Groundwater Storage Changes Derived from GRACE and GLDAS on Smaller River Basins—A Case Study in Poland

geosciences

Article Groundwater Storage Changes Derived from GRACE and GLDAS on Smaller River Basins—A Case Study in Poland

Zoﬁa Rzepecka and Monika Birylo *

Faculty of Geoengineering, University of Warmia and Mazury in Olsztyn, 10-719 Olsztyn, Poland; zoﬁ[email protected] * Correspondence: [email protected]

Received: 11 March 2020; Accepted: 27 March 2020; Published: 31 March 2020

Abstract: In the era of global climate change, the monitoring of water resources, including groundwater, is of fundamental importance for nature, agriculture, economy and society. The purpose of this paper is to check compliance of changes in groundwater level obtained from direct measurements in wells with groundwater storage (GWS) anomalies calculated using gravity recovery and climate experiment (GRACE) observations in Poland. Data from the global land data assimilation (GLDAS), in the form of soil moisture (SM) and snow water equivalence (SWE), were used to convert GRACE observations into a series of GWS changes. It was found that very high consistency occurs between GRACE observations and changes in water level in wells, while the GWS series obtained from GRACE and GLDAS do not provide adequate compatibility. Further research presented in the paper was devoted to attempts to explain this phenomenon. In addition, time series of GRACE, GLDAS and groundwater head series were analyzed.

Keywords: GRACE; GLDAS; water storage; groundwater; small basin

1. Introduction The gravity recovery and climate experiment (GRACE) mission operated from 2002 to 2017. In this 15+ year period, it provided a great deal of global observations of the mass distribution and ﬂow, on and underneath the surface of the Earth. These observations explained many large scale processes connected with, among others, changes in polar ice, soil moisture, surface and ground water storage and ocean mass dynamics. GRACE observations have proved so valuable in many areas of earth science, that shortly after GRACE mission completion [1,2], another mission was initiated, called GRACE FO (gravity recovery and climate experiment follow-on) [3]. The principle of both missions is similar: measurements of satellite orbits, using GNSS (global navigation satellite systems) and laser tracking, are supplemented with very accurate measurements of the distance between two twin GRACE satellites. We can distinguish three levels of GRACE observations:

Raw measurement on Level-1 (L1), • Geopotential in a form of a spherical harmonics coeﬃcients on Level-2 (L2), • Monthly values of a terrestrial water storage (TWS) on Level-3 (L3). • Calculation centers provide GRACE observations in a form of Release Notes, the newest version is RL06 [4]. In comparison to the latest version, the new one has improved corrections (tides, atmosphere and oceans). GRACE observations can be acquired from the three main computational centers, i.e., GFZ (GeoForschungsZentrum, Potsdam), CSR (Center for Space Research at University of Texas, Austin) and

Geosciences 2020, 10, 124; doi:10.3390/geosciences10040124 www.mdpi.com/journal/geosciences Geosciences 2020, 10, 124 2 of 14

JPL (Jet Propulsion Laboratory). Data can be acquired in two forms: spherical harmonics coefficients and mascons. Spherical harmonics coefficient usage is the oldest method for geoid computation. It is based on extending harmonics up to a dedicated degree and order. Due to the fact that the model determined in such a way is very noisy, it needs spatial or temporal filtering. Noise can be observed in a final model, in the form of north–south stripes, so the model requires de-striping [5]—filters to remove errors, like averaging with Gaussian filtering, anisotropic non-symmetric filters or one of the anisotropic decorrelation filter a decision-directed Kalman - DDK filters (reducing the error stripes). The other method of model determination and presenting is a mascon technique—mass concentration computation. This alternative technique is designed as the native basis function, so every mascon has a known particular localization. An advantage of such a solution is that it does not need to be de-striped or smoothed. Moreover, due to the mascon approach, it is possible to easily separate land and ocean signals. The gravity changes are caused by mass changes. These mass variations can be understood as a change in a very thin concentrated layer of water thickness (it means near the Earth’s surface). Usually, gravity changes are caused by water storage changes (in basins or the land hydrosphere, melting ice or mass exchange between an atmosphere and land/ocean). The vertical change caused by water mass change can then be recomputed into total water storage changes (TWS). In many applications, the GRACE observations are combined with data from various land data assimilation systems, e.g., global land data assimilation (GLDAS), MERRA (modern era retrospective-analysis for research and applications) and climatic models. In the presented paper, the GLDAS model (the global land data assimilation system) was used [6,7]. The GLDAS aim is to gather both satellite and in situ data, together with advanced land surface modeling and data assimilation techniques [6]. GLDAS contains 28 types of data, such as a 1-km global vegetation dataset, soil and elevation parameters, observation-based precipitation and downward radiation products. The global model simulations provided by GLDAS are widely used in many applications, e.g., weather and climate prediction, water resource applications and water cycle investigations. Simulations are provided in 1-degree and 0.25-degree resolution, from 1948 up to now in four sub-models, NOAH (National Centers for Environmental Prediction/Oregon State University/Air Force/Hydrologic Research Lab Model), CLM (community land surface models), VIC (variable infiltration capacity) and Mosaic. After separation contributions to temporal mass changes, groundwater changes can be computed [8]. It is recommended to resolve water mass variability with GRACE, using a minimum region size of approximately 200,000 km2 [9]. The purpose of this paper is to verify the possibility of successfully using GRACE observations in smaller areas. The two largest Polish basins (Vistula and Odra) do not meet the requirements of [10]. The Vistula basin covers an area of about 194,500 km2, and the Odra basin covers about 118,900 km2. There are many determinations of groundwater using satellite models and observations and comparison of these determinations with a terrestrial data. It was concluded in [11] that GRACE data can increase the correlation between satellite-based observations and well-groundwater data. It was also noted that when taking into account groundwater data from wells, GRACE observations strongly and positively impacts time series of groundwater storage. Another application of both GRACE and well data for groundwater storage comparison was presented for the area of Alberta, Canada [12]. It was concluded that successful isolating the groundwater storage (GWS) component from the GRACE TWS is mostly dependent on the accuracy of the soil moisture and snow water values. Determining groundwater storage allowed the authors to notice that accurate final determination needs a dense distribution of terrestrial wells and realistic evaluation of a porosity coefficient at wells’ localization. Final results of comparison GRACE-derived GWS and 256 well data revealed that only 36 wells were significantly correlated with the GWS from GRACE (correlation coefficient of 0.68). A site factor (standard deviation ratio) at all the 36 wells is strongly dependent on geological patterns at the area [13]. Geosciences 2020, 10, 124 3 of 14

The groundwater storage was also examined for Western India, in Rajasthan, where many contrasting patterns were observed when analyzing data—an increasing trend was observed for wells, while for GRACE derived groundwater storage the trend was negative, which resulted in a negative correlation of 0.14. On the other hand, when analyzing Gujarat, for well and GRACE observations − the same pattern was noticed—a positive relationship of 0.64 [14]. In [15] a GWS determination in the areas of sparse hydrogeological databases (southern Mali, Africa) was presented—only 16 wells within the region. The analysis showed a strong correlation between the GRACE-derived GWS and those from direct well measurements. When GRACE data was corrected with the soil moisture, the magnitude and relative timing of groundwater-storage changes was predicted more accurately. Based on the research it was concluded that GRACE could become a valuable resource management tool in regions lacking hydrogeological data. In the paper, the following procedure was applied: a deduction of GRACE TWS data to deeper water storage using GLDAS information and a comparison of results with water level variations in chosen Polish wells. The detailed procedure used was developed on the basis of the Level-3 Data Product User Handbook [4]. For validation, a groundwater level from measurement wells was taken. In situ measurements are carried out by the National Hydrogeological Service (Polish abbreviation: PSH). The PSH provides groundwater measurements of water quantity and quality, fulfilling the necessity of assessing the quantitative and chemical status of groundwater. Groundwater monitoring is very important in terms of water resource management and protection. Over 2000 measurement wells are located in the area of Poland. Monitoring of wells is carried out at different time scales, depending on their function. The water table measurement is performed every day at the first order hydrogeological stations; and once a week at the second order hydrogeological stations. In some of the first and second order hydrogeological stations, automatic measurements of the groundwater level were introduced. Diagnostic monitoring takes place every three years and covers the entire country. In the years between diagnostic monitoring, operational monitoring is carried out, during which uniform parts are sampled once or twice a year, threatened by failure to achieve good condition in the perspective of 2021 [16]. The subject of monitoring of equivalent parts of groundwater (EPG) according to division into 172 uniform parts and separated from the basis by appropriately selected criteria fragments: subparts EPG. Due to the geological and hydrogeological analysis for the most area of Poland and the fact that groundwater resources in EPG are in multilevel structures, monitoring of numerous aquifers, levels and stories are not possible. Therefore, levels and/or stories were grouped into three aquifers complexes, taking into account hydrogeological conditions, dynamics and pressure exerted on them. An aquifer complex is a levels’ set connected with each other with a specific characteristics, like: lithological (sand, sand–gravel), stratigraphic (quaternary–tertiary), structural (kw of the valleys and lowlands), chemical (kw of sweet water), etc. The first complex is a groundwater reaching low-permeable level where pumping takes from a few days up to several months. It is a complex with an unconfined table that corresponds to the first aquifer (FA defined for the purposes of developing the Hydrogeological Map of Poland (HMP) in the scale of 1:50,000). The complex fed directly by precipitation infiltration. They do not have to meet the conditions specified for useful aquifers, it is possible to isolate these waters from the surface in a small area with a discontinuous packet of poorly permeable formations of low thickness (e.g., <2 m). The second complex are aquifers with a confined table (deep waters), insulated from the upper surface by a packet of poorly permeable formations, of considerable thickness (e.g., 2 m), fed with water filtration from a higher level with an unconfined table. Infiltration takes up to hundreds of years. The third complex is the water of the lowest occurring or the lowest of the identified usable aquifers, contacting or being able to contact the lower occurring levels of salt water. This complex is at risk of salt water ascension (the so-called deep water in hydraulic contact with deep water, which are most often brines) [17,18]. In the presented paper only the first complex is taken into account. Geosciences 2020, 10, 124 4 of 14

The approach to obtaining a representative monitoring result for the examined wells requires taking into account: its purpose, size of the research area, complications of geological structure and hydrogeological conditions, type and strength of economy pressure [18]. From this point of view, the following were considered:

Partial representativeness, ﬁrst of all taking into account the structure and parameters of • aquifers/aquifers, location of pressure foci and is mainly relevant for determining the optimal location and depth of the research point; Temporal representativeness taking into account the speed of hydrogeological processes, which is • combined with determining the appropriate frequency of measurements and tests (sampling). Determination of the structure and density of the observation and research network, as well as indication of locations of monitoring points in the area of a particular JCWPd (in Polish: Jednolite cz˛esciwód podziemnych–Groundwater plain parts) of the selected aquifer, took place so as to obtain spatial representativeness of the network.

For research points of groundwater table location and source eﬃciency as well as diagnostic chemical monitoring, because it applies to all JCWPd, the following densities were adopted in individual aquifers:

At groundwater level or usable aquifer with unconﬁned water table (when there is no insulation • from the area)—1 point per 500 km2, but not less than 3 points within JCWPd.

The aim of the study is to check compliance of changes in groundwater level obtained from direct measurements in wells with groundwater storage (GWS) anomalies calculated using GRACE observations in Poland.

2. Data Used for the Study

2.1. GRACE Data The GRACE TWS data was obtained from the JPL NASA [19], in the form of monthly gravity mascon solutions with a CRI ﬁlter (a Coastline Resolution Improvement) applied [20,21]. The JPL mascon data are given with the resolution of 0.5◦ in cm of equivalent water height. In the calculations, data given monthly, for the period from November 2006 to October 2016 were used. Missing epochs were completed by linear interpolation using the “approx” function of R [22]. This procedure gave 120 epochs (months) of monthly data, referenced to the 15th day of each month. All of the GRACE data were optimized to reduce the leakage eﬀect, using scaling factors given together with the mascon JPL data. It should be noted that GRACE data are given in the form of anomalies in relation to the average value obtained in the period from January 2004 to December 2009. Any other period can be used to calculate the anomaly. In this paper we changed the period against which anomalies were calculated for January 2007 to December 2012. This was due to the fact that we used data for the wells for the period November 2006 to October 2016. Conversion to an anomaly relative to the average of another period is very simple and involves subtracting the new average from all previous anomaly values.

2.2. GLDAS Data As recommended by the Level-3 Data Product User Handbook [4], the GLDAS NOAH model with a resolution of 0.25◦ was used to estimate the total amount of water contained in the surface of the investigated area. Water content in soil was modeled to the depth of 2 m in this model. It is given in the form of the soil moisture (SM), which is a static value expressed in kg/m2, which can easily be recomputed to the equivalent water height in cm. Other forms of water contained in the surface of the terrain include water contained in snow and water contained in all plants growing in a given area. The ﬁrst value is given in the NOAH model as snow water equivalent (SWE), and the second Geosciences 2020, 10, 124 5 of 14

as canopy (CA). Units are the same as in the soil moisture. Total water content estimated within the NOAH model is the sum of SM, SWE and CA. As noted previously, this expresses all forms of water Geosciencescontained 2020, 10 on, x andFOR PEER under REVIEW the surface, to the depth of 2 m. The same period of 120 months5 as of in14 the case of the GRACE data was used. From all the data, the averages January 2007 to December 2012 werewere removed, removed, thus thus the thedata data presented presented are areanomalies anomalies comparabl comparablee with with the theGRACE GRACE data. data. It is Itworth is worth mentioningmentioning that that the the GLDAS GLDAS model, model, in in addition addition to to the the N NOAHOAH submodel, alsoalso containscontains threethree other other land landassimilation assimilation models: models: The The community community land land modelmodel (CLM)(CLM) [[2323],], thethe mosaicmosaic (MOS)(MOS) modelmodel [[2424]] andand the the variablevariable inﬁltrationinfiltration capacity capacity (VIC) (VIC) model model [25 [2].5 The]. The other other models models were were used used for thefor purposethe purpose of looking of lookingfor the for best the correlation.best correlation.

2.3. 2.3.Polish Polish Wells Wells TheThe groundwater groundwater level direct direct measurement measurement data weredata obtained were obtained from the Polish from Hydrogeological the Polish HydrogeologicalAnnual Reports, Annual from Reports, the years from of 2007–2016 the years of [26 2007]. Above–2016 one[26]. thousand Above one wells thousand were reported,wells were from reported,which 215 from wells which were 215 selected, wells only were those selected, that wereonly continuously those that were measured continuously throughout measured the whole throughoutperiod of the November whole period 2006 to of October November 2016 2006 (without to October gaps). 2016When (without spatially gaps) averaging. When all spatially time-series averagingover the all basins, time-series 122 wells over were the basins assigned, 122 to wells the Vistula, were assigned 70 to the to Odra the Vistula, basin and 70 the to the remaining Odra basin 23 were andoutside the remaining the basin 23 areaswere (Figureoutside1 a).the Itbasin needs areas to be (Figure added 1a) that. It the need averages to be over added the that series the may average or may overnot the give series a good may approximationor may not give of a the good real approximation average of groundwater of the real headaverage series, of groundwater so a possible head bias due seriesto, the so a location possible needs bias due to be to taken the location into consideration. needs to be taken into consideration.

FigureFigure 1. Polish 1. Polish well welllocalization localization and andapproximate approximate depths depths (a) and (a) andexample example depths depths variations variations (b). (b).

PolishPolish wells wells are arevery very diversified, diversified, both both due due to the to thedepth depth of the of thewater water surface surface and and seasonal seasonal changes changes in level.in level. Figure Figure 1b 1showsb shows some some examples examples of the of the anomalies anomalies of the of the unconfined unconfined water water level level of chosen of chosen wellswells taken taken for calculations. for calculations. Two Two wells wells were were removed removed from from the calculations, the calculations, due dueto unusual to unusual behavior, behavior, likelike the thewell well 428. 428. It can It canbe seen be seen that that depth depth variations variations of individual of individual well well levels levels differ diffedered significantly significantly betweenbetween each each other. other. However, However, the thecalculated calculated average average variations variations for the for theVistula Vistula and and Oder Oder basins basins were were similarsimilar,, see seeFigure Figure 3. These 3. These resulting resulting averages averages were were adopted adopted for comparisons for comparisons with with GWS GWS and and TWS TWS in in furtherfurther parts parts of the of thepaper. paper. Let Letus remind us remind that that TWS TWS stands stands for forGRACE GRACE derived derived total total water water storage, storage, whilewhile GWS GWS stands stands for ground for ground water water storage storage computed computed based based on TWS on TWS and and GLDA GLDASS data, data, see seeEquation Equation (1) below.(1) below.

3. Methods3. Methods To workTo work together together with with the theGRACE GRACE and and GLDAS GLDAS data, data, we ha wedhad to bring to bring them them to a touniform a uniform form. form. AfterAfter unification uniﬁcation of ofunits units to tocm cm of of equivalent equivalent water water height, height, we we must present thethe NOAHNOAH data data in in the the form formof of anomalies anomalies in in relation relation to to the the average average for for the the period period 2007.000–2012.999 2007.000–2012.999 and and then then aggregate aggregate the datathe to datathe to coarser the coarser resolution resolution of 0.5 ◦ ofof 0.5 the° GRACEof the GRACE data. To data. reduce To resolution, reduce resolution, the “aggregate” the “aggregate function from” functionthe R from raster the package R raster was package used [ 22was,27 used]. [22,27]. Next, for all the raster cells and all the time epochs, the groundwater storage (GWS) anomalies were computed. It should be emphasized that all the water contained beneath the depth of 2 m, i.e., the water not taken into allowance in NOAH model, is referred to as the groundwater here. GWS was computed as the difference between the JPL GRACE TWS and the sum of GLDAS contents: = − ( + + ) (1)

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Next, for all the raster cells and all the time epochs, the groundwater storage (GWS) anomalies were computed. It should be emphasized that all the water contained beneath the depth of 2 m, i.e., the water not taken into allowance in NOAH model, is referred to as the groundwater here. GWS was computed as the diﬀerence between the JPL GRACE TWS and the sum of GLDAS contents:

GWS = TWS (SM + SWE + CA) (1) Geosciences 2020, 10, x FOR PEER REVIEW − 6 of 14 Units of all quantities in the above equation are cm of equivalent water height. The obtained Units of all quantities in the above equation are cm of equivalent water height. The obtained rasterraster of GWS of GWS data, data, for for the the ﬁrst first month month taken taken for for analyses, analyses, is given given in in Figure Figure 2.2 .

FigureFigure 2. Groundwater 2. Groundwater storage storage (GWS) (GWS raster) raster computed computed for for November November 2002, 2002, with with marked marked areas areas used used for averagingfor averaging (green: (green: Vistula Vistula basin, basin, red: red: Odra Odra basin). basin).

Next,Next, the raster the raster cell values cell values were were averaged averaged over over the generalized the generalized areas areas of Polish of Polish river river basins basins (Vistula and Odra).(Vistula The and obtained Odra). The means obtained were means further were analyzed. further analyzed.

4. Analysis4. Analysis of Results of Results

4.1. Comparison4.1. Comparison of GWS of GWS with with Polish Polish Well Well Data Data in in 2006–20162006–2016 This analysis used data from 215 wells, located as presented in Figure 1a and covering the This analysis used data from 215 wells, located as presented in Figure1a and covering the period period of November 2006 to October 2016. The thicknesses of the unsaturated zone at the location of of Novemberthe well and 2006 GWS to October data averaged 2016. over The thicknessesthe Vistula basin, of the Odra unsaturated basin and over zone the at thetotal location area of the of two the well and GWSbasins data were averaged compared. over The thetime Vistula series of basin, averaged Odra data basin are plotted and over in Fig theure total 3a,b area. of the two basins were compared.It can be The seen time that seriesthe amplitudes of averaged of the data thickness are plotted of the unsaturated in Figure3a,b. zone at the location of the Itwell can changes be seen were that generally the amplitudes about four of the times thickness greater ofthan the the unsaturated amplitudes zoneof the at GRACE/NOAH the location of the well changesGWS variations. were generally A conclusion about on four the timesmean soil greater porosity than can the be amplitudes derived: it was of the approximately GRACE/NOAH equal GWS variations.to 0.25. AThis conclusion means that on to theraise mean the water soil level porosity by an can average be derived: of 1 cm on it 1 was square approximately meter of the area, equal to 3 0.25.you This need means to pour that 2500 to raise cubic the centimete waterr levels of water by an—instead average of of10,000 1 cm cm on in 1 an square empty meter space. ofThis the is area, only an approximate value due to the fact that information is lost when calculating the mean over you need to pour 2500 cubic centimeters of water—instead of 10,000 cm3 in an empty space. This is the area. Thus, the obtained value of 0.25 can be considered as a conversion factor between the mean only an approximate value due to the fact that information is lost when calculating the mean over total storage (GWS) variation and the mean level (GWL) variation. The cross-correlations between the area.the thickness Thus, the of obtained the unsaturated value ofzone 0.25 at canthe location be considered of the well as and a conversion GRACE/NOAH factor GWS between variations the mean total storagewere also (GWS) computed. variation Maximum and correlation the mean between level (GWL) GWS variation.and the thickness The cross-correlations of the unsaturated zone between at the location of the well is obtained for the time lag of three months for the both Vistula and Odra basins. Correlations between time series of the thickness of the unsaturated zone at the location of the well and GRACE TWS were much greater and less shifted, what is more, the shift is in a different direction. If a maximum of the mean thickness of the unsaturated zone at the location of the well

Geosciences 2020, 10, 124 7 of 14 the thickness of the unsaturated zone at the location of the well and GRACE/NOAH GWS variations were also computed. Maximum correlation between GWS and the thickness of the unsaturated zone at the location of the well is obtained for the time lag of three months for the both Vistula and Odra basins. Correlations between time series of the thickness of the unsaturated zone at the location of the well and GRACE TWS were much greater and less shifted, what is more, the shift is in a different direction.Geosciences 20 If20, a 10 maximum, x FOR PEER REVIEW of the mean thickness of the unsaturated zone at the location7 of of 14 the well occurs on June, then the appropriate maximum of GWS occurs in September, and that of GRACE in May.occurs Shifts on June, between then the GRACE appropriate and maximum the thickness of GWS of theoccurs unsaturated in September, zone and at that the of location GRACE ofin the well May. Shifts between GRACE and the thickness of the unsaturated zone at the location of the well seem more logical than between GWS and the thickness of the unsaturated zone at the location of the seem more logical than between GWS and the thickness of the unsaturated zone at the location of the well: first, let us say in May, there is a lot of water (rain and humidity), then it soaks into the ground well: first, let us say in May, there is a lot of water (rain and humidity), then it soaks into the ground andand causes causes (after(after one one month, month, let let us us say say in June) in June) an increase an increase of the of water the waterlevel in level wells. in However, wells. However, it is it is muchmuch more more didifficultfficult to explainexplain the the situation situation with with GWS GWS and and the the thickness thickness of the of theunsaturated unsaturated zone zoneat at the locationthe location of the of well,the well, when when there there is alreadyis already a a lot lot of of water water in in thethe wells,wells, and the the calculated calculated GWS GWS reacts onlyreact afters only three after months.three months. It looks It looks like thelike usethe use of the of the NOAH NOAH model model to to convert convert GRACE GRACE TWSTWS to GWS in PolandGWS in was Poland not givingwas not goodgiving results. good results. Precise Precise values values of the of cross-correlationthe cross-correlation functions functions (CCFs) (CCFs) are given inare Table given1. in Further Table 1. analysis Further wasanalysis aimed was at aimed finding at finding an explanation an explanation of this of phenomenon.this phenomenon.

Figure 3. Average thickness of the unsaturated zone at the location of the well, gravity recovery and Figure 3. Average thickness of the unsaturated zone at the location of the well, gravity recovery and climateclimate experimentexperiment ( (GRACE)GRACE)/NOAH/NOAH GWS GWS and and GRACE GRACE terrestrial terrestrial water water storage storage (TWS (TWS)) anomalies anomalies on theon areathe area of Vistulaof Vistula basin basin (a ()a and) and Odra Odra basinbasin (b)).. Table 1. Cross-correlation function (CCF) values between the thickness of the unsaturated zone at the Table 1. Cross-correlation function (CCF) values between the thickness of the unsaturated zone at location of the well and GWS or GRACE TWS values. the location of the well and GWS or GRACE TWS values.

CCFCCF Values Values Vistula Vistula Basin BasinOdra Basin Odra Basin CCF(GWS~wells)CCF(GWS~wells) atat laglag = 00 0.20 0.200.21 0.21 Max CCF(GWS~wells) = CCF(GWS~wells) at lag = 3 0.61 0.59 Max CCF(GWS~wells)CCF(GRACE~wells)= CCF(GWS~wells) at lag = 0 at lag = 30.78 0.610.89 0.59 Max CCF(GRACE~wells)CCF(GRACE~wells) = CCF(GRACE~wells) at lag = 0 at lag = −1 0.82 0.780.90 0.89 Max CCF(GRACE~wells) = CCF(GRACE~wells) at lag = 1 0.82 0.90 4.2. Analyses Concerning Well Depths − Firstly, it is worth examining the relationship of mutual time correlations between the thickness of the unsaturated zone at the location of the well, GWS, GRACE and the depth of the wells. As it was mentioned, NOAH models water content in soil (as the soil moisture, SM) to the depth of 2 m. In that case, acceptance of the thickness of the unsaturated zone at the location of the well only with depths greater than 2 m for averaging and comparison, should improve compatibility between GWS and the thickness of the unsaturated zone at the location of the well.

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4.2. Analyses Concerning Well Depths Firstly, it is worth examining the relationship of mutual time correlations between the thickness of the unsaturated zone at the location of the well, GWS, GRACE and the depth of the wells. As it was mentioned, NOAH models water content in soil (as the soil moisture, SM) to the depth of 2 m. In that case, acceptance of the thickness of the unsaturated zone at the location of the well only with depths greaterGeosciences than 2020 2, m10, forx FOR averaging PEER REVIEW and comparison, should improve compatibility between GWS and8 theof 14 thickness of the unsaturated zone at the location of the well. ItIt can can bebe seenseen fromfrom FigureFigure 44aa thatthat timetime series of average average thickness thickness of of the the unsaturated unsaturated zone zone at atthe thelocation location of of the the well well changes changes for for different different depths depths were were not shifted shifted significantly. significantly. For For example, example, the the correlationcorrelation coe coefficientfficient calculated calculated for for wells wells up to up 2 m to deep 2 m and deep deeper and than deeper 2 m than was 0.88. 2 m Thewas maximum 0.88. The ofmaximum CCF for theseof CCF two for groupsthese two of wellsgroups occurred of wells atoccur lagred= at1 andlag = was −1 and equal was to equal 0.89. to It 0.89. suggests It suggests a very a − slightvery slight shift between shift between the two the time two series, time series, probably probably smaller smaller than one than month, one month, and the and direction the direction of the of shift the wasshift logical: was logical: deeper deeper wells werewells delayedwere delayed relative relative to shallower to shallower ones. Theones. delay The delay was probably was probably less than less onethan month. one month.

FigureFigure 4. 4.Average Average groundwater groundwater head head for for 6 6 di differentﬀerent classes classes of of screen screen depth depth ( a()a) and and number number of of wells wells withwith di differentﬀerent depths depths (b ().b).

InIn general, general, it can it can be summarized be summarized that thatdespite despite the fact the that fact the that analyses the analyses were hindered were hindered by a different by a numberdifferent of number wells belonging of wells tobelonging different to depth different ranges depth and byranges performing and by calculationsperforming oncalculations data with on a monthlydata with period a monthly when itperiod is known when that it variousis known changes that various can occur changes faster, can it can occur be seenfaster, that it dicanfferences be seen inthat well differences depths causing in well di depthsfferences causing in soaking differences time to in these soaking wells time could to notthese explain wells thecould 3-month not explain shift betweenthe 3-month the GWS shift seriesbetween and the the GWS thickness series of and the the unsaturated thickness zoneof the at unsaturated the location zone of the atwell. the location Based onof Table the well2, it. can Based be concluded on Table 2, that it the can shifts be concluded between the that thickness the shifts of between the unsaturated the thickness zone at of the the locationunsaturated of the zone well at and the GWSlocation were of the greater well theand shallowerGWS were the greater wells the were. shallower Of course, the wells it should were. be Of rememberedcourse, it should that we be were remembered dealing with that data we whose were annualdealing signal with was data dominant, whose annual so a 4-month signal shiftwas candominant, be considered so a 4-month as an 8-month shift can shift be considered to the other as direction. an 8-month However, shift to the the analysis other direction. of Figure However,3 rather contradictedthe analysis thisof Figure hypothesis. 3 rather Shifts contradict in suched a waythis thathypothesis. GWS was Shifts on average in such abouta way three that monthsGWS was later, on andaverage for shallow about wellsthree evenmonths five later, months and later for thanshallow wells, wells were even diffi fivecult tomonths explain. later than wells, were difficultThere to were explain. no such interpretation difficulties for the data from not reduced GRACE TWS. Firstly, the correlations in this study were much larger, and secondly, the shifts were in the right direction. For shallowerTable 2. Correlation wells (up toof 2the m), thickness the largest of th correlationse unsaturated were zone obtainedat the location for non-shifted of the well variations series (rapid soakingwith/sinking), changes for of GWS deeper (GRACE/NOAH) wells, the shift and was TWS one (GRACE month (depthalone). range from 2 to 10 m), and for even deeper (depths greater than 10 m) the shift amounted to two months. The shift direction was such that Cor(GWL Lag[max], Cor(TWS Lag[max], Depths (m) No. of Wells there was a maximum of TWS first, and then~well)[0] the water levelMax in the wells~well)[0] increased. Max It can be seen that the deeper the wells,0 ÷ the 2 longer the30 time of soaking−0.17 water5 (0.61) into them. 0.88 0 (0.88) Over 2 161 0.27 3 (0.62) 0.82 −1 (0.86) 2 ÷ 5 68 0.06 4 (0.61) 0.86 −1 (0.86) 5 ÷ 10 54 0.25 3 (0.61) 0.75 −1 (0.82) 10 ÷ 20 23 0.48 1 (0.55) 0.71 −2 (0.78) Over 20 15 0.52 1 (0.56) 0.62 −2 (0.73) 0 ÷ 5 99 0.02 4 (0.62) 0.87 0 (0.87) 0 ÷ 10 154 0.10 3 (0.61) 0.75 −1 (0.85) Over 10 38 0.51 1 (0.57) 0.68 −2 (0.77) There were no such interpretation difficulties for the data from not reduced GRACE TWS. Firstly, the correlations in this study were much larger, and secondly, the shifts were in the right direction. For shallower wells (up to 2 m), the largest correlations were obtained for non-shifted series (rapid soaking/sinking), for deeper wells, the shift was one month (depth range from 2 to 10 m), and for even deeper (depths greater than 10 m) the shift amounted to two months. The shift

Geosciences 2020, 10, 124 9 of 14

Table 2. Correlation of the thickness of the unsaturated zone at the location of the well variations with changes of GWS (GRACE/NOAH) and TWS (GRACE alone).

No. of Cor(GWL Lag[max], Cor(TWS Lag[max], Depths (m) Wells ~well)[0] Max ~well)[0] Max 0 2 30 0.17 5 (0.61) 0.88 0 (0.88) ÷ − Over 2 161 0.27 3 (0.62) 0.82 1 (0.86) − 2 5 68 0.06 4 (0.61) 0.86 1 (0.86) ÷ − 5 10 54 0.25 3 (0.61) 0.75 1 (0.82) ÷ − 10 20 23 0.48 1 (0.55) 0.71 2 (0.78) ÷ − Over 20 15 0.52 1 (0.56) 0.62 2 (0.73) − 0 5 99 0.02 4 (0.62) 0.87 0 (0.87) Geosciences 2020, 10÷, x FOR PEER REVIEW 9 of 14 0 10 154 0.10 3 (0.61) 0.75 1 (0.85) ÷ − direction wasOver such 10 that there 38 was a maximum 0.51 of TWS 1 (0.57) first, and then 0.68 the water2 level (0.77) in the wells increased. It can be seen that the deeper the wells, the longer the time of soaking− water into them. From Figure 5 it can be seen that there was a small correlation between the depth and the degreeFrom of Figure correlation5 it can of be the seen thickness that there of wasthe aunsaturated small correlation zone betweenat the location the depth of the and well the degreewith GWS of correlationand GRACE, of the however, thickness it can of the be unsaturatedseen that there zone was at thea large location dispersion of the wellbetween with the GWS fitted and regression GRACE, however,line andit the can data. be seen It that is also there seen was that a large the dispersion correlations between of GRACE the ﬁtted versus regression the thickness line and of the the data.unsaturated It is also zone seen at that the the location correlations of the ofwell GRACE were much versus larger the thickness than the ofcorrelations the unsaturated of GWS zone versus at thethe location thickness of o thef the well unsaturated were much zone larger at the than location the correlations of the well of, and GWS that versus most wells the thickness had depths of the less unsaturatedthan 10 m, so zone that at they the ha locationd the greatest of the well, impact and on that the most results. wells At hadany depthsrate, it can less be than seen 10 that m, soGRACE that theybetter had reflect the greatested the behavior impact on of thethe results.water level At anyin the rate, wells it can tha ben the seen GWS that obtained GRACE betterfrom the reﬂected merger theof behaviorGRACE and of the NOAH water [27,28 level]. in the wells than the GWS obtained from the merger of GRACE and NOAH [27,28].

Figure 5. Correlations versus well depths: between GWS and the thickness of the unsaturated zone Figure 5. Correlations versus well depths: between GWS and the thickness of the unsaturated zone at at the location of the well (a) and between GRACE and the thickness of the unsaturated zone at the the location of the well (a) and between GRACE and the thickness of the unsaturated zone at the location of the well (b). location of the well (b).

Geosciences 2020, 10, 124 10 of 14

4.3. Dependence on Localization Changes in water conditions depend on climate conditions, the amount of water extraction for consumption, irrigation, industry and on the type of soil. Soil porosity (the sum of all free spaces in the soil) is of especially great importance for relations between the total water storage and the groundwater level. For the area of Poland, the porosity coefficient was estimated, e.g., in [29]. It obtained similar values in the Vistula and Odra basins (around 0.4). The two basin areas divide Poland into the eastern and western parts, while the different climate zones are rather arranged in latitudinal zones: in the south, there are mountains with more rainfall, in the north, the influence of the Baltic Sea is observed, which causes lower annual temperature amplitudes. To see if these changing climatic and soil conditions can affect the compatibility between the thickness of the unsaturated zone at the location of the well and GWS and the thickness of the unsaturated zone at the location of the well and GRACE, Figure6 shows the correlations obtained on the area of Poland. Again, it can easily be Geosciences 2020, 10, x FOR PEER REVIEW 10 of 14 seen that individual thickness of the unsaturated zone at the location of the well were very weakly correlatedcorrelated with a series ofof GWSGWS changes,changes, onlyonly a a few few thickness thickness of of the the unsaturated unsaturated zone zone at at the the location location of ofthe the thickness thickness of of the the unsaturated unsaturated zone zone at theat the location location of theof the well well obtained obtained correlations correlations greater greater than than 0.2, 0.2,most most thickness thickness of the of unsaturated the unsaturated zone zone at the at location the location of the of well the have well negative have negative correlations correlations (which (whichwas also was visible also invisible Figure in5 Figure). In contrast, 5). In contrast, compatibility compatibility between between GRACE GRACE and individual and individual wells was wells at wasa high at a level, high onlylevel, single only single wells wells have correlationshave correlations less than less than 0.2. In0.2. both In both cases, cases, no dependenceno dependence on theon thelocation location of the of the well well can can be seen.be seen. Thus, Thus, the the local local conditions conditions surrounding surrounding the the individual individual wells wells did did not notexplain explain the the lack lack of compliance of compliance (3-month (3-month shift) shift) between between the average the average changes changes in water in water level level in the in wells the wellsand the and GWS the GWS series. series.

FigureFigure 6. 6. CorrelationsCorrelations between between the the thickness thickness of of the the unsaturated unsaturated zone zone at at the the location location of of the the well well and and GWSGWS ( (aa)) and and the the thickness thickness of of the the unsaturated unsaturated zone zone at at the the location location of of the the well well and G GRACERACE ( b))..

4.44.4.. Dependence Dependence on on the the LDAS LDAS Model Model Admitted Admitted AsAs already mentioned,mentioned, thethe most most recommended recommended GLDAS GLDAS model model was was NOAH NOAH but, but,in addition, in addition, there thereare three are models three models available available from NASA: from CLM, NASA: MOS CLM, and MOS VIC [ and30]. For VIC completeness, [30]. For completeness, the correlations the correlationsobtained for obtained the other for three the modelsother three were models also examined, were also see examined, Figure7. see Figure 7.

Figure 7. Correlations between the thickness of the unsaturated zone at the location of the well variations and GWS series obtained based on the community land model (CLM; a), the mosaic (MOS;

Geosciences 2020, 10, x FOR PEER REVIEW 10 of 14 correlated with a series of GWS changes, only a few thickness of the unsaturated zone at the location of the thickness of the unsaturated zone at the location of the well obtained correlations greater than 0.2, most thickness of the unsaturated zone at the location of the well have negative correlations (which was also visible in Figure 5). In contrast, compatibility between GRACE and individual wells was at a high level, only single wells have correlations less than 0.2. In both cases, no dependence on the location of the well can be seen. Thus, the local conditions surrounding the individual wells did not explain the lack of compliance (3-month shift) between the average changes in water level in the wells and the GWS series.

Figure 6. Correlations between the thickness of the unsaturated zone at the location of the well and GWS (a) and the thickness of the unsaturated zone at the location of the well and GRACE (b).

4.4. Dependence on the LDAS Model Admitted As already mentioned, the most recommended GLDAS model was NOAH but, in addition, thereGeosciences are three2020 , models10, 124 available from NASA: CLM, MOS and VIC [30]. For completeness, the11 of 14 correlations obtained for the other three models were also examined, see Figure 7.

FigureFigure 7. Correlations 7. Correlations between between the the thickness thickness of the of the unsaturated unsaturated zone zone at the at the location location of the of the well well variationsvariations and and GWS GWS series series obtained obtained based based on onthe the community community land land m modelodel (CLM (CLM;; a),a ),the the m mosaicosaic (MOS (MOS;; b) and variable inﬁltration capacity (VIC; c) models of global land data assimilation (GLDAS); (d) shows GLDAS TWS = soil moisture (SM) + snow water equivalent (SWE) + canopy (CA) from the four GLDAS models.

It can be seen in Figure7 that the GWS results obtained were very di fferent depending on which GLDAS model was used to convert GRACE TWS observations to groundwater head series. For MOS and VIC models, the correlations were very low, mostly negative. For CLM, the correlations were much greater, mostly positive and greater than 0.2. The correlation between GWS calculated from GRACE and CLM averaged over Poland and water level changes in wells, averaged over all wells, was equal to 0.74. It is, therefore, lower than the corresponding correlation coefficient for GRACE itself (see Table1), but much higher than the correlations obtained based on other models. Does it follow that the TWS calculated from CLM and NOAH is shifted between each other by some months? No, it can be seen from Figure7d that the phase of GLDAS TWS changes from both models fit together very well, the correlation coefficient between them was 0.92. The problem lies in the amplitude of the changes—the amplitudes calculated from the NOAH model were much larger than the amplitudes obtained for the CLM model. Let us recall the Equation (1), on the basis of which GRACE TWS is converted to GWS. In this equation, there is a difference between TWS from GRACE and TWS from the model admitted. In the case of differentiation of the time series, which have periodic components (in our case mainly annual), it is of great significance for the phase of the resulting signal, which are the magnitudes of the amplitudes of differentiated signals. If the amplitude of the NOAH annual changes were smaller, then the phase of the obtained GWS series would match the phase of mean well levels and GRACE TWS changes. The amplitudes of changes of the four examined models were different, which resulted in different phases of the GWS series obtained. It is well seen also in Figure8. Geosciences 2020, 10, x FOR PEER REVIEW 11 of 14

b) and variable infiltration capacity (VIC; c) models of global land data assimilation (GLDAS); (d) shows GLDAS TWS = soil moisture (SM) + snow water equivalent (SWE) + canopy (CA) from the four GLDAS models.

It can be seen in Figure 7 that the GWS results obtained were very different depending on which GLDAS model was used to convert GRACE TWS observations to groundwater head series. For MOS and VIC models, the correlations were very low, mostly negative. For CLM, the correlations were much greater, mostly positive and greater than 0.2. The correlation between GWS calculated from GRACE and CLM averaged over Poland and water level changes in wells, averaged over all wells, was equal to 0.74. It is, therefore, lower than the corresponding correlation coefficient for GRACE itself (see Table 1), but much higher than the correlations obtained based on other models. Does it follow that the TWS calculated from CLM and NOAH is shifted between each other by some months? No, it can be seen from Figure 7d that the phase of GLDAS TWS changes from both models fit together very well, the correlation coefficient between them was 0.92. The problem lies in the amplitude of the changes—the amplitudes calculated from the NOAH model were much larger than the amplitudes obtained for the CLM model. Let us recall the Equation (1), on the basis of which GRACE TWS is converted to GWS. In this equation, there is a difference between TWS from GRACE and TWS from the model admitted. In the case of differentiation of the time series, which have periodic components (in our case mainly annual), it is of great significance for the phase of the resulting signal, which are the magnitudes of the amplitudes of differentiated signals. If the amplitude of the NOAH annual changes were smaller, then the phase of the obtained GWS series would match the phase of mean well levels and GRACE TWS changes. The amplitudes of changes of the four examined models were different, which Geosciences 2020, 10, 124 12 of 14 resulted in different phases of the GWS series obtained. It is well seen also in Figure 8.

Figure 8. Well data compared to GRACE and GLDAS TWS (a,b) and to GWS (c,d). Figure 8. Well data compared to GRACE and GLDAS TWS (a, b) and to GWS (c, d). 5. Conclusions 5. Conclusions 1. GRACE and the thickness of the unsaturated zone at the location of the well in Poland were highly correlated, wells data were delayed by one month on average. The cross-correlation function values were equal to 0.78 and 0.82 for Vistula and Odra basins at lag = 0, and to 0.82 and 0.90 respectively at lag = 1. − 2. After applying GLDAS NOAH to GRACE data, the resulting GWS were shifted in respect to direct measurements in wells by three months (GWS was delayed). The achieved values of the cross-correlation function were in this case much smaller (appropriate values were 0.20 and 0.21 for lag = 0, and 0.61 and 0.59 for lag = 3). 3. No clear dependence of well depths and locations on the correlations could be observed. 4. It seems that the GLDAS NOAH data had too large amplitudes of changes in comparison with the GRACE data on the area of the Polish basins studied. 5. It seems that the CLM model fit much better in Poland for computation of groundwater storage variation values. Its annual amplitudes of changes were significantly smaller than the NOAH amplitudes. Due to this, the phase of TWS signal from GRACE did not change when performing differentiating according to Equation (1). 6. However, it seems that GRACE data alone, not reduced by any model, when properly shifted, best reflected the behavior of the water level in the wells. The time shifts obtained between the GRACE series and the thickness of the unsaturated zone at the location of the well were logical and easy to interpret. 7. It can be seen from the data that the changes in water levels in the wells were much greater than the changes in TWS from GRACE or GWS from GRACE and GLDAS. This is probably due to the mean soil porosity. Since the amplitudes of the thickness of the unsaturated zone at the location of the well changes were generally about four times greater than the amplitudes of the GRACE/NOAH GWS variations consequently a conclusion on the mean soil porosity could be derived: it was approximately equal to 0.25. Geosciences 2020, 10, 124 13 of 14

Author Contributions: Conceptualization, Z.R. and M.B.; methodology, Z.R. and M.B.; software, Z.R.; validation, Z.R. and M.B.; formal analysis, M.B.; investigation, Z.R. and M.B.; resources, M.B.; data curation, Z.R.; writing—original draft preparation, Z.R. and M.B.; writing—review and editing, Z.R. and M.B.; visualization, Z.R. and M.B.; supervision, Z.R. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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