Based on the forward-modeled TSH coefficients, the coseismic gravity changes Δ*g* and gravity gradient changes of the components (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in the LNOF on a sphere with a height of 260 km above the WGS84 reference ellipsoid were computed, which are shown in Figures 5 and 6. Figure 5 shows that the magnitude of the forward-modeled coseismic gravity changes is approximately 1.2 μGal. The maximum magnitude of the components (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) is approximately 0.1 mE, which corresponds to the radial component. Compared to Figures 3 and 4, the spatial patterns of Figures 5 and 6 are no longer dipole patterns, and instead show multiple extrema. Additionally, the gravity changes Δ*g* and the changes in the gravity gradient components Δ*Vyy* and Δ*Vzz* show multiple rings. The spatial patterns of Δ*g* and Δ*Vzz* are very similar and nearly isotropic. According to Figure 6, the components (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) have different spatial patterns. The components Δ*Vxx* and Δ*Vxz* have similar spatial patterns, namely, nearly west-to-east stripes and multiple poles in the North-South direction. The Δ*Vyy* component has a spatial pattern with nearly North-South stripes and multiple poles in the west-to-east direction. Moreover, we also use two other fault slip models, provided by the GSI (Geospatial Information Authority of Japan) and the USGS (United States Geological Survey), to compute the coseismic gravity gradient changes from the TSH coefficients(see the supplementary materials). Compared with the Caltech fault slip model (as mentioned in Section 2.5), the GSI and USGS models have different depth extends. The slips extend to 70 km and 58 km in depth for the GSI and USGS models, respectively, while for the Caltech model, the maximum depth of slip is 47 km. The dip angles of the three slip models are very close, all around 10◦. Although calculated with different fault slip models, the spatial patterns of the gravity and gravity gradient changes are similar to the signals plotted in Figures 5 and 6.

**Figure 5.** Gravity changes on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from the forward model with a Gaussian filter applied. The SH degree range is 30–95 and the radius of the filter is 210 km. The unit is μGal.

**Figure 6.** Gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in Local North-Oriented Frame on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from the forward-modeled coseismic signals with a Gaussian filter applied. The SH degree range is 30–95 and the radius of the filter is 210 km. The units are mE.

#### *3.2. Post-seismic Gravity Changes from the Viscoelastic Model*

We compute the 1-year mean post-seismic radial gravity gradient changes (Δ*Vzz*) based on the TSH coefficients method from the computed viscoelastic relaxation models in Section 2.6, which are shown in Figure 7. A Gaussian filter with the smoothing radius 210 km is applied to the TSH coefficients. The maximum and minimum values of the radial gravity gradient changes from the viscoelastic relaxation model are 0.0095 mE, and -0.0047 mE, respectively. This 1-year mean field will be used in removing the post-seismic effect, and deriving the coseismic gravity signals both from the GOCE and GRACE data (in Sections 3.4 and 3.5). Comparison between our viscoelastic relaxation results and those from Han et al. [46] under the SH degree 60 truncation has also been provided in the supplementary of the manuscript.

**Figure 7.** Radial gravity gradient changes (Δ*Vzz*) in Local North-Oriented Frame on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from the viscoelastic relaxation model with a Gaussian filter applied. The SH degree range is 30–95 and the radius of the filter is 210 km. The units are mE.

#### *3.3. Coseismic Gravity Changes from the Hydrological and Oceanic Mass Redistributions*

Based on the TSH coefficients method, we compute the coseismic radial gravity gradient changes (Δ*Vzz*), which are shown in Figure 8. According to Figure 8, the radial gravity gradient changes derived from the hydrological and oceanic mass redistributions are very small. The maximum and minimum value of the radial gravity gradient changes from both of GLDAS and ECCO-OBP are 0.0022 mE, and −0.0027 mE, respectively. Nevertheless, the contribution from the hydrological and oceanic mass redistributions will be removed in deriving the coseismic gravity signals both from GOCE and GRACE data.

**Figure 8.** Radial gravity gradient changes (Δ*Vzz*) in Local North-Oriented Frame on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from GLDAS (**a**), ECCO-OBP (**b**) and both of GLDAS and ECCO-OBP (**c**) with a Gaussian filter applied. The SH degree range is 30–95 and the radius of the filter is 210 km. The units are mE.

#### *3.4. GRACE-derived Coseismic Gravity Changes and Gravity Gradient Changes*

The coseismic gravity changes and gravity gradient changes from GRACE are shown in Figures 9 and 10. It should be noted that before computing the coseismic gravity changes, we removed the post-seismic effects from the one-year mean post-seismic model, and the contribution from the hydrological and oceanic mass redistributions. According to Figures 9 and 10, the coseismic gravity and gravity gradient changes from GRACE have nearly the same spatial pattern, showing only clear multi-pole characteristics in the North-South direction alongside west-to-east stripes. Only the gravity gradient changes Δ*Vxx* and Δ*Vxz* have similar spatial patterns compared to the forward-modeled coseismic signals plotted in Figure 6. Additionally, the gravity changes and the gravity gradient components Δ*Vyy* and Δ*Vzz* have very different spatial patterns compared to those from the forward-modeled coseismic signals. The spatial stripes for the component Δ*Vyy* are oriented west-to-east, which is completely different from the North-South stripes of the forward-modeled

coseismic signal. The reason for this situation should be that GRACE's satellite is in a polar orbit with an inclination of 89.5◦, so the inter-satellite range-rate observations along the orbit are almost in the North-South direction. Thus, these inter-satellite range-rate observations are not sensitive to signals in the west-to-east direction.

**Figure 9.** Gravity changes on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from GRACE (the Gravity field Recovery and Climate Experiment). The SH degree range is 30–95. The unit is μGal.

**Figure 10.** Gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in Local North-Oriented Frame on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from GRACE. The SH degree range is 30–95. The units are mE.

Furthermore, when comparing the forward-modeled coseismic results in Figures 5 and 6 with those from the GRACE data in Figures 9 and 10, the magnitudes of the coseismic gravity changes from GRACE are smaller than those from the forward model.

#### *3.5. GOCE-derived Coseismic Gravity Changes and Gravity Gradient Changes*

We use the same method of processing the forward-modeled coseismic signals to compute the coseismic gravity and gravity gradient changes from GOCE, which are shown in Figures 11 and 12. The post-seismic effects and the contribution from the hydrological and oceanic mass redistributions are also removed like GRACE-derived coseismic gravity signals. A Gaussian filter with a radius of

210 km was also applied. Figure 11 shows that the magnitude of the forward-modeled coseismic gravity changes is approximately 2.4 μGal. The maximum magnitude of the components (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) is approximately 0.15 mE, which corresponds to the radial component.

**Figure 11.** Gravity changes on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from the GOCE observations with a Gaussian filter applied. The SH degree range is 30–95, and the radius of the filter is 210 km. The unit is μGal.

**Figure 12.** Gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in Local North-Oriented Frame on a sphere with a height of 260 km computed by the tailored spherical harmonic coefficients from the GOCE observations with a Gaussian filter applied. The SH degree range is 30–95, and the radius of the filter is 210 km. The units are mE.

#### **4. Discussion**

When compared to the forward-modeled coseismic signals in Figures 7 and 8, the spatial patterns of the coseismic signals in Figures 11 and 12 from the GOCE observations, although noisy, are somewhat similar, exhibiting multiple extrema. The spatial patterns of the gravity changes Δ*g* and gravity gradient changes of the radial component Δ*Vzz* exhibit multiple rings. According to Figure 12, the components Δ*Vxx* and Δ*Vxz* show similar spatial patterns, i.e., the west-to-east stripes and multiple poles in the North-South direction. Note that, there are more gravity gradient change peaks compared to the modeled gravity gradient changes in the area of interest, which is the same situation with Figure 8 in Fuchs et al. [28]. Referring to Fuchs et al. [28], we also use the averaged accuracy of gravity gradients before the 2011 earthquake to represent the accuracy of the derived coseismic gravity gradients. The deviations of the mean (1σ) in 0.5◦ grid cells for the differences of gravity gradients (Δ*Vxx*, Δ*Vyy*, Δ*Vzz* and Δ*Vxz*) between the GOCE-derived pre-earthquake model and the GOCO03S [32] are computed, which are 0.018, 0.022, 0.036 and 0.024 mE, respectively. According to Figure 12, we could see that there is a significant change (greater than 3σ) in gravity gradients between pre- and post-earthquake gravity gradients.

We note that the uncertainties (σ) might be underestimated because the two models are not completely independent and the errors are not stationary, but we will not do further assessment here. Additionally, according to Figures 5, 6, 11 and 12, the amplitudes of the coseismic gravity gradient changes are larger than the forward-modeled coseismic signals, and the geographical positions of the multi-poles are different, which is similar to what is seen in Fuchs et al. [28]. The geographic positions of these multi-poles from the GOCE data are located approximately 200 km to the northeast of the modeled results. The reasons for these discrepancies are still not very clear. According to Fuchs et al. [28], Heki et al. [51] and Feng et al. [52], the differences between the results from the forward model and GOCE data might be caused by systematic errors in the SGG observations and the weak sensitivity of SGG observations to the location of the earthquake. In addition, the large uncertainties of fault slip models also contribute to the discrepancies. Dai et al. [16] show that the fault slip model still leads to around 40% relative difference of gravity changes compared to the GRACE observations, even inverted with a multiple data source, which is likely, because the current commonly-used dislocation models are not sophisticated enough. The noticeable differences between model prediction and observation need to be investigated by further studies. According to Figures 7, 10 and 12, the maximum and minimum values from the viscoelastic relaxation model are nearly 15–21% of the ones (max: 0.031 mE, min: −0.046 mE) derived from the GRACE one-year mean field differences, and nearly 3–6% of the ones (max: 0.161 mE, min: −0.167 mE) derived from the GOCE one-year mean field differences. According to Figures 8 and 12, the maximum and minimum value of the radial gravity gradient changes from both of GLDAS and ECCO-OBP are nearly two orders of magnitude smaller than the GOCE-derived coseismic gravity gradient signals.

In order to show the gravity change time series, we processed the GOCE SGG data to obtain the monthly gravity field models with the time period from November 2009 to May 2012. The data processing strategies are the same with that determining the pre-earthquake and post-earthquake models above. According to the GOCE daily reports EGG [53], there are a lot of special events, several data gaps and frequent calibrating operations (about once a month), from November 2009 to May 2012. Therefore, we are unlikely to be able to derive continuous monthly time-variable gravity field models due to the practical data quality. In addition, the solutions after the earthquake have larger oscillations, which agree with the fact that there are more special events in SGG data after the earthquake than those before the earthquake for most months [53]. Figure 13a,b show the radial gravity gradient changes at A (40.6◦, 141.2◦) and B (40.2◦, 147.2◦) points on Figure 12 derived from the monthly time-variable gravity field models before and after the earthquake, while Figure 13c,d shows the average radial gravity gradient changes at a negative area [(40◦~41◦), (140.5◦~142.5◦)] around A and a positive area [(39◦~40.5◦), (147~148.5◦)] around B.

According to Figure 13, although the radial gravity gradient change time series contain some significant oscillations, they are still comparable with the co-seismic gravity change time series from GRACE for some smaller earthquake (Mw ≈ 8.5) given by some previous studies (see as Figure 2 of Han et al. [54], and Figures 6 and 7 of Chao and Liau [55]). In order to show the changes more clearly, we use a 1D median filter (with 5th order) to process those four time series, and the obtained filtered results denoted by the red curves in Figure 13. Those filtered curves show obvious steps before and after (gray areas in Figure 13) the earthquake. We further use step functions to fit the original observations (the obtained fitting curves are also plotted in Figure 13; blue curves), and the step values can be estimated at the same time (see Figure 13). Here we use a bootstrap procedure (a Monte Carlo process, see Efron and Tibshirani [56]) to estimate the uncertainties for those step values. This method has been widely used for the uncertainty estimations in different geophysical research [57–62]. Here we give a simple example to explain the error estimation process (more details can be found in Shen and Ding [60]):

From Figure 13, we can see that the step values are clearly over three times their corresponding uncertainties (the double uncertainties are denoted by the blue areas in Figure 13 as the corresponding two standard deviations). Statistically, we may suggest that those steps represent the coseismic gravity gradient change signals caused by the 2011 Tohoku-Oki earthquake.

**Figure 13.** Radial gravity gradient changes at A (**a**), B (**b**) points and two selected areas around A and B (**c**,**d**) before and after earthquake. The red curves denote the filtered results after using a 1D median filter to the original time series, the blue curves are the fitted step functions. The double uncertainties are denoted by the blue areas.

To reveal how the spatial patterns of the GOCE and modeled gravity gradient changes agree with each other, we computed the correlation coefficients (see Table 2) of the gravity changes and gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, Δ*Vxz* and Δg) between the observed models (GOCE and GRACE) and the forward model for the TSH coefficients (see Figure 2). The Root Mean Square (RMS) of observed (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, Δ*Vxz* and Δg) of GOCE/GRACE, and the differences between the observed and forward modeling signals, are also computed and shown in Table 2. According to Table 2, both of GOCE and GRACE do not perform well, because all the correlation coefficients are less than or equal to 0.85. Although most correlation coefficients corresponding to GOCE are lower than those of the GRACE time-variable gravity field models, the correlation coefficient corresponding to the

Δ*Vyy* component from GOCE is slightly larger than the one of GRACE. Thus, for the SH degree range 30–95, the GOCE mission could reveal a greater signal of coseismic gravity gradient changes in the west-to-east direction than GRACE, because GRACE has sensitive observations along the North-South direction. The coefficient for Δ*Vzz* is very close to the value in Fuchs et al. [28]. All RMS of observed signals are reduced after subtracting the forward-modeled coseismic signals from the GOCE-derived results. However, because the amplitude of the results from GRACE is only about half of the one from the forward model, the RMS of GRACE's Δ*Vyy* increases when the modeled signal is subtracted from the observed signal and the RMS of Δ*Vyy* doesn't change. Of course, compared to GOCE, GRACE performs relatively well in the SH degree range 30–95, especially for the Δ*Vxx* component, which has the maximum correlation coefficient because only inter-satellite range-rates are observed along its orbit.

**Table 2.** Correlation coefficients, RMS of observed gravity and gravity gradients (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, Δ*Vxz* and Δg), RMS of the differences between the observed and forward modeling signals. The observed signals are from GRACE and GOCE. The positions for the computation are located in the region of 28◦N–48◦N, 132◦E–152◦E. The unit of Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz* is mE and the unit of Δg is μGal.

#### **5. Conclusions**

We employed the least squares method with a bandpass auto regression moving average filter, to recover two global gravity field models up to degree and order 220, from GOCE satellite gravity gradient data from the 15 March 2011 to the 31 May 2012 after the 2011 Japan Tohoku-Oki earthquake event. Then, we used the recovered models to estimate the coseismic gravity and gravity gradient changes that were caused by the earthquake by subtracting the pre-earthquake model from the post-earthquake model. This approach is different from that in Fuchs et al. [28]. They used the diagonal components (*Vxx*, *Vyy*, and *Vzz*) along the orbit to construct the new vertical gravity gradient *Vzz*, which was used to present the coseismic gravity gradient changes. To extract the coseismic gravity signals from the recovered global gravity field models, we proposed TSH coefficients according to the influences of colored noise in the SGG data and the polar gap problem on the recovered models.

The gravity changes Δ*g* and the gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) were computed by the GOCE-derived tailored spherical harmonic (TSH) coefficients, GRACE-derived TSH coefficients and the forward-modeled TSH coefficients. In data processing, the degree range 30–95 was used to obtain the TSH coefficients. A Gaussian filter with a radius of 210 km was also applied to the TSH coefficients according to the maximum frequency of 95. When comparing the coseismic gravity signals from GOCE, the forward model, and GRACE, the spatial patterns of the coseismic gravity and gravity gradient changes from GOCE were analogous to those from the forward model. There is a significant change (greater than 3σ) in the gravity gradients between the pre- and post-earthquake gravity gradients, which is associated with the earthquake. Moreover, the radial gravity gradient changes from the derived monthly time-variable gravity field models before and after the earthquake show obvious steps before and after the earthquake, whose amplitudes are at a level over three times that of their corresponding uncertainties, and thus significant. Statistically, it is reasonable to infer that these steps represent the coseismic gravity gradient change signals caused by the 2011 Tohoku-Oki earthquake. For the GGT components (Δ*Vxx*, Δ*Vzz*, and Δ*Vxz*), the correlation between the GOCE-derived coseismic gravity signals and the forward-modeled coseismic results was weaker than that from GRACE. However, the correlation coefficient that corresponded to the Δ*Vyy* component from GOCE is larger than that from GRACE. The component Δ*Vyy* had spatial patterns that included North-South stripes and multiple poles in the west-to-east direction. This situation means

that the GOCE mission might reveal more coseismic gravity signals in the West-East direction than GRACE in the SH degree range 30–95. The estimated time series of radial gravity gradient changes (see Figure 13) suggest that the coseismic gravity changes can be reproduced from GOCE observations through the proposed method.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2072-4292/11/11/1295/s1, Figure S1: Gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in LNOF on a sphere with a height of 260 km computed by the TSH coefficients from the forward-modeled signals of the GSI fault slip model with a Gaussian filter applied, Figure S2: Gravity gradient changes (Δ*Vxx*, Δ*Vyy*, Δ*Vzz*, and Δ*Vxz*) in LNOF on a sphere with a height of 260 km computed by the TSH coefficients from the forward-modeled signals of the USGS fault slip model with a Gaussian filter applied, Figure S3: The observation (the fitted step has been removed) and the inputted noise (a), and their Fourier power spectra (b) (logarithmic scale in dB), Figure S4: Postseismic gravity changes (Δ*g*) on the ground from the spherical harmonic coefficients up to d/o 60 of the viscoelastic relaxation model computed in the paper (left) and provided by Han (right).

**Author Contributions:** Conceptualization X.X.; methodology, X.X. and H.D.; investigation, X.X. and H.D.; resources, J.L. and M.H.; data curation, Y.Z.; writing—original draft preparation, X.X.; writing—review and editing, X.X., H.D., and J.L.

**Funding:** This research was financially supported by the National Natural Science Foundation of China (Grant No. 41574019, 41774020, 11873075). DAAD Thematic Network Project (57421148). The Major Project of High resolution Earth Observation System. The Natural Science Foundation of Shanghai (17ZR1435600).

**Acknowledgments:** The authors thank Shin-Chan Han for the help in our post-seismic effect evaluation and providing the viscoelastic and afterslip models of the Tohuku-Oki earthquake for the verification of our post-seismic models. We thank Wenbin Shen for useful discussion. We also acknowledge the European Space Agency for providing the GOCE data. We are also grateful to the three anomalous reviewers who have provided constructive comments and suggestions to improve our work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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**2.2 Management of postoperative hemorrhage**

Recognized as an uncommon complication of hysterectomy, postoperative hemorrhage represents a true challenge in routine practice [8]; irrespective of the procedure, a close follow-up of the patient in a high-dependency unit is indicated in order to exclude recurrence of bleeding [6, 7].

The key to successful management is timely intervention meaning prompt diagnosis, urgent resuscitation if necessary and rapid decision for either arterial embolization or reoperation according to the severity of bleeding and the hemodynamic stability of the patient. Both techniques are highly effective to control bleeding; nevertheless, if the patient is hemodynamically unstable or of the interval since surgery is under 24 hours suggesting rapid hemorrhage, the emergency return to the operating theater to arrest the bleeding is preferred [6, 7, 9].

Current options for managing hemorrhage include [6, 7, 9]:

A simplified algorithm to describe steps after gynecological surgery and potential post-surgery bleeding is provided in **Figure 1**.

A closer look at the holistic management of postoperative blood should also underpin the following [9]:

#### **Figure 1.**

*A simplified algorithm of post-surgery bleeding approach.*

#### *2.2.1 Reoperation*

In hemodynamically unstable women (rapid pulse, falling blood pressure, with or without renal impairment) or if the bleeding occurs shortly in post-surgery (the socalled reactionary hemorrhage), it is desirable to return to the operating room [5–9].

A preoperative abdominal and pelvic ultrasound or CT scan is routinely required to visualize the source of bleeding as being intra- or retro-peritoneal, as well as adequate local examination without or under anesthesia. Moreover, the operative procedure should be mentally revised to identify any potential bleeding issue [9].

Surgical revision for postoperative bleeding may be performed transvaginally, laparoscopically, or both [5–9, 13, 14].

Postoperative hemorrhage from the vaginal vault recurrently originates from the vaginal artery in the lateral vaginal fornix or from one of its branches, since the lateral vaginal angle which includes the vaginal artery may not be accurately protected or turn into disligated [9, 13, 14].  Vaginal bleeding can be controlled by clamping and ligating the bleeding point as well as by delayed-absorbable transfixion suturing of the vaginal mucosa and paravaginal tissue [9, 13, 14]. If such techniques are not enough or bleeding vessels have retracted, other tactics should be intended [8].

When no noticeable vaginal source, bleeding after abdominal or vaginal hysterectomy is traditionally treated by laparotomy or laparoscopy [7, 9]. While laparotomy is recommended in cases of intraperitoneal bleeding or unsuccessful conservative transvaginal treatment, operative laparoscopy is clearly indicated if the source of bleeding cannot be identified by the means of vaginal examination and/or if an intraabdominal bleeding source is suspected [7, 9, 13].

#### *2.2.2 Laparotomy*

Post-surgery bleeding requires laparotomy in two situations.

*Bleeding after Hysterectomy: Recommendations and What to Expect DOI: http://dx.doi.org/10.5772/intechopen.101384*

Firstly, if the surgical hemostasis cannot be achieved transvaginally, laparotomy may be necessary [9].

Secondly, if the patient underwent an abdominal hysterectomy, the incision should be reopened, succeeding the following steps (i) clots and blood evacuation from the abdomen and pelvic area; (ii) searching of the potential bleeding sites, commencing with the most expected places; (iii) ligating, suturing, or clipping of the identified bleeding sites; (iv) verifying the ureteral integrity as high risk of ureteral damage during reoperation; and (v) closing second time after a completely dry abdomen and pelvis [9].

#### *2.2.3 Laparoscopy*

The laparoscopic approach to postoperative bleeding following laparoscopic hysterectomy, vaginal hysterectomy, or laparoscopic-assisted vaginal hysterectomy is an attractive alternative to the abdominal surgical approach in the majority of patients [6, 7, 9, 13]. The procedure can be used to adequately evaluate the pelvis and the abdominal wall, which is occasionally the source of hemorrhage after laparoscopic hysterectomy. Moreover, whether the bleeding is from the abdominal wall, the surgical pedicles, or the vaginal cuff, it can be managed laparoscopically [8, 9]. Evidently, hemostasis can be more easily obtained in laparoscopic surgery because of magnification, close inspection, routine use of suction irrigation, and bipolar coagulation [7, 9]. Besides, bipolar coagulation, a Foley catheter introduced in the port-site bleeding, or a collagen-fibrin agent can be used to achieve local hemostasis during laparoscopy [7, 9].

Following laparoscopic irrigation/suction using Ringer's solution to clear the operative field, a combination of laparoscopic suturing using absorbable suture material and laparoscopic bipolar coagulation is commonly recommended [6, 8, 9]. Also, electrosurgery is effective in controlling bleeding during laparoscopic surgery. Furthermore, different forms of fibrin adhesive are tested in gynecologic open surgery in order to stop oozing hemorrhages after primary hemostatic treatment with a high efficacy rate (98%) [6]. Holub and Kliment reported successful treatment of hemorrhage from damaged tissue near important pelvic structures using the laparoscope to apply collagen fleece combined with fibrin glue [7, 17].

To avoid further risk of injury to the abdominal wall and to improve the recovery time from surgery, *single incision laparoscopic surgery* is a viable option for the management of hemorrhage, particularly for those patients whose original surgery was accomplished via single incision laparoscopic surgery. Curlin et al. reported a case where single incision laparoscopy was used to manage postoperative hemorrhage after total laparoscopic hysterectomy with right salpingectomy and left salpingooophorectomy [8].

#### **2.3 Arterial embolization**

Conversely, if the patient is reasonably stable and there is not abrupt early bleeding (based on the volume of blood in the abdomen or retroperitoneal space as estimated by ultrasound and the time from surgery), it seems realistic to try to identify the bleeding artery and embolize it by transcatheter interventional radiological techniques [2–4, 9, 10].

Arterial embolization remains an important minimally invasive option for the management of delayed postoperative hemorrhage [2–4, 8, 9, 18]. Transcatheter arterial embolization has been shown to be an effective tool for the management of postoperative hemorrhage after gynecologic laparoscopy, but also after abdominal and vaginal hysterectomy [8, 9]. Selective angiographic arterial

embolization is a quite simple and safe procedure with a clinical success rate up to 90% in routine practice and usually a low complication rate less than 10%, including a mild postembolization syndrome with pain, fever, high leucocyte count related to vascular thrombosis and tissue necrosis [8, 9]. Bladder necrosis, vesicovaginal fistula, neuropathies as well as renal toxicity are uncommon, isolated side effects [9].

Arterial embolization technique comprises the following main steps—(i) identification of the site of bleeding by angiofluoroscopy if more than 2–3 mL/ min bleeding rate; (ii) percutaneous catheterization of the femoral artery or, uncommonly, brachial artery under local anesthesia with retrograde direct access to the hypogastric artery; (iii) canulation of the hypogastric artery or specific collateral vessel if appropriate; (iv) injection of the embolization material under angiographic observation (metal coins, autologous clot, small pieces of gelfoam, small silastic spheres, subcutaneous tissue, or other hemostatic materials; (v) repeat angiography to demonstrate the occlusion of the bleeding vessel; (vi) remove of the catheter followed by careful monitoring for further bleeding [8–10].

Although second surgery is often the initial choice for postoperative hemorrhage, for a patient who is hemodynamically stable but is experiencing postoperative hemorrhage, transcatheter arterial embolization is a welcome alternative to a second surgery [8, 9]. However, if rapid access to interventional radiology is not available or if transcatheter arterial embolization is unsuccessful, laparoscopy can still be considered [8, 9]. Besides, a potential advantage of surgical management of postoperative hemorrhage over transcatheter arterial embolization is the ability to evacuate the hemoperitoneum, which may decrease postoperative pain, the risk of infection, and the risk of ileus [8, 9].


**Conflict of interest**

Financial support of the studies *Softia S* and *Softia G* was provided by the Ministry of Agriculture, Forestry and Fisheries of Japan; NUTRI participated in the design of the studies *Softia S* and *Softia G* and discussion of the results.


**Preface to "Assessing Water Quality by Statistical Methods"**

Water, indispensable for life, has became scarcer in the last period due to overexploitation and pollution. Deforestation, urbanization, and, generally, agricultural and economic development lead to the water quality decreasing not only of the surface water, but also of the groundwater, endangering the water reserve. Toxic substances reaching water bodies without satisfactory treatment and climate change negatively impact water quality. Moreover, billions of inhabitants worldwide suffer from water scarcity, having limited or challenging access to drinking water. Therefore, evaluating the groundwater vulnerability and the threats to the surface waters, like detecting the pollution sources, their seasonal and spatial extent, and assessing the water quality are essential for making insight decisions on reducing and eliminating, if possible, the pollution impact.

Recent studies on water quality increasingly used statistical methods to select the water parameters that significantly impact the water quality or address pollution extent. They highlighted the advantages of the proposed approach in terms of time and cost savings. The advantage of using statistical methods also relies on validating the result that may be used in the next phase of forecasting. Therefore, the Special Issue "Assessing the Water Quality by Statistical Methods" of "Water" the book is based on contains articles on the following topics:

The topics may interest water resources scientists and the larger public, treating actual environmental problems. Some methodologies proposed in the articles can be used or adapted to analyze other complex databases or solve spatiotemporal environmental problems.

The editor thanks the authors for sharing their research, and the reviewers whose valuable suggestions significantly improved the submitted articles.

We also thank the editorial staff, who ensured an excellent editorial process.

**Alina Barbulescu** *Editor*

### *Editorial* **Assessing Water Quality by Statistical Methods**

**Alina Bărbulescu 1,\* and Cristian S, tefan Dumitriu 2,\***

Water is one of the natural resources most affected by anthropogenic activities, like industry, agriculture, and traffic. Moreover, pollutants resulting from different sources are reaching water bodies with insufficient or without proper treatment. Climate change impacts the water quality as well, reducing the quantities of drinking water. Apart from human health, profoundly affected by water pollution, organisms living in the water and many ecosystems are affected more and more. Considering the difficult access to the drinking water of the population from different parts of the world, preserving the water resources, assessing their quality, and taking measures for the remediation of the water bodies' natural properties is a must.

In this context, the Special Issue with the title "Assessing Water Quality by Statistical Methods" addressed topics related to groundwater vulnerability [1–4], estimating water quality parameters in natural and artificial lakes and gulfs [5–7], investigating the causes of Rivers pollution [8–10], and proposing new tools for estimating the regional extent [11] and mitigating the effects of high precipitations on the water quality [12].

The single review [1] published in this volume addresses the groundwater vulnerability evaluation by the DRASTIC method and DRASTIC-like approaches, without including the particular case of the karst aquifer. Since its proposal, DRASTIC has become an essential tool for assessing the groundwater vulnerability, being adapted to different cases, like lithology, regions, land-uses, pollutants, land cover, and types of human settlements (rural and urban). The review is based on 128 articles, giving a detailed image of the previous work and opening possible study directions.

The article of Baena-Ruiz and Pulido-Velazquez [2] adapts the DRASTIC index to obtain reliable assessments in carbonate aquifers while maintaining its original conceptual formulation. The authors combine spatial statistics and decision trees to establish the DRASTIC parameters' domains and their associated weights. Comparisons of the new method's results with those obtained using the COP for the karst aquifer [13] show a concordance on 75% of the study area, the Upper Guadiana Basin. Given its good output, this approach should be validated in future studies.

In the same idea of evaluating the groundwater quality, in another part of the world the United Arab Emirates—the article [3] proposes a combined approach involving a multivariate statistical analysis and water quality indices' use. The study relies on a database containing 42 concentration series of 19 water parameters collected in the Liwa area. Since the hypothesis that the series of water parameters recorded at different locations are similar was rejected, the samples were grouped in clusters and the main parameters that determined the differences between the clusters were determined by Principal Component Analysis (PCA). Finally, a quality index for assessing the water suitability for drinking was computed in two scenarios. The authors emphasized the necessity of using more than one technique to evaluate water quality for different purposes and to cross-validate the results [3].

Du et al. [4] employed the Factorial Analysis (FA) and Correspondence Analysis (CA), combined with geospatial tools, to identify the sources of inorganic nitrogen compounds

**Citation:** B˘arbulescu, A.; Dumitriu, C.S, . Assessing Water Quality by Statistical Methods. *Water* **2021**, *13*, 1026. https://doi.org/10.3390/ w13081026

Received: 5 April 2021 Accepted: 7 April 2021 Published: 9 April 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

in shallow groundwater, to determine the governing influencing factors and analyze the formation process in an agricultural area in Northeast China [4].

In the article [5], the authors investigated the long-term time series of salinity and water level of Techirghiol Lake (Romania), renowned in Europe for its sapropelic mud's therapeutic properties. These variables trends have been studied as functions of the precipitation, overland flow, groundwater recharge, and the hydraulic works from the lake's neighborhood. The study shows that the Techirghiol Lake is a heavily modified water body.

Mamun et al. [6] realized a comprehensive spatial and temporal analysis of the water quality of the Paldang reservoir (Korea), which is an important source of freshwater. The tools utilized to carry out the research were the PCA, FA, and stepwise spatial discriminant analysis (DA), together with the Trophic State Index (TSI) and Trophic State Index deviation (TSID). They show that anthropogenic activity is mainly responsible for the significant spatial variations of most water parameters. The water parameters that significantly vary during different seasons are the temperature, the biological oxygen demand, and total suspended solids. The water parameters that significantly vary at different sites are the water temperature, the electrical conductivity, the total nitrogen, the ratio biological oxygen demand: chemical oxygen demand, and total nitrogen: total phosphorus.

In their research, Al-Taani et al. [7] investigated the water quality of the Aqaba Gulf in Jordan, a zone with high touristic potential. The investigation of 19 parameters of water samples collected in different parts of the Littoral did not present specific patterns, except for the metal contents that showed increasing values close to an industrial complex by comparison to other sampling places.

The article *Characteristics and Causes of Long-Term Water Quality Variation in Lixiahe Abdominal Area, China* [8] presents the results of a set of statistical tests (the Mann–Kendall trend test and Sen's slope estimator) and the analysis of the correlation between the water quality variation, the water level, and the water diversion employing the cross wavelet transform and wavelet coherence. The results show that the comprehensive water quality index (CWQI) included periodic fluctuations on multiple scales from 0.25 to 5 years [8].

Yu et al. [9] analyzed twenty water parameters from samples collected during March, May, July, September, and November 2010 in Chaobai River (China). They found that the eutrophication level was severe in most locations where the water was collected, and the water was not appropriate for irrigation water (indicated by the sodium adsorption ratio). Cluster analysis was used to determine the significant spatial and temporal variation among different data series. The Gibbs plot indicated that the water–rock interaction mainly controls the water chemistry, whereas the PCA showed that river water had undergone the minerals dissolution.

Kim et al. [10] study the land-cover influence on the streams water quality in urban zones from South Korea. After classifying the watersheds in three clusters, the factorial analysis is used to select the water parameters that participate in the computation of a newly defined water quality indicator (WQImin), further employed to estimate the degree of water contamination. WQImin appears as a competitor for the other water quality indexes already known.

Costache et al. [11] introduced an integrated framework for detecting the areas prone to flooding generated by flash-floods in small river catchments as an indicator for water quality. Three models were generated in the first stage, by a combination of frequency ratio (FR), weights of evidence (WOE), and statistical index (SI), with fuzzy analytical hierarchy process (FAHP), and the best one (FAHP-WOE) was selected. In the next stage, the first step's output was weighted using the flow accumulation method to determine the valleys with different levels of susceptibility to flood. Finally, ten flood conditioning factors were used to determine flood susceptibility through the analytical hierarchy process model. Given that the higher the susceptibility to flooding is, the higher the pollution with different sediments and other materials carried by the water is, this method provides an interesting tool for pollution warning in small river catchments.

The article [12] proposes a new evolutionary approach for determining an optimal parameter in the Inverse Distance Weighting Interpolation (IDW) method that has a large applicability in the spatial interpolation of regional data series. Proposed for the scenario, the algorithm was tested on 41 series collected at ten locations, in Dobrogea, Romania. In terms of the mean absolute error (MAE) and the mean standard error (MSE) the new algorithm outperformed the classical IDW, the ordinary kriging, and the Particle Swarm Optimization of IDW. The algorithm should be validated on other data sets.

**Author Contributions:** Conceptualization, A.B. and C.S, .D.; methodology, A.B. and C.S, .D.; formal analysis, C.S, .D.; writing—A.B. and C.S, .D.; writing—review and editing, A.B.; supervision, A.B.; project administration, A.B. 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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