a. Datasets

In the first part of our investigation we analyze the forecasts produced operationally by the Met Office for June, July, and August for each of the six years 2012–17. Over this period, the MetUM has been initialized four times per day (at 0000, 0600, 1200, and 1800 UTC), but we restrict this part of the investigation to the forecasts starting at 0000 and 1200 UTC out to 120 h, since the forecasts starting at 0600 and 1800 UTC were only produced up to 60 h. The operational setup was upgraded during the 6-yr period, so the analysis covers more than one version of the MetUM. In 2012 the MetUM was run operationally in the Global Atmosphere 3.1 (GA3.1) configuration (Walters et al. 2011) at N512 resolution (37 km at 20°N). This was upgraded on 15 July 2014 to the GA6.1 configuration (Walters et al. 2017) at N768 resolution (25 km at 20°N), and a further resolution upgrade was implemented on 12 July 2017 to N1280 (15 km at 20°N). The observational data we used for comparison were TRMM data (Huffman et al. 2007; Hou et al. 2014); the dataset used was 3B42, version 7 (Huffman et al. 2010).

For the moisture budget evaluation, which comprises most of our investigation, we use output from the forecasts produced operationally by the Met Office for 2012. Here we use forecasts starting at all four available times. We use instantaneous (i.e., model time step) values of precipitation P, surface upward moisture flux E and, defined on model levels, pressure p, specific humidity q, and horizontal wind V. We also use surface latent heat flux h, defined as a 6-h mean, to calibrate the surface upward moisture flux (see appendix).

For both investigations, quantities have been averaged over forecasts initialized in June, July, and August. We have restricted to valid times from 6 June until 31 August—constant for each forecast lead time—so that for a perfect forecast each term should be independent of lead time. The evolution of the quantities with forecast lead time therefore gives an indication as to how quantities change as the forecast develops.

b. Moisture budget calculation

The moisture conservation of the MetUM can be tested by comparing ${\mathrm{\mathbb{Q}}}_t$ and ${\mathbb{M}}_A-\mathrm{\mathbb{P}}$, since both can be calculated directly from different model outputs. We take ${\mathrm{\mathbb{Q}}}_t\left[{\tau }_{\left(n-1\right)/2}\right]\approx \left[\mathrm{\mathbb{Q}}\left({\tau }_n\right)-\mathrm{\mathbb{Q}}\left({\tau }_{n-1}\right)\right]/\text{Δ}\tau$, where n represents the individual forecast lead times separated by Δτ = 12 h, and $\mathrm{\mathbb{Q}}=1/g\iiint q{d}^{2}A\hspace{0.17em}dp$. Any discrepancies between ${\mathrm{\mathbb{Q}}}_t$ and ${\mathbb{M}}_A-\mathrm{\mathbb{P}}$ would suggest a lack of moisture conservation, although could also be caused by the somewhat coarse temporal discretization used to define ${\mathrm{\mathbb{Q}}}_t$.

c. Separation into moisture and wind effects

a. General rainfall climatology

Figure 2 shows the evolution of the total rainfall, within the green box in Fig. 1, as a function of forecast lead time, for the years 2012–17. The values are 12-h accumulations, and each accumulation is plotted against the whole period to which it applies. Also plotted is the observed rainfall for the same area, for which there is a single value independent of forecast lead time since the forecast valid time does not change.

The 12-h accumulated rainfall in the green box shown in Fig. 1, for June, July, and August of six different years, as a function of forecast lead time (thick lines) and observed (thin lines). The values have been converted to mm h⁻¹. Although the direction of the bias of the forecast against the observations varies, all six years show a drying tendency as the forecast develops.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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The 12-h accumulated rainfall in the green box shown in Fig. 1, for June, July, and August of six different years, as a function of forecast lead time (thick lines) and observed (thin lines). The values have been converted to mm h⁻¹. Although the direction of the bias of the forecast against the observations varies, all six years show a drying tendency as the forecast develops.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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The 12-h accumulated rainfall in the green box shown in Fig. 1, for June, July, and August of six different years, as a function of forecast lead time (thick lines) and observed (thin lines). The values have been converted to mm h⁻¹. Although the direction of the bias of the forecast against the observations varies, all six years show a drying tendency as the forecast develops.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Although the forecast rainfall bias is positive compared with observations for some years at some lead times, all years exhibit a drying tendency from the start of the forecast to 5 days so that the bias against observations is always negative after 5 days. This reduction is largely monotonic, although there is some increase in rainfall earlier in the forecast, particularly for 2015 and 2016. The upgrade in model version that took place in 2014 coincides with a shift from an initial dry bias to an initial wet bias, but both versions clearly show a drying tendency over 5 days.

Figure 3 shows how the bias in the climate simulation, shown in Fig. 1a, varies from year to year, for the same green box in Fig. 1. Although there is of course much variability, reflecting the different meteorological conditions in each year, there is no clear general trend in the behavior. The same is seen for northern India, suggesting that, for both regions, the dry bias develops quickly within the climate simulation, and then is a permanent feature of it.

Rainfall bias averaged over the green box shown in Fig. 1, and a region over northern India, for a MetUM climate simulation against GPCP rainfall data. Values are averaged over June, July, and August for each year. The regions are both bounded by longitudes 71.89° and 85.96°E. The green box is bounded by latitudes 9.02° and 21.45°N, and the region over northern India is bounded by latitudes 21.45° and 28.95°N.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Rainfall bias averaged over the green box shown in Fig. 1, and a region over northern India, for a MetUM climate simulation against GPCP rainfall data. Values are averaged over June, July, and August for each year. The regions are both bounded by longitudes 71.89° and 85.96°E. The green box is bounded by latitudes 9.02° and 21.45°N, and the region over northern India is bounded by latitudes 21.45° and 28.95°N.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Rainfall bias averaged over the green box shown in Fig. 1, and a region over northern India, for a MetUM climate simulation against GPCP rainfall data. Values are averaged over June, July, and August for each year. The regions are both bounded by longitudes 71.89° and 85.96°E. The green box is bounded by latitudes 9.02° and 21.45°N, and the region over northern India is bounded by latitudes 21.45° and 28.95°N.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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These results suggest that an insight into the dry bias over India can be achieved by looking at the development of the forecast and how the bias compares at later and earlier lead times. For the rest of this study we therefore restrict the investigation to model fields (including the model analysis field), in order to investigate the first few days of its drying tendency. We also restrict the rest of the study to 2012, since it displays a clear monotonic drying tendency in rainfall and, given that this drying is robust over the full 6-yr period investigated, it would be expected that the conclusions drawn in the rest of the study would apply broadly to other recent years.

b. Evaluation of moisture budget for 2012

The moisture flux terms are plotted, as a function of lead time, in Fig. 4. The general behavior is that there is a steady decrease in rainfall $\mathrm{\mathbb{P}}$ alongside a decrease in total available moisture ${\mathbb{M}}_A$ from advection and evaporation. Overall, there is a roughly constant moisture flux $\mathbb{E}$ at the surface, which is lower than $\mathbb{P}$, suggesting that the net reduction in rainfall is driven by moisture advection changes. The budget is characterized by a strong westerly flow, so ${\mathbb{M}}_{\mathrm{W}}$ and ${\mathbb{M}}_{\mathrm{E}}$ are much greater in magnitude than the other terms. We have therefore subtracted 1 mm h⁻¹ from the westerly and easterly flow components (leaving no net effect on the budget) in Fig. 4 for clarity. It is clear that the flow from the western, northern, and southern sides of the box are net sources of moisture in the model, with the flow from the eastern side a net sink of moisture (i.e., net flow out of the box).

Behavior of each of the moisture budget terms as a function of forecast lead time. An offset of 1 mm h⁻¹ equivalent westerly flux has been removed. The precipitation $\mathbb{P}$ follows the “available” moisture ${\mathbb{M}}_A$, and the budget is approximately balanced (blue lines near zero). The vertical gray dotted lines identify the three periods defined in the text, for each of which the behavior of the moisture budget terms seems to fit into one of three coherent regimes. The thin dotted lines show the 95% confidence interval for the quantity shown in the same color.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Behavior of each of the moisture budget terms as a function of forecast lead time. An offset of 1 mm h⁻¹ equivalent westerly flux has been removed. The precipitation $\mathbb{P}$ follows the “available” moisture ${\mathbb{M}}_A$, and the budget is approximately balanced (blue lines near zero). The vertical gray dotted lines identify the three periods defined in the text, for each of which the behavior of the moisture budget terms seems to fit into one of three coherent regimes. The thin dotted lines show the 95% confidence interval for the quantity shown in the same color.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Behavior of each of the moisture budget terms as a function of forecast lead time. An offset of 1 mm h⁻¹ equivalent westerly flux has been removed. The precipitation $\mathbb{P}$ follows the “available” moisture ${\mathbb{M}}_A$, and the budget is approximately balanced (blue lines near zero). The vertical gray dotted lines identify the three periods defined in the text, for each of which the behavior of the moisture budget terms seems to fit into one of three coherent regimes. The thin dotted lines show the 95% confidence interval for the quantity shown in the same color.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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The actual values of ${\mathrm{\mathbb{Q}}}_t$ and ${\mathbb{M}}_A-\mathbb{P}$ are approximately zero at τ = 0 (although significantly above, rather than below, zero), indicating that the moisture in the box is fairly constant from one analysis to the next over the 3-month period. They are also approximately equal to each other, suggesting that the MetUM keeps an approximately balanced moisture budget (relative to the magnitude of the tendencies) for the duration of the forecast. The variation in ${\mathbb{M}}_A$, $\mathbb{P}$, and ${\mathrm{\mathbb{Q}}}_t$ can be broadly divided into three stages. During the first day of the forecast (which we define as period I), ${\mathbb{M}}_A$ and $\mathrm{\mathbb{P}}$ are approximately constant, with ${\mathbb{M}}_A$ slightly larger than $\mathrm{\mathbb{P}}$ so that there is a moistening of the box during this period; although the significance interval allows for some possibility of $\mathrm{\mathbb{P}}$ being larger than ${\mathbb{M}}_A$, ${\mathrm{\mathbb{Q}}}_t$ is significantly positive. From days 1 to 3 (period II), both quantities decrease, but ${\mathbb{M}}_A$ decreases rather faster. Again, the significance intervals suggest that this will vary depending on the precise period used for the calculation, but ${\mathrm{\mathbb{Q}}}_t$ is significantly negative, suggesting a drying of the box during this period. From days 3 to 5 (period III), ${\mathbb{M}}_A$ levels off and even increases slightly, while $\mathrm{\mathbb{P}}$ continues to decrease so that the box continues to dry but at a slower and slower rate, until at day 5 the budget becomes approximately balanced (here ${\mathrm{\mathbb{Q}}}_t$ is significantly negative at the start of the period, but approaches zero toward the end of the period).

The zonal moisture advection also seems to follow a three-stage pattern, as ${\mathbb{M}}_{\mathrm{W}}$ and ${\mathbb{M}}_{\mathrm{E}}$ both increase in magnitude during period I, start to reduce slowly in magnitude during period II, and then reduce more quickly in magnitude during period III. The flow into the south of the box ${\mathbb{M}}_{\mathrm{S}}$ varies rather less (following a similar pattern to ${\mathrm{\mathbb{Q}}}_t$), and the flow into the north of the box ${\mathbb{M}}_{\mathrm{N}}$ decreases monotonically throughout the forecast, although this decrease is slower during period III than during the other periods.

Figure 4 suggests that the fastest processes during the first day of the forecast do not contribute immediately to the reduction in rainfall, and are likely due to model spinup and adjustment to analysis, but that the processes on time scales of a few days do make a significant contribution.

Figure 5 shows the separation of $\mathrm{\mathbb{P}}$ and $\mathbb{E}$ into land and ocean components. It can be seen that the steady reduction in $\mathrm{\mathbb{P}}$ occurs over both land and ocean, and roughly to the same extent. The behavior of $\mathbb{E}$ is, however, different over land and over ocean. Over ocean it increases at the beginning of the forecast and seems to approach an asymptotic value, while over land there is a steady decrease, although this is much less pronounced than the decrease in $\mathrm{\mathbb{P}}$. The effects over land and ocean cancel each other somewhat, leading to the approximately constant value of $\mathbb{E}$ with lead time over the region as a whole.

Behavior of upward surface water flux and precipitation as a function of forecast lead time, restricted to land points only (dotted lines) and ocean points only (dashed lines).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Behavior of upward surface water flux and precipitation as a function of forecast lead time, restricted to land points only (dotted lines) and ocean points only (dashed lines).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Behavior of upward surface water flux and precipitation as a function of forecast lead time, restricted to land points only (dotted lines) and ocean points only (dashed lines).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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c. Separation into components

Figure 6 shows the variation in the total horizontal moisture flux (the sum of the individual horizontal flux terms, equal to ${\mathbb{M}}_A-\mathbb{E}$) and its components $\mathrm{ℍ}$ (which represents the evolution with forecast lead time due to humidity changes only) and $\mathbb{S}$ (which represents the evolution with forecast lead time due to wind speed changes only). The term $\mathbb{S}$ is constant during period I and reduces throughout period II before increasing slightly during period III. The term $\mathrm{ℍ}$ follows a similar pattern, but starts to decrease earlier during period I, and also stops decreasing earlier during period II.

Total horizontal flux $\mathbb{M}$ (solid line) into the green box in Fig. 1, with separation into variation due to humidity changes $\mathrm{ℍ}$ (dashed line) and variation due to horizontal wind changes $\mathbb{S}$ (dotted line). Also plotted is the variation due to these individual components added together (stars; $\mathbb{M}\left\{0\right\}+\mathrm{ℍ}\left\{\tau \right\}-\mathrm{ℍ}\left\{0\right\}+\mathbb{S}\left\{\tau \right\}-\mathbb{S}\left\{0\right\}$).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total horizontal flux $\mathbb{M}$ (solid line) into the green box in Fig. 1, with separation into variation due to humidity changes $\mathrm{ℍ}$ (dashed line) and variation due to horizontal wind changes $\mathbb{S}$ (dotted line). Also plotted is the variation due to these individual components added together (stars; $\mathbb{M}\left\{0\right\}+\mathrm{ℍ}\left\{\tau \right\}-\mathrm{ℍ}\left\{0\right\}+\mathbb{S}\left\{\tau \right\}-\mathbb{S}\left\{0\right\}$).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total horizontal flux $\mathbb{M}$ (solid line) into the green box in Fig. 1, with separation into variation due to humidity changes $\mathrm{ℍ}$ (dashed line) and variation due to horizontal wind changes $\mathbb{S}$ (dotted line). Also plotted is the variation due to these individual components added together (stars; $\mathbb{M}\left\{0\right\}+\mathrm{ℍ}\left\{\tau \right\}-\mathrm{ℍ}\left\{0\right\}+\mathbb{S}\left\{\tau \right\}-\mathbb{S}\left\{0\right\}$).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Also plotted is $\mathbb{M}\left\{0\right\}+\left(\mathrm{ℍ}\left\{\tau \right\}-\mathrm{ℍ}\left\{0\right\}\right)+\left(\mathbb{S}\left\{\tau \right\}-\mathbb{S}\left\{0\right\}\right)=\mathrm{ℍ}\left\{\tau \right\}+\mathbb{S}\left\{\tau \right\}-\mathbb{M}\left\{0\right\}$, which represents the sum of the variation due to wind and the variation due to moisture, without any interaction between the two. This is approximately equal to $\mathbb{M}$, suggesting that the errors in the two quantities do not interact, and that investigating the errors in $\mathrm{ℍ}$ and $\mathbb{S}$ individually is sufficient to understand the overall errors.

Figure 7 shows the variation in the individual horizontal flux terms $\mathbb{M}$ (as in Fig. 4, but with no offset removed), and their components $\mathrm{ℍ}$ and $\mathbb{S}$. It is clear that, for the three terms other than ${\mathbb{M}}_{\mathrm{W}}$, the variation is driven almost completely by the wind speed, with the humidity having a minimal effect on the evolution with forecast lead time. The reduction in $\mathrm{ℍ}$ seen in Fig. 6 is driven almost entirely by a reduction in humidity entering the box from the west. The behavior of $\mathbb{S}$ in Fig. 6 during period II seems to be driven principally by a reduction in wind speed into the northern edge of the box, whereas the behavior during period III is complicated, with the inflow to the north and west decreasing, the inflow to the south increasing and the outflow to the east decreasing.

Separation of the individual horizontal flux terms $\mathbb{M}$ into variation due to humidity changes $\mathrm{ℍ}$ and variation due to horizontal wind changes $\mathbb{S}$. The variation in each term is dominated by the horizontal wind changes, except for the western side of the box where the humidity changes have a significant effect.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Separation of the individual horizontal flux terms $\mathbb{M}$ into variation due to humidity changes $\mathrm{ℍ}$ and variation due to horizontal wind changes $\mathbb{S}$. The variation in each term is dominated by the horizontal wind changes, except for the western side of the box where the humidity changes have a significant effect.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Separation of the individual horizontal flux terms $\mathbb{M}$ into variation due to humidity changes $\mathrm{ℍ}$ and variation due to horizontal wind changes $\mathbb{S}$. The variation in each term is dominated by the horizontal wind changes, except for the western side of the box where the humidity changes have a significant effect.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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d. Spatial variation of horizontal flux terms

Figures 8 and 9 show the spatial variation of H dp{τ} and S dp{τ}, respectively, in both the horizontal and vertical. These quantities refer to (respectively) $\mathrm{ℍ}$ and $\mathbb{S}$ without the spatial average in Eqs. (13) and (14) but with the average over all the forecasts during the period 6 June–31 August. The top row in each figure shows the analysis field, which is the same for both figures because H dp{0} = S dp{0} = M dp{0}; blue colors here represent flow into the box and red colors represent flow out of the box. The middle rows show the bias that accumulates during periods I and II combined, and the bottom rows show the bias that accumulates during all three periods; here blue colors represent either an increase in flow into the box or a decrease in flow out of the box, and red colors represent either a decrease in flow into the box or an increase in flow out of the box.

Spatial variation of H dp (horizontal moisture flux into box, with variation due to humidity only). Quantities are plotted at (top) analysis time, along with the bias against analysis after (middle) 3 days (corresponding to the end of period II) and (bottom) 5 days (corresponding to the end of period III). The quantity qV(dp/dz)δz is converted into a mm h⁻¹ equivalent by multiplying by (3600/A)δl, where δl is the length of each grid element (constant for each panel, but different for each of the four directions). In this way, each pixel of a given color contributes equally to the total amount of moisture entering or leaving the box. Note that the color bar is set up so that blue always represents flow into the box, or a net increase in flow into the box, and red always represents flow out of the box, or a net decrease in flow into the box. The horizontal dashed green line represents the height z_b = 1.1 km identified in the text.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Spatial variation of H dp (horizontal moisture flux into box, with variation due to humidity only). Quantities are plotted at (top) analysis time, along with the bias against analysis after (middle) 3 days (corresponding to the end of period II) and (bottom) 5 days (corresponding to the end of period III). The quantity qV(dp/dz)δz is converted into a mm h⁻¹ equivalent by multiplying by (3600/A)δl, where δl is the length of each grid element (constant for each panel, but different for each of the four directions). In this way, each pixel of a given color contributes equally to the total amount of moisture entering or leaving the box. Note that the color bar is set up so that blue always represents flow into the box, or a net increase in flow into the box, and red always represents flow out of the box, or a net decrease in flow into the box. The horizontal dashed green line represents the height z_b = 1.1 km identified in the text.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Spatial variation of H dp (horizontal moisture flux into box, with variation due to humidity only). Quantities are plotted at (top) analysis time, along with the bias against analysis after (middle) 3 days (corresponding to the end of period II) and (bottom) 5 days (corresponding to the end of period III). The quantity qV(dp/dz)δz is converted into a mm h⁻¹ equivalent by multiplying by (3600/A)δl, where δl is the length of each grid element (constant for each panel, but different for each of the four directions). In this way, each pixel of a given color contributes equally to the total amount of moisture entering or leaving the box. Note that the color bar is set up so that blue always represents flow into the box, or a net increase in flow into the box, and red always represents flow out of the box, or a net decrease in flow into the box. The horizontal dashed green line represents the height z_b = 1.1 km identified in the text.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Spatial variation of S dp (horizontal moisture flux into box, with variation due to wind speed only). See caption of Fig. 8 for details.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Spatial variation of S dp (horizontal moisture flux into box, with variation due to wind speed only). See caption of Fig. 8 for details.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Spatial variation of S dp (horizontal moisture flux into box, with variation due to wind speed only). See caption of Fig. 8 for details.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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The predominantly westerly flow into the western side and out of the eastern side of the box is clearly seen, and occurs throughout the depth and width of both of those two box sides. The flow at the southern side of the box has more variation in the horizontal, and seems to be cyclonic, although this in fact represents an undulation in the westerly flow so that it is northwesterly in the western half of the southern side, and southwesterly in the eastern half of the southern side, as will be discussed in a later subsection. The flow at the northern side of the box varies more in the vertical, with predominantly an inflow above z_b = 1.1 km, and more variation below z_b. We have defined z_b = 1.1 km subjectively as a height that demarcates the flow (and its bias) into separate regimes; this height could be interpreted physically as roughly representing the depth of the boundary layer.

The spatial structure of the variation of H dp (due to humidity changes) with forecast lead time is relatively simple. There is a decrease in the westerly inflow of moisture, which becomes greater with forecast lead time, and this decrease occurs mainly above z_b. There is a corresponding, but much smaller, decrease in the outflow of moisture from the eastern side of the box. The variation in the other terms is rather small.

The spatial structure of the variation of S dp (due to wind speed changes) with forecast lead time is more complicated. The bias during periods I and II is that the westerly flow (into the western side and out of the eastern side) has strengthened, although some parts of the eastern side of the box show a reduction in the flow out of the box. The flow into the box at the southern side increases below z_b and decreases above z_b. The flow into the box at the northern side is almost uniformly reduced. Many of these effects are due to an anticyclonic bias, which will be discussed in a later subsection.

The variation of S dp continues in a similar way through period III, except that the westerly flow is now weaker than it was at the end of period II. The flow into the box from the southwest starts to reduce; this represents a significant departure from the behavior during periods I and II.

Because S dp displays significant biases both above and below z_b = 1.1 km, we show $\mathbb{S}$ for the sum of fluxes in all directions in Fig. 10. We define ${\mathbb{S}}^l$ from Eq. (16) with the upper vertical integration limit set to z = z_b (i.e., restricting to quantities below z_b), and ${\mathbb{S}}^u$ from Eq. (16) with the lower vertical integration limit set to z = z_b (i.e., restricting to quantities above z_b). Figure 10 shows that the flux above z_b decreases fairly monotonically with forecast lead time, although the decrease has essentially stopped by the end of period II. The flux below z_b increases during period I, decreases during period II, and then increases slightly during period III. It is possible that the behavior early in the forecast is due to spinup effects, since the winds near the surface are likely to be more affected by the observations going into the analysis.

Total horizontal moisture flux with variation due to wind speed $\mathbb{S}$ only (solid line), with separation into flux ${\mathbb{S}}^l$ below z_b = 1.1 km (dashed line) and ${\mathbb{S}}^u$ above z_b (dotted line).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total horizontal moisture flux with variation due to wind speed $\mathbb{S}$ only (solid line), with separation into flux ${\mathbb{S}}^l$ below z_b = 1.1 km (dashed line) and ${\mathbb{S}}^u$ above z_b (dotted line).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total horizontal moisture flux with variation due to wind speed $\mathbb{S}$ only (solid line), with separation into flux ${\mathbb{S}}^l$ below z_b = 1.1 km (dashed line) and ${\mathbb{S}}^u$ above z_b (dotted line).

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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e. Horizontal structure of humidity field and biases

In Fig. 11 we show how the bias in the humidity develops with forecast lead time. There is a large dry bias to the northwest of India, which is present from day 1 and increases further as the forecast develops. It is also apparent that the air being advected over India from the west becomes increasingly too dry. These two effects are responsible for the reduction in $\mathrm{ℍ}$ with forecast lead time seen in Fig. 6.

Total column moisture ${\displaystyle {\int }_0^{P_s}q\left\{\tau \right\}\hspace{0.17em}dp/g}$, overlaid with moisture flux vectors ${\displaystyle {\int }_{z_b}^{\infty }\left[q\left\{0\right\}V\left\{\tau \right\}\left(dp/dz\right)\left\{0\right\}\hspace{0.17em}dz\right]/g}$ (i.e., holding the humidity field constant at its analysis value while allowing the velocity field to vary with forecast lead time, so relevant to the quantity ${\mathbb{S}}^u$ defined in the text). (a) The analysis (τ = 0) value, and biases between the two values of τ denoted in the panel title are shown in the other three panels, that is, the bias that develops during (b) period I, (c) period II, and (d) period III. Note that the humidity is integrated upward from the surface whereas the moisture fluxes are integrated upward from z_b = 1.1 km.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total column moisture ${\displaystyle {\int }_0^{P_s}q\left\{\tau \right\}\hspace{0.17em}dp/g}$, overlaid with moisture flux vectors ${\displaystyle {\int }_{z_b}^{\infty }\left[q\left\{0\right\}V\left\{\tau \right\}\left(dp/dz\right)\left\{0\right\}\hspace{0.17em}dz\right]/g}$ (i.e., holding the humidity field constant at its analysis value while allowing the velocity field to vary with forecast lead time, so relevant to the quantity ${\mathbb{S}}^u$ defined in the text). (a) The analysis (τ = 0) value, and biases between the two values of τ denoted in the panel title are shown in the other three panels, that is, the bias that develops during (b) period I, (c) period II, and (d) period III. Note that the humidity is integrated upward from the surface whereas the moisture fluxes are integrated upward from z_b = 1.1 km.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Total column moisture ${\displaystyle {\int }_0^{P_s}q\left\{\tau \right\}\hspace{0.17em}dp/g}$, overlaid with moisture flux vectors ${\displaystyle {\int }_{z_b}^{\infty }\left[q\left\{0\right\}V\left\{\tau \right\}\left(dp/dz\right)\left\{0\right\}\hspace{0.17em}dz\right]/g}$ (i.e., holding the humidity field constant at its analysis value while allowing the velocity field to vary with forecast lead time, so relevant to the quantity ${\mathbb{S}}^u$ defined in the text). (a) The analysis (τ = 0) value, and biases between the two values of τ denoted in the panel title are shown in the other three panels, that is, the bias that develops during (b) period I, (c) period II, and (d) period III. Note that the humidity is integrated upward from the surface whereas the moisture fluxes are integrated upward from z_b = 1.1 km.

Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0650.1

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Parker et al. (2016) showed that the Indian monsoon is characterized by a competition between moist flow advected over the Indian Ocean from the southwest and dry air advected over the arid land from the northwest. These “dry intrusions” from the northwest were identified by Krishnamurti et al. (2010) as being partly responsible for dry spells in the Indian monsoon. It is possible that the MetUM is simulating these dry intrusions too strongly, leading to too-dry air coming from the northwest that erroneously suppresses the convection in the model. The air over the northwest of India was identified by Pathak et al. (2017) as making a relatively small contribution of moisture to the monsoon rainfall, but possibly enough that if its moisture content is heavily reduced this could make a significant contribution to the reduction in rainfall seen in the MetUM.

The flow entering the box from the Arabian Sea to the west and southwest appears to originate in the western and southern Indian Ocean; these regions have previously been identified as the most important moisture sources for the Indian monsoon (Pathak et al. 2017). Sahana et al. (2019) showed that inaccurate representation of these moisture sources is partly responsible for the Indian monsoon dry bias in CFSv2, a coupled model used by the National Centers for Environmental Prediction for seasonal forecasting. It is apparent from Figs. 1 and 11 that the air in the equatorial Indian Ocean directly to the south of India is too moist and produces too much rainfall in the MetUM. However, this region is identified by Pathak et al. (2017) and Sahana et al. (2019) as being a less important moisture source for the Indian monsoon, and this appears from Figs. 1 and 11 to be also the case for shorter time scales. Indeed, there is some evidence that moistening in this region is related to moisture being diverted away from the peninsular region, at least during period II.

f. Horizontal structure of wind speed field and biases

The variation of moisture flux vectors due to wind speed (∫S dp) is also shown in Fig. 11. These were calculated by taking the wind velocity at a given forecast lead time, multiplying by the humidity field at analysis time and integrating vertically above z_b. In this way, they are relevant to the quantity ${\mathbb{S}}^u$. Another physical interpretation is that Fig. 11 shows the evolution of the wind vectors, but weighted toward air that is more humid at analysis time.

The westerly flow is clear to see in Fig. 11a, and the effect of this flow is to transport moisture into the box from the west and out of the box to the east. As discussed in the previous subsection, this moisture comes from two sources: air coming from the southwest of the box (which would be expected to be moister), and air coming from the northwest of the box (which would be expected to be drier). The westerly flow also undulates, and the effect of this on the southern side of the box is that it transports moisture out of the box farther west and back into the box farther east. The moisture flux is also characterized by cyclonic flow to the northeast of India, which may be associated with the monsoon trough or the passage of monsoon depressions.

The reduction in wind flow from the western side of the box also makes an important contribution to the drying of the box leading to reduced rainfall in the NWP forecast. This only manifests itself after approximately 3 days (i.e., during period III), suggesting that it could be due to errors farther upstream, over the Arabian Sea. This connection has been presented in previous work on longer time scales. Levine and Martin (2018) used a set of regional climate model simulations with differing lateral boundary locations to show that the most significant regions of influence on the biases around the Indian Peninsula were those to the south and to the west. Further, it was shown by Bush et al. (2015) that increasing the entrainment rate in the MetUM over the equatorial Indian Ocean (and thereby suppressing convection and alleviating the moist bias over that region) leads to an enhanced southwesterly flow (i.e., reducing the wind bias) and a reduction in the dry bias over India. Willetts et al. (2017) also showed that rainfall over India could be increased by using a convection-permitting model, and that this is partly achieved by increasing the flow of moist air from the Arabian Sea into India, and Chakraborty and Agrawal (2017) showed that an earlier monsoon onset tends to coincide with a stronger low-level jet over the Arabian Sea. Roxy et al. (2017) showed that extreme rainfall events are often related to variability in moisture from the Arabian Sea.

The moisture flux exhibits an anticyclonic bias centered near the eastern edge of the box, which is present for all three periods but shifts northward as the forecast develops. Its effect near the beginning of the forecast is to advect less air in through the northern side of the box, while later in the forecast its effect is to advect less air out through the eastern side of the box. It is possible that this anticyclonic bias corresponds to a weaker monsoon trough, which would lead to a reduction in rainfall overall. A climatological anticyclonic bias was identified by Martin and Levine (2012) and Levine and Martin (2018) in climate simulations, although the positioning of the bias was not the same as in our investigation. Indeed, we have shown that the location of this bias changes as the forecast develops; it also is possible that it would be in a different location in a different monsoon year. Bush et al. (2015) showed that this anticyclonic bias could be reduced by increasing the entrainment rate over the equatorial Indian Ocean, a change that, as mentioned above, also reduced the dry bias over India.

There is a northerly bias during period II on the southern side of the box, which could be indicative of divergent flow toward the equatorial Indian Ocean, where the model produces too much rainfall (Fig. 1). During period III the southern side of the box is near a saddle point in a somewhat complex bias flow, and the northerly bias here seems to be contingent on the precise location of the saddle point. This suggests that correctly simulating smaller-scale features of the flow is important for capturing the flux through the southern edge of the box correctly.

Suggestions for future work

We have confined this study to looking at the mean flux terms over most of the monsoon season as a whole, and future work will investigate how these terms vary as the monsoon progresses. In particular, we shall determine whether it is possible to identify relatively short periods within the monsoon, which account for a relatively large amount of the overall negative rainfall bias. If this is the case, then it will be possible to run relatively inexpensive further simulations for just these short periods, and to test the likely effects of model changes on the dry bias in the MetUM. Similarly, we have been careful to eliminate the effects of the diurnal cycle on our overall budget, but it would also be interesting to carry out an analysis on shorter time scales and to investigate how the diurnal cycle varies as the forecast progresses.

Having shown that the drying tendency is common to all years of a 6-yr period, we have focused on a single year as representative of the recent past. We are currently working on repeating the full analysis for all the years 2011–18, in order to investigate to what extent conclusions hold for other years (in particular those with a different model version), and to enable an enhanced significance testing of the conclusions arrived at in this study. Initial results suggest that the decrease in moisture flux into the region from around day 3, as well as the drying of the air to the west and northwest of the region, is seen in other recent years. Some other years show evidence of an anticyclonic bias, although in varying locations meaning it has a varying effect on the moisture fluxes, particularly into the northern side of the region.

The detailed moisture budget investigation, carried out in this study for weather forecasts, could also be applied to climate simulations. This would involve a somewhat different approach, since there would only be a single simulation for the whole period, rather than several shorter, overlapping simulations, and the simulations would have to be compared with, for example, reanalysis datasets, instead of against the same model analysis. However, it would be useful to investigate how the dry bias, and the moisture budget terms, develop on the longer time scales of a climate simulation, and this might further inform the discussion of similarities and differences in the dry bias between climate simulations and weather forecasts using the MetUM.

It will be interesting to carry out a similar analysis for other regions, particularly that to the south of India, where there is a wet bias, and over northern India, where the biases in the weather and climate simulations are different. For northern India, initial analysis suggests that there is a similar steady decrease in total moisture flux into the region (to that for southern India), but that the rainfall increases initially before steadily decreasing later in the forecast. This rainfall behavior is also seen over southern India in other recent years (see Fig. 2), so extending the analysis to these years may clarify the comparison between the climate simulations and weather forecasts.

The effects of initial conditions on the dry bias should also be considered. It is possible that a model captures the monsoon system correctly, but incorrect initial conditions cause it to develop toward an equilibrium state that produces less rainfall than the real atmosphere. We have conducted forecast experiments for 2012, similar to those analyzed in this study, with different initial conditions, and analysis of these experiments will also form the basis of a future study.