to digest a wide array of observations from many variables into dynamical weather models. With spatial interpolation, missing values can be estimated based on surrounding observations. Spatial interpolation can digest lower station densities, but does typically not include information from other variables (see e.g., Becker et al., 2013;I. Harris et al., 2020). Statistical or data-driven up-scaling is typically performed to predict missing values in gridded data by uncovering the relation between a time series of spatially sparse in situ observations and donor variables that are available on regular grids using machine learning. Subsequently, this relation is employed to derive gridded estimates of the considered variable. Up-scaling can be viewed as "interpolation in climate space" compared to the more common approach to interpolate in geographic space. Up-scaling procedures have been regularly employed in recent years to develop global estimates of variables such as evapotranspiration (Jung et al., 2009(Jung et al., , 2011(Jung et al., , 2019Martens et al., 2017), runoff (Ghiggi et al., 2021;Gudmundsson & Seneviratne, 2015) and soil moisture (O. & Orth, 2021;Zhang et al., 2021). The resulting data products are regularly used in a wide array of applications including climate monitoring (e.g., Martens et al., 2018), physical model evaluation (e.g., H. Guo et al., 2022), evaluation of remote sensing products (e.g., W. Dorigo et al., 2017), constraining statistical models (e.g., Kraft et al., 2022) or process studies (e.g., Miralles et al., 2019).
Irrespective of the method, a major obstacle for gridded products derived from station measurements is the uneven distribution of stations across the globe. For example, the gridded CRU TS data set (I. , comprised of interpolated weather station observations, shows a lower performance in the tropics for temperature and precipitation, where the station network is less dense. The WMO has thus articulated the need for closing the gaps in the observation system and has initiated the Systematic Observation Financing Facility to raise and redistribute money for building stations in under-represented regions (WMO, 2021). In the realm of data assimilation, the ECMWF has noted that in situ observations are still, even in the age of massive satellite remote sensing, the main drivers of model performance and that sparse in situ observation in the Southern Hemisphere are more influential than their counterparts in the Northern Hemisphere, as their impact on the forecast and forecast error is larger (Ingleby, 2021). The ISMN station network is exceptionally unevenly distributed, making up-scaling these observations to global soil moisture estimates challenging. For example, O. and Orth (2021) have up-scaled ISMN data using a neural network-based approach. They get overall satisfactory results, but also note that performance depends on data availability, and missing in situ data leads to low performance in tropical regions.

Objectives
The irregular soil moisture station network hampers global and regional monitoring, up-scaling efforts, and the detection of ongoing and future drying trends or drought occurrences. The current de-facto approach is building stations where wealthy countries place an emphasis on their observation networks, where field campaigns are running and at locations that are relatively easy to access. Installing new stations is urgently necessary, but associated with significant costs. Placing future stations should hence focus on closing gaps in the observation net most efficiently. It is however not immediately straightforward where future stations should ideally be placed to achieve this goal. A spatially uniform measurement network might seem like the obvious choice, but this disregards the current network and the distribution of climates across the globe, where environmentally similar regions can be far distant from one another. Within this study, we address this problem by examining different strategies for future station placement and estimating the impact of possible future measurement stations in currently under-represented areas of the world.
As we cannot observe future soil moisture, we fall back on an ensemble of future model projections of the sixth phase of the coupled model inter-comparison project (CMIP6, see Eyring et al. (2016)) as a surrogate for future observations. We acknowledge that model grid points are not generally representative of station data and a point measurement can only be compared to a certain degree with the respective grid point of model output. Nevertheless, by focusing on monthly anomalies of soil moisture observations from 2.5-degree harmonized CMIP6 model output, we concentrate on the climate signal and not the local heterogeneous soil conditions that control it on smaller scales (O. & Orth, 2021;Mittelbach & Seneviratne, 2012;Robock et al., 1998). Furthermore, since we cannot change the observations of the past, we build on the current network and propose possible extensions.

Data Preprocessing
We consider monthly mean total soil moisture from near-future (2015-2050) SSP (shared socioeconomic pathway) 3 RCP (representative concentration pathway) 7.0 climate model simulations contributing to CMIP6 model ensemble that were re-gridded to a common 2.5° resolution (Brunner et al., 2020). We extract the locations of currently active ISMN stations that have at least one sensor reporting valid measurements, irrespective of the actual depth of the sensor. These locations are then matched with their respective CMIP6 grid point that contains the station (see Figure S1 in Supporting Information S1). Grid points on land that contain an ISMN station are labeled observed, all other grid points are defined as unobserved.

Focus on Relevant Areas With Strong Land-Atmosphere Coupling
We allow the placement of new virtual soil moisture stations only in "human affected and human affecting" (Vogel et al., 2019) areas or areas where the land-atmosphere coupling is strong enough to be able to influence local climate. To achieve this we include regions where (a) the cropland fraction of the grid point is larger than 10% (data from Potapov (2022)), (b) the human population density is above 100 km −2 (data from CIESIN (2017)) or (c) where the Pearson correlation between the inter-annual variability of evapotranspiration and soil moisture of the driest three consecutive months is below 0.2, indicating a transitional soil moisture regime and therefore land-atmosphere coupling . Local smoothing is applied to this mask to reduce spurious holes. In addition, oceans, deserts (defined as Köppen-Geiger climate BW Köppen, 1884)) and permanently glaciated areas (Greenland and Antarctica) are masked prior to analysis to focus only on regions with active and non-negligible land hydrological cycles. Areas with permafrost (soil temperature of deepest layer below 0°C in 2014-2015 average, after Slater and Lawrence (2013)) are excluded since soil-moisture sensors are only suitable for observing liquid soil water. The resulting mask of relevant regions for future station placement is shown in Figure S2 in Supporting Information S1.

Statistical Up-Scaling Model
At the center of the analysis is an up-scaling model adapted from Gudmundsson and Seneviratne (2015), where a random forest (Breiman, 2001) is trained to estimate local grid-point level soil moisture from temperature and precipitation of the current month and last 12 months: where x and y are the latitude and longitude of the grid point, respectively, and m is the monthly time step. sm indicates the monthly mean all-layer soil moisture [kg m −2 ], t is the monthly mean 2 m temperature [K], and p monthly summed precipitation [kg m −2 s −1 ]. The function f is a random forest regression. In doing that we assume that temperature and precipitation from the last 12 months are sufficient to estimate the current soil moisture.

Performance Metrics
Two main properties of future soil moisture are key to informing its future influence on local climate: (a) The inter-annual variability of dry-season soil moisture and (b) the long-term trend in dry-season soil moisture. To extract the dry season, for each grid point the driest 3 consecutive months are calculated from the 2015-2050 climatology and extracted for each year. Then the linear trend and the anomalies are calculated from the yearly averages, respectively (see Text S1 in Supporting Information S1).
The experiment described in Section 4.3 is performed for each of those properties individually. In the first case, the performance of the up-scaling is judged by the correlation of the inter-annual variability between the original CMIP6 model data and the prediction of the up-scaling model. In the second run, the difference between the trend estimates of both CMIP6 model data and up-scaling model prediction expressed as Mean Absolute Error (MAE), are compared. The difference between the results of the up-scaling model and the original CMIP6 values at unobserved points, for both performance metrics, is subsequently called prediction error.

Experiment
For each model in the CMIP6 ensemble individually, a random forest model (Equation 1) is trained using all observed grid points. The trained model is then applied to predict soil moisture at all unobserved grid points, creating globally coherent gridded soil moisture estimates per month.
This procedure is repeated iteratively. In each iteration, 100 new virtual soil moisture stations are added to previously unobserved grid points. In other words, after training the up-scaling model, we add 100 new grid points at once to the set of observed grid points, practically expanding the observed land area. This is repeated until all model grid points on land are observed.
The following three strategies for station placement are explored: First, we randomly place stations onto the unobserved part of the model world (random strategy). Second, we set stations at grid points that are geographically most distant from the existing ones (geographical distance strategy). Lastly, new stations are added where the previous up-scaling had the highest prediction error for the respective performance metric, that is, lowest skill (skill-based strategy). Note that the placement of the stations can differ between the two performance metrics.

Comparing Different Strategies of Station Placement
With the current station net, around 15% of grid points on land contain a station. With increasing percentage of added stations, soil moisture estimates improve for both trend and variability ( Figure 2). This result is robust across strategies, models, and metrics. Although models have differences in the magnitude of correlation and MAE, the relative increase toward higher fractions of the observed land mass is consistent across all models.
Placing new stations according to the skill-based strategy increases global mean soil moisture estimates for both performance metrics faster than placing stations randomly or by placement based on geographical distance. This is seen in the multi-model mean, but also the majority of the considered models show that skill-based grid point selection has lower prediction errors than the other two strategies (see individual results per model in Figure S4 in Supporting Information S1). Notably, there is little difference between random and geographical distance station placement strategy. Geographical distance is therefore only a poor predictor of climatic similarity.
In summary, placing future soil-moisture observation stations skill-based has the lowest errors across metrics and models. In the next sections, we will therefore focus on this strategy only.

Distribution of Newly Placed Stations With Skill-Based Strategy
Figures 3a and 3c shows the order of the selected grid cells for trend and variability optimization averaged over all models, expressed as normalized rank. Lower normalized ranks indicate this grid point is chosen earlier, that is, deemed under-represented in the current observation net. For example, if the rank is below 10%, the grid point is chosen among the first 10% of all grid points in this model. This is accompanied by Figures 3b and 3d that shows the standard deviation in ranks across models.
With the skill-based strategy, future soil moisture stations are initially placed in African subtropics and continental Asia, if optimized for inter-annual variability. When looking at soil moisture trends, the inner tropics are predominantly chosen for early station placement. These are all regions with low station density in the current ISMN. Europe and the US, with a currently high station net, are selected later.
10.1029/2022GL101667 6 of 11 The standard deviation of normalized ranks across the CMIP6 model ensemble is a measure of disagreement in station placement across models. Model disagreement is generally larger for placing stations when optimizing for future soil-moisture trends as compared to future inter-annual variability. Model disagreement is especially high in the tropics.   Figure S3 in Supporting Information S1.

Impact of Doubling Current Number of Stations With Skill-Based Strategy
Doubling the global number of stations from roughly 18%-36% of covered land area with the skill-based strategy increases station density differently for different IPCC regions. When optimizing for inter-annual variability, new stations are placed predominantly in the tropics and continental Asia (Figure 4a). In contrast, when optimizing for estimating trends the algorithm places stations almost exclusively in the inner tropics (Figure 4b).
Although the new stations are placed only in a few regions, it is noteworthy that the performance of the up-scaling model increases not only at the locations with new stations but in all IPCC regions included in the analysis (Figures 4c and 4d). This indicates that placing stations does not only benefit the area close to the newly added soil moisture station but has non-local effects on similar climates across the world.
Figures 4e-4f additionally shows the results for current and future station numbers aggregated to Köppen-Geiger climates. When optimizing for trend estimation, tropical A climates have the largest increase in station density, which is accompanied by a considerable error reduction. When optimizing for inter-annual variability in dry-season soil moisture, the increase in correlation is more equally distributed across climates. Temperate C climates show little increase in station density and skill, but this is expected since their density and skill are already high. Overall, skill-based station placement leads to a decrease in the difference in station densities and skills across the different climates, effectively lifting global differences in observational coverage.

Discussion and Conclusion
Observations of root-zone soil moisture are vital for monitoring future drought and drying trends. In situ observations included in the ISMN are the largest collection of their kind. However, they are distributed unequally across the globe, favoring the US and Europe. 40% of IPCC regions and 76% of all countries do not have a single soil moisture station. This is an obstacle to global analysis of current and future soil moisture variability and trends.
In this study, we present a way to inform future station placement that can potentially increase the accuracy of the future global in situ soil moisture station network. This can help in deciding on future station placement.
We test placing future soil moisture stations virtually in a CMIP6 model world according to the error of an up-scaling model. Stations are placed where the up-scaling model trained from the current station net distribution shows the lowest performance, that is, stations are placed where the current climate space is most under-represented. This strategy of station placement outperforms strategies where future soil moisture stations are placed randomly or according to geographical distance, for two key properties of future soil moisture: dry-season inter-annual variability and dry-season long-term trends. The two latter placement strategies show little difference, that is, geographical distance is only a poor predictor of climatic similarity. These results show up in the multi-model mean of the CMIP6 model ensemble and the majority of individual CMIP6 models. As such, the results suggest that future stations should be placed according to climatological and not geographical distance and can for example, be informed by the framework presented in this study.
Doubling the number of current ISMN stations for a future station network with the newly proposed skill-based strategy considerably increases the skill of soil moisture anomaly and soil moisture trend estimation, alleviates the uneven global distribution of stations, and reduces differences in skill across climates and regions. The framework chooses tropical A climates as the most important for placing new stations, especially when optimizing for long-term drying trends. Many tropical regions are projected to dry in the near future (Arias et al., 2021;Cook et al., 2020) and their low inter-annual variability implies that trends can move soil moisture values more easily being outside the currently observed variability. When inter-annual variability of dry-season soil moisture is chosen as the performance measure, stations are additionally placed in regions that are covered by climates with a currently low station density: Arid regions like Western South America, Mongolia, and western China as well as dry winter climates (Cw, Dw) prevalent in North India and southern China. Thus we conclude that it is vital that future station placement focuses on these regions as it might improve observational coverage of future soil moisture drying trends and droughts.
Adequately defining the root zone is important for capturing the full extent of the land-atmosphere coupling. The soil moisture in the CMIP6 models is summed over all layers, but the depth of these layers is different across the models. Depending on the vegetation and climate, the actual rooting depth of plants varies (Kleidon & Heimann, 1998) and might be deeper than the maximum layer depth of individual CMIP6 models. Results on station placement are limited to the soil depth captured by the models, even if actual rooting depth especially in the tropics is likely higher.
Some studies indicate that station densities exhibit spatial dependence: Nicolai-Shaw et al. (2015); Orlowsky and Seneviratne (2014) show that the representative area of a point observation depends on the variable, the season, topography, and vegetation. The WMO defines recommended station densities depending on six physiographic regions and five hydrological variables, ranging from 10 stations per million km 2 to 100,000 per Mio km 2 (WMO, 2008). Station density also likely depends on temporal resolution. At yearly time-scales, CRU TS precipitation (I.  and GPCC precipitation (Becker et al., 2013) datasets have comparable skill, although their station densities (around 66 and 566 stations per million km 2 , respectively) are vastly different. This suggests either that yearly timescales need lower station densities than monthly time scales or that inter-annual variability is already well captured if recommended station densities for interpolation are met. We consequently emphasize that depending on the spatial and temporal scales chosen, the results of the framework presented in this study can differ.
In a wider context, other properties of the specific setup can affect the results as well: The statistical or physical model chosen, and especially the variable and its spatial and temporal resolution can influence future station 9 of 11 placement recommendations created by this framework. While exploring all options is out of scope for this study, such considerations are indeed interesting and relevant for the future development of similar in situ station networks. For example, the presented framework can be applied to networks of other sensors or variables, for example, temperature, precipitation (I. Rohde & Hausfather, 2020), streamflow (Sheffield et al., 2018) or soil moisture via cosmic-ray neutron sensors (Andreasen et al., 2017) to suggest new station placements. By matching their specific design requirements, for example, considering different performance metrics or different temporal resolutions (e.g., yearly or daily values), the framework can be tailored to these specific measurement networks.
For many regions, the observed change in soil moisture drought is uncertain. Arias et al. (2021) differentiates two sources of uncertainty: a low agreement in the data or missing data. But when observations are sparse, conclusions drawn from them have high uncertainty and might not agree with each other. Fundamentally, both sources of uncertainty are the same and depend on each other. If we don't close the gaps in in situ observation of vegetation-relevant root-zone soil moisture, the local future change in soil moisture droughts can remain uncertain. This may have severe implications for future drought monitoring, as it may lead to poorly constrained or validated model projections. Increasing the number of in situ stations in these regions is therefore crucial for local and regional climate change mitigation.