Quantifying Raindrop Evaporation Deficit in General Circulation Models from Observed and Model Rain Isotope Ratios on the West Coast of India

Abstract

Raindrop evaporation is an important sub-cloud process that modifies rainfall amount and rainwater isotope values. Earlier studies have shown that various general circulation models (GCMs) do not incorporate this process properly during the simulation of water isotope ratios (oxygen and hydrogen). Our recent study has demonstrated that an inadequate estimation of this process for the Indian Summer Monsoon (ISM) results in significant biases (model-observed values) in the simulation of various GCMs on a monthly scale. However, a quantitative estimation was lacking. The magnitude of raindrop evaporation depends upon ambient humidity and temperature, which vary considerably during the ISM. Consequently, the isotope biases would also vary over various time scales. The present study aims to investigate the magnitude of the monthly scale variation in raindrop evaporation in the simulations and its causal connection with the corresponding variation in isotope biases. Towards this, we compare an 11-year-long (1997–2007) dataset of rain isotope ratios (both oxygen and hydrogen) from an Indian station, Kozhikode (Kerala), obtained under the Global Network of Isotopes in Precipitation (GNIP) programme of the International Atomic Energy Agency (IAEA) with the corresponding outputs of two isotope-enabled nudged GCMs—ISOGSM and LMDZ4. The raindrop evaporation fractions are estimated for 44 ISM months (June–September) of the study period using the Stewart (1975) formalism. Using a simple condensation–accretion model based on equilibrium fractionation from vapour, obtained from two adopted vapour isotope profiles, we estimate the liquid water isotope ratios at the cloud base. Considering this water as the initial rain, the raindrop evaporation fractions are estimated using the observed oxygen and hydrogen isotope ratios of Kozhikode surface rain samples. The estimated fractions show strong positive correlations with the isotope biases (R² = 0.60 and 0.66). This suggests that lower estimates of raindrop evaporation could be responsible for the rain isotope biases in these two GCMs.

1. Introduction

The oxygen and hydrogen isotope ratios in water have long been considered important tracers of the hydrologic cycle [1,2,3,4]. These ratios are primarily affected by various physical processes involving phase changes during liquid–vapor transition (evaporation or condensation). Since different water sources in the hydrologic cycle have different evaporation and condensation histories, they usually have different isotopic ratios. Isotope-enabled general circulation models (GCMs) constitute a useful tool to investigate the relationship between water isotopes and climate, since many climatic processes are considered in these models [5,6,7]. These processes include evaporation, advection, condensation, evaporative isotope exchange of raindrops, and the recycling of moisture through evaporation and evapotranspiration. The models have been used to simulate water isotope tracers in the atmosphere [8,9,10,11], the ocean/ice system [12,13,14] and the coupled ocean atmosphere system [15,16,17]. Historical simulation (in multi-decadal scales) of these models is often compared with proxy isotope values for constraining past atmospheric circulation [18,19]. These GCMs reproduce the direction and large-scale patterns of past climate changes successfully. However, they cannot accurately simulate the magnitude of regional changes archived in the local climate proxies [20,21]. The accurate simulation of water isotopes in these models is required not only to correctly estimate the extent of these changes in the modern climate but also to reconstruct/project the past/future climate. However, the accuracy in the simulation can be achieved only by the correct representation of the controlling physical processes.

The Indian sub-continent experiences rainfall governed primarily by the seasonal variation in atmospheric circulation [22]. Most of the rainfall occurs during the Indian Summer Monsoon (ISM; June–September) season. The sub-continent and the adjacent Tibetan Plateau host a rich repository of natural archives from which decadal to centennial-scale climates have been reconstructed [23,24,25]. However, due to the paucity of long-term rain isotope data, studies evaluating the performances of GCMs in this region are limited [26,27]. A recent study by Shi et al. [28] documented a strong seasonality in the rain isotope ratios over the Tibetan Plateau (TP). Their analyses indicate that most GCMs underestimate seasonality of the isotopic composition in the precipitation and vapour. In the southern TP, the upwind precipitation seasonality controls the inter-model spread in isotopic seasonality. This observation is consistent with the findings of our recent study [27], which demonstrated that the rain δ¹⁸O biases in North India are inversely proportional to the rainfall biases over the monsoon trough. In addition, this study suggested that the efficacy of these models in Western India depends on how accurately they simulate (a) vapour isotope values in the mid-troposphere and (b) the raindrop evaporation. Raindrops, while falling through the sub-cloud layer of unsaturated atmosphere, exchange isotopes with the ambient vapour [29,30]. The isotopic composition of the falling raindrops changes due to evaporation and exchange. It is difficult to quantify raindrop evaporation directly from the satellite-based meteorological data. However, using water isotope analysis and various parameterization equations, the magnitude of isotope exchange and drop evaporation can be estimated [30,31]. Normally, the isotope exchange model proposed by Stewart [32] is used in most of the GCMs. In that model, the fall of a raindrop in the atmosphere is associated with equilibrium exchange and diffusive transport of vapour isotopologues between the drop surface and the environment. Under certain simplifying assumptions, the Stewart model estimates the final isotopic composition of a raindrop as a function of temperature, normalized relative humidity, isotope ratios of the initial raindrop and ambient vapour, and ratio of the final mass to the initial mass of the drop (see later in Section 3.2).

While most of the GCMs use this evaporation-exchange scheme to compute final isotope ratios of the raindrops at the ground level, there is no way we can separate out the sub-cloud evaporation contribution, which plays a major role [30]. The present study is an attempt to evaluate this contribution. Using a model vapour isotope profile, we can estimate the composition of the cloud droplets at various levels inside a cloud, assuming equilibrium condensation and zero evaporation (saturated humidity assumption). These cloud droplets can grow and combine to make rain droplets that descend through the cloud to reach the cloud base. The raindrop composition at the cloud base is estimated by the isotope mass balance of these droplets. This composition serves as the initial isotope ratio to be used for obtaining the sub-cloud evaporation.

In an earlier study dealing with the improper estimation of drop evaporation in the GCMs, we adjusted their simulated vapour isotope profiles to match the available surface and satellite based data [27]. Since the objective of that study was to carry out an inter-comparison of seven different GCMs, a long-term mean isotope profile of a common time window (1997–2007) was considered. However, the magnitude of the sub-cloud raindrop evaporation depends on the ambient air temperature and humidity and should vary in various summer monsoonal months. Especially in the latter part of the summer monsoon (August–September), less evaporation is expected due to high humidity in the atmosphere [33]. These aspects were not addressed in that study. In the present work, we explore the monthly variation in drop evaporation during the ISM months and corresponding rain isotope biases of the GCMs.

2. Data and Methods

2.1. Study Area and Choice of GCMs

The limited available studies dealing with the performance of the GCMs over the Asian monsoon region show that two nudged models—LMDZ4 and IsoGSM Nudged [26,27,28]—perform better over these regions. The other models, in contrast, show large biases in various physical fields like temperature, humidity, wind etc., both in monthly and seasonal scales. Therefore, we decided to consider only IsoGSM and LMDZ4 models for the estimation of raindrop evaporation effects. The model outputs are available at the Stable Water Isotope Intercomparison Group, Phase 2 (SWING2; https://data.giss.nasa.gov/swing2/swing2_mirror/; [34], accessed on 8 April 2023). Monthly outputs of simulated rain isotope values (δ¹⁸O and δD) for summer monsoon (June–September) months are extracted for the period (1997–2007) over the location Kozhikode (11.25° N; 75.77° E), where corresponding observed isotope data are available for the same time window. Kozhikode, situated on the west coast of India at an altitude of 1 masl, falls under the Global Network of Isotopes in Precipitation (GNIP) program [35]. The station experiences a tropical monsoon climate with brief spells of pre-monsoon (April–May) shower. It receives a substantial rainfall (average monsoonal rainfall = 2237 mm) during the summer monsoon (June–September) and a sizable amount (on average 444 mm) of rain during the winter monsoon (October–December). During the summer monsoon months, the daytime air temperature remains nearly constant at around 26 °C (https://imdpune.gov.in/library/public/1981-2010%20CLIM%20NORMALS%20%28STATWISE%29.pdf, accessed on 8 April 2023). Considering the availability and continuity of the observed and model rain/vapour isotope datasets, Kozhikode serves as an appropriate location for this analysis. Furthermore, being situated on the coast, the contribution of inland moisture recycling through evaporation and evapotranspiration is insignificant compared to the advected moisture flux during the ISM (Figure 1).

2.2. Gridded Meteorological Data

For estimating the effect of evaporation on the monthly rain isotope ratios, monthly gridded data (relative humidity, air temperature, specific humidity, wind (both zonal and meridional) and specific cloud liquid water content (CLWC) for the pressure levels 1000 to 100 mb from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA 5) reanalysis dataset with a resolution of 0.25° × 0.25° [36] are used. Vertically integrated moisture transport (VIMT) is calculated from the specific humidity, zonal and meridional wind components, integrated from 300 to 1000 mb using the standard equation [37]. The mean monsoon VIMT and moisture fluxes are shown in Figure 1. The moisture fluxes are very large and a comparison with precipitation indicates that only about 15% of this moisture is precipitated [38]. Moreover, the contribution from evapotranspiration is negligible compared to this flux.

2.3. Satellite-Based Vapour Isotope Data

To investigate how the models simulate vapour isotope values at various pressure levels, we compare them with the Tropospheric Emission Spectrometer (TES) Level 2 (Nadir-Lite-Version 6) retrievals of HDO and H₂O profiles. The data are available for the period (2005–2007) [39,40]. Vapour δD data are obtained from 17 pressure levels with a 5.3 km × 8.4 km footprint. These observations have a precision of 1–2‰ when the zonal average of this data is considered [34,41]. All valid TES observations of HDO and H₂O concentrations over a box (6°–14° N and 69°–78° E) are extracted (Figure 1). This box includes Kozhikode and part of the Arabian Sea.

3. Model for Estimation of Raindrop Evaporation Effect

We carry out the calculations in two steps for estimating the raindrop evaporation effects: (1) calculations that are involved in vapour to cloud droplets and cloud droplets to raindrop formation processes inside the convective cloud system and (2) sub-cloud evaporative exchange below the cloud base until the raindrops reach the ground.

3.1. Rain Forming Processes and Raindrop Isotopic Composition at the Cloud Base Height

The rainfall over Kozhikode during the ISM season (JJAS) occurs mainly due to orography-induced convective processes [42,43]. In these cases, rains form due to rapid uplift of moisture-laden vapour that originates by evaporation from the Arabian Sea. The vapour is carried inland by strong westerly winds impinging on the coast in a perpendicular direction (Figure 1). The available ceilometer observations suggest that majority of the clouds occur at a low level (LLC; average Cloud Base height (CBH) = 800 m) for rains over the study region during the ISM [44]. The ceilometer study also shows that clouds hover around the LLC region about 90% of the time during the active phases of the ISM. In addition, the occurrence of clouds is rare above 6 km, a region where the ice phase forms [45]. For simplicity, we assume that the contribution from higher-level clouds or ice phase is small and can be neglected. This implies that most of the rainfall over the Western Ghat region is induced by shallow convection.

The cloud droplets form from the ambient vapour and an isotopic fractionation occurs during condensation. Therefore, to estimate isotope ratios of the cloud droplets, the composition of the ambient vapour needs to be known/estimated at various heights. It is known that certain suitable adjustments and zonal integrations provide observational validation for the profiles of the two chosen models used here [6,7]. The height-specific monthly average vapour δD and δ¹⁸O values from the IsoGSM/LMDZ4 outputs (see later in Section 4) are obtained for the JJAS monsoon months over the period 1997–2007. All gridded meteorological data and model vapour isotope outputs are averaged over the box surrounding Kozhikode (6–14° N; 74–78° E; Figure 1). The parameters used in the calculations (for Section 3.1 and Section 3.2) are the following: air temperature, relative humidity, vertical profiles of CLWC, model vapour isotope ratios, and observed ground-level rain isotope ratios at Kozhikode.

Available CLWC data show that cloud droplets exist at various pressure levels (from 1000 mb to 100 mb), with major liquid water peaks at 550 and 900 mb levels. Raindrops form by the collision and coalescence of the small cloud water droplets. The bigger drops come down without suffering any exchange or evaporation effect within the clouds. This situation prevails because the presence of significant amount of cloud water at these levels is indicative of super-saturated humidity, where evaporative exchange is minimal [29,30]. The ground-level rain (collected over a period) is derived from a uniform mix of these raindrops that arrive at the cloud base without alteration. It is important to mention here that the presence of CLWC does not explicitly confirm rain formation. The rain liquid water content (RLWC) is a better indicator for that. The connection between the CLWC and RLWC is not always clear. However, in a study based on a micro-rain radar, Zhang et al. [46] showed that the Cloud Liquid Water Path (CLWP) is larger than the Rain Liquid Water Path (RLWP; integral for the rain water concentrations up to the top of the atmosphere), but they both show a similar variation. They also found that both CLWP and RLWP are positively correlated with the rain rate, and the precipitation efficiency (100% × RLWP/CLWP) is high (about 50%) when precipitation finally happens. From a case study in central China, they showed that during the period of increasing precipitation, both CLWC and RLWC increase with height (up to about 3 km) in a similar fashion (see Figure 2). The RLWC data require micro rain radar measurements, which are not available in and around our study area for the said period. Therefore, for the present purpose, we assume that in case it rains, the raindrop formation rate would be in direct proportion to the CLWC values in the average profile.

We use the available CLWC average monthly profile to estimate the altitude variation in the rain formation rate by taking the CLWC values as statistical weights in the rain liquid water content as a function of height. Following earlier studies [29,32,47], we also consider that condensation takes place in equilibrium, and there is no fractionation during the coalescence of cloud drops in the course of raindrop formation. The fractionation factors for the condensation of vapour to liquid at various temperatures corresponding to the altitudes are determined using the formula of Horita and Wesolowski, 1994 [48], for both δD and δ¹⁸O. The isotope ratios (δ_i) of the rains formed at different altitudes (ith level) are determined using these fractionation factors. In this approach, we cannot determine the amount of total rain but only the average isotope ratios of the total rain at the cloud base height (CBH) for different months using the following equation:

$${{\mathsf{\delta }}_{}}_{\mathrm{r}\left(\mathrm{C}\mathrm{B}\mathrm{H}\right)}=\frac{\sum _{\mathrm{i}=1000 \mathrm{m}\mathrm{b}}^{\mathrm{i}=100 \mathrm{m}\mathrm{b}}{\mathsf{\delta }}_{\mathrm{i}}\ast \mathrm{ }{\mathrm{C}}_{\mathrm{i}}\ast ∆{\mathrm{h}}_{\mathrm{i}}}{\sum _{\mathrm{i}=1000 \mathrm{m}\mathrm{b}}^{\mathrm{i}=100 \mathrm{m}\mathrm{b}}{\mathrm{C}}_{\mathrm{i}}\ast ∆{\mathrm{h}}_{\mathrm{i}}}$$

(1)

The subscript “i” refers to the altitude/pressure level (1000 mbar to 100 mbar in 25 mbar intervals up to 750 and then in 50 mbar intervals, denoted by Δh). C_i denotes the CLWC values at the ith level.

The above procedure is a simplified version of the condensation and coalescence process (hereafter referred to as the condensation-accretion process) that allows us to calculate the isotope ratio of the liquid rain at the cloud base. We made the following assumptions: (1) no in-cloud exchange or evaporation takes place, (2) no updraft or downdraft occurs, (3) condensation occurs in equilibrium between the vapour and liquid at various altitudes within the cloud, and (4) liquid rain amount is proportional to the CLWC. In actual practice, rain formation and its downward migration is a complex process. Admittedly, since no data for the isotope ratio of liquid rain leaving the cloud base are available, the procedure that we follow cannot be verified. However, we note that the IsoGSM-Nudged model simulates a δD value of −77‰ (Kei Yoshimura, Personal Communication) for the liquid at the average CBH over Kozhikode, which is only 10‰ lower compared to our average accretion model estimate of −67‰ for the same period [27]. The accumulated raindrops at CBH (varying from 820 mbar to 925 mbar) then fall into the sub-cloud region where the air is under-saturated and warmer. The falling raindrops undergo evaporative exchange with the environmental vapour, and their isotope ratios are modified. We use the Stewart model [32] to estimate the magnitude of this evaporative enrichment.

3.2. Sub-Cloud Evaporative Exchange

The Stewart (1975) model is essentially a Craig–Gordon [2,49]-type model, which deals with the evaporation of water drops falling through the atmosphere with varying relative humidity and temperature levels and exchanging isotopes with the ambient moisture of different isotopic compositions. The isotope ratio of falling raindrops increases due to evaporation and exchange with ambient vapour (which has higher isotope ratios relative to the higher-level vapour inside the cloud) in the sub-cloud layer. The evaporation/exchange process simulated by Stewart [32] is usually adopted by all GCMs, where the isotopic composition of falling raindrops is given by,

[R_r(g) − γR_v(amb)] = [R_r(cb) − γR_v(amb)] × f^β

(2)

where R_r(g) and R_r(cb) represent the ground level (g subscript) and cloud base (cb subscript) isotope ratios of the drop, and R_v(amb) is the ratio of the ambient (amb subscript) vapour. The parameter f denotes the fraction of the raindrop mass remaining. The constants γ and β involve three parameters: fractionation factor, relative humidity, and diffusivity ratios, as given below:

$$\beta =\frac{1-{\alpha }_p{(D/D\prime )}^n(1-h)}{{\alpha }_p{(D/D\prime )}^n(1-h)}$$

(3)

$$\mathit{\gamma }=\frac{{\alpha }_{p}h}{1-{\alpha }_p{(D/D\prime )}^n(1-h)}$$

(4)

where α_p is the equilibrium fractionation factor (liquid to vapour), D and D′ are the diffusivities for H₂¹⁶O and HD¹⁶O (or H₂¹⁸O), n = 0.58, and h is the relative humidity. We assume that the isotope ratio of the sub-cloud vapour, the RH and temperature do not change significantly between the cloud base and ground, and we can use the average values of the temperature, RH, R_v(amb), and the fractionation factor for water to vapour conversion for the calculations. Using the three R-values and the two constants in equation 2 corresponding to the D/H and ¹⁸O/¹⁶O ratios, we finally estimate the remaining fraction of the rain (f) for the 44 ISM months. The raindrop evaporation fraction is then given by (1-f). The simulated rain δD and δ¹⁸O values of two GCMs, our estimated liquid isotope values at CBH, the observed rain isotopes at Kozhikode, and estimated raindrop evaporation fractions are given in

Table 1. The model and observed δD values at Kozhikode along with the estimates of evaporation.

Months 1 (YYYY-MM)	GNIP	ISOGSM			LMDZ4
	2 Observed Rain δD (‰)	3 Model Rain δD (‰)	4 Estimated Rain δD at CBH (‰)	5 Estimated Rain Evaporation Fraction	3 Model Rain δD (‰)	4 Estimated Rain δD at CBH (‰)	5 Estimated Rain Evaporation Fraction
1997-06	−7	−23	−47	0.27	−11	−108	0.33
1997-07	−14	−16	−61	0.18	−33	−114	0.29
1997-08	−3	−13	−45	0.32	−27	−106	0.36
1997-09	−40	−19	−92	0.12	3	−90	0.10
1998-06	−6	−21	−62	0.47	−51	−155	0.31
1998-07	−1	−11	−86	0.40	−25	−103	0.47
1998-08	−17	−19	−98	0.21	−9	−98	0.20
1998-09	−8	−19	−97	0.29	−13	−113	0.30
1999-06	−5	−14	−34	0.28	−20	−104	0.40
1999-07	−5	−19	−70	0.35	−28	−113	0.34
1999-08	4	−12	−54	0.49	−16	−89	0.52
1999-09	−8	NA	−77	0.32	NA	−93	0.30
2000-06	0	−16	−47	0.48	−22	−109	0.54
2000-07	1	−25	−57	0.44	−23	−119	0.50
2000-08	−9	−15	−91	0.31	−16	−97	0.24
2000-09	−26	−29	−86	0.17	−1	−83	0.14
2001-06	4	−16	−57	0.52	−26	−129	0.57
2001-07	−2	−8	−64	0.41	−50	−133	0.20
2001-08	−1	−17	−65	0.46	−24	−83	0.27
2001-09	−12	−15	−67	0.19	9	−90	0.23
2002-06	−39	−19	−44	0.02	−16	−101	0.14
2002-07	1	−11	−20	0.43	−19	−96	0.43
2002-08	1	−13	−44	0.56	−3	−93	0.32
2002-09	2	−16	−62	0.41	6	−59	0.30
2003-06	5	−19	−74	0.47	−34	−112	0.51
2003-07	−11	−16	−90		−37	−127	0.46
2003-08	3	−17	−64	0.44	−8	−91	0.47
2003-09	−8	−12	−71	0.26	3	−84	0.25
2004-06	−10	−14	−42	0.21	−15	−112	0.40
2004-07	−2	−15	−69	0.50	−34	−104	0.53
2004-08	3	−15	−46	0.49	−25	−112	0.55
2004-09	−26	−24	−88	0.17	−19	−119	0.19
2005-06	−9	−18	−54	0.22	−30	−98	0.32
2005-07	−11	−14	−72	0.28	−52	−72	0.28
2005-08	−4	−15	−61	0.33	−7	−84	0.27
2005-09	−7	−23	−78	0.25	5	−95	0.25
2006-06	−7	−15	−75	0.35	−20	−114	0.40
2006-07	−3	−11	−34	0.26	−33	−93	0.38
2006-08	−7	−17	−72	0.34	−33	−95	0.30
2006-09	−30	−15	−91	0.16
2007-06	−33	−16	−106	0.18
2007-07	−4	−19	−77	0.32
2007-08	−10	−13	−86	0.27
2007−09	−8		−90	0.34
Average	−8	−16	−67	0.32	−20	−102	0.34

¹ Monthly composite/average data of isotopes (both observed and model) for the following months are calculated; ² Monthly average rain δD data (1997–2007) of Kozhikode under the Global Network of Isotopes in Precipitation (GNIP) are given here; ³ Monthly average rain δD data extracted from the nudged models IsoGSM (1997–2007) and LMDZ4 (1997–2006) over the grid covering Kozhikode are given here. The data are available at SWING2 repository. ⁴ Liquid δD value at cloud base height is estimated in Section 3.1 using vapour δD values of the respective model; ⁵ Raindrop evaporation fraction (1-f) is estimated from liquid δD values at CBH and observed rain δD values (Section 3.2).

(δD) and

Table 2. The model and observed δ¹⁸O values at Kozhikode along with the estimates of evaporation.

Months (YYYY-MM) 1	GNIP	ISOGSM			LMDZ4
	Observed Rain δ18O (‰) 2	Model Rain δ18O (‰) 3	Estimated Rain δ18O at CBH (‰) 4	Estimated Rain Evaporation Fraction 5	Model Rain δ18O (‰) 3	Estimated Rain δ18O at CBH (‰) 4	Estimated Rain Evaporation Fraction 5
1997-06	−1.6	−4.2	−8.2	0.21	−2.4	−13.2	0.24
1997-07	−3.3	−3.4	−9.6	0.12	−5.2	−14.6	0.19
1997-08	−1.5	−3.1	−7.6	0.17	−4.7	−14.0	0.11
1997-09	−6.7	−3.6	−13.3	0.09	−0.9	−12.6	0.08
1998-06	−2.1	−3.8	−9.5	0.20	−6.9	−9.6	0.20
1998-07	−1.1	−2.5	−12.7	0.24	−4.3	−13.4	0.30
1998-08	−3.1	−3.3	−14.1	0.17	−2.1	−13.2	0.16
1998-09	−2.2	−3.6	−14.3	0.20	−2.6	−15.2	0.22
1999-06	−1.8	−3.0	−6.4	0.15	−4.3	−12.6	0.25
1999-07	−2.0	−3.4	−10.8	0.23	−4.8	−14.0	0.22
1999-08	−0.7	−2.7	−8.7	0.24	−3.1	−11.8	0.24
1999-09	−2.3		−11.6	0.20		−12.7	0.21
2000-06	−1.3	−3.4	−7.9	0.22	−4.1	−13.2	0.25
2000-07	−1.2	−4.3	−9.1	0.22	−3.9	−9.7	0.27
2000-08	−2.3	−3.3	−13.2	0.20	−3.8	−13.1	0.18
2000-09	−4.4	−5.0	−12.8	0.14	−0.8	−11.5	0.11
2001-06	−1.0	−3.8	−9.1	0.24	−4.9	−9.1	0.25
2001-07	−1.5	−2.6	−9.9	0.20	−7.2	−17.3	0.27
2001-08	−1.6	−3.2	−10.2	0.19	−4.5	−16.1	0.18
2001-09	−2.8	−2.7	−10.1	0.14	0.0	−11.8	0.16
2002-06	−6.3	−3.7	−7.9	0.03	−3.5	−12.0	0.08
2002-07	−0.9	−2.6	−4.6	0.16	−3.8	−11.5	0.24
2002-08	−1.0	−2.5	−7.5	0.20	−1.2	−13.3	0.30
2002-09	−1.0	−3.1	−9.9	0.23	−0.3	−10.1	0.22
2003-06	−0.6	−3.6	−12.0	0.28	−5.6	−14.5	0.30
2003-07	−2.7	−2.5	−13.8	0.28	−6.0	−12.6	0.15
2003-08	−0.8	−3.2	−9.9	0.25	−2.1	−12.4	0.41
2003-09	−2.6	−2.6	−11.2	0.17	−0.7	−12.1	0.17
2004-06	−2.6	−3.3	−7.6	0.13	−3.5	−13.1	0.20
2004-07	−1.6	−3.2	−10.3	0.24	−5.6	−12.0	0.19
2004-08	−1.2	−2.8	−7.8	0.19	−4.3	−14.2	0.33
2004-09	−4.4	−4.2	−13.4	0.14	−3.1	−16.0	0.17
2005-06	−2.6	−3.6	−9.1	0.15	−5.1	−10.3	0.16
2005-07	−2.7	−3.3	−11.0	0.17	−7.6	−15.2	0.18
2005-08	−1.3	−2.6	−9.3	0.21	−2.0	−13.2	0.47
2005-09	−2.1	−3.9	−11.8	0.18	−0.7	−12.8	0.18
2006-06	−2.6	−3.1	−11.9	0.20	−3.5	−13.4	0.20
2006-07	−1.6	−2.6	−6.5	0.14	−5.5	−12.8	0.21
2006-08	−2.1	−3.4	−10.8	0.20	−5.0	−11.3	0.20
2006-09	−4.8	−3.2	−13.2	0.13
2007-06	−5.6	−3.3	−15.4	0.14
2007-07	−1.8	−3.5	−11.8	0.19
2007-08	−2.9	−3.0	−12.6	0.17
2007-09	−2.3		−13.3	0.20
Average	−2.3	−3.3	−10.4	0.18	−3.7	−12.9	0.22

^1. Monthly composite/average data of isotopes (both observed and model) for the following months are studied, ² Monthly average rain δ¹⁸O data (1997–2007) of Kozhikode under the Global Network of Isotopes in Precipitation (GNIP) are given here, ³ Monthly average rain δ¹⁸O data extracted from the nudged models IsoGSM (1997–2007) and LMDZ4 (1997–2006) over the grid covering Kozhikode are given here. The data are available at SWING2 repository, ⁴ Liquid δ¹⁸O values at cloud base height estimated in Section 3.1 using vapour δ¹⁸O values of the respective model, ⁵ Raindrop evaporation fraction (1-f) is estimated from liquid δ¹⁸O composition at CBH and observed rain δ¹⁸O values (Section 3.2).

(δ¹⁸O).

3.3. Uncertainty Calculation by Numerical Quadrature Method

The uncertainty in the evaporation estimates is obtained by varying the values of the variables in the Stewart equation. The evaporation depends on five parameters: temperature, relative humidity, initial rain composition at the CBH, final rain composition at the ground, and the sub-cloud vapour isotope composition. Each of these parameters can vary and affect the final estimated value of evaporation. The uncertainty in the evaporation is calculated by the following formula:

$$\mathrm{Assume} x=f\left(u,v,\dots \right).$$

$${\sigma }_{x }^2\simeq {\sigma }_{u }^2{\left(\frac{\delta x}{\delta u}\right)}^2+ {\sigma }_v^2{\left(\frac{\delta x}{\delta v}\right)}^2+\cdots$$

(5)

We assume that the errors in the parameters are as follows: σ(T) = 2 °C, σ(RH) = 2%, σ(δD_ini) = ±2‰, σ(δD_fin) = ±2‰, and σ(δD_amb) = ±2‰. For example,

Table 3. An example of the uncertainty calculation in the evaporation parameter (1-f) corresponding to the IsoGSM model for June 1997 (see Table 1, first row, fifth column).

Variable	Range	Values	diff	Ratio = Diff/Range	Sigma Terms	Total	1σ Error
Temp (C)	296	0.2477	0.0786	0.0197	0.0015445	0.00369	0.060709
	298	0.2802
	300	0.3263					0.27 ± 0.06
RH (%)	85	0.2738	−0.0067	−0.0017	1.122 × 10−5		(Table 1)
	87	0.2691
	89	0.2671
Ro (δo)	−44	0.2623	0.0105	0.0026	2.756 × 10−5
‰	−46	0.2677
	−48	0.2728
Ramb	−84	0.2316	0.0584	0.0146	0.0008526
(δamb)	−86	0.2566
‰	−88	0.2900
Rf (δf)	−5	0.3087	−0.0707	−0.0177	0.0012496
‰	−7	0.2691
	−9	0.2380

shows the calculated final error in the evaporation (1-f) for the case of June 1997 (IsoGSM), corresponding to the first entry in Table 1. The sigma column indicates individual error terms, and the final column gives the error (calculated by quadrature) in the evaporation (1-f), which is 0.27 ± 0.06 (for the chosen month), or about 27%. The sensitivity is highest for the temperature, followed by the ambient vapour and the final rain isotope ratios. Considering all the other entries, typical error values are ±20%.

4. Results

As mentioned earlier (Section 2.3), the TES observations of δD values are available for a smaller period compared to their model counterparts, while to check the performances of the models, we need to use their vapour isotope profiles for the 44 months during 1997–2009. Therefore, for validation, we compared the results obtained by using the TES and the two models’ vapour isotope profiles over a common interval. Mean averaging kernels of all valid observations for the summer monsoon months of 2005–2007 suggest that the TES observations over the study region between the pressure levels 750 mb and 400 mb are of acceptable quality. Therefore, all such observations at different pressure levels for the summer monsoon months of 2005–2007 are averaged over the box (Figure 1). Notably, the TES observations are not very sensitive in the atmospheric boundary layer, especially below 750 mb in our study area. To circumvent this issue, we used the available surface vapour isotope observations (mean monsoon δD ~78‰; [33]) at the location Wayanad (around 70 km away) as the surface value and extrapolated the curve from the surface to 750 mb and above 400 mb to construct the adopted vapour δD profiles for TES. The mean monsoon vapour δD profiles of TES and the two models (IsoGSM and LMDZ4) over the box for the synchronous period are shown in Figure 3. The average TES profile is considered as representing the ‘true’ atmospheric situation (called ‘observed’). The figure shows that IsoGSM values reasonably agree with the TES values from the surface to 400 mb and deviate only slightly above that level. However, notable differences (mean model—TES) of about −30‰ exist for LMDZ4. To explore whether these differences have any impact on the drop evaporation estimates, we determined the rain δD composition at the CBH by using the three vapour δD profiles (TES and the two models) following our condensation-accretion model discussed in Section 3.1. The drop evaporation fraction is estimated from the difference between the liquid δD at CBH (acting as the initial rain) calculated for each model and the observed GNIP average rain value at the ground (acting as the final rain). The values given in

Table 4. Comparison of the estimated rain isotope ratios at cloud base height (CBH) and the magnitude of the average evaporation fraction (2005–2007). For computation of the reference (1-f) fraction, vapor δD values at multiple levels obtained from TES, and temperature, specific humidity data from ERA-5 have been used. Similarly, the δD, temperature, and specific humidity values from the model simulations are used in corresponding calculations for the models. Data from GNIP are used as the observed value for the rain δD at the ground level.

Model	Rain δD at CBH (‰)	Observed Value (‰)	Rain Evaporation Fraction
TES (as Reference)	−74	−39	0.08
IsoGSM	−78	−39	0.11
LMDZ4	−112	−39	0.15

show that the calculated evaporation differs only by 2% for IsoGSM and 7% for LMDZ4; these two differences are small (within and slightly above the uncertainty of the estimates, respectively). This provides adequate validation of our conceived condensation-accretion model along with its assumptions.

5. Discussion

5.1. Comparison between Observed and Model Rain Isotope Values

Table 1 and Table 2 show that barring 5 cases out of 44, all IsoGSM simulations are lower compared to the observed values. An overall negative rain isotope bias is observed for both models (on average −8‰ in δD and −1‰ in δ¹⁸O for IsoGSM; −12‰ in δD and −1.4‰ in δ¹⁸O for LMDZ4; Table 1 and Table 2). The rain δ¹⁸O and δD biases are strongly correlated for both models (Figure 4), suggesting that same processes control both isotope biases. The data points fall reasonably well with a mean regression line: δD = 7.3 (±0.27) × δ¹⁸O −1.4 (±0.47) for IsoGSM and δD = 7.9 (±0.17) × δ¹⁸O − 0.96 (±0.52) for LMDZ4. The model, IsoGSM (LMDZ4), under or (over) estimates the range of variation (δD varying −8‰ to −29‰ for IsoGSM and +9‰ to −53‰ for LMDZ4) as compared to observed values (5‰ to −40‰; Table 1). The difference in the range of variations (between observed and model values) is clearly evident in the frequency distribution of δD values (Figure 5). The negative isotope biases in the models during the ISM have also been reported in a few earlier studies [26,28,50]. In our earlier study [27], we identified that the underestimation of the mean isotope values can be due to (a) an inaccurate vapour isotope profile and (b) a lower estimate of the raindrop evaporation. By comparing the IsoGSM simulation with the TES estimation for the same period (2005–2007), we see that the difference (at the CBH) could be at most 4‰ (in δD) due to the isotope profile difference (Table 4), which is too small to account for the discrepancy, assuming the TES represents a realistic profile. However, the aforementioned difference is large (38‰) for LMDZ4. Therefore, for LMDZ4, we cannot rule out a significant contribution from the vapour isotope bias towards the negative rain isotope bias. The above result suggests that we should look for a lower evaporation estimate as the main factor for the models’ discrepancy.

5.2. Rain Evaporation Estimates and Their Relations with Model Rain Isotope Biases

Table 1 shows that average raindrop evaporation required to match the observed δD values at Kozhikode is about 32% (±12%). If the IsoGSM model rain isotope values were taken as the final rain isotope values (instead of the observed rain isotope values), the average evaporation required to reproduce them would be about 22%. This suggests a shortfall of about 10% in evaporation (though evaporative effects, sensu stricto, do not add linearly) in the IsoGSM. On the other hand, the mean rain evaporation required for the LMDZ4 model to match the observed values is 34% (±12%), and the corresponding shortfall is about 12%.

We also carried out similar exercises using the δ¹⁸O values simulated by IsoGSM and LMDZ4. Table 2 shows that the evaporation required to match the observed δ¹⁸O values is on average about 18% (±5%) for IsoGSM and 22% (±8%) for LMDZ4. The discrepancy between the two estimates (i.e., based on δD and δ¹⁸O vapour profiles) using the condensation-accretion process is quite large. We explore the reason for this difference below. Since the only input from the models is the vapour isotope values, it seems reasonable to assume that an inconsistency in the two isotope profiles (δD and δ¹⁸O) may be responsible for this discrepancy. As the TES observations do not provide δ¹⁸O values, the corresponding model outputs could not be validated. Therefore, it is possible that model vapour δ¹⁸O values are higher than they should be (considering what one expects from the δD profile), which results in slightly more enriched liquid δ¹⁸O simulations at the CBH, thus requiring less evaporation. This suggestion is corroborated by the δD-δ¹⁸O correlation plots (Figure 6 and Figure 7). The δD-δ¹⁸O correlations for the observed and models’ rains are shown in Figure 6. The same correlations for model vapour and estimated liquid isotopes at CBH are displayed in Figure 7. The local meteoric water line constructed on the basis of simulated rain at Kozhikode (δD = 6.8 (±0.5) × δ¹⁸O + 5.9 (±1.68); Figure 6) and the vapour profile over Kozhikode (δD = 6.63 (±0.06) × δ¹⁸O −11.92 (±3.12); Figure 7a) in IsoGSM have lower slopes and intercepts compared to the observed values: δD = 7.7 (±0.17) × δ¹⁸O + 9.6 (±0.46); (Figure 6). In contrast, the estimated liquid values at the cloud base based on our condensation-accretion process align with δD = 8 (±0.12) × δ¹⁸O + 16.8 (±1.35); (Figure 7b). The δ(δD)/δ(δ¹⁸O) differential is much less for the IsoGSM simulation (both vapours; Figure 7a and ground rain; Figure 6) and indicates a relatively higher value of δ¹⁸O vapour with respect to the δD vapour in the profiles. We cannot identify the real reason, but this could be caused by nonequilibrium fractionation like the diffusion of vapour inside the cloud. In the case of equilibrium fractionation, we obtain:

$$\frac{d{\delta }^{2}H}{d{\delta }^{18}O}=\frac{{\alpha }^{2}H-1}{{\alpha }^{18}O-1} \approx \frac{8}{1}$$

(6)

However, in the case of diffusion (like raindrop evaporation in an unsaturated environment), the smaller diffusion velocities of HD¹⁶O and H₂¹⁸O compared to H₂¹⁶O lead to additional fractionation. Since H₂¹⁸O is heavier than HD¹⁶O, nonequilibrium fractionation is slightly stronger for H₂¹⁸O than for HD¹⁶O. In our condensation-accretion model, we have considered only equilibrium fractionation, leading to a slope close to 8.

The cross-plots of model isotope biases (both δD and δ¹⁸O) against the evaporation fraction (1-f) estimated from δD and δ¹⁸O are shown in Figure 8a,b, respectively. Both models show good correlation between δD bias and (1-f) (Figure 8a); this is expected if the discrepancy originates from a deficiency in raindrop evaporation. Since model values are less than the observed GNIP values, the bias is negative in sign. More negative values imply more evaporation is needed to match the observed values.

However, the correlations are relatively weak for both models in the case of δ¹⁸O bias and the (1-f) cross-plot (Figure 8b). The raindrop evaporation fractions calculated by δ¹⁸O and δD show a stronger correlation for IsoGSM (Figure 8c). The possible reason behind the different estimation of (1-f) for the two models has been discussed above. In addition, as we discussed earlier (Section 4), the vapour isotope values have been largely underestimated in the LMDZ4 model, which can affect the (1-f) estimation following our model. This could be a possible reason for obtaining very different slope, intercept, and correlation values in various correlation plots for the LMDZ4 model. However, even with this limitation, the rain δD bias in this model is correlated with (1-f), suggesting that raindrop evaporation must have notable control on the simulation. Decoupling the effect of this vapour isotope bias from the estimated (1-f) values for this model is beyond the scope of the present study. Based on the above discussion, we propose that the lower isotope values simulated by IsoGSM are due to lower estimates of evaporation (by about 10%) of the IsoGSM in Kozhikode rain samples.

Although our simple model could estimate the liquid isotopic composition at the cloud base and subsequently the drop evaporation amounts that should be adjusted in the GCMs for the correct simulation of rain isotope ratios, our study has some limitations. As mentioned in Section 3.1, our model does not consider any updraft, downdraft, or advection. Moreover, we consider that drop evaporation occurs only below the CBH (Section 3.2), whereas evaporation can take place wherever the relative humidity is <100%, even above the CBH. Therefore, further improvement of our approach is required after taking care of these shortcomings to refine the evaporation estimates reported in the study.

6. Conclusions and Implications

• The rain and vapour isotope simulations of IsoGSM and LMDZ4 models are compared with the observations from Kozhikode (GNIP data). Both models underestimate the long-term mean monsoon rain δD and δ¹⁸O values at Kozhikode, on average by 8‰ and 1.0‰ for IsoGSM and 12‰ and 1.4‰ for LMDZ4, respectively. However, the observed variation in rain isotope values (from +5 to −40‰ for δD and −0.6 to −6.7‰ for δ¹⁸O) is underestimated in IsoGSM but overestimated in LMDZ4.
• To estimate the magnitude of this underestimation, we first determined the isotope ratios of the accumulated liquid water at the cloud base height (CBH) using the GCMs’ vapour isotope profiles and a simple condensation-accretion process (without any in-cloud modification). Treating this composition as the initial rain isotope composition and the observed values as the final rain composition, we used the Stewart model to estimate the raindrop evaporation fractions on monthly scale.
• The evaporation fraction (1-f) varies from 2% to 56% with a mean of 32% (±12%) for IsoGSM when the fraction is computed from δD values. The same value for the LMDZ4 varies from 10% to 55% with a mean of 34% (±12%). We propose that the lower isotope values simulated by IsoGSM and LMDZ4 are due to lower estimates of evaporation (by about 10%) in those models.
• The evaporation is also calculated using the vapour δ¹⁸O profiles for both models. The evaporations required in this case are much less: 18% ± 5% for IsoGSM and 22% ± 8% for LMDZ4. This can be traced to the inconsistency of the adopted δ¹⁸O profile compared to that expected from the δD profile. The inconsistency can possibly happen because of the δ¹⁸O profile, which cannot be validated against the TES observation.
• To estimate the raindrop evaporation fraction on monthly scale, we rely on the vapour δD profiles obtained from the models. Although vapour δD values for the IsoGSM model reasonably agree with the TES observation on a long-term mean seasonal scale, LMDZ4 shows a significant negative bias. For the same reason, the liquid water compositions at CBH estimated from TES profiles grossly agree with the same obtained from the IsoGSM model (TES: −73.5‰; IsoGSM: −77.7‰). However, the value is much lower—about −112‰ for the LMDZ model. Even with stronger bias in the vapour values, raindrop evaporation fractions estimated by LMDZ4 strongly correlate with rain δD biases, suggesting raindrop evaporation indeed affects the rain isotope simulation.
• Our study region is very close to several climate proxies (speleothem and tree ring) locations in the Western Ghat Mountains. The isotope studies of these proxies provided valuable information on past rainfall variability in centennial scales. The present study shows that a monthly variation in raindrop evaporation fractions strongly affects rain isotope simulation. Therefore, the improvement of evaporation schemes in the GCMs may result in better rain isotope simulation, which would be useful in understanding past atmospheric circulation.